KILLED proof of input_dan5Anqs7b.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 3 ms] (26) CdtProblem (27) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms] (32) CdtProblem (33) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 60 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (80) CdtProblem (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 53 ms] (86) CdtProblem (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 391 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 30 ms] (100) CdtProblem (101) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 134 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 17 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16.0 s] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16.6 s] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 312 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 872 ms] (120) CdtProblem (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 15 ms] (122) CdtProblem (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 3646 ms] (124) 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__first(0, X) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) a__from(X) -> cons(mark(X), from(s(X))) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(from(X)) -> a__from(mark(X)) mark(0) -> 0 mark(nil) -> nil mark(s(X)) -> s(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) a__first(X1, X2) -> first(X1, X2) 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__first(0', X) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) a__from(X) -> cons(mark(X), from(s(X))) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(from(X)) -> a__from(mark(X)) mark(0') -> 0' mark(nil) -> nil mark(s(X)) -> s(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) a__first(X1, X2) -> first(X1, X2) 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__first(0, X) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) a__from(X) -> cons(mark(X), from(s(X))) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(from(X)) -> a__from(mark(X)) mark(0) -> 0 mark(nil) -> nil mark(s(X)) -> s(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) a__first(X1, X2) -> first(X1, X2) 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__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__from(X) -> cons(mark(X), from(s(X))) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(from(X)) -> a__from(mark(X)) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] a__first(X1, X2) -> first(X1, X2) [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__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__from(X) -> cons(mark(X), from(s(X))) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(from(X)) -> a__from(mark(X)) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] a__first(X1, X2) -> first(X1, X2) [1] a__from(X) -> from(X) [1] The TRS has the following type information: a__first :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from 0 :: 0:nil:s:cons:first:from nil :: 0:nil:s:cons:first:from s :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from cons :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from mark :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from first :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from a__from :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from from :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from 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__from_1 a__first_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__from(X) -> cons(mark(X), from(s(X))) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(from(X)) -> a__from(mark(X)) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] a__first(X1, X2) -> first(X1, X2) [1] a__from(X) -> from(X) [1] The TRS has the following type information: a__first :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from 0 :: 0:nil:s:cons:first:from nil :: 0:nil:s:cons:first:from s :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from cons :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from mark :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from first :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from a__from :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from from :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from 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__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__from(X) -> cons(mark(X), from(s(X))) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(from(first(X113, X213))) -> a__from(a__first(mark(X113), mark(X213))) [2] mark(from(from(X33))) -> a__from(a__from(mark(X33))) [2] mark(from(0)) -> a__from(0) [2] mark(from(nil)) -> a__from(nil) [2] mark(from(s(X34))) -> a__from(s(mark(X34))) [2] mark(from(cons(X114, X214))) -> a__from(cons(mark(X114), X214)) [2] mark(0) -> 0 [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] a__first(X1, X2) -> first(X1, X2) [1] a__from(X) -> from(X) [1] The TRS has the following type information: a__first :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from 0 :: 0:nil:s:cons:first:from nil :: 0:nil:s:cons:first:from s :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from cons :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from mark :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from first :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from a__from :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from from :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from Rewrite Strategy: INNERMOST ---------------------------------------- (13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 nil => 1 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: a__first(z, z') -{ 1 }-> 1 :|: z' = X, X >= 0, z = 0 a__first(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + X + Z) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z 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(X33))) :|: X33 >= 0, z = 1 + (1 + X33) mark(z) -{ 2 }-> a__from(a__first(mark(X113), mark(X213))) :|: X113 >= 0, X213 >= 0, z = 1 + (1 + X113 + X213) mark(z) -{ 2 }-> a__from(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__from(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__from(1 + mark(X34)) :|: z = 1 + (1 + X34), X34 >= 0 mark(z) -{ 2 }-> a__from(1 + mark(X114) + X214) :|: X114 >= 0, X214 >= 0, z = 1 + (1 + X114 + X214) mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (15) 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__first(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0 a__first(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + (z - 1) + Z) :|: Z >= 0, Y >= 0, z - 1 >= 0, z' = 1 + Y + Z 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__first(mark(X113), mark(X213))) :|: X113 >= 0, X213 >= 0, z = 1 + (1 + X113 + X213) mark(z) -{ 2 }-> a__from(1) :|: z = 1 + 1 mark(z) -{ 2 }-> 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(X114) + X214) :|: X114 >= 0, X214 >= 0, z = 1 + (1 + X114 + X214) mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (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: none And the following fresh constants: none ---------------------------------------- (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__first(0, X) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__from(X) -> cons(mark(X), from(s(X))) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(from(X)) -> a__from(mark(X)) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] mark(s(X)) -> s(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] a__first(X1, X2) -> first(X1, X2) [1] a__from(X) -> from(X) [1] The TRS has the following type information: a__first :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from 0 :: 0:nil:s:cons:first:from nil :: 0:nil:s:cons:first:from s :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from cons :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from mark :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from first :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from a__from :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from from :: 0:nil:s:cons:first:from -> 0:nil:s:cons:first:from 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: 0 => 0 nil => 1 ---------------------------------------- (20) Obligation: Complexity RNTS consisting of the following rules: a__first(z, z') -{ 1 }-> 1 :|: z' = X, X >= 0, z = 0 a__first(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + X + Z) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z 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__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (21) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (22) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(0, z0) -> c A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FIRST(z0, z1) -> c2 A__FROM(z0) -> c3(MARK(z0)) A__FROM(z0) -> c4 MARK(first(z0, z1)) -> c5(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c6(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(0) -> c8 MARK(nil) -> c9 MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) S tuples: A__FIRST(0, z0) -> c A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FIRST(z0, z1) -> c2 A__FROM(z0) -> c3(MARK(z0)) A__FROM(z0) -> c4 MARK(first(z0, z1)) -> c5(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c6(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(0) -> c8 MARK(nil) -> c9 MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c, c1_1, c2, c3_1, c4, c5_2, c6_2, c7_2, c8, c9, c10_1, c11_1 ---------------------------------------- (23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: A__FIRST(z0, z1) -> c2 MARK(0) -> c8 A__FROM(z0) -> c4 MARK(nil) -> c9 A__FIRST(0, z0) -> c ---------------------------------------- (24) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(first(z0, z1)) -> c5(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c6(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(first(z0, z1)) -> c5(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c6(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c5_2, c6_2, c7_2, c10_1, c11_1 ---------------------------------------- (25) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(z0, z1)) -> c5(A__FIRST(mark(z0), mark(z1)), MARK(z0)) by MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c5(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c5(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(x0, s(z0))) -> c5(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(0, x1)) -> c5(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c5(A__FIRST(nil, mark(x1)), MARK(nil)) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c5(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(first(z0, z1)) -> c6(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c5(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c5(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(x0, s(z0))) -> c5(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(0, x1)) -> c5(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c5(A__FIRST(nil, mark(x1)), MARK(nil)) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c5(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(first(z0, z1)) -> c6(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c5(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c5(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(x0, s(z0))) -> c5(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(0, x1)) -> c5(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c5(A__FIRST(nil, mark(x1)), MARK(nil)) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c5(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c6_2, c7_2, c10_1, c11_1, c5_2 ---------------------------------------- (27) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(nil, x1)) -> c5(A__FIRST(nil, mark(x1)), MARK(nil)) MARK(first(0, x1)) -> c5(A__FIRST(0, mark(x1)), MARK(0)) ---------------------------------------- (28) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(first(z0, z1)) -> c6(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c5(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c5(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(x0, s(z0))) -> c5(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c5(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(first(z0, z1)) -> c6(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c5(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c5(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(x0, s(z0))) -> c5(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c5(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c6_2, c7_2, c10_1, c11_1, c5_2 ---------------------------------------- (29) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (30) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(first(z0, z1)) -> c6(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(first(z0, z1)) -> c6(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c6_2, c7_2, c10_1, c11_1, c5_2, c5_1 ---------------------------------------- (31) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(z0, z1)) -> c6(A__FIRST(mark(z0), mark(z1)), MARK(z1)) by MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, 0)) -> c6(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c6(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(x0, s(z0))) -> c6(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c6(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c6(A__FIRST(nil, mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, 0)) -> c6(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c6(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(x0, s(z0))) -> c6(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c6(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c6(A__FIRST(nil, mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, 0)) -> c6(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c6(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(x0, s(z0))) -> c6(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c6(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c6(A__FIRST(nil, mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2 ---------------------------------------- (33) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(x0, 0)) -> c6(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c6(A__FIRST(mark(x0), nil), MARK(nil)) ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, s(z0))) -> c6(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c6(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c6(A__FIRST(nil, mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, s(z0))) -> c6(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c6(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c6(A__FIRST(nil, mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2 ---------------------------------------- (35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (37) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, first(z0, z1))) -> c5(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) by MARK(first(x0, first(x1, x2))) -> c5(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(0, first(x1, x2))) -> c5(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, first(x1, x2))) -> c5(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil)) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, x2))) -> c5(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(0, first(x1, x2))) -> c5(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, first(x1, x2))) -> c5(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil)) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, x2))) -> c5(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(0, first(x1, x2))) -> c5(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, first(x1, x2))) -> c5(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil)) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(nil, first(x1, x2))) -> c5(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil)) MARK(first(0, first(x1, x2))) -> c5(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0)) ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, x2))) -> c5(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, x2))) -> c5(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (43) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, from(z0))) -> c5(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) by MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), from(mark(x1))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(0, from(x1))) -> c5(A__FIRST(0, a__from(mark(x1))), MARK(0)) MARK(first(nil, from(x1))) -> c5(A__FIRST(nil, a__from(mark(x1))), MARK(nil)) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(cons(z0, z1), from(x1))) -> c5(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(cons(z0, z1))) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), from(mark(x1))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(0, from(x1))) -> c5(A__FIRST(0, a__from(mark(x1))), MARK(0)) MARK(first(nil, from(x1))) -> c5(A__FIRST(nil, a__from(mark(x1))), MARK(nil)) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(cons(z0, z1), from(x1))) -> c5(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(cons(z0, z1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), from(mark(x1))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(0, from(x1))) -> c5(A__FIRST(0, a__from(mark(x1))), MARK(0)) MARK(first(nil, from(x1))) -> c5(A__FIRST(nil, a__from(mark(x1))), MARK(nil)) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(cons(z0, z1), from(x1))) -> c5(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (45) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(0, from(x1))) -> c5(A__FIRST(0, a__from(mark(x1))), MARK(0)) MARK(first(nil, from(x1))) -> c5(A__FIRST(nil, a__from(mark(x1))), MARK(nil)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), from(mark(x1))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(cons(z0, z1), from(x1))) -> c5(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(cons(z0, z1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), from(mark(x1))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(cons(z0, z1), from(x1))) -> c5(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, cons(z0, z1))) -> c5(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) by MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(0, cons(x1, x2))) -> c5(A__FIRST(0, cons(mark(x1), x2)), MARK(0)) MARK(first(nil, cons(x1, x2))) -> c5(A__FIRST(nil, cons(mark(x1), x2)), MARK(nil)) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(0, cons(x1, x2))) -> c5(A__FIRST(0, cons(mark(x1), x2)), MARK(0)) MARK(first(nil, cons(x1, x2))) -> c5(A__FIRST(nil, cons(mark(x1), x2)), MARK(nil)) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(0, cons(x1, x2))) -> c5(A__FIRST(0, cons(mark(x1), x2)), MARK(0)) MARK(first(nil, cons(x1, x2))) -> c5(A__FIRST(nil, cons(mark(x1), x2)), MARK(nil)) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (51) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(0, cons(x1, x2))) -> c5(A__FIRST(0, cons(mark(x1), x2)), MARK(0)) MARK(first(nil, cons(x1, x2))) -> c5(A__FIRST(nil, cons(mark(x1), x2)), MARK(nil)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(first(z0, z1), x1)) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) by MARK(first(first(x0, x1), first(z0, z1))) -> c5(A__FIRST(a__first(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(x0, x1))) MARK(first(first(x0, x1), from(z0))) -> c5(A__FIRST(a__first(mark(x0), mark(x1)), a__from(mark(z0))), MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c5(A__FIRST(a__first(mark(x0), mark(x1)), 0), MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(A__FIRST(a__first(mark(x0), mark(x1)), nil), MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(A__FIRST(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(first(x0, x1))) MARK(first(first(x0, x1), cons(z0, z1))) -> c5(A__FIRST(a__first(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(A__FIRST(first(mark(x0), mark(x1)), mark(x2)), MARK(first(x0, x1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, x1), 0)) -> c5(A__FIRST(a__first(mark(x0), mark(x1)), 0), MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(A__FIRST(a__first(mark(x0), mark(x1)), nil), MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(A__FIRST(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(A__FIRST(first(mark(x0), mark(x1)), mark(x2)), MARK(first(x0, x1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, x1), 0)) -> c5(A__FIRST(a__first(mark(x0), mark(x1)), 0), MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(A__FIRST(a__first(mark(x0), mark(x1)), nil), MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(A__FIRST(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(A__FIRST(first(mark(x0), mark(x1)), mark(x2)), MARK(first(x0, x1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(from(z0), x1)) -> c5(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) by MARK(first(from(x0), first(z0, z1))) -> c5(A__FIRST(a__from(mark(x0)), a__first(mark(z0), mark(z1))), MARK(from(x0))) MARK(first(from(x0), from(z0))) -> c5(A__FIRST(a__from(mark(x0)), a__from(mark(z0))), MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(A__FIRST(a__from(mark(x0)), 0), MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(A__FIRST(a__from(mark(x0)), nil), MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(A__FIRST(a__from(mark(x0)), s(mark(z0))), MARK(from(x0))) MARK(first(from(x0), cons(z0, z1))) -> c5(A__FIRST(a__from(mark(x0)), cons(mark(z0), z1)), MARK(from(x0))) MARK(first(from(x0), x1)) -> c5(A__FIRST(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1)), MARK(from(x0))) MARK(first(from(x0), x1)) -> c5(A__FIRST(from(mark(x0)), mark(x1)), MARK(from(x0))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(x0), 0)) -> c5(A__FIRST(a__from(mark(x0)), 0), MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(A__FIRST(a__from(mark(x0)), nil), MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(A__FIRST(a__from(mark(x0)), s(mark(z0))), MARK(from(x0))) MARK(first(from(x0), x1)) -> c5(A__FIRST(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1)), MARK(from(x0))) MARK(first(from(x0), x1)) -> c5(A__FIRST(from(mark(x0)), mark(x1)), MARK(from(x0))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(x0), 0)) -> c5(A__FIRST(a__from(mark(x0)), 0), MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(A__FIRST(a__from(mark(x0)), nil), MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(A__FIRST(a__from(mark(x0)), s(mark(z0))), MARK(from(x0))) MARK(first(from(x0), x1)) -> c5(A__FIRST(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1)), MARK(from(x0))) MARK(first(from(x0), x1)) -> c5(A__FIRST(from(mark(x0)), mark(x1)), MARK(from(x0))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_2, c5_1, c6_2, c6_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(s(z0), x1)) -> c5(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) by MARK(first(s(x0), first(z0, z1))) -> c5(A__FIRST(s(mark(x0)), a__first(mark(z0), mark(z1))), MARK(s(x0))) MARK(first(s(x0), from(z0))) -> c5(A__FIRST(s(mark(x0)), a__from(mark(z0))), MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(A__FIRST(s(mark(x0)), 0), MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(A__FIRST(s(mark(x0)), nil), MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(A__FIRST(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(first(s(x0), cons(z0, z1))) -> c5(A__FIRST(s(mark(x0)), cons(mark(z0), z1)), MARK(s(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(x0), 0)) -> c5(A__FIRST(s(mark(x0)), 0), MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(A__FIRST(s(mark(x0)), nil), MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(A__FIRST(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(x0), 0)) -> c5(A__FIRST(s(mark(x0)), 0), MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(A__FIRST(s(mark(x0)), nil), MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(A__FIRST(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, first(z0, z1))) -> c6(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) by MARK(first(x0, first(x1, x2))) -> c6(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, x2))) -> c6(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, x2))) -> c6(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, from(z0))) -> c6(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) by MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(0, from(x1))) -> c6(A__FIRST(0, a__from(mark(x1))), MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(A__FIRST(nil, a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(0, from(x1))) -> c6(A__FIRST(0, a__from(mark(x1))), MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(A__FIRST(nil, a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(0, from(x1))) -> c6(A__FIRST(0, a__from(mark(x1))), MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(A__FIRST(nil, a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, cons(z0, z1))) -> c6(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) by MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(A__FIRST(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(A__FIRST(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(A__FIRST(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(A__FIRST(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(A__FIRST(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(A__FIRST(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), 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a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), 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c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), 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c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, 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mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(first(z0, z1), x1)) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by MARK(first(first(x0, x1), first(z0, z1))) -> c6(A__FIRST(a__first(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(first(x0, x1), from(z0))) -> c6(A__FIRST(a__first(mark(x0), mark(x1)), a__from(mark(z0))), MARK(from(z0))) MARK(first(first(x0, x1), 0)) -> c6(A__FIRST(a__first(mark(x0), mark(x1)), 0), MARK(0)) MARK(first(first(x0, x1), nil)) -> c6(A__FIRST(a__first(mark(x0), mark(x1)), nil), MARK(nil)) MARK(first(first(x0, x1), s(z0))) -> c6(A__FIRST(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(first(first(x0, x1), cons(z0, z1))) -> c6(A__FIRST(a__first(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(x0, x1), x2)) -> c6(A__FIRST(first(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, 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MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, x1), 0)) -> c6(A__FIRST(a__first(mark(x0), mark(x1)), 0), MARK(0)) MARK(first(first(x0, x1), nil)) -> c6(A__FIRST(a__first(mark(x0), mark(x1)), nil), MARK(nil)) MARK(first(first(x0, x1), s(z0))) -> c6(A__FIRST(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(A__FIRST(first(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(first(x0, x1), 0)) -> c6(A__FIRST(a__first(mark(x0), mark(x1)), 0), MARK(0)) MARK(first(first(x0, x1), nil)) -> c6(A__FIRST(a__first(mark(x0), mark(x1)), nil), MARK(nil)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> 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c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, x1), s(z0))) -> c6(A__FIRST(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(A__FIRST(first(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(from(z0), x1)) -> c6(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) by MARK(first(from(x0), first(z0, z1))) -> c6(A__FIRST(a__from(mark(x0)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(from(x0), from(z0))) -> c6(A__FIRST(a__from(mark(x0)), a__from(mark(z0))), MARK(from(z0))) MARK(first(from(x0), 0)) -> c6(A__FIRST(a__from(mark(x0)), 0), MARK(0)) MARK(first(from(x0), nil)) -> c6(A__FIRST(a__from(mark(x0)), nil), MARK(nil)) MARK(first(from(x0), s(z0))) -> c6(A__FIRST(a__from(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(from(x0), cons(z0, z1))) -> c6(A__FIRST(a__from(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(x0), x1)) -> c6(A__FIRST(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1)), MARK(x1)) MARK(first(from(x0), x1)) -> c6(A__FIRST(from(mark(x0)), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(x0), 0)) -> c6(A__FIRST(a__from(mark(x0)), 0), MARK(0)) MARK(first(from(x0), nil)) -> c6(A__FIRST(a__from(mark(x0)), nil), MARK(nil)) MARK(first(from(x0), s(z0))) -> c6(A__FIRST(a__from(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(A__FIRST(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1)), MARK(x1)) MARK(first(from(x0), x1)) -> c6(A__FIRST(from(mark(x0)), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(x0), 0)) -> c6(A__FIRST(a__from(mark(x0)), 0), MARK(0)) MARK(first(from(x0), nil)) -> c6(A__FIRST(a__from(mark(x0)), nil), MARK(nil)) MARK(first(from(x0), s(z0))) -> c6(A__FIRST(a__from(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(A__FIRST(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1)), MARK(x1)) MARK(first(from(x0), x1)) -> c6(A__FIRST(from(mark(x0)), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(from(x0), nil)) -> c6(A__FIRST(a__from(mark(x0)), nil), MARK(nil)) MARK(first(from(x0), 0)) -> c6(A__FIRST(a__from(mark(x0)), 0), MARK(0)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) 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MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, 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MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(x0), s(z0))) -> c6(A__FIRST(a__from(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(A__FIRST(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1)), MARK(x1)) MARK(first(from(x0), x1)) -> c6(A__FIRST(from(mark(x0)), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), 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c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, 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c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, 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c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_2, c6_1, c5_2 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(s(z0), x1)) -> c6(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) by MARK(first(s(x0), first(z0, z1))) -> c6(A__FIRST(s(mark(x0)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(s(x0), from(z0))) -> c6(A__FIRST(s(mark(x0)), a__from(mark(z0))), MARK(from(z0))) MARK(first(s(x0), 0)) -> c6(A__FIRST(s(mark(x0)), 0), MARK(0)) MARK(first(s(x0), nil)) -> c6(A__FIRST(s(mark(x0)), nil), MARK(nil)) MARK(first(s(x0), s(z0))) -> c6(A__FIRST(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(s(x0), cons(z0, z1))) -> c6(A__FIRST(s(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, 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MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(x0), 0)) -> c6(A__FIRST(s(mark(x0)), 0), MARK(0)) MARK(first(s(x0), nil)) -> c6(A__FIRST(s(mark(x0)), nil), MARK(nil)) MARK(first(s(x0), s(z0))) -> c6(A__FIRST(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_1, c5_2, c6_2 ---------------------------------------- (93) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(s(x0), 0)) -> c6(A__FIRST(s(mark(x0)), 0), MARK(0)) MARK(first(s(x0), nil)) -> c6(A__FIRST(s(mark(x0)), nil), MARK(nil)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) 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MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(A__FIRST(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_1, c5_2, c6_2 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> 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c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) S tuples: A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, 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c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FIRST_2, A__FROM_1, MARK_1 Compound Symbols: c1_1, c3_1, c7_2, c10_1, c11_1, c5_1, c6_1, c5_2, c6_2 ---------------------------------------- (97) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__FIRST(s(z0), cons(z1, z2)) -> c1(MARK(z1)) by A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 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cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) S tuples: A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c5(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(0, x2))) -> c6(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FROM_1, MARK_1, A__FIRST_2 Compound Symbols: c3_1, c7_2, c10_1, c11_1, c5_1, c6_1, c5_2, c6_2, c1_1 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, 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from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) S tuples: A__FROM(z0) -> c3(MARK(z0)) MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), 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A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: A__FROM_1, MARK_1, A__FIRST_2 Compound Symbols: c3_1, c7_2, c10_1, c11_1, c5_1, c6_1, c5_2, c6_2, c1_1 ---------------------------------------- (101) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A__FROM(z0) -> c3(MARK(z0)) by A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, 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z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) S tuples: MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), 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y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__FIRST_2, A__FROM_1 Compound Symbols: c7_2, c10_1, c11_1, c5_1, c6_1, c5_2, c6_2, c1_1, c3_1 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(from(z0)) -> c7(A__FROM(mark(z0)), MARK(z0)) by MARK(from(first(z0, z1))) -> c7(A__FROM(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(0)) -> c7(A__FROM(0), MARK(0)) MARK(from(nil)) -> c7(A__FROM(nil), MARK(nil)) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(first(z0, z1))) -> c7(A__FROM(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(0)) -> c7(A__FROM(0), MARK(0)) MARK(from(nil)) -> c7(A__FROM(nil), MARK(nil)) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) S tuples: MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(first(z0, z1))) -> c7(A__FROM(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(0)) -> c7(A__FROM(0), MARK(0)) MARK(from(nil)) -> c7(A__FROM(nil), MARK(nil)) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__FIRST_2, A__FROM_1 Compound Symbols: c10_1, c11_1, c5_1, c6_1, c5_2, c6_2, c1_1, c3_1, c7_2 ---------------------------------------- (105) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(from(0)) -> c7(A__FROM(0), MARK(0)) MARK(from(nil)) -> c7(A__FROM(nil), MARK(nil)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> 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c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), 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A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) 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MARK(cons(z0, z1))) S tuples: MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, 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c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), 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a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(first(z0, z1))) -> c7(A__FROM(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__FIRST_2, A__FROM_1 Compound Symbols: c10_1, c11_1, c5_1, c6_1, c5_2, c6_2, c1_1, c3_1, c7_2 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), 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A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) 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A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(first(z0, z1))) -> c7(A__FROM(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) S tuples: MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> 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y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(first(z0, z1))) -> c7(A__FROM(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__FIRST_2, A__FROM_1 Compound Symbols: c10_1, c11_1, c5_1, c6_1, c5_2, c6_2, c1_1, c3_1, c7_2 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(from(first(z0, z1))) -> c7(A__FROM(a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) by MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) 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c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) S tuples: MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> 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c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> 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a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), 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c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> 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x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(from(z0))) -> c7(A__FROM(a__from(mark(z0))), MARK(from(z0))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__FIRST_2, A__FROM_1 Compound Symbols: c10_1, c11_1, c5_1, c6_1, c5_2, c6_2, c1_1, c3_1, c7_2 ---------------------------------------- (111) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(0))) -> c7(A__FROM(a__from(0)), MARK(from(0))) MARK(from(from(nil))) -> c7(A__FROM(a__from(nil)), MARK(from(nil))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), 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c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(0))) -> c7(A__FROM(a__from(0)), MARK(from(0))) MARK(from(from(nil))) -> c7(A__FROM(a__from(nil)), MARK(from(nil))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) S tuples: MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), 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z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(0))) -> c7(A__FROM(a__from(0)), MARK(from(0))) MARK(from(from(nil))) -> c7(A__FROM(a__from(nil)), MARK(from(nil))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__FIRST_2, A__FROM_1 Compound Symbols: c10_1, c11_1, c5_1, c6_1, c5_2, c6_2, c1_1, c3_1, c7_2 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> 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-> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(0))) -> c7(A__FROM(a__from(0))) MARK(from(from(nil))) -> c7(A__FROM(a__from(nil))) S tuples: MARK(s(z0)) -> c10(MARK(z0)) MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, 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z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(0))) -> c7(A__FROM(a__from(0))) MARK(from(from(nil))) -> c7(A__FROM(a__from(nil))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__FIRST_2, A__FROM_1 Compound Symbols: c10_1, c11_1, c5_1, c6_1, c5_2, c6_2, c1_1, c3_1, c7_2, c7_1 ---------------------------------------- (115) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(s(z0)) -> c10(MARK(z0)) by MARK(s(s(y0))) -> c10(MARK(s(y0))) MARK(s(cons(y0, y1))) -> c10(MARK(cons(y0, y1))) MARK(s(first(y0, 0))) -> c10(MARK(first(y0, 0))) MARK(s(first(y0, nil))) -> c10(MARK(first(y0, nil))) MARK(s(first(y0, s(y1)))) -> c10(MARK(first(y0, s(y1)))) MARK(s(first(cons(y0, y1), y2))) -> c10(MARK(first(cons(y0, y1), y2))) MARK(s(first(0, y0))) -> c10(MARK(first(0, y0))) MARK(s(first(nil, y0))) -> c10(MARK(first(nil, y0))) MARK(s(first(y0, first(y1, first(y2, y3))))) -> c10(MARK(first(y0, first(y1, first(y2, y3))))) MARK(s(first(y0, first(y1, from(y2))))) -> c10(MARK(first(y0, first(y1, from(y2))))) MARK(s(first(y0, first(y1, 0)))) -> c10(MARK(first(y0, first(y1, 0)))) MARK(s(first(y0, first(y1, nil)))) -> c10(MARK(first(y0, first(y1, nil)))) MARK(s(first(y0, first(y1, s(y2))))) -> c10(MARK(first(y0, first(y1, s(y2))))) MARK(s(first(y0, first(y1, cons(y2, y3))))) -> c10(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(s(first(y0, first(first(y1, y2), y3)))) -> c10(MARK(first(y0, first(first(y1, y2), y3)))) MARK(s(first(y0, first(from(y1), y2)))) -> c10(MARK(first(y0, first(from(y1), y2)))) MARK(s(first(y0, first(0, y1)))) -> c10(MARK(first(y0, first(0, y1)))) MARK(s(first(y0, first(nil, y1)))) -> c10(MARK(first(y0, first(nil, y1)))) MARK(s(first(y0, first(s(y1), y2)))) -> c10(MARK(first(y0, first(s(y1), y2)))) MARK(s(first(y0, first(cons(y1, y2), y3)))) -> c10(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), first(y2, y3)))) -> c10(MARK(first(first(y0, y1), first(y2, y3)))) MARK(s(first(from(y0), first(y1, y2)))) -> c10(MARK(first(from(y0), first(y1, y2)))) MARK(s(first(s(y0), first(y1, y2)))) -> c10(MARK(first(s(y0), first(y1, y2)))) MARK(s(first(y0, first(y1, y2)))) -> c10(MARK(first(y0, first(y1, y2)))) MARK(s(first(cons(y0, y1), first(y2, y3)))) -> c10(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(s(first(y0, from(y1)))) -> c10(MARK(first(y0, from(y1)))) MARK(s(first(y0, from(first(y1, y2))))) -> c10(MARK(first(y0, from(first(y1, y2))))) MARK(s(first(y0, from(from(y1))))) -> c10(MARK(first(y0, from(from(y1))))) MARK(s(first(y0, from(0)))) -> c10(MARK(first(y0, from(0)))) MARK(s(first(y0, from(nil)))) -> c10(MARK(first(y0, from(nil)))) MARK(s(first(y0, from(s(y1))))) -> c10(MARK(first(y0, from(s(y1))))) MARK(s(first(y0, from(cons(y1, y2))))) -> c10(MARK(first(y0, from(cons(y1, y2))))) MARK(s(first(first(y0, y1), from(y2)))) -> c10(MARK(first(first(y0, y1), from(y2)))) MARK(s(first(from(y0), from(y1)))) -> c10(MARK(first(from(y0), from(y1)))) MARK(s(first(s(y0), from(y1)))) -> c10(MARK(first(s(y0), from(y1)))) MARK(s(first(cons(y0, y1), from(y2)))) -> c10(MARK(first(cons(y0, y1), from(y2)))) MARK(s(first(y0, cons(first(y1, y2), y3)))) -> c10(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(s(first(y0, cons(from(y1), y2)))) -> c10(MARK(first(y0, cons(from(y1), y2)))) MARK(s(first(y0, cons(s(y1), y2)))) -> c10(MARK(first(y0, cons(s(y1), y2)))) MARK(s(first(y0, cons(cons(y1, y2), y3)))) -> c10(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), cons(y2, y3)))) -> c10(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(s(first(from(y0), cons(y1, y2)))) -> c10(MARK(first(from(y0), cons(y1, y2)))) MARK(s(first(s(y0), cons(y1, y2)))) -> c10(MARK(first(s(y0), cons(y1, y2)))) MARK(s(first(cons(y0, y1), cons(y2, y3)))) -> c10(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(s(first(first(y0, first(y1, y2)), y3))) -> c10(MARK(first(first(y0, first(y1, y2)), y3))) MARK(s(first(first(y0, from(y1)), y2))) -> c10(MARK(first(first(y0, from(y1)), y2))) MARK(s(first(first(y0, 0), y1))) -> c10(MARK(first(first(y0, 0), y1))) MARK(s(first(first(y0, nil), y1))) -> c10(MARK(first(first(y0, nil), y1))) MARK(s(first(first(y0, s(y1)), y2))) -> c10(MARK(first(first(y0, s(y1)), y2))) MARK(s(first(first(y0, cons(y1, y2)), y3))) -> c10(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(s(first(first(first(y0, y1), y2), y3))) -> c10(MARK(first(first(first(y0, y1), y2), y3))) MARK(s(first(first(from(y0), y1), y2))) -> c10(MARK(first(first(from(y0), y1), y2))) MARK(s(first(first(0, y0), y1))) -> c10(MARK(first(first(0, y0), y1))) MARK(s(first(first(nil, y0), y1))) -> c10(MARK(first(first(nil, y0), y1))) MARK(s(first(first(s(y0), y1), y2))) -> c10(MARK(first(first(s(y0), y1), y2))) MARK(s(first(first(cons(y0, y1), y2), y3))) -> c10(MARK(first(first(cons(y0, y1), y2), y3))) MARK(s(first(first(y0, y1), 0))) -> c10(MARK(first(first(y0, y1), 0))) MARK(s(first(first(y0, y1), nil))) -> c10(MARK(first(first(y0, y1), nil))) MARK(s(first(first(y0, y1), s(y2)))) -> c10(MARK(first(first(y0, y1), s(y2)))) MARK(s(first(first(y0, y1), y2))) -> c10(MARK(first(first(y0, y1), y2))) MARK(s(first(from(first(y0, y1)), y2))) -> c10(MARK(first(from(first(y0, y1)), y2))) MARK(s(first(from(from(y0)), y1))) -> c10(MARK(first(from(from(y0)), y1))) MARK(s(first(from(s(y0)), y1))) -> c10(MARK(first(from(s(y0)), y1))) MARK(s(first(from(cons(y0, y1)), y2))) -> c10(MARK(first(from(cons(y0, y1)), y2))) MARK(s(first(from(y0), y1))) -> c10(MARK(first(from(y0), y1))) MARK(s(first(from(y0), 0))) -> c10(MARK(first(from(y0), 0))) MARK(s(first(from(y0), nil))) -> c10(MARK(first(from(y0), nil))) MARK(s(first(from(y0), s(y1)))) -> c10(MARK(first(from(y0), s(y1)))) MARK(s(first(s(first(y0, y1)), y2))) -> c10(MARK(first(s(first(y0, y1)), y2))) MARK(s(first(s(from(y0)), y1))) -> c10(MARK(first(s(from(y0)), y1))) MARK(s(first(s(0), y0))) -> c10(MARK(first(s(0), y0))) MARK(s(first(s(nil), y0))) -> c10(MARK(first(s(nil), y0))) MARK(s(first(s(s(y0)), y1))) -> c10(MARK(first(s(s(y0)), y1))) MARK(s(first(s(cons(y0, y1)), y2))) -> c10(MARK(first(s(cons(y0, y1)), y2))) MARK(s(first(s(y0), y1))) -> c10(MARK(first(s(y0), y1))) MARK(s(first(s(y0), 0))) -> c10(MARK(first(s(y0), 0))) MARK(s(first(s(y0), nil))) -> c10(MARK(first(s(y0), nil))) MARK(s(first(s(y0), s(y1)))) -> c10(MARK(first(s(y0), s(y1)))) MARK(s(first(0, first(y0, y1)))) -> c10(MARK(first(0, first(y0, y1)))) MARK(s(first(nil, first(y0, y1)))) -> c10(MARK(first(nil, first(y0, y1)))) MARK(s(first(0, from(y0)))) -> c10(MARK(first(0, from(y0)))) MARK(s(first(nil, from(y0)))) -> c10(MARK(first(nil, from(y0)))) MARK(s(first(y0, cons(y1, y2)))) -> c10(MARK(first(y0, cons(y1, y2)))) MARK(s(first(0, cons(y0, y1)))) -> c10(MARK(first(0, cons(y0, y1)))) MARK(s(first(nil, cons(y0, y1)))) -> c10(MARK(first(nil, cons(y0, y1)))) MARK(s(first(from(0), y0))) -> c10(MARK(first(from(0), y0))) MARK(s(first(from(nil), y0))) -> c10(MARK(first(from(nil), y0))) MARK(s(first(y0, cons(0, y1)))) -> c10(MARK(first(y0, cons(0, y1)))) MARK(s(first(y0, cons(nil, y1)))) -> c10(MARK(first(y0, cons(nil, y1)))) MARK(s(from(s(y0)))) -> c10(MARK(from(s(y0)))) MARK(s(from(cons(y0, y1)))) -> c10(MARK(from(cons(y0, y1)))) MARK(s(from(first(y0, y1)))) -> c10(MARK(from(first(y0, y1)))) MARK(s(from(first(y0, first(y1, y2))))) -> c10(MARK(from(first(y0, first(y1, y2))))) MARK(s(from(first(y0, from(y1))))) -> c10(MARK(from(first(y0, from(y1))))) MARK(s(from(first(y0, 0)))) -> c10(MARK(from(first(y0, 0)))) MARK(s(from(first(y0, nil)))) -> c10(MARK(from(first(y0, nil)))) MARK(s(from(first(y0, s(y1))))) -> c10(MARK(from(first(y0, s(y1))))) MARK(s(from(first(y0, cons(y1, y2))))) -> c10(MARK(from(first(y0, cons(y1, y2))))) MARK(s(from(first(first(y0, y1), y2)))) -> c10(MARK(from(first(first(y0, y1), y2)))) MARK(s(from(first(from(y0), y1)))) -> c10(MARK(from(first(from(y0), y1)))) MARK(s(from(first(0, y0)))) -> c10(MARK(from(first(0, y0)))) MARK(s(from(first(nil, y0)))) -> c10(MARK(from(first(nil, y0)))) MARK(s(from(first(s(y0), y1)))) -> c10(MARK(from(first(s(y0), y1)))) MARK(s(from(first(cons(y0, y1), y2)))) -> c10(MARK(from(first(cons(y0, y1), y2)))) MARK(s(from(from(y0)))) -> c10(MARK(from(from(y0)))) MARK(s(from(from(first(y0, y1))))) -> c10(MARK(from(from(first(y0, y1))))) MARK(s(from(from(from(y0))))) -> c10(MARK(from(from(from(y0))))) MARK(s(from(from(s(y0))))) -> c10(MARK(from(from(s(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c10(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(0)))) -> c10(MARK(from(from(0)))) MARK(s(from(from(nil)))) -> c10(MARK(from(from(nil)))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) 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A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(0))) -> c7(A__FROM(a__from(0))) MARK(from(from(nil))) -> c7(A__FROM(a__from(nil))) MARK(s(s(y0))) -> c10(MARK(s(y0))) MARK(s(cons(y0, y1))) -> c10(MARK(cons(y0, y1))) MARK(s(first(y0, 0))) -> c10(MARK(first(y0, 0))) MARK(s(first(y0, nil))) -> c10(MARK(first(y0, nil))) MARK(s(first(y0, s(y1)))) -> c10(MARK(first(y0, s(y1)))) MARK(s(first(cons(y0, y1), y2))) -> c10(MARK(first(cons(y0, y1), y2))) MARK(s(first(0, y0))) -> c10(MARK(first(0, y0))) MARK(s(first(nil, y0))) -> c10(MARK(first(nil, y0))) MARK(s(first(y0, first(y1, first(y2, y3))))) -> c10(MARK(first(y0, first(y1, first(y2, y3))))) MARK(s(first(y0, first(y1, from(y2))))) -> c10(MARK(first(y0, first(y1, from(y2))))) MARK(s(first(y0, first(y1, 0)))) -> c10(MARK(first(y0, first(y1, 0)))) MARK(s(first(y0, first(y1, nil)))) -> c10(MARK(first(y0, first(y1, nil)))) MARK(s(first(y0, first(y1, s(y2))))) -> c10(MARK(first(y0, first(y1, s(y2))))) MARK(s(first(y0, first(y1, cons(y2, y3))))) -> c10(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(s(first(y0, first(first(y1, y2), y3)))) -> c10(MARK(first(y0, first(first(y1, y2), y3)))) MARK(s(first(y0, first(from(y1), y2)))) -> c10(MARK(first(y0, first(from(y1), y2)))) MARK(s(first(y0, first(0, y1)))) -> c10(MARK(first(y0, first(0, y1)))) MARK(s(first(y0, first(nil, y1)))) -> c10(MARK(first(y0, first(nil, y1)))) MARK(s(first(y0, first(s(y1), y2)))) -> c10(MARK(first(y0, first(s(y1), y2)))) MARK(s(first(y0, first(cons(y1, y2), y3)))) -> c10(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), first(y2, y3)))) -> c10(MARK(first(first(y0, y1), first(y2, y3)))) MARK(s(first(from(y0), first(y1, y2)))) -> c10(MARK(first(from(y0), first(y1, y2)))) MARK(s(first(s(y0), first(y1, y2)))) -> c10(MARK(first(s(y0), first(y1, y2)))) MARK(s(first(y0, first(y1, y2)))) -> c10(MARK(first(y0, first(y1, y2)))) MARK(s(first(cons(y0, y1), first(y2, y3)))) -> c10(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(s(first(y0, from(y1)))) -> c10(MARK(first(y0, from(y1)))) MARK(s(first(y0, from(first(y1, y2))))) -> c10(MARK(first(y0, from(first(y1, y2))))) MARK(s(first(y0, from(from(y1))))) -> c10(MARK(first(y0, from(from(y1))))) MARK(s(first(y0, from(0)))) -> c10(MARK(first(y0, from(0)))) MARK(s(first(y0, from(nil)))) -> c10(MARK(first(y0, from(nil)))) MARK(s(first(y0, from(s(y1))))) -> c10(MARK(first(y0, from(s(y1))))) MARK(s(first(y0, from(cons(y1, y2))))) -> c10(MARK(first(y0, from(cons(y1, y2))))) MARK(s(first(first(y0, y1), from(y2)))) -> c10(MARK(first(first(y0, y1), from(y2)))) MARK(s(first(from(y0), from(y1)))) -> c10(MARK(first(from(y0), from(y1)))) MARK(s(first(s(y0), from(y1)))) -> c10(MARK(first(s(y0), from(y1)))) MARK(s(first(cons(y0, y1), from(y2)))) -> c10(MARK(first(cons(y0, y1), from(y2)))) MARK(s(first(y0, cons(first(y1, y2), y3)))) -> c10(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(s(first(y0, cons(from(y1), y2)))) -> c10(MARK(first(y0, cons(from(y1), y2)))) MARK(s(first(y0, cons(s(y1), y2)))) -> c10(MARK(first(y0, cons(s(y1), y2)))) MARK(s(first(y0, cons(cons(y1, y2), y3)))) -> c10(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), cons(y2, y3)))) -> c10(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(s(first(from(y0), cons(y1, y2)))) -> c10(MARK(first(from(y0), cons(y1, y2)))) MARK(s(first(s(y0), cons(y1, y2)))) -> c10(MARK(first(s(y0), cons(y1, y2)))) MARK(s(first(cons(y0, y1), cons(y2, y3)))) -> c10(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(s(first(first(y0, first(y1, y2)), y3))) -> c10(MARK(first(first(y0, first(y1, y2)), y3))) MARK(s(first(first(y0, from(y1)), y2))) -> c10(MARK(first(first(y0, from(y1)), y2))) MARK(s(first(first(y0, 0), y1))) -> c10(MARK(first(first(y0, 0), y1))) MARK(s(first(first(y0, nil), y1))) -> c10(MARK(first(first(y0, nil), y1))) MARK(s(first(first(y0, s(y1)), y2))) -> c10(MARK(first(first(y0, s(y1)), y2))) MARK(s(first(first(y0, cons(y1, y2)), y3))) -> c10(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(s(first(first(first(y0, y1), y2), y3))) -> c10(MARK(first(first(first(y0, y1), y2), y3))) MARK(s(first(first(from(y0), y1), y2))) -> c10(MARK(first(first(from(y0), y1), y2))) MARK(s(first(first(0, y0), y1))) -> c10(MARK(first(first(0, y0), y1))) MARK(s(first(first(nil, y0), y1))) -> c10(MARK(first(first(nil, y0), y1))) MARK(s(first(first(s(y0), y1), y2))) -> c10(MARK(first(first(s(y0), y1), y2))) MARK(s(first(first(cons(y0, y1), y2), y3))) -> c10(MARK(first(first(cons(y0, y1), y2), y3))) MARK(s(first(first(y0, y1), 0))) -> c10(MARK(first(first(y0, y1), 0))) MARK(s(first(first(y0, y1), nil))) -> c10(MARK(first(first(y0, y1), nil))) MARK(s(first(first(y0, y1), s(y2)))) -> c10(MARK(first(first(y0, y1), s(y2)))) MARK(s(first(first(y0, y1), y2))) -> c10(MARK(first(first(y0, y1), y2))) MARK(s(first(from(first(y0, y1)), y2))) -> c10(MARK(first(from(first(y0, y1)), y2))) MARK(s(first(from(from(y0)), y1))) -> c10(MARK(first(from(from(y0)), y1))) MARK(s(first(from(s(y0)), y1))) -> c10(MARK(first(from(s(y0)), y1))) MARK(s(first(from(cons(y0, y1)), y2))) -> c10(MARK(first(from(cons(y0, y1)), y2))) MARK(s(first(from(y0), y1))) -> c10(MARK(first(from(y0), y1))) MARK(s(first(from(y0), 0))) -> c10(MARK(first(from(y0), 0))) MARK(s(first(from(y0), nil))) -> c10(MARK(first(from(y0), nil))) MARK(s(first(from(y0), s(y1)))) -> c10(MARK(first(from(y0), s(y1)))) MARK(s(first(s(first(y0, y1)), y2))) -> c10(MARK(first(s(first(y0, y1)), y2))) MARK(s(first(s(from(y0)), y1))) -> c10(MARK(first(s(from(y0)), y1))) MARK(s(first(s(0), y0))) -> c10(MARK(first(s(0), y0))) MARK(s(first(s(nil), y0))) -> c10(MARK(first(s(nil), y0))) MARK(s(first(s(s(y0)), y1))) -> c10(MARK(first(s(s(y0)), y1))) MARK(s(first(s(cons(y0, y1)), y2))) -> c10(MARK(first(s(cons(y0, y1)), y2))) MARK(s(first(s(y0), y1))) -> c10(MARK(first(s(y0), y1))) MARK(s(first(s(y0), 0))) -> c10(MARK(first(s(y0), 0))) MARK(s(first(s(y0), nil))) -> c10(MARK(first(s(y0), nil))) MARK(s(first(s(y0), s(y1)))) -> c10(MARK(first(s(y0), s(y1)))) MARK(s(first(0, first(y0, y1)))) -> c10(MARK(first(0, first(y0, y1)))) MARK(s(first(nil, first(y0, y1)))) -> c10(MARK(first(nil, first(y0, y1)))) MARK(s(first(0, from(y0)))) -> c10(MARK(first(0, from(y0)))) MARK(s(first(nil, from(y0)))) -> c10(MARK(first(nil, from(y0)))) MARK(s(first(y0, cons(y1, y2)))) -> c10(MARK(first(y0, cons(y1, y2)))) MARK(s(first(0, cons(y0, y1)))) -> c10(MARK(first(0, cons(y0, y1)))) MARK(s(first(nil, cons(y0, y1)))) -> c10(MARK(first(nil, cons(y0, y1)))) MARK(s(first(from(0), y0))) -> c10(MARK(first(from(0), y0))) MARK(s(first(from(nil), y0))) -> c10(MARK(first(from(nil), y0))) MARK(s(first(y0, cons(0, y1)))) -> c10(MARK(first(y0, cons(0, y1)))) MARK(s(first(y0, cons(nil, y1)))) -> c10(MARK(first(y0, cons(nil, y1)))) MARK(s(from(s(y0)))) -> c10(MARK(from(s(y0)))) MARK(s(from(cons(y0, y1)))) -> c10(MARK(from(cons(y0, y1)))) MARK(s(from(first(y0, y1)))) -> c10(MARK(from(first(y0, y1)))) MARK(s(from(first(y0, first(y1, y2))))) -> c10(MARK(from(first(y0, first(y1, y2))))) MARK(s(from(first(y0, from(y1))))) -> c10(MARK(from(first(y0, from(y1))))) MARK(s(from(first(y0, 0)))) -> c10(MARK(from(first(y0, 0)))) MARK(s(from(first(y0, nil)))) -> c10(MARK(from(first(y0, nil)))) MARK(s(from(first(y0, s(y1))))) -> c10(MARK(from(first(y0, s(y1))))) MARK(s(from(first(y0, cons(y1, y2))))) -> c10(MARK(from(first(y0, cons(y1, y2))))) MARK(s(from(first(first(y0, y1), y2)))) -> c10(MARK(from(first(first(y0, y1), y2)))) MARK(s(from(first(from(y0), y1)))) -> c10(MARK(from(first(from(y0), y1)))) MARK(s(from(first(0, y0)))) -> c10(MARK(from(first(0, y0)))) MARK(s(from(first(nil, y0)))) -> c10(MARK(from(first(nil, y0)))) MARK(s(from(first(s(y0), y1)))) -> c10(MARK(from(first(s(y0), y1)))) MARK(s(from(first(cons(y0, y1), y2)))) -> c10(MARK(from(first(cons(y0, y1), y2)))) MARK(s(from(from(y0)))) -> c10(MARK(from(from(y0)))) MARK(s(from(from(first(y0, y1))))) -> c10(MARK(from(from(first(y0, y1))))) MARK(s(from(from(from(y0))))) -> c10(MARK(from(from(from(y0))))) MARK(s(from(from(s(y0))))) -> c10(MARK(from(from(s(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c10(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(0)))) -> c10(MARK(from(from(0)))) MARK(s(from(from(nil)))) -> c10(MARK(from(from(nil)))) S tuples: MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) 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c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), 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MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(0))) -> c7(A__FROM(a__from(0))) MARK(from(from(nil))) -> c7(A__FROM(a__from(nil))) MARK(s(s(y0))) -> c10(MARK(s(y0))) MARK(s(cons(y0, y1))) -> c10(MARK(cons(y0, y1))) MARK(s(first(y0, 0))) -> c10(MARK(first(y0, 0))) MARK(s(first(y0, nil))) -> c10(MARK(first(y0, nil))) MARK(s(first(y0, s(y1)))) -> c10(MARK(first(y0, s(y1)))) MARK(s(first(cons(y0, y1), y2))) -> c10(MARK(first(cons(y0, y1), y2))) MARK(s(first(0, y0))) -> c10(MARK(first(0, y0))) MARK(s(first(nil, y0))) -> c10(MARK(first(nil, y0))) MARK(s(first(y0, first(y1, first(y2, y3))))) -> c10(MARK(first(y0, first(y1, first(y2, y3))))) MARK(s(first(y0, first(y1, from(y2))))) -> c10(MARK(first(y0, first(y1, from(y2))))) MARK(s(first(y0, first(y1, 0)))) -> c10(MARK(first(y0, first(y1, 0)))) MARK(s(first(y0, first(y1, nil)))) -> c10(MARK(first(y0, first(y1, nil)))) MARK(s(first(y0, first(y1, s(y2))))) -> c10(MARK(first(y0, first(y1, s(y2))))) MARK(s(first(y0, first(y1, cons(y2, y3))))) -> c10(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(s(first(y0, first(first(y1, y2), y3)))) -> c10(MARK(first(y0, first(first(y1, y2), y3)))) MARK(s(first(y0, first(from(y1), y2)))) -> c10(MARK(first(y0, first(from(y1), y2)))) MARK(s(first(y0, first(0, y1)))) -> c10(MARK(first(y0, first(0, y1)))) MARK(s(first(y0, first(nil, y1)))) -> c10(MARK(first(y0, first(nil, y1)))) MARK(s(first(y0, first(s(y1), y2)))) -> c10(MARK(first(y0, first(s(y1), y2)))) MARK(s(first(y0, first(cons(y1, y2), y3)))) -> c10(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), first(y2, y3)))) -> c10(MARK(first(first(y0, y1), first(y2, y3)))) MARK(s(first(from(y0), first(y1, y2)))) -> c10(MARK(first(from(y0), first(y1, y2)))) MARK(s(first(s(y0), first(y1, y2)))) -> c10(MARK(first(s(y0), first(y1, y2)))) MARK(s(first(y0, first(y1, y2)))) -> c10(MARK(first(y0, first(y1, y2)))) MARK(s(first(cons(y0, y1), first(y2, y3)))) -> c10(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(s(first(y0, from(y1)))) -> c10(MARK(first(y0, from(y1)))) MARK(s(first(y0, from(first(y1, y2))))) -> c10(MARK(first(y0, from(first(y1, y2))))) MARK(s(first(y0, from(from(y1))))) -> c10(MARK(first(y0, from(from(y1))))) MARK(s(first(y0, from(0)))) -> c10(MARK(first(y0, from(0)))) MARK(s(first(y0, from(nil)))) -> c10(MARK(first(y0, from(nil)))) MARK(s(first(y0, from(s(y1))))) -> c10(MARK(first(y0, from(s(y1))))) MARK(s(first(y0, from(cons(y1, y2))))) -> c10(MARK(first(y0, from(cons(y1, y2))))) MARK(s(first(first(y0, y1), from(y2)))) -> c10(MARK(first(first(y0, y1), from(y2)))) MARK(s(first(from(y0), from(y1)))) -> c10(MARK(first(from(y0), from(y1)))) MARK(s(first(s(y0), from(y1)))) -> c10(MARK(first(s(y0), from(y1)))) MARK(s(first(cons(y0, y1), from(y2)))) -> c10(MARK(first(cons(y0, y1), from(y2)))) MARK(s(first(y0, cons(first(y1, y2), y3)))) -> c10(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(s(first(y0, cons(from(y1), y2)))) -> c10(MARK(first(y0, cons(from(y1), y2)))) MARK(s(first(y0, cons(s(y1), y2)))) -> c10(MARK(first(y0, cons(s(y1), y2)))) MARK(s(first(y0, cons(cons(y1, y2), y3)))) -> c10(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), cons(y2, y3)))) -> c10(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(s(first(from(y0), cons(y1, y2)))) -> c10(MARK(first(from(y0), cons(y1, y2)))) MARK(s(first(s(y0), cons(y1, y2)))) -> c10(MARK(first(s(y0), cons(y1, y2)))) MARK(s(first(cons(y0, y1), cons(y2, y3)))) -> c10(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(s(first(first(y0, first(y1, y2)), y3))) -> c10(MARK(first(first(y0, first(y1, y2)), y3))) MARK(s(first(first(y0, from(y1)), y2))) -> c10(MARK(first(first(y0, from(y1)), y2))) MARK(s(first(first(y0, 0), y1))) -> c10(MARK(first(first(y0, 0), y1))) MARK(s(first(first(y0, nil), y1))) -> c10(MARK(first(first(y0, nil), y1))) MARK(s(first(first(y0, s(y1)), y2))) -> c10(MARK(first(first(y0, s(y1)), y2))) MARK(s(first(first(y0, cons(y1, y2)), y3))) -> c10(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(s(first(first(first(y0, y1), y2), y3))) -> c10(MARK(first(first(first(y0, y1), y2), y3))) MARK(s(first(first(from(y0), y1), y2))) -> c10(MARK(first(first(from(y0), y1), y2))) MARK(s(first(first(0, y0), y1))) -> c10(MARK(first(first(0, y0), y1))) MARK(s(first(first(nil, y0), y1))) -> c10(MARK(first(first(nil, y0), y1))) MARK(s(first(first(s(y0), y1), y2))) -> c10(MARK(first(first(s(y0), y1), y2))) MARK(s(first(first(cons(y0, y1), y2), y3))) -> c10(MARK(first(first(cons(y0, y1), y2), y3))) MARK(s(first(first(y0, y1), 0))) -> c10(MARK(first(first(y0, y1), 0))) MARK(s(first(first(y0, y1), nil))) -> c10(MARK(first(first(y0, y1), nil))) MARK(s(first(first(y0, y1), s(y2)))) -> c10(MARK(first(first(y0, y1), s(y2)))) MARK(s(first(first(y0, y1), y2))) -> c10(MARK(first(first(y0, y1), y2))) MARK(s(first(from(first(y0, y1)), y2))) -> c10(MARK(first(from(first(y0, y1)), y2))) MARK(s(first(from(from(y0)), y1))) -> c10(MARK(first(from(from(y0)), y1))) MARK(s(first(from(s(y0)), y1))) -> c10(MARK(first(from(s(y0)), y1))) MARK(s(first(from(cons(y0, y1)), y2))) -> c10(MARK(first(from(cons(y0, y1)), y2))) MARK(s(first(from(y0), y1))) -> c10(MARK(first(from(y0), y1))) MARK(s(first(from(y0), 0))) -> c10(MARK(first(from(y0), 0))) MARK(s(first(from(y0), nil))) -> c10(MARK(first(from(y0), nil))) MARK(s(first(from(y0), s(y1)))) -> c10(MARK(first(from(y0), s(y1)))) MARK(s(first(s(first(y0, y1)), y2))) -> c10(MARK(first(s(first(y0, y1)), y2))) MARK(s(first(s(from(y0)), y1))) -> c10(MARK(first(s(from(y0)), y1))) MARK(s(first(s(0), y0))) -> c10(MARK(first(s(0), y0))) MARK(s(first(s(nil), y0))) -> c10(MARK(first(s(nil), y0))) MARK(s(first(s(s(y0)), y1))) -> c10(MARK(first(s(s(y0)), y1))) MARK(s(first(s(cons(y0, y1)), y2))) -> c10(MARK(first(s(cons(y0, y1)), y2))) MARK(s(first(s(y0), y1))) -> c10(MARK(first(s(y0), y1))) MARK(s(first(s(y0), 0))) -> c10(MARK(first(s(y0), 0))) MARK(s(first(s(y0), nil))) -> c10(MARK(first(s(y0), nil))) MARK(s(first(s(y0), s(y1)))) -> c10(MARK(first(s(y0), s(y1)))) MARK(s(first(0, first(y0, y1)))) -> c10(MARK(first(0, first(y0, y1)))) MARK(s(first(nil, first(y0, y1)))) -> c10(MARK(first(nil, first(y0, y1)))) MARK(s(first(0, from(y0)))) -> c10(MARK(first(0, from(y0)))) MARK(s(first(nil, from(y0)))) -> c10(MARK(first(nil, from(y0)))) MARK(s(first(y0, cons(y1, y2)))) -> c10(MARK(first(y0, cons(y1, y2)))) MARK(s(first(0, cons(y0, y1)))) -> c10(MARK(first(0, cons(y0, y1)))) MARK(s(first(nil, cons(y0, y1)))) -> c10(MARK(first(nil, cons(y0, y1)))) MARK(s(first(from(0), y0))) -> c10(MARK(first(from(0), y0))) MARK(s(first(from(nil), y0))) -> c10(MARK(first(from(nil), y0))) MARK(s(first(y0, cons(0, y1)))) -> c10(MARK(first(y0, cons(0, y1)))) MARK(s(first(y0, cons(nil, y1)))) -> c10(MARK(first(y0, cons(nil, y1)))) MARK(s(from(s(y0)))) -> c10(MARK(from(s(y0)))) MARK(s(from(cons(y0, y1)))) -> c10(MARK(from(cons(y0, y1)))) MARK(s(from(first(y0, y1)))) -> c10(MARK(from(first(y0, y1)))) MARK(s(from(first(y0, first(y1, y2))))) -> c10(MARK(from(first(y0, first(y1, y2))))) MARK(s(from(first(y0, from(y1))))) -> c10(MARK(from(first(y0, from(y1))))) MARK(s(from(first(y0, 0)))) -> c10(MARK(from(first(y0, 0)))) MARK(s(from(first(y0, nil)))) -> c10(MARK(from(first(y0, nil)))) MARK(s(from(first(y0, s(y1))))) -> c10(MARK(from(first(y0, s(y1))))) MARK(s(from(first(y0, cons(y1, y2))))) -> c10(MARK(from(first(y0, cons(y1, y2))))) MARK(s(from(first(first(y0, y1), y2)))) -> c10(MARK(from(first(first(y0, y1), y2)))) MARK(s(from(first(from(y0), y1)))) -> c10(MARK(from(first(from(y0), y1)))) MARK(s(from(first(0, y0)))) -> c10(MARK(from(first(0, y0)))) MARK(s(from(first(nil, y0)))) -> c10(MARK(from(first(nil, y0)))) MARK(s(from(first(s(y0), y1)))) -> c10(MARK(from(first(s(y0), y1)))) MARK(s(from(first(cons(y0, y1), y2)))) -> c10(MARK(from(first(cons(y0, y1), y2)))) MARK(s(from(from(y0)))) -> c10(MARK(from(from(y0)))) MARK(s(from(from(first(y0, y1))))) -> c10(MARK(from(from(first(y0, y1))))) MARK(s(from(from(from(y0))))) -> c10(MARK(from(from(from(y0))))) MARK(s(from(from(s(y0))))) -> c10(MARK(from(from(s(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c10(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(0)))) -> c10(MARK(from(from(0)))) MARK(s(from(from(nil)))) -> c10(MARK(from(from(nil)))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__FIRST_2, A__FROM_1 Compound Symbols: c11_1, c5_1, c6_1, c5_2, c6_2, c1_1, c3_1, c7_2, c7_1, c10_1 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(0))) -> c7(A__FROM(a__from(0))) MARK(from(from(nil))) -> c7(A__FROM(a__from(nil))) MARK(s(s(y0))) -> c10(MARK(s(y0))) MARK(s(cons(y0, y1))) -> c10(MARK(cons(y0, y1))) MARK(s(first(y0, 0))) -> c10(MARK(first(y0, 0))) MARK(s(first(y0, nil))) -> c10(MARK(first(y0, nil))) MARK(s(first(y0, s(y1)))) -> c10(MARK(first(y0, s(y1)))) MARK(s(first(cons(y0, y1), y2))) -> c10(MARK(first(cons(y0, y1), y2))) MARK(s(first(0, y0))) -> c10(MARK(first(0, y0))) MARK(s(first(nil, y0))) -> c10(MARK(first(nil, y0))) MARK(s(first(y0, first(y1, first(y2, y3))))) -> c10(MARK(first(y0, first(y1, first(y2, y3))))) MARK(s(first(y0, first(y1, from(y2))))) -> c10(MARK(first(y0, first(y1, from(y2))))) MARK(s(first(y0, first(y1, 0)))) -> c10(MARK(first(y0, first(y1, 0)))) MARK(s(first(y0, first(y1, nil)))) -> c10(MARK(first(y0, first(y1, nil)))) MARK(s(first(y0, first(y1, s(y2))))) -> c10(MARK(first(y0, first(y1, s(y2))))) MARK(s(first(y0, first(y1, cons(y2, y3))))) -> c10(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(s(first(y0, first(first(y1, y2), y3)))) -> c10(MARK(first(y0, first(first(y1, y2), y3)))) MARK(s(first(y0, first(from(y1), y2)))) -> c10(MARK(first(y0, first(from(y1), y2)))) MARK(s(first(y0, first(0, y1)))) -> c10(MARK(first(y0, first(0, y1)))) MARK(s(first(y0, first(nil, y1)))) -> c10(MARK(first(y0, first(nil, y1)))) MARK(s(first(y0, first(s(y1), y2)))) -> c10(MARK(first(y0, first(s(y1), y2)))) MARK(s(first(y0, first(cons(y1, y2), y3)))) -> c10(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), first(y2, y3)))) -> c10(MARK(first(first(y0, y1), first(y2, y3)))) MARK(s(first(from(y0), first(y1, y2)))) -> c10(MARK(first(from(y0), first(y1, y2)))) MARK(s(first(s(y0), first(y1, y2)))) -> c10(MARK(first(s(y0), first(y1, y2)))) MARK(s(first(y0, first(y1, y2)))) -> c10(MARK(first(y0, first(y1, y2)))) MARK(s(first(cons(y0, y1), first(y2, y3)))) -> c10(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(s(first(y0, from(y1)))) -> c10(MARK(first(y0, from(y1)))) MARK(s(first(y0, from(first(y1, y2))))) -> c10(MARK(first(y0, from(first(y1, y2))))) MARK(s(first(y0, from(from(y1))))) -> c10(MARK(first(y0, from(from(y1))))) MARK(s(first(y0, from(0)))) -> c10(MARK(first(y0, from(0)))) MARK(s(first(y0, from(nil)))) -> c10(MARK(first(y0, from(nil)))) MARK(s(first(y0, from(s(y1))))) -> c10(MARK(first(y0, from(s(y1))))) MARK(s(first(y0, from(cons(y1, y2))))) -> c10(MARK(first(y0, from(cons(y1, y2))))) MARK(s(first(first(y0, y1), from(y2)))) -> c10(MARK(first(first(y0, y1), from(y2)))) MARK(s(first(from(y0), from(y1)))) -> c10(MARK(first(from(y0), from(y1)))) MARK(s(first(s(y0), from(y1)))) -> c10(MARK(first(s(y0), from(y1)))) MARK(s(first(cons(y0, y1), from(y2)))) -> c10(MARK(first(cons(y0, y1), from(y2)))) MARK(s(first(y0, cons(first(y1, y2), y3)))) -> c10(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(s(first(y0, cons(from(y1), y2)))) -> c10(MARK(first(y0, cons(from(y1), y2)))) MARK(s(first(y0, cons(s(y1), y2)))) -> c10(MARK(first(y0, cons(s(y1), y2)))) MARK(s(first(y0, cons(cons(y1, y2), y3)))) -> c10(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), cons(y2, y3)))) -> c10(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(s(first(from(y0), cons(y1, y2)))) -> c10(MARK(first(from(y0), cons(y1, y2)))) MARK(s(first(s(y0), cons(y1, y2)))) -> c10(MARK(first(s(y0), cons(y1, y2)))) MARK(s(first(cons(y0, y1), cons(y2, y3)))) -> c10(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(s(first(first(y0, first(y1, y2)), y3))) -> c10(MARK(first(first(y0, first(y1, y2)), y3))) MARK(s(first(first(y0, from(y1)), y2))) -> c10(MARK(first(first(y0, from(y1)), y2))) MARK(s(first(first(y0, 0), y1))) -> c10(MARK(first(first(y0, 0), y1))) MARK(s(first(first(y0, nil), y1))) -> c10(MARK(first(first(y0, nil), y1))) MARK(s(first(first(y0, s(y1)), y2))) -> c10(MARK(first(first(y0, s(y1)), y2))) MARK(s(first(first(y0, cons(y1, y2)), y3))) -> c10(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(s(first(first(first(y0, y1), y2), y3))) -> c10(MARK(first(first(first(y0, y1), y2), y3))) MARK(s(first(first(from(y0), y1), y2))) -> c10(MARK(first(first(from(y0), y1), y2))) MARK(s(first(first(0, y0), y1))) -> c10(MARK(first(first(0, y0), y1))) MARK(s(first(first(nil, y0), y1))) -> c10(MARK(first(first(nil, y0), y1))) MARK(s(first(first(s(y0), y1), y2))) -> c10(MARK(first(first(s(y0), y1), y2))) MARK(s(first(first(cons(y0, y1), y2), y3))) -> c10(MARK(first(first(cons(y0, y1), y2), y3))) MARK(s(first(first(y0, y1), 0))) -> c10(MARK(first(first(y0, y1), 0))) MARK(s(first(first(y0, y1), nil))) -> c10(MARK(first(first(y0, y1), nil))) MARK(s(first(first(y0, y1), s(y2)))) -> c10(MARK(first(first(y0, y1), s(y2)))) MARK(s(first(first(y0, y1), y2))) -> c10(MARK(first(first(y0, y1), y2))) MARK(s(first(from(first(y0, y1)), y2))) -> c10(MARK(first(from(first(y0, y1)), y2))) MARK(s(first(from(from(y0)), y1))) -> c10(MARK(first(from(from(y0)), y1))) MARK(s(first(from(s(y0)), y1))) -> c10(MARK(first(from(s(y0)), y1))) MARK(s(first(from(cons(y0, y1)), y2))) -> c10(MARK(first(from(cons(y0, y1)), y2))) MARK(s(first(from(y0), y1))) -> c10(MARK(first(from(y0), y1))) MARK(s(first(from(y0), 0))) -> c10(MARK(first(from(y0), 0))) MARK(s(first(from(y0), nil))) -> c10(MARK(first(from(y0), nil))) MARK(s(first(from(y0), s(y1)))) -> c10(MARK(first(from(y0), s(y1)))) MARK(s(first(s(first(y0, y1)), y2))) -> c10(MARK(first(s(first(y0, y1)), y2))) MARK(s(first(s(from(y0)), y1))) -> c10(MARK(first(s(from(y0)), y1))) MARK(s(first(s(0), y0))) -> c10(MARK(first(s(0), y0))) MARK(s(first(s(nil), y0))) -> c10(MARK(first(s(nil), y0))) MARK(s(first(s(s(y0)), y1))) -> c10(MARK(first(s(s(y0)), y1))) MARK(s(first(s(cons(y0, y1)), y2))) -> c10(MARK(first(s(cons(y0, y1)), y2))) MARK(s(first(s(y0), y1))) -> c10(MARK(first(s(y0), y1))) MARK(s(first(s(y0), 0))) -> c10(MARK(first(s(y0), 0))) MARK(s(first(s(y0), nil))) -> c10(MARK(first(s(y0), nil))) MARK(s(first(s(y0), s(y1)))) -> c10(MARK(first(s(y0), s(y1)))) MARK(s(first(0, first(y0, y1)))) -> c10(MARK(first(0, first(y0, y1)))) MARK(s(first(nil, first(y0, y1)))) -> c10(MARK(first(nil, first(y0, y1)))) MARK(s(first(0, from(y0)))) -> c10(MARK(first(0, from(y0)))) MARK(s(first(nil, from(y0)))) -> c10(MARK(first(nil, from(y0)))) MARK(s(first(y0, cons(y1, y2)))) -> c10(MARK(first(y0, cons(y1, y2)))) MARK(s(first(0, cons(y0, y1)))) -> c10(MARK(first(0, cons(y0, y1)))) MARK(s(first(nil, cons(y0, y1)))) -> c10(MARK(first(nil, cons(y0, y1)))) MARK(s(first(from(0), y0))) -> c10(MARK(first(from(0), y0))) MARK(s(first(from(nil), y0))) -> c10(MARK(first(from(nil), y0))) MARK(s(first(y0, cons(0, y1)))) -> c10(MARK(first(y0, cons(0, y1)))) MARK(s(first(y0, cons(nil, y1)))) -> c10(MARK(first(y0, cons(nil, y1)))) MARK(s(from(s(y0)))) -> c10(MARK(from(s(y0)))) MARK(s(from(cons(y0, y1)))) -> c10(MARK(from(cons(y0, y1)))) MARK(s(from(first(y0, y1)))) -> c10(MARK(from(first(y0, y1)))) MARK(s(from(first(y0, first(y1, y2))))) -> c10(MARK(from(first(y0, first(y1, y2))))) MARK(s(from(first(y0, from(y1))))) -> c10(MARK(from(first(y0, from(y1))))) MARK(s(from(first(y0, 0)))) -> c10(MARK(from(first(y0, 0)))) MARK(s(from(first(y0, nil)))) -> c10(MARK(from(first(y0, nil)))) MARK(s(from(first(y0, s(y1))))) -> c10(MARK(from(first(y0, s(y1))))) MARK(s(from(first(y0, cons(y1, y2))))) -> c10(MARK(from(first(y0, cons(y1, y2))))) MARK(s(from(first(first(y0, y1), y2)))) -> c10(MARK(from(first(first(y0, y1), y2)))) MARK(s(from(first(from(y0), y1)))) -> c10(MARK(from(first(from(y0), y1)))) MARK(s(from(first(0, y0)))) -> c10(MARK(from(first(0, y0)))) MARK(s(from(first(nil, y0)))) -> c10(MARK(from(first(nil, y0)))) MARK(s(from(first(s(y0), y1)))) -> c10(MARK(from(first(s(y0), y1)))) MARK(s(from(first(cons(y0, y1), y2)))) -> c10(MARK(from(first(cons(y0, y1), y2)))) MARK(s(from(from(y0)))) -> c10(MARK(from(from(y0)))) MARK(s(from(from(first(y0, y1))))) -> c10(MARK(from(from(first(y0, y1))))) MARK(s(from(from(from(y0))))) -> c10(MARK(from(from(from(y0))))) MARK(s(from(from(s(y0))))) -> c10(MARK(from(from(s(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c10(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(0)))) -> c10(MARK(from(from(0)))) MARK(s(from(from(nil)))) -> c10(MARK(from(from(nil)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1))) S tuples: MARK(cons(z0, z1)) -> c11(MARK(z0)) MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, 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A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(0))) -> c7(A__FROM(a__from(0))) MARK(from(from(nil))) -> c7(A__FROM(a__from(nil))) MARK(s(s(y0))) -> c10(MARK(s(y0))) MARK(s(cons(y0, y1))) -> c10(MARK(cons(y0, y1))) MARK(s(first(y0, 0))) -> c10(MARK(first(y0, 0))) MARK(s(first(y0, nil))) -> c10(MARK(first(y0, nil))) MARK(s(first(y0, s(y1)))) -> c10(MARK(first(y0, s(y1)))) MARK(s(first(cons(y0, y1), y2))) -> c10(MARK(first(cons(y0, y1), y2))) MARK(s(first(0, y0))) -> c10(MARK(first(0, y0))) MARK(s(first(nil, y0))) -> c10(MARK(first(nil, y0))) MARK(s(first(y0, first(y1, first(y2, y3))))) -> c10(MARK(first(y0, first(y1, first(y2, y3))))) MARK(s(first(y0, first(y1, from(y2))))) -> c10(MARK(first(y0, first(y1, from(y2))))) MARK(s(first(y0, first(y1, 0)))) -> c10(MARK(first(y0, first(y1, 0)))) MARK(s(first(y0, first(y1, nil)))) -> c10(MARK(first(y0, first(y1, nil)))) MARK(s(first(y0, first(y1, s(y2))))) -> c10(MARK(first(y0, first(y1, s(y2))))) MARK(s(first(y0, first(y1, cons(y2, y3))))) -> c10(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(s(first(y0, first(first(y1, y2), y3)))) -> c10(MARK(first(y0, first(first(y1, y2), y3)))) MARK(s(first(y0, first(from(y1), y2)))) -> c10(MARK(first(y0, first(from(y1), y2)))) MARK(s(first(y0, first(0, y1)))) -> c10(MARK(first(y0, first(0, y1)))) MARK(s(first(y0, first(nil, y1)))) -> c10(MARK(first(y0, first(nil, y1)))) MARK(s(first(y0, first(s(y1), y2)))) -> c10(MARK(first(y0, first(s(y1), y2)))) MARK(s(first(y0, first(cons(y1, y2), y3)))) -> c10(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), first(y2, y3)))) -> c10(MARK(first(first(y0, y1), first(y2, y3)))) MARK(s(first(from(y0), first(y1, y2)))) -> c10(MARK(first(from(y0), first(y1, y2)))) MARK(s(first(s(y0), first(y1, y2)))) -> c10(MARK(first(s(y0), first(y1, y2)))) MARK(s(first(y0, first(y1, y2)))) -> c10(MARK(first(y0, first(y1, y2)))) MARK(s(first(cons(y0, y1), first(y2, y3)))) -> c10(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(s(first(y0, from(y1)))) -> c10(MARK(first(y0, from(y1)))) MARK(s(first(y0, from(first(y1, y2))))) -> c10(MARK(first(y0, from(first(y1, y2))))) MARK(s(first(y0, from(from(y1))))) -> c10(MARK(first(y0, from(from(y1))))) MARK(s(first(y0, from(0)))) -> c10(MARK(first(y0, from(0)))) MARK(s(first(y0, from(nil)))) -> c10(MARK(first(y0, from(nil)))) MARK(s(first(y0, from(s(y1))))) -> c10(MARK(first(y0, from(s(y1))))) MARK(s(first(y0, from(cons(y1, y2))))) -> c10(MARK(first(y0, from(cons(y1, y2))))) MARK(s(first(first(y0, y1), from(y2)))) -> c10(MARK(first(first(y0, y1), from(y2)))) MARK(s(first(from(y0), from(y1)))) -> c10(MARK(first(from(y0), from(y1)))) MARK(s(first(s(y0), from(y1)))) -> c10(MARK(first(s(y0), from(y1)))) MARK(s(first(cons(y0, y1), from(y2)))) -> c10(MARK(first(cons(y0, y1), from(y2)))) MARK(s(first(y0, cons(first(y1, y2), y3)))) -> c10(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(s(first(y0, cons(from(y1), y2)))) -> c10(MARK(first(y0, cons(from(y1), y2)))) MARK(s(first(y0, cons(s(y1), y2)))) -> c10(MARK(first(y0, cons(s(y1), y2)))) MARK(s(first(y0, cons(cons(y1, y2), y3)))) -> c10(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), cons(y2, y3)))) -> c10(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(s(first(from(y0), cons(y1, y2)))) -> c10(MARK(first(from(y0), cons(y1, y2)))) MARK(s(first(s(y0), cons(y1, y2)))) -> c10(MARK(first(s(y0), cons(y1, y2)))) MARK(s(first(cons(y0, y1), cons(y2, y3)))) -> c10(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(s(first(first(y0, first(y1, y2)), y3))) -> c10(MARK(first(first(y0, first(y1, y2)), y3))) MARK(s(first(first(y0, from(y1)), y2))) -> c10(MARK(first(first(y0, from(y1)), y2))) MARK(s(first(first(y0, 0), y1))) -> c10(MARK(first(first(y0, 0), y1))) MARK(s(first(first(y0, nil), y1))) -> c10(MARK(first(first(y0, nil), y1))) MARK(s(first(first(y0, s(y1)), y2))) -> c10(MARK(first(first(y0, s(y1)), y2))) MARK(s(first(first(y0, cons(y1, y2)), y3))) -> c10(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(s(first(first(first(y0, y1), y2), y3))) -> c10(MARK(first(first(first(y0, y1), y2), y3))) MARK(s(first(first(from(y0), y1), y2))) -> c10(MARK(first(first(from(y0), y1), y2))) MARK(s(first(first(0, y0), y1))) -> c10(MARK(first(first(0, y0), y1))) MARK(s(first(first(nil, y0), y1))) -> c10(MARK(first(first(nil, y0), y1))) MARK(s(first(first(s(y0), y1), y2))) -> c10(MARK(first(first(s(y0), y1), y2))) MARK(s(first(first(cons(y0, y1), y2), y3))) -> c10(MARK(first(first(cons(y0, y1), y2), y3))) MARK(s(first(first(y0, y1), 0))) -> c10(MARK(first(first(y0, y1), 0))) MARK(s(first(first(y0, y1), nil))) -> c10(MARK(first(first(y0, y1), nil))) MARK(s(first(first(y0, y1), s(y2)))) -> c10(MARK(first(first(y0, y1), s(y2)))) MARK(s(first(first(y0, y1), y2))) -> c10(MARK(first(first(y0, y1), y2))) MARK(s(first(from(first(y0, y1)), y2))) -> c10(MARK(first(from(first(y0, y1)), y2))) MARK(s(first(from(from(y0)), y1))) -> c10(MARK(first(from(from(y0)), y1))) MARK(s(first(from(s(y0)), y1))) -> c10(MARK(first(from(s(y0)), y1))) MARK(s(first(from(cons(y0, y1)), y2))) -> c10(MARK(first(from(cons(y0, y1)), y2))) MARK(s(first(from(y0), y1))) -> c10(MARK(first(from(y0), y1))) MARK(s(first(from(y0), 0))) -> c10(MARK(first(from(y0), 0))) MARK(s(first(from(y0), nil))) -> c10(MARK(first(from(y0), nil))) MARK(s(first(from(y0), s(y1)))) -> c10(MARK(first(from(y0), s(y1)))) MARK(s(first(s(first(y0, y1)), y2))) -> c10(MARK(first(s(first(y0, y1)), y2))) MARK(s(first(s(from(y0)), y1))) -> c10(MARK(first(s(from(y0)), y1))) MARK(s(first(s(0), y0))) -> c10(MARK(first(s(0), y0))) MARK(s(first(s(nil), y0))) -> c10(MARK(first(s(nil), y0))) MARK(s(first(s(s(y0)), y1))) -> c10(MARK(first(s(s(y0)), y1))) MARK(s(first(s(cons(y0, y1)), y2))) -> c10(MARK(first(s(cons(y0, y1)), y2))) MARK(s(first(s(y0), y1))) -> c10(MARK(first(s(y0), y1))) MARK(s(first(s(y0), 0))) -> c10(MARK(first(s(y0), 0))) MARK(s(first(s(y0), nil))) -> c10(MARK(first(s(y0), nil))) MARK(s(first(s(y0), s(y1)))) -> c10(MARK(first(s(y0), s(y1)))) MARK(s(first(0, first(y0, y1)))) -> c10(MARK(first(0, first(y0, y1)))) MARK(s(first(nil, first(y0, y1)))) -> c10(MARK(first(nil, first(y0, y1)))) MARK(s(first(0, from(y0)))) -> c10(MARK(first(0, from(y0)))) MARK(s(first(nil, from(y0)))) -> c10(MARK(first(nil, from(y0)))) MARK(s(first(y0, cons(y1, y2)))) -> c10(MARK(first(y0, cons(y1, y2)))) MARK(s(first(0, cons(y0, y1)))) -> c10(MARK(first(0, cons(y0, y1)))) MARK(s(first(nil, cons(y0, y1)))) -> c10(MARK(first(nil, cons(y0, y1)))) MARK(s(first(from(0), y0))) -> c10(MARK(first(from(0), y0))) MARK(s(first(from(nil), y0))) -> c10(MARK(first(from(nil), y0))) MARK(s(first(y0, cons(0, y1)))) -> c10(MARK(first(y0, cons(0, y1)))) MARK(s(first(y0, cons(nil, y1)))) -> c10(MARK(first(y0, cons(nil, y1)))) MARK(s(from(s(y0)))) -> c10(MARK(from(s(y0)))) MARK(s(from(cons(y0, y1)))) -> c10(MARK(from(cons(y0, y1)))) MARK(s(from(first(y0, y1)))) -> c10(MARK(from(first(y0, y1)))) MARK(s(from(first(y0, first(y1, y2))))) -> c10(MARK(from(first(y0, first(y1, y2))))) MARK(s(from(first(y0, from(y1))))) -> c10(MARK(from(first(y0, from(y1))))) MARK(s(from(first(y0, 0)))) -> c10(MARK(from(first(y0, 0)))) MARK(s(from(first(y0, nil)))) -> c10(MARK(from(first(y0, nil)))) MARK(s(from(first(y0, s(y1))))) -> c10(MARK(from(first(y0, s(y1))))) MARK(s(from(first(y0, cons(y1, y2))))) -> c10(MARK(from(first(y0, cons(y1, y2))))) MARK(s(from(first(first(y0, y1), y2)))) -> c10(MARK(from(first(first(y0, y1), y2)))) MARK(s(from(first(from(y0), y1)))) -> c10(MARK(from(first(from(y0), y1)))) MARK(s(from(first(0, y0)))) -> c10(MARK(from(first(0, y0)))) MARK(s(from(first(nil, y0)))) -> c10(MARK(from(first(nil, y0)))) MARK(s(from(first(s(y0), y1)))) -> c10(MARK(from(first(s(y0), y1)))) MARK(s(from(first(cons(y0, y1), y2)))) -> c10(MARK(from(first(cons(y0, y1), y2)))) MARK(s(from(from(y0)))) -> c10(MARK(from(from(y0)))) MARK(s(from(from(first(y0, y1))))) -> c10(MARK(from(from(first(y0, y1))))) MARK(s(from(from(from(y0))))) -> c10(MARK(from(from(from(y0))))) MARK(s(from(from(s(y0))))) -> c10(MARK(from(from(s(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c10(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(0)))) -> c10(MARK(from(from(0)))) MARK(s(from(from(nil)))) -> c10(MARK(from(from(nil)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__FIRST_2, A__FROM_1 Compound Symbols: c11_1, c5_1, c6_1, c5_2, c6_2, c1_1, c3_1, c7_2, c7_1, c10_1 ---------------------------------------- (119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(cons(z0, z1)) -> c11(MARK(z0)) by MARK(cons(cons(y0, y1), z1)) -> c11(MARK(cons(y0, y1))) MARK(cons(first(y0, 0), z1)) -> c11(MARK(first(y0, 0))) MARK(cons(first(y0, nil), z1)) -> c11(MARK(first(y0, nil))) MARK(cons(first(y0, s(y1)), z1)) -> c11(MARK(first(y0, s(y1)))) MARK(cons(first(cons(y0, y1), y2), z1)) -> c11(MARK(first(cons(y0, y1), y2))) MARK(cons(first(0, y0), z1)) -> c11(MARK(first(0, y0))) MARK(cons(first(nil, y0), z1)) -> c11(MARK(first(nil, y0))) MARK(cons(first(y0, first(y1, first(y2, y3))), z1)) -> c11(MARK(first(y0, first(y1, first(y2, y3))))) MARK(cons(first(y0, first(y1, from(y2))), z1)) -> c11(MARK(first(y0, first(y1, from(y2))))) MARK(cons(first(y0, first(y1, 0)), z1)) -> c11(MARK(first(y0, first(y1, 0)))) MARK(cons(first(y0, first(y1, nil)), z1)) -> c11(MARK(first(y0, first(y1, nil)))) MARK(cons(first(y0, first(y1, s(y2))), z1)) -> c11(MARK(first(y0, first(y1, s(y2))))) MARK(cons(first(y0, first(y1, cons(y2, y3))), z1)) -> c11(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(cons(first(y0, first(first(y1, y2), y3)), z1)) -> c11(MARK(first(y0, first(first(y1, y2), y3)))) MARK(cons(first(y0, first(from(y1), y2)), z1)) -> c11(MARK(first(y0, first(from(y1), y2)))) MARK(cons(first(y0, first(0, y1)), z1)) -> c11(MARK(first(y0, first(0, y1)))) MARK(cons(first(y0, first(nil, y1)), z1)) -> c11(MARK(first(y0, first(nil, y1)))) MARK(cons(first(y0, first(s(y1), y2)), z1)) -> c11(MARK(first(y0, first(s(y1), y2)))) MARK(cons(first(y0, first(cons(y1, y2), y3)), z1)) -> c11(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(cons(first(first(y0, y1), first(y2, y3)), z1)) -> c11(MARK(first(first(y0, y1), first(y2, y3)))) MARK(cons(first(from(y0), first(y1, y2)), z1)) -> c11(MARK(first(from(y0), first(y1, y2)))) MARK(cons(first(s(y0), first(y1, y2)), z1)) -> c11(MARK(first(s(y0), first(y1, y2)))) MARK(cons(first(y0, first(y1, y2)), z1)) -> c11(MARK(first(y0, first(y1, y2)))) MARK(cons(first(cons(y0, y1), first(y2, y3)), z1)) -> c11(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(cons(first(y0, from(y1)), z1)) -> c11(MARK(first(y0, from(y1)))) MARK(cons(first(y0, from(first(y1, y2))), z1)) -> c11(MARK(first(y0, from(first(y1, y2))))) MARK(cons(first(y0, from(from(y1))), z1)) -> c11(MARK(first(y0, from(from(y1))))) MARK(cons(first(y0, from(0)), z1)) -> c11(MARK(first(y0, from(0)))) MARK(cons(first(y0, from(nil)), z1)) -> c11(MARK(first(y0, from(nil)))) MARK(cons(first(y0, from(s(y1))), z1)) -> c11(MARK(first(y0, from(s(y1))))) MARK(cons(first(y0, from(cons(y1, y2))), z1)) -> c11(MARK(first(y0, from(cons(y1, y2))))) MARK(cons(first(first(y0, y1), from(y2)), z1)) -> c11(MARK(first(first(y0, y1), from(y2)))) MARK(cons(first(from(y0), from(y1)), z1)) -> c11(MARK(first(from(y0), from(y1)))) MARK(cons(first(s(y0), from(y1)), z1)) -> c11(MARK(first(s(y0), from(y1)))) MARK(cons(first(cons(y0, y1), from(y2)), z1)) -> c11(MARK(first(cons(y0, y1), from(y2)))) MARK(cons(first(y0, cons(first(y1, y2), y3)), z1)) -> c11(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(cons(first(y0, cons(from(y1), y2)), z1)) -> c11(MARK(first(y0, cons(from(y1), y2)))) MARK(cons(first(y0, cons(s(y1), y2)), z1)) -> c11(MARK(first(y0, cons(s(y1), y2)))) MARK(cons(first(y0, cons(cons(y1, y2), y3)), z1)) -> c11(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(cons(first(first(y0, y1), cons(y2, y3)), z1)) -> c11(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(cons(first(from(y0), cons(y1, y2)), z1)) -> c11(MARK(first(from(y0), cons(y1, y2)))) MARK(cons(first(s(y0), cons(y1, y2)), z1)) -> c11(MARK(first(s(y0), cons(y1, y2)))) MARK(cons(first(cons(y0, y1), cons(y2, y3)), z1)) -> c11(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(cons(first(first(y0, first(y1, y2)), y3), z1)) -> c11(MARK(first(first(y0, first(y1, y2)), y3))) MARK(cons(first(first(y0, from(y1)), y2), z1)) -> c11(MARK(first(first(y0, from(y1)), y2))) MARK(cons(first(first(y0, 0), y1), z1)) -> c11(MARK(first(first(y0, 0), y1))) MARK(cons(first(first(y0, nil), y1), z1)) -> c11(MARK(first(first(y0, nil), y1))) MARK(cons(first(first(y0, s(y1)), y2), z1)) -> c11(MARK(first(first(y0, s(y1)), y2))) MARK(cons(first(first(y0, cons(y1, y2)), y3), z1)) -> c11(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(cons(first(first(first(y0, y1), y2), y3), z1)) -> c11(MARK(first(first(first(y0, y1), y2), y3))) MARK(cons(first(first(from(y0), y1), y2), z1)) -> c11(MARK(first(first(from(y0), y1), y2))) MARK(cons(first(first(0, y0), y1), z1)) -> c11(MARK(first(first(0, y0), y1))) MARK(cons(first(first(nil, y0), y1), z1)) -> c11(MARK(first(first(nil, y0), y1))) MARK(cons(first(first(s(y0), y1), y2), z1)) -> c11(MARK(first(first(s(y0), y1), y2))) MARK(cons(first(first(cons(y0, y1), y2), y3), z1)) -> c11(MARK(first(first(cons(y0, y1), y2), y3))) MARK(cons(first(first(y0, y1), 0), z1)) -> c11(MARK(first(first(y0, y1), 0))) MARK(cons(first(first(y0, y1), nil), z1)) -> c11(MARK(first(first(y0, y1), nil))) MARK(cons(first(first(y0, y1), s(y2)), z1)) -> c11(MARK(first(first(y0, y1), s(y2)))) MARK(cons(first(first(y0, y1), y2), z1)) -> c11(MARK(first(first(y0, y1), y2))) MARK(cons(first(from(first(y0, y1)), y2), z1)) -> c11(MARK(first(from(first(y0, y1)), y2))) MARK(cons(first(from(from(y0)), y1), z1)) -> c11(MARK(first(from(from(y0)), y1))) MARK(cons(first(from(s(y0)), y1), z1)) -> c11(MARK(first(from(s(y0)), y1))) MARK(cons(first(from(cons(y0, y1)), y2), z1)) -> c11(MARK(first(from(cons(y0, y1)), y2))) MARK(cons(first(from(y0), y1), z1)) -> c11(MARK(first(from(y0), y1))) MARK(cons(first(from(y0), 0), z1)) -> c11(MARK(first(from(y0), 0))) MARK(cons(first(from(y0), nil), z1)) -> c11(MARK(first(from(y0), nil))) MARK(cons(first(from(y0), s(y1)), z1)) -> c11(MARK(first(from(y0), s(y1)))) MARK(cons(first(s(first(y0, y1)), y2), z1)) -> c11(MARK(first(s(first(y0, y1)), y2))) MARK(cons(first(s(from(y0)), y1), z1)) -> c11(MARK(first(s(from(y0)), y1))) MARK(cons(first(s(s(y0)), y1), z1)) -> c11(MARK(first(s(s(y0)), y1))) MARK(cons(first(s(cons(y0, y1)), y2), z1)) -> c11(MARK(first(s(cons(y0, y1)), y2))) MARK(cons(first(s(y0), y1), z1)) -> c11(MARK(first(s(y0), y1))) MARK(cons(first(s(y0), 0), z1)) -> c11(MARK(first(s(y0), 0))) MARK(cons(first(s(y0), nil), z1)) -> c11(MARK(first(s(y0), nil))) MARK(cons(first(s(y0), s(y1)), z1)) -> c11(MARK(first(s(y0), s(y1)))) MARK(cons(first(0, first(y0, y1)), z1)) -> c11(MARK(first(0, first(y0, y1)))) MARK(cons(first(nil, first(y0, y1)), z1)) -> c11(MARK(first(nil, first(y0, y1)))) MARK(cons(first(0, from(y0)), z1)) -> c11(MARK(first(0, from(y0)))) MARK(cons(first(nil, from(y0)), z1)) -> c11(MARK(first(nil, from(y0)))) MARK(cons(first(y0, cons(y1, y2)), z1)) -> c11(MARK(first(y0, cons(y1, y2)))) MARK(cons(first(0, cons(y0, y1)), z1)) -> c11(MARK(first(0, cons(y0, y1)))) MARK(cons(first(nil, cons(y0, y1)), z1)) -> c11(MARK(first(nil, cons(y0, y1)))) MARK(cons(first(from(0), y0), z1)) -> c11(MARK(first(from(0), y0))) MARK(cons(first(from(nil), y0), z1)) -> c11(MARK(first(from(nil), y0))) MARK(cons(first(s(0), y0), z1)) -> c11(MARK(first(s(0), y0))) MARK(cons(first(s(nil), y0), z1)) -> c11(MARK(first(s(nil), y0))) MARK(cons(first(y0, cons(0, y1)), z1)) -> c11(MARK(first(y0, cons(0, y1)))) MARK(cons(first(y0, cons(nil, y1)), z1)) -> c11(MARK(first(y0, cons(nil, y1)))) MARK(cons(from(s(y0)), z1)) -> c11(MARK(from(s(y0)))) MARK(cons(from(cons(y0, y1)), z1)) -> c11(MARK(from(cons(y0, y1)))) MARK(cons(from(first(y0, y1)), z1)) -> c11(MARK(from(first(y0, y1)))) MARK(cons(from(first(y0, first(y1, y2))), z1)) -> c11(MARK(from(first(y0, first(y1, y2))))) MARK(cons(from(first(y0, from(y1))), z1)) -> c11(MARK(from(first(y0, from(y1))))) MARK(cons(from(first(y0, 0)), z1)) -> c11(MARK(from(first(y0, 0)))) MARK(cons(from(first(y0, nil)), z1)) -> c11(MARK(from(first(y0, nil)))) MARK(cons(from(first(y0, s(y1))), z1)) -> c11(MARK(from(first(y0, s(y1))))) MARK(cons(from(first(y0, cons(y1, y2))), z1)) -> c11(MARK(from(first(y0, cons(y1, y2))))) MARK(cons(from(first(first(y0, y1), y2)), z1)) -> c11(MARK(from(first(first(y0, y1), y2)))) MARK(cons(from(first(from(y0), y1)), z1)) -> c11(MARK(from(first(from(y0), y1)))) MARK(cons(from(first(0, y0)), z1)) -> c11(MARK(from(first(0, y0)))) MARK(cons(from(first(nil, y0)), z1)) -> c11(MARK(from(first(nil, y0)))) MARK(cons(from(first(s(y0), y1)), z1)) -> c11(MARK(from(first(s(y0), y1)))) MARK(cons(from(first(cons(y0, y1), y2)), z1)) -> c11(MARK(from(first(cons(y0, y1), y2)))) MARK(cons(from(from(y0)), z1)) -> c11(MARK(from(from(y0)))) MARK(cons(from(from(first(y0, y1))), z1)) -> c11(MARK(from(from(first(y0, y1))))) MARK(cons(from(from(from(y0))), z1)) -> c11(MARK(from(from(from(y0))))) MARK(cons(from(from(s(y0))), z1)) -> c11(MARK(from(from(s(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c11(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(0)), z1)) -> c11(MARK(from(from(0)))) MARK(cons(from(from(nil)), z1)) -> c11(MARK(from(from(nil)))) MARK(cons(s(s(y0)), z1)) -> c11(MARK(s(s(y0)))) MARK(cons(s(cons(y0, y1)), z1)) -> c11(MARK(s(cons(y0, y1)))) MARK(cons(s(first(y0, 0)), z1)) -> c11(MARK(s(first(y0, 0)))) MARK(cons(s(first(y0, nil)), z1)) -> c11(MARK(s(first(y0, nil)))) MARK(cons(s(first(y0, s(y1))), z1)) -> c11(MARK(s(first(y0, s(y1))))) MARK(cons(s(first(cons(y0, y1), y2)), z1)) -> c11(MARK(s(first(cons(y0, y1), y2)))) MARK(cons(s(first(0, y0)), z1)) -> c11(MARK(s(first(0, y0)))) MARK(cons(s(first(nil, y0)), z1)) -> c11(MARK(s(first(nil, y0)))) MARK(cons(s(first(y0, first(y1, first(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, first(y2, y3)))))) MARK(cons(s(first(y0, first(y1, from(y2)))), z1)) -> c11(MARK(s(first(y0, first(y1, from(y2)))))) MARK(cons(s(first(y0, first(y1, 0))), z1)) -> c11(MARK(s(first(y0, first(y1, 0))))) MARK(cons(s(first(y0, first(y1, nil))), z1)) -> c11(MARK(s(first(y0, first(y1, nil))))) MARK(cons(s(first(y0, first(y1, s(y2)))), z1)) -> c11(MARK(s(first(y0, first(y1, s(y2)))))) MARK(cons(s(first(y0, first(y1, cons(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, cons(y2, y3)))))) MARK(cons(s(first(y0, first(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, first(first(y1, y2), y3))))) MARK(cons(s(first(y0, first(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, first(from(y1), y2))))) MARK(cons(s(first(y0, first(0, y1))), z1)) -> c11(MARK(s(first(y0, first(0, y1))))) MARK(cons(s(first(y0, first(nil, y1))), z1)) -> c11(MARK(s(first(y0, first(nil, y1))))) MARK(cons(s(first(y0, first(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, first(s(y1), y2))))) MARK(cons(s(first(y0, first(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, first(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), first(y2, y3))))) MARK(cons(s(first(from(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), first(y1, y2))))) MARK(cons(s(first(s(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), first(y1, y2))))) MARK(cons(s(first(y0, first(y1, y2))), z1)) -> c11(MARK(s(first(y0, first(y1, y2))))) MARK(cons(s(first(cons(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), first(y2, y3))))) MARK(cons(s(first(y0, from(y1))), z1)) -> c11(MARK(s(first(y0, from(y1))))) MARK(cons(s(first(y0, from(first(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(first(y1, y2)))))) MARK(cons(s(first(y0, from(from(y1)))), z1)) -> c11(MARK(s(first(y0, from(from(y1)))))) MARK(cons(s(first(y0, from(0))), z1)) -> c11(MARK(s(first(y0, from(0))))) MARK(cons(s(first(y0, from(nil))), z1)) -> c11(MARK(s(first(y0, from(nil))))) MARK(cons(s(first(y0, from(s(y1)))), z1)) -> c11(MARK(s(first(y0, from(s(y1)))))) MARK(cons(s(first(y0, from(cons(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(cons(y1, y2)))))) MARK(cons(s(first(first(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), from(y2))))) MARK(cons(s(first(from(y0), from(y1))), z1)) -> c11(MARK(s(first(from(y0), from(y1))))) MARK(cons(s(first(s(y0), from(y1))), z1)) -> c11(MARK(s(first(s(y0), from(y1))))) MARK(cons(s(first(cons(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(cons(y0, y1), from(y2))))) MARK(cons(s(first(y0, cons(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(first(y1, y2), y3))))) MARK(cons(s(first(y0, cons(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(from(y1), y2))))) MARK(cons(s(first(y0, cons(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(s(y1), y2))))) MARK(cons(s(first(y0, cons(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), cons(y2, y3))))) MARK(cons(s(first(from(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), cons(y1, y2))))) MARK(cons(s(first(s(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), cons(y1, y2))))) MARK(cons(s(first(cons(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), cons(y2, y3))))) MARK(cons(s(first(first(y0, first(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, first(y1, y2)), y3)))) MARK(cons(s(first(first(y0, from(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, from(y1)), y2)))) MARK(cons(s(first(first(y0, 0), y1)), z1)) -> c11(MARK(s(first(first(y0, 0), y1)))) MARK(cons(s(first(first(y0, nil), y1)), z1)) -> c11(MARK(s(first(first(y0, nil), y1)))) MARK(cons(s(first(first(y0, s(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, s(y1)), y2)))) MARK(cons(s(first(first(y0, cons(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, cons(y1, y2)), y3)))) MARK(cons(s(first(first(first(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(first(y0, y1), y2), y3)))) MARK(cons(s(first(first(from(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(from(y0), y1), y2)))) MARK(cons(s(first(first(0, y0), y1)), z1)) -> c11(MARK(s(first(first(0, y0), y1)))) MARK(cons(s(first(first(nil, y0), y1)), z1)) -> c11(MARK(s(first(first(nil, y0), y1)))) MARK(cons(s(first(first(s(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(s(y0), y1), y2)))) MARK(cons(s(first(first(cons(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(cons(y0, y1), y2), y3)))) MARK(cons(s(first(first(y0, y1), 0)), z1)) -> c11(MARK(s(first(first(y0, y1), 0)))) MARK(cons(s(first(first(y0, y1), nil)), z1)) -> c11(MARK(s(first(first(y0, y1), nil)))) MARK(cons(s(first(first(y0, y1), s(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), s(y2))))) MARK(cons(s(first(first(y0, y1), y2)), z1)) -> c11(MARK(s(first(first(y0, y1), y2)))) MARK(cons(s(first(from(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(first(y0, y1)), y2)))) MARK(cons(s(first(from(from(y0)), y1)), z1)) -> c11(MARK(s(first(from(from(y0)), y1)))) MARK(cons(s(first(from(s(y0)), y1)), z1)) -> c11(MARK(s(first(from(s(y0)), y1)))) MARK(cons(s(first(from(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(cons(y0, y1)), y2)))) MARK(cons(s(first(from(y0), y1)), z1)) -> c11(MARK(s(first(from(y0), y1)))) MARK(cons(s(first(from(y0), 0)), z1)) -> c11(MARK(s(first(from(y0), 0)))) MARK(cons(s(first(from(y0), nil)), z1)) -> c11(MARK(s(first(from(y0), nil)))) MARK(cons(s(first(from(y0), s(y1))), z1)) -> c11(MARK(s(first(from(y0), s(y1))))) MARK(cons(s(first(s(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(first(y0, y1)), y2)))) MARK(cons(s(first(s(from(y0)), y1)), z1)) -> c11(MARK(s(first(s(from(y0)), y1)))) MARK(cons(s(first(s(0), y0)), z1)) -> c11(MARK(s(first(s(0), y0)))) MARK(cons(s(first(s(nil), y0)), z1)) -> c11(MARK(s(first(s(nil), y0)))) MARK(cons(s(first(s(s(y0)), y1)), z1)) -> c11(MARK(s(first(s(s(y0)), y1)))) MARK(cons(s(first(s(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(cons(y0, y1)), y2)))) MARK(cons(s(first(s(y0), y1)), z1)) -> c11(MARK(s(first(s(y0), y1)))) MARK(cons(s(first(s(y0), 0)), z1)) -> c11(MARK(s(first(s(y0), 0)))) MARK(cons(s(first(s(y0), nil)), z1)) -> c11(MARK(s(first(s(y0), nil)))) MARK(cons(s(first(s(y0), s(y1))), z1)) -> c11(MARK(s(first(s(y0), s(y1))))) MARK(cons(s(first(0, first(y0, y1))), z1)) -> c11(MARK(s(first(0, first(y0, y1))))) MARK(cons(s(first(nil, first(y0, y1))), z1)) -> c11(MARK(s(first(nil, first(y0, y1))))) MARK(cons(s(first(0, from(y0))), z1)) -> c11(MARK(s(first(0, from(y0))))) MARK(cons(s(first(nil, from(y0))), z1)) -> c11(MARK(s(first(nil, from(y0))))) MARK(cons(s(first(y0, cons(y1, y2))), z1)) -> c11(MARK(s(first(y0, cons(y1, y2))))) MARK(cons(s(first(0, cons(y0, y1))), z1)) -> c11(MARK(s(first(0, cons(y0, y1))))) MARK(cons(s(first(nil, cons(y0, y1))), z1)) -> c11(MARK(s(first(nil, cons(y0, y1))))) MARK(cons(s(first(from(0), y0)), z1)) -> c11(MARK(s(first(from(0), y0)))) MARK(cons(s(first(from(nil), y0)), z1)) -> c11(MARK(s(first(from(nil), y0)))) MARK(cons(s(first(y0, cons(0, y1))), z1)) -> c11(MARK(s(first(y0, cons(0, y1))))) MARK(cons(s(first(y0, cons(nil, y1))), z1)) -> c11(MARK(s(first(y0, cons(nil, y1))))) MARK(cons(s(from(s(y0))), z1)) -> c11(MARK(s(from(s(y0))))) MARK(cons(s(from(cons(y0, y1))), z1)) -> c11(MARK(s(from(cons(y0, y1))))) MARK(cons(s(from(first(y0, y1))), z1)) -> c11(MARK(s(from(first(y0, y1))))) MARK(cons(s(from(first(y0, first(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, first(y1, y2)))))) MARK(cons(s(from(first(y0, from(y1)))), z1)) -> c11(MARK(s(from(first(y0, from(y1)))))) MARK(cons(s(from(first(y0, 0))), z1)) -> c11(MARK(s(from(first(y0, 0))))) MARK(cons(s(from(first(y0, nil))), z1)) -> c11(MARK(s(from(first(y0, nil))))) MARK(cons(s(from(first(y0, s(y1)))), z1)) -> c11(MARK(s(from(first(y0, s(y1)))))) MARK(cons(s(from(first(y0, cons(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, cons(y1, y2)))))) MARK(cons(s(from(first(first(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(first(y0, y1), y2))))) MARK(cons(s(from(first(from(y0), y1))), z1)) -> c11(MARK(s(from(first(from(y0), y1))))) MARK(cons(s(from(first(0, y0))), z1)) -> c11(MARK(s(from(first(0, y0))))) MARK(cons(s(from(first(nil, y0))), z1)) -> c11(MARK(s(from(first(nil, y0))))) MARK(cons(s(from(first(s(y0), y1))), z1)) -> c11(MARK(s(from(first(s(y0), y1))))) MARK(cons(s(from(first(cons(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(cons(y0, y1), y2))))) MARK(cons(s(from(from(y0))), z1)) -> c11(MARK(s(from(from(y0))))) MARK(cons(s(from(from(first(y0, y1)))), z1)) -> c11(MARK(s(from(from(first(y0, y1)))))) MARK(cons(s(from(from(from(y0)))), z1)) -> c11(MARK(s(from(from(from(y0)))))) MARK(cons(s(from(from(s(y0)))), z1)) -> c11(MARK(s(from(from(s(y0)))))) MARK(cons(s(from(from(cons(y0, y1)))), z1)) -> c11(MARK(s(from(from(cons(y0, y1)))))) MARK(cons(s(from(from(0))), z1)) -> c11(MARK(s(from(from(0))))) MARK(cons(s(from(from(nil))), z1)) -> c11(MARK(s(from(from(nil))))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(0))) -> c7(A__FROM(a__from(0))) MARK(from(from(nil))) -> c7(A__FROM(a__from(nil))) MARK(s(s(y0))) -> c10(MARK(s(y0))) MARK(s(cons(y0, y1))) -> c10(MARK(cons(y0, y1))) MARK(s(first(y0, 0))) -> c10(MARK(first(y0, 0))) MARK(s(first(y0, nil))) -> c10(MARK(first(y0, nil))) MARK(s(first(y0, s(y1)))) -> c10(MARK(first(y0, s(y1)))) MARK(s(first(cons(y0, y1), y2))) -> c10(MARK(first(cons(y0, y1), y2))) MARK(s(first(0, y0))) -> c10(MARK(first(0, y0))) MARK(s(first(nil, y0))) -> c10(MARK(first(nil, y0))) MARK(s(first(y0, first(y1, first(y2, y3))))) -> c10(MARK(first(y0, first(y1, first(y2, y3))))) MARK(s(first(y0, first(y1, from(y2))))) -> c10(MARK(first(y0, first(y1, from(y2))))) MARK(s(first(y0, first(y1, 0)))) -> c10(MARK(first(y0, first(y1, 0)))) MARK(s(first(y0, first(y1, nil)))) -> c10(MARK(first(y0, first(y1, nil)))) MARK(s(first(y0, first(y1, s(y2))))) -> c10(MARK(first(y0, first(y1, s(y2))))) MARK(s(first(y0, first(y1, cons(y2, y3))))) -> c10(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(s(first(y0, first(first(y1, y2), y3)))) -> c10(MARK(first(y0, first(first(y1, y2), y3)))) MARK(s(first(y0, first(from(y1), y2)))) -> c10(MARK(first(y0, first(from(y1), y2)))) MARK(s(first(y0, first(0, y1)))) -> c10(MARK(first(y0, first(0, y1)))) MARK(s(first(y0, first(nil, y1)))) -> c10(MARK(first(y0, first(nil, y1)))) MARK(s(first(y0, first(s(y1), y2)))) -> c10(MARK(first(y0, first(s(y1), y2)))) MARK(s(first(y0, first(cons(y1, y2), y3)))) -> c10(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), first(y2, y3)))) -> c10(MARK(first(first(y0, y1), first(y2, y3)))) MARK(s(first(from(y0), first(y1, y2)))) -> c10(MARK(first(from(y0), first(y1, y2)))) MARK(s(first(s(y0), first(y1, y2)))) -> c10(MARK(first(s(y0), first(y1, y2)))) MARK(s(first(y0, first(y1, y2)))) -> c10(MARK(first(y0, first(y1, y2)))) MARK(s(first(cons(y0, y1), first(y2, y3)))) -> c10(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(s(first(y0, from(y1)))) -> c10(MARK(first(y0, from(y1)))) MARK(s(first(y0, from(first(y1, y2))))) -> c10(MARK(first(y0, from(first(y1, y2))))) MARK(s(first(y0, from(from(y1))))) -> c10(MARK(first(y0, from(from(y1))))) MARK(s(first(y0, from(0)))) -> c10(MARK(first(y0, from(0)))) MARK(s(first(y0, from(nil)))) -> c10(MARK(first(y0, from(nil)))) MARK(s(first(y0, from(s(y1))))) -> c10(MARK(first(y0, from(s(y1))))) MARK(s(first(y0, from(cons(y1, y2))))) -> c10(MARK(first(y0, from(cons(y1, y2))))) MARK(s(first(first(y0, y1), from(y2)))) -> c10(MARK(first(first(y0, y1), from(y2)))) MARK(s(first(from(y0), from(y1)))) -> c10(MARK(first(from(y0), from(y1)))) MARK(s(first(s(y0), from(y1)))) -> c10(MARK(first(s(y0), from(y1)))) MARK(s(first(cons(y0, y1), from(y2)))) -> c10(MARK(first(cons(y0, y1), from(y2)))) MARK(s(first(y0, cons(first(y1, y2), y3)))) -> c10(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(s(first(y0, cons(from(y1), y2)))) -> c10(MARK(first(y0, cons(from(y1), y2)))) MARK(s(first(y0, cons(s(y1), y2)))) -> c10(MARK(first(y0, cons(s(y1), y2)))) MARK(s(first(y0, cons(cons(y1, y2), y3)))) -> c10(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), cons(y2, y3)))) -> c10(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(s(first(from(y0), cons(y1, y2)))) -> c10(MARK(first(from(y0), cons(y1, y2)))) MARK(s(first(s(y0), cons(y1, y2)))) -> c10(MARK(first(s(y0), cons(y1, y2)))) MARK(s(first(cons(y0, y1), cons(y2, y3)))) -> c10(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(s(first(first(y0, first(y1, y2)), y3))) -> c10(MARK(first(first(y0, first(y1, y2)), y3))) MARK(s(first(first(y0, from(y1)), y2))) -> c10(MARK(first(first(y0, from(y1)), y2))) MARK(s(first(first(y0, 0), y1))) -> c10(MARK(first(first(y0, 0), y1))) MARK(s(first(first(y0, nil), y1))) -> c10(MARK(first(first(y0, nil), y1))) MARK(s(first(first(y0, s(y1)), y2))) -> c10(MARK(first(first(y0, s(y1)), y2))) MARK(s(first(first(y0, cons(y1, y2)), 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MARK(cons(first(first(s(y0), y1), y2), z1)) -> c11(MARK(first(first(s(y0), y1), y2))) MARK(cons(first(first(cons(y0, y1), y2), y3), z1)) -> c11(MARK(first(first(cons(y0, y1), y2), y3))) MARK(cons(first(first(y0, y1), 0), z1)) -> c11(MARK(first(first(y0, y1), 0))) MARK(cons(first(first(y0, y1), nil), z1)) -> c11(MARK(first(first(y0, y1), nil))) MARK(cons(first(first(y0, y1), s(y2)), z1)) -> c11(MARK(first(first(y0, y1), s(y2)))) MARK(cons(first(first(y0, y1), y2), z1)) -> c11(MARK(first(first(y0, y1), y2))) MARK(cons(first(from(first(y0, y1)), y2), z1)) -> c11(MARK(first(from(first(y0, y1)), y2))) MARK(cons(first(from(from(y0)), y1), z1)) -> c11(MARK(first(from(from(y0)), y1))) MARK(cons(first(from(s(y0)), y1), z1)) -> c11(MARK(first(from(s(y0)), y1))) MARK(cons(first(from(cons(y0, y1)), y2), z1)) -> c11(MARK(first(from(cons(y0, y1)), y2))) MARK(cons(first(from(y0), y1), z1)) -> c11(MARK(first(from(y0), y1))) MARK(cons(first(from(y0), 0), z1)) -> c11(MARK(first(from(y0), 0))) MARK(cons(first(from(y0), nil), z1)) -> c11(MARK(first(from(y0), nil))) MARK(cons(first(from(y0), s(y1)), z1)) -> c11(MARK(first(from(y0), s(y1)))) MARK(cons(first(s(first(y0, y1)), y2), z1)) -> c11(MARK(first(s(first(y0, y1)), y2))) MARK(cons(first(s(from(y0)), y1), z1)) -> c11(MARK(first(s(from(y0)), y1))) MARK(cons(first(s(s(y0)), y1), z1)) -> c11(MARK(first(s(s(y0)), y1))) MARK(cons(first(s(cons(y0, y1)), y2), z1)) -> c11(MARK(first(s(cons(y0, y1)), y2))) MARK(cons(first(s(y0), y1), z1)) -> c11(MARK(first(s(y0), y1))) MARK(cons(first(s(y0), 0), z1)) -> c11(MARK(first(s(y0), 0))) MARK(cons(first(s(y0), nil), z1)) -> c11(MARK(first(s(y0), nil))) MARK(cons(first(s(y0), s(y1)), z1)) -> c11(MARK(first(s(y0), s(y1)))) MARK(cons(first(0, first(y0, y1)), z1)) -> c11(MARK(first(0, first(y0, y1)))) MARK(cons(first(nil, first(y0, y1)), z1)) -> c11(MARK(first(nil, first(y0, y1)))) MARK(cons(first(0, from(y0)), z1)) -> c11(MARK(first(0, from(y0)))) MARK(cons(first(nil, from(y0)), z1)) -> 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MARK(cons(from(from(from(y0))), z1)) -> c11(MARK(from(from(from(y0))))) MARK(cons(from(from(s(y0))), z1)) -> c11(MARK(from(from(s(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c11(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(0)), z1)) -> c11(MARK(from(from(0)))) MARK(cons(from(from(nil)), z1)) -> c11(MARK(from(from(nil)))) MARK(cons(s(s(y0)), z1)) -> c11(MARK(s(s(y0)))) MARK(cons(s(cons(y0, y1)), z1)) -> c11(MARK(s(cons(y0, y1)))) MARK(cons(s(first(y0, 0)), z1)) -> c11(MARK(s(first(y0, 0)))) MARK(cons(s(first(y0, nil)), z1)) -> c11(MARK(s(first(y0, nil)))) MARK(cons(s(first(y0, s(y1))), z1)) -> c11(MARK(s(first(y0, s(y1))))) MARK(cons(s(first(cons(y0, y1), y2)), z1)) -> c11(MARK(s(first(cons(y0, y1), y2)))) MARK(cons(s(first(0, y0)), z1)) -> c11(MARK(s(first(0, y0)))) MARK(cons(s(first(nil, y0)), z1)) -> c11(MARK(s(first(nil, y0)))) MARK(cons(s(first(y0, first(y1, first(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, first(y2, y3)))))) MARK(cons(s(first(y0, first(y1, 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y2), y3))))) MARK(cons(s(first(first(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), first(y2, y3))))) MARK(cons(s(first(from(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), first(y1, y2))))) MARK(cons(s(first(s(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), first(y1, y2))))) MARK(cons(s(first(y0, first(y1, y2))), z1)) -> c11(MARK(s(first(y0, first(y1, y2))))) MARK(cons(s(first(cons(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), first(y2, y3))))) MARK(cons(s(first(y0, from(y1))), z1)) -> c11(MARK(s(first(y0, from(y1))))) MARK(cons(s(first(y0, from(first(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(first(y1, y2)))))) MARK(cons(s(first(y0, from(from(y1)))), z1)) -> c11(MARK(s(first(y0, from(from(y1)))))) MARK(cons(s(first(y0, from(0))), z1)) -> c11(MARK(s(first(y0, from(0))))) MARK(cons(s(first(y0, from(nil))), z1)) -> c11(MARK(s(first(y0, from(nil))))) MARK(cons(s(first(y0, from(s(y1)))), z1)) -> c11(MARK(s(first(y0, from(s(y1)))))) MARK(cons(s(first(y0, from(cons(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(cons(y1, y2)))))) MARK(cons(s(first(first(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), from(y2))))) MARK(cons(s(first(from(y0), from(y1))), z1)) -> c11(MARK(s(first(from(y0), from(y1))))) MARK(cons(s(first(s(y0), from(y1))), z1)) -> c11(MARK(s(first(s(y0), from(y1))))) MARK(cons(s(first(cons(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(cons(y0, y1), from(y2))))) MARK(cons(s(first(y0, cons(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(first(y1, y2), y3))))) MARK(cons(s(first(y0, cons(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(from(y1), y2))))) MARK(cons(s(first(y0, cons(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(s(y1), y2))))) MARK(cons(s(first(y0, cons(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), cons(y2, y3))))) MARK(cons(s(first(from(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), cons(y1, y2))))) MARK(cons(s(first(s(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), cons(y1, y2))))) MARK(cons(s(first(cons(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), cons(y2, y3))))) MARK(cons(s(first(first(y0, first(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, first(y1, y2)), y3)))) MARK(cons(s(first(first(y0, from(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, from(y1)), y2)))) MARK(cons(s(first(first(y0, 0), y1)), z1)) -> c11(MARK(s(first(first(y0, 0), y1)))) MARK(cons(s(first(first(y0, nil), y1)), z1)) -> c11(MARK(s(first(first(y0, nil), y1)))) MARK(cons(s(first(first(y0, s(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, s(y1)), y2)))) MARK(cons(s(first(first(y0, cons(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, cons(y1, y2)), y3)))) MARK(cons(s(first(first(first(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(first(y0, y1), y2), y3)))) MARK(cons(s(first(first(from(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(from(y0), y1), y2)))) MARK(cons(s(first(first(0, y0), y1)), z1)) -> c11(MARK(s(first(first(0, y0), y1)))) MARK(cons(s(first(first(nil, y0), y1)), z1)) -> c11(MARK(s(first(first(nil, y0), y1)))) MARK(cons(s(first(first(s(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(s(y0), y1), y2)))) MARK(cons(s(first(first(cons(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(cons(y0, y1), y2), y3)))) MARK(cons(s(first(first(y0, y1), 0)), z1)) -> c11(MARK(s(first(first(y0, y1), 0)))) MARK(cons(s(first(first(y0, y1), nil)), z1)) -> c11(MARK(s(first(first(y0, y1), nil)))) MARK(cons(s(first(first(y0, y1), s(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), s(y2))))) MARK(cons(s(first(first(y0, y1), y2)), z1)) -> c11(MARK(s(first(first(y0, y1), y2)))) MARK(cons(s(first(from(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(first(y0, y1)), y2)))) MARK(cons(s(first(from(from(y0)), y1)), z1)) -> c11(MARK(s(first(from(from(y0)), y1)))) MARK(cons(s(first(from(s(y0)), y1)), z1)) -> c11(MARK(s(first(from(s(y0)), y1)))) MARK(cons(s(first(from(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(cons(y0, y1)), y2)))) MARK(cons(s(first(from(y0), y1)), z1)) -> c11(MARK(s(first(from(y0), y1)))) MARK(cons(s(first(from(y0), 0)), z1)) -> c11(MARK(s(first(from(y0), 0)))) MARK(cons(s(first(from(y0), nil)), z1)) -> c11(MARK(s(first(from(y0), nil)))) MARK(cons(s(first(from(y0), s(y1))), z1)) -> c11(MARK(s(first(from(y0), s(y1))))) MARK(cons(s(first(s(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(first(y0, y1)), y2)))) MARK(cons(s(first(s(from(y0)), y1)), z1)) -> c11(MARK(s(first(s(from(y0)), y1)))) MARK(cons(s(first(s(0), y0)), z1)) -> c11(MARK(s(first(s(0), y0)))) MARK(cons(s(first(s(nil), y0)), z1)) -> c11(MARK(s(first(s(nil), y0)))) MARK(cons(s(first(s(s(y0)), y1)), z1)) -> c11(MARK(s(first(s(s(y0)), y1)))) MARK(cons(s(first(s(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(cons(y0, y1)), y2)))) MARK(cons(s(first(s(y0), y1)), z1)) -> c11(MARK(s(first(s(y0), y1)))) MARK(cons(s(first(s(y0), 0)), z1)) -> c11(MARK(s(first(s(y0), 0)))) MARK(cons(s(first(s(y0), nil)), z1)) -> c11(MARK(s(first(s(y0), nil)))) MARK(cons(s(first(s(y0), s(y1))), z1)) -> c11(MARK(s(first(s(y0), s(y1))))) MARK(cons(s(first(0, first(y0, y1))), z1)) -> c11(MARK(s(first(0, first(y0, y1))))) MARK(cons(s(first(nil, first(y0, y1))), z1)) -> c11(MARK(s(first(nil, first(y0, y1))))) MARK(cons(s(first(0, from(y0))), z1)) -> c11(MARK(s(first(0, from(y0))))) MARK(cons(s(first(nil, from(y0))), z1)) -> c11(MARK(s(first(nil, from(y0))))) MARK(cons(s(first(y0, cons(y1, y2))), z1)) -> c11(MARK(s(first(y0, cons(y1, y2))))) MARK(cons(s(first(0, cons(y0, y1))), z1)) -> c11(MARK(s(first(0, cons(y0, y1))))) MARK(cons(s(first(nil, cons(y0, y1))), z1)) -> c11(MARK(s(first(nil, cons(y0, y1))))) MARK(cons(s(first(from(0), y0)), z1)) -> c11(MARK(s(first(from(0), y0)))) MARK(cons(s(first(from(nil), y0)), z1)) -> c11(MARK(s(first(from(nil), y0)))) MARK(cons(s(first(y0, cons(0, y1))), z1)) -> c11(MARK(s(first(y0, cons(0, y1))))) MARK(cons(s(first(y0, cons(nil, y1))), z1)) -> c11(MARK(s(first(y0, cons(nil, y1))))) MARK(cons(s(from(s(y0))), z1)) -> c11(MARK(s(from(s(y0))))) MARK(cons(s(from(cons(y0, y1))), z1)) -> c11(MARK(s(from(cons(y0, y1))))) MARK(cons(s(from(first(y0, y1))), z1)) -> c11(MARK(s(from(first(y0, y1))))) MARK(cons(s(from(first(y0, first(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, first(y1, y2)))))) MARK(cons(s(from(first(y0, from(y1)))), z1)) -> c11(MARK(s(from(first(y0, from(y1)))))) MARK(cons(s(from(first(y0, 0))), z1)) -> c11(MARK(s(from(first(y0, 0))))) MARK(cons(s(from(first(y0, nil))), z1)) -> c11(MARK(s(from(first(y0, nil))))) MARK(cons(s(from(first(y0, s(y1)))), z1)) -> c11(MARK(s(from(first(y0, s(y1)))))) MARK(cons(s(from(first(y0, cons(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, cons(y1, y2)))))) MARK(cons(s(from(first(first(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(first(y0, y1), y2))))) MARK(cons(s(from(first(from(y0), y1))), z1)) -> c11(MARK(s(from(first(from(y0), y1))))) MARK(cons(s(from(first(0, y0))), z1)) -> c11(MARK(s(from(first(0, y0))))) MARK(cons(s(from(first(nil, y0))), z1)) -> c11(MARK(s(from(first(nil, y0))))) MARK(cons(s(from(first(s(y0), y1))), z1)) -> c11(MARK(s(from(first(s(y0), y1))))) MARK(cons(s(from(first(cons(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(cons(y0, y1), y2))))) MARK(cons(s(from(from(y0))), z1)) -> c11(MARK(s(from(from(y0))))) MARK(cons(s(from(from(first(y0, y1)))), z1)) -> c11(MARK(s(from(from(first(y0, y1)))))) MARK(cons(s(from(from(from(y0)))), z1)) -> c11(MARK(s(from(from(from(y0)))))) MARK(cons(s(from(from(s(y0)))), z1)) -> c11(MARK(s(from(from(s(y0)))))) MARK(cons(s(from(from(cons(y0, y1)))), z1)) -> c11(MARK(s(from(from(cons(y0, y1)))))) MARK(cons(s(from(from(0))), z1)) -> c11(MARK(s(from(from(0))))) MARK(cons(s(from(from(nil))), z1)) -> c11(MARK(s(from(from(nil))))) S tuples: MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, 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c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(0))) -> 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MARK(cons(from(first(y0, nil)), z1)) -> c11(MARK(from(first(y0, nil)))) MARK(cons(from(first(y0, s(y1))), z1)) -> c11(MARK(from(first(y0, s(y1))))) MARK(cons(from(first(y0, cons(y1, y2))), z1)) -> c11(MARK(from(first(y0, cons(y1, y2))))) MARK(cons(from(first(first(y0, y1), y2)), z1)) -> c11(MARK(from(first(first(y0, y1), y2)))) MARK(cons(from(first(from(y0), y1)), z1)) -> c11(MARK(from(first(from(y0), y1)))) MARK(cons(from(first(0, y0)), z1)) -> c11(MARK(from(first(0, y0)))) MARK(cons(from(first(nil, y0)), z1)) -> c11(MARK(from(first(nil, y0)))) MARK(cons(from(first(s(y0), y1)), z1)) -> c11(MARK(from(first(s(y0), y1)))) MARK(cons(from(first(cons(y0, y1), y2)), z1)) -> c11(MARK(from(first(cons(y0, y1), y2)))) MARK(cons(from(from(y0)), z1)) -> c11(MARK(from(from(y0)))) MARK(cons(from(from(first(y0, y1))), z1)) -> c11(MARK(from(from(first(y0, y1))))) MARK(cons(from(from(from(y0))), z1)) -> c11(MARK(from(from(from(y0))))) MARK(cons(from(from(s(y0))), z1)) -> c11(MARK(from(from(s(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c11(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(0)), z1)) -> c11(MARK(from(from(0)))) MARK(cons(from(from(nil)), z1)) -> c11(MARK(from(from(nil)))) MARK(cons(s(s(y0)), z1)) -> c11(MARK(s(s(y0)))) MARK(cons(s(cons(y0, y1)), z1)) -> c11(MARK(s(cons(y0, y1)))) MARK(cons(s(first(y0, 0)), z1)) -> c11(MARK(s(first(y0, 0)))) MARK(cons(s(first(y0, nil)), z1)) -> c11(MARK(s(first(y0, nil)))) MARK(cons(s(first(y0, s(y1))), z1)) -> c11(MARK(s(first(y0, s(y1))))) MARK(cons(s(first(cons(y0, y1), y2)), z1)) -> c11(MARK(s(first(cons(y0, y1), y2)))) MARK(cons(s(first(0, y0)), z1)) -> c11(MARK(s(first(0, y0)))) MARK(cons(s(first(nil, y0)), z1)) -> c11(MARK(s(first(nil, y0)))) MARK(cons(s(first(y0, first(y1, first(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, first(y2, y3)))))) MARK(cons(s(first(y0, first(y1, from(y2)))), z1)) -> c11(MARK(s(first(y0, first(y1, from(y2)))))) MARK(cons(s(first(y0, first(y1, 0))), z1)) -> c11(MARK(s(first(y0, first(y1, 0))))) MARK(cons(s(first(y0, first(y1, nil))), z1)) -> c11(MARK(s(first(y0, first(y1, nil))))) MARK(cons(s(first(y0, first(y1, s(y2)))), z1)) -> c11(MARK(s(first(y0, first(y1, s(y2)))))) MARK(cons(s(first(y0, first(y1, cons(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, cons(y2, y3)))))) MARK(cons(s(first(y0, first(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, first(first(y1, y2), y3))))) MARK(cons(s(first(y0, first(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, first(from(y1), y2))))) MARK(cons(s(first(y0, first(0, y1))), z1)) -> c11(MARK(s(first(y0, first(0, y1))))) MARK(cons(s(first(y0, first(nil, y1))), z1)) -> c11(MARK(s(first(y0, first(nil, y1))))) MARK(cons(s(first(y0, first(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, first(s(y1), y2))))) MARK(cons(s(first(y0, first(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, first(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), first(y2, y3))))) MARK(cons(s(first(from(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), first(y1, y2))))) MARK(cons(s(first(s(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), first(y1, y2))))) MARK(cons(s(first(y0, first(y1, y2))), z1)) -> c11(MARK(s(first(y0, first(y1, y2))))) MARK(cons(s(first(cons(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), first(y2, y3))))) MARK(cons(s(first(y0, from(y1))), z1)) -> c11(MARK(s(first(y0, from(y1))))) MARK(cons(s(first(y0, from(first(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(first(y1, y2)))))) MARK(cons(s(first(y0, from(from(y1)))), z1)) -> c11(MARK(s(first(y0, from(from(y1)))))) MARK(cons(s(first(y0, from(0))), z1)) -> c11(MARK(s(first(y0, from(0))))) MARK(cons(s(first(y0, from(nil))), z1)) -> c11(MARK(s(first(y0, from(nil))))) MARK(cons(s(first(y0, from(s(y1)))), z1)) -> c11(MARK(s(first(y0, from(s(y1)))))) MARK(cons(s(first(y0, from(cons(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(cons(y1, y2)))))) MARK(cons(s(first(first(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), from(y2))))) MARK(cons(s(first(from(y0), from(y1))), z1)) -> c11(MARK(s(first(from(y0), from(y1))))) MARK(cons(s(first(s(y0), from(y1))), z1)) -> c11(MARK(s(first(s(y0), from(y1))))) MARK(cons(s(first(cons(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(cons(y0, y1), from(y2))))) MARK(cons(s(first(y0, cons(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(first(y1, y2), y3))))) MARK(cons(s(first(y0, cons(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(from(y1), y2))))) MARK(cons(s(first(y0, cons(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(s(y1), y2))))) MARK(cons(s(first(y0, cons(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), cons(y2, y3))))) MARK(cons(s(first(from(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), cons(y1, y2))))) MARK(cons(s(first(s(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), cons(y1, y2))))) MARK(cons(s(first(cons(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), cons(y2, y3))))) MARK(cons(s(first(first(y0, first(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, first(y1, y2)), y3)))) MARK(cons(s(first(first(y0, from(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, from(y1)), y2)))) MARK(cons(s(first(first(y0, 0), y1)), z1)) -> c11(MARK(s(first(first(y0, 0), y1)))) MARK(cons(s(first(first(y0, nil), y1)), z1)) -> c11(MARK(s(first(first(y0, nil), y1)))) MARK(cons(s(first(first(y0, s(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, s(y1)), y2)))) MARK(cons(s(first(first(y0, cons(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, cons(y1, y2)), y3)))) MARK(cons(s(first(first(first(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(first(y0, y1), y2), y3)))) MARK(cons(s(first(first(from(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(from(y0), y1), y2)))) MARK(cons(s(first(first(0, y0), y1)), z1)) -> c11(MARK(s(first(first(0, y0), y1)))) MARK(cons(s(first(first(nil, y0), y1)), z1)) -> c11(MARK(s(first(first(nil, y0), y1)))) MARK(cons(s(first(first(s(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(s(y0), y1), y2)))) MARK(cons(s(first(first(cons(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(cons(y0, y1), y2), y3)))) MARK(cons(s(first(first(y0, y1), 0)), z1)) -> c11(MARK(s(first(first(y0, y1), 0)))) MARK(cons(s(first(first(y0, y1), nil)), z1)) -> c11(MARK(s(first(first(y0, y1), nil)))) MARK(cons(s(first(first(y0, y1), s(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), s(y2))))) MARK(cons(s(first(first(y0, y1), y2)), z1)) -> c11(MARK(s(first(first(y0, y1), y2)))) MARK(cons(s(first(from(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(first(y0, y1)), y2)))) MARK(cons(s(first(from(from(y0)), y1)), z1)) -> c11(MARK(s(first(from(from(y0)), y1)))) MARK(cons(s(first(from(s(y0)), y1)), z1)) -> c11(MARK(s(first(from(s(y0)), y1)))) MARK(cons(s(first(from(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(cons(y0, y1)), y2)))) MARK(cons(s(first(from(y0), y1)), z1)) -> c11(MARK(s(first(from(y0), y1)))) MARK(cons(s(first(from(y0), 0)), z1)) -> c11(MARK(s(first(from(y0), 0)))) MARK(cons(s(first(from(y0), nil)), z1)) -> c11(MARK(s(first(from(y0), nil)))) MARK(cons(s(first(from(y0), s(y1))), z1)) -> c11(MARK(s(first(from(y0), s(y1))))) MARK(cons(s(first(s(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(first(y0, y1)), y2)))) MARK(cons(s(first(s(from(y0)), y1)), z1)) -> c11(MARK(s(first(s(from(y0)), y1)))) MARK(cons(s(first(s(0), y0)), z1)) -> c11(MARK(s(first(s(0), y0)))) MARK(cons(s(first(s(nil), y0)), z1)) -> c11(MARK(s(first(s(nil), y0)))) MARK(cons(s(first(s(s(y0)), y1)), z1)) -> c11(MARK(s(first(s(s(y0)), y1)))) MARK(cons(s(first(s(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(cons(y0, y1)), y2)))) MARK(cons(s(first(s(y0), y1)), z1)) -> c11(MARK(s(first(s(y0), y1)))) MARK(cons(s(first(s(y0), 0)), z1)) -> c11(MARK(s(first(s(y0), 0)))) MARK(cons(s(first(s(y0), nil)), z1)) -> c11(MARK(s(first(s(y0), nil)))) MARK(cons(s(first(s(y0), s(y1))), z1)) -> c11(MARK(s(first(s(y0), s(y1))))) MARK(cons(s(first(0, first(y0, y1))), z1)) -> c11(MARK(s(first(0, first(y0, y1))))) MARK(cons(s(first(nil, first(y0, y1))), z1)) -> c11(MARK(s(first(nil, first(y0, y1))))) MARK(cons(s(first(0, from(y0))), z1)) -> c11(MARK(s(first(0, from(y0))))) MARK(cons(s(first(nil, from(y0))), z1)) -> c11(MARK(s(first(nil, from(y0))))) MARK(cons(s(first(y0, cons(y1, y2))), z1)) -> c11(MARK(s(first(y0, cons(y1, y2))))) MARK(cons(s(first(0, cons(y0, y1))), z1)) -> c11(MARK(s(first(0, cons(y0, y1))))) MARK(cons(s(first(nil, cons(y0, y1))), z1)) -> c11(MARK(s(first(nil, cons(y0, y1))))) MARK(cons(s(first(from(0), y0)), z1)) -> c11(MARK(s(first(from(0), y0)))) MARK(cons(s(first(from(nil), y0)), z1)) -> c11(MARK(s(first(from(nil), y0)))) MARK(cons(s(first(y0, cons(0, y1))), z1)) -> c11(MARK(s(first(y0, cons(0, y1))))) MARK(cons(s(first(y0, cons(nil, y1))), z1)) -> c11(MARK(s(first(y0, cons(nil, y1))))) MARK(cons(s(from(s(y0))), z1)) -> c11(MARK(s(from(s(y0))))) MARK(cons(s(from(cons(y0, y1))), z1)) -> c11(MARK(s(from(cons(y0, y1))))) MARK(cons(s(from(first(y0, y1))), z1)) -> c11(MARK(s(from(first(y0, y1))))) MARK(cons(s(from(first(y0, first(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, first(y1, y2)))))) MARK(cons(s(from(first(y0, from(y1)))), z1)) -> c11(MARK(s(from(first(y0, from(y1)))))) MARK(cons(s(from(first(y0, 0))), z1)) -> c11(MARK(s(from(first(y0, 0))))) MARK(cons(s(from(first(y0, nil))), z1)) -> c11(MARK(s(from(first(y0, nil))))) MARK(cons(s(from(first(y0, s(y1)))), z1)) -> c11(MARK(s(from(first(y0, s(y1)))))) MARK(cons(s(from(first(y0, cons(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, cons(y1, y2)))))) MARK(cons(s(from(first(first(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(first(y0, y1), y2))))) MARK(cons(s(from(first(from(y0), y1))), z1)) -> c11(MARK(s(from(first(from(y0), y1))))) MARK(cons(s(from(first(0, y0))), z1)) -> c11(MARK(s(from(first(0, y0))))) MARK(cons(s(from(first(nil, y0))), z1)) -> c11(MARK(s(from(first(nil, y0))))) MARK(cons(s(from(first(s(y0), y1))), z1)) -> c11(MARK(s(from(first(s(y0), y1))))) MARK(cons(s(from(first(cons(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(cons(y0, y1), y2))))) MARK(cons(s(from(from(y0))), z1)) -> c11(MARK(s(from(from(y0))))) MARK(cons(s(from(from(first(y0, y1)))), z1)) -> c11(MARK(s(from(from(first(y0, y1)))))) MARK(cons(s(from(from(from(y0)))), z1)) -> c11(MARK(s(from(from(from(y0)))))) MARK(cons(s(from(from(s(y0)))), z1)) -> c11(MARK(s(from(from(s(y0)))))) MARK(cons(s(from(from(cons(y0, y1)))), z1)) -> c11(MARK(s(from(from(cons(y0, y1)))))) MARK(cons(s(from(from(0))), z1)) -> c11(MARK(s(from(from(0))))) MARK(cons(s(from(from(nil))), z1)) -> c11(MARK(s(from(from(nil))))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__FIRST_2, A__FROM_1 Compound Symbols: c5_1, c6_1, c5_2, c6_2, c1_1, c3_1, c7_2, c7_1, c10_1, c11_1 ---------------------------------------- (121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(x0, cons(0, x2))) -> c6(MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c6(MARK(cons(nil, x2))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) 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MARK(s(first(y0, from(nil)))) -> c10(MARK(first(y0, from(nil)))) MARK(s(first(y0, from(s(y1))))) -> c10(MARK(first(y0, from(s(y1))))) MARK(s(first(y0, from(cons(y1, y2))))) -> c10(MARK(first(y0, from(cons(y1, y2))))) MARK(s(first(first(y0, y1), from(y2)))) -> c10(MARK(first(first(y0, y1), from(y2)))) MARK(s(first(from(y0), from(y1)))) -> c10(MARK(first(from(y0), from(y1)))) MARK(s(first(s(y0), from(y1)))) -> c10(MARK(first(s(y0), from(y1)))) MARK(s(first(cons(y0, y1), from(y2)))) -> c10(MARK(first(cons(y0, y1), from(y2)))) MARK(s(first(y0, cons(first(y1, y2), y3)))) -> c10(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(s(first(y0, cons(from(y1), y2)))) -> c10(MARK(first(y0, cons(from(y1), y2)))) MARK(s(first(y0, cons(s(y1), y2)))) -> c10(MARK(first(y0, cons(s(y1), y2)))) MARK(s(first(y0, cons(cons(y1, y2), y3)))) -> c10(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), cons(y2, y3)))) -> c10(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(s(first(from(y0), cons(y1, 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MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1))) MARK(cons(cons(y0, y1), z1)) -> c11(MARK(cons(y0, y1))) MARK(cons(first(y0, 0), z1)) -> c11(MARK(first(y0, 0))) MARK(cons(first(y0, nil), z1)) -> c11(MARK(first(y0, nil))) MARK(cons(first(y0, s(y1)), z1)) -> c11(MARK(first(y0, s(y1)))) MARK(cons(first(cons(y0, y1), y2), z1)) -> c11(MARK(first(cons(y0, y1), y2))) MARK(cons(first(0, y0), z1)) -> c11(MARK(first(0, y0))) MARK(cons(first(nil, y0), z1)) -> c11(MARK(first(nil, y0))) MARK(cons(first(y0, first(y1, first(y2, y3))), z1)) -> c11(MARK(first(y0, first(y1, first(y2, y3))))) MARK(cons(first(y0, first(y1, from(y2))), z1)) -> c11(MARK(first(y0, first(y1, from(y2))))) MARK(cons(first(y0, first(y1, 0)), z1)) -> c11(MARK(first(y0, first(y1, 0)))) MARK(cons(first(y0, first(y1, nil)), z1)) -> c11(MARK(first(y0, first(y1, nil)))) MARK(cons(first(y0, first(y1, s(y2))), z1)) -> c11(MARK(first(y0, first(y1, s(y2))))) MARK(cons(first(y0, first(y1, cons(y2, y3))), z1)) -> c11(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(cons(first(y0, first(first(y1, y2), y3)), z1)) -> c11(MARK(first(y0, first(first(y1, y2), y3)))) MARK(cons(first(y0, first(from(y1), y2)), z1)) -> c11(MARK(first(y0, first(from(y1), y2)))) MARK(cons(first(y0, first(0, y1)), z1)) -> c11(MARK(first(y0, first(0, y1)))) MARK(cons(first(y0, first(nil, y1)), z1)) -> c11(MARK(first(y0, first(nil, y1)))) MARK(cons(first(y0, first(s(y1), y2)), z1)) -> c11(MARK(first(y0, first(s(y1), y2)))) MARK(cons(first(y0, first(cons(y1, y2), y3)), z1)) -> c11(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(cons(first(first(y0, y1), first(y2, y3)), z1)) -> c11(MARK(first(first(y0, y1), first(y2, y3)))) MARK(cons(first(from(y0), first(y1, y2)), z1)) -> c11(MARK(first(from(y0), first(y1, y2)))) MARK(cons(first(s(y0), first(y1, y2)), z1)) -> c11(MARK(first(s(y0), first(y1, y2)))) MARK(cons(first(y0, first(y1, y2)), z1)) -> c11(MARK(first(y0, first(y1, y2)))) MARK(cons(first(cons(y0, y1), first(y2, y3)), z1)) -> c11(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(cons(first(y0, from(y1)), z1)) -> c11(MARK(first(y0, from(y1)))) MARK(cons(first(y0, from(first(y1, y2))), z1)) -> c11(MARK(first(y0, from(first(y1, y2))))) MARK(cons(first(y0, from(from(y1))), z1)) -> c11(MARK(first(y0, from(from(y1))))) MARK(cons(first(y0, from(0)), z1)) -> c11(MARK(first(y0, from(0)))) MARK(cons(first(y0, from(nil)), z1)) -> c11(MARK(first(y0, from(nil)))) MARK(cons(first(y0, from(s(y1))), z1)) -> c11(MARK(first(y0, from(s(y1))))) MARK(cons(first(y0, from(cons(y1, y2))), z1)) -> c11(MARK(first(y0, from(cons(y1, y2))))) MARK(cons(first(first(y0, y1), from(y2)), z1)) -> c11(MARK(first(first(y0, y1), from(y2)))) MARK(cons(first(from(y0), from(y1)), z1)) -> c11(MARK(first(from(y0), from(y1)))) MARK(cons(first(s(y0), from(y1)), z1)) -> c11(MARK(first(s(y0), from(y1)))) MARK(cons(first(cons(y0, y1), from(y2)), z1)) -> c11(MARK(first(cons(y0, y1), from(y2)))) MARK(cons(first(y0, cons(first(y1, y2), y3)), z1)) -> c11(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(cons(first(y0, cons(from(y1), y2)), z1)) -> c11(MARK(first(y0, cons(from(y1), y2)))) MARK(cons(first(y0, cons(s(y1), y2)), z1)) -> c11(MARK(first(y0, cons(s(y1), y2)))) MARK(cons(first(y0, cons(cons(y1, y2), y3)), z1)) -> c11(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(cons(first(first(y0, y1), cons(y2, y3)), z1)) -> c11(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(cons(first(from(y0), cons(y1, y2)), z1)) -> c11(MARK(first(from(y0), cons(y1, y2)))) MARK(cons(first(s(y0), cons(y1, y2)), z1)) -> c11(MARK(first(s(y0), cons(y1, y2)))) MARK(cons(first(cons(y0, y1), cons(y2, y3)), z1)) -> c11(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(cons(first(first(y0, first(y1, y2)), y3), z1)) -> c11(MARK(first(first(y0, first(y1, y2)), y3))) MARK(cons(first(first(y0, from(y1)), y2), z1)) -> c11(MARK(first(first(y0, from(y1)), y2))) MARK(cons(first(first(y0, 0), y1), z1)) -> c11(MARK(first(first(y0, 0), y1))) MARK(cons(first(first(y0, nil), y1), z1)) -> c11(MARK(first(first(y0, nil), y1))) MARK(cons(first(first(y0, s(y1)), y2), z1)) -> c11(MARK(first(first(y0, s(y1)), y2))) MARK(cons(first(first(y0, cons(y1, y2)), y3), z1)) -> c11(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(cons(first(first(first(y0, y1), y2), y3), z1)) -> c11(MARK(first(first(first(y0, y1), y2), y3))) MARK(cons(first(first(from(y0), y1), y2), z1)) -> c11(MARK(first(first(from(y0), y1), y2))) MARK(cons(first(first(0, y0), y1), z1)) -> c11(MARK(first(first(0, y0), y1))) MARK(cons(first(first(nil, y0), y1), z1)) -> c11(MARK(first(first(nil, y0), y1))) MARK(cons(first(first(s(y0), y1), y2), z1)) -> c11(MARK(first(first(s(y0), y1), y2))) MARK(cons(first(first(cons(y0, y1), y2), y3), z1)) -> c11(MARK(first(first(cons(y0, y1), y2), y3))) MARK(cons(first(first(y0, y1), 0), z1)) -> c11(MARK(first(first(y0, y1), 0))) MARK(cons(first(first(y0, y1), nil), z1)) -> c11(MARK(first(first(y0, y1), 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c11(MARK(first(s(s(y0)), y1))) MARK(cons(first(s(cons(y0, y1)), y2), z1)) -> c11(MARK(first(s(cons(y0, y1)), y2))) MARK(cons(first(s(y0), y1), z1)) -> c11(MARK(first(s(y0), y1))) MARK(cons(first(s(y0), 0), z1)) -> c11(MARK(first(s(y0), 0))) MARK(cons(first(s(y0), nil), z1)) -> c11(MARK(first(s(y0), nil))) MARK(cons(first(s(y0), s(y1)), z1)) -> c11(MARK(first(s(y0), s(y1)))) MARK(cons(first(0, first(y0, y1)), z1)) -> c11(MARK(first(0, first(y0, y1)))) MARK(cons(first(nil, first(y0, y1)), z1)) -> c11(MARK(first(nil, first(y0, y1)))) MARK(cons(first(0, from(y0)), z1)) -> c11(MARK(first(0, from(y0)))) MARK(cons(first(nil, from(y0)), z1)) -> c11(MARK(first(nil, from(y0)))) MARK(cons(first(y0, cons(y1, y2)), z1)) -> c11(MARK(first(y0, cons(y1, y2)))) MARK(cons(first(0, cons(y0, y1)), z1)) -> c11(MARK(first(0, cons(y0, y1)))) MARK(cons(first(nil, cons(y0, y1)), z1)) -> c11(MARK(first(nil, cons(y0, y1)))) MARK(cons(first(from(0), y0), z1)) -> c11(MARK(first(from(0), y0))) MARK(cons(first(from(nil), y0), z1)) -> c11(MARK(first(from(nil), y0))) MARK(cons(first(s(0), y0), z1)) -> c11(MARK(first(s(0), y0))) MARK(cons(first(s(nil), y0), z1)) -> c11(MARK(first(s(nil), y0))) MARK(cons(first(y0, cons(0, y1)), z1)) -> c11(MARK(first(y0, cons(0, y1)))) MARK(cons(first(y0, cons(nil, y1)), z1)) -> c11(MARK(first(y0, cons(nil, y1)))) MARK(cons(from(s(y0)), z1)) -> c11(MARK(from(s(y0)))) MARK(cons(from(cons(y0, y1)), z1)) -> c11(MARK(from(cons(y0, y1)))) MARK(cons(from(first(y0, y1)), z1)) -> c11(MARK(from(first(y0, y1)))) MARK(cons(from(first(y0, first(y1, y2))), z1)) -> c11(MARK(from(first(y0, first(y1, y2))))) MARK(cons(from(first(y0, from(y1))), z1)) -> c11(MARK(from(first(y0, from(y1))))) MARK(cons(from(first(y0, 0)), z1)) -> c11(MARK(from(first(y0, 0)))) MARK(cons(from(first(y0, nil)), z1)) -> c11(MARK(from(first(y0, nil)))) MARK(cons(from(first(y0, s(y1))), z1)) -> c11(MARK(from(first(y0, s(y1))))) MARK(cons(from(first(y0, cons(y1, y2))), z1)) -> c11(MARK(from(first(y0, cons(y1, y2))))) MARK(cons(from(first(first(y0, y1), y2)), z1)) -> c11(MARK(from(first(first(y0, y1), y2)))) MARK(cons(from(first(from(y0), y1)), z1)) -> c11(MARK(from(first(from(y0), y1)))) MARK(cons(from(first(0, y0)), z1)) -> c11(MARK(from(first(0, y0)))) MARK(cons(from(first(nil, y0)), z1)) -> c11(MARK(from(first(nil, y0)))) MARK(cons(from(first(s(y0), y1)), z1)) -> c11(MARK(from(first(s(y0), y1)))) MARK(cons(from(first(cons(y0, y1), y2)), z1)) -> c11(MARK(from(first(cons(y0, y1), y2)))) MARK(cons(from(from(y0)), z1)) -> c11(MARK(from(from(y0)))) MARK(cons(from(from(first(y0, y1))), z1)) -> c11(MARK(from(from(first(y0, y1))))) MARK(cons(from(from(from(y0))), z1)) -> c11(MARK(from(from(from(y0))))) MARK(cons(from(from(s(y0))), z1)) -> c11(MARK(from(from(s(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c11(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(0)), z1)) -> c11(MARK(from(from(0)))) MARK(cons(from(from(nil)), z1)) -> c11(MARK(from(from(nil)))) MARK(cons(s(s(y0)), z1)) -> c11(MARK(s(s(y0)))) MARK(cons(s(cons(y0, y1)), z1)) -> c11(MARK(s(cons(y0, y1)))) MARK(cons(s(first(y0, 0)), z1)) -> c11(MARK(s(first(y0, 0)))) MARK(cons(s(first(y0, nil)), z1)) -> c11(MARK(s(first(y0, nil)))) MARK(cons(s(first(y0, s(y1))), z1)) -> c11(MARK(s(first(y0, s(y1))))) MARK(cons(s(first(cons(y0, y1), y2)), z1)) -> c11(MARK(s(first(cons(y0, y1), y2)))) MARK(cons(s(first(0, y0)), z1)) -> c11(MARK(s(first(0, y0)))) MARK(cons(s(first(nil, y0)), z1)) -> c11(MARK(s(first(nil, y0)))) MARK(cons(s(first(y0, first(y1, first(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, first(y2, y3)))))) MARK(cons(s(first(y0, first(y1, from(y2)))), z1)) -> c11(MARK(s(first(y0, first(y1, from(y2)))))) MARK(cons(s(first(y0, first(y1, 0))), z1)) -> c11(MARK(s(first(y0, first(y1, 0))))) MARK(cons(s(first(y0, first(y1, nil))), z1)) -> c11(MARK(s(first(y0, first(y1, nil))))) MARK(cons(s(first(y0, first(y1, s(y2)))), z1)) -> c11(MARK(s(first(y0, first(y1, s(y2)))))) MARK(cons(s(first(y0, first(y1, cons(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, cons(y2, y3)))))) MARK(cons(s(first(y0, first(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, first(first(y1, y2), y3))))) MARK(cons(s(first(y0, first(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, first(from(y1), y2))))) MARK(cons(s(first(y0, first(0, y1))), z1)) -> c11(MARK(s(first(y0, first(0, y1))))) MARK(cons(s(first(y0, first(nil, y1))), z1)) -> c11(MARK(s(first(y0, first(nil, y1))))) MARK(cons(s(first(y0, first(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, first(s(y1), y2))))) MARK(cons(s(first(y0, first(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, first(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), first(y2, y3))))) MARK(cons(s(first(from(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), first(y1, y2))))) MARK(cons(s(first(s(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), first(y1, y2))))) MARK(cons(s(first(y0, first(y1, y2))), z1)) -> c11(MARK(s(first(y0, first(y1, y2))))) MARK(cons(s(first(cons(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), first(y2, y3))))) MARK(cons(s(first(y0, from(y1))), z1)) -> c11(MARK(s(first(y0, from(y1))))) MARK(cons(s(first(y0, from(first(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(first(y1, y2)))))) MARK(cons(s(first(y0, from(from(y1)))), z1)) -> c11(MARK(s(first(y0, from(from(y1)))))) MARK(cons(s(first(y0, from(0))), z1)) -> c11(MARK(s(first(y0, from(0))))) MARK(cons(s(first(y0, from(nil))), z1)) -> c11(MARK(s(first(y0, from(nil))))) MARK(cons(s(first(y0, from(s(y1)))), z1)) -> c11(MARK(s(first(y0, from(s(y1)))))) MARK(cons(s(first(y0, from(cons(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(cons(y1, y2)))))) MARK(cons(s(first(first(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), from(y2))))) MARK(cons(s(first(from(y0), from(y1))), z1)) -> c11(MARK(s(first(from(y0), from(y1))))) MARK(cons(s(first(s(y0), from(y1))), z1)) -> c11(MARK(s(first(s(y0), from(y1))))) MARK(cons(s(first(cons(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(cons(y0, y1), from(y2))))) MARK(cons(s(first(y0, cons(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(first(y1, y2), y3))))) MARK(cons(s(first(y0, cons(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(from(y1), y2))))) MARK(cons(s(first(y0, cons(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(s(y1), y2))))) MARK(cons(s(first(y0, cons(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), cons(y2, y3))))) MARK(cons(s(first(from(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), cons(y1, y2))))) MARK(cons(s(first(s(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), cons(y1, y2))))) MARK(cons(s(first(cons(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), cons(y2, y3))))) MARK(cons(s(first(first(y0, first(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, first(y1, y2)), y3)))) MARK(cons(s(first(first(y0, from(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, from(y1)), y2)))) MARK(cons(s(first(first(y0, 0), y1)), z1)) -> c11(MARK(s(first(first(y0, 0), y1)))) MARK(cons(s(first(first(y0, nil), y1)), z1)) -> c11(MARK(s(first(first(y0, nil), y1)))) MARK(cons(s(first(first(y0, s(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, s(y1)), y2)))) MARK(cons(s(first(first(y0, cons(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, cons(y1, y2)), y3)))) MARK(cons(s(first(first(first(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(first(y0, y1), y2), y3)))) MARK(cons(s(first(first(from(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(from(y0), y1), y2)))) MARK(cons(s(first(first(0, y0), y1)), z1)) -> c11(MARK(s(first(first(0, y0), y1)))) MARK(cons(s(first(first(nil, y0), y1)), z1)) -> c11(MARK(s(first(first(nil, y0), y1)))) MARK(cons(s(first(first(s(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(s(y0), y1), y2)))) MARK(cons(s(first(first(cons(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(cons(y0, y1), y2), y3)))) MARK(cons(s(first(first(y0, y1), 0)), z1)) -> c11(MARK(s(first(first(y0, y1), 0)))) MARK(cons(s(first(first(y0, y1), nil)), z1)) -> c11(MARK(s(first(first(y0, y1), nil)))) MARK(cons(s(first(first(y0, y1), s(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), s(y2))))) MARK(cons(s(first(first(y0, y1), y2)), z1)) -> c11(MARK(s(first(first(y0, y1), y2)))) MARK(cons(s(first(from(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(first(y0, y1)), y2)))) MARK(cons(s(first(from(from(y0)), y1)), z1)) -> c11(MARK(s(first(from(from(y0)), y1)))) MARK(cons(s(first(from(s(y0)), y1)), z1)) -> c11(MARK(s(first(from(s(y0)), y1)))) MARK(cons(s(first(from(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(cons(y0, y1)), y2)))) MARK(cons(s(first(from(y0), y1)), z1)) -> c11(MARK(s(first(from(y0), y1)))) MARK(cons(s(first(from(y0), 0)), z1)) -> c11(MARK(s(first(from(y0), 0)))) MARK(cons(s(first(from(y0), nil)), z1)) -> c11(MARK(s(first(from(y0), nil)))) MARK(cons(s(first(from(y0), s(y1))), z1)) -> c11(MARK(s(first(from(y0), s(y1))))) MARK(cons(s(first(s(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(first(y0, y1)), y2)))) MARK(cons(s(first(s(from(y0)), y1)), z1)) -> c11(MARK(s(first(s(from(y0)), y1)))) MARK(cons(s(first(s(0), y0)), z1)) -> c11(MARK(s(first(s(0), y0)))) MARK(cons(s(first(s(nil), y0)), z1)) -> c11(MARK(s(first(s(nil), y0)))) MARK(cons(s(first(s(s(y0)), y1)), z1)) -> c11(MARK(s(first(s(s(y0)), y1)))) MARK(cons(s(first(s(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(cons(y0, y1)), y2)))) MARK(cons(s(first(s(y0), y1)), z1)) -> c11(MARK(s(first(s(y0), y1)))) MARK(cons(s(first(s(y0), 0)), z1)) -> c11(MARK(s(first(s(y0), 0)))) MARK(cons(s(first(s(y0), nil)), z1)) -> c11(MARK(s(first(s(y0), nil)))) MARK(cons(s(first(s(y0), s(y1))), z1)) -> c11(MARK(s(first(s(y0), s(y1))))) MARK(cons(s(first(0, first(y0, y1))), z1)) -> c11(MARK(s(first(0, first(y0, y1))))) MARK(cons(s(first(nil, first(y0, y1))), z1)) -> c11(MARK(s(first(nil, first(y0, y1))))) MARK(cons(s(first(0, from(y0))), z1)) -> c11(MARK(s(first(0, from(y0))))) MARK(cons(s(first(nil, from(y0))), z1)) -> c11(MARK(s(first(nil, from(y0))))) MARK(cons(s(first(y0, cons(y1, y2))), z1)) -> c11(MARK(s(first(y0, cons(y1, y2))))) MARK(cons(s(first(0, cons(y0, y1))), z1)) -> c11(MARK(s(first(0, cons(y0, y1))))) MARK(cons(s(first(nil, cons(y0, y1))), z1)) -> c11(MARK(s(first(nil, cons(y0, y1))))) MARK(cons(s(first(from(0), y0)), z1)) -> c11(MARK(s(first(from(0), y0)))) MARK(cons(s(first(from(nil), y0)), z1)) -> c11(MARK(s(first(from(nil), y0)))) MARK(cons(s(first(y0, cons(0, y1))), z1)) -> c11(MARK(s(first(y0, cons(0, y1))))) MARK(cons(s(first(y0, cons(nil, y1))), z1)) -> c11(MARK(s(first(y0, cons(nil, y1))))) MARK(cons(s(from(s(y0))), z1)) -> c11(MARK(s(from(s(y0))))) MARK(cons(s(from(cons(y0, y1))), z1)) -> c11(MARK(s(from(cons(y0, y1))))) MARK(cons(s(from(first(y0, y1))), z1)) -> c11(MARK(s(from(first(y0, y1))))) MARK(cons(s(from(first(y0, first(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, first(y1, y2)))))) MARK(cons(s(from(first(y0, from(y1)))), z1)) -> c11(MARK(s(from(first(y0, from(y1)))))) MARK(cons(s(from(first(y0, 0))), z1)) -> c11(MARK(s(from(first(y0, 0))))) MARK(cons(s(from(first(y0, nil))), z1)) -> c11(MARK(s(from(first(y0, nil))))) MARK(cons(s(from(first(y0, s(y1)))), z1)) -> c11(MARK(s(from(first(y0, s(y1)))))) MARK(cons(s(from(first(y0, cons(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, cons(y1, y2)))))) MARK(cons(s(from(first(first(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(first(y0, y1), y2))))) MARK(cons(s(from(first(from(y0), y1))), z1)) -> c11(MARK(s(from(first(from(y0), y1))))) MARK(cons(s(from(first(0, y0))), z1)) -> c11(MARK(s(from(first(0, y0))))) MARK(cons(s(from(first(nil, y0))), z1)) -> c11(MARK(s(from(first(nil, y0))))) MARK(cons(s(from(first(s(y0), y1))), z1)) -> c11(MARK(s(from(first(s(y0), y1))))) MARK(cons(s(from(first(cons(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(cons(y0, y1), y2))))) MARK(cons(s(from(from(y0))), z1)) -> c11(MARK(s(from(from(y0))))) MARK(cons(s(from(from(first(y0, y1)))), z1)) -> c11(MARK(s(from(from(first(y0, y1)))))) MARK(cons(s(from(from(from(y0)))), z1)) -> c11(MARK(s(from(from(from(y0)))))) MARK(cons(s(from(from(s(y0)))), z1)) -> c11(MARK(s(from(from(s(y0)))))) MARK(cons(s(from(from(cons(y0, y1)))), z1)) -> c11(MARK(s(from(from(cons(y0, y1)))))) MARK(cons(s(from(from(0))), z1)) -> c11(MARK(s(from(from(0))))) MARK(cons(s(from(from(nil))), z1)) -> c11(MARK(s(from(from(nil))))) S tuples: MARK(first(x0, 0)) -> c5(MARK(x0)) MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, 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MARK(cons(first(first(y0, s(y1)), y2), z1)) -> c11(MARK(first(first(y0, s(y1)), y2))) MARK(cons(first(first(y0, cons(y1, y2)), y3), z1)) -> c11(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(cons(first(first(first(y0, y1), y2), y3), z1)) -> c11(MARK(first(first(first(y0, y1), y2), y3))) MARK(cons(first(first(from(y0), y1), y2), z1)) -> c11(MARK(first(first(from(y0), y1), y2))) MARK(cons(first(first(0, y0), y1), z1)) -> c11(MARK(first(first(0, y0), y1))) MARK(cons(first(first(nil, y0), y1), z1)) -> c11(MARK(first(first(nil, y0), y1))) MARK(cons(first(first(s(y0), y1), y2), z1)) -> c11(MARK(first(first(s(y0), y1), y2))) MARK(cons(first(first(cons(y0, y1), y2), y3), z1)) -> c11(MARK(first(first(cons(y0, y1), y2), y3))) MARK(cons(first(first(y0, y1), 0), z1)) -> c11(MARK(first(first(y0, y1), 0))) MARK(cons(first(first(y0, y1), nil), z1)) -> c11(MARK(first(first(y0, y1), nil))) MARK(cons(first(first(y0, y1), s(y2)), z1)) -> c11(MARK(first(first(y0, y1), s(y2)))) MARK(cons(first(first(y0, y1), y2), z1)) -> c11(MARK(first(first(y0, y1), y2))) MARK(cons(first(from(first(y0, y1)), y2), z1)) -> c11(MARK(first(from(first(y0, y1)), y2))) MARK(cons(first(from(from(y0)), y1), z1)) -> c11(MARK(first(from(from(y0)), y1))) MARK(cons(first(from(s(y0)), y1), z1)) -> c11(MARK(first(from(s(y0)), y1))) MARK(cons(first(from(cons(y0, y1)), y2), z1)) -> c11(MARK(first(from(cons(y0, y1)), y2))) MARK(cons(first(from(y0), y1), z1)) -> c11(MARK(first(from(y0), y1))) MARK(cons(first(from(y0), 0), z1)) -> c11(MARK(first(from(y0), 0))) MARK(cons(first(from(y0), nil), z1)) -> c11(MARK(first(from(y0), nil))) MARK(cons(first(from(y0), s(y1)), z1)) -> c11(MARK(first(from(y0), s(y1)))) MARK(cons(first(s(first(y0, y1)), y2), z1)) -> c11(MARK(first(s(first(y0, y1)), y2))) MARK(cons(first(s(from(y0)), y1), z1)) -> c11(MARK(first(s(from(y0)), y1))) MARK(cons(first(s(s(y0)), y1), z1)) -> c11(MARK(first(s(s(y0)), y1))) MARK(cons(first(s(cons(y0, y1)), y2), z1)) -> c11(MARK(first(s(cons(y0, y1)), y2))) MARK(cons(first(s(y0), y1), z1)) -> c11(MARK(first(s(y0), y1))) MARK(cons(first(s(y0), 0), z1)) -> c11(MARK(first(s(y0), 0))) MARK(cons(first(s(y0), nil), z1)) -> c11(MARK(first(s(y0), nil))) MARK(cons(first(s(y0), s(y1)), z1)) -> c11(MARK(first(s(y0), s(y1)))) MARK(cons(first(0, first(y0, y1)), z1)) -> c11(MARK(first(0, first(y0, y1)))) MARK(cons(first(nil, first(y0, y1)), z1)) -> c11(MARK(first(nil, first(y0, y1)))) MARK(cons(first(0, from(y0)), z1)) -> c11(MARK(first(0, from(y0)))) MARK(cons(first(nil, from(y0)), z1)) -> c11(MARK(first(nil, from(y0)))) MARK(cons(first(y0, cons(y1, y2)), z1)) -> c11(MARK(first(y0, cons(y1, y2)))) MARK(cons(first(0, cons(y0, y1)), z1)) -> c11(MARK(first(0, cons(y0, y1)))) MARK(cons(first(nil, cons(y0, y1)), z1)) -> c11(MARK(first(nil, cons(y0, y1)))) MARK(cons(first(from(0), y0), z1)) -> c11(MARK(first(from(0), y0))) MARK(cons(first(from(nil), y0), z1)) -> c11(MARK(first(from(nil), y0))) MARK(cons(first(s(0), y0), z1)) -> c11(MARK(first(s(0), y0))) MARK(cons(first(s(nil), y0), z1)) -> c11(MARK(first(s(nil), y0))) MARK(cons(first(y0, cons(0, y1)), z1)) -> c11(MARK(first(y0, cons(0, y1)))) MARK(cons(first(y0, cons(nil, y1)), z1)) -> c11(MARK(first(y0, cons(nil, y1)))) MARK(cons(from(s(y0)), z1)) -> c11(MARK(from(s(y0)))) MARK(cons(from(cons(y0, y1)), z1)) -> c11(MARK(from(cons(y0, y1)))) MARK(cons(from(first(y0, y1)), z1)) -> c11(MARK(from(first(y0, y1)))) MARK(cons(from(first(y0, first(y1, y2))), z1)) -> c11(MARK(from(first(y0, first(y1, y2))))) MARK(cons(from(first(y0, from(y1))), z1)) -> c11(MARK(from(first(y0, from(y1))))) MARK(cons(from(first(y0, 0)), z1)) -> c11(MARK(from(first(y0, 0)))) MARK(cons(from(first(y0, nil)), z1)) -> c11(MARK(from(first(y0, nil)))) MARK(cons(from(first(y0, s(y1))), z1)) -> c11(MARK(from(first(y0, s(y1))))) MARK(cons(from(first(y0, cons(y1, y2))), z1)) -> c11(MARK(from(first(y0, cons(y1, y2))))) MARK(cons(from(first(first(y0, y1), y2)), z1)) -> c11(MARK(from(first(first(y0, y1), y2)))) MARK(cons(from(first(from(y0), y1)), z1)) -> c11(MARK(from(first(from(y0), y1)))) MARK(cons(from(first(0, y0)), z1)) -> c11(MARK(from(first(0, y0)))) MARK(cons(from(first(nil, y0)), z1)) -> c11(MARK(from(first(nil, y0)))) MARK(cons(from(first(s(y0), y1)), z1)) -> c11(MARK(from(first(s(y0), y1)))) MARK(cons(from(first(cons(y0, y1), y2)), z1)) -> c11(MARK(from(first(cons(y0, y1), y2)))) MARK(cons(from(from(y0)), z1)) -> c11(MARK(from(from(y0)))) MARK(cons(from(from(first(y0, y1))), z1)) -> c11(MARK(from(from(first(y0, y1))))) MARK(cons(from(from(from(y0))), z1)) -> c11(MARK(from(from(from(y0))))) MARK(cons(from(from(s(y0))), z1)) -> c11(MARK(from(from(s(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c11(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(0)), z1)) -> c11(MARK(from(from(0)))) MARK(cons(from(from(nil)), z1)) -> c11(MARK(from(from(nil)))) MARK(cons(s(s(y0)), z1)) -> c11(MARK(s(s(y0)))) MARK(cons(s(cons(y0, y1)), z1)) -> c11(MARK(s(cons(y0, y1)))) MARK(cons(s(first(y0, 0)), z1)) -> c11(MARK(s(first(y0, 0)))) MARK(cons(s(first(y0, nil)), z1)) -> c11(MARK(s(first(y0, nil)))) MARK(cons(s(first(y0, s(y1))), z1)) -> c11(MARK(s(first(y0, s(y1))))) MARK(cons(s(first(cons(y0, y1), y2)), z1)) -> c11(MARK(s(first(cons(y0, y1), y2)))) MARK(cons(s(first(0, y0)), z1)) -> c11(MARK(s(first(0, y0)))) MARK(cons(s(first(nil, y0)), z1)) -> c11(MARK(s(first(nil, y0)))) MARK(cons(s(first(y0, first(y1, first(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, first(y2, y3)))))) MARK(cons(s(first(y0, first(y1, from(y2)))), z1)) -> c11(MARK(s(first(y0, first(y1, from(y2)))))) MARK(cons(s(first(y0, first(y1, 0))), z1)) -> c11(MARK(s(first(y0, first(y1, 0))))) MARK(cons(s(first(y0, first(y1, nil))), z1)) -> c11(MARK(s(first(y0, first(y1, nil))))) MARK(cons(s(first(y0, first(y1, s(y2)))), z1)) -> c11(MARK(s(first(y0, first(y1, s(y2)))))) MARK(cons(s(first(y0, first(y1, cons(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, cons(y2, y3)))))) MARK(cons(s(first(y0, first(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, first(first(y1, y2), y3))))) MARK(cons(s(first(y0, first(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, first(from(y1), y2))))) MARK(cons(s(first(y0, first(0, y1))), z1)) -> c11(MARK(s(first(y0, first(0, y1))))) MARK(cons(s(first(y0, first(nil, y1))), z1)) -> c11(MARK(s(first(y0, first(nil, y1))))) MARK(cons(s(first(y0, first(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, first(s(y1), y2))))) MARK(cons(s(first(y0, first(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, first(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), first(y2, y3))))) MARK(cons(s(first(from(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), first(y1, y2))))) MARK(cons(s(first(s(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), first(y1, y2))))) MARK(cons(s(first(y0, first(y1, y2))), z1)) -> c11(MARK(s(first(y0, first(y1, y2))))) MARK(cons(s(first(cons(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), first(y2, y3))))) MARK(cons(s(first(y0, from(y1))), z1)) -> c11(MARK(s(first(y0, from(y1))))) MARK(cons(s(first(y0, from(first(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(first(y1, y2)))))) MARK(cons(s(first(y0, from(from(y1)))), z1)) -> c11(MARK(s(first(y0, from(from(y1)))))) MARK(cons(s(first(y0, from(0))), z1)) -> c11(MARK(s(first(y0, from(0))))) MARK(cons(s(first(y0, from(nil))), z1)) -> c11(MARK(s(first(y0, from(nil))))) MARK(cons(s(first(y0, from(s(y1)))), z1)) -> c11(MARK(s(first(y0, from(s(y1)))))) MARK(cons(s(first(y0, from(cons(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(cons(y1, y2)))))) MARK(cons(s(first(first(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), from(y2))))) MARK(cons(s(first(from(y0), from(y1))), z1)) -> c11(MARK(s(first(from(y0), from(y1))))) MARK(cons(s(first(s(y0), from(y1))), z1)) -> c11(MARK(s(first(s(y0), from(y1))))) MARK(cons(s(first(cons(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(cons(y0, y1), from(y2))))) MARK(cons(s(first(y0, cons(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(first(y1, y2), y3))))) MARK(cons(s(first(y0, cons(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(from(y1), y2))))) MARK(cons(s(first(y0, cons(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(s(y1), y2))))) MARK(cons(s(first(y0, cons(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), cons(y2, y3))))) MARK(cons(s(first(from(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), cons(y1, y2))))) MARK(cons(s(first(s(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), cons(y1, y2))))) MARK(cons(s(first(cons(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), cons(y2, y3))))) MARK(cons(s(first(first(y0, first(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, first(y1, y2)), y3)))) MARK(cons(s(first(first(y0, from(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, from(y1)), y2)))) MARK(cons(s(first(first(y0, 0), y1)), z1)) -> c11(MARK(s(first(first(y0, 0), y1)))) MARK(cons(s(first(first(y0, nil), y1)), z1)) -> c11(MARK(s(first(first(y0, nil), y1)))) MARK(cons(s(first(first(y0, s(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, s(y1)), y2)))) MARK(cons(s(first(first(y0, cons(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, cons(y1, y2)), y3)))) MARK(cons(s(first(first(first(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(first(y0, y1), y2), y3)))) MARK(cons(s(first(first(from(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(from(y0), y1), y2)))) MARK(cons(s(first(first(0, y0), y1)), z1)) -> c11(MARK(s(first(first(0, y0), y1)))) MARK(cons(s(first(first(nil, y0), y1)), z1)) -> c11(MARK(s(first(first(nil, y0), y1)))) MARK(cons(s(first(first(s(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(s(y0), y1), y2)))) MARK(cons(s(first(first(cons(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(cons(y0, y1), y2), y3)))) MARK(cons(s(first(first(y0, y1), 0)), z1)) -> c11(MARK(s(first(first(y0, y1), 0)))) MARK(cons(s(first(first(y0, y1), nil)), z1)) -> c11(MARK(s(first(first(y0, y1), nil)))) MARK(cons(s(first(first(y0, y1), s(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), s(y2))))) MARK(cons(s(first(first(y0, y1), y2)), z1)) -> c11(MARK(s(first(first(y0, y1), y2)))) MARK(cons(s(first(from(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(first(y0, y1)), y2)))) MARK(cons(s(first(from(from(y0)), y1)), z1)) -> c11(MARK(s(first(from(from(y0)), y1)))) MARK(cons(s(first(from(s(y0)), y1)), z1)) -> c11(MARK(s(first(from(s(y0)), y1)))) MARK(cons(s(first(from(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(cons(y0, y1)), y2)))) MARK(cons(s(first(from(y0), y1)), z1)) -> c11(MARK(s(first(from(y0), y1)))) MARK(cons(s(first(from(y0), 0)), z1)) -> c11(MARK(s(first(from(y0), 0)))) MARK(cons(s(first(from(y0), nil)), z1)) -> c11(MARK(s(first(from(y0), nil)))) MARK(cons(s(first(from(y0), s(y1))), z1)) -> c11(MARK(s(first(from(y0), s(y1))))) MARK(cons(s(first(s(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(first(y0, y1)), y2)))) MARK(cons(s(first(s(from(y0)), y1)), z1)) -> c11(MARK(s(first(s(from(y0)), y1)))) MARK(cons(s(first(s(0), y0)), z1)) -> c11(MARK(s(first(s(0), y0)))) MARK(cons(s(first(s(nil), y0)), z1)) -> c11(MARK(s(first(s(nil), y0)))) MARK(cons(s(first(s(s(y0)), y1)), z1)) -> c11(MARK(s(first(s(s(y0)), y1)))) MARK(cons(s(first(s(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(cons(y0, y1)), y2)))) MARK(cons(s(first(s(y0), y1)), z1)) -> c11(MARK(s(first(s(y0), y1)))) MARK(cons(s(first(s(y0), 0)), z1)) -> c11(MARK(s(first(s(y0), 0)))) MARK(cons(s(first(s(y0), nil)), z1)) -> c11(MARK(s(first(s(y0), nil)))) MARK(cons(s(first(s(y0), s(y1))), z1)) -> c11(MARK(s(first(s(y0), s(y1))))) MARK(cons(s(first(0, first(y0, y1))), z1)) -> c11(MARK(s(first(0, first(y0, y1))))) MARK(cons(s(first(nil, first(y0, y1))), z1)) -> c11(MARK(s(first(nil, first(y0, y1))))) MARK(cons(s(first(0, from(y0))), z1)) -> c11(MARK(s(first(0, from(y0))))) MARK(cons(s(first(nil, from(y0))), z1)) -> c11(MARK(s(first(nil, from(y0))))) MARK(cons(s(first(y0, cons(y1, y2))), z1)) -> c11(MARK(s(first(y0, cons(y1, y2))))) MARK(cons(s(first(0, cons(y0, y1))), z1)) -> c11(MARK(s(first(0, cons(y0, y1))))) MARK(cons(s(first(nil, cons(y0, y1))), z1)) -> c11(MARK(s(first(nil, cons(y0, y1))))) MARK(cons(s(first(from(0), y0)), z1)) -> c11(MARK(s(first(from(0), y0)))) MARK(cons(s(first(from(nil), y0)), z1)) -> c11(MARK(s(first(from(nil), y0)))) MARK(cons(s(first(y0, cons(0, y1))), z1)) -> c11(MARK(s(first(y0, cons(0, y1))))) MARK(cons(s(first(y0, cons(nil, y1))), z1)) -> c11(MARK(s(first(y0, cons(nil, y1))))) MARK(cons(s(from(s(y0))), z1)) -> c11(MARK(s(from(s(y0))))) MARK(cons(s(from(cons(y0, y1))), z1)) -> c11(MARK(s(from(cons(y0, y1))))) MARK(cons(s(from(first(y0, y1))), z1)) -> c11(MARK(s(from(first(y0, y1))))) MARK(cons(s(from(first(y0, first(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, first(y1, y2)))))) MARK(cons(s(from(first(y0, from(y1)))), z1)) -> c11(MARK(s(from(first(y0, from(y1)))))) MARK(cons(s(from(first(y0, 0))), z1)) -> c11(MARK(s(from(first(y0, 0))))) MARK(cons(s(from(first(y0, nil))), z1)) -> c11(MARK(s(from(first(y0, nil))))) MARK(cons(s(from(first(y0, s(y1)))), z1)) -> c11(MARK(s(from(first(y0, s(y1)))))) MARK(cons(s(from(first(y0, cons(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, cons(y1, y2)))))) MARK(cons(s(from(first(first(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(first(y0, y1), y2))))) MARK(cons(s(from(first(from(y0), y1))), z1)) -> c11(MARK(s(from(first(from(y0), y1))))) MARK(cons(s(from(first(0, y0))), z1)) -> c11(MARK(s(from(first(0, y0))))) MARK(cons(s(from(first(nil, y0))), z1)) -> c11(MARK(s(from(first(nil, y0))))) MARK(cons(s(from(first(s(y0), y1))), z1)) -> c11(MARK(s(from(first(s(y0), y1))))) MARK(cons(s(from(first(cons(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(cons(y0, y1), y2))))) MARK(cons(s(from(from(y0))), z1)) -> c11(MARK(s(from(from(y0))))) MARK(cons(s(from(from(first(y0, y1)))), z1)) -> c11(MARK(s(from(from(first(y0, y1)))))) MARK(cons(s(from(from(from(y0)))), z1)) -> c11(MARK(s(from(from(from(y0)))))) MARK(cons(s(from(from(s(y0)))), z1)) -> c11(MARK(s(from(from(s(y0)))))) MARK(cons(s(from(from(cons(y0, y1)))), z1)) -> c11(MARK(s(from(from(cons(y0, y1)))))) MARK(cons(s(from(from(0))), z1)) -> c11(MARK(s(from(from(0))))) MARK(cons(s(from(from(nil))), z1)) -> c11(MARK(s(from(from(nil))))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__FIRST_2, A__FROM_1 Compound Symbols: c5_1, c6_1, c5_2, c6_2, c1_1, c3_1, c7_2, c7_1, c10_1, c11_1 ---------------------------------------- (123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace MARK(first(x0, 0)) -> c5(MARK(x0)) by MARK(first(first(y0, 0), 0)) -> c5(MARK(first(y0, 0))) MARK(first(first(y0, nil), 0)) -> c5(MARK(first(y0, nil))) MARK(first(first(y0, s(y1)), 0)) -> c5(MARK(first(y0, s(y1)))) MARK(first(first(cons(y0, y1), y2), 0)) -> c5(MARK(first(cons(y0, y1), y2))) MARK(first(first(0, y0), 0)) -> c5(MARK(first(0, y0))) MARK(first(first(nil, y0), 0)) -> c5(MARK(first(nil, y0))) MARK(first(first(y0, first(y1, first(y2, y3))), 0)) -> c5(MARK(first(y0, first(y1, first(y2, y3))))) MARK(first(first(y0, first(y1, from(y2))), 0)) -> c5(MARK(first(y0, first(y1, from(y2))))) MARK(first(first(y0, first(y1, 0)), 0)) -> c5(MARK(first(y0, first(y1, 0)))) MARK(first(first(y0, first(y1, nil)), 0)) -> c5(MARK(first(y0, first(y1, nil)))) MARK(first(first(y0, first(y1, s(y2))), 0)) -> c5(MARK(first(y0, first(y1, s(y2))))) MARK(first(first(y0, first(y1, cons(y2, y3))), 0)) -> c5(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(first(first(y0, first(first(y1, y2), y3)), 0)) -> c5(MARK(first(y0, first(first(y1, y2), y3)))) MARK(first(first(y0, first(from(y1), y2)), 0)) -> c5(MARK(first(y0, first(from(y1), y2)))) MARK(first(first(y0, first(0, y1)), 0)) -> c5(MARK(first(y0, first(0, 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MARK(first(cons(from(from(nil)), y0), 0)) -> c5(MARK(cons(from(from(nil)), y0))) MARK(first(cons(s(s(y0)), y1), 0)) -> c5(MARK(cons(s(s(y0)), y1))) MARK(first(cons(s(cons(y0, y1)), y2), 0)) -> c5(MARK(cons(s(cons(y0, y1)), y2))) MARK(first(cons(s(first(y0, 0)), y1), 0)) -> c5(MARK(cons(s(first(y0, 0)), y1))) MARK(first(cons(s(first(y0, nil)), y1), 0)) -> c5(MARK(cons(s(first(y0, nil)), y1))) MARK(first(cons(s(first(y0, s(y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, s(y1))), y2))) MARK(first(cons(s(first(cons(y0, y1), y2)), y3), 0)) -> c5(MARK(cons(s(first(cons(y0, y1), y2)), y3))) MARK(first(cons(s(first(0, y0)), y1), 0)) -> c5(MARK(cons(s(first(0, y0)), y1))) MARK(first(cons(s(first(nil, y0)), y1), 0)) -> c5(MARK(cons(s(first(nil, y0)), y1))) MARK(first(cons(s(first(y0, first(y1, first(y2, y3)))), y4), 0)) -> c5(MARK(cons(s(first(y0, first(y1, first(y2, y3)))), y4))) MARK(first(cons(s(first(y0, first(y1, from(y2)))), y3), 0)) -> c5(MARK(cons(s(first(y0, first(y1, from(y2)))), y3))) MARK(first(cons(s(first(y0, first(y1, 0))), y2), 0)) -> c5(MARK(cons(s(first(y0, first(y1, 0))), y2))) MARK(first(cons(s(first(y0, first(y1, nil))), y2), 0)) -> c5(MARK(cons(s(first(y0, first(y1, nil))), y2))) MARK(first(cons(s(first(y0, first(y1, s(y2)))), y3), 0)) -> c5(MARK(cons(s(first(y0, first(y1, s(y2)))), y3))) MARK(first(cons(s(first(y0, first(y1, cons(y2, y3)))), y4), 0)) -> c5(MARK(cons(s(first(y0, first(y1, cons(y2, y3)))), y4))) MARK(first(cons(s(first(y0, first(first(y1, y2), y3))), y4), 0)) -> c5(MARK(cons(s(first(y0, first(first(y1, y2), y3))), y4))) MARK(first(cons(s(first(y0, first(from(y1), y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, first(from(y1), y2))), y3))) MARK(first(cons(s(first(y0, first(0, y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, first(0, y1))), y2))) MARK(first(cons(s(first(y0, first(nil, y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, first(nil, y1))), y2))) MARK(first(cons(s(first(y0, first(s(y1), y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, first(s(y1), y2))), y3))) MARK(first(cons(s(first(y0, first(cons(y1, y2), y3))), y4), 0)) -> c5(MARK(cons(s(first(y0, first(cons(y1, y2), y3))), y4))) MARK(first(cons(s(first(first(y0, y1), first(y2, y3))), y4), 0)) -> c5(MARK(cons(s(first(first(y0, y1), first(y2, y3))), y4))) MARK(first(cons(s(first(from(y0), first(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(from(y0), first(y1, y2))), y3))) MARK(first(cons(s(first(s(y0), first(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(s(y0), first(y1, y2))), y3))) MARK(first(cons(s(first(y0, first(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, first(y1, y2))), y3))) MARK(first(cons(s(first(cons(y0, y1), first(y2, y3))), y4), 0)) -> c5(MARK(cons(s(first(cons(y0, y1), first(y2, y3))), y4))) MARK(first(cons(s(first(y0, from(y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, from(y1))), y2))) MARK(first(cons(s(first(y0, from(first(y1, y2)))), y3), 0)) -> c5(MARK(cons(s(first(y0, from(first(y1, y2)))), y3))) MARK(first(cons(s(first(y0, from(from(y1)))), y2), 0)) -> c5(MARK(cons(s(first(y0, from(from(y1)))), y2))) MARK(first(cons(s(first(y0, from(0))), y1), 0)) -> c5(MARK(cons(s(first(y0, from(0))), y1))) MARK(first(cons(s(first(y0, from(nil))), y1), 0)) -> c5(MARK(cons(s(first(y0, from(nil))), y1))) MARK(first(cons(s(first(y0, from(s(y1)))), y2), 0)) -> c5(MARK(cons(s(first(y0, from(s(y1)))), y2))) MARK(first(cons(s(first(y0, from(cons(y1, y2)))), y3), 0)) -> c5(MARK(cons(s(first(y0, from(cons(y1, y2)))), y3))) MARK(first(cons(s(first(first(y0, y1), from(y2))), y3), 0)) -> c5(MARK(cons(s(first(first(y0, y1), from(y2))), y3))) MARK(first(cons(s(first(from(y0), from(y1))), y2), 0)) -> c5(MARK(cons(s(first(from(y0), from(y1))), y2))) MARK(first(cons(s(first(s(y0), from(y1))), y2), 0)) -> c5(MARK(cons(s(first(s(y0), from(y1))), y2))) MARK(first(cons(s(first(cons(y0, y1), from(y2))), y3), 0)) -> c5(MARK(cons(s(first(cons(y0, y1), from(y2))), y3))) MARK(first(cons(s(first(y0, cons(first(y1, y2), y3))), y4), 0)) -> c5(MARK(cons(s(first(y0, cons(first(y1, y2), y3))), y4))) MARK(first(cons(s(first(y0, cons(from(y1), y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, cons(from(y1), y2))), y3))) MARK(first(cons(s(first(y0, cons(s(y1), y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, cons(s(y1), y2))), y3))) MARK(first(cons(s(first(y0, cons(cons(y1, y2), y3))), y4), 0)) -> c5(MARK(cons(s(first(y0, cons(cons(y1, y2), y3))), y4))) MARK(first(cons(s(first(first(y0, y1), cons(y2, y3))), y4), 0)) -> c5(MARK(cons(s(first(first(y0, y1), cons(y2, y3))), y4))) MARK(first(cons(s(first(from(y0), cons(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(from(y0), cons(y1, y2))), y3))) MARK(first(cons(s(first(s(y0), cons(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(s(y0), cons(y1, y2))), y3))) MARK(first(cons(s(first(cons(y0, y1), cons(y2, y3))), y4), 0)) -> c5(MARK(cons(s(first(cons(y0, y1), cons(y2, y3))), y4))) MARK(first(cons(s(first(first(y0, first(y1, y2)), y3)), y4), 0)) -> c5(MARK(cons(s(first(first(y0, first(y1, y2)), y3)), y4))) MARK(first(cons(s(first(first(y0, from(y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(y0, from(y1)), y2)), y3))) MARK(first(cons(s(first(first(y0, 0), y1)), y2), 0)) -> c5(MARK(cons(s(first(first(y0, 0), y1)), y2))) MARK(first(cons(s(first(first(y0, nil), y1)), y2), 0)) -> c5(MARK(cons(s(first(first(y0, nil), y1)), y2))) MARK(first(cons(s(first(first(y0, s(y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(y0, s(y1)), y2)), y3))) MARK(first(cons(s(first(first(y0, cons(y1, y2)), y3)), y4), 0)) -> c5(MARK(cons(s(first(first(y0, cons(y1, y2)), y3)), y4))) MARK(first(cons(s(first(first(first(y0, y1), y2), y3)), y4), 0)) -> c5(MARK(cons(s(first(first(first(y0, y1), y2), y3)), y4))) MARK(first(cons(s(first(first(from(y0), y1), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(from(y0), y1), y2)), y3))) MARK(first(cons(s(first(first(0, y0), y1)), y2), 0)) -> c5(MARK(cons(s(first(first(0, y0), y1)), y2))) MARK(first(cons(s(first(first(nil, y0), y1)), y2), 0)) -> c5(MARK(cons(s(first(first(nil, y0), y1)), y2))) MARK(first(cons(s(first(first(s(y0), y1), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(s(y0), y1), y2)), y3))) MARK(first(cons(s(first(first(cons(y0, y1), y2), y3)), y4), 0)) -> c5(MARK(cons(s(first(first(cons(y0, y1), y2), y3)), y4))) MARK(first(cons(s(first(first(y0, y1), 0)), y2), 0)) -> c5(MARK(cons(s(first(first(y0, y1), 0)), y2))) MARK(first(cons(s(first(first(y0, y1), nil)), y2), 0)) -> c5(MARK(cons(s(first(first(y0, y1), nil)), y2))) MARK(first(cons(s(first(first(y0, y1), s(y2))), y3), 0)) -> c5(MARK(cons(s(first(first(y0, y1), s(y2))), y3))) MARK(first(cons(s(first(first(y0, y1), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(y0, y1), y2)), y3))) MARK(first(cons(s(first(from(first(y0, y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(from(first(y0, y1)), y2)), y3))) MARK(first(cons(s(first(from(from(y0)), y1)), y2), 0)) -> c5(MARK(cons(s(first(from(from(y0)), y1)), y2))) MARK(first(cons(s(first(from(s(y0)), y1)), y2), 0)) -> c5(MARK(cons(s(first(from(s(y0)), y1)), y2))) MARK(first(cons(s(first(from(cons(y0, y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(from(cons(y0, y1)), y2)), y3))) MARK(first(cons(s(first(from(y0), y1)), y2), 0)) -> c5(MARK(cons(s(first(from(y0), y1)), y2))) MARK(first(cons(s(first(from(y0), 0)), y1), 0)) -> c5(MARK(cons(s(first(from(y0), 0)), y1))) MARK(first(cons(s(first(from(y0), nil)), y1), 0)) -> c5(MARK(cons(s(first(from(y0), nil)), y1))) MARK(first(cons(s(first(from(y0), s(y1))), y2), 0)) -> c5(MARK(cons(s(first(from(y0), s(y1))), y2))) MARK(first(cons(s(first(s(first(y0, y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(s(first(y0, y1)), y2)), y3))) MARK(first(cons(s(first(s(from(y0)), y1)), y2), 0)) -> c5(MARK(cons(s(first(s(from(y0)), y1)), y2))) MARK(first(cons(s(first(s(0), y0)), y1), 0)) -> c5(MARK(cons(s(first(s(0), y0)), y1))) MARK(first(cons(s(first(s(nil), y0)), y1), 0)) -> c5(MARK(cons(s(first(s(nil), y0)), y1))) MARK(first(cons(s(first(s(s(y0)), y1)), y2), 0)) -> c5(MARK(cons(s(first(s(s(y0)), y1)), y2))) MARK(first(cons(s(first(s(cons(y0, y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(s(cons(y0, y1)), y2)), y3))) MARK(first(cons(s(first(s(y0), y1)), y2), 0)) -> c5(MARK(cons(s(first(s(y0), y1)), y2))) MARK(first(cons(s(first(s(y0), 0)), y1), 0)) -> c5(MARK(cons(s(first(s(y0), 0)), y1))) MARK(first(cons(s(first(s(y0), nil)), y1), 0)) -> c5(MARK(cons(s(first(s(y0), nil)), y1))) MARK(first(cons(s(first(s(y0), s(y1))), y2), 0)) -> c5(MARK(cons(s(first(s(y0), s(y1))), y2))) MARK(first(cons(s(first(0, first(y0, y1))), y2), 0)) -> c5(MARK(cons(s(first(0, first(y0, y1))), y2))) MARK(first(cons(s(first(nil, first(y0, y1))), y2), 0)) -> c5(MARK(cons(s(first(nil, first(y0, y1))), y2))) MARK(first(cons(s(first(0, from(y0))), y1), 0)) -> c5(MARK(cons(s(first(0, from(y0))), y1))) MARK(first(cons(s(first(nil, from(y0))), y1), 0)) -> c5(MARK(cons(s(first(nil, from(y0))), y1))) MARK(first(cons(s(first(y0, cons(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, cons(y1, y2))), y3))) MARK(first(cons(s(first(0, cons(y0, y1))), y2), 0)) -> c5(MARK(cons(s(first(0, cons(y0, y1))), y2))) MARK(first(cons(s(first(nil, cons(y0, y1))), y2), 0)) -> c5(MARK(cons(s(first(nil, cons(y0, y1))), y2))) MARK(first(cons(s(first(from(0), y0)), y1), 0)) -> c5(MARK(cons(s(first(from(0), y0)), y1))) MARK(first(cons(s(first(from(nil), y0)), y1), 0)) -> c5(MARK(cons(s(first(from(nil), y0)), y1))) MARK(first(cons(s(first(y0, cons(0, y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, cons(0, y1))), y2))) MARK(first(cons(s(first(y0, cons(nil, y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, cons(nil, y1))), y2))) MARK(first(cons(s(from(s(y0))), y1), 0)) -> c5(MARK(cons(s(from(s(y0))), y1))) MARK(first(cons(s(from(cons(y0, y1))), y2), 0)) -> c5(MARK(cons(s(from(cons(y0, y1))), y2))) MARK(first(cons(s(from(first(y0, y1))), y2), 0)) -> c5(MARK(cons(s(from(first(y0, y1))), y2))) MARK(first(cons(s(from(first(y0, first(y1, y2)))), y3), 0)) -> c5(MARK(cons(s(from(first(y0, first(y1, y2)))), y3))) MARK(first(cons(s(from(first(y0, from(y1)))), y2), 0)) -> c5(MARK(cons(s(from(first(y0, from(y1)))), y2))) MARK(first(cons(s(from(first(y0, 0))), y1), 0)) -> c5(MARK(cons(s(from(first(y0, 0))), y1))) MARK(first(cons(s(from(first(y0, nil))), y1), 0)) -> c5(MARK(cons(s(from(first(y0, nil))), y1))) MARK(first(cons(s(from(first(y0, s(y1)))), y2), 0)) -> c5(MARK(cons(s(from(first(y0, s(y1)))), y2))) MARK(first(cons(s(from(first(y0, cons(y1, y2)))), y3), 0)) -> c5(MARK(cons(s(from(first(y0, cons(y1, y2)))), y3))) MARK(first(cons(s(from(first(first(y0, y1), y2))), y3), 0)) -> c5(MARK(cons(s(from(first(first(y0, y1), y2))), y3))) MARK(first(cons(s(from(first(from(y0), y1))), y2), 0)) -> c5(MARK(cons(s(from(first(from(y0), y1))), y2))) MARK(first(cons(s(from(first(0, y0))), y1), 0)) -> c5(MARK(cons(s(from(first(0, y0))), y1))) MARK(first(cons(s(from(first(nil, y0))), y1), 0)) -> c5(MARK(cons(s(from(first(nil, y0))), y1))) MARK(first(cons(s(from(first(s(y0), y1))), y2), 0)) -> c5(MARK(cons(s(from(first(s(y0), y1))), y2))) MARK(first(cons(s(from(first(cons(y0, y1), y2))), y3), 0)) -> c5(MARK(cons(s(from(first(cons(y0, y1), y2))), y3))) MARK(first(cons(s(from(from(y0))), y1), 0)) -> c5(MARK(cons(s(from(from(y0))), y1))) MARK(first(cons(s(from(from(first(y0, y1)))), y2), 0)) -> c5(MARK(cons(s(from(from(first(y0, y1)))), y2))) MARK(first(cons(s(from(from(from(y0)))), y1), 0)) -> c5(MARK(cons(s(from(from(from(y0)))), y1))) MARK(first(cons(s(from(from(s(y0)))), y1), 0)) -> c5(MARK(cons(s(from(from(s(y0)))), y1))) MARK(first(cons(s(from(from(cons(y0, y1)))), y2), 0)) -> c5(MARK(cons(s(from(from(cons(y0, y1)))), y2))) MARK(first(cons(s(from(from(0))), y0), 0)) -> c5(MARK(cons(s(from(from(0))), y0))) MARK(first(cons(s(from(from(nil))), y0), 0)) -> c5(MARK(cons(s(from(from(nil))), y0))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(from(z0)) -> a__from(mark(z0)) mark(0) -> 0 mark(nil) -> nil mark(s(z0)) -> s(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) Tuples: MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> 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A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), 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c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(0))) -> c7(A__FROM(a__from(0))) MARK(from(from(nil))) -> c7(A__FROM(a__from(nil))) MARK(s(s(y0))) -> c10(MARK(s(y0))) MARK(s(cons(y0, y1))) -> c10(MARK(cons(y0, y1))) MARK(s(first(y0, 0))) -> c10(MARK(first(y0, 0))) MARK(s(first(y0, nil))) -> c10(MARK(first(y0, nil))) MARK(s(first(y0, s(y1)))) -> c10(MARK(first(y0, s(y1)))) MARK(s(first(cons(y0, y1), y2))) -> c10(MARK(first(cons(y0, y1), y2))) MARK(s(first(0, y0))) -> c10(MARK(first(0, y0))) MARK(s(first(nil, y0))) -> c10(MARK(first(nil, y0))) MARK(s(first(y0, first(y1, first(y2, y3))))) -> c10(MARK(first(y0, first(y1, first(y2, y3))))) MARK(s(first(y0, first(y1, from(y2))))) -> c10(MARK(first(y0, first(y1, from(y2))))) MARK(s(first(y0, first(y1, 0)))) -> c10(MARK(first(y0, first(y1, 0)))) MARK(s(first(y0, first(y1, nil)))) -> c10(MARK(first(y0, first(y1, nil)))) MARK(s(first(y0, first(y1, s(y2))))) -> c10(MARK(first(y0, first(y1, s(y2))))) MARK(s(first(y0, first(y1, cons(y2, y3))))) -> c10(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(s(first(y0, first(first(y1, y2), y3)))) -> c10(MARK(first(y0, first(first(y1, y2), y3)))) MARK(s(first(y0, first(from(y1), y2)))) -> c10(MARK(first(y0, first(from(y1), y2)))) MARK(s(first(y0, first(0, y1)))) -> c10(MARK(first(y0, first(0, y1)))) MARK(s(first(y0, first(nil, y1)))) -> c10(MARK(first(y0, first(nil, y1)))) MARK(s(first(y0, first(s(y1), y2)))) -> c10(MARK(first(y0, first(s(y1), y2)))) MARK(s(first(y0, first(cons(y1, y2), y3)))) -> c10(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), first(y2, y3)))) -> c10(MARK(first(first(y0, y1), first(y2, y3)))) MARK(s(first(from(y0), first(y1, y2)))) -> c10(MARK(first(from(y0), first(y1, y2)))) MARK(s(first(s(y0), first(y1, y2)))) -> c10(MARK(first(s(y0), first(y1, y2)))) MARK(s(first(y0, first(y1, y2)))) -> c10(MARK(first(y0, first(y1, y2)))) MARK(s(first(cons(y0, y1), first(y2, y3)))) -> c10(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(s(first(y0, from(y1)))) -> c10(MARK(first(y0, from(y1)))) MARK(s(first(y0, from(first(y1, y2))))) -> c10(MARK(first(y0, from(first(y1, y2))))) MARK(s(first(y0, from(from(y1))))) -> c10(MARK(first(y0, from(from(y1))))) MARK(s(first(y0, from(0)))) -> c10(MARK(first(y0, from(0)))) MARK(s(first(y0, from(nil)))) -> c10(MARK(first(y0, from(nil)))) MARK(s(first(y0, from(s(y1))))) -> c10(MARK(first(y0, from(s(y1))))) MARK(s(first(y0, from(cons(y1, y2))))) -> c10(MARK(first(y0, from(cons(y1, y2))))) MARK(s(first(first(y0, y1), from(y2)))) -> c10(MARK(first(first(y0, y1), from(y2)))) MARK(s(first(from(y0), from(y1)))) -> c10(MARK(first(from(y0), from(y1)))) MARK(s(first(s(y0), from(y1)))) -> c10(MARK(first(s(y0), from(y1)))) MARK(s(first(cons(y0, y1), from(y2)))) -> c10(MARK(first(cons(y0, y1), from(y2)))) MARK(s(first(y0, cons(first(y1, y2), y3)))) -> c10(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(s(first(y0, cons(from(y1), y2)))) -> c10(MARK(first(y0, cons(from(y1), y2)))) MARK(s(first(y0, cons(s(y1), y2)))) -> c10(MARK(first(y0, cons(s(y1), y2)))) MARK(s(first(y0, cons(cons(y1, y2), y3)))) -> c10(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), cons(y2, y3)))) -> c10(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(s(first(from(y0), cons(y1, y2)))) -> c10(MARK(first(from(y0), cons(y1, y2)))) MARK(s(first(s(y0), cons(y1, y2)))) -> c10(MARK(first(s(y0), cons(y1, y2)))) MARK(s(first(cons(y0, y1), cons(y2, y3)))) -> c10(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(s(first(first(y0, first(y1, y2)), y3))) -> c10(MARK(first(first(y0, first(y1, y2)), y3))) MARK(s(first(first(y0, from(y1)), y2))) -> c10(MARK(first(first(y0, from(y1)), y2))) MARK(s(first(first(y0, 0), y1))) -> c10(MARK(first(first(y0, 0), y1))) MARK(s(first(first(y0, nil), y1))) -> c10(MARK(first(first(y0, nil), y1))) MARK(s(first(first(y0, s(y1)), y2))) -> c10(MARK(first(first(y0, s(y1)), y2))) MARK(s(first(first(y0, cons(y1, y2)), y3))) -> c10(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(s(first(first(first(y0, y1), y2), y3))) -> c10(MARK(first(first(first(y0, y1), y2), y3))) MARK(s(first(first(from(y0), y1), y2))) -> c10(MARK(first(first(from(y0), y1), y2))) MARK(s(first(first(0, y0), y1))) -> c10(MARK(first(first(0, y0), y1))) MARK(s(first(first(nil, y0), y1))) -> c10(MARK(first(first(nil, y0), y1))) MARK(s(first(first(s(y0), y1), y2))) -> c10(MARK(first(first(s(y0), y1), y2))) MARK(s(first(first(cons(y0, y1), y2), y3))) -> c10(MARK(first(first(cons(y0, y1), y2), y3))) MARK(s(first(first(y0, y1), 0))) -> c10(MARK(first(first(y0, y1), 0))) MARK(s(first(first(y0, y1), nil))) -> c10(MARK(first(first(y0, y1), nil))) MARK(s(first(first(y0, y1), s(y2)))) -> c10(MARK(first(first(y0, y1), s(y2)))) MARK(s(first(first(y0, y1), y2))) -> c10(MARK(first(first(y0, y1), y2))) MARK(s(first(from(first(y0, y1)), y2))) -> c10(MARK(first(from(first(y0, y1)), y2))) MARK(s(first(from(from(y0)), y1))) -> c10(MARK(first(from(from(y0)), y1))) MARK(s(first(from(s(y0)), y1))) -> c10(MARK(first(from(s(y0)), y1))) MARK(s(first(from(cons(y0, y1)), y2))) -> c10(MARK(first(from(cons(y0, y1)), y2))) MARK(s(first(from(y0), y1))) -> c10(MARK(first(from(y0), y1))) MARK(s(first(from(y0), 0))) -> c10(MARK(first(from(y0), 0))) MARK(s(first(from(y0), nil))) -> c10(MARK(first(from(y0), nil))) MARK(s(first(from(y0), s(y1)))) -> c10(MARK(first(from(y0), s(y1)))) MARK(s(first(s(first(y0, y1)), y2))) -> c10(MARK(first(s(first(y0, y1)), y2))) MARK(s(first(s(from(y0)), y1))) -> c10(MARK(first(s(from(y0)), y1))) MARK(s(first(s(0), y0))) -> c10(MARK(first(s(0), y0))) MARK(s(first(s(nil), y0))) -> c10(MARK(first(s(nil), y0))) MARK(s(first(s(s(y0)), y1))) -> c10(MARK(first(s(s(y0)), y1))) MARK(s(first(s(cons(y0, y1)), y2))) -> c10(MARK(first(s(cons(y0, y1)), y2))) MARK(s(first(s(y0), y1))) -> c10(MARK(first(s(y0), y1))) MARK(s(first(s(y0), 0))) -> c10(MARK(first(s(y0), 0))) MARK(s(first(s(y0), nil))) -> c10(MARK(first(s(y0), nil))) MARK(s(first(s(y0), s(y1)))) -> c10(MARK(first(s(y0), s(y1)))) MARK(s(first(0, first(y0, y1)))) -> c10(MARK(first(0, first(y0, y1)))) MARK(s(first(nil, first(y0, y1)))) -> c10(MARK(first(nil, first(y0, y1)))) MARK(s(first(0, from(y0)))) -> c10(MARK(first(0, from(y0)))) MARK(s(first(nil, from(y0)))) -> c10(MARK(first(nil, from(y0)))) MARK(s(first(y0, cons(y1, y2)))) -> c10(MARK(first(y0, cons(y1, y2)))) MARK(s(first(0, cons(y0, y1)))) -> c10(MARK(first(0, cons(y0, y1)))) MARK(s(first(nil, cons(y0, y1)))) -> c10(MARK(first(nil, cons(y0, y1)))) MARK(s(first(from(0), y0))) -> c10(MARK(first(from(0), y0))) MARK(s(first(from(nil), y0))) -> c10(MARK(first(from(nil), y0))) MARK(s(first(y0, cons(0, y1)))) -> c10(MARK(first(y0, cons(0, y1)))) MARK(s(first(y0, cons(nil, y1)))) -> c10(MARK(first(y0, cons(nil, y1)))) MARK(s(from(s(y0)))) -> c10(MARK(from(s(y0)))) MARK(s(from(cons(y0, y1)))) -> c10(MARK(from(cons(y0, y1)))) MARK(s(from(first(y0, y1)))) -> c10(MARK(from(first(y0, y1)))) MARK(s(from(first(y0, first(y1, y2))))) -> c10(MARK(from(first(y0, first(y1, y2))))) MARK(s(from(first(y0, from(y1))))) -> c10(MARK(from(first(y0, from(y1))))) MARK(s(from(first(y0, 0)))) -> c10(MARK(from(first(y0, 0)))) MARK(s(from(first(y0, nil)))) -> c10(MARK(from(first(y0, nil)))) MARK(s(from(first(y0, s(y1))))) -> c10(MARK(from(first(y0, s(y1))))) MARK(s(from(first(y0, cons(y1, y2))))) -> c10(MARK(from(first(y0, cons(y1, y2))))) MARK(s(from(first(first(y0, y1), y2)))) -> c10(MARK(from(first(first(y0, y1), y2)))) MARK(s(from(first(from(y0), y1)))) -> c10(MARK(from(first(from(y0), y1)))) MARK(s(from(first(0, y0)))) -> c10(MARK(from(first(0, y0)))) MARK(s(from(first(nil, y0)))) -> c10(MARK(from(first(nil, y0)))) MARK(s(from(first(s(y0), y1)))) -> c10(MARK(from(first(s(y0), y1)))) MARK(s(from(first(cons(y0, y1), y2)))) -> c10(MARK(from(first(cons(y0, y1), y2)))) MARK(s(from(from(y0)))) -> c10(MARK(from(from(y0)))) MARK(s(from(from(first(y0, y1))))) -> c10(MARK(from(from(first(y0, y1))))) MARK(s(from(from(from(y0))))) -> c10(MARK(from(from(from(y0))))) MARK(s(from(from(s(y0))))) -> c10(MARK(from(from(s(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c10(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(0)))) -> c10(MARK(from(from(0)))) MARK(s(from(from(nil)))) -> c10(MARK(from(from(nil)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1))) MARK(cons(cons(y0, y1), z1)) -> c11(MARK(cons(y0, y1))) MARK(cons(first(y0, 0), z1)) -> c11(MARK(first(y0, 0))) MARK(cons(first(y0, nil), z1)) -> c11(MARK(first(y0, nil))) MARK(cons(first(y0, s(y1)), z1)) -> c11(MARK(first(y0, s(y1)))) MARK(cons(first(cons(y0, y1), y2), z1)) -> c11(MARK(first(cons(y0, y1), y2))) MARK(cons(first(0, y0), z1)) -> c11(MARK(first(0, y0))) MARK(cons(first(nil, y0), z1)) -> c11(MARK(first(nil, y0))) MARK(cons(first(y0, first(y1, first(y2, y3))), z1)) -> c11(MARK(first(y0, first(y1, first(y2, y3))))) MARK(cons(first(y0, first(y1, from(y2))), z1)) -> c11(MARK(first(y0, first(y1, from(y2))))) MARK(cons(first(y0, first(y1, 0)), z1)) -> c11(MARK(first(y0, first(y1, 0)))) MARK(cons(first(y0, first(y1, nil)), z1)) -> c11(MARK(first(y0, first(y1, nil)))) MARK(cons(first(y0, first(y1, s(y2))), z1)) -> c11(MARK(first(y0, first(y1, s(y2))))) MARK(cons(first(y0, first(y1, cons(y2, y3))), z1)) -> c11(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(cons(first(y0, first(first(y1, y2), y3)), z1)) -> c11(MARK(first(y0, first(first(y1, y2), y3)))) MARK(cons(first(y0, first(from(y1), y2)), z1)) -> c11(MARK(first(y0, first(from(y1), y2)))) MARK(cons(first(y0, first(0, y1)), z1)) -> c11(MARK(first(y0, first(0, y1)))) MARK(cons(first(y0, first(nil, y1)), z1)) -> c11(MARK(first(y0, first(nil, y1)))) MARK(cons(first(y0, first(s(y1), y2)), z1)) -> c11(MARK(first(y0, first(s(y1), y2)))) MARK(cons(first(y0, first(cons(y1, y2), y3)), z1)) -> c11(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(cons(first(first(y0, y1), first(y2, y3)), z1)) -> c11(MARK(first(first(y0, y1), first(y2, y3)))) MARK(cons(first(from(y0), first(y1, y2)), z1)) -> c11(MARK(first(from(y0), first(y1, y2)))) MARK(cons(first(s(y0), first(y1, y2)), z1)) -> c11(MARK(first(s(y0), first(y1, y2)))) MARK(cons(first(y0, first(y1, y2)), z1)) -> c11(MARK(first(y0, first(y1, y2)))) MARK(cons(first(cons(y0, y1), first(y2, y3)), z1)) -> c11(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(cons(first(y0, from(y1)), z1)) -> c11(MARK(first(y0, from(y1)))) MARK(cons(first(y0, from(first(y1, y2))), z1)) -> c11(MARK(first(y0, from(first(y1, y2))))) MARK(cons(first(y0, from(from(y1))), z1)) -> c11(MARK(first(y0, from(from(y1))))) MARK(cons(first(y0, from(0)), z1)) -> c11(MARK(first(y0, from(0)))) MARK(cons(first(y0, from(nil)), z1)) -> c11(MARK(first(y0, from(nil)))) MARK(cons(first(y0, from(s(y1))), z1)) -> c11(MARK(first(y0, from(s(y1))))) MARK(cons(first(y0, from(cons(y1, y2))), z1)) -> c11(MARK(first(y0, from(cons(y1, y2))))) MARK(cons(first(first(y0, y1), from(y2)), z1)) -> c11(MARK(first(first(y0, y1), from(y2)))) MARK(cons(first(from(y0), from(y1)), z1)) -> c11(MARK(first(from(y0), from(y1)))) MARK(cons(first(s(y0), from(y1)), z1)) -> c11(MARK(first(s(y0), from(y1)))) MARK(cons(first(cons(y0, y1), from(y2)), z1)) -> c11(MARK(first(cons(y0, y1), from(y2)))) MARK(cons(first(y0, cons(first(y1, y2), y3)), z1)) -> c11(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(cons(first(y0, cons(from(y1), y2)), z1)) -> c11(MARK(first(y0, cons(from(y1), y2)))) MARK(cons(first(y0, cons(s(y1), y2)), z1)) -> c11(MARK(first(y0, cons(s(y1), y2)))) MARK(cons(first(y0, cons(cons(y1, y2), y3)), z1)) -> c11(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(cons(first(first(y0, y1), cons(y2, y3)), z1)) -> c11(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(cons(first(from(y0), cons(y1, y2)), z1)) -> c11(MARK(first(from(y0), cons(y1, y2)))) MARK(cons(first(s(y0), cons(y1, y2)), z1)) -> c11(MARK(first(s(y0), cons(y1, y2)))) MARK(cons(first(cons(y0, y1), cons(y2, y3)), z1)) -> c11(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(cons(first(first(y0, first(y1, y2)), y3), z1)) -> c11(MARK(first(first(y0, first(y1, y2)), y3))) MARK(cons(first(first(y0, from(y1)), y2), z1)) -> c11(MARK(first(first(y0, from(y1)), y2))) MARK(cons(first(first(y0, 0), y1), z1)) -> c11(MARK(first(first(y0, 0), y1))) MARK(cons(first(first(y0, nil), y1), z1)) -> c11(MARK(first(first(y0, nil), y1))) MARK(cons(first(first(y0, s(y1)), y2), z1)) -> c11(MARK(first(first(y0, s(y1)), y2))) MARK(cons(first(first(y0, cons(y1, y2)), y3), z1)) -> c11(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(cons(first(first(first(y0, y1), y2), y3), z1)) -> c11(MARK(first(first(first(y0, y1), y2), y3))) MARK(cons(first(first(from(y0), y1), y2), z1)) -> c11(MARK(first(first(from(y0), y1), y2))) MARK(cons(first(first(0, y0), y1), z1)) -> c11(MARK(first(first(0, y0), y1))) MARK(cons(first(first(nil, y0), y1), z1)) -> c11(MARK(first(first(nil, y0), y1))) MARK(cons(first(first(s(y0), y1), y2), z1)) -> c11(MARK(first(first(s(y0), y1), y2))) MARK(cons(first(first(cons(y0, y1), y2), y3), z1)) -> c11(MARK(first(first(cons(y0, y1), y2), y3))) MARK(cons(first(first(y0, y1), 0), z1)) -> c11(MARK(first(first(y0, y1), 0))) MARK(cons(first(first(y0, y1), nil), z1)) -> c11(MARK(first(first(y0, y1), nil))) MARK(cons(first(first(y0, y1), s(y2)), z1)) -> c11(MARK(first(first(y0, y1), s(y2)))) MARK(cons(first(first(y0, y1), y2), z1)) -> c11(MARK(first(first(y0, y1), y2))) MARK(cons(first(from(first(y0, y1)), y2), z1)) -> c11(MARK(first(from(first(y0, y1)), y2))) MARK(cons(first(from(from(y0)), y1), z1)) -> c11(MARK(first(from(from(y0)), y1))) MARK(cons(first(from(s(y0)), y1), z1)) -> c11(MARK(first(from(s(y0)), y1))) MARK(cons(first(from(cons(y0, y1)), y2), z1)) -> c11(MARK(first(from(cons(y0, y1)), y2))) MARK(cons(first(from(y0), y1), z1)) -> c11(MARK(first(from(y0), y1))) MARK(cons(first(from(y0), 0), z1)) -> c11(MARK(first(from(y0), 0))) MARK(cons(first(from(y0), nil), z1)) -> c11(MARK(first(from(y0), nil))) MARK(cons(first(from(y0), s(y1)), z1)) -> c11(MARK(first(from(y0), s(y1)))) MARK(cons(first(s(first(y0, y1)), y2), z1)) -> c11(MARK(first(s(first(y0, y1)), y2))) MARK(cons(first(s(from(y0)), y1), z1)) -> c11(MARK(first(s(from(y0)), y1))) MARK(cons(first(s(s(y0)), y1), z1)) -> c11(MARK(first(s(s(y0)), y1))) MARK(cons(first(s(cons(y0, y1)), y2), z1)) -> c11(MARK(first(s(cons(y0, y1)), y2))) MARK(cons(first(s(y0), y1), z1)) -> c11(MARK(first(s(y0), y1))) MARK(cons(first(s(y0), 0), z1)) -> c11(MARK(first(s(y0), 0))) MARK(cons(first(s(y0), nil), z1)) -> c11(MARK(first(s(y0), nil))) MARK(cons(first(s(y0), s(y1)), z1)) -> c11(MARK(first(s(y0), s(y1)))) MARK(cons(first(0, first(y0, y1)), z1)) -> c11(MARK(first(0, first(y0, y1)))) MARK(cons(first(nil, first(y0, y1)), z1)) -> c11(MARK(first(nil, first(y0, y1)))) MARK(cons(first(0, from(y0)), z1)) -> c11(MARK(first(0, from(y0)))) MARK(cons(first(nil, from(y0)), z1)) -> c11(MARK(first(nil, from(y0)))) MARK(cons(first(y0, cons(y1, y2)), z1)) -> c11(MARK(first(y0, cons(y1, y2)))) MARK(cons(first(0, cons(y0, y1)), z1)) -> c11(MARK(first(0, cons(y0, y1)))) MARK(cons(first(nil, cons(y0, y1)), z1)) -> c11(MARK(first(nil, cons(y0, y1)))) MARK(cons(first(from(0), y0), z1)) -> c11(MARK(first(from(0), y0))) MARK(cons(first(from(nil), y0), z1)) -> c11(MARK(first(from(nil), y0))) MARK(cons(first(s(0), y0), z1)) -> c11(MARK(first(s(0), y0))) MARK(cons(first(s(nil), y0), z1)) -> c11(MARK(first(s(nil), y0))) MARK(cons(first(y0, cons(0, y1)), z1)) -> c11(MARK(first(y0, cons(0, y1)))) MARK(cons(first(y0, cons(nil, y1)), z1)) -> c11(MARK(first(y0, cons(nil, y1)))) MARK(cons(from(s(y0)), z1)) -> c11(MARK(from(s(y0)))) MARK(cons(from(cons(y0, y1)), z1)) -> c11(MARK(from(cons(y0, y1)))) MARK(cons(from(first(y0, y1)), z1)) -> c11(MARK(from(first(y0, y1)))) MARK(cons(from(first(y0, first(y1, y2))), z1)) -> c11(MARK(from(first(y0, first(y1, y2))))) MARK(cons(from(first(y0, from(y1))), z1)) -> c11(MARK(from(first(y0, from(y1))))) MARK(cons(from(first(y0, 0)), z1)) -> c11(MARK(from(first(y0, 0)))) MARK(cons(from(first(y0, nil)), z1)) -> c11(MARK(from(first(y0, nil)))) MARK(cons(from(first(y0, s(y1))), z1)) -> c11(MARK(from(first(y0, s(y1))))) MARK(cons(from(first(y0, cons(y1, y2))), z1)) -> c11(MARK(from(first(y0, cons(y1, y2))))) MARK(cons(from(first(first(y0, y1), y2)), z1)) -> c11(MARK(from(first(first(y0, y1), y2)))) MARK(cons(from(first(from(y0), y1)), z1)) -> c11(MARK(from(first(from(y0), y1)))) MARK(cons(from(first(0, y0)), z1)) -> c11(MARK(from(first(0, y0)))) MARK(cons(from(first(nil, y0)), z1)) -> c11(MARK(from(first(nil, y0)))) MARK(cons(from(first(s(y0), y1)), z1)) -> c11(MARK(from(first(s(y0), y1)))) MARK(cons(from(first(cons(y0, y1), y2)), z1)) -> c11(MARK(from(first(cons(y0, y1), y2)))) MARK(cons(from(from(y0)), z1)) -> c11(MARK(from(from(y0)))) MARK(cons(from(from(first(y0, y1))), z1)) -> c11(MARK(from(from(first(y0, y1))))) MARK(cons(from(from(from(y0))), z1)) -> c11(MARK(from(from(from(y0))))) MARK(cons(from(from(s(y0))), z1)) -> c11(MARK(from(from(s(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c11(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(0)), z1)) -> c11(MARK(from(from(0)))) MARK(cons(from(from(nil)), z1)) -> c11(MARK(from(from(nil)))) MARK(cons(s(s(y0)), z1)) -> c11(MARK(s(s(y0)))) MARK(cons(s(cons(y0, y1)), z1)) -> c11(MARK(s(cons(y0, y1)))) MARK(cons(s(first(y0, 0)), z1)) -> c11(MARK(s(first(y0, 0)))) MARK(cons(s(first(y0, nil)), z1)) -> c11(MARK(s(first(y0, nil)))) MARK(cons(s(first(y0, s(y1))), z1)) -> c11(MARK(s(first(y0, s(y1))))) MARK(cons(s(first(cons(y0, y1), y2)), z1)) -> c11(MARK(s(first(cons(y0, y1), y2)))) MARK(cons(s(first(0, y0)), z1)) -> c11(MARK(s(first(0, y0)))) MARK(cons(s(first(nil, y0)), z1)) -> c11(MARK(s(first(nil, y0)))) MARK(cons(s(first(y0, first(y1, first(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, first(y2, y3)))))) MARK(cons(s(first(y0, first(y1, from(y2)))), z1)) -> c11(MARK(s(first(y0, first(y1, from(y2)))))) MARK(cons(s(first(y0, first(y1, 0))), z1)) -> c11(MARK(s(first(y0, first(y1, 0))))) MARK(cons(s(first(y0, first(y1, nil))), z1)) -> c11(MARK(s(first(y0, first(y1, nil))))) MARK(cons(s(first(y0, first(y1, s(y2)))), z1)) -> c11(MARK(s(first(y0, first(y1, s(y2)))))) MARK(cons(s(first(y0, first(y1, cons(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, cons(y2, y3)))))) MARK(cons(s(first(y0, first(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, first(first(y1, y2), y3))))) MARK(cons(s(first(y0, first(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, first(from(y1), y2))))) MARK(cons(s(first(y0, first(0, y1))), z1)) -> c11(MARK(s(first(y0, first(0, y1))))) MARK(cons(s(first(y0, first(nil, y1))), z1)) -> c11(MARK(s(first(y0, first(nil, y1))))) MARK(cons(s(first(y0, first(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, first(s(y1), y2))))) MARK(cons(s(first(y0, first(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, first(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), first(y2, y3))))) MARK(cons(s(first(from(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), first(y1, y2))))) MARK(cons(s(first(s(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), first(y1, y2))))) MARK(cons(s(first(y0, first(y1, y2))), z1)) -> c11(MARK(s(first(y0, first(y1, y2))))) MARK(cons(s(first(cons(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), first(y2, y3))))) MARK(cons(s(first(y0, from(y1))), z1)) -> c11(MARK(s(first(y0, from(y1))))) MARK(cons(s(first(y0, from(first(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(first(y1, y2)))))) MARK(cons(s(first(y0, from(from(y1)))), z1)) -> c11(MARK(s(first(y0, from(from(y1)))))) MARK(cons(s(first(y0, from(0))), z1)) -> c11(MARK(s(first(y0, from(0))))) MARK(cons(s(first(y0, from(nil))), z1)) -> c11(MARK(s(first(y0, from(nil))))) MARK(cons(s(first(y0, from(s(y1)))), z1)) -> c11(MARK(s(first(y0, from(s(y1)))))) MARK(cons(s(first(y0, from(cons(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(cons(y1, y2)))))) MARK(cons(s(first(first(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), from(y2))))) MARK(cons(s(first(from(y0), from(y1))), z1)) -> c11(MARK(s(first(from(y0), from(y1))))) MARK(cons(s(first(s(y0), from(y1))), z1)) -> c11(MARK(s(first(s(y0), from(y1))))) MARK(cons(s(first(cons(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(cons(y0, y1), from(y2))))) MARK(cons(s(first(y0, cons(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(first(y1, y2), y3))))) MARK(cons(s(first(y0, cons(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(from(y1), y2))))) MARK(cons(s(first(y0, cons(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(s(y1), y2))))) MARK(cons(s(first(y0, cons(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), cons(y2, y3))))) MARK(cons(s(first(from(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), cons(y1, y2))))) MARK(cons(s(first(s(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), cons(y1, y2))))) MARK(cons(s(first(cons(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), cons(y2, y3))))) MARK(cons(s(first(first(y0, first(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, first(y1, y2)), y3)))) MARK(cons(s(first(first(y0, from(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, from(y1)), y2)))) MARK(cons(s(first(first(y0, 0), y1)), z1)) -> c11(MARK(s(first(first(y0, 0), y1)))) MARK(cons(s(first(first(y0, nil), y1)), z1)) -> c11(MARK(s(first(first(y0, nil), y1)))) MARK(cons(s(first(first(y0, s(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, s(y1)), y2)))) MARK(cons(s(first(first(y0, cons(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, cons(y1, y2)), y3)))) MARK(cons(s(first(first(first(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(first(y0, y1), y2), y3)))) MARK(cons(s(first(first(from(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(from(y0), y1), y2)))) MARK(cons(s(first(first(0, y0), y1)), z1)) -> c11(MARK(s(first(first(0, y0), y1)))) MARK(cons(s(first(first(nil, y0), y1)), z1)) -> c11(MARK(s(first(first(nil, y0), y1)))) MARK(cons(s(first(first(s(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(s(y0), y1), y2)))) MARK(cons(s(first(first(cons(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(cons(y0, y1), y2), y3)))) MARK(cons(s(first(first(y0, y1), 0)), z1)) -> c11(MARK(s(first(first(y0, y1), 0)))) MARK(cons(s(first(first(y0, y1), nil)), z1)) -> c11(MARK(s(first(first(y0, y1), nil)))) MARK(cons(s(first(first(y0, y1), s(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), s(y2))))) MARK(cons(s(first(first(y0, y1), y2)), z1)) -> c11(MARK(s(first(first(y0, y1), y2)))) MARK(cons(s(first(from(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(first(y0, y1)), y2)))) MARK(cons(s(first(from(from(y0)), y1)), z1)) -> c11(MARK(s(first(from(from(y0)), y1)))) MARK(cons(s(first(from(s(y0)), y1)), z1)) -> c11(MARK(s(first(from(s(y0)), y1)))) MARK(cons(s(first(from(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(cons(y0, y1)), y2)))) MARK(cons(s(first(from(y0), y1)), z1)) -> c11(MARK(s(first(from(y0), y1)))) MARK(cons(s(first(from(y0), 0)), z1)) -> c11(MARK(s(first(from(y0), 0)))) MARK(cons(s(first(from(y0), nil)), z1)) -> c11(MARK(s(first(from(y0), nil)))) MARK(cons(s(first(from(y0), s(y1))), z1)) -> c11(MARK(s(first(from(y0), s(y1))))) MARK(cons(s(first(s(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(first(y0, y1)), y2)))) MARK(cons(s(first(s(from(y0)), y1)), z1)) -> c11(MARK(s(first(s(from(y0)), y1)))) MARK(cons(s(first(s(0), y0)), z1)) -> c11(MARK(s(first(s(0), y0)))) MARK(cons(s(first(s(nil), y0)), z1)) -> c11(MARK(s(first(s(nil), y0)))) MARK(cons(s(first(s(s(y0)), y1)), z1)) -> c11(MARK(s(first(s(s(y0)), y1)))) MARK(cons(s(first(s(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(cons(y0, y1)), y2)))) MARK(cons(s(first(s(y0), y1)), z1)) -> c11(MARK(s(first(s(y0), y1)))) MARK(cons(s(first(s(y0), 0)), z1)) -> c11(MARK(s(first(s(y0), 0)))) MARK(cons(s(first(s(y0), nil)), z1)) -> c11(MARK(s(first(s(y0), nil)))) MARK(cons(s(first(s(y0), s(y1))), z1)) -> c11(MARK(s(first(s(y0), s(y1))))) MARK(cons(s(first(0, first(y0, y1))), z1)) -> c11(MARK(s(first(0, first(y0, y1))))) MARK(cons(s(first(nil, first(y0, y1))), z1)) -> c11(MARK(s(first(nil, first(y0, y1))))) MARK(cons(s(first(0, from(y0))), z1)) -> c11(MARK(s(first(0, from(y0))))) MARK(cons(s(first(nil, from(y0))), z1)) -> c11(MARK(s(first(nil, from(y0))))) MARK(cons(s(first(y0, cons(y1, y2))), z1)) -> c11(MARK(s(first(y0, cons(y1, y2))))) MARK(cons(s(first(0, cons(y0, y1))), z1)) -> c11(MARK(s(first(0, cons(y0, y1))))) MARK(cons(s(first(nil, cons(y0, y1))), z1)) -> c11(MARK(s(first(nil, cons(y0, y1))))) MARK(cons(s(first(from(0), y0)), z1)) -> c11(MARK(s(first(from(0), y0)))) MARK(cons(s(first(from(nil), y0)), z1)) -> c11(MARK(s(first(from(nil), y0)))) MARK(cons(s(first(y0, cons(0, y1))), z1)) -> c11(MARK(s(first(y0, cons(0, y1))))) MARK(cons(s(first(y0, cons(nil, y1))), z1)) -> c11(MARK(s(first(y0, cons(nil, y1))))) MARK(cons(s(from(s(y0))), z1)) -> c11(MARK(s(from(s(y0))))) MARK(cons(s(from(cons(y0, y1))), z1)) -> c11(MARK(s(from(cons(y0, y1))))) MARK(cons(s(from(first(y0, y1))), z1)) -> c11(MARK(s(from(first(y0, y1))))) MARK(cons(s(from(first(y0, first(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, first(y1, y2)))))) MARK(cons(s(from(first(y0, from(y1)))), z1)) -> c11(MARK(s(from(first(y0, from(y1)))))) MARK(cons(s(from(first(y0, 0))), z1)) -> c11(MARK(s(from(first(y0, 0))))) MARK(cons(s(from(first(y0, nil))), z1)) -> c11(MARK(s(from(first(y0, nil))))) MARK(cons(s(from(first(y0, s(y1)))), z1)) -> c11(MARK(s(from(first(y0, s(y1)))))) MARK(cons(s(from(first(y0, cons(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, cons(y1, y2)))))) MARK(cons(s(from(first(first(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(first(y0, y1), y2))))) MARK(cons(s(from(first(from(y0), y1))), z1)) -> c11(MARK(s(from(first(from(y0), y1))))) MARK(cons(s(from(first(0, y0))), z1)) -> c11(MARK(s(from(first(0, y0))))) MARK(cons(s(from(first(nil, y0))), z1)) -> c11(MARK(s(from(first(nil, y0))))) MARK(cons(s(from(first(s(y0), y1))), z1)) -> c11(MARK(s(from(first(s(y0), y1))))) MARK(cons(s(from(first(cons(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(cons(y0, y1), y2))))) MARK(cons(s(from(from(y0))), z1)) -> c11(MARK(s(from(from(y0))))) MARK(cons(s(from(from(first(y0, y1)))), z1)) -> c11(MARK(s(from(from(first(y0, y1)))))) MARK(cons(s(from(from(from(y0)))), z1)) -> c11(MARK(s(from(from(from(y0)))))) MARK(cons(s(from(from(s(y0)))), z1)) -> c11(MARK(s(from(from(s(y0)))))) MARK(cons(s(from(from(cons(y0, y1)))), z1)) -> c11(MARK(s(from(from(cons(y0, y1)))))) MARK(cons(s(from(from(0))), z1)) -> c11(MARK(s(from(from(0))))) MARK(cons(s(from(from(nil))), z1)) -> c11(MARK(s(from(from(nil))))) MARK(first(first(y0, 0), 0)) -> c5(MARK(first(y0, 0))) MARK(first(first(y0, nil), 0)) -> c5(MARK(first(y0, nil))) MARK(first(first(y0, s(y1)), 0)) -> c5(MARK(first(y0, s(y1)))) MARK(first(first(cons(y0, y1), y2), 0)) -> c5(MARK(first(cons(y0, y1), y2))) MARK(first(first(0, y0), 0)) -> c5(MARK(first(0, y0))) MARK(first(first(nil, y0), 0)) -> c5(MARK(first(nil, y0))) MARK(first(first(y0, first(y1, first(y2, y3))), 0)) -> c5(MARK(first(y0, first(y1, first(y2, y3))))) MARK(first(first(y0, first(y1, from(y2))), 0)) -> c5(MARK(first(y0, first(y1, from(y2))))) MARK(first(first(y0, first(y1, 0)), 0)) -> c5(MARK(first(y0, first(y1, 0)))) MARK(first(first(y0, first(y1, nil)), 0)) -> c5(MARK(first(y0, first(y1, nil)))) MARK(first(first(y0, first(y1, s(y2))), 0)) -> c5(MARK(first(y0, first(y1, s(y2))))) MARK(first(first(y0, first(y1, cons(y2, y3))), 0)) -> c5(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(first(first(y0, first(first(y1, y2), y3)), 0)) -> c5(MARK(first(y0, first(first(y1, y2), y3)))) MARK(first(first(y0, first(from(y1), y2)), 0)) -> c5(MARK(first(y0, first(from(y1), y2)))) MARK(first(first(y0, first(0, y1)), 0)) -> c5(MARK(first(y0, first(0, y1)))) MARK(first(first(y0, first(nil, y1)), 0)) -> c5(MARK(first(y0, first(nil, y1)))) MARK(first(first(y0, first(s(y1), y2)), 0)) -> c5(MARK(first(y0, first(s(y1), y2)))) MARK(first(first(y0, first(cons(y1, y2), y3)), 0)) -> c5(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(first(first(first(y0, y1), first(y2, y3)), 0)) -> c5(MARK(first(first(y0, y1), first(y2, y3)))) MARK(first(first(from(y0), first(y1, y2)), 0)) -> c5(MARK(first(from(y0), first(y1, y2)))) MARK(first(first(s(y0), first(y1, y2)), 0)) -> c5(MARK(first(s(y0), first(y1, y2)))) MARK(first(first(y0, first(y1, y2)), 0)) -> c5(MARK(first(y0, first(y1, y2)))) MARK(first(first(cons(y0, y1), first(y2, y3)), 0)) -> c5(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(first(first(y0, from(y1)), 0)) -> c5(MARK(first(y0, from(y1)))) MARK(first(first(y0, from(first(y1, y2))), 0)) -> c5(MARK(first(y0, from(first(y1, y2))))) MARK(first(first(y0, from(from(y1))), 0)) -> c5(MARK(first(y0, from(from(y1))))) MARK(first(first(y0, from(0)), 0)) -> c5(MARK(first(y0, from(0)))) MARK(first(first(y0, from(nil)), 0)) -> c5(MARK(first(y0, from(nil)))) MARK(first(first(y0, from(s(y1))), 0)) -> c5(MARK(first(y0, from(s(y1))))) MARK(first(first(y0, from(cons(y1, y2))), 0)) -> c5(MARK(first(y0, from(cons(y1, y2))))) MARK(first(first(first(y0, y1), from(y2)), 0)) -> c5(MARK(first(first(y0, y1), from(y2)))) MARK(first(first(from(y0), from(y1)), 0)) -> c5(MARK(first(from(y0), from(y1)))) MARK(first(first(s(y0), from(y1)), 0)) -> c5(MARK(first(s(y0), from(y1)))) MARK(first(first(cons(y0, y1), from(y2)), 0)) -> c5(MARK(first(cons(y0, y1), from(y2)))) MARK(first(first(y0, cons(first(y1, y2), y3)), 0)) -> c5(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(first(first(y0, 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c5(MARK(s(first(s(from(y0)), y1)))) MARK(first(s(first(s(0), y0)), 0)) -> c5(MARK(s(first(s(0), y0)))) MARK(first(s(first(s(nil), y0)), 0)) -> c5(MARK(s(first(s(nil), y0)))) MARK(first(s(first(s(s(y0)), y1)), 0)) -> c5(MARK(s(first(s(s(y0)), y1)))) MARK(first(s(first(s(cons(y0, y1)), y2)), 0)) -> c5(MARK(s(first(s(cons(y0, y1)), y2)))) MARK(first(s(first(s(y0), y1)), 0)) -> c5(MARK(s(first(s(y0), y1)))) MARK(first(s(first(s(y0), 0)), 0)) -> c5(MARK(s(first(s(y0), 0)))) MARK(first(s(first(s(y0), nil)), 0)) -> c5(MARK(s(first(s(y0), nil)))) MARK(first(s(first(s(y0), s(y1))), 0)) -> c5(MARK(s(first(s(y0), s(y1))))) MARK(first(s(first(0, first(y0, y1))), 0)) -> c5(MARK(s(first(0, first(y0, y1))))) MARK(first(s(first(nil, first(y0, y1))), 0)) -> c5(MARK(s(first(nil, first(y0, y1))))) MARK(first(s(first(0, from(y0))), 0)) -> c5(MARK(s(first(0, from(y0))))) MARK(first(s(first(nil, from(y0))), 0)) -> c5(MARK(s(first(nil, from(y0))))) MARK(first(s(first(y0, cons(y1, y2))), 0)) -> c5(MARK(s(first(y0, cons(y1, y2))))) MARK(first(s(first(0, cons(y0, y1))), 0)) -> c5(MARK(s(first(0, cons(y0, y1))))) MARK(first(s(first(nil, cons(y0, y1))), 0)) -> c5(MARK(s(first(nil, cons(y0, y1))))) MARK(first(s(first(from(0), y0)), 0)) -> c5(MARK(s(first(from(0), y0)))) MARK(first(s(first(from(nil), y0)), 0)) -> c5(MARK(s(first(from(nil), y0)))) MARK(first(s(first(y0, cons(0, y1))), 0)) -> c5(MARK(s(first(y0, cons(0, y1))))) MARK(first(s(first(y0, cons(nil, y1))), 0)) -> c5(MARK(s(first(y0, cons(nil, y1))))) MARK(first(s(from(s(y0))), 0)) -> c5(MARK(s(from(s(y0))))) MARK(first(s(from(cons(y0, y1))), 0)) -> c5(MARK(s(from(cons(y0, y1))))) MARK(first(s(from(first(y0, y1))), 0)) -> c5(MARK(s(from(first(y0, y1))))) MARK(first(s(from(first(y0, first(y1, y2)))), 0)) -> c5(MARK(s(from(first(y0, first(y1, y2)))))) MARK(first(s(from(first(y0, from(y1)))), 0)) -> c5(MARK(s(from(first(y0, from(y1)))))) MARK(first(s(from(first(y0, 0))), 0)) -> c5(MARK(s(from(first(y0, 0))))) MARK(first(s(from(first(y0, nil))), 0)) -> c5(MARK(s(from(first(y0, nil))))) MARK(first(s(from(first(y0, s(y1)))), 0)) -> c5(MARK(s(from(first(y0, s(y1)))))) MARK(first(s(from(first(y0, cons(y1, y2)))), 0)) -> c5(MARK(s(from(first(y0, cons(y1, y2)))))) MARK(first(s(from(first(first(y0, y1), y2))), 0)) -> c5(MARK(s(from(first(first(y0, y1), y2))))) MARK(first(s(from(first(from(y0), y1))), 0)) -> c5(MARK(s(from(first(from(y0), y1))))) MARK(first(s(from(first(0, y0))), 0)) -> c5(MARK(s(from(first(0, y0))))) MARK(first(s(from(first(nil, y0))), 0)) -> c5(MARK(s(from(first(nil, y0))))) MARK(first(s(from(first(s(y0), y1))), 0)) -> c5(MARK(s(from(first(s(y0), y1))))) MARK(first(s(from(first(cons(y0, y1), y2))), 0)) -> c5(MARK(s(from(first(cons(y0, y1), y2))))) MARK(first(s(from(from(y0))), 0)) -> c5(MARK(s(from(from(y0))))) MARK(first(s(from(from(first(y0, y1)))), 0)) -> c5(MARK(s(from(from(first(y0, y1)))))) MARK(first(s(from(from(from(y0)))), 0)) -> c5(MARK(s(from(from(from(y0)))))) MARK(first(s(from(from(s(y0)))), 0)) -> c5(MARK(s(from(from(s(y0)))))) MARK(first(s(from(from(cons(y0, y1)))), 0)) -> c5(MARK(s(from(from(cons(y0, y1)))))) MARK(first(s(from(from(0))), 0)) -> c5(MARK(s(from(from(0))))) MARK(first(s(from(from(nil))), 0)) -> c5(MARK(s(from(from(nil))))) MARK(first(cons(cons(y0, y1), y2), 0)) -> c5(MARK(cons(cons(y0, y1), y2))) MARK(first(cons(first(y0, 0), y1), 0)) -> c5(MARK(cons(first(y0, 0), y1))) MARK(first(cons(first(y0, nil), y1), 0)) -> c5(MARK(cons(first(y0, nil), y1))) MARK(first(cons(first(y0, s(y1)), y2), 0)) -> c5(MARK(cons(first(y0, s(y1)), y2))) MARK(first(cons(first(cons(y0, y1), y2), y3), 0)) -> c5(MARK(cons(first(cons(y0, y1), y2), y3))) MARK(first(cons(first(0, y0), y1), 0)) -> c5(MARK(cons(first(0, y0), y1))) MARK(first(cons(first(nil, y0), y1), 0)) -> c5(MARK(cons(first(nil, y0), y1))) MARK(first(cons(first(y0, first(y1, first(y2, y3))), y4), 0)) -> c5(MARK(cons(first(y0, first(y1, first(y2, y3))), y4))) MARK(first(cons(first(y0, first(y1, from(y2))), y3), 0)) -> c5(MARK(cons(first(y0, first(y1, from(y2))), y3))) MARK(first(cons(first(y0, first(y1, 0)), y2), 0)) -> c5(MARK(cons(first(y0, first(y1, 0)), y2))) MARK(first(cons(first(y0, first(y1, nil)), y2), 0)) -> c5(MARK(cons(first(y0, first(y1, nil)), y2))) MARK(first(cons(first(y0, first(y1, s(y2))), y3), 0)) -> c5(MARK(cons(first(y0, first(y1, s(y2))), y3))) MARK(first(cons(first(y0, first(y1, cons(y2, y3))), y4), 0)) -> c5(MARK(cons(first(y0, first(y1, cons(y2, y3))), y4))) MARK(first(cons(first(y0, first(first(y1, y2), y3)), y4), 0)) -> c5(MARK(cons(first(y0, first(first(y1, y2), y3)), y4))) MARK(first(cons(first(y0, first(from(y1), y2)), y3), 0)) -> c5(MARK(cons(first(y0, first(from(y1), y2)), y3))) MARK(first(cons(first(y0, first(0, y1)), y2), 0)) -> c5(MARK(cons(first(y0, first(0, y1)), y2))) MARK(first(cons(first(y0, first(nil, y1)), y2), 0)) -> c5(MARK(cons(first(y0, first(nil, y1)), y2))) MARK(first(cons(first(y0, first(s(y1), y2)), y3), 0)) -> c5(MARK(cons(first(y0, first(s(y1), y2)), y3))) MARK(first(cons(first(y0, first(cons(y1, y2), y3)), y4), 0)) -> c5(MARK(cons(first(y0, first(cons(y1, y2), y3)), y4))) MARK(first(cons(first(first(y0, y1), first(y2, y3)), y4), 0)) -> c5(MARK(cons(first(first(y0, y1), first(y2, y3)), y4))) MARK(first(cons(first(from(y0), first(y1, y2)), y3), 0)) -> c5(MARK(cons(first(from(y0), first(y1, y2)), y3))) MARK(first(cons(first(s(y0), first(y1, y2)), y3), 0)) -> c5(MARK(cons(first(s(y0), first(y1, y2)), y3))) MARK(first(cons(first(y0, first(y1, y2)), y3), 0)) -> c5(MARK(cons(first(y0, first(y1, y2)), y3))) MARK(first(cons(first(cons(y0, y1), first(y2, y3)), y4), 0)) -> c5(MARK(cons(first(cons(y0, y1), first(y2, y3)), y4))) MARK(first(cons(first(y0, from(y1)), y2), 0)) -> c5(MARK(cons(first(y0, from(y1)), y2))) MARK(first(cons(first(y0, from(first(y1, y2))), y3), 0)) -> c5(MARK(cons(first(y0, from(first(y1, y2))), y3))) MARK(first(cons(first(y0, from(from(y1))), y2), 0)) -> c5(MARK(cons(first(y0, from(from(y1))), y2))) MARK(first(cons(first(y0, from(0)), y1), 0)) -> c5(MARK(cons(first(y0, from(0)), y1))) MARK(first(cons(first(y0, from(nil)), y1), 0)) -> c5(MARK(cons(first(y0, from(nil)), y1))) MARK(first(cons(first(y0, from(s(y1))), y2), 0)) -> c5(MARK(cons(first(y0, from(s(y1))), y2))) MARK(first(cons(first(y0, from(cons(y1, y2))), y3), 0)) -> c5(MARK(cons(first(y0, from(cons(y1, y2))), y3))) MARK(first(cons(first(first(y0, y1), from(y2)), y3), 0)) -> c5(MARK(cons(first(first(y0, y1), from(y2)), y3))) MARK(first(cons(first(from(y0), from(y1)), y2), 0)) -> c5(MARK(cons(first(from(y0), from(y1)), y2))) MARK(first(cons(first(s(y0), from(y1)), y2), 0)) -> c5(MARK(cons(first(s(y0), from(y1)), y2))) MARK(first(cons(first(cons(y0, y1), from(y2)), y3), 0)) -> c5(MARK(cons(first(cons(y0, y1), from(y2)), y3))) MARK(first(cons(first(y0, cons(first(y1, y2), y3)), y4), 0)) -> c5(MARK(cons(first(y0, cons(first(y1, y2), y3)), y4))) MARK(first(cons(first(y0, cons(from(y1), y2)), y3), 0)) -> c5(MARK(cons(first(y0, cons(from(y1), y2)), y3))) MARK(first(cons(first(y0, cons(s(y1), y2)), y3), 0)) -> c5(MARK(cons(first(y0, cons(s(y1), y2)), y3))) MARK(first(cons(first(y0, cons(cons(y1, y2), y3)), y4), 0)) -> c5(MARK(cons(first(y0, cons(cons(y1, y2), y3)), y4))) MARK(first(cons(first(first(y0, y1), cons(y2, y3)), y4), 0)) -> c5(MARK(cons(first(first(y0, y1), cons(y2, y3)), y4))) MARK(first(cons(first(from(y0), cons(y1, y2)), y3), 0)) -> c5(MARK(cons(first(from(y0), cons(y1, y2)), y3))) MARK(first(cons(first(s(y0), cons(y1, y2)), y3), 0)) -> c5(MARK(cons(first(s(y0), cons(y1, y2)), y3))) MARK(first(cons(first(cons(y0, y1), cons(y2, y3)), y4), 0)) -> c5(MARK(cons(first(cons(y0, y1), cons(y2, y3)), y4))) MARK(first(cons(first(first(y0, first(y1, y2)), y3), y4), 0)) -> c5(MARK(cons(first(first(y0, first(y1, y2)), y3), y4))) MARK(first(cons(first(first(y0, from(y1)), y2), y3), 0)) -> c5(MARK(cons(first(first(y0, from(y1)), y2), y3))) MARK(first(cons(first(first(y0, 0), y1), y2), 0)) -> c5(MARK(cons(first(first(y0, 0), y1), y2))) MARK(first(cons(first(first(y0, nil), y1), y2), 0)) -> c5(MARK(cons(first(first(y0, nil), y1), y2))) MARK(first(cons(first(first(y0, s(y1)), y2), y3), 0)) -> c5(MARK(cons(first(first(y0, s(y1)), y2), y3))) MARK(first(cons(first(first(y0, cons(y1, y2)), y3), y4), 0)) -> c5(MARK(cons(first(first(y0, cons(y1, y2)), y3), y4))) MARK(first(cons(first(first(first(y0, y1), y2), y3), y4), 0)) -> c5(MARK(cons(first(first(first(y0, y1), y2), y3), y4))) MARK(first(cons(first(first(from(y0), y1), y2), y3), 0)) -> c5(MARK(cons(first(first(from(y0), y1), y2), y3))) MARK(first(cons(first(first(0, y0), y1), y2), 0)) -> c5(MARK(cons(first(first(0, y0), y1), y2))) MARK(first(cons(first(first(nil, y0), y1), y2), 0)) -> c5(MARK(cons(first(first(nil, y0), y1), y2))) MARK(first(cons(first(first(s(y0), y1), y2), y3), 0)) -> c5(MARK(cons(first(first(s(y0), y1), y2), y3))) MARK(first(cons(first(first(cons(y0, y1), y2), y3), y4), 0)) -> c5(MARK(cons(first(first(cons(y0, y1), y2), y3), y4))) MARK(first(cons(first(first(y0, y1), 0), y2), 0)) -> c5(MARK(cons(first(first(y0, y1), 0), y2))) MARK(first(cons(first(first(y0, y1), nil), y2), 0)) -> c5(MARK(cons(first(first(y0, y1), nil), y2))) MARK(first(cons(first(first(y0, y1), s(y2)), y3), 0)) -> c5(MARK(cons(first(first(y0, y1), s(y2)), y3))) MARK(first(cons(first(first(y0, y1), y2), y3), 0)) -> c5(MARK(cons(first(first(y0, y1), y2), y3))) MARK(first(cons(first(from(first(y0, y1)), y2), y3), 0)) -> c5(MARK(cons(first(from(first(y0, y1)), y2), y3))) MARK(first(cons(first(from(from(y0)), y1), y2), 0)) -> c5(MARK(cons(first(from(from(y0)), y1), y2))) MARK(first(cons(first(from(s(y0)), y1), y2), 0)) -> c5(MARK(cons(first(from(s(y0)), y1), y2))) MARK(first(cons(first(from(cons(y0, y1)), y2), y3), 0)) -> c5(MARK(cons(first(from(cons(y0, y1)), y2), y3))) MARK(first(cons(first(from(y0), y1), y2), 0)) -> c5(MARK(cons(first(from(y0), y1), y2))) MARK(first(cons(first(from(y0), 0), y1), 0)) -> c5(MARK(cons(first(from(y0), 0), y1))) MARK(first(cons(first(from(y0), nil), y1), 0)) -> c5(MARK(cons(first(from(y0), nil), y1))) MARK(first(cons(first(from(y0), s(y1)), y2), 0)) -> c5(MARK(cons(first(from(y0), s(y1)), y2))) MARK(first(cons(first(s(first(y0, y1)), y2), y3), 0)) -> c5(MARK(cons(first(s(first(y0, y1)), y2), y3))) MARK(first(cons(first(s(from(y0)), y1), y2), 0)) -> c5(MARK(cons(first(s(from(y0)), y1), y2))) MARK(first(cons(first(s(s(y0)), y1), y2), 0)) -> c5(MARK(cons(first(s(s(y0)), y1), y2))) MARK(first(cons(first(s(cons(y0, y1)), y2), y3), 0)) -> c5(MARK(cons(first(s(cons(y0, y1)), y2), y3))) MARK(first(cons(first(s(y0), y1), y2), 0)) -> c5(MARK(cons(first(s(y0), y1), y2))) MARK(first(cons(first(s(y0), 0), y1), 0)) -> c5(MARK(cons(first(s(y0), 0), y1))) MARK(first(cons(first(s(y0), nil), y1), 0)) -> c5(MARK(cons(first(s(y0), nil), y1))) MARK(first(cons(first(s(y0), s(y1)), y2), 0)) -> c5(MARK(cons(first(s(y0), s(y1)), y2))) MARK(first(cons(first(0, first(y0, y1)), y2), 0)) -> c5(MARK(cons(first(0, first(y0, y1)), y2))) MARK(first(cons(first(nil, first(y0, y1)), y2), 0)) -> c5(MARK(cons(first(nil, first(y0, y1)), y2))) MARK(first(cons(first(0, from(y0)), y1), 0)) -> c5(MARK(cons(first(0, from(y0)), y1))) MARK(first(cons(first(nil, from(y0)), y1), 0)) -> c5(MARK(cons(first(nil, from(y0)), y1))) MARK(first(cons(first(y0, cons(y1, y2)), y3), 0)) -> c5(MARK(cons(first(y0, cons(y1, y2)), y3))) MARK(first(cons(first(0, cons(y0, y1)), y2), 0)) -> c5(MARK(cons(first(0, cons(y0, y1)), y2))) MARK(first(cons(first(nil, cons(y0, y1)), y2), 0)) -> c5(MARK(cons(first(nil, cons(y0, y1)), y2))) MARK(first(cons(first(from(0), y0), y1), 0)) -> c5(MARK(cons(first(from(0), y0), y1))) MARK(first(cons(first(from(nil), y0), y1), 0)) -> c5(MARK(cons(first(from(nil), y0), y1))) MARK(first(cons(first(s(0), y0), y1), 0)) -> c5(MARK(cons(first(s(0), y0), y1))) MARK(first(cons(first(s(nil), y0), y1), 0)) -> c5(MARK(cons(first(s(nil), y0), y1))) MARK(first(cons(first(y0, cons(0, y1)), y2), 0)) -> c5(MARK(cons(first(y0, cons(0, y1)), y2))) MARK(first(cons(first(y0, cons(nil, y1)), y2), 0)) -> c5(MARK(cons(first(y0, cons(nil, y1)), y2))) MARK(first(cons(from(s(y0)), y1), 0)) -> c5(MARK(cons(from(s(y0)), y1))) MARK(first(cons(from(cons(y0, y1)), y2), 0)) -> c5(MARK(cons(from(cons(y0, y1)), y2))) MARK(first(cons(from(first(y0, y1)), y2), 0)) -> c5(MARK(cons(from(first(y0, y1)), y2))) MARK(first(cons(from(first(y0, first(y1, y2))), y3), 0)) -> c5(MARK(cons(from(first(y0, first(y1, y2))), y3))) MARK(first(cons(from(first(y0, from(y1))), y2), 0)) -> c5(MARK(cons(from(first(y0, from(y1))), y2))) MARK(first(cons(from(first(y0, 0)), y1), 0)) -> c5(MARK(cons(from(first(y0, 0)), y1))) MARK(first(cons(from(first(y0, nil)), y1), 0)) -> c5(MARK(cons(from(first(y0, nil)), y1))) MARK(first(cons(from(first(y0, s(y1))), y2), 0)) -> c5(MARK(cons(from(first(y0, s(y1))), y2))) MARK(first(cons(from(first(y0, cons(y1, y2))), y3), 0)) -> c5(MARK(cons(from(first(y0, cons(y1, y2))), y3))) MARK(first(cons(from(first(first(y0, y1), y2)), y3), 0)) -> c5(MARK(cons(from(first(first(y0, y1), y2)), y3))) MARK(first(cons(from(first(from(y0), y1)), y2), 0)) -> c5(MARK(cons(from(first(from(y0), y1)), y2))) MARK(first(cons(from(first(0, y0)), y1), 0)) -> c5(MARK(cons(from(first(0, y0)), y1))) MARK(first(cons(from(first(nil, y0)), y1), 0)) -> c5(MARK(cons(from(first(nil, y0)), y1))) MARK(first(cons(from(first(s(y0), y1)), y2), 0)) -> c5(MARK(cons(from(first(s(y0), y1)), y2))) MARK(first(cons(from(first(cons(y0, y1), y2)), y3), 0)) -> c5(MARK(cons(from(first(cons(y0, y1), y2)), y3))) MARK(first(cons(from(from(y0)), y1), 0)) -> c5(MARK(cons(from(from(y0)), y1))) MARK(first(cons(from(from(first(y0, y1))), y2), 0)) -> c5(MARK(cons(from(from(first(y0, y1))), y2))) MARK(first(cons(from(from(from(y0))), y1), 0)) -> c5(MARK(cons(from(from(from(y0))), y1))) MARK(first(cons(from(from(s(y0))), y1), 0)) -> c5(MARK(cons(from(from(s(y0))), y1))) MARK(first(cons(from(from(cons(y0, y1))), y2), 0)) -> c5(MARK(cons(from(from(cons(y0, y1))), y2))) MARK(first(cons(from(from(0)), y0), 0)) -> c5(MARK(cons(from(from(0)), y0))) MARK(first(cons(from(from(nil)), y0), 0)) -> c5(MARK(cons(from(from(nil)), y0))) MARK(first(cons(s(s(y0)), y1), 0)) -> c5(MARK(cons(s(s(y0)), y1))) MARK(first(cons(s(cons(y0, y1)), y2), 0)) -> c5(MARK(cons(s(cons(y0, y1)), y2))) MARK(first(cons(s(first(y0, 0)), y1), 0)) -> c5(MARK(cons(s(first(y0, 0)), y1))) MARK(first(cons(s(first(y0, nil)), y1), 0)) -> c5(MARK(cons(s(first(y0, nil)), y1))) MARK(first(cons(s(first(y0, s(y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, s(y1))), y2))) MARK(first(cons(s(first(cons(y0, y1), y2)), y3), 0)) -> c5(MARK(cons(s(first(cons(y0, y1), y2)), y3))) MARK(first(cons(s(first(0, y0)), y1), 0)) -> c5(MARK(cons(s(first(0, y0)), y1))) MARK(first(cons(s(first(nil, y0)), y1), 0)) -> c5(MARK(cons(s(first(nil, y0)), y1))) MARK(first(cons(s(first(y0, first(y1, first(y2, y3)))), y4), 0)) -> c5(MARK(cons(s(first(y0, first(y1, first(y2, y3)))), y4))) MARK(first(cons(s(first(y0, first(y1, from(y2)))), y3), 0)) -> c5(MARK(cons(s(first(y0, first(y1, from(y2)))), y3))) MARK(first(cons(s(first(y0, first(y1, 0))), y2), 0)) -> c5(MARK(cons(s(first(y0, first(y1, 0))), y2))) MARK(first(cons(s(first(y0, first(y1, nil))), y2), 0)) -> c5(MARK(cons(s(first(y0, first(y1, nil))), y2))) MARK(first(cons(s(first(y0, first(y1, s(y2)))), y3), 0)) -> c5(MARK(cons(s(first(y0, first(y1, s(y2)))), y3))) MARK(first(cons(s(first(y0, first(y1, cons(y2, y3)))), y4), 0)) -> c5(MARK(cons(s(first(y0, first(y1, cons(y2, y3)))), y4))) MARK(first(cons(s(first(y0, first(first(y1, y2), y3))), y4), 0)) -> c5(MARK(cons(s(first(y0, first(first(y1, y2), y3))), y4))) MARK(first(cons(s(first(y0, first(from(y1), y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, first(from(y1), y2))), y3))) MARK(first(cons(s(first(y0, first(0, y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, first(0, y1))), y2))) MARK(first(cons(s(first(y0, first(nil, y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, first(nil, y1))), y2))) MARK(first(cons(s(first(y0, first(s(y1), y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, first(s(y1), y2))), y3))) MARK(first(cons(s(first(y0, first(cons(y1, y2), y3))), y4), 0)) -> c5(MARK(cons(s(first(y0, first(cons(y1, y2), y3))), y4))) MARK(first(cons(s(first(first(y0, y1), first(y2, y3))), y4), 0)) -> c5(MARK(cons(s(first(first(y0, y1), first(y2, y3))), y4))) MARK(first(cons(s(first(from(y0), first(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(from(y0), first(y1, y2))), y3))) MARK(first(cons(s(first(s(y0), first(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(s(y0), first(y1, y2))), y3))) MARK(first(cons(s(first(y0, first(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, first(y1, y2))), y3))) MARK(first(cons(s(first(cons(y0, y1), first(y2, y3))), y4), 0)) -> c5(MARK(cons(s(first(cons(y0, y1), first(y2, y3))), y4))) MARK(first(cons(s(first(y0, from(y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, from(y1))), y2))) MARK(first(cons(s(first(y0, from(first(y1, y2)))), y3), 0)) -> c5(MARK(cons(s(first(y0, from(first(y1, y2)))), y3))) MARK(first(cons(s(first(y0, from(from(y1)))), y2), 0)) -> c5(MARK(cons(s(first(y0, from(from(y1)))), y2))) MARK(first(cons(s(first(y0, from(0))), y1), 0)) -> c5(MARK(cons(s(first(y0, from(0))), y1))) MARK(first(cons(s(first(y0, from(nil))), y1), 0)) -> c5(MARK(cons(s(first(y0, from(nil))), y1))) MARK(first(cons(s(first(y0, from(s(y1)))), y2), 0)) -> c5(MARK(cons(s(first(y0, from(s(y1)))), y2))) MARK(first(cons(s(first(y0, from(cons(y1, y2)))), y3), 0)) -> c5(MARK(cons(s(first(y0, from(cons(y1, y2)))), y3))) MARK(first(cons(s(first(first(y0, y1), from(y2))), y3), 0)) -> c5(MARK(cons(s(first(first(y0, y1), from(y2))), y3))) MARK(first(cons(s(first(from(y0), from(y1))), y2), 0)) -> c5(MARK(cons(s(first(from(y0), from(y1))), y2))) MARK(first(cons(s(first(s(y0), from(y1))), y2), 0)) -> c5(MARK(cons(s(first(s(y0), from(y1))), y2))) MARK(first(cons(s(first(cons(y0, y1), from(y2))), y3), 0)) -> c5(MARK(cons(s(first(cons(y0, y1), from(y2))), y3))) MARK(first(cons(s(first(y0, cons(first(y1, y2), y3))), y4), 0)) -> c5(MARK(cons(s(first(y0, cons(first(y1, y2), y3))), y4))) MARK(first(cons(s(first(y0, cons(from(y1), y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, cons(from(y1), y2))), y3))) MARK(first(cons(s(first(y0, cons(s(y1), y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, cons(s(y1), y2))), y3))) MARK(first(cons(s(first(y0, cons(cons(y1, y2), y3))), y4), 0)) -> c5(MARK(cons(s(first(y0, cons(cons(y1, y2), y3))), y4))) MARK(first(cons(s(first(first(y0, y1), cons(y2, y3))), y4), 0)) -> c5(MARK(cons(s(first(first(y0, y1), cons(y2, y3))), y4))) MARK(first(cons(s(first(from(y0), cons(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(from(y0), cons(y1, y2))), y3))) MARK(first(cons(s(first(s(y0), cons(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(s(y0), cons(y1, y2))), y3))) MARK(first(cons(s(first(cons(y0, y1), cons(y2, y3))), y4), 0)) -> c5(MARK(cons(s(first(cons(y0, y1), cons(y2, y3))), y4))) MARK(first(cons(s(first(first(y0, first(y1, y2)), y3)), y4), 0)) -> c5(MARK(cons(s(first(first(y0, first(y1, y2)), y3)), y4))) MARK(first(cons(s(first(first(y0, from(y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(y0, from(y1)), y2)), y3))) MARK(first(cons(s(first(first(y0, 0), y1)), y2), 0)) -> c5(MARK(cons(s(first(first(y0, 0), y1)), y2))) MARK(first(cons(s(first(first(y0, nil), y1)), y2), 0)) -> c5(MARK(cons(s(first(first(y0, nil), y1)), y2))) MARK(first(cons(s(first(first(y0, s(y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(y0, s(y1)), y2)), y3))) MARK(first(cons(s(first(first(y0, cons(y1, y2)), y3)), y4), 0)) -> c5(MARK(cons(s(first(first(y0, cons(y1, y2)), y3)), y4))) MARK(first(cons(s(first(first(first(y0, y1), y2), y3)), y4), 0)) -> c5(MARK(cons(s(first(first(first(y0, y1), y2), y3)), y4))) MARK(first(cons(s(first(first(from(y0), y1), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(from(y0), y1), y2)), y3))) MARK(first(cons(s(first(first(0, y0), y1)), y2), 0)) -> c5(MARK(cons(s(first(first(0, y0), y1)), y2))) MARK(first(cons(s(first(first(nil, y0), y1)), y2), 0)) -> c5(MARK(cons(s(first(first(nil, y0), y1)), y2))) MARK(first(cons(s(first(first(s(y0), y1), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(s(y0), y1), y2)), y3))) MARK(first(cons(s(first(first(cons(y0, y1), y2), y3)), y4), 0)) -> c5(MARK(cons(s(first(first(cons(y0, y1), y2), y3)), y4))) MARK(first(cons(s(first(first(y0, y1), 0)), y2), 0)) -> c5(MARK(cons(s(first(first(y0, y1), 0)), y2))) MARK(first(cons(s(first(first(y0, y1), nil)), y2), 0)) -> c5(MARK(cons(s(first(first(y0, y1), nil)), y2))) MARK(first(cons(s(first(first(y0, y1), s(y2))), y3), 0)) -> c5(MARK(cons(s(first(first(y0, y1), s(y2))), y3))) MARK(first(cons(s(first(first(y0, y1), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(y0, y1), y2)), y3))) MARK(first(cons(s(first(from(first(y0, y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(from(first(y0, y1)), y2)), y3))) MARK(first(cons(s(first(from(from(y0)), y1)), y2), 0)) -> c5(MARK(cons(s(first(from(from(y0)), y1)), y2))) MARK(first(cons(s(first(from(s(y0)), y1)), y2), 0)) -> c5(MARK(cons(s(first(from(s(y0)), y1)), y2))) MARK(first(cons(s(first(from(cons(y0, y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(from(cons(y0, y1)), y2)), y3))) MARK(first(cons(s(first(from(y0), y1)), y2), 0)) -> c5(MARK(cons(s(first(from(y0), y1)), y2))) MARK(first(cons(s(first(from(y0), 0)), y1), 0)) -> c5(MARK(cons(s(first(from(y0), 0)), y1))) MARK(first(cons(s(first(from(y0), nil)), y1), 0)) -> c5(MARK(cons(s(first(from(y0), nil)), y1))) MARK(first(cons(s(first(from(y0), s(y1))), y2), 0)) -> c5(MARK(cons(s(first(from(y0), s(y1))), y2))) MARK(first(cons(s(first(s(first(y0, y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(s(first(y0, y1)), y2)), y3))) MARK(first(cons(s(first(s(from(y0)), y1)), y2), 0)) -> c5(MARK(cons(s(first(s(from(y0)), y1)), y2))) MARK(first(cons(s(first(s(0), y0)), y1), 0)) -> c5(MARK(cons(s(first(s(0), y0)), y1))) MARK(first(cons(s(first(s(nil), y0)), y1), 0)) -> c5(MARK(cons(s(first(s(nil), y0)), y1))) MARK(first(cons(s(first(s(s(y0)), y1)), y2), 0)) -> c5(MARK(cons(s(first(s(s(y0)), y1)), y2))) MARK(first(cons(s(first(s(cons(y0, y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(s(cons(y0, y1)), y2)), y3))) MARK(first(cons(s(first(s(y0), y1)), y2), 0)) -> c5(MARK(cons(s(first(s(y0), y1)), y2))) MARK(first(cons(s(first(s(y0), 0)), y1), 0)) -> c5(MARK(cons(s(first(s(y0), 0)), y1))) MARK(first(cons(s(first(s(y0), nil)), y1), 0)) -> c5(MARK(cons(s(first(s(y0), nil)), y1))) MARK(first(cons(s(first(s(y0), s(y1))), y2), 0)) -> c5(MARK(cons(s(first(s(y0), s(y1))), y2))) MARK(first(cons(s(first(0, first(y0, y1))), y2), 0)) -> c5(MARK(cons(s(first(0, first(y0, y1))), y2))) MARK(first(cons(s(first(nil, first(y0, y1))), y2), 0)) -> c5(MARK(cons(s(first(nil, first(y0, y1))), y2))) MARK(first(cons(s(first(0, from(y0))), y1), 0)) -> c5(MARK(cons(s(first(0, from(y0))), y1))) MARK(first(cons(s(first(nil, from(y0))), y1), 0)) -> c5(MARK(cons(s(first(nil, from(y0))), y1))) MARK(first(cons(s(first(y0, cons(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, cons(y1, y2))), y3))) MARK(first(cons(s(first(0, cons(y0, y1))), y2), 0)) -> c5(MARK(cons(s(first(0, cons(y0, y1))), y2))) MARK(first(cons(s(first(nil, cons(y0, y1))), y2), 0)) -> c5(MARK(cons(s(first(nil, cons(y0, y1))), y2))) MARK(first(cons(s(first(from(0), y0)), y1), 0)) -> c5(MARK(cons(s(first(from(0), y0)), y1))) MARK(first(cons(s(first(from(nil), y0)), y1), 0)) -> c5(MARK(cons(s(first(from(nil), y0)), y1))) MARK(first(cons(s(first(y0, cons(0, y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, cons(0, y1))), y2))) MARK(first(cons(s(first(y0, cons(nil, y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, cons(nil, y1))), y2))) MARK(first(cons(s(from(s(y0))), y1), 0)) -> c5(MARK(cons(s(from(s(y0))), y1))) MARK(first(cons(s(from(cons(y0, y1))), y2), 0)) -> c5(MARK(cons(s(from(cons(y0, y1))), y2))) MARK(first(cons(s(from(first(y0, y1))), y2), 0)) -> c5(MARK(cons(s(from(first(y0, y1))), y2))) MARK(first(cons(s(from(first(y0, first(y1, y2)))), y3), 0)) -> c5(MARK(cons(s(from(first(y0, first(y1, y2)))), y3))) MARK(first(cons(s(from(first(y0, from(y1)))), y2), 0)) -> c5(MARK(cons(s(from(first(y0, from(y1)))), y2))) MARK(first(cons(s(from(first(y0, 0))), y1), 0)) -> c5(MARK(cons(s(from(first(y0, 0))), y1))) MARK(first(cons(s(from(first(y0, nil))), y1), 0)) -> c5(MARK(cons(s(from(first(y0, nil))), y1))) MARK(first(cons(s(from(first(y0, s(y1)))), y2), 0)) -> c5(MARK(cons(s(from(first(y0, s(y1)))), y2))) MARK(first(cons(s(from(first(y0, cons(y1, y2)))), y3), 0)) -> c5(MARK(cons(s(from(first(y0, cons(y1, y2)))), y3))) MARK(first(cons(s(from(first(first(y0, y1), y2))), y3), 0)) -> c5(MARK(cons(s(from(first(first(y0, y1), y2))), y3))) MARK(first(cons(s(from(first(from(y0), y1))), y2), 0)) -> c5(MARK(cons(s(from(first(from(y0), y1))), y2))) MARK(first(cons(s(from(first(0, y0))), y1), 0)) -> c5(MARK(cons(s(from(first(0, y0))), y1))) MARK(first(cons(s(from(first(nil, y0))), y1), 0)) -> c5(MARK(cons(s(from(first(nil, y0))), y1))) MARK(first(cons(s(from(first(s(y0), y1))), y2), 0)) -> c5(MARK(cons(s(from(first(s(y0), y1))), y2))) MARK(first(cons(s(from(first(cons(y0, y1), y2))), y3), 0)) -> c5(MARK(cons(s(from(first(cons(y0, y1), y2))), y3))) MARK(first(cons(s(from(from(y0))), y1), 0)) -> c5(MARK(cons(s(from(from(y0))), y1))) MARK(first(cons(s(from(from(first(y0, y1)))), y2), 0)) -> c5(MARK(cons(s(from(from(first(y0, y1)))), y2))) MARK(first(cons(s(from(from(from(y0)))), y1), 0)) -> c5(MARK(cons(s(from(from(from(y0)))), y1))) MARK(first(cons(s(from(from(s(y0)))), y1), 0)) -> c5(MARK(cons(s(from(from(s(y0)))), y1))) MARK(first(cons(s(from(from(cons(y0, y1)))), y2), 0)) -> c5(MARK(cons(s(from(from(cons(y0, y1)))), y2))) MARK(first(cons(s(from(from(0))), y0), 0)) -> c5(MARK(cons(s(from(from(0))), y0))) MARK(first(cons(s(from(from(nil))), y0), 0)) -> c5(MARK(cons(s(from(from(nil))), y0))) S tuples: MARK(first(x0, nil)) -> c5(MARK(x0)) MARK(first(x0, s(z0))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c5(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c6(MARK(s(z0))) MARK(first(0, x1)) -> c6(MARK(x1)) MARK(first(nil, x1)) -> c6(MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c6(MARK(x1)) MARK(first(x0, first(x1, first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c5(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c5(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c5(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(first(z0, z1), first(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(from(z0), first(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(s(z0), first(x1, x2))) -> c5(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, from(x1))) -> c5(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c5(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c5(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c5(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c5(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c5(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(first(z0, z1), from(x1))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(from(z0), from(x1))) -> c5(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(s(z0), from(x1))) -> c5(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c5(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c5(MARK(cons(z0, z1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(from(z0), x2))) -> c5(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c5(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c5(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(first(z0, z1), cons(x1, x2))) -> c5(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(from(z0), cons(x1, x2))) -> c5(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(s(z0), cons(x1, x2))) -> c5(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c5(MARK(cons(z0, z1))) MARK(first(first(x0, first(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, from(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, 0), x2)) -> c5(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c5(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(x0, s(z0)), x2)) -> c5(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c5(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(first(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(from(z0), x1), x2)) -> c5(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(0, x1), x2)) -> c5(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c5(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(s(z0), x1), x2)) -> c5(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c5(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(x0, x1), 0)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c5(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c5(MARK(first(x0, x1))) MARK(first(from(first(z0, z1)), x1)) -> c5(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(from(z0)), x1)) -> c5(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(s(z0)), x1)) -> c5(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(cons(z0, z1)), x1)) -> c5(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(x0), x1)) -> c5(MARK(from(x0))) MARK(first(from(x0), 0)) -> c5(MARK(from(x0))) MARK(first(from(x0), nil)) -> c5(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c5(MARK(from(x0))) MARK(first(s(first(z0, z1)), x1)) -> c5(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(from(z0)), x1)) -> c5(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(s(z0)), x1)) -> c5(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(cons(z0, z1)), x1)) -> c5(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(x0), x1)) -> c5(MARK(s(x0))) MARK(first(s(x0), 0)) -> c5(MARK(s(x0))) MARK(first(s(x0), nil)) -> c5(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c5(MARK(s(x0))) MARK(first(x0, first(x1, first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, from(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, 0))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(x1, s(z0)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(from(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(0, x2))) -> c6(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c6(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(x0, first(s(z0), x2))) -> c6(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(from(z0), first(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c6(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c6(MARK(first(x1, x2))) MARK(first(x0, from(x1))) -> c6(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(first(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(from(z0)))) -> c6(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(s(z0)))) -> c6(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(cons(z0, z1)))) -> c6(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(first(z0, z1), from(x1))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(from(z0), from(x1))) -> c6(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c6(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c6(MARK(from(x1))) MARK(first(0, from(x1))) -> c6(MARK(from(x1))) MARK(first(nil, from(x1))) -> c6(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c6(MARK(from(x1))) MARK(first(x0, cons(first(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(from(z0), x2))) -> c6(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(s(z0), x2))) -> c6(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c6(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c6(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(from(z0), cons(x1, x2))) -> c6(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c6(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c6(MARK(cons(x1, x2))) MARK(first(first(x0, first(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c6(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c6(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c6(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c6(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c6(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c6(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c6(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c6(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c6(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c6(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c6(MARK(x2)) MARK(first(from(first(z0, z1)), x1)) -> c6(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c6(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c6(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c6(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c6(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c6(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c6(MARK(s(z0))) MARK(first(from(x0), x1)) -> c6(MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c6(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(from(z0)), x1)) -> c6(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c6(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c6(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c6(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c6(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c6(MARK(s(z0))) A__FIRST(s(z0), cons(from(y0), z2)) -> c1(MARK(from(y0))) A__FIRST(s(z0), cons(s(y0), z2)) -> c1(MARK(s(y0))) A__FIRST(s(z0), cons(cons(y0, y1), z2)) -> c1(MARK(cons(y0, y1))) A__FIRST(s(z0), cons(first(y0, 0), z2)) -> c1(MARK(first(y0, 0))) A__FIRST(s(z0), cons(first(y0, nil), z2)) -> c1(MARK(first(y0, nil))) A__FIRST(s(z0), cons(first(y0, s(y1)), z2)) -> c1(MARK(first(y0, s(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), y2), z2)) -> c1(MARK(first(cons(y0, y1), y2))) A__FIRST(s(z0), cons(first(0, y0), z2)) -> c1(MARK(first(0, y0))) A__FIRST(s(z0), cons(first(nil, y0), z2)) -> c1(MARK(first(nil, y0))) A__FIRST(s(z0), cons(first(y0, first(y1, first(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, first(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(y1, from(y2))), z2)) -> c1(MARK(first(y0, first(y1, from(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, 0)), z2)) -> c1(MARK(first(y0, first(y1, 0)))) A__FIRST(s(z0), cons(first(y0, first(y1, nil)), z2)) -> c1(MARK(first(y0, first(y1, nil)))) A__FIRST(s(z0), cons(first(y0, first(y1, s(y2))), z2)) -> c1(MARK(first(y0, first(y1, s(y2))))) A__FIRST(s(z0), cons(first(y0, first(y1, cons(y2, y3))), z2)) -> c1(MARK(first(y0, first(y1, cons(y2, y3))))) A__FIRST(s(z0), cons(first(y0, first(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, first(from(y1), y2)), z2)) -> c1(MARK(first(y0, first(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(0, y1)), z2)) -> c1(MARK(first(y0, first(0, y1)))) A__FIRST(s(z0), cons(first(y0, first(nil, y1)), z2)) -> c1(MARK(first(y0, first(nil, y1)))) A__FIRST(s(z0), cons(first(y0, first(s(y1), y2)), z2)) -> c1(MARK(first(y0, first(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, first(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, first(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), first(y1, y2)), z2)) -> c1(MARK(first(from(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), first(y1, y2)), z2)) -> c1(MARK(first(s(y0), first(y1, y2)))) A__FIRST(s(z0), cons(first(y0, first(y1, y2)), z2)) -> c1(MARK(first(y0, first(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), first(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), first(y2, y3)))) A__FIRST(s(z0), cons(first(y0, from(y1)), z2)) -> c1(MARK(first(y0, from(y1)))) A__FIRST(s(z0), cons(first(y0, from(first(y1, y2))), z2)) -> c1(MARK(first(y0, from(first(y1, y2))))) A__FIRST(s(z0), cons(first(y0, from(from(y1))), z2)) -> c1(MARK(first(y0, from(from(y1))))) A__FIRST(s(z0), cons(first(y0, from(0)), z2)) -> c1(MARK(first(y0, from(0)))) A__FIRST(s(z0), cons(first(y0, from(nil)), z2)) -> c1(MARK(first(y0, from(nil)))) A__FIRST(s(z0), cons(first(y0, from(s(y1))), z2)) -> c1(MARK(first(y0, from(s(y1))))) A__FIRST(s(z0), cons(first(y0, from(cons(y1, y2))), z2)) -> c1(MARK(first(y0, from(cons(y1, y2))))) A__FIRST(s(z0), cons(first(first(y0, y1), from(y2)), z2)) -> c1(MARK(first(first(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(from(y0), from(y1)), z2)) -> c1(MARK(first(from(y0), from(y1)))) A__FIRST(s(z0), cons(first(s(y0), from(y1)), z2)) -> c1(MARK(first(s(y0), from(y1)))) A__FIRST(s(z0), cons(first(cons(y0, y1), from(y2)), z2)) -> c1(MARK(first(cons(y0, y1), from(y2)))) A__FIRST(s(z0), cons(first(y0, cons(first(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(first(y1, y2), y3)))) A__FIRST(s(z0), cons(first(y0, cons(from(y1), y2)), z2)) -> c1(MARK(first(y0, cons(from(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(0, y1)), z2)) -> c1(MARK(first(y0, cons(0, y1)))) A__FIRST(s(z0), cons(first(y0, cons(nil, y1)), z2)) -> c1(MARK(first(y0, cons(nil, y1)))) A__FIRST(s(z0), cons(first(y0, cons(s(y1), y2)), z2)) -> c1(MARK(first(y0, cons(s(y1), y2)))) A__FIRST(s(z0), cons(first(y0, cons(cons(y1, y2), y3)), z2)) -> c1(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FIRST(s(z0), cons(first(first(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(first(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(from(y0), cons(y1, y2)), z2)) -> c1(MARK(first(from(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(s(y0), cons(y1, y2)), z2)) -> c1(MARK(first(s(y0), cons(y1, y2)))) A__FIRST(s(z0), cons(first(cons(y0, y1), cons(y2, y3)), z2)) -> c1(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FIRST(s(z0), cons(first(first(y0, first(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, first(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(y0, from(y1)), y2), z2)) -> c1(MARK(first(first(y0, from(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, 0), y1), z2)) -> c1(MARK(first(first(y0, 0), y1))) A__FIRST(s(z0), cons(first(first(y0, nil), y1), z2)) -> c1(MARK(first(first(y0, nil), y1))) A__FIRST(s(z0), cons(first(first(y0, s(y1)), y2), z2)) -> c1(MARK(first(first(y0, s(y1)), y2))) A__FIRST(s(z0), cons(first(first(y0, cons(y1, y2)), y3), z2)) -> c1(MARK(first(first(y0, cons(y1, y2)), y3))) A__FIRST(s(z0), cons(first(first(first(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(first(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(from(y0), y1), y2), z2)) -> c1(MARK(first(first(from(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(0, y0), y1), z2)) -> c1(MARK(first(first(0, y0), y1))) A__FIRST(s(z0), cons(first(first(nil, y0), y1), z2)) -> c1(MARK(first(first(nil, y0), y1))) A__FIRST(s(z0), cons(first(first(s(y0), y1), y2), z2)) -> c1(MARK(first(first(s(y0), y1), y2))) A__FIRST(s(z0), cons(first(first(cons(y0, y1), y2), y3), z2)) -> c1(MARK(first(first(cons(y0, y1), y2), y3))) A__FIRST(s(z0), cons(first(first(y0, y1), 0), z2)) -> c1(MARK(first(first(y0, y1), 0))) A__FIRST(s(z0), cons(first(first(y0, y1), nil), z2)) -> c1(MARK(first(first(y0, y1), nil))) A__FIRST(s(z0), cons(first(first(y0, y1), s(y2)), z2)) -> c1(MARK(first(first(y0, y1), s(y2)))) A__FIRST(s(z0), cons(first(first(y0, y1), y2), z2)) -> c1(MARK(first(first(y0, y1), y2))) A__FIRST(s(z0), cons(first(from(first(y0, y1)), y2), z2)) -> c1(MARK(first(from(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(from(y0)), y1), z2)) -> c1(MARK(first(from(from(y0)), y1))) A__FIRST(s(z0), cons(first(from(0), y0), z2)) -> c1(MARK(first(from(0), y0))) A__FIRST(s(z0), cons(first(from(nil), y0), z2)) -> c1(MARK(first(from(nil), y0))) A__FIRST(s(z0), cons(first(from(s(y0)), y1), z2)) -> c1(MARK(first(from(s(y0)), y1))) A__FIRST(s(z0), cons(first(from(cons(y0, y1)), y2), z2)) -> c1(MARK(first(from(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(from(y0), y1), z2)) -> c1(MARK(first(from(y0), y1))) A__FIRST(s(z0), cons(first(from(y0), 0), z2)) -> c1(MARK(first(from(y0), 0))) A__FIRST(s(z0), cons(first(from(y0), nil), z2)) -> c1(MARK(first(from(y0), nil))) A__FIRST(s(z0), cons(first(from(y0), s(y1)), z2)) -> c1(MARK(first(from(y0), s(y1)))) A__FIRST(s(z0), cons(first(s(first(y0, y1)), y2), z2)) -> c1(MARK(first(s(first(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(from(y0)), y1), z2)) -> c1(MARK(first(s(from(y0)), y1))) A__FIRST(s(z0), cons(first(s(0), y0), z2)) -> c1(MARK(first(s(0), y0))) A__FIRST(s(z0), cons(first(s(nil), y0), z2)) -> c1(MARK(first(s(nil), y0))) A__FIRST(s(z0), cons(first(s(s(y0)), y1), z2)) -> c1(MARK(first(s(s(y0)), y1))) A__FIRST(s(z0), cons(first(s(cons(y0, y1)), y2), z2)) -> c1(MARK(first(s(cons(y0, y1)), y2))) A__FIRST(s(z0), cons(first(s(y0), y1), z2)) -> c1(MARK(first(s(y0), y1))) A__FIRST(s(z0), cons(first(s(y0), 0), z2)) -> c1(MARK(first(s(y0), 0))) A__FIRST(s(z0), cons(first(s(y0), nil), z2)) -> c1(MARK(first(s(y0), nil))) A__FIRST(s(z0), cons(first(s(y0), s(y1)), z2)) -> c1(MARK(first(s(y0), s(y1)))) A__FIRST(s(z0), cons(first(0, first(y0, y1)), z2)) -> c1(MARK(first(0, first(y0, y1)))) A__FIRST(s(z0), cons(first(nil, first(y0, y1)), z2)) -> c1(MARK(first(nil, first(y0, y1)))) A__FIRST(s(z0), cons(first(0, from(y0)), z2)) -> c1(MARK(first(0, from(y0)))) A__FIRST(s(z0), cons(first(nil, from(y0)), z2)) -> c1(MARK(first(nil, from(y0)))) A__FIRST(s(z0), cons(first(y0, cons(y1, y2)), z2)) -> c1(MARK(first(y0, cons(y1, y2)))) A__FIRST(s(z0), cons(first(0, cons(y0, y1)), z2)) -> c1(MARK(first(0, cons(y0, y1)))) A__FIRST(s(z0), cons(first(nil, cons(y0, y1)), z2)) -> c1(MARK(first(nil, cons(y0, y1)))) MARK(first(x0, cons(0, x2))) -> c5(MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c5(MARK(x0)) A__FROM(from(y0)) -> c3(MARK(from(y0))) A__FROM(s(y0)) -> c3(MARK(s(y0))) A__FROM(cons(y0, y1)) -> c3(MARK(cons(y0, y1))) A__FROM(first(y0, 0)) -> c3(MARK(first(y0, 0))) A__FROM(first(y0, nil)) -> c3(MARK(first(y0, nil))) A__FROM(first(y0, s(y1))) -> c3(MARK(first(y0, s(y1)))) A__FROM(first(cons(y0, y1), y2)) -> c3(MARK(first(cons(y0, y1), y2))) A__FROM(first(0, y0)) -> c3(MARK(first(0, y0))) A__FROM(first(nil, y0)) -> c3(MARK(first(nil, y0))) A__FROM(first(y0, first(y1, first(y2, y3)))) -> c3(MARK(first(y0, first(y1, first(y2, y3))))) A__FROM(first(y0, first(y1, from(y2)))) -> c3(MARK(first(y0, first(y1, from(y2))))) A__FROM(first(y0, first(y1, 0))) -> c3(MARK(first(y0, first(y1, 0)))) A__FROM(first(y0, first(y1, nil))) -> c3(MARK(first(y0, first(y1, nil)))) A__FROM(first(y0, first(y1, s(y2)))) -> c3(MARK(first(y0, first(y1, s(y2))))) A__FROM(first(y0, first(y1, cons(y2, y3)))) -> c3(MARK(first(y0, first(y1, cons(y2, y3))))) A__FROM(first(y0, first(first(y1, y2), y3))) -> c3(MARK(first(y0, first(first(y1, y2), y3)))) A__FROM(first(y0, first(from(y1), y2))) -> c3(MARK(first(y0, first(from(y1), y2)))) A__FROM(first(y0, first(0, y1))) -> c3(MARK(first(y0, first(0, y1)))) A__FROM(first(y0, first(nil, y1))) -> c3(MARK(first(y0, first(nil, y1)))) A__FROM(first(y0, first(s(y1), y2))) -> c3(MARK(first(y0, first(s(y1), y2)))) A__FROM(first(y0, first(cons(y1, y2), y3))) -> c3(MARK(first(y0, first(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), first(y2, y3))) -> c3(MARK(first(first(y0, y1), first(y2, y3)))) A__FROM(first(from(y0), first(y1, y2))) -> c3(MARK(first(from(y0), first(y1, y2)))) A__FROM(first(s(y0), first(y1, y2))) -> c3(MARK(first(s(y0), first(y1, y2)))) A__FROM(first(y0, first(y1, y2))) -> c3(MARK(first(y0, first(y1, y2)))) A__FROM(first(cons(y0, y1), first(y2, y3))) -> c3(MARK(first(cons(y0, y1), first(y2, y3)))) A__FROM(first(y0, from(y1))) -> c3(MARK(first(y0, from(y1)))) A__FROM(first(y0, from(first(y1, y2)))) -> c3(MARK(first(y0, from(first(y1, y2))))) A__FROM(first(y0, from(from(y1)))) -> c3(MARK(first(y0, from(from(y1))))) A__FROM(first(y0, from(0))) -> c3(MARK(first(y0, from(0)))) A__FROM(first(y0, from(nil))) -> c3(MARK(first(y0, from(nil)))) A__FROM(first(y0, from(s(y1)))) -> c3(MARK(first(y0, from(s(y1))))) A__FROM(first(y0, from(cons(y1, y2)))) -> c3(MARK(first(y0, from(cons(y1, y2))))) A__FROM(first(first(y0, y1), from(y2))) -> c3(MARK(first(first(y0, y1), from(y2)))) A__FROM(first(from(y0), from(y1))) -> c3(MARK(first(from(y0), from(y1)))) A__FROM(first(s(y0), from(y1))) -> c3(MARK(first(s(y0), from(y1)))) A__FROM(first(cons(y0, y1), from(y2))) -> c3(MARK(first(cons(y0, y1), from(y2)))) A__FROM(first(y0, cons(first(y1, y2), y3))) -> c3(MARK(first(y0, cons(first(y1, y2), y3)))) A__FROM(first(y0, cons(from(y1), y2))) -> c3(MARK(first(y0, cons(from(y1), y2)))) A__FROM(first(y0, cons(s(y1), y2))) -> c3(MARK(first(y0, cons(s(y1), y2)))) A__FROM(first(y0, cons(cons(y1, y2), y3))) -> c3(MARK(first(y0, cons(cons(y1, y2), y3)))) A__FROM(first(first(y0, y1), cons(y2, y3))) -> c3(MARK(first(first(y0, y1), cons(y2, y3)))) A__FROM(first(from(y0), cons(y1, y2))) -> c3(MARK(first(from(y0), cons(y1, y2)))) A__FROM(first(s(y0), cons(y1, y2))) -> c3(MARK(first(s(y0), cons(y1, y2)))) A__FROM(first(cons(y0, y1), cons(y2, y3))) -> c3(MARK(first(cons(y0, y1), cons(y2, y3)))) A__FROM(first(first(y0, first(y1, y2)), y3)) -> c3(MARK(first(first(y0, first(y1, y2)), y3))) A__FROM(first(first(y0, from(y1)), y2)) -> c3(MARK(first(first(y0, from(y1)), y2))) A__FROM(first(first(y0, 0), y1)) -> c3(MARK(first(first(y0, 0), y1))) A__FROM(first(first(y0, nil), y1)) -> c3(MARK(first(first(y0, nil), y1))) A__FROM(first(first(y0, s(y1)), y2)) -> c3(MARK(first(first(y0, s(y1)), y2))) A__FROM(first(first(y0, cons(y1, y2)), y3)) -> c3(MARK(first(first(y0, cons(y1, y2)), y3))) A__FROM(first(first(first(y0, y1), y2), y3)) -> c3(MARK(first(first(first(y0, y1), y2), y3))) A__FROM(first(first(from(y0), y1), y2)) -> c3(MARK(first(first(from(y0), y1), y2))) A__FROM(first(first(0, y0), y1)) -> c3(MARK(first(first(0, y0), y1))) A__FROM(first(first(nil, y0), y1)) -> c3(MARK(first(first(nil, y0), y1))) A__FROM(first(first(s(y0), y1), y2)) -> c3(MARK(first(first(s(y0), y1), y2))) A__FROM(first(first(cons(y0, y1), y2), y3)) -> c3(MARK(first(first(cons(y0, y1), y2), y3))) A__FROM(first(first(y0, y1), 0)) -> c3(MARK(first(first(y0, y1), 0))) A__FROM(first(first(y0, y1), nil)) -> c3(MARK(first(first(y0, y1), nil))) A__FROM(first(first(y0, y1), s(y2))) -> c3(MARK(first(first(y0, y1), s(y2)))) A__FROM(first(first(y0, y1), y2)) -> c3(MARK(first(first(y0, y1), y2))) A__FROM(first(from(first(y0, y1)), y2)) -> c3(MARK(first(from(first(y0, y1)), y2))) A__FROM(first(from(from(y0)), y1)) -> c3(MARK(first(from(from(y0)), y1))) A__FROM(first(from(0), y0)) -> c3(MARK(first(from(0), y0))) A__FROM(first(from(nil), y0)) -> c3(MARK(first(from(nil), y0))) A__FROM(first(from(s(y0)), y1)) -> c3(MARK(first(from(s(y0)), y1))) A__FROM(first(from(cons(y0, y1)), y2)) -> c3(MARK(first(from(cons(y0, y1)), y2))) A__FROM(first(from(y0), y1)) -> c3(MARK(first(from(y0), y1))) A__FROM(first(from(y0), 0)) -> c3(MARK(first(from(y0), 0))) A__FROM(first(from(y0), nil)) -> c3(MARK(first(from(y0), nil))) A__FROM(first(from(y0), s(y1))) -> c3(MARK(first(from(y0), s(y1)))) A__FROM(first(s(first(y0, y1)), y2)) -> c3(MARK(first(s(first(y0, y1)), y2))) A__FROM(first(s(from(y0)), y1)) -> c3(MARK(first(s(from(y0)), y1))) A__FROM(first(s(0), y0)) -> c3(MARK(first(s(0), y0))) A__FROM(first(s(nil), y0)) -> c3(MARK(first(s(nil), y0))) A__FROM(first(s(s(y0)), y1)) -> c3(MARK(first(s(s(y0)), y1))) A__FROM(first(s(cons(y0, y1)), y2)) -> c3(MARK(first(s(cons(y0, y1)), y2))) A__FROM(first(s(y0), y1)) -> c3(MARK(first(s(y0), y1))) A__FROM(first(s(y0), 0)) -> c3(MARK(first(s(y0), 0))) A__FROM(first(s(y0), nil)) -> c3(MARK(first(s(y0), nil))) A__FROM(first(s(y0), s(y1))) -> c3(MARK(first(s(y0), s(y1)))) A__FROM(first(0, first(y0, y1))) -> c3(MARK(first(0, first(y0, y1)))) A__FROM(first(nil, first(y0, y1))) -> c3(MARK(first(nil, first(y0, y1)))) A__FROM(first(0, from(y0))) -> c3(MARK(first(0, from(y0)))) A__FROM(first(nil, from(y0))) -> c3(MARK(first(nil, from(y0)))) A__FROM(first(y0, cons(y1, y2))) -> c3(MARK(first(y0, cons(y1, y2)))) A__FROM(first(0, cons(y0, y1))) -> c3(MARK(first(0, cons(y0, y1)))) A__FROM(first(nil, cons(y0, y1))) -> c3(MARK(first(nil, cons(y0, y1)))) A__FROM(first(y0, cons(0, y1))) -> c3(MARK(first(y0, cons(0, y1)))) A__FROM(first(y0, cons(nil, y1))) -> c3(MARK(first(y0, cons(nil, y1)))) MARK(from(s(z0))) -> c7(A__FROM(s(mark(z0))), MARK(s(z0))) MARK(from(cons(z0, z1))) -> c7(A__FROM(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(0), x1)) -> c5(A__FIRST(a__from(0), mark(x1))) MARK(first(from(nil), x1)) -> c5(A__FIRST(a__from(nil), mark(x1))) MARK(first(x0, from(0))) -> c6(A__FIRST(mark(x0), a__from(0))) MARK(first(x0, from(nil))) -> c6(A__FIRST(mark(x0), a__from(nil))) MARK(from(first(x0, x1))) -> c7(A__FROM(first(mark(x0), mark(x1))), MARK(first(x0, x1))) MARK(from(first(x0, first(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), a__first(mark(z0), mark(z1)))), MARK(first(x0, first(z0, z1)))) MARK(from(first(x0, from(z0)))) -> c7(A__FROM(a__first(mark(x0), a__from(mark(z0)))), MARK(first(x0, from(z0)))) MARK(from(first(x0, 0))) -> c7(A__FROM(a__first(mark(x0), 0)), MARK(first(x0, 0))) MARK(from(first(x0, nil))) -> c7(A__FROM(a__first(mark(x0), nil)), MARK(first(x0, nil))) MARK(from(first(x0, s(z0)))) -> c7(A__FROM(a__first(mark(x0), s(mark(z0)))), MARK(first(x0, s(z0)))) MARK(from(first(x0, cons(z0, z1)))) -> c7(A__FROM(a__first(mark(x0), cons(mark(z0), z1))), MARK(first(x0, cons(z0, z1)))) MARK(from(first(first(z0, z1), x1))) -> c7(A__FROM(a__first(a__first(mark(z0), mark(z1)), mark(x1))), MARK(first(first(z0, z1), x1))) MARK(from(first(from(z0), x1))) -> c7(A__FROM(a__first(a__from(mark(z0)), mark(x1))), MARK(first(from(z0), x1))) MARK(from(first(0, x1))) -> c7(A__FROM(a__first(0, mark(x1))), MARK(first(0, x1))) MARK(from(first(nil, x1))) -> c7(A__FROM(a__first(nil, mark(x1))), MARK(first(nil, x1))) MARK(from(first(s(z0), x1))) -> c7(A__FROM(a__first(s(mark(z0)), mark(x1))), MARK(first(s(z0), x1))) MARK(from(first(cons(z0, z1), x1))) -> c7(A__FROM(a__first(cons(mark(z0), z1), mark(x1))), MARK(first(cons(z0, z1), x1))) 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(first(z0, z1)))) -> c7(A__FROM(a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(from(from(from(z0)))) -> c7(A__FROM(a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(from(from(s(z0)))) -> c7(A__FROM(a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(from(from(cons(z0, z1)))) -> c7(A__FROM(a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(from(from(0))) -> c7(A__FROM(a__from(0))) MARK(from(from(nil))) -> c7(A__FROM(a__from(nil))) MARK(s(s(y0))) -> c10(MARK(s(y0))) MARK(s(cons(y0, y1))) -> c10(MARK(cons(y0, y1))) MARK(s(first(y0, 0))) -> c10(MARK(first(y0, 0))) MARK(s(first(y0, nil))) -> c10(MARK(first(y0, nil))) MARK(s(first(y0, s(y1)))) -> c10(MARK(first(y0, s(y1)))) MARK(s(first(cons(y0, y1), y2))) -> c10(MARK(first(cons(y0, y1), y2))) MARK(s(first(0, y0))) -> c10(MARK(first(0, y0))) MARK(s(first(nil, y0))) -> c10(MARK(first(nil, y0))) MARK(s(first(y0, first(y1, first(y2, y3))))) -> c10(MARK(first(y0, first(y1, first(y2, y3))))) MARK(s(first(y0, first(y1, from(y2))))) -> c10(MARK(first(y0, first(y1, from(y2))))) MARK(s(first(y0, first(y1, 0)))) -> c10(MARK(first(y0, first(y1, 0)))) MARK(s(first(y0, first(y1, nil)))) -> c10(MARK(first(y0, first(y1, nil)))) MARK(s(first(y0, first(y1, s(y2))))) -> c10(MARK(first(y0, first(y1, s(y2))))) MARK(s(first(y0, first(y1, cons(y2, y3))))) -> c10(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(s(first(y0, first(first(y1, y2), y3)))) -> c10(MARK(first(y0, first(first(y1, y2), y3)))) MARK(s(first(y0, first(from(y1), y2)))) -> c10(MARK(first(y0, first(from(y1), y2)))) MARK(s(first(y0, first(0, y1)))) -> c10(MARK(first(y0, first(0, y1)))) MARK(s(first(y0, first(nil, y1)))) -> c10(MARK(first(y0, first(nil, y1)))) MARK(s(first(y0, first(s(y1), y2)))) -> c10(MARK(first(y0, first(s(y1), y2)))) MARK(s(first(y0, first(cons(y1, y2), y3)))) -> c10(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), first(y2, y3)))) -> c10(MARK(first(first(y0, y1), first(y2, y3)))) MARK(s(first(from(y0), first(y1, y2)))) -> c10(MARK(first(from(y0), first(y1, y2)))) MARK(s(first(s(y0), first(y1, y2)))) -> c10(MARK(first(s(y0), first(y1, y2)))) MARK(s(first(y0, first(y1, y2)))) -> c10(MARK(first(y0, first(y1, y2)))) MARK(s(first(cons(y0, y1), first(y2, y3)))) -> c10(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(s(first(y0, from(y1)))) -> c10(MARK(first(y0, from(y1)))) MARK(s(first(y0, from(first(y1, y2))))) -> c10(MARK(first(y0, from(first(y1, y2))))) MARK(s(first(y0, from(from(y1))))) -> c10(MARK(first(y0, from(from(y1))))) MARK(s(first(y0, from(0)))) -> c10(MARK(first(y0, from(0)))) MARK(s(first(y0, from(nil)))) -> c10(MARK(first(y0, from(nil)))) MARK(s(first(y0, from(s(y1))))) -> c10(MARK(first(y0, from(s(y1))))) MARK(s(first(y0, from(cons(y1, y2))))) -> c10(MARK(first(y0, from(cons(y1, y2))))) MARK(s(first(first(y0, y1), from(y2)))) -> c10(MARK(first(first(y0, y1), from(y2)))) MARK(s(first(from(y0), from(y1)))) -> c10(MARK(first(from(y0), from(y1)))) MARK(s(first(s(y0), from(y1)))) -> c10(MARK(first(s(y0), from(y1)))) MARK(s(first(cons(y0, y1), from(y2)))) -> c10(MARK(first(cons(y0, y1), from(y2)))) MARK(s(first(y0, cons(first(y1, y2), y3)))) -> c10(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(s(first(y0, cons(from(y1), y2)))) -> c10(MARK(first(y0, cons(from(y1), y2)))) MARK(s(first(y0, cons(s(y1), y2)))) -> c10(MARK(first(y0, cons(s(y1), y2)))) MARK(s(first(y0, cons(cons(y1, y2), y3)))) -> c10(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(s(first(first(y0, y1), cons(y2, y3)))) -> c10(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(s(first(from(y0), cons(y1, y2)))) -> c10(MARK(first(from(y0), cons(y1, y2)))) MARK(s(first(s(y0), cons(y1, y2)))) -> c10(MARK(first(s(y0), cons(y1, y2)))) MARK(s(first(cons(y0, y1), cons(y2, y3)))) -> c10(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(s(first(first(y0, first(y1, y2)), y3))) -> c10(MARK(first(first(y0, first(y1, y2)), y3))) MARK(s(first(first(y0, from(y1)), y2))) -> c10(MARK(first(first(y0, from(y1)), y2))) MARK(s(first(first(y0, 0), y1))) -> c10(MARK(first(first(y0, 0), y1))) MARK(s(first(first(y0, nil), y1))) -> c10(MARK(first(first(y0, nil), y1))) MARK(s(first(first(y0, s(y1)), y2))) -> c10(MARK(first(first(y0, s(y1)), y2))) MARK(s(first(first(y0, cons(y1, y2)), y3))) -> c10(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(s(first(first(first(y0, y1), y2), y3))) -> c10(MARK(first(first(first(y0, y1), y2), y3))) MARK(s(first(first(from(y0), y1), y2))) -> c10(MARK(first(first(from(y0), y1), y2))) MARK(s(first(first(0, y0), y1))) -> c10(MARK(first(first(0, y0), y1))) MARK(s(first(first(nil, y0), y1))) -> c10(MARK(first(first(nil, y0), y1))) MARK(s(first(first(s(y0), y1), y2))) -> c10(MARK(first(first(s(y0), y1), y2))) MARK(s(first(first(cons(y0, y1), y2), y3))) -> c10(MARK(first(first(cons(y0, y1), y2), y3))) MARK(s(first(first(y0, y1), 0))) -> c10(MARK(first(first(y0, y1), 0))) MARK(s(first(first(y0, y1), nil))) -> c10(MARK(first(first(y0, y1), nil))) MARK(s(first(first(y0, y1), s(y2)))) -> c10(MARK(first(first(y0, y1), s(y2)))) MARK(s(first(first(y0, y1), y2))) -> c10(MARK(first(first(y0, y1), y2))) MARK(s(first(from(first(y0, y1)), y2))) -> c10(MARK(first(from(first(y0, y1)), y2))) MARK(s(first(from(from(y0)), y1))) -> c10(MARK(first(from(from(y0)), y1))) MARK(s(first(from(s(y0)), y1))) -> c10(MARK(first(from(s(y0)), y1))) MARK(s(first(from(cons(y0, y1)), y2))) -> c10(MARK(first(from(cons(y0, y1)), y2))) MARK(s(first(from(y0), y1))) -> c10(MARK(first(from(y0), y1))) MARK(s(first(from(y0), 0))) -> c10(MARK(first(from(y0), 0))) MARK(s(first(from(y0), nil))) -> c10(MARK(first(from(y0), nil))) MARK(s(first(from(y0), s(y1)))) -> c10(MARK(first(from(y0), s(y1)))) MARK(s(first(s(first(y0, y1)), y2))) -> c10(MARK(first(s(first(y0, y1)), y2))) MARK(s(first(s(from(y0)), y1))) -> c10(MARK(first(s(from(y0)), y1))) MARK(s(first(s(0), y0))) -> c10(MARK(first(s(0), y0))) MARK(s(first(s(nil), y0))) -> c10(MARK(first(s(nil), y0))) MARK(s(first(s(s(y0)), y1))) -> c10(MARK(first(s(s(y0)), y1))) MARK(s(first(s(cons(y0, y1)), y2))) -> c10(MARK(first(s(cons(y0, y1)), y2))) MARK(s(first(s(y0), y1))) -> c10(MARK(first(s(y0), y1))) MARK(s(first(s(y0), 0))) -> c10(MARK(first(s(y0), 0))) MARK(s(first(s(y0), nil))) -> c10(MARK(first(s(y0), nil))) MARK(s(first(s(y0), s(y1)))) -> c10(MARK(first(s(y0), s(y1)))) MARK(s(first(0, first(y0, y1)))) -> c10(MARK(first(0, first(y0, y1)))) MARK(s(first(nil, first(y0, y1)))) -> c10(MARK(first(nil, first(y0, y1)))) MARK(s(first(0, from(y0)))) -> c10(MARK(first(0, from(y0)))) MARK(s(first(nil, from(y0)))) -> c10(MARK(first(nil, from(y0)))) MARK(s(first(y0, cons(y1, y2)))) -> c10(MARK(first(y0, cons(y1, y2)))) MARK(s(first(0, cons(y0, y1)))) -> c10(MARK(first(0, cons(y0, y1)))) MARK(s(first(nil, cons(y0, y1)))) -> c10(MARK(first(nil, cons(y0, y1)))) MARK(s(first(from(0), y0))) -> c10(MARK(first(from(0), y0))) MARK(s(first(from(nil), y0))) -> c10(MARK(first(from(nil), y0))) MARK(s(first(y0, cons(0, y1)))) -> c10(MARK(first(y0, cons(0, y1)))) MARK(s(first(y0, cons(nil, y1)))) -> c10(MARK(first(y0, cons(nil, y1)))) MARK(s(from(s(y0)))) -> c10(MARK(from(s(y0)))) MARK(s(from(cons(y0, y1)))) -> c10(MARK(from(cons(y0, y1)))) MARK(s(from(first(y0, y1)))) -> c10(MARK(from(first(y0, y1)))) MARK(s(from(first(y0, first(y1, y2))))) -> c10(MARK(from(first(y0, first(y1, y2))))) MARK(s(from(first(y0, from(y1))))) -> c10(MARK(from(first(y0, from(y1))))) MARK(s(from(first(y0, 0)))) -> c10(MARK(from(first(y0, 0)))) MARK(s(from(first(y0, nil)))) -> c10(MARK(from(first(y0, nil)))) MARK(s(from(first(y0, s(y1))))) -> c10(MARK(from(first(y0, s(y1))))) MARK(s(from(first(y0, cons(y1, y2))))) -> c10(MARK(from(first(y0, cons(y1, y2))))) MARK(s(from(first(first(y0, y1), y2)))) -> c10(MARK(from(first(first(y0, y1), y2)))) MARK(s(from(first(from(y0), y1)))) -> c10(MARK(from(first(from(y0), y1)))) MARK(s(from(first(0, y0)))) -> c10(MARK(from(first(0, y0)))) MARK(s(from(first(nil, y0)))) -> c10(MARK(from(first(nil, y0)))) MARK(s(from(first(s(y0), y1)))) -> c10(MARK(from(first(s(y0), y1)))) MARK(s(from(first(cons(y0, y1), y2)))) -> c10(MARK(from(first(cons(y0, y1), y2)))) MARK(s(from(from(y0)))) -> c10(MARK(from(from(y0)))) MARK(s(from(from(first(y0, y1))))) -> c10(MARK(from(from(first(y0, y1))))) MARK(s(from(from(from(y0))))) -> c10(MARK(from(from(from(y0))))) MARK(s(from(from(s(y0))))) -> c10(MARK(from(from(s(y0))))) MARK(s(from(from(cons(y0, y1))))) -> c10(MARK(from(from(cons(y0, y1))))) MARK(s(from(from(0)))) -> c10(MARK(from(from(0)))) MARK(s(from(from(nil)))) -> c10(MARK(from(from(nil)))) MARK(first(s(0), x1)) -> c5(A__FIRST(s(0), mark(x1))) MARK(first(s(nil), x1)) -> c5(A__FIRST(s(nil), mark(x1))) MARK(cons(cons(y0, y1), z1)) -> c11(MARK(cons(y0, y1))) MARK(cons(first(y0, 0), z1)) -> c11(MARK(first(y0, 0))) MARK(cons(first(y0, nil), z1)) -> c11(MARK(first(y0, nil))) MARK(cons(first(y0, s(y1)), z1)) -> c11(MARK(first(y0, s(y1)))) MARK(cons(first(cons(y0, y1), y2), z1)) -> c11(MARK(first(cons(y0, y1), y2))) MARK(cons(first(0, y0), z1)) -> c11(MARK(first(0, y0))) MARK(cons(first(nil, y0), z1)) -> c11(MARK(first(nil, y0))) MARK(cons(first(y0, first(y1, first(y2, y3))), z1)) -> c11(MARK(first(y0, first(y1, first(y2, y3))))) MARK(cons(first(y0, first(y1, from(y2))), z1)) -> c11(MARK(first(y0, first(y1, from(y2))))) MARK(cons(first(y0, first(y1, 0)), z1)) -> c11(MARK(first(y0, first(y1, 0)))) MARK(cons(first(y0, first(y1, nil)), z1)) -> c11(MARK(first(y0, first(y1, nil)))) MARK(cons(first(y0, first(y1, s(y2))), z1)) -> c11(MARK(first(y0, first(y1, s(y2))))) MARK(cons(first(y0, first(y1, cons(y2, y3))), z1)) -> c11(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(cons(first(y0, first(first(y1, y2), y3)), z1)) -> c11(MARK(first(y0, first(first(y1, y2), y3)))) MARK(cons(first(y0, first(from(y1), y2)), z1)) -> c11(MARK(first(y0, first(from(y1), y2)))) MARK(cons(first(y0, first(0, y1)), z1)) -> c11(MARK(first(y0, first(0, y1)))) MARK(cons(first(y0, first(nil, y1)), z1)) -> c11(MARK(first(y0, first(nil, y1)))) MARK(cons(first(y0, first(s(y1), y2)), z1)) -> c11(MARK(first(y0, first(s(y1), y2)))) MARK(cons(first(y0, first(cons(y1, y2), y3)), z1)) -> c11(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(cons(first(first(y0, y1), first(y2, y3)), z1)) -> c11(MARK(first(first(y0, y1), first(y2, y3)))) MARK(cons(first(from(y0), first(y1, y2)), z1)) -> c11(MARK(first(from(y0), first(y1, y2)))) MARK(cons(first(s(y0), first(y1, y2)), z1)) -> c11(MARK(first(s(y0), first(y1, y2)))) MARK(cons(first(y0, first(y1, y2)), z1)) -> c11(MARK(first(y0, first(y1, y2)))) MARK(cons(first(cons(y0, y1), first(y2, y3)), z1)) -> c11(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(cons(first(y0, from(y1)), z1)) -> c11(MARK(first(y0, from(y1)))) MARK(cons(first(y0, from(first(y1, y2))), z1)) -> c11(MARK(first(y0, from(first(y1, y2))))) MARK(cons(first(y0, from(from(y1))), z1)) -> c11(MARK(first(y0, from(from(y1))))) MARK(cons(first(y0, from(0)), z1)) -> c11(MARK(first(y0, from(0)))) MARK(cons(first(y0, from(nil)), z1)) -> c11(MARK(first(y0, from(nil)))) MARK(cons(first(y0, from(s(y1))), z1)) -> c11(MARK(first(y0, from(s(y1))))) MARK(cons(first(y0, from(cons(y1, y2))), z1)) -> c11(MARK(first(y0, from(cons(y1, y2))))) MARK(cons(first(first(y0, y1), from(y2)), z1)) -> c11(MARK(first(first(y0, y1), from(y2)))) MARK(cons(first(from(y0), from(y1)), z1)) -> c11(MARK(first(from(y0), from(y1)))) MARK(cons(first(s(y0), from(y1)), z1)) -> c11(MARK(first(s(y0), from(y1)))) MARK(cons(first(cons(y0, y1), from(y2)), z1)) -> c11(MARK(first(cons(y0, y1), from(y2)))) MARK(cons(first(y0, cons(first(y1, y2), y3)), z1)) -> c11(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(cons(first(y0, cons(from(y1), y2)), z1)) -> c11(MARK(first(y0, cons(from(y1), y2)))) MARK(cons(first(y0, cons(s(y1), y2)), z1)) -> c11(MARK(first(y0, cons(s(y1), y2)))) MARK(cons(first(y0, cons(cons(y1, y2), y3)), z1)) -> c11(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(cons(first(first(y0, y1), cons(y2, y3)), z1)) -> c11(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(cons(first(from(y0), cons(y1, y2)), z1)) -> c11(MARK(first(from(y0), cons(y1, y2)))) MARK(cons(first(s(y0), cons(y1, y2)), z1)) -> c11(MARK(first(s(y0), cons(y1, y2)))) MARK(cons(first(cons(y0, y1), cons(y2, y3)), z1)) -> c11(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(cons(first(first(y0, first(y1, y2)), y3), z1)) -> c11(MARK(first(first(y0, first(y1, y2)), y3))) MARK(cons(first(first(y0, from(y1)), y2), z1)) -> c11(MARK(first(first(y0, from(y1)), y2))) MARK(cons(first(first(y0, 0), y1), z1)) -> c11(MARK(first(first(y0, 0), y1))) MARK(cons(first(first(y0, nil), y1), z1)) -> c11(MARK(first(first(y0, nil), y1))) MARK(cons(first(first(y0, s(y1)), y2), z1)) -> c11(MARK(first(first(y0, s(y1)), y2))) MARK(cons(first(first(y0, cons(y1, y2)), y3), z1)) -> c11(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(cons(first(first(first(y0, y1), y2), y3), z1)) -> c11(MARK(first(first(first(y0, y1), y2), y3))) MARK(cons(first(first(from(y0), y1), y2), z1)) -> c11(MARK(first(first(from(y0), y1), y2))) MARK(cons(first(first(0, y0), y1), z1)) -> c11(MARK(first(first(0, y0), y1))) MARK(cons(first(first(nil, y0), y1), z1)) -> c11(MARK(first(first(nil, y0), y1))) MARK(cons(first(first(s(y0), y1), y2), z1)) -> c11(MARK(first(first(s(y0), y1), y2))) MARK(cons(first(first(cons(y0, y1), y2), y3), z1)) -> c11(MARK(first(first(cons(y0, y1), y2), y3))) MARK(cons(first(first(y0, y1), 0), z1)) -> c11(MARK(first(first(y0, y1), 0))) MARK(cons(first(first(y0, y1), nil), z1)) -> c11(MARK(first(first(y0, y1), nil))) MARK(cons(first(first(y0, y1), s(y2)), z1)) -> c11(MARK(first(first(y0, y1), s(y2)))) MARK(cons(first(first(y0, y1), y2), z1)) -> c11(MARK(first(first(y0, y1), y2))) MARK(cons(first(from(first(y0, y1)), y2), z1)) -> c11(MARK(first(from(first(y0, y1)), y2))) MARK(cons(first(from(from(y0)), y1), z1)) -> c11(MARK(first(from(from(y0)), y1))) MARK(cons(first(from(s(y0)), y1), z1)) -> c11(MARK(first(from(s(y0)), y1))) MARK(cons(first(from(cons(y0, y1)), y2), z1)) -> c11(MARK(first(from(cons(y0, y1)), y2))) MARK(cons(first(from(y0), y1), z1)) -> c11(MARK(first(from(y0), y1))) MARK(cons(first(from(y0), 0), z1)) -> c11(MARK(first(from(y0), 0))) MARK(cons(first(from(y0), nil), z1)) -> c11(MARK(first(from(y0), nil))) MARK(cons(first(from(y0), s(y1)), z1)) -> c11(MARK(first(from(y0), s(y1)))) MARK(cons(first(s(first(y0, y1)), y2), z1)) -> c11(MARK(first(s(first(y0, y1)), y2))) MARK(cons(first(s(from(y0)), y1), z1)) -> c11(MARK(first(s(from(y0)), y1))) MARK(cons(first(s(s(y0)), y1), z1)) -> c11(MARK(first(s(s(y0)), y1))) MARK(cons(first(s(cons(y0, y1)), y2), z1)) -> c11(MARK(first(s(cons(y0, y1)), y2))) MARK(cons(first(s(y0), y1), z1)) -> c11(MARK(first(s(y0), y1))) MARK(cons(first(s(y0), 0), z1)) -> c11(MARK(first(s(y0), 0))) MARK(cons(first(s(y0), nil), z1)) -> c11(MARK(first(s(y0), nil))) MARK(cons(first(s(y0), s(y1)), z1)) -> c11(MARK(first(s(y0), s(y1)))) MARK(cons(first(0, first(y0, y1)), z1)) -> c11(MARK(first(0, first(y0, y1)))) MARK(cons(first(nil, first(y0, y1)), z1)) -> c11(MARK(first(nil, first(y0, y1)))) MARK(cons(first(0, from(y0)), z1)) -> c11(MARK(first(0, from(y0)))) MARK(cons(first(nil, from(y0)), z1)) -> c11(MARK(first(nil, from(y0)))) MARK(cons(first(y0, cons(y1, y2)), z1)) -> c11(MARK(first(y0, cons(y1, y2)))) MARK(cons(first(0, cons(y0, y1)), z1)) -> c11(MARK(first(0, cons(y0, y1)))) MARK(cons(first(nil, cons(y0, y1)), z1)) -> c11(MARK(first(nil, cons(y0, y1)))) MARK(cons(first(from(0), y0), z1)) -> c11(MARK(first(from(0), y0))) MARK(cons(first(from(nil), y0), z1)) -> c11(MARK(first(from(nil), y0))) MARK(cons(first(s(0), y0), z1)) -> c11(MARK(first(s(0), y0))) MARK(cons(first(s(nil), y0), z1)) -> c11(MARK(first(s(nil), y0))) MARK(cons(first(y0, cons(0, y1)), z1)) -> c11(MARK(first(y0, cons(0, y1)))) MARK(cons(first(y0, cons(nil, y1)), z1)) -> c11(MARK(first(y0, cons(nil, y1)))) MARK(cons(from(s(y0)), z1)) -> c11(MARK(from(s(y0)))) MARK(cons(from(cons(y0, y1)), z1)) -> c11(MARK(from(cons(y0, y1)))) MARK(cons(from(first(y0, y1)), z1)) -> c11(MARK(from(first(y0, y1)))) MARK(cons(from(first(y0, first(y1, y2))), z1)) -> c11(MARK(from(first(y0, first(y1, y2))))) MARK(cons(from(first(y0, from(y1))), z1)) -> c11(MARK(from(first(y0, from(y1))))) MARK(cons(from(first(y0, 0)), z1)) -> c11(MARK(from(first(y0, 0)))) MARK(cons(from(first(y0, nil)), z1)) -> c11(MARK(from(first(y0, nil)))) MARK(cons(from(first(y0, s(y1))), z1)) -> c11(MARK(from(first(y0, s(y1))))) MARK(cons(from(first(y0, cons(y1, y2))), z1)) -> c11(MARK(from(first(y0, cons(y1, y2))))) MARK(cons(from(first(first(y0, y1), y2)), z1)) -> c11(MARK(from(first(first(y0, y1), y2)))) MARK(cons(from(first(from(y0), y1)), z1)) -> c11(MARK(from(first(from(y0), y1)))) MARK(cons(from(first(0, y0)), z1)) -> c11(MARK(from(first(0, y0)))) MARK(cons(from(first(nil, y0)), z1)) -> c11(MARK(from(first(nil, y0)))) MARK(cons(from(first(s(y0), y1)), z1)) -> c11(MARK(from(first(s(y0), y1)))) MARK(cons(from(first(cons(y0, y1), y2)), z1)) -> c11(MARK(from(first(cons(y0, y1), y2)))) MARK(cons(from(from(y0)), z1)) -> c11(MARK(from(from(y0)))) MARK(cons(from(from(first(y0, y1))), z1)) -> c11(MARK(from(from(first(y0, y1))))) MARK(cons(from(from(from(y0))), z1)) -> c11(MARK(from(from(from(y0))))) MARK(cons(from(from(s(y0))), z1)) -> c11(MARK(from(from(s(y0))))) MARK(cons(from(from(cons(y0, y1))), z1)) -> c11(MARK(from(from(cons(y0, y1))))) MARK(cons(from(from(0)), z1)) -> c11(MARK(from(from(0)))) MARK(cons(from(from(nil)), z1)) -> c11(MARK(from(from(nil)))) MARK(cons(s(s(y0)), z1)) -> c11(MARK(s(s(y0)))) MARK(cons(s(cons(y0, y1)), z1)) -> c11(MARK(s(cons(y0, y1)))) MARK(cons(s(first(y0, 0)), z1)) -> c11(MARK(s(first(y0, 0)))) MARK(cons(s(first(y0, nil)), z1)) -> c11(MARK(s(first(y0, nil)))) MARK(cons(s(first(y0, s(y1))), z1)) -> c11(MARK(s(first(y0, s(y1))))) MARK(cons(s(first(cons(y0, y1), y2)), z1)) -> c11(MARK(s(first(cons(y0, y1), y2)))) MARK(cons(s(first(0, y0)), z1)) -> c11(MARK(s(first(0, y0)))) MARK(cons(s(first(nil, y0)), z1)) -> c11(MARK(s(first(nil, y0)))) MARK(cons(s(first(y0, first(y1, first(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, first(y2, y3)))))) MARK(cons(s(first(y0, first(y1, from(y2)))), z1)) -> c11(MARK(s(first(y0, first(y1, from(y2)))))) MARK(cons(s(first(y0, first(y1, 0))), z1)) -> c11(MARK(s(first(y0, first(y1, 0))))) MARK(cons(s(first(y0, first(y1, nil))), z1)) -> c11(MARK(s(first(y0, first(y1, nil))))) MARK(cons(s(first(y0, first(y1, s(y2)))), z1)) -> c11(MARK(s(first(y0, first(y1, s(y2)))))) MARK(cons(s(first(y0, first(y1, cons(y2, y3)))), z1)) -> c11(MARK(s(first(y0, first(y1, cons(y2, y3)))))) MARK(cons(s(first(y0, first(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, first(first(y1, y2), y3))))) MARK(cons(s(first(y0, first(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, first(from(y1), y2))))) MARK(cons(s(first(y0, first(0, y1))), z1)) -> c11(MARK(s(first(y0, first(0, y1))))) MARK(cons(s(first(y0, first(nil, y1))), z1)) -> c11(MARK(s(first(y0, first(nil, y1))))) MARK(cons(s(first(y0, first(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, first(s(y1), y2))))) MARK(cons(s(first(y0, first(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, first(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), first(y2, y3))))) MARK(cons(s(first(from(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), first(y1, y2))))) MARK(cons(s(first(s(y0), first(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), first(y1, y2))))) MARK(cons(s(first(y0, first(y1, y2))), z1)) -> c11(MARK(s(first(y0, first(y1, y2))))) MARK(cons(s(first(cons(y0, y1), first(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), first(y2, y3))))) MARK(cons(s(first(y0, from(y1))), z1)) -> c11(MARK(s(first(y0, from(y1))))) MARK(cons(s(first(y0, from(first(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(first(y1, y2)))))) MARK(cons(s(first(y0, from(from(y1)))), z1)) -> c11(MARK(s(first(y0, from(from(y1)))))) MARK(cons(s(first(y0, from(0))), z1)) -> c11(MARK(s(first(y0, from(0))))) MARK(cons(s(first(y0, from(nil))), z1)) -> c11(MARK(s(first(y0, from(nil))))) MARK(cons(s(first(y0, from(s(y1)))), z1)) -> c11(MARK(s(first(y0, from(s(y1)))))) MARK(cons(s(first(y0, from(cons(y1, y2)))), z1)) -> c11(MARK(s(first(y0, from(cons(y1, y2)))))) MARK(cons(s(first(first(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), from(y2))))) MARK(cons(s(first(from(y0), from(y1))), z1)) -> c11(MARK(s(first(from(y0), from(y1))))) MARK(cons(s(first(s(y0), from(y1))), z1)) -> c11(MARK(s(first(s(y0), from(y1))))) MARK(cons(s(first(cons(y0, y1), from(y2))), z1)) -> c11(MARK(s(first(cons(y0, y1), from(y2))))) MARK(cons(s(first(y0, cons(first(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(first(y1, y2), y3))))) MARK(cons(s(first(y0, cons(from(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(from(y1), y2))))) MARK(cons(s(first(y0, cons(s(y1), y2))), z1)) -> c11(MARK(s(first(y0, cons(s(y1), y2))))) MARK(cons(s(first(y0, cons(cons(y1, y2), y3))), z1)) -> c11(MARK(s(first(y0, cons(cons(y1, y2), y3))))) MARK(cons(s(first(first(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(first(y0, y1), cons(y2, y3))))) MARK(cons(s(first(from(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(from(y0), cons(y1, y2))))) MARK(cons(s(first(s(y0), cons(y1, y2))), z1)) -> c11(MARK(s(first(s(y0), cons(y1, y2))))) MARK(cons(s(first(cons(y0, y1), cons(y2, y3))), z1)) -> c11(MARK(s(first(cons(y0, y1), cons(y2, y3))))) MARK(cons(s(first(first(y0, first(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, first(y1, y2)), y3)))) MARK(cons(s(first(first(y0, from(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, from(y1)), y2)))) MARK(cons(s(first(first(y0, 0), y1)), z1)) -> c11(MARK(s(first(first(y0, 0), y1)))) MARK(cons(s(first(first(y0, nil), y1)), z1)) -> c11(MARK(s(first(first(y0, nil), y1)))) MARK(cons(s(first(first(y0, s(y1)), y2)), z1)) -> c11(MARK(s(first(first(y0, s(y1)), y2)))) MARK(cons(s(first(first(y0, cons(y1, y2)), y3)), z1)) -> c11(MARK(s(first(first(y0, cons(y1, y2)), y3)))) MARK(cons(s(first(first(first(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(first(y0, y1), y2), y3)))) MARK(cons(s(first(first(from(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(from(y0), y1), y2)))) MARK(cons(s(first(first(0, y0), y1)), z1)) -> c11(MARK(s(first(first(0, y0), y1)))) MARK(cons(s(first(first(nil, y0), y1)), z1)) -> c11(MARK(s(first(first(nil, y0), y1)))) MARK(cons(s(first(first(s(y0), y1), y2)), z1)) -> c11(MARK(s(first(first(s(y0), y1), y2)))) MARK(cons(s(first(first(cons(y0, y1), y2), y3)), z1)) -> c11(MARK(s(first(first(cons(y0, y1), y2), y3)))) MARK(cons(s(first(first(y0, y1), 0)), z1)) -> c11(MARK(s(first(first(y0, y1), 0)))) MARK(cons(s(first(first(y0, y1), nil)), z1)) -> c11(MARK(s(first(first(y0, y1), nil)))) MARK(cons(s(first(first(y0, y1), s(y2))), z1)) -> c11(MARK(s(first(first(y0, y1), s(y2))))) MARK(cons(s(first(first(y0, y1), y2)), z1)) -> c11(MARK(s(first(first(y0, y1), y2)))) MARK(cons(s(first(from(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(first(y0, y1)), y2)))) MARK(cons(s(first(from(from(y0)), y1)), z1)) -> c11(MARK(s(first(from(from(y0)), y1)))) MARK(cons(s(first(from(s(y0)), y1)), z1)) -> c11(MARK(s(first(from(s(y0)), y1)))) MARK(cons(s(first(from(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(from(cons(y0, y1)), y2)))) MARK(cons(s(first(from(y0), y1)), z1)) -> c11(MARK(s(first(from(y0), y1)))) MARK(cons(s(first(from(y0), 0)), z1)) -> c11(MARK(s(first(from(y0), 0)))) MARK(cons(s(first(from(y0), nil)), z1)) -> c11(MARK(s(first(from(y0), nil)))) MARK(cons(s(first(from(y0), s(y1))), z1)) -> c11(MARK(s(first(from(y0), s(y1))))) MARK(cons(s(first(s(first(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(first(y0, y1)), y2)))) MARK(cons(s(first(s(from(y0)), y1)), z1)) -> c11(MARK(s(first(s(from(y0)), y1)))) MARK(cons(s(first(s(0), y0)), z1)) -> c11(MARK(s(first(s(0), y0)))) MARK(cons(s(first(s(nil), y0)), z1)) -> c11(MARK(s(first(s(nil), y0)))) MARK(cons(s(first(s(s(y0)), y1)), z1)) -> c11(MARK(s(first(s(s(y0)), y1)))) MARK(cons(s(first(s(cons(y0, y1)), y2)), z1)) -> c11(MARK(s(first(s(cons(y0, y1)), y2)))) MARK(cons(s(first(s(y0), y1)), z1)) -> c11(MARK(s(first(s(y0), y1)))) MARK(cons(s(first(s(y0), 0)), z1)) -> c11(MARK(s(first(s(y0), 0)))) MARK(cons(s(first(s(y0), nil)), z1)) -> c11(MARK(s(first(s(y0), nil)))) MARK(cons(s(first(s(y0), s(y1))), z1)) -> c11(MARK(s(first(s(y0), s(y1))))) MARK(cons(s(first(0, first(y0, y1))), z1)) -> c11(MARK(s(first(0, first(y0, y1))))) MARK(cons(s(first(nil, first(y0, y1))), z1)) -> c11(MARK(s(first(nil, first(y0, y1))))) MARK(cons(s(first(0, from(y0))), z1)) -> c11(MARK(s(first(0, from(y0))))) MARK(cons(s(first(nil, from(y0))), z1)) -> c11(MARK(s(first(nil, from(y0))))) MARK(cons(s(first(y0, cons(y1, y2))), z1)) -> c11(MARK(s(first(y0, cons(y1, y2))))) MARK(cons(s(first(0, cons(y0, y1))), z1)) -> c11(MARK(s(first(0, cons(y0, y1))))) MARK(cons(s(first(nil, cons(y0, y1))), z1)) -> c11(MARK(s(first(nil, cons(y0, y1))))) MARK(cons(s(first(from(0), y0)), z1)) -> c11(MARK(s(first(from(0), y0)))) MARK(cons(s(first(from(nil), y0)), z1)) -> c11(MARK(s(first(from(nil), y0)))) MARK(cons(s(first(y0, cons(0, y1))), z1)) -> c11(MARK(s(first(y0, cons(0, y1))))) MARK(cons(s(first(y0, cons(nil, y1))), z1)) -> c11(MARK(s(first(y0, cons(nil, y1))))) MARK(cons(s(from(s(y0))), z1)) -> c11(MARK(s(from(s(y0))))) MARK(cons(s(from(cons(y0, y1))), z1)) -> c11(MARK(s(from(cons(y0, y1))))) MARK(cons(s(from(first(y0, y1))), z1)) -> c11(MARK(s(from(first(y0, y1))))) MARK(cons(s(from(first(y0, first(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, first(y1, y2)))))) MARK(cons(s(from(first(y0, from(y1)))), z1)) -> c11(MARK(s(from(first(y0, from(y1)))))) MARK(cons(s(from(first(y0, 0))), z1)) -> c11(MARK(s(from(first(y0, 0))))) MARK(cons(s(from(first(y0, nil))), z1)) -> c11(MARK(s(from(first(y0, nil))))) MARK(cons(s(from(first(y0, s(y1)))), z1)) -> c11(MARK(s(from(first(y0, s(y1)))))) MARK(cons(s(from(first(y0, cons(y1, y2)))), z1)) -> c11(MARK(s(from(first(y0, cons(y1, y2)))))) MARK(cons(s(from(first(first(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(first(y0, y1), y2))))) MARK(cons(s(from(first(from(y0), y1))), z1)) -> c11(MARK(s(from(first(from(y0), y1))))) MARK(cons(s(from(first(0, y0))), z1)) -> c11(MARK(s(from(first(0, y0))))) MARK(cons(s(from(first(nil, y0))), z1)) -> c11(MARK(s(from(first(nil, y0))))) MARK(cons(s(from(first(s(y0), y1))), z1)) -> c11(MARK(s(from(first(s(y0), y1))))) MARK(cons(s(from(first(cons(y0, y1), y2))), z1)) -> c11(MARK(s(from(first(cons(y0, y1), y2))))) MARK(cons(s(from(from(y0))), z1)) -> c11(MARK(s(from(from(y0))))) MARK(cons(s(from(from(first(y0, y1)))), z1)) -> c11(MARK(s(from(from(first(y0, y1)))))) MARK(cons(s(from(from(from(y0)))), z1)) -> c11(MARK(s(from(from(from(y0)))))) MARK(cons(s(from(from(s(y0)))), z1)) -> c11(MARK(s(from(from(s(y0)))))) MARK(cons(s(from(from(cons(y0, y1)))), z1)) -> c11(MARK(s(from(from(cons(y0, y1)))))) MARK(cons(s(from(from(0))), z1)) -> c11(MARK(s(from(from(0))))) MARK(cons(s(from(from(nil))), z1)) -> c11(MARK(s(from(from(nil))))) MARK(first(first(y0, 0), 0)) -> c5(MARK(first(y0, 0))) MARK(first(first(y0, nil), 0)) -> c5(MARK(first(y0, nil))) MARK(first(first(y0, s(y1)), 0)) -> c5(MARK(first(y0, s(y1)))) MARK(first(first(cons(y0, y1), y2), 0)) -> c5(MARK(first(cons(y0, y1), y2))) MARK(first(first(0, y0), 0)) -> c5(MARK(first(0, y0))) MARK(first(first(nil, y0), 0)) -> c5(MARK(first(nil, y0))) MARK(first(first(y0, first(y1, first(y2, y3))), 0)) -> c5(MARK(first(y0, first(y1, first(y2, y3))))) MARK(first(first(y0, first(y1, from(y2))), 0)) -> c5(MARK(first(y0, first(y1, from(y2))))) MARK(first(first(y0, first(y1, 0)), 0)) -> c5(MARK(first(y0, first(y1, 0)))) MARK(first(first(y0, first(y1, nil)), 0)) -> c5(MARK(first(y0, first(y1, nil)))) MARK(first(first(y0, first(y1, s(y2))), 0)) -> c5(MARK(first(y0, first(y1, s(y2))))) MARK(first(first(y0, first(y1, cons(y2, y3))), 0)) -> c5(MARK(first(y0, first(y1, cons(y2, y3))))) MARK(first(first(y0, first(first(y1, y2), y3)), 0)) -> c5(MARK(first(y0, first(first(y1, y2), y3)))) MARK(first(first(y0, first(from(y1), y2)), 0)) -> c5(MARK(first(y0, first(from(y1), y2)))) MARK(first(first(y0, first(0, y1)), 0)) -> c5(MARK(first(y0, first(0, y1)))) MARK(first(first(y0, first(nil, y1)), 0)) -> c5(MARK(first(y0, first(nil, y1)))) MARK(first(first(y0, first(s(y1), y2)), 0)) -> c5(MARK(first(y0, first(s(y1), y2)))) MARK(first(first(y0, first(cons(y1, y2), y3)), 0)) -> c5(MARK(first(y0, first(cons(y1, y2), y3)))) MARK(first(first(first(y0, y1), first(y2, y3)), 0)) -> c5(MARK(first(first(y0, y1), first(y2, y3)))) MARK(first(first(from(y0), first(y1, y2)), 0)) -> c5(MARK(first(from(y0), first(y1, y2)))) MARK(first(first(s(y0), first(y1, y2)), 0)) -> c5(MARK(first(s(y0), first(y1, y2)))) MARK(first(first(y0, first(y1, y2)), 0)) -> c5(MARK(first(y0, first(y1, y2)))) MARK(first(first(cons(y0, y1), first(y2, y3)), 0)) -> c5(MARK(first(cons(y0, y1), first(y2, y3)))) MARK(first(first(y0, from(y1)), 0)) -> c5(MARK(first(y0, from(y1)))) MARK(first(first(y0, from(first(y1, y2))), 0)) -> c5(MARK(first(y0, from(first(y1, y2))))) MARK(first(first(y0, from(from(y1))), 0)) -> c5(MARK(first(y0, from(from(y1))))) MARK(first(first(y0, from(0)), 0)) -> c5(MARK(first(y0, from(0)))) MARK(first(first(y0, from(nil)), 0)) -> c5(MARK(first(y0, from(nil)))) MARK(first(first(y0, from(s(y1))), 0)) -> c5(MARK(first(y0, from(s(y1))))) MARK(first(first(y0, from(cons(y1, y2))), 0)) -> c5(MARK(first(y0, from(cons(y1, y2))))) MARK(first(first(first(y0, y1), from(y2)), 0)) -> c5(MARK(first(first(y0, y1), from(y2)))) MARK(first(first(from(y0), from(y1)), 0)) -> c5(MARK(first(from(y0), from(y1)))) MARK(first(first(s(y0), from(y1)), 0)) -> c5(MARK(first(s(y0), from(y1)))) MARK(first(first(cons(y0, y1), from(y2)), 0)) -> c5(MARK(first(cons(y0, y1), from(y2)))) MARK(first(first(y0, cons(first(y1, y2), y3)), 0)) -> c5(MARK(first(y0, cons(first(y1, y2), y3)))) MARK(first(first(y0, cons(from(y1), y2)), 0)) -> c5(MARK(first(y0, cons(from(y1), y2)))) MARK(first(first(y0, cons(s(y1), y2)), 0)) -> c5(MARK(first(y0, cons(s(y1), y2)))) MARK(first(first(y0, cons(cons(y1, y2), y3)), 0)) -> c5(MARK(first(y0, cons(cons(y1, y2), y3)))) MARK(first(first(first(y0, y1), cons(y2, y3)), 0)) -> c5(MARK(first(first(y0, y1), cons(y2, y3)))) MARK(first(first(from(y0), cons(y1, y2)), 0)) -> c5(MARK(first(from(y0), cons(y1, y2)))) MARK(first(first(s(y0), cons(y1, y2)), 0)) -> c5(MARK(first(s(y0), cons(y1, y2)))) MARK(first(first(cons(y0, y1), cons(y2, y3)), 0)) -> c5(MARK(first(cons(y0, y1), cons(y2, y3)))) MARK(first(first(first(y0, first(y1, y2)), y3), 0)) -> c5(MARK(first(first(y0, first(y1, y2)), y3))) MARK(first(first(first(y0, from(y1)), y2), 0)) -> c5(MARK(first(first(y0, from(y1)), y2))) MARK(first(first(first(y0, 0), y1), 0)) -> c5(MARK(first(first(y0, 0), y1))) MARK(first(first(first(y0, nil), y1), 0)) -> c5(MARK(first(first(y0, nil), y1))) MARK(first(first(first(y0, s(y1)), y2), 0)) -> c5(MARK(first(first(y0, s(y1)), y2))) MARK(first(first(first(y0, cons(y1, y2)), y3), 0)) -> c5(MARK(first(first(y0, cons(y1, y2)), y3))) MARK(first(first(first(first(y0, y1), y2), y3), 0)) -> c5(MARK(first(first(first(y0, y1), y2), y3))) MARK(first(first(first(from(y0), y1), y2), 0)) -> c5(MARK(first(first(from(y0), y1), y2))) MARK(first(first(first(0, y0), y1), 0)) -> c5(MARK(first(first(0, y0), y1))) MARK(first(first(first(nil, y0), y1), 0)) -> c5(MARK(first(first(nil, y0), y1))) MARK(first(first(first(s(y0), y1), y2), 0)) -> c5(MARK(first(first(s(y0), y1), y2))) MARK(first(first(first(cons(y0, y1), y2), y3), 0)) -> c5(MARK(first(first(cons(y0, y1), y2), y3))) MARK(first(first(first(y0, y1), 0), 0)) -> c5(MARK(first(first(y0, y1), 0))) MARK(first(first(first(y0, y1), nil), 0)) -> c5(MARK(first(first(y0, y1), nil))) MARK(first(first(first(y0, y1), s(y2)), 0)) -> c5(MARK(first(first(y0, y1), s(y2)))) MARK(first(first(first(y0, y1), y2), 0)) -> c5(MARK(first(first(y0, y1), y2))) MARK(first(first(from(first(y0, y1)), y2), 0)) -> c5(MARK(first(from(first(y0, y1)), y2))) MARK(first(first(from(from(y0)), y1), 0)) -> c5(MARK(first(from(from(y0)), y1))) MARK(first(first(from(s(y0)), y1), 0)) -> c5(MARK(first(from(s(y0)), y1))) MARK(first(first(from(cons(y0, y1)), y2), 0)) -> c5(MARK(first(from(cons(y0, y1)), y2))) MARK(first(first(from(y0), y1), 0)) -> c5(MARK(first(from(y0), y1))) MARK(first(first(from(y0), 0), 0)) -> c5(MARK(first(from(y0), 0))) MARK(first(first(from(y0), nil), 0)) -> c5(MARK(first(from(y0), nil))) MARK(first(first(from(y0), s(y1)), 0)) -> c5(MARK(first(from(y0), s(y1)))) MARK(first(first(s(first(y0, y1)), y2), 0)) -> c5(MARK(first(s(first(y0, y1)), y2))) MARK(first(first(s(from(y0)), y1), 0)) -> c5(MARK(first(s(from(y0)), y1))) MARK(first(first(s(s(y0)), y1), 0)) -> c5(MARK(first(s(s(y0)), y1))) MARK(first(first(s(cons(y0, y1)), y2), 0)) -> c5(MARK(first(s(cons(y0, y1)), y2))) MARK(first(first(s(y0), y1), 0)) -> c5(MARK(first(s(y0), y1))) MARK(first(first(s(y0), 0), 0)) -> c5(MARK(first(s(y0), 0))) MARK(first(first(s(y0), nil), 0)) -> c5(MARK(first(s(y0), nil))) MARK(first(first(s(y0), s(y1)), 0)) -> c5(MARK(first(s(y0), s(y1)))) MARK(first(first(0, first(y0, y1)), 0)) -> c5(MARK(first(0, first(y0, y1)))) MARK(first(first(nil, first(y0, y1)), 0)) -> c5(MARK(first(nil, first(y0, y1)))) MARK(first(first(0, from(y0)), 0)) -> c5(MARK(first(0, from(y0)))) MARK(first(first(nil, from(y0)), 0)) -> c5(MARK(first(nil, from(y0)))) MARK(first(first(y0, cons(y1, y2)), 0)) -> c5(MARK(first(y0, cons(y1, y2)))) MARK(first(first(0, cons(y0, y1)), 0)) -> c5(MARK(first(0, cons(y0, y1)))) MARK(first(first(nil, cons(y0, y1)), 0)) -> c5(MARK(first(nil, cons(y0, y1)))) MARK(first(first(from(0), y0), 0)) -> c5(MARK(first(from(0), y0))) MARK(first(first(from(nil), y0), 0)) -> c5(MARK(first(from(nil), y0))) MARK(first(first(s(0), y0), 0)) -> c5(MARK(first(s(0), y0))) MARK(first(first(s(nil), y0), 0)) -> c5(MARK(first(s(nil), y0))) MARK(first(first(y0, cons(0, y1)), 0)) -> c5(MARK(first(y0, cons(0, y1)))) MARK(first(first(y0, cons(nil, y1)), 0)) -> c5(MARK(first(y0, cons(nil, y1)))) MARK(first(from(s(y0)), 0)) -> c5(MARK(from(s(y0)))) MARK(first(from(cons(y0, y1)), 0)) -> c5(MARK(from(cons(y0, y1)))) MARK(first(from(first(y0, y1)), 0)) -> c5(MARK(from(first(y0, y1)))) MARK(first(from(first(y0, first(y1, y2))), 0)) -> c5(MARK(from(first(y0, first(y1, y2))))) MARK(first(from(first(y0, from(y1))), 0)) -> c5(MARK(from(first(y0, from(y1))))) MARK(first(from(first(y0, 0)), 0)) -> c5(MARK(from(first(y0, 0)))) MARK(first(from(first(y0, nil)), 0)) -> c5(MARK(from(first(y0, nil)))) MARK(first(from(first(y0, s(y1))), 0)) -> c5(MARK(from(first(y0, s(y1))))) MARK(first(from(first(y0, cons(y1, y2))), 0)) -> c5(MARK(from(first(y0, cons(y1, y2))))) MARK(first(from(first(first(y0, y1), y2)), 0)) -> c5(MARK(from(first(first(y0, y1), y2)))) MARK(first(from(first(from(y0), y1)), 0)) -> c5(MARK(from(first(from(y0), y1)))) MARK(first(from(first(0, y0)), 0)) -> c5(MARK(from(first(0, y0)))) MARK(first(from(first(nil, y0)), 0)) -> c5(MARK(from(first(nil, y0)))) MARK(first(from(first(s(y0), y1)), 0)) -> c5(MARK(from(first(s(y0), y1)))) MARK(first(from(first(cons(y0, y1), y2)), 0)) -> c5(MARK(from(first(cons(y0, y1), y2)))) MARK(first(from(from(y0)), 0)) -> c5(MARK(from(from(y0)))) MARK(first(from(from(first(y0, y1))), 0)) -> c5(MARK(from(from(first(y0, y1))))) MARK(first(from(from(from(y0))), 0)) -> c5(MARK(from(from(from(y0))))) MARK(first(from(from(s(y0))), 0)) -> c5(MARK(from(from(s(y0))))) MARK(first(from(from(cons(y0, y1))), 0)) -> c5(MARK(from(from(cons(y0, y1))))) MARK(first(from(from(0)), 0)) -> c5(MARK(from(from(0)))) MARK(first(from(from(nil)), 0)) -> c5(MARK(from(from(nil)))) MARK(first(s(s(y0)), 0)) -> c5(MARK(s(s(y0)))) MARK(first(s(cons(y0, y1)), 0)) -> c5(MARK(s(cons(y0, y1)))) MARK(first(s(first(y0, 0)), 0)) -> c5(MARK(s(first(y0, 0)))) MARK(first(s(first(y0, nil)), 0)) -> c5(MARK(s(first(y0, nil)))) MARK(first(s(first(y0, s(y1))), 0)) -> c5(MARK(s(first(y0, s(y1))))) MARK(first(s(first(cons(y0, y1), y2)), 0)) -> c5(MARK(s(first(cons(y0, y1), y2)))) MARK(first(s(first(0, y0)), 0)) -> c5(MARK(s(first(0, y0)))) MARK(first(s(first(nil, y0)), 0)) -> c5(MARK(s(first(nil, y0)))) MARK(first(s(first(y0, first(y1, first(y2, y3)))), 0)) -> c5(MARK(s(first(y0, first(y1, first(y2, y3)))))) MARK(first(s(first(y0, first(y1, from(y2)))), 0)) -> c5(MARK(s(first(y0, first(y1, from(y2)))))) MARK(first(s(first(y0, first(y1, 0))), 0)) -> c5(MARK(s(first(y0, first(y1, 0))))) MARK(first(s(first(y0, first(y1, nil))), 0)) -> c5(MARK(s(first(y0, first(y1, nil))))) MARK(first(s(first(y0, first(y1, s(y2)))), 0)) -> c5(MARK(s(first(y0, first(y1, s(y2)))))) MARK(first(s(first(y0, first(y1, cons(y2, y3)))), 0)) -> c5(MARK(s(first(y0, first(y1, cons(y2, y3)))))) MARK(first(s(first(y0, first(first(y1, y2), y3))), 0)) -> c5(MARK(s(first(y0, first(first(y1, y2), y3))))) MARK(first(s(first(y0, first(from(y1), y2))), 0)) -> c5(MARK(s(first(y0, first(from(y1), y2))))) MARK(first(s(first(y0, first(0, y1))), 0)) -> c5(MARK(s(first(y0, first(0, y1))))) MARK(first(s(first(y0, first(nil, y1))), 0)) -> c5(MARK(s(first(y0, first(nil, y1))))) MARK(first(s(first(y0, first(s(y1), y2))), 0)) -> c5(MARK(s(first(y0, first(s(y1), y2))))) MARK(first(s(first(y0, first(cons(y1, y2), y3))), 0)) -> c5(MARK(s(first(y0, first(cons(y1, y2), y3))))) MARK(first(s(first(first(y0, y1), first(y2, y3))), 0)) -> c5(MARK(s(first(first(y0, y1), first(y2, y3))))) MARK(first(s(first(from(y0), first(y1, y2))), 0)) -> c5(MARK(s(first(from(y0), first(y1, y2))))) MARK(first(s(first(s(y0), first(y1, y2))), 0)) -> c5(MARK(s(first(s(y0), first(y1, y2))))) MARK(first(s(first(y0, first(y1, y2))), 0)) -> c5(MARK(s(first(y0, first(y1, y2))))) MARK(first(s(first(cons(y0, y1), first(y2, y3))), 0)) -> c5(MARK(s(first(cons(y0, y1), first(y2, y3))))) MARK(first(s(first(y0, from(y1))), 0)) -> c5(MARK(s(first(y0, from(y1))))) MARK(first(s(first(y0, from(first(y1, y2)))), 0)) -> c5(MARK(s(first(y0, from(first(y1, y2)))))) MARK(first(s(first(y0, from(from(y1)))), 0)) -> c5(MARK(s(first(y0, from(from(y1)))))) MARK(first(s(first(y0, from(0))), 0)) -> c5(MARK(s(first(y0, from(0))))) MARK(first(s(first(y0, from(nil))), 0)) -> c5(MARK(s(first(y0, from(nil))))) MARK(first(s(first(y0, from(s(y1)))), 0)) -> c5(MARK(s(first(y0, from(s(y1)))))) MARK(first(s(first(y0, from(cons(y1, y2)))), 0)) -> c5(MARK(s(first(y0, from(cons(y1, y2)))))) MARK(first(s(first(first(y0, y1), from(y2))), 0)) -> c5(MARK(s(first(first(y0, y1), from(y2))))) MARK(first(s(first(from(y0), from(y1))), 0)) -> c5(MARK(s(first(from(y0), from(y1))))) MARK(first(s(first(s(y0), from(y1))), 0)) -> c5(MARK(s(first(s(y0), from(y1))))) MARK(first(s(first(cons(y0, y1), from(y2))), 0)) -> c5(MARK(s(first(cons(y0, y1), from(y2))))) MARK(first(s(first(y0, cons(first(y1, y2), y3))), 0)) -> c5(MARK(s(first(y0, cons(first(y1, y2), y3))))) MARK(first(s(first(y0, cons(from(y1), y2))), 0)) -> c5(MARK(s(first(y0, cons(from(y1), y2))))) MARK(first(s(first(y0, cons(s(y1), y2))), 0)) -> c5(MARK(s(first(y0, cons(s(y1), y2))))) MARK(first(s(first(y0, cons(cons(y1, y2), y3))), 0)) -> c5(MARK(s(first(y0, cons(cons(y1, y2), y3))))) MARK(first(s(first(first(y0, y1), cons(y2, y3))), 0)) -> c5(MARK(s(first(first(y0, y1), cons(y2, y3))))) MARK(first(s(first(from(y0), cons(y1, y2))), 0)) -> c5(MARK(s(first(from(y0), cons(y1, y2))))) MARK(first(s(first(s(y0), cons(y1, y2))), 0)) -> c5(MARK(s(first(s(y0), cons(y1, y2))))) MARK(first(s(first(cons(y0, y1), cons(y2, y3))), 0)) -> c5(MARK(s(first(cons(y0, y1), cons(y2, y3))))) MARK(first(s(first(first(y0, first(y1, y2)), y3)), 0)) -> c5(MARK(s(first(first(y0, first(y1, y2)), y3)))) MARK(first(s(first(first(y0, from(y1)), y2)), 0)) -> c5(MARK(s(first(first(y0, from(y1)), y2)))) MARK(first(s(first(first(y0, 0), y1)), 0)) -> c5(MARK(s(first(first(y0, 0), y1)))) MARK(first(s(first(first(y0, nil), y1)), 0)) -> c5(MARK(s(first(first(y0, nil), y1)))) MARK(first(s(first(first(y0, s(y1)), y2)), 0)) -> c5(MARK(s(first(first(y0, s(y1)), y2)))) MARK(first(s(first(first(y0, cons(y1, y2)), y3)), 0)) -> c5(MARK(s(first(first(y0, cons(y1, y2)), y3)))) MARK(first(s(first(first(first(y0, y1), y2), y3)), 0)) -> c5(MARK(s(first(first(first(y0, y1), y2), y3)))) MARK(first(s(first(first(from(y0), y1), y2)), 0)) -> c5(MARK(s(first(first(from(y0), y1), y2)))) MARK(first(s(first(first(0, y0), y1)), 0)) -> c5(MARK(s(first(first(0, y0), y1)))) MARK(first(s(first(first(nil, y0), y1)), 0)) -> c5(MARK(s(first(first(nil, y0), y1)))) MARK(first(s(first(first(s(y0), y1), y2)), 0)) -> c5(MARK(s(first(first(s(y0), y1), y2)))) MARK(first(s(first(first(cons(y0, y1), y2), y3)), 0)) -> c5(MARK(s(first(first(cons(y0, y1), y2), y3)))) MARK(first(s(first(first(y0, y1), 0)), 0)) -> c5(MARK(s(first(first(y0, y1), 0)))) MARK(first(s(first(first(y0, y1), nil)), 0)) -> c5(MARK(s(first(first(y0, y1), nil)))) MARK(first(s(first(first(y0, y1), s(y2))), 0)) -> c5(MARK(s(first(first(y0, y1), s(y2))))) MARK(first(s(first(first(y0, y1), y2)), 0)) -> c5(MARK(s(first(first(y0, y1), y2)))) MARK(first(s(first(from(first(y0, y1)), y2)), 0)) -> c5(MARK(s(first(from(first(y0, y1)), y2)))) MARK(first(s(first(from(from(y0)), y1)), 0)) -> c5(MARK(s(first(from(from(y0)), y1)))) MARK(first(s(first(from(s(y0)), y1)), 0)) -> c5(MARK(s(first(from(s(y0)), y1)))) MARK(first(s(first(from(cons(y0, y1)), y2)), 0)) -> c5(MARK(s(first(from(cons(y0, y1)), y2)))) MARK(first(s(first(from(y0), y1)), 0)) -> c5(MARK(s(first(from(y0), y1)))) MARK(first(s(first(from(y0), 0)), 0)) -> c5(MARK(s(first(from(y0), 0)))) MARK(first(s(first(from(y0), nil)), 0)) -> c5(MARK(s(first(from(y0), nil)))) MARK(first(s(first(from(y0), s(y1))), 0)) -> c5(MARK(s(first(from(y0), s(y1))))) MARK(first(s(first(s(first(y0, y1)), y2)), 0)) -> c5(MARK(s(first(s(first(y0, y1)), y2)))) MARK(first(s(first(s(from(y0)), y1)), 0)) -> c5(MARK(s(first(s(from(y0)), y1)))) MARK(first(s(first(s(0), y0)), 0)) -> c5(MARK(s(first(s(0), y0)))) MARK(first(s(first(s(nil), y0)), 0)) -> c5(MARK(s(first(s(nil), y0)))) MARK(first(s(first(s(s(y0)), y1)), 0)) -> c5(MARK(s(first(s(s(y0)), y1)))) MARK(first(s(first(s(cons(y0, y1)), y2)), 0)) -> c5(MARK(s(first(s(cons(y0, y1)), y2)))) MARK(first(s(first(s(y0), y1)), 0)) -> c5(MARK(s(first(s(y0), y1)))) MARK(first(s(first(s(y0), 0)), 0)) -> c5(MARK(s(first(s(y0), 0)))) MARK(first(s(first(s(y0), nil)), 0)) -> c5(MARK(s(first(s(y0), nil)))) MARK(first(s(first(s(y0), s(y1))), 0)) -> c5(MARK(s(first(s(y0), s(y1))))) MARK(first(s(first(0, first(y0, y1))), 0)) -> c5(MARK(s(first(0, first(y0, y1))))) MARK(first(s(first(nil, first(y0, y1))), 0)) -> c5(MARK(s(first(nil, first(y0, y1))))) MARK(first(s(first(0, from(y0))), 0)) -> c5(MARK(s(first(0, from(y0))))) MARK(first(s(first(nil, from(y0))), 0)) -> c5(MARK(s(first(nil, from(y0))))) MARK(first(s(first(y0, cons(y1, y2))), 0)) -> c5(MARK(s(first(y0, cons(y1, y2))))) MARK(first(s(first(0, cons(y0, y1))), 0)) -> c5(MARK(s(first(0, cons(y0, y1))))) MARK(first(s(first(nil, cons(y0, y1))), 0)) -> c5(MARK(s(first(nil, cons(y0, y1))))) MARK(first(s(first(from(0), y0)), 0)) -> c5(MARK(s(first(from(0), y0)))) MARK(first(s(first(from(nil), y0)), 0)) -> c5(MARK(s(first(from(nil), y0)))) MARK(first(s(first(y0, cons(0, y1))), 0)) -> c5(MARK(s(first(y0, cons(0, y1))))) MARK(first(s(first(y0, cons(nil, y1))), 0)) -> c5(MARK(s(first(y0, cons(nil, y1))))) MARK(first(s(from(s(y0))), 0)) -> c5(MARK(s(from(s(y0))))) MARK(first(s(from(cons(y0, y1))), 0)) -> c5(MARK(s(from(cons(y0, y1))))) MARK(first(s(from(first(y0, y1))), 0)) -> c5(MARK(s(from(first(y0, y1))))) MARK(first(s(from(first(y0, first(y1, y2)))), 0)) -> c5(MARK(s(from(first(y0, first(y1, y2)))))) MARK(first(s(from(first(y0, from(y1)))), 0)) -> c5(MARK(s(from(first(y0, from(y1)))))) MARK(first(s(from(first(y0, 0))), 0)) -> c5(MARK(s(from(first(y0, 0))))) MARK(first(s(from(first(y0, nil))), 0)) -> c5(MARK(s(from(first(y0, nil))))) MARK(first(s(from(first(y0, s(y1)))), 0)) -> c5(MARK(s(from(first(y0, s(y1)))))) MARK(first(s(from(first(y0, cons(y1, y2)))), 0)) -> c5(MARK(s(from(first(y0, cons(y1, y2)))))) MARK(first(s(from(first(first(y0, y1), y2))), 0)) -> c5(MARK(s(from(first(first(y0, y1), y2))))) MARK(first(s(from(first(from(y0), y1))), 0)) -> c5(MARK(s(from(first(from(y0), 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MARK(first(cons(s(first(from(y0), first(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(from(y0), first(y1, y2))), y3))) MARK(first(cons(s(first(s(y0), first(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(s(y0), first(y1, y2))), y3))) MARK(first(cons(s(first(y0, first(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, first(y1, y2))), y3))) MARK(first(cons(s(first(cons(y0, y1), first(y2, y3))), y4), 0)) -> c5(MARK(cons(s(first(cons(y0, y1), first(y2, y3))), y4))) MARK(first(cons(s(first(y0, from(y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, from(y1))), y2))) MARK(first(cons(s(first(y0, from(first(y1, y2)))), y3), 0)) -> c5(MARK(cons(s(first(y0, from(first(y1, y2)))), y3))) MARK(first(cons(s(first(y0, from(from(y1)))), y2), 0)) -> c5(MARK(cons(s(first(y0, from(from(y1)))), y2))) MARK(first(cons(s(first(y0, from(0))), y1), 0)) -> c5(MARK(cons(s(first(y0, from(0))), y1))) MARK(first(cons(s(first(y0, from(nil))), y1), 0)) -> c5(MARK(cons(s(first(y0, from(nil))), y1))) MARK(first(cons(s(first(y0, 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MARK(first(cons(s(first(y0, cons(cons(y1, y2), y3))), y4), 0)) -> c5(MARK(cons(s(first(y0, cons(cons(y1, y2), y3))), y4))) MARK(first(cons(s(first(first(y0, y1), cons(y2, y3))), y4), 0)) -> c5(MARK(cons(s(first(first(y0, y1), cons(y2, y3))), y4))) MARK(first(cons(s(first(from(y0), cons(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(from(y0), cons(y1, y2))), y3))) MARK(first(cons(s(first(s(y0), cons(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(s(y0), cons(y1, y2))), y3))) MARK(first(cons(s(first(cons(y0, y1), cons(y2, y3))), y4), 0)) -> c5(MARK(cons(s(first(cons(y0, y1), cons(y2, y3))), y4))) MARK(first(cons(s(first(first(y0, first(y1, y2)), y3)), y4), 0)) -> c5(MARK(cons(s(first(first(y0, first(y1, y2)), y3)), y4))) MARK(first(cons(s(first(first(y0, from(y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(y0, from(y1)), y2)), y3))) MARK(first(cons(s(first(first(y0, 0), y1)), y2), 0)) -> c5(MARK(cons(s(first(first(y0, 0), y1)), y2))) MARK(first(cons(s(first(first(y0, nil), y1)), y2), 0)) -> c5(MARK(cons(s(first(first(y0, nil), y1)), y2))) MARK(first(cons(s(first(first(y0, s(y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(y0, s(y1)), y2)), y3))) MARK(first(cons(s(first(first(y0, cons(y1, y2)), y3)), y4), 0)) -> c5(MARK(cons(s(first(first(y0, cons(y1, y2)), y3)), y4))) MARK(first(cons(s(first(first(first(y0, y1), y2), y3)), y4), 0)) -> c5(MARK(cons(s(first(first(first(y0, y1), y2), y3)), y4))) MARK(first(cons(s(first(first(from(y0), y1), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(from(y0), y1), y2)), y3))) MARK(first(cons(s(first(first(0, y0), y1)), y2), 0)) -> c5(MARK(cons(s(first(first(0, y0), y1)), y2))) MARK(first(cons(s(first(first(nil, y0), y1)), y2), 0)) -> c5(MARK(cons(s(first(first(nil, y0), y1)), y2))) MARK(first(cons(s(first(first(s(y0), y1), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(s(y0), y1), y2)), y3))) MARK(first(cons(s(first(first(cons(y0, y1), y2), y3)), y4), 0)) -> c5(MARK(cons(s(first(first(cons(y0, y1), y2), y3)), y4))) MARK(first(cons(s(first(first(y0, y1), 0)), y2), 0)) -> c5(MARK(cons(s(first(first(y0, y1), 0)), y2))) MARK(first(cons(s(first(first(y0, y1), nil)), y2), 0)) -> c5(MARK(cons(s(first(first(y0, y1), nil)), y2))) MARK(first(cons(s(first(first(y0, y1), s(y2))), y3), 0)) -> c5(MARK(cons(s(first(first(y0, y1), s(y2))), y3))) MARK(first(cons(s(first(first(y0, y1), y2)), y3), 0)) -> c5(MARK(cons(s(first(first(y0, y1), y2)), y3))) MARK(first(cons(s(first(from(first(y0, y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(from(first(y0, y1)), y2)), y3))) MARK(first(cons(s(first(from(from(y0)), y1)), y2), 0)) -> c5(MARK(cons(s(first(from(from(y0)), y1)), y2))) MARK(first(cons(s(first(from(s(y0)), y1)), y2), 0)) -> c5(MARK(cons(s(first(from(s(y0)), y1)), y2))) MARK(first(cons(s(first(from(cons(y0, y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(from(cons(y0, y1)), y2)), y3))) MARK(first(cons(s(first(from(y0), y1)), y2), 0)) -> c5(MARK(cons(s(first(from(y0), y1)), y2))) MARK(first(cons(s(first(from(y0), 0)), y1), 0)) -> c5(MARK(cons(s(first(from(y0), 0)), y1))) MARK(first(cons(s(first(from(y0), nil)), y1), 0)) -> c5(MARK(cons(s(first(from(y0), nil)), y1))) MARK(first(cons(s(first(from(y0), s(y1))), y2), 0)) -> c5(MARK(cons(s(first(from(y0), s(y1))), y2))) MARK(first(cons(s(first(s(first(y0, y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(s(first(y0, y1)), y2)), y3))) MARK(first(cons(s(first(s(from(y0)), y1)), y2), 0)) -> c5(MARK(cons(s(first(s(from(y0)), y1)), y2))) MARK(first(cons(s(first(s(0), y0)), y1), 0)) -> c5(MARK(cons(s(first(s(0), y0)), y1))) MARK(first(cons(s(first(s(nil), y0)), y1), 0)) -> c5(MARK(cons(s(first(s(nil), y0)), y1))) MARK(first(cons(s(first(s(s(y0)), y1)), y2), 0)) -> c5(MARK(cons(s(first(s(s(y0)), y1)), y2))) MARK(first(cons(s(first(s(cons(y0, y1)), y2)), y3), 0)) -> c5(MARK(cons(s(first(s(cons(y0, y1)), y2)), y3))) MARK(first(cons(s(first(s(y0), y1)), y2), 0)) -> c5(MARK(cons(s(first(s(y0), y1)), y2))) MARK(first(cons(s(first(s(y0), 0)), y1), 0)) -> c5(MARK(cons(s(first(s(y0), 0)), y1))) MARK(first(cons(s(first(s(y0), nil)), y1), 0)) -> c5(MARK(cons(s(first(s(y0), nil)), y1))) MARK(first(cons(s(first(s(y0), s(y1))), y2), 0)) -> c5(MARK(cons(s(first(s(y0), s(y1))), y2))) MARK(first(cons(s(first(0, first(y0, y1))), y2), 0)) -> c5(MARK(cons(s(first(0, first(y0, y1))), y2))) MARK(first(cons(s(first(nil, first(y0, y1))), y2), 0)) -> c5(MARK(cons(s(first(nil, first(y0, y1))), y2))) MARK(first(cons(s(first(0, from(y0))), y1), 0)) -> c5(MARK(cons(s(first(0, from(y0))), y1))) MARK(first(cons(s(first(nil, from(y0))), y1), 0)) -> c5(MARK(cons(s(first(nil, from(y0))), y1))) MARK(first(cons(s(first(y0, cons(y1, y2))), y3), 0)) -> c5(MARK(cons(s(first(y0, cons(y1, y2))), y3))) MARK(first(cons(s(first(0, cons(y0, y1))), y2), 0)) -> c5(MARK(cons(s(first(0, cons(y0, y1))), y2))) MARK(first(cons(s(first(nil, cons(y0, y1))), y2), 0)) -> c5(MARK(cons(s(first(nil, cons(y0, y1))), y2))) MARK(first(cons(s(first(from(0), y0)), y1), 0)) -> c5(MARK(cons(s(first(from(0), y0)), y1))) MARK(first(cons(s(first(from(nil), y0)), y1), 0)) -> c5(MARK(cons(s(first(from(nil), y0)), y1))) MARK(first(cons(s(first(y0, cons(0, y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, cons(0, y1))), y2))) MARK(first(cons(s(first(y0, cons(nil, y1))), y2), 0)) -> c5(MARK(cons(s(first(y0, cons(nil, y1))), y2))) MARK(first(cons(s(from(s(y0))), y1), 0)) -> c5(MARK(cons(s(from(s(y0))), y1))) MARK(first(cons(s(from(cons(y0, y1))), y2), 0)) -> c5(MARK(cons(s(from(cons(y0, y1))), y2))) MARK(first(cons(s(from(first(y0, y1))), y2), 0)) -> c5(MARK(cons(s(from(first(y0, y1))), y2))) MARK(first(cons(s(from(first(y0, first(y1, y2)))), y3), 0)) -> c5(MARK(cons(s(from(first(y0, first(y1, y2)))), y3))) MARK(first(cons(s(from(first(y0, from(y1)))), y2), 0)) -> c5(MARK(cons(s(from(first(y0, from(y1)))), y2))) MARK(first(cons(s(from(first(y0, 0))), y1), 0)) -> c5(MARK(cons(s(from(first(y0, 0))), y1))) MARK(first(cons(s(from(first(y0, nil))), y1), 0)) -> c5(MARK(cons(s(from(first(y0, nil))), y1))) MARK(first(cons(s(from(first(y0, s(y1)))), y2), 0)) -> c5(MARK(cons(s(from(first(y0, s(y1)))), y2))) MARK(first(cons(s(from(first(y0, cons(y1, y2)))), y3), 0)) -> c5(MARK(cons(s(from(first(y0, cons(y1, y2)))), y3))) MARK(first(cons(s(from(first(first(y0, y1), y2))), y3), 0)) -> c5(MARK(cons(s(from(first(first(y0, y1), y2))), y3))) MARK(first(cons(s(from(first(from(y0), y1))), y2), 0)) -> c5(MARK(cons(s(from(first(from(y0), y1))), y2))) MARK(first(cons(s(from(first(0, y0))), y1), 0)) -> c5(MARK(cons(s(from(first(0, y0))), y1))) MARK(first(cons(s(from(first(nil, y0))), y1), 0)) -> c5(MARK(cons(s(from(first(nil, y0))), y1))) MARK(first(cons(s(from(first(s(y0), y1))), y2), 0)) -> c5(MARK(cons(s(from(first(s(y0), y1))), y2))) MARK(first(cons(s(from(first(cons(y0, y1), y2))), y3), 0)) -> c5(MARK(cons(s(from(first(cons(y0, y1), y2))), y3))) MARK(first(cons(s(from(from(y0))), y1), 0)) -> c5(MARK(cons(s(from(from(y0))), y1))) MARK(first(cons(s(from(from(first(y0, y1)))), y2), 0)) -> c5(MARK(cons(s(from(from(first(y0, y1)))), y2))) MARK(first(cons(s(from(from(from(y0)))), y1), 0)) -> c5(MARK(cons(s(from(from(from(y0)))), y1))) MARK(first(cons(s(from(from(s(y0)))), y1), 0)) -> c5(MARK(cons(s(from(from(s(y0)))), y1))) MARK(first(cons(s(from(from(cons(y0, y1)))), y2), 0)) -> c5(MARK(cons(s(from(from(cons(y0, y1)))), y2))) MARK(first(cons(s(from(from(0))), y0), 0)) -> c5(MARK(cons(s(from(from(0))), y0))) MARK(first(cons(s(from(from(nil))), y0), 0)) -> c5(MARK(cons(s(from(from(nil))), y0))) K tuples:none Defined Rule Symbols: a__first_2, a__from_1, mark_1 Defined Pair Symbols: MARK_1, A__FIRST_2, A__FROM_1 Compound Symbols: c5_1, c6_1, c5_2, c6_2, c1_1, c3_1, c7_2, c7_1, c10_1, c11_1