/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 155 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 2625 ms] (14) BOUNDS(1, INF) (15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (16) CpxTRS (17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (18) CpxRelTRS (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxWeightedTrs (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxTypedWeightedTrs (23) CompletionProof [UPPER BOUND(ID), 0 ms] (24) CpxTypedWeightedCompleteTrs (25) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CpxTypedWeightedCompleteTrs (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxRNTS (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (36) CdtProblem (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (42) CdtProblem (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1 ms] (104) CdtProblem (105) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 320 ms] (106) CdtProblem (107) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1926 ms] (108) CdtProblem ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(a, f(a, f(a, f(x, b)))) -> f(f(a, f(a, f(a, x))), b) f(f(f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(a, f(a, f(a, f(x, b)))) -> f(f(a, f(a, f(a, x))), b) f(f(f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) The (relative) TRS S consists of the following rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(a, f(a, f(a, f(x, b)))) -> f(f(a, f(a, f(a, x))), b) f(f(f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) The (relative) TRS S consists of the following rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(a, f(a, f(a, f(x, b)))) -> f(f(a, f(a, f(a, x))), b) f(f(f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) The (relative) TRS S consists of the following rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b Rewrite Strategy: INNERMOST ---------------------------------------- (7) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(a, f(a, f(a, f(x, b)))) -> f(f(a, f(a, f(a, x))), b) f(f(f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) The (relative) TRS S consists of the following rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: f(a, f(a, f(a, f(x, b)))) -> f(f(a, f(a, f(a, x))), b) f(f(f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b Types: f :: a:b:cons_f -> a:b:cons_f -> a:b:cons_f a :: a:b:cons_f b :: a:b:cons_f encArg :: a:b:cons_f -> a:b:cons_f cons_f :: a:b:cons_f -> a:b:cons_f -> a:b:cons_f encode_f :: a:b:cons_f -> a:b:cons_f -> a:b:cons_f encode_a :: a:b:cons_f encode_b :: a:b:cons_f hole_a:b:cons_f1_0 :: a:b:cons_f gen_a:b:cons_f2_0 :: Nat -> a:b:cons_f ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: f, encArg They will be analysed ascendingly in the following order: f < encArg ---------------------------------------- (12) Obligation: Innermost TRS: Rules: f(a, f(a, f(a, f(x, b)))) -> f(f(a, f(a, f(a, x))), b) f(f(f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b Types: f :: a:b:cons_f -> a:b:cons_f -> a:b:cons_f a :: a:b:cons_f b :: a:b:cons_f encArg :: a:b:cons_f -> a:b:cons_f cons_f :: a:b:cons_f -> a:b:cons_f -> a:b:cons_f encode_f :: a:b:cons_f -> a:b:cons_f -> a:b:cons_f encode_a :: a:b:cons_f encode_b :: a:b:cons_f hole_a:b:cons_f1_0 :: a:b:cons_f gen_a:b:cons_f2_0 :: Nat -> a:b:cons_f Generator Equations: gen_a:b:cons_f2_0(0) <=> a gen_a:b:cons_f2_0(+(x, 1)) <=> cons_f(a, gen_a:b:cons_f2_0(x)) The following defined symbols remain to be analysed: f, encArg They will be analysed ascendingly in the following order: f < encArg ---------------------------------------- (13) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_a:b:cons_f2_0(n12_0)) -> *3_0, rt in Omega(0) Induction Base: encArg(gen_a:b:cons_f2_0(0)) Induction Step: encArg(gen_a:b:cons_f2_0(+(n12_0, 1))) ->_R^Omega(0) f(encArg(a), encArg(gen_a:b:cons_f2_0(n12_0))) ->_R^Omega(0) f(a, encArg(gen_a:b:cons_f2_0(n12_0))) ->_IH f(a, *3_0) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (14) BOUNDS(1, INF) ---------------------------------------- (15) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (16) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(a, f(a, f(a, f(x, b)))) -> f(f(a, f(a, f(a, x))), b) f(f(f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (17) NonCtorToCtorProof (UPPER BOUND(ID)) transformed non-ctor to ctor-system ---------------------------------------- (18) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: f(a, c_f(a, c_f(a, c_f(x, b)))) -> f(f(a, f(a, f(a, x))), b) f(c_f(c_f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) The (relative) TRS S consists of the following rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) encode_a -> a encode_b -> b f(x0, x1) -> c_f(x0, x1) Rewrite Strategy: INNERMOST ---------------------------------------- (19) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (20) 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: f(a, c_f(a, c_f(a, c_f(x, b)))) -> f(f(a, f(a, f(a, x))), b) [1] f(c_f(c_f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) [1] encArg(a) -> a [0] encArg(b) -> b [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_a -> a [0] encode_b -> b [0] f(x0, x1) -> c_f(x0, x1) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (21) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (22) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: f(a, c_f(a, c_f(a, c_f(x, b)))) -> f(f(a, f(a, f(a, x))), b) [1] f(c_f(c_f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) [1] encArg(a) -> a [0] encArg(b) -> b [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_a -> a [0] encode_b -> b [0] f(x0, x1) -> c_f(x0, x1) [0] The TRS has the following type information: f :: a:b:c_f:cons_f -> a:b:c_f:cons_f -> a:b:c_f:cons_f a :: a:b:c_f:cons_f c_f :: a:b:c_f:cons_f -> a:b:c_f:cons_f -> a:b:c_f:cons_f b :: a:b:c_f:cons_f encArg :: a:b:c_f:cons_f -> a:b:c_f:cons_f cons_f :: a:b:c_f:cons_f -> a:b:c_f:cons_f -> a:b:c_f:cons_f encode_f :: a:b:c_f:cons_f -> a:b:c_f:cons_f -> a:b:c_f:cons_f encode_a :: a:b:c_f:cons_f encode_b :: a:b:c_f:cons_f Rewrite Strategy: INNERMOST ---------------------------------------- (23) 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: encArg_1 encode_f_2 encode_a encode_b f_2 Due to the following rules being added: encArg(v0) -> null_encArg [0] encode_f(v0, v1) -> null_encode_f [0] encode_a -> null_encode_a [0] encode_b -> null_encode_b [0] f(v0, v1) -> null_f [0] And the following fresh constants: null_encArg, null_encode_f, null_encode_a, null_encode_b, null_f ---------------------------------------- (24) 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: f(a, c_f(a, c_f(a, c_f(x, b)))) -> f(f(a, f(a, f(a, x))), b) [1] f(c_f(c_f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) [1] encArg(a) -> a [0] encArg(b) -> b [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_a -> a [0] encode_b -> b [0] f(x0, x1) -> c_f(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_f(v0, v1) -> null_encode_f [0] encode_a -> null_encode_a [0] encode_b -> null_encode_b [0] f(v0, v1) -> null_f [0] The TRS has the following type information: f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f a :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f c_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f b :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encArg :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f cons_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_a :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_b :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encArg :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_a :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_b :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f Rewrite Strategy: INNERMOST ---------------------------------------- (25) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (26) 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: f(a, c_f(a, c_f(a, c_f(c_f(a, c_f(a, c_f(x', b))), b)))) -> f(f(a, f(a, f(f(a, f(a, f(a, x'))), b))), b) [2] f(a, c_f(a, c_f(a, c_f(x, b)))) -> f(f(a, f(a, c_f(a, x))), b) [1] f(a, c_f(a, c_f(a, c_f(x, b)))) -> f(f(a, f(a, null_f)), b) [1] f(c_f(c_f(a, c_f(c_f(a, x''), b)), b), b) -> f(f(a, f(f(f(a, f(f(x'', b), b)), b), b)), b) [2] f(c_f(c_f(a, x), b), b) -> f(f(a, f(c_f(x, b), b)), b) [1] f(c_f(c_f(a, x), b), b) -> f(f(a, f(null_f, b)), b) [1] encArg(a) -> a [0] encArg(b) -> b [0] encArg(cons_f(a, a)) -> f(a, a) [0] encArg(cons_f(a, b)) -> f(a, b) [0] encArg(cons_f(a, cons_f(x_1'', x_2''))) -> f(a, f(encArg(x_1''), encArg(x_2''))) [0] encArg(cons_f(a, x_2)) -> f(a, null_encArg) [0] encArg(cons_f(b, a)) -> f(b, a) [0] encArg(cons_f(b, b)) -> f(b, b) [0] encArg(cons_f(b, cons_f(x_11, x_21))) -> f(b, f(encArg(x_11), encArg(x_21))) [0] encArg(cons_f(b, x_2)) -> f(b, null_encArg) [0] encArg(cons_f(cons_f(x_1', x_2'), a)) -> f(f(encArg(x_1'), encArg(x_2')), a) [0] encArg(cons_f(cons_f(x_1', x_2'), b)) -> f(f(encArg(x_1'), encArg(x_2')), b) [0] encArg(cons_f(cons_f(x_1', x_2'), cons_f(x_12, x_22))) -> f(f(encArg(x_1'), encArg(x_2')), f(encArg(x_12), encArg(x_22))) [0] encArg(cons_f(cons_f(x_1', x_2'), x_2)) -> f(f(encArg(x_1'), encArg(x_2')), null_encArg) [0] encArg(cons_f(x_1, a)) -> f(null_encArg, a) [0] encArg(cons_f(x_1, b)) -> f(null_encArg, b) [0] encArg(cons_f(x_1, cons_f(x_13, x_23))) -> f(null_encArg, f(encArg(x_13), encArg(x_23))) [0] encArg(cons_f(x_1, x_2)) -> f(null_encArg, null_encArg) [0] encode_f(a, a) -> f(a, a) [0] encode_f(a, b) -> f(a, b) [0] encode_f(a, cons_f(x_15, x_25)) -> f(a, f(encArg(x_15), encArg(x_25))) [0] encode_f(a, x_2) -> f(a, null_encArg) [0] encode_f(b, a) -> f(b, a) [0] encode_f(b, b) -> f(b, b) [0] encode_f(b, cons_f(x_16, x_26)) -> f(b, f(encArg(x_16), encArg(x_26))) [0] encode_f(b, x_2) -> f(b, null_encArg) [0] encode_f(cons_f(x_14, x_24), a) -> f(f(encArg(x_14), encArg(x_24)), a) [0] encode_f(cons_f(x_14, x_24), b) -> f(f(encArg(x_14), encArg(x_24)), b) [0] encode_f(cons_f(x_14, x_24), cons_f(x_17, x_27)) -> f(f(encArg(x_14), encArg(x_24)), f(encArg(x_17), encArg(x_27))) [0] encode_f(cons_f(x_14, x_24), x_2) -> f(f(encArg(x_14), encArg(x_24)), null_encArg) [0] encode_f(x_1, a) -> f(null_encArg, a) [0] encode_f(x_1, b) -> f(null_encArg, b) [0] encode_f(x_1, cons_f(x_18, x_28)) -> f(null_encArg, f(encArg(x_18), encArg(x_28))) [0] encode_f(x_1, x_2) -> f(null_encArg, null_encArg) [0] encode_a -> a [0] encode_b -> b [0] f(x0, x1) -> c_f(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_f(v0, v1) -> null_encode_f [0] encode_a -> null_encode_a [0] encode_b -> null_encode_b [0] f(v0, v1) -> null_f [0] The TRS has the following type information: f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f a :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f c_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f b :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encArg :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f cons_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_a :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_b :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encArg :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_a :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_b :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f Rewrite Strategy: INNERMOST ---------------------------------------- (27) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: a => 0 b => 1 null_encArg => 0 null_encode_f => 0 null_encode_a => 0 null_encode_b => 0 null_f => 0 ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), f(encArg(x_12), encArg(x_22))) :|: x_2' >= 0, z = 1 + (1 + x_1' + x_2') + (1 + x_12 + x_22), x_1' >= 0, x_12 >= 0, x_22 >= 0 encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 1) :|: z = 1 + (1 + x_1' + x_2') + 1, x_2' >= 0, x_1' >= 0 encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, x_1' >= 0, z = 1 + (1 + x_1' + x_2') + 0 encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 0) :|: z = 1 + (1 + x_1' + x_2') + x_2, x_2' >= 0, x_1' >= 0, x_2 >= 0 encArg(z) -{ 0 }-> f(1, f(encArg(x_11), encArg(x_21))) :|: x_11 >= 0, z = 1 + 1 + (1 + x_11 + x_21), x_21 >= 0 encArg(z) -{ 0 }-> f(1, 1) :|: z = 1 + 1 + 1 encArg(z) -{ 0 }-> f(1, 0) :|: z = 1 + 1 + 0 encArg(z) -{ 0 }-> f(1, 0) :|: z = 1 + 1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> f(0, f(encArg(x_1''), encArg(x_2''))) :|: x_1'' >= 0, z = 1 + 0 + (1 + x_1'' + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> f(0, f(encArg(x_13), encArg(x_23))) :|: x_1 >= 0, x_13 >= 0, z = 1 + x_1 + (1 + x_13 + x_23), x_23 >= 0 encArg(z) -{ 0 }-> f(0, 1) :|: z = 1 + 0 + 1 encArg(z) -{ 0 }-> f(0, 1) :|: x_1 >= 0, z = 1 + x_1 + 1 encArg(z) -{ 0 }-> f(0, 0) :|: z = 1 + 0 + 0 encArg(z) -{ 0 }-> f(0, 0) :|: z = 1 + 0 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> f(0, 0) :|: z = 1 + x_1 + 0, x_1 >= 0 encArg(z) -{ 0 }-> f(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_a -{ 0 }-> 0 :|: encode_b -{ 0 }-> 1 :|: encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), f(encArg(x_17), encArg(x_27))) :|: x_14 >= 0, x_17 >= 0, x_24 >= 0, x_27 >= 0, z' = 1 + x_17 + x_27, z = 1 + x_14 + x_24 encode_f(z, z') -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), 1) :|: x_14 >= 0, x_24 >= 0, z' = 1, z = 1 + x_14 + x_24 encode_f(z, z') -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), 0) :|: x_14 >= 0, x_24 >= 0, z = 1 + x_14 + x_24, z' = 0 encode_f(z, z') -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), 0) :|: x_14 >= 0, x_24 >= 0, x_2 >= 0, z' = x_2, z = 1 + x_14 + x_24 encode_f(z, z') -{ 0 }-> f(1, f(encArg(x_16), encArg(x_26))) :|: x_16 >= 0, z = 1, z' = 1 + x_16 + x_26, x_26 >= 0 encode_f(z, z') -{ 0 }-> f(1, 1) :|: z = 1, z' = 1 encode_f(z, z') -{ 0 }-> f(1, 0) :|: z = 1, z' = 0 encode_f(z, z') -{ 0 }-> f(1, 0) :|: z = 1, x_2 >= 0, z' = x_2 encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_15), encArg(x_25))) :|: x_15 >= 0, z' = 1 + x_15 + x_25, x_25 >= 0, z = 0 encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_18), encArg(x_28))) :|: x_1 >= 0, z' = 1 + x_18 + x_28, z = x_1, x_18 >= 0, x_28 >= 0 encode_f(z, z') -{ 0 }-> f(0, 1) :|: z' = 1, z = 0 encode_f(z, z') -{ 0 }-> f(0, 1) :|: x_1 >= 0, z' = 1, z = x_1 encode_f(z, z') -{ 0 }-> f(0, 0) :|: z = 0, z' = 0 encode_f(z, z') -{ 0 }-> f(0, 0) :|: x_2 >= 0, z' = x_2, z = 0 encode_f(z, z') -{ 0 }-> f(0, 0) :|: x_1 >= 0, z = x_1, z' = 0 encode_f(z, z') -{ 0 }-> f(0, 0) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 f(z, z') -{ 2 }-> f(f(0, f(f(f(0, f(f(x'', 1), 1)), 1), 1)), 1) :|: z' = 1, z = 1 + (1 + 0 + (1 + (1 + 0 + x'') + 1)) + 1, x'' >= 0 f(z, z') -{ 2 }-> f(f(0, f(0, f(f(0, f(0, f(0, x'))), 1))), 1) :|: x' >= 0, z = 0, z' = 1 + 0 + (1 + 0 + (1 + (1 + 0 + (1 + 0 + (1 + x' + 1))) + 1)) f(z, z') -{ 1 }-> f(f(0, f(0, 1)), 1) :|: z = 1 + (1 + 0 + x) + 1, x >= 0, z' = 1 f(z, z') -{ 1 }-> f(f(0, f(0, 0)), 1) :|: x >= 0, z' = 1 + 0 + (1 + 0 + (1 + x + 1)), z = 0 f(z, z') -{ 1 }-> f(f(0, f(0, 1 + 0 + x)), 1) :|: x >= 0, z' = 1 + 0 + (1 + 0 + (1 + x + 1)), z = 0 f(z, z') -{ 1 }-> f(f(0, f(1 + x + 1, 1)), 1) :|: z = 1 + (1 + 0 + x) + 1, x >= 0, z' = 1 f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 f(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 ---------------------------------------- (29) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), f(encArg(x_12), encArg(x_22))) :|: x_2' >= 0, z = 1 + (1 + x_1' + x_2') + (1 + x_12 + x_22), x_1' >= 0, x_12 >= 0, x_22 >= 0 encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 1) :|: z = 1 + (1 + x_1' + x_2') + 1, x_2' >= 0, x_1' >= 0 encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, x_1' >= 0, z = 1 + (1 + x_1' + x_2') + 0 encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 0) :|: z = 1 + (1 + x_1' + x_2') + x_2, x_2' >= 0, x_1' >= 0, x_2 >= 0 encArg(z) -{ 0 }-> f(1, f(encArg(x_11), encArg(x_21))) :|: x_11 >= 0, z = 1 + 1 + (1 + x_11 + x_21), x_21 >= 0 encArg(z) -{ 0 }-> f(1, 1) :|: z = 1 + 1 + 1 encArg(z) -{ 0 }-> f(1, 0) :|: z = 1 + 1 + 0 encArg(z) -{ 0 }-> f(1, 0) :|: z - 2 >= 0 encArg(z) -{ 0 }-> f(0, f(encArg(x_1''), encArg(x_2''))) :|: x_1'' >= 0, z = 1 + 0 + (1 + x_1'' + x_2''), x_2'' >= 0 encArg(z) -{ 0 }-> f(0, f(encArg(x_13), encArg(x_23))) :|: x_1 >= 0, x_13 >= 0, z = 1 + x_1 + (1 + x_13 + x_23), x_23 >= 0 encArg(z) -{ 0 }-> f(0, 1) :|: z = 1 + 0 + 1 encArg(z) -{ 0 }-> f(0, 1) :|: z - 2 >= 0 encArg(z) -{ 0 }-> f(0, 0) :|: z = 1 + 0 + 0 encArg(z) -{ 0 }-> f(0, 0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> f(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encode_a -{ 0 }-> 0 :|: encode_b -{ 0 }-> 1 :|: encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), f(encArg(x_17), encArg(x_27))) :|: x_14 >= 0, x_17 >= 0, x_24 >= 0, x_27 >= 0, z' = 1 + x_17 + x_27, z = 1 + x_14 + x_24 encode_f(z, z') -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), 1) :|: x_14 >= 0, x_24 >= 0, z' = 1, z = 1 + x_14 + x_24 encode_f(z, z') -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), 0) :|: x_14 >= 0, x_24 >= 0, z = 1 + x_14 + x_24, z' = 0 encode_f(z, z') -{ 0 }-> f(f(encArg(x_14), encArg(x_24)), 0) :|: x_14 >= 0, x_24 >= 0, z' >= 0, z = 1 + x_14 + x_24 encode_f(z, z') -{ 0 }-> f(1, f(encArg(x_16), encArg(x_26))) :|: x_16 >= 0, z = 1, z' = 1 + x_16 + x_26, x_26 >= 0 encode_f(z, z') -{ 0 }-> f(1, 1) :|: z = 1, z' = 1 encode_f(z, z') -{ 0 }-> f(1, 0) :|: z = 1, z' = 0 encode_f(z, z') -{ 0 }-> f(1, 0) :|: z = 1, z' >= 0 encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_15), encArg(x_25))) :|: x_15 >= 0, z' = 1 + x_15 + x_25, x_25 >= 0, z = 0 encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_18), encArg(x_28))) :|: z >= 0, z' = 1 + x_18 + x_28, x_18 >= 0, x_28 >= 0 encode_f(z, z') -{ 0 }-> f(0, 1) :|: z' = 1, z = 0 encode_f(z, z') -{ 0 }-> f(0, 1) :|: z >= 0, z' = 1 encode_f(z, z') -{ 0 }-> f(0, 0) :|: z = 0, z' = 0 encode_f(z, z') -{ 0 }-> f(0, 0) :|: z' >= 0, z = 0 encode_f(z, z') -{ 0 }-> f(0, 0) :|: z >= 0, z' = 0 encode_f(z, z') -{ 0 }-> f(0, 0) :|: z >= 0, z' >= 0 encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 f(z, z') -{ 2 }-> f(f(0, f(f(f(0, f(f(z - 6, 1), 1)), 1), 1)), 1) :|: z' = 1, z - 6 >= 0 f(z, z') -{ 2 }-> f(f(0, f(0, f(f(0, f(0, f(0, z' - 8))), 1))), 1) :|: z' - 8 >= 0, z = 0 f(z, z') -{ 1 }-> f(f(0, f(0, 1)), 1) :|: z - 3 >= 0, z' = 1 f(z, z') -{ 1 }-> f(f(0, f(0, 0)), 1) :|: z' - 4 >= 0, z = 0 f(z, z') -{ 1 }-> f(f(0, f(0, 1 + 0 + (z' - 4))), 1) :|: z' - 4 >= 0, z = 0 f(z, z') -{ 1 }-> f(f(0, f(1 + (z - 3) + 1, 1)), 1) :|: z - 3 >= 0, z' = 1 f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 f(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 ---------------------------------------- (31) 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: encArg(v0) -> null_encArg [0] encode_f(v0, v1) -> null_encode_f [0] encode_a -> null_encode_a [0] encode_b -> null_encode_b [0] f(v0, v1) -> null_f [0] And the following fresh constants: null_encArg, null_encode_f, null_encode_a, null_encode_b, null_f ---------------------------------------- (32) 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: f(a, c_f(a, c_f(a, c_f(x, b)))) -> f(f(a, f(a, f(a, x))), b) [1] f(c_f(c_f(a, x), b), b) -> f(f(a, f(f(x, b), b)), b) [1] encArg(a) -> a [0] encArg(b) -> b [0] encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0] encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0] encode_a -> a [0] encode_b -> b [0] f(x0, x1) -> c_f(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_f(v0, v1) -> null_encode_f [0] encode_a -> null_encode_a [0] encode_b -> null_encode_b [0] f(v0, v1) -> null_f [0] The TRS has the following type information: f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f a :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f c_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f b :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encArg :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f cons_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f -> a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_a :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f encode_b :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encArg :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_a :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_encode_b :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f null_f :: a:b:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_f Rewrite Strategy: INNERMOST ---------------------------------------- (33) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: a => 0 b => 1 null_encArg => 0 null_encode_f => 0 null_encode_a => 0 null_encode_b => 0 null_f => 0 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_a -{ 0 }-> 0 :|: encode_b -{ 0 }-> 1 :|: encode_b -{ 0 }-> 0 :|: encode_f(z, z') -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 f(z, z') -{ 1 }-> f(f(0, f(f(x, 1), 1)), 1) :|: z = 1 + (1 + 0 + x) + 1, x >= 0, z' = 1 f(z, z') -{ 1 }-> f(f(0, f(0, f(0, x))), 1) :|: x >= 0, z' = 1 + 0 + (1 + 0 + (1 + x + 1)), z = 0 f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 f(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (35) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) encode_f(z0, z1) -> f(encArg(z0), encArg(z1)) encode_a -> a encode_b -> b f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(a) -> c ENCARG(b) -> c1 ENCARG(cons_f(z0, z1)) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_F(z0, z1) -> c3(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_A -> c4 ENCODE_B -> c5 F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) S tuples: F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) K tuples:none Defined Rule Symbols: f_2, encArg_1, encode_f_2, encode_a, encode_b Defined Pair Symbols: ENCARG_1, ENCODE_F_2, ENCODE_A, ENCODE_B, F_2 Compound Symbols: c, c1, c2_3, c3_3, c4, c5, c6_4, c7_4 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing nodes: ENCODE_B -> c5 ENCARG(a) -> c ENCARG(b) -> c1 ENCODE_A -> c4 ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) encode_f(z0, z1) -> f(encArg(z0), encArg(z1)) encode_a -> a encode_b -> b f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(z0, z1)) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_F(z0, z1) -> c3(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) S tuples: F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) K tuples:none Defined Rule Symbols: f_2, encArg_1, encode_f_2, encode_a, encode_b Defined Pair Symbols: ENCARG_1, ENCODE_F_2, F_2 Compound Symbols: c2_3, c3_3, c6_4, c7_4 ---------------------------------------- (39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) encode_f(z0, z1) -> f(encArg(z0), encArg(z1)) encode_a -> a encode_b -> b f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(z0, z1)) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) ENCODE_F(z0, z1) -> c(ENCARG(z0)) ENCODE_F(z0, z1) -> c(ENCARG(z1)) S tuples: F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) K tuples:none Defined Rule Symbols: f_2, encArg_1, encode_f_2, encode_a, encode_b Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c6_4, c7_4, c_1 ---------------------------------------- (41) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_F(z0, z1) -> c(ENCARG(z0)) ENCODE_F(z0, z1) -> c(ENCARG(z1)) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) encode_f(z0, z1) -> f(encArg(z0), encArg(z1)) encode_a -> a encode_b -> b f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(z0, z1)) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) S tuples: F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) K tuples:none Defined Rule Symbols: f_2, encArg_1, encode_f_2, encode_a, encode_b Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c6_4, c7_4, c_1 ---------------------------------------- (43) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_f(z0, z1) -> f(encArg(z0), encArg(z1)) encode_a -> a encode_b -> b ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(z0, z1)) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) S tuples: F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c6_4, c7_4, c_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_f(z0, z1)) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0), ENCARG(a)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0), ENCARG(b)) ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(a), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(b), ENCARG(x1)) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) ENCARG(cons_f(x0, a)) -> c2(F(encArg(x0), a), ENCARG(x0), ENCARG(a)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0), ENCARG(b)) ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(a), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(F(b, encArg(x1)), ENCARG(b), ENCARG(x1)) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) S tuples: F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c6_4, c7_4, c_1, c2_3 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing tuple parts ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) S tuples: F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c6_4, c7_4, c_1, c2_3, c2_1, c2_2 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(a, f(a, f(a, f(z0, b)))) -> c6(F(f(a, f(a, f(a, z0))), b), F(a, f(a, f(a, z0))), F(a, f(a, z0)), F(a, z0)) by F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b)))), F(a, f(a, f(z0, b))), F(a, f(z0, b))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b)))), F(a, f(a, f(z0, b)))) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b)))), F(a, f(a, f(z0, b))), F(a, f(z0, b))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b)))), F(a, f(a, f(z0, b)))) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) S tuples: F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b)))), F(a, f(a, f(z0, b))), F(a, f(z0, b))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b)))), F(a, f(a, f(z0, b)))) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_4, c_1, c2_3, c2_1, c2_2, c6_4 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) S tuples: F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCODE_F_2, ENCARG_1 Compound Symbols: c7_4, c_1, c2_3, c2_1, c2_2, c6_4, c6_2, c6_3 ---------------------------------------- (53) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(f(f(a, z0), b), b) -> c7(F(f(a, f(f(z0, b), b)), b), F(a, f(f(z0, b), b)), F(f(z0, b), b), F(z0, b)) by F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b), F(f(a, z0), b)) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b), F(f(a, z0), b)) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) S tuples: F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b), F(f(a, z0), b)) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCODE_F_2, ENCARG_1, F_2 Compound Symbols: c_1, c2_3, c2_1, c2_2, c6_4, c6_2, c6_3, c7_4 ---------------------------------------- (55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) S tuples: F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCODE_F_2, ENCARG_1, F_2 Compound Symbols: c_1, c2_3, c2_1, c2_2, c6_4, c6_2, c6_3, c7_4, c7_3 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) by ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) S tuples: F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_1, c2_2, c6_4, c6_2, c6_3, c7_4, c7_3, c_1 ---------------------------------------- (59) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_F(b, x1) -> c(F(b, encArg(x1))) ENCODE_F(x0, a) -> c(F(encArg(x0), a)) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) S tuples: F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_1, c2_2, c6_4, c6_2, c6_3, c7_4, c7_3, c_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_f(x0, cons_f(z0, z1))) -> c2(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) by ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(a), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(b), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(a), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(F(b, f(encArg(x1), encArg(x2))), ENCARG(b), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) S tuples: F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_1, c2_2, c6_4, c6_2, c6_3, c7_4, c7_3, c_1 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) S tuples: F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_3, c2_1, c2_2, c6_4, c6_2, c6_3, c7_4, c7_3, c_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_f(cons_f(z0, z1), x1)) -> c2(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) by ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)), ENCARG(a)) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)), ENCARG(b)) ENCARG(cons_f(cons_f(x0, x1), cons_f(z0, z1))) -> c2(F(f(encArg(x0), encArg(x1)), f(encArg(z0), encArg(z1))), ENCARG(cons_f(x0, x1)), ENCARG(cons_f(z0, z1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)), ENCARG(a)) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)), ENCARG(b)) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) S tuples: F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c2_2, c6_4, c6_2, c6_3, c7_4, c7_3, c_1, c2_3 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) S tuples: F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c2_2, c6_4, c6_2, c6_3, c7_4, c7_3, c_1, c2_3 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_f(x0, b)) -> c2(F(encArg(x0), b), ENCARG(x0)) by ENCARG(cons_f(a, b)) -> c2(F(a, b), ENCARG(a)) ENCARG(cons_f(b, b)) -> c2(F(b, b), ENCARG(b)) ENCARG(cons_f(cons_f(z0, z1), b)) -> c2(F(f(encArg(z0), encArg(z1)), b), ENCARG(cons_f(z0, z1))) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(a, b)) -> c2(F(a, b), ENCARG(a)) ENCARG(cons_f(b, b)) -> c2(F(b, b), ENCARG(b)) S tuples: F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c2_2, c6_4, c6_2, c6_3, c7_4, c7_3, c_1, c2_3 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_f(a, b)) -> c2(F(a, b), ENCARG(a)) ENCARG(cons_f(b, b)) -> c2(F(b, b), ENCARG(b)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) S tuples: F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c2_2, c6_4, c6_2, c6_3, c7_4, c7_3, c_1, c2_3 ---------------------------------------- (73) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_f(a, x1)) -> c2(F(a, encArg(x1)), ENCARG(x1)) by ENCARG(cons_f(a, a)) -> c2(F(a, a), ENCARG(a)) ENCARG(cons_f(a, b)) -> c2(F(a, b), ENCARG(b)) ENCARG(cons_f(a, cons_f(z0, z1))) -> c2(F(a, f(encArg(z0), encArg(z1))), ENCARG(cons_f(z0, z1))) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) ENCARG(cons_f(a, a)) -> c2(F(a, a), ENCARG(a)) ENCARG(cons_f(a, b)) -> c2(F(a, b), ENCARG(b)) S tuples: F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_4, c6_2, c6_3, c7_4, c7_3, c_1, c2_3, c2_2 ---------------------------------------- (75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCARG(cons_f(a, b)) -> c2(F(a, b), ENCARG(b)) ENCARG(cons_f(a, a)) -> c2(F(a, a), ENCARG(a)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) S tuples: F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_4, c6_2, c6_3, c7_4, c7_3, c_1, c2_3, c2_2 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b), F(a, f(a, f(a, f(a, f(a, f(z0, b)))))), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) by F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c6_3, c7_4, c7_3, c_1, c2_3, c2_2, c6_4 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(a, f(a, f(a, f(f(a, f(z0, b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(a, z0))), b)), b), F(a, f(a, f(a, f(a, f(z0, b))))), F(a, f(a, f(a, f(z0, b))))) by F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c7_4, c7_3, c_1, c2_3, c2_2, c6_4, c6_3, c6_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(f(f(a, f(f(a, z0), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), F(a, f(f(f(f(a, z0), b), b), b)), F(f(f(f(a, z0), b), b), b), F(f(f(a, z0), b), b)) by F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c7_3, c_1, c2_3, c2_2, c6_4, c6_3, c6_1, c7_4, c7_2 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace F(f(f(a, f(a, z0)), b), b) -> c7(F(f(a, f(f(a, f(f(z0, b), b)), b)), b), F(a, f(f(f(a, z0), b), b)), F(f(f(a, z0), b), b)) by F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCODE_F(x0, b) -> c(F(encArg(x0), b)) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c_1, c2_3, c2_2, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_F(x0, b) -> c(F(encArg(x0), b)) by ENCODE_F(a, b) -> c(F(a, b)) ENCODE_F(b, b) -> c(F(b, b)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ENCODE_F(a, b) -> c(F(a, b)) ENCODE_F(b, b) -> c(F(b, b)) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c_1, c2_3, c2_2, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_F(b, b) -> c(F(b, b)) ENCODE_F(a, b) -> c(F(a, b)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c_1, c2_3, c2_2, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) by ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c_1, c2_3, c2_2, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a))) ENCODE_F(b, cons_f(x1, x2)) -> c(F(b, f(encArg(x1), encArg(x2)))) ENCODE_F(x0, cons_f(b, x2)) -> c(F(encArg(x0), f(b, encArg(x2)))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCODE_F(a, x1) -> c(F(a, encArg(x1))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c_1, c2_3, c2_2, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_F(a, x1) -> c(F(a, encArg(x1))) by ENCODE_F(a, a) -> c(F(a, a)) ENCODE_F(a, b) -> c(F(a, b)) ENCODE_F(a, cons_f(z0, z1)) -> c(F(a, f(encArg(z0), encArg(z1)))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(a, a) -> c(F(a, a)) ENCODE_F(a, b) -> c(F(a, b)) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c_1, c2_3, c2_2, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1 ---------------------------------------- (95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: ENCODE_F(a, b) -> c(F(a, b)) ENCODE_F(a, a) -> c(F(a, a)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c_1, c2_3, c2_2, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) by ENCODE_F(cons_f(x0, x1), a) -> c(F(f(encArg(x0), encArg(x1)), a)) ENCODE_F(cons_f(x0, x1), b) -> c(F(f(encArg(x0), encArg(x1)), b)) ENCODE_F(cons_f(x0, x1), cons_f(z0, z1)) -> c(F(f(encArg(x0), encArg(x1)), f(encArg(z0), encArg(z1)))) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, x1), a) -> c(F(f(encArg(x0), encArg(x1)), a)) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c2_3, c2_2, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1, c_1 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: ENCODE_F(cons_f(b, x1), x2) -> c(F(f(b, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2))) ENCODE_F(cons_f(x0, x1), a) -> c(F(f(encArg(x0), encArg(x1)), a)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c2_3, c2_2, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1, c_1 ---------------------------------------- (101) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_f(x0, a)) -> c2(ENCARG(x0)) by ENCARG(cons_f(cons_f(y0, a), a)) -> c2(ENCARG(cons_f(y0, a))) ENCARG(cons_f(cons_f(b, y0), a)) -> c2(ENCARG(cons_f(b, y0))) ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, b)))) ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3))))) ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c2(ENCARG(cons_f(y0, cons_f(a, y1)))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3)))) ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3)))) ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, a)))) ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a)) -> c2(ENCARG(cons_f(y0, cons_f(b, y1)))) ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c2(ENCARG(cons_f(a, cons_f(y0, y1)))) ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a)) -> c2(ENCARG(cons_f(b, cons_f(y0, y1)))) ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a)) -> c2(ENCARG(cons_f(cons_f(y0, b), y1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3))) ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c2(ENCARG(cons_f(cons_f(a, y0), y1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3))) ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), b))) ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c2(ENCARG(cons_f(cons_f(y0, a), y1))) ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a)) -> c2(ENCARG(cons_f(cons_f(b, y0), y1))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) ENCARG(cons_f(cons_f(y0, a), a)) -> c2(ENCARG(cons_f(y0, a))) ENCARG(cons_f(cons_f(b, y0), a)) -> c2(ENCARG(cons_f(b, y0))) ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, b)))) ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3))))) ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c2(ENCARG(cons_f(y0, cons_f(a, y1)))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3)))) ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3)))) ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, a)))) ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a)) -> c2(ENCARG(cons_f(y0, cons_f(b, y1)))) ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c2(ENCARG(cons_f(a, cons_f(y0, y1)))) ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a)) -> c2(ENCARG(cons_f(b, cons_f(y0, y1)))) ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a)) -> c2(ENCARG(cons_f(cons_f(y0, b), y1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3))) ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c2(ENCARG(cons_f(cons_f(a, y0), y1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3))) ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), b))) ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c2(ENCARG(cons_f(cons_f(y0, a), y1))) ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a)) -> c2(ENCARG(cons_f(cons_f(b, y0), y1))) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: ENCARG_1, F_2, ENCODE_F_2 Compound Symbols: c2_1, c6_2, c2_3, c2_2, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1, c_1 ---------------------------------------- (103) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_f(b, x1)) -> c2(ENCARG(x1)) by ENCARG(cons_f(b, cons_f(b, y0))) -> c2(ENCARG(cons_f(b, y0))) ENCARG(cons_f(b, cons_f(y0, cons_f(y1, b)))) -> c2(ENCARG(cons_f(y0, cons_f(y1, b)))) ENCARG(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3))))) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3))))) ENCARG(cons_f(b, cons_f(y0, cons_f(a, y1)))) -> c2(ENCARG(cons_f(y0, cons_f(a, y1)))) ENCARG(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3)))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3)))) ENCARG(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3)))) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3)))) ENCARG(cons_f(b, cons_f(y0, cons_f(y1, a)))) -> c2(ENCARG(cons_f(y0, cons_f(y1, a)))) ENCARG(cons_f(b, cons_f(y0, cons_f(b, y1)))) -> c2(ENCARG(cons_f(y0, cons_f(b, y1)))) ENCARG(cons_f(b, cons_f(a, cons_f(y0, y1)))) -> c2(ENCARG(cons_f(a, cons_f(y0, y1)))) ENCARG(cons_f(b, cons_f(b, cons_f(y0, y1)))) -> c2(ENCARG(cons_f(b, cons_f(y0, y1)))) ENCARG(cons_f(b, cons_f(cons_f(y0, b), y1))) -> c2(ENCARG(cons_f(cons_f(y0, b), y1))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3))) ENCARG(cons_f(b, cons_f(cons_f(a, y0), y1))) -> c2(ENCARG(cons_f(cons_f(a, y0), y1))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3))) ENCARG(cons_f(b, cons_f(cons_f(y0, y1), a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, y1), b))) -> c2(ENCARG(cons_f(cons_f(y0, y1), b))) ENCARG(cons_f(b, cons_f(cons_f(y0, a), y1))) -> c2(ENCARG(cons_f(cons_f(y0, a), y1))) ENCARG(cons_f(b, cons_f(cons_f(b, y0), y1))) -> c2(ENCARG(cons_f(cons_f(b, y0), y1))) ENCARG(cons_f(b, cons_f(cons_f(y0, a), a))) -> c2(ENCARG(cons_f(cons_f(y0, a), a))) ENCARG(cons_f(b, cons_f(cons_f(b, y0), a))) -> c2(ENCARG(cons_f(cons_f(b, y0), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a))) -> c2(ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) ENCARG(cons_f(cons_f(y0, a), a)) -> c2(ENCARG(cons_f(y0, a))) ENCARG(cons_f(cons_f(b, y0), a)) -> c2(ENCARG(cons_f(b, y0))) ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, b)))) ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3))))) ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c2(ENCARG(cons_f(y0, cons_f(a, y1)))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3)))) ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3)))) ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, a)))) ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a)) -> c2(ENCARG(cons_f(y0, cons_f(b, y1)))) ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c2(ENCARG(cons_f(a, cons_f(y0, y1)))) ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a)) -> c2(ENCARG(cons_f(b, cons_f(y0, y1)))) ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a)) -> c2(ENCARG(cons_f(cons_f(y0, b), y1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3))) ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c2(ENCARG(cons_f(cons_f(a, y0), y1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3))) ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), b))) ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c2(ENCARG(cons_f(cons_f(y0, a), y1))) ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a)) -> c2(ENCARG(cons_f(cons_f(b, y0), y1))) ENCARG(cons_f(b, cons_f(b, y0))) -> c2(ENCARG(cons_f(b, y0))) ENCARG(cons_f(b, cons_f(y0, cons_f(y1, b)))) -> c2(ENCARG(cons_f(y0, cons_f(y1, b)))) ENCARG(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3))))) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3))))) ENCARG(cons_f(b, cons_f(y0, cons_f(a, y1)))) -> c2(ENCARG(cons_f(y0, cons_f(a, y1)))) ENCARG(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3)))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3)))) ENCARG(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3)))) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3)))) ENCARG(cons_f(b, cons_f(y0, cons_f(y1, a)))) -> c2(ENCARG(cons_f(y0, cons_f(y1, a)))) ENCARG(cons_f(b, cons_f(y0, cons_f(b, y1)))) -> c2(ENCARG(cons_f(y0, cons_f(b, y1)))) ENCARG(cons_f(b, cons_f(a, cons_f(y0, y1)))) -> c2(ENCARG(cons_f(a, cons_f(y0, y1)))) ENCARG(cons_f(b, cons_f(b, cons_f(y0, y1)))) -> c2(ENCARG(cons_f(b, cons_f(y0, y1)))) ENCARG(cons_f(b, cons_f(cons_f(y0, b), y1))) -> c2(ENCARG(cons_f(cons_f(y0, b), y1))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3))) ENCARG(cons_f(b, cons_f(cons_f(a, y0), y1))) -> c2(ENCARG(cons_f(cons_f(a, y0), y1))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3))) ENCARG(cons_f(b, cons_f(cons_f(y0, y1), a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, y1), b))) -> c2(ENCARG(cons_f(cons_f(y0, y1), b))) ENCARG(cons_f(b, cons_f(cons_f(y0, a), y1))) -> c2(ENCARG(cons_f(cons_f(y0, a), y1))) ENCARG(cons_f(b, cons_f(cons_f(b, y0), y1))) -> c2(ENCARG(cons_f(cons_f(b, y0), y1))) ENCARG(cons_f(b, cons_f(cons_f(y0, a), a))) -> c2(ENCARG(cons_f(cons_f(y0, a), a))) ENCARG(cons_f(b, cons_f(cons_f(b, y0), a))) -> c2(ENCARG(cons_f(cons_f(b, y0), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a))) -> c2(ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a))) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCARG_1, ENCODE_F_2 Compound Symbols: c6_2, c2_3, c2_2, c2_1, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1, c_1 ---------------------------------------- (105) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_f(x0, cons_f(x1, a))) -> c2(ENCARG(x0), ENCARG(cons_f(x1, a))) by ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(y1, b))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(a, y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(y1, a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(b, y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(a, cons_f(y0, y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(y0, b), y1), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, b), y1)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, b), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, b), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(y1, y2)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a))) ENCARG(cons_f(cons_f(cons_f(a, y0), y1), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(a, y0), y1)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(a, y0), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(a, y0), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, y1), y2), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, y1), a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), b), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), b)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(y0, a), y1), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, a), y1)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, a), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, a), a))) ENCARG(cons_f(cons_f(cons_f(b, y0), y1), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(b, y0), y1)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(b, y0), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(b, y0), a))) ENCARG(cons_f(cons_f(cons_f(y0, a), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, a), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(b, y0), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(b, y0), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, b)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(y1, b)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(a, y1)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(a, y1)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, a)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(y1, a)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(b, y1)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(b, y1)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a))) ENCARG(cons_f(cons_f(cons_f(a, cons_f(y0, y1)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(a, cons_f(y0, y1)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, y1)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(b, cons_f(y0, y1)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, b), y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, b), y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(a, y0), y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(a, y0), y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), a), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, y1), a), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), b), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, y1), b), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, a), y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, a), y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(b, y0), y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(b, y0), y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a))) ENCARG(cons_f(cons_f(b, cons_f(b, y0)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(b, y0))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, b))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, b)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3))))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(a, y1))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(a, y1)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, a))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, a)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(b, y1))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(b, y1)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(a, cons_f(y0, y1))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(a, cons_f(y0, y1)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(b, cons_f(y0, y1))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(b, cons_f(y0, y1)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, b), y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, b), y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, y0), y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(a, y0), y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), b)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), b))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, a), y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, y0), y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, a), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, y0), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a))), ENCARG(cons_f(z1, a))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) ENCARG(cons_f(cons_f(y0, a), a)) -> c2(ENCARG(cons_f(y0, a))) ENCARG(cons_f(cons_f(b, y0), a)) -> c2(ENCARG(cons_f(b, y0))) ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, b)))) ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3))))) ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c2(ENCARG(cons_f(y0, cons_f(a, y1)))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3)))) ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3)))) ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, a)))) ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a)) -> c2(ENCARG(cons_f(y0, cons_f(b, y1)))) ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c2(ENCARG(cons_f(a, cons_f(y0, y1)))) ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a)) -> c2(ENCARG(cons_f(b, cons_f(y0, y1)))) ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a)) -> c2(ENCARG(cons_f(cons_f(y0, b), y1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3))) ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c2(ENCARG(cons_f(cons_f(a, y0), y1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3))) ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), b))) ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c2(ENCARG(cons_f(cons_f(y0, a), y1))) ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a)) -> c2(ENCARG(cons_f(cons_f(b, y0), y1))) ENCARG(cons_f(b, cons_f(b, y0))) -> c2(ENCARG(cons_f(b, y0))) ENCARG(cons_f(b, cons_f(y0, cons_f(y1, b)))) -> c2(ENCARG(cons_f(y0, cons_f(y1, b)))) ENCARG(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3))))) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3))))) ENCARG(cons_f(b, cons_f(y0, cons_f(a, y1)))) -> c2(ENCARG(cons_f(y0, cons_f(a, y1)))) ENCARG(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3)))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3)))) ENCARG(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3)))) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3)))) ENCARG(cons_f(b, cons_f(y0, cons_f(y1, a)))) -> c2(ENCARG(cons_f(y0, cons_f(y1, a)))) ENCARG(cons_f(b, cons_f(y0, cons_f(b, y1)))) -> c2(ENCARG(cons_f(y0, cons_f(b, y1)))) ENCARG(cons_f(b, cons_f(a, cons_f(y0, y1)))) -> c2(ENCARG(cons_f(a, cons_f(y0, y1)))) ENCARG(cons_f(b, cons_f(b, cons_f(y0, y1)))) -> c2(ENCARG(cons_f(b, cons_f(y0, y1)))) ENCARG(cons_f(b, cons_f(cons_f(y0, b), y1))) -> c2(ENCARG(cons_f(cons_f(y0, b), y1))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3))) ENCARG(cons_f(b, cons_f(cons_f(a, y0), y1))) -> c2(ENCARG(cons_f(cons_f(a, y0), y1))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3))) ENCARG(cons_f(b, cons_f(cons_f(y0, y1), a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, y1), b))) -> c2(ENCARG(cons_f(cons_f(y0, y1), b))) ENCARG(cons_f(b, cons_f(cons_f(y0, a), y1))) -> c2(ENCARG(cons_f(cons_f(y0, a), y1))) ENCARG(cons_f(b, cons_f(cons_f(b, y0), y1))) -> c2(ENCARG(cons_f(cons_f(b, y0), y1))) ENCARG(cons_f(b, cons_f(cons_f(y0, a), a))) -> c2(ENCARG(cons_f(cons_f(y0, a), a))) ENCARG(cons_f(b, cons_f(cons_f(b, y0), a))) -> c2(ENCARG(cons_f(cons_f(b, y0), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a))) -> c2(ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a))) ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(y1, b))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(a, y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(y1, a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(b, y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(a, cons_f(y0, y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(y0, b), y1), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, b), y1)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, b), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, b), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(y1, y2)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a))) ENCARG(cons_f(cons_f(cons_f(a, y0), y1), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(a, y0), y1)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(a, y0), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(a, y0), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, y1), y2), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, y1), a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), b), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), b)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(y0, a), y1), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, a), y1)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, a), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, a), a))) ENCARG(cons_f(cons_f(cons_f(b, y0), y1), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(b, y0), y1)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(b, y0), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(b, y0), a))) ENCARG(cons_f(cons_f(cons_f(y0, a), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, a), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(b, y0), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(b, y0), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, b)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(y1, b)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(a, y1)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(a, y1)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, a)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(y1, a)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(b, y1)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(b, y1)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a))) ENCARG(cons_f(cons_f(cons_f(a, cons_f(y0, y1)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(a, cons_f(y0, y1)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, y1)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(b, cons_f(y0, y1)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, b), y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, b), y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(a, y0), y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(a, y0), y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), a), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, y1), a), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), b), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, y1), b), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, a), y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, a), y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(b, y0), y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(b, y0), y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a))) ENCARG(cons_f(cons_f(b, cons_f(b, y0)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(b, y0))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, b))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, b)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3))))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(a, y1))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(a, y1)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, a))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, a)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(b, y1))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(b, y1)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(a, cons_f(y0, y1))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(a, cons_f(y0, y1)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(b, cons_f(y0, y1))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(b, cons_f(y0, y1)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, b), y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, b), y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, y0), y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(a, y0), y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), b)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), b))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, a), y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, y0), y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, a), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, y0), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a))), ENCARG(cons_f(z1, a))) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCARG_1, ENCODE_F_2 Compound Symbols: c6_2, c2_3, c2_2, c2_1, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1, c_1 ---------------------------------------- (107) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_f(x0, cons_f(b, x2))) -> c2(ENCARG(x0), ENCARG(cons_f(b, x2))) by ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(y1, b))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y1, b)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y1, b)))) ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y1, cons_f(y2, y3))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y1, cons_f(y2, y3))))) ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(a, y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(a, y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(a, y1)))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y1, y2), y3)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y1, y2), y3)))) ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(b, y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(b, y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(b, y1)))) ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(a, cons_f(y0, y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, y1)))) ENCARG(cons_f(cons_f(cons_f(y0, b), y1), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, b), y1)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(a, y0), y1), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(a, y0), y1)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, y1), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, y1), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, y1), b), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, y1), b)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, a), y1), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, a), y1)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, y0), y1), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, y0), y1)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, a), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, a), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, y0), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, y0), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, b)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(a, y1)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, a)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(b, y1)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(a, cons_f(y0, y1)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, y1)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, b), y1), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(a, y0), y1), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), a), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), b), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, a), y1), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(b, y0), y1), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(b, cons_f(b, y0)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(b, y0))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, b))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, b)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, cons_f(y1, b))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, cons_f(y1, b))))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3))))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(a, y1))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(a, y1)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, cons_f(a, y1))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, cons_f(a, y1))))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, a))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, a)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, cons_f(y1, a))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, cons_f(y1, a))))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(b, y1))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(b, y1)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, cons_f(b, y1))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, cons_f(b, y1))))) ENCARG(cons_f(cons_f(b, cons_f(a, cons_f(y0, y1))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(a, cons_f(y0, y1)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(a, cons_f(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(a, cons_f(y0, y1))))) ENCARG(cons_f(cons_f(b, cons_f(b, cons_f(y0, y1))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(b, cons_f(y0, y1)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(b, cons_f(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(b, cons_f(y0, y1))))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, b), y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, b), y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, b), y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, b), y1)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, y0), y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(a, y0), y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(a, y0), y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(a, y0), y1)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, y1), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, y1), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), b)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), b))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, y1), b)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, y1), b)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, a), y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, a), y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, a), y1)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, y0), y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(b, y0), y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(b, y0), y1)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, a), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, a), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, a), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, y0), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(b, y0), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(b, y0), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, b)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(a, y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(b, y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(a, cons_f(y0, y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, b), y1), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, b), y1), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, b), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, b), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y1, b), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y1, b), a)))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, y3)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, y3)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y1, cons_f(y2, y3)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y1, cons_f(y2, y3)), a)))) ENCARG(cons_f(cons_f(cons_f(cons_f(a, y0), y1), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, y0), y1), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(a, y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(a, y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(a, y1), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(a, y1), a)))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), y3), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), y3), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y1, y2), y3), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y1, y2), y3), a)))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), b), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), b), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, a), y1), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), y1), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, a), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, a), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(b, y0), y1), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), y1), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(b, y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(b, y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, a), a), cons_f(y1, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), a), cons_f(y1, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(b, y0), a), cons_f(y1, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), a), cons_f(y1, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, b)), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, b)), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, b)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, b)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, cons_f(y3, y4))), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, cons_f(y3, y4))), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(a, y1)), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(a, y1)), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(a, y2)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(a, y2)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(cons_f(y2, y3), y4)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(cons_f(y2, y3), y4)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), cons_f(y3, y4)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), cons_f(y3, y4)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, a)), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, a)), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, a)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, a)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(b, y1)), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(b, y1)), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(b, y2)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(b, y2)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(a, cons_f(y0, y1)), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, cons_f(y0, y1)), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(a, cons_f(y1, y2)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(a, cons_f(y1, y2)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(b, cons_f(y0, y1)), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, y1)), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(b, cons_f(y1, y2)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(b, cons_f(y1, y2)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, b), y1), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, b), y1), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, b), y2), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, b), y2), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, cons_f(y2, y3)), y4), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, cons_f(y2, y3)), y4), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(a, y0), y1), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(a, y0), y1), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(a, y1), y2), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(a, y1), y2), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(cons_f(y1, y2), y3), y4), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(cons_f(y1, y2), y3), y4), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), a), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), a), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), a), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), a), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), b), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), b), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), b), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), b), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, a), y1), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, a), y1), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, a), y2), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, a), y2), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(b, y0), y1), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(b, y0), y1), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(b, y1), y2), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(b, y1), y2), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(b, y0)), cons_f(y1, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(b, y0)), cons_f(y1, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, cons_f(y1, b))), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, b))), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, cons_f(a, y1))), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(a, y1))), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, cons_f(y1, a))), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, a))), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, cons_f(b, y1))), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(b, y1))), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(a, cons_f(y0, y1))), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(a, cons_f(y0, y1))), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(b, cons_f(y0, y1))), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(b, cons_f(y0, y1))), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, b), y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, b), y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(a, y0), y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, y0), y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, y1), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, y1), b)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), b)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, a), y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(b, y0), y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, a), a)), cons_f(y1, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), a)), cons_f(y1, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(b, y0), a)), cons_f(y1, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), a)), cons_f(y1, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a) -> a encArg(b) -> b encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1)) f(a, f(a, f(a, f(z0, b)))) -> f(f(a, f(a, f(a, z0))), b) f(f(f(a, z0), b), b) -> f(f(a, f(f(z0, b), b)), b) Tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) ENCARG(cons_f(x0, cons_f(x1, b))) -> c2(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b))) ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c2(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1)))) ENCARG(cons_f(x0, cons_f(a, x2))) -> c2(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2))) ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c2(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2))) ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c2(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(a, cons_f(x1, x2))) -> c2(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2))) ENCARG(cons_f(b, cons_f(x1, x2))) -> c2(ENCARG(cons_f(x1, x2))) ENCARG(cons_f(cons_f(x0, b), x2)) -> c2(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c2(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2)) ENCARG(cons_f(cons_f(a, x1), x2)) -> c2(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c2(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_f(cons_f(x0, x1), a)) -> c2(ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, x1), b)) -> c2(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1))) ENCARG(cons_f(cons_f(x0, a), x2)) -> c2(ENCARG(cons_f(x0, a)), ENCARG(x2)) ENCARG(cons_f(cons_f(b, x1), x2)) -> c2(ENCARG(cons_f(b, x1)), ENCARG(x2)) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) ENCODE_F(cons_f(z0, z1), b) -> c(F(f(encArg(z0), encArg(z1)), b)) ENCODE_F(x0, cons_f(x1, b)) -> c(F(encArg(x0), f(encArg(x1), b))) ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1))))) ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2)))) ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2)))) ENCODE_F(cons_f(x0, b), x2) -> c(F(f(encArg(x0), b), encArg(x2))) ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2))) ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) ENCARG(cons_f(cons_f(y0, a), a)) -> c2(ENCARG(cons_f(y0, a))) ENCARG(cons_f(cons_f(b, y0), a)) -> c2(ENCARG(cons_f(b, y0))) ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, b)))) ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3))))) ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c2(ENCARG(cons_f(y0, cons_f(a, y1)))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3)))) ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3)))) ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c2(ENCARG(cons_f(y0, cons_f(y1, a)))) ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a)) -> c2(ENCARG(cons_f(y0, cons_f(b, y1)))) ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c2(ENCARG(cons_f(a, cons_f(y0, y1)))) ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a)) -> c2(ENCARG(cons_f(b, cons_f(y0, y1)))) ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a)) -> c2(ENCARG(cons_f(cons_f(y0, b), y1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3))) ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c2(ENCARG(cons_f(cons_f(a, y0), y1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3))) ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a)) -> c2(ENCARG(cons_f(cons_f(y0, y1), b))) ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c2(ENCARG(cons_f(cons_f(y0, a), y1))) ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a)) -> c2(ENCARG(cons_f(cons_f(b, y0), y1))) ENCARG(cons_f(b, cons_f(b, y0))) -> c2(ENCARG(cons_f(b, y0))) ENCARG(cons_f(b, cons_f(y0, cons_f(y1, b)))) -> c2(ENCARG(cons_f(y0, cons_f(y1, b)))) ENCARG(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3))))) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3))))) ENCARG(cons_f(b, cons_f(y0, cons_f(a, y1)))) -> c2(ENCARG(cons_f(y0, cons_f(a, y1)))) ENCARG(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3)))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3)))) ENCARG(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3)))) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3)))) ENCARG(cons_f(b, cons_f(y0, cons_f(y1, a)))) -> c2(ENCARG(cons_f(y0, cons_f(y1, a)))) ENCARG(cons_f(b, cons_f(y0, cons_f(b, y1)))) -> c2(ENCARG(cons_f(y0, cons_f(b, y1)))) ENCARG(cons_f(b, cons_f(a, cons_f(y0, y1)))) -> c2(ENCARG(cons_f(a, cons_f(y0, y1)))) ENCARG(cons_f(b, cons_f(b, cons_f(y0, y1)))) -> c2(ENCARG(cons_f(b, cons_f(y0, y1)))) ENCARG(cons_f(b, cons_f(cons_f(y0, b), y1))) -> c2(ENCARG(cons_f(cons_f(y0, b), y1))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3))) ENCARG(cons_f(b, cons_f(cons_f(a, y0), y1))) -> c2(ENCARG(cons_f(cons_f(a, y0), y1))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3))) ENCARG(cons_f(b, cons_f(cons_f(y0, y1), a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, y1), b))) -> c2(ENCARG(cons_f(cons_f(y0, y1), b))) ENCARG(cons_f(b, cons_f(cons_f(y0, a), y1))) -> c2(ENCARG(cons_f(cons_f(y0, a), y1))) ENCARG(cons_f(b, cons_f(cons_f(b, y0), y1))) -> c2(ENCARG(cons_f(cons_f(b, y0), y1))) ENCARG(cons_f(b, cons_f(cons_f(y0, a), a))) -> c2(ENCARG(cons_f(cons_f(y0, a), a))) ENCARG(cons_f(b, cons_f(cons_f(b, y0), a))) -> c2(ENCARG(cons_f(cons_f(b, y0), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a))) ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a))) -> c2(ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a))) ENCARG(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a))) ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(y1, b))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(a, y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(y1, a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(y0, cons_f(b, y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(a, cons_f(y0, y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(y0, b), y1), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, b), y1)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, b), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, b), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(y1, y2)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a))) ENCARG(cons_f(cons_f(cons_f(a, y0), y1), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(a, y0), y1)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(a, y0), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(a, y0), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, y1), y2), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, y1), a))) ENCARG(cons_f(cons_f(cons_f(y0, y1), b), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, y1), b)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(y0, a), y1), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, a), y1)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, a), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, a), a))) ENCARG(cons_f(cons_f(cons_f(b, y0), y1), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(b, y0), y1)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(b, y0), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(b, y0), a))) ENCARG(cons_f(cons_f(cons_f(y0, a), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, a), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(b, y0), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(b, y0), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, b)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(y1, b)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(a, y1)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(a, y1)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, a)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(y1, a)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(b, y1)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(y0, cons_f(b, y1)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a))) ENCARG(cons_f(cons_f(cons_f(a, cons_f(y0, y1)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(a, cons_f(y0, y1)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, y1)), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(b, cons_f(y0, y1)), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, b), y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, b), y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(a, y0), y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(a, y0), y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), a), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, y1), a), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), b), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, y1), b), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, a), y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(y0, a), y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a))) ENCARG(cons_f(cons_f(cons_f(cons_f(b, y0), y1), a), cons_f(z1, a))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a)), ENCARG(cons_f(z1, a))) ENCARG(cons_f(z0, cons_f(cons_f(cons_f(b, y0), y1), a))) -> c2(ENCARG(z0), ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a))) ENCARG(cons_f(cons_f(b, cons_f(b, y0)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(b, y0))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, b))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, b)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3))))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(a, y1))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(a, y1)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, a))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, a)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(b, y1))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(b, y1)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(a, cons_f(y0, y1))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(a, cons_f(y0, y1)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(b, cons_f(y0, y1))), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(b, cons_f(y0, y1)))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, b), y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, b), y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, y0), y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(a, y0), y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), b)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), b))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, a), y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), y1)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, y0), y1))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, a), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, y0), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)), cons_f(z1, a))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a))), ENCARG(cons_f(z1, a))) ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(y1, b))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y1, b)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y1, b)))) ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y1, cons_f(y2, y3))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y1, cons_f(y2, y3))))) ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(a, y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(a, y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(a, y1)))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y1, y2), y3)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y1, y2), y3)))) ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(b, y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(b, y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(b, y1)))) ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(a, cons_f(y0, y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, y1)))) ENCARG(cons_f(cons_f(cons_f(y0, b), y1), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, b), y1)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(a, y0), y1), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(a, y0), y1)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, y1), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, y1), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, y1), b), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, y1), b)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, a), y1), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, a), y1)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, y0), y1), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, y0), y1)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, a), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, a), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, y0), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, y0), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, b)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(a, y1)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, a)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(b, y1)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(a, cons_f(y0, y1)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, y1)), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, b), y1), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, b), y1), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(a, y0), y1), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), a), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), b), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), b), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, a), y1), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(b, y0), y1), a), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), y1), a)), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(b, cons_f(b, y0)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(b, y0))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, b))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, b)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, cons_f(y1, b))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, cons_f(y1, b))))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3))))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(a, y1))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(a, y1)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, cons_f(a, y1))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, cons_f(a, y1))))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, a))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(y1, a)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, cons_f(y1, a))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, cons_f(y1, a))))) ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(b, y1))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(y0, cons_f(b, y1)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(y0, cons_f(b, y1))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(y0, cons_f(b, y1))))) ENCARG(cons_f(cons_f(b, cons_f(a, cons_f(y0, y1))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(a, cons_f(y0, y1)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(a, cons_f(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(a, cons_f(y0, y1))))) ENCARG(cons_f(cons_f(b, cons_f(b, cons_f(y0, y1))), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(b, cons_f(y0, y1)))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(b, cons_f(y0, y1))))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(b, cons_f(y0, y1))))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, b), y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, b), y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, b), y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, b), y1)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, y0), y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(a, y0), y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(a, y0), y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(a, y0), y1)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, y1), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, y1), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), b)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, y1), b))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, y1), b)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, y1), b)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, a), y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, a), y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, a), y1)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), y1)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, y0), y1))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(b, y0), y1)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(b, y0), y1)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, a), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, a), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, a), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, y0), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(b, y0), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(b, y0), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)))) ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, b)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, b)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(a, y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(y0, cons_f(b, y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(y0, cons_f(b, y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(a, cons_f(y0, y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, b), y1), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, b), y1), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, b), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, b), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y1, b), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y1, b), a)))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, y3)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, y3)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(y1, cons_f(y2, y3)), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(y1, cons_f(y2, y3)), a)))) ENCARG(cons_f(cons_f(cons_f(cons_f(a, y0), y1), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, y0), y1), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(a, y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(a, y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(a, y1), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(a, y1), a)))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), y3), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), y3), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(z0, cons_f(b, cons_f(cons_f(cons_f(y1, y2), y3), a)))) -> c2(ENCARG(z0), ENCARG(cons_f(b, cons_f(cons_f(cons_f(y1, y2), y3), a)))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), b), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, y1), b), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, a), y1), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), y1), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, a), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, a), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(b, y0), y1), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), y1), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(b, y1), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(b, y1), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, a), a), cons_f(y1, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, a), a), cons_f(y1, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(b, y0), a), cons_f(y1, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, y0), a), cons_f(y1, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, b)), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, b)), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, b)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, b)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, cons_f(y3, y4))), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, cons_f(y3, y4))), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(a, y1)), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(a, y1)), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(a, y2)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(a, y2)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(cons_f(y2, y3), y4)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(cons_f(y2, y3), y4)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), cons_f(y3, y4)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), cons_f(y3, y4)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, a)), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, a)), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, a)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(y2, a)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(b, y1)), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(y0, cons_f(b, y1)), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, cons_f(b, y2)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(y1, cons_f(b, y2)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(a, cons_f(y0, y1)), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(a, cons_f(y0, y1)), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(a, cons_f(y1, y2)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(a, cons_f(y1, y2)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(b, cons_f(y0, y1)), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, y1)), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(b, cons_f(y1, y2)), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(b, cons_f(y1, y2)), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, b), y1), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, b), y1), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, b), y2), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, b), y2), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, cons_f(y2, y3)), y4), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, cons_f(y2, y3)), y4), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(a, y0), y1), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(a, y0), y1), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(a, y1), y2), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(a, y1), y2), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(cons_f(y1, y2), y3), y4), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(cons_f(y1, y2), y3), y4), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), a), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), a), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), a), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), a), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, y1), b), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), b), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), b), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, y2), b), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(y0, a), y1), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(y0, a), y1), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(y1, a), y2), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(y1, a), y2), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(cons_f(cons_f(b, y0), y1), a), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(cons_f(cons_f(b, y0), y1), a), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(y0, cons_f(cons_f(cons_f(b, y1), y2), a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(y0, cons_f(cons_f(cons_f(b, y1), y2), a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(b, y0)), cons_f(y1, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(b, y0)), cons_f(y1, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, cons_f(y1, b))), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, b))), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, cons_f(y2, y3)))), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, cons_f(a, y1))), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(a, y1))), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(cons_f(y1, y2), y3))), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), cons_f(y2, y3))), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, cons_f(y1, a))), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(y1, a))), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(y0, cons_f(b, y1))), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(y0, cons_f(b, y1))), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(a, cons_f(y0, y1))), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(a, cons_f(y0, y1))), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(b, cons_f(y0, y1))), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(b, cons_f(y0, y1))), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, b), y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, b), y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, y2)), y3)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(a, y0), y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, y0), y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), y2), y3)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, y1), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, y1), b)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, y1), b)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, a), y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(b, y0), y1)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), y1)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, a), a)), cons_f(y1, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, a), a)), cons_f(y1, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(b, y0), a)), cons_f(y1, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, y0), a)), cons_f(y1, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, b)), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(a, y1)), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(y1, a)), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(y0, cons_f(b, y1)), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(a, cons_f(y0, y1)), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(b, cons_f(y0, y1)), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, b), y1), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(a, y0), y1), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), cons_f(y4, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)), cons_f(y4, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), a), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, y1), b), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(y0, a), y1), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) ENCARG(cons_f(cons_f(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)), cons_f(y2, a)), cons_f(b, z1))) -> c2(ENCARG(cons_f(cons_f(b, cons_f(cons_f(cons_f(b, y0), y1), a)), cons_f(y2, a))), ENCARG(cons_f(b, z1))) S tuples: F(a, f(a, f(a, f(f(z0, b), b)))) -> c6(F(f(f(a, f(a, f(a, z0))), b), b), F(a, f(a, f(a, f(z0, b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(z0, b), b))), b)))) -> c6(F(f(a, f(a, f(f(f(a, f(a, f(a, z0))), b), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(z0, b), b)))))), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(z0, b)), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(z0, b))), b))), b)))) -> c6(F(f(a, f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b))), b), F(a, f(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b)))))), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(a, f(x0, b))), b)))) -> c6(F(a, f(a, f(a, f(a, f(a, f(x0, b)))))), F(a, f(a, f(a, f(a, f(x0, b)))))) F(a, f(a, f(a, f(f(a, f(f(z0, b), b)), b)))) -> c6(F(f(a, f(f(f(a, f(a, f(a, z0))), b), b)), b), F(a, f(a, f(a, f(a, f(f(z0, b), b))))), F(a, f(a, f(a, f(f(z0, b), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(z0, b)), b)), b)))) -> c6(F(f(a, f(f(a, f(f(a, f(a, f(a, z0))), b)), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(z0, b)), b))))), F(a, f(a, f(a, f(f(a, f(z0, b)), b))))) F(a, f(a, f(a, f(f(a, f(f(a, f(a, f(z0, b))), b)), b)))) -> c6(F(f(a, f(f(a, f(a, f(f(a, f(a, f(a, z0))), b))), b)), b), F(a, f(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))), F(a, f(a, f(a, f(f(a, f(a, f(z0, b))), b))))) F(a, f(a, f(a, f(f(a, f(x0, b)), b)))) -> c6(F(a, f(a, f(a, f(a, f(x0, b)))))) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(f(a, f(f(a, f(f(f(f(x0, b), b), b), b)), b)), b), F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b), F(f(f(a, x0), b), b)) F(f(f(a, f(f(a, f(a, z0)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(a, f(f(z0, b), b)), b)), b), b)), b), F(a, f(f(f(f(a, f(a, z0)), b), b), b)), F(f(f(f(a, f(a, z0)), b), b), b), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(f(a, f(f(a, z0), b)), b)), b), b) -> c7(F(f(a, f(f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b), b)), b), F(a, f(f(f(f(a, f(f(a, z0), b)), b), b), b)), F(f(f(f(a, f(f(a, z0), b)), b), b), b), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(f(a, x0), b)), b), b) -> c7(F(a, f(f(f(f(a, x0), b), b), b)), F(f(f(f(a, x0), b), b), b)) F(f(f(a, f(a, f(a, z0))), b), b) -> c7(F(f(a, f(f(a, f(f(a, f(f(z0, b), b)), b)), b)), b), F(a, f(f(f(a, f(a, z0)), b), b)), F(f(f(a, f(a, z0)), b), b)) F(f(f(a, f(a, f(f(a, z0), b))), b), b) -> c7(F(f(a, f(f(a, f(f(f(a, f(f(z0, b), b)), b), b)), b)), b), F(a, f(f(f(a, f(f(a, z0), b)), b), b)), F(f(f(a, f(f(a, z0), b)), b), b)) F(f(f(a, f(a, x0)), b), b) -> c7(F(a, f(f(f(a, x0), b), b))) K tuples:none Defined Rule Symbols: encArg_1, f_2 Defined Pair Symbols: F_2, ENCARG_1, ENCODE_F_2 Compound Symbols: c6_2, c2_3, c2_2, c2_1, c6_4, c6_3, c6_1, c7_4, c7_2, c7_3, c7_1, c_1