/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).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), 56 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), 7 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 454 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 [ComplexityIfPolyImplication, 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), 3 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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 3 ms] (134) CdtProblem (135) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (136) 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: a(a(a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) 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(b(x_1)) -> b(encArg(x_1)) encArg(cons_a(x_1)) -> a(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) ---------------------------------------- (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: a(a(a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) The (relative) TRS S consists of the following rules: encArg(b(x_1)) -> b(encArg(x_1)) encArg(cons_a(x_1)) -> a(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) 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: a(a(a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) The (relative) TRS S consists of the following rules: encArg(b(x_1)) -> b(encArg(x_1)) encArg(cons_a(x_1)) -> a(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) 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: a(a(a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) The (relative) TRS S consists of the following rules: encArg(b(x_1)) -> b(encArg(x_1)) encArg(cons_a(x_1)) -> a(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) 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: a(a(a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) The (relative) TRS S consists of the following rules: encArg(b(x_1)) -> b(encArg(x_1)) encArg(cons_a(x_1)) -> a(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: a(a(a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) encArg(b(x_1)) -> b(encArg(x_1)) encArg(cons_a(x_1)) -> a(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) Types: a :: b:cons_a -> b:cons_a b :: b:cons_a -> b:cons_a encArg :: b:cons_a -> b:cons_a cons_a :: b:cons_a -> b:cons_a encode_a :: b:cons_a -> b:cons_a encode_b :: b:cons_a -> b:cons_a hole_b:cons_a1_0 :: b:cons_a gen_b:cons_a2_0 :: Nat -> b:cons_a ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: a, encArg They will be analysed ascendingly in the following order: a < encArg ---------------------------------------- (12) Obligation: Innermost TRS: Rules: a(a(a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) encArg(b(x_1)) -> b(encArg(x_1)) encArg(cons_a(x_1)) -> a(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) Types: a :: b:cons_a -> b:cons_a b :: b:cons_a -> b:cons_a encArg :: b:cons_a -> b:cons_a cons_a :: b:cons_a -> b:cons_a encode_a :: b:cons_a -> b:cons_a encode_b :: b:cons_a -> b:cons_a hole_b:cons_a1_0 :: b:cons_a gen_b:cons_a2_0 :: Nat -> b:cons_a Generator Equations: gen_b:cons_a2_0(0) <=> hole_b:cons_a1_0 gen_b:cons_a2_0(+(x, 1)) <=> b(gen_b:cons_a2_0(x)) The following defined symbols remain to be analysed: a, encArg They will be analysed ascendingly in the following order: a < encArg ---------------------------------------- (13) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_b:cons_a2_0(+(1, n8_0))) -> *3_0, rt in Omega(0) Induction Base: encArg(gen_b:cons_a2_0(+(1, 0))) Induction Step: encArg(gen_b:cons_a2_0(+(1, +(n8_0, 1)))) ->_R^Omega(0) b(encArg(gen_b:cons_a2_0(+(1, n8_0)))) ->_IH b(*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: a(a(a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) encArg(b(x_1)) -> b(encArg(x_1)) encArg(cons_a(x_1)) -> a(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) 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: a(c_a(c_a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) The (relative) TRS S consists of the following rules: encArg(b(x_1)) -> b(encArg(x_1)) encArg(cons_a(x_1)) -> a(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) a(x0) -> c_a(x0) 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: a(c_a(c_a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) [1] encArg(b(x_1)) -> b(encArg(x_1)) [0] encArg(cons_a(x_1)) -> a(encArg(x_1)) [0] encode_a(x_1) -> a(encArg(x_1)) [0] encode_b(x_1) -> b(encArg(x_1)) [0] a(x0) -> c_a(x0) [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: a(c_a(c_a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) [1] encArg(b(x_1)) -> b(encArg(x_1)) [0] encArg(cons_a(x_1)) -> a(encArg(x_1)) [0] encode_a(x_1) -> a(encArg(x_1)) [0] encode_b(x_1) -> b(encArg(x_1)) [0] a(x0) -> c_a(x0) [0] The TRS has the following type information: a :: b:c_a:cons_a -> b:c_a:cons_a c_a :: b:c_a:cons_a -> b:c_a:cons_a b :: b:c_a:cons_a -> b:c_a:cons_a encArg :: b:c_a:cons_a -> b:c_a:cons_a cons_a :: b:c_a:cons_a -> b:c_a:cons_a encode_a :: b:c_a:cons_a -> b:c_a:cons_a encode_b :: b:c_a:cons_a -> b:c_a:cons_a 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_a_1 encode_b_1 a_1 Due to the following rules being added: encArg(v0) -> const [0] encode_a(v0) -> const [0] encode_b(v0) -> const [0] a(v0) -> const [0] And the following fresh constants: const ---------------------------------------- (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: a(c_a(c_a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) [1] encArg(b(x_1)) -> b(encArg(x_1)) [0] encArg(cons_a(x_1)) -> a(encArg(x_1)) [0] encode_a(x_1) -> a(encArg(x_1)) [0] encode_b(x_1) -> b(encArg(x_1)) [0] a(x0) -> c_a(x0) [0] encArg(v0) -> const [0] encode_a(v0) -> const [0] encode_b(v0) -> const [0] a(v0) -> const [0] The TRS has the following type information: a :: b:c_a:cons_a:const -> b:c_a:cons_a:const c_a :: b:c_a:cons_a:const -> b:c_a:cons_a:const b :: b:c_a:cons_a:const -> b:c_a:cons_a:const encArg :: b:c_a:cons_a:const -> b:c_a:cons_a:const cons_a :: b:c_a:cons_a:const -> b:c_a:cons_a:const encode_a :: b:c_a:cons_a:const -> b:c_a:cons_a:const encode_b :: b:c_a:cons_a:const -> b:c_a:cons_a:const const :: b:c_a:cons_a:const 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: a(c_a(c_a(b(b(b(c_a(c_a(b(b(b(x1'))))))))))) -> b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(x1'))))))))))))))) [2] a(c_a(c_a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(c_a(x1)))))))) [1] a(c_a(c_a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(const))))))) [1] encArg(b(x_1)) -> b(encArg(x_1)) [0] encArg(cons_a(b(x_1'))) -> a(b(encArg(x_1'))) [0] encArg(cons_a(cons_a(x_1''))) -> a(a(encArg(x_1''))) [0] encArg(cons_a(x_1)) -> a(const) [0] encode_a(b(x_11)) -> a(b(encArg(x_11))) [0] encode_a(cons_a(x_12)) -> a(a(encArg(x_12))) [0] encode_a(x_1) -> a(const) [0] encode_b(x_1) -> b(encArg(x_1)) [0] a(x0) -> c_a(x0) [0] encArg(v0) -> const [0] encode_a(v0) -> const [0] encode_b(v0) -> const [0] a(v0) -> const [0] The TRS has the following type information: a :: b:c_a:cons_a:const -> b:c_a:cons_a:const c_a :: b:c_a:cons_a:const -> b:c_a:cons_a:const b :: b:c_a:cons_a:const -> b:c_a:cons_a:const encArg :: b:c_a:cons_a:const -> b:c_a:cons_a:const cons_a :: b:c_a:cons_a:const -> b:c_a:cons_a:const encode_a :: b:c_a:cons_a:const -> b:c_a:cons_a:const encode_b :: b:c_a:cons_a:const -> b:c_a:cons_a:const const :: b:c_a:cons_a:const 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: const => 0 ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 a(z) -{ 1 }-> 1 + (1 + (1 + (1 + a(a(a(0)))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1)))) a(z) -{ 1 }-> 1 + (1 + (1 + (1 + a(a(a(1 + x1)))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1)))) a(z) -{ 2 }-> 1 + (1 + (1 + (1 + a(a(a(1 + (1 + (1 + (1 + a(a(a(a(x1'))))))))))))) :|: x1' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1'))))))))) encArg(z) -{ 0 }-> a(a(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0 encArg(z) -{ 0 }-> a(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> a(1 + encArg(x_1')) :|: z = 1 + (1 + x_1'), x_1' >= 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0 encode_a(z) -{ 0 }-> a(a(encArg(x_12))) :|: z = 1 + x_12, x_12 >= 0 encode_a(z) -{ 0 }-> a(0) :|: x_1 >= 0, z = x_1 encode_a(z) -{ 0 }-> a(1 + encArg(x_11)) :|: x_11 >= 0, z = 1 + x_11 encode_a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_b(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 ---------------------------------------- (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: a(z) -{ 0 }-> 0 :|: z >= 0 a(z) -{ 0 }-> 1 + z :|: z >= 0 a(z) -{ 1 }-> 1 + (1 + (1 + (1 + a(a(a(0)))))) :|: z - 5 >= 0 a(z) -{ 1 }-> 1 + (1 + (1 + (1 + a(a(a(1 + (z - 5))))))) :|: z - 5 >= 0 a(z) -{ 2 }-> 1 + (1 + (1 + (1 + a(a(a(1 + (1 + (1 + (1 + a(a(a(a(z - 10))))))))))))) :|: z - 10 >= 0 encArg(z) -{ 0 }-> a(a(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> a(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> a(1 + encArg(z - 2)) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0 encode_a(z) -{ 0 }-> a(a(encArg(z - 1))) :|: z - 1 >= 0 encode_a(z) -{ 0 }-> a(0) :|: z >= 0 encode_a(z) -{ 0 }-> a(1 + encArg(z - 1)) :|: z - 1 >= 0 encode_a(z) -{ 0 }-> 0 :|: z >= 0 encode_b(z) -{ 0 }-> 0 :|: z >= 0 encode_b(z) -{ 0 }-> 1 + encArg(z) :|: 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_a(v0) -> null_encode_a [0] encode_b(v0) -> null_encode_b [0] a(v0) -> null_a [0] And the following fresh constants: null_encArg, null_encode_a, null_encode_b, null_a ---------------------------------------- (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: a(c_a(c_a(b(b(b(x1)))))) -> b(b(b(b(a(a(a(a(x1)))))))) [1] encArg(b(x_1)) -> b(encArg(x_1)) [0] encArg(cons_a(x_1)) -> a(encArg(x_1)) [0] encode_a(x_1) -> a(encArg(x_1)) [0] encode_b(x_1) -> b(encArg(x_1)) [0] a(x0) -> c_a(x0) [0] encArg(v0) -> null_encArg [0] encode_a(v0) -> null_encode_a [0] encode_b(v0) -> null_encode_b [0] a(v0) -> null_a [0] The TRS has the following type information: a :: b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a c_a :: b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a b :: b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a encArg :: b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a cons_a :: b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a encode_a :: b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a encode_b :: b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a null_encArg :: b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a null_encode_a :: b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a null_encode_b :: b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a null_a :: b:c_a:cons_a:null_encArg:null_encode_a:null_encode_b:null_a 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: null_encArg => 0 null_encode_a => 0 null_encode_b => 0 null_a => 0 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 a(z) -{ 1 }-> 1 + (1 + (1 + (1 + a(a(a(a(x1))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1)))) encArg(z) -{ 0 }-> a(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0 encode_a(z) -{ 0 }-> a(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_b(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 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(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) encode_a(z0) -> a(encArg(z0)) encode_b(z0) -> b(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0)) ENCODE_A(z0) -> c2(A(encArg(z0)), ENCARG(z0)) ENCODE_B(z0) -> c3(ENCARG(z0)) A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) S tuples: A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) K tuples:none Defined Rule Symbols: a_1, encArg_1, encode_a_1, encode_b_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, ENCODE_B_1, A_1 Compound Symbols: c_1, c1_2, c2_2, c3_1, c4_4 ---------------------------------------- (37) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: ENCODE_B(z0) -> c3(ENCARG(z0)) ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) encode_a(z0) -> a(encArg(z0)) encode_b(z0) -> b(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0)) ENCODE_A(z0) -> c2(A(encArg(z0)), ENCARG(z0)) A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) S tuples: A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) K tuples:none Defined Rule Symbols: a_1, encArg_1, encode_a_1, encode_b_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c_1, c1_2, c2_2, c4_4 ---------------------------------------- (39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) encode_a(z0) -> a(encArg(z0)) encode_b(z0) -> b(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0)) A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) ENCODE_A(z0) -> c3(A(encArg(z0))) ENCODE_A(z0) -> c3(ENCARG(z0)) S tuples: A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) K tuples:none Defined Rule Symbols: a_1, encArg_1, encode_a_1, encode_b_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_2, c4_4, c3_1 ---------------------------------------- (41) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: ENCODE_A(z0) -> c3(ENCARG(z0)) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) encode_a(z0) -> a(encArg(z0)) encode_b(z0) -> b(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0)) A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) ENCODE_A(z0) -> c3(A(encArg(z0))) S tuples: A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) K tuples:none Defined Rule Symbols: a_1, encArg_1, encode_a_1, encode_b_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_2, c4_4, c3_1 ---------------------------------------- (43) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_a(z0) -> a(encArg(z0)) encode_b(z0) -> b(encArg(z0)) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0)) A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) ENCODE_A(z0) -> c3(A(encArg(z0))) S tuples: A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_2, c4_4, c3_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0)) by ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0))) ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0))) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) ENCODE_A(z0) -> c3(A(encArg(z0))) ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0))) ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0))) S tuples: A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c4_4, c3_1, c1_2 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) ENCODE_A(z0) -> c3(A(encArg(z0))) ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0))) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) S tuples: A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c4_4, c3_1, c1_2, c1_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A(a(a(b(b(b(z0)))))) -> c4(A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0)) by A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(b(b(b(b(a(a(a(a(z0))))))))), A(a(a(b(b(b(z0)))))), A(a(b(b(b(z0))))), A(b(b(b(z0))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(b(b(b(b(a(a(a(a(z0)))))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0)))))), A(a(b(b(b(z0)))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCODE_A(z0) -> c3(A(encArg(z0))) ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0))) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(b(b(b(b(a(a(a(a(z0))))))))), A(a(a(b(b(b(z0)))))), A(a(b(b(b(z0))))), A(b(b(b(z0))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(b(b(b(b(a(a(a(a(z0)))))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0)))))), A(a(b(b(b(z0)))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) S tuples: A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(b(b(b(b(a(a(a(a(z0))))))))), A(a(a(b(b(b(z0)))))), A(a(b(b(b(z0))))), A(b(b(b(z0))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(b(b(b(b(a(a(a(a(z0)))))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0)))))), A(a(b(b(b(z0)))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c_1, c3_1, c1_2, c1_1, c4_4 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCODE_A(z0) -> c3(A(encArg(z0))) ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0))) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) S tuples: A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c_1, c3_1, c1_2, c1_1, c4_4, c4_1, c4_2 ---------------------------------------- (53) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_A(z0) -> c3(A(encArg(z0))) by ENCODE_A(b(z0)) -> c3(A(b(encArg(z0)))) ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0)))) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0))) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) ENCODE_A(b(z0)) -> c3(A(b(encArg(z0)))) ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0)))) S tuples: A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_2, c1_1, c4_4, c4_1, c4_2, c3_1 ---------------------------------------- (55) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCODE_A(b(z0)) -> c3(A(b(encArg(z0)))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0))) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0)))) S tuples: A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_2, c1_1, c4_4, c4_1, c4_2, c3_1 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0))) by ENCARG(cons_a(cons_a(b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(b(z0)))) ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0)))) ENCARG(cons_a(cons_a(b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(b(z0)))) ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) S tuples: A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_1, c4_4, c4_1, c4_2, c3_1, c1_2 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0)))) ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCARG(cons_a(cons_a(b(z0)))) -> c1(ENCARG(cons_a(b(z0)))) S tuples: A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_1, c4_4, c4_1, c4_2, c3_1, c1_2 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(a(z0))))))))))), A(a(a(a(a(b(b(b(z0)))))))), A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) by A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(a(b(b(b(b(a(a(a(a(z0)))))))))))))))), A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(b(b(b(b(a(a(a(a(z0))))))))))))))))), A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0)))) ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCARG(cons_a(cons_a(b(z0)))) -> c1(ENCARG(cons_a(b(z0)))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(a(b(b(b(b(a(a(a(a(z0)))))))))))))))), A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(b(b(b(b(a(a(a(a(z0))))))))))))))))), A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) S tuples: A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(a(b(b(b(b(a(a(a(a(z0)))))))))))))))), A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(b(b(b(b(a(a(a(a(z0))))))))))))))))), A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_1, c4_1, c4_2, c3_1, c1_2, c4_4 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0)))) ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCARG(cons_a(cons_a(b(z0)))) -> c1(ENCARG(cons_a(b(z0)))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) S tuples: A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_1, c4_1, c4_2, c3_1, c1_2, c4_4, c4_3 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(a(b(b(b(z0))))))), A(a(a(b(b(b(z0))))))) by A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(b(b(b(b(a(a(a(a(z0))))))))), A(a(a(b(b(b(z0))))))) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0)))) ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCARG(cons_a(cons_a(b(z0)))) -> c1(ENCARG(cons_a(b(z0)))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(b(b(b(b(a(a(a(a(z0))))))))), A(a(a(b(b(b(z0))))))) S tuples: A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(b(b(b(b(a(a(a(a(z0))))))))), A(a(a(b(b(b(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_1, c4_1, c3_1, c1_2, c4_4, c4_2, c4_3 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0)))) ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCARG(cons_a(cons_a(b(z0)))) -> c1(ENCARG(cons_a(b(z0)))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) S tuples: A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_1, c4_1, c3_1, c1_2, c4_4, c4_2, c4_3 ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0)))) by ENCODE_A(cons_a(b(z0))) -> c3(A(a(b(encArg(z0))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCARG(cons_a(cons_a(b(z0)))) -> c1(ENCARG(cons_a(b(z0)))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(b(z0))) -> c3(A(a(b(encArg(z0))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) S tuples: A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_1, c4_1, c1_2, c4_4, c4_2, c4_3, c3_1 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCODE_A(cons_a(b(z0))) -> c3(A(a(b(encArg(z0))))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(b(z0)) -> c(ENCARG(z0)) ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCARG(cons_a(cons_a(b(z0)))) -> c1(ENCARG(cons_a(b(z0)))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) S tuples: A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c_1, c1_1, c4_1, c1_2, c4_4, c4_2, c4_3, c3_1 ---------------------------------------- (73) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(b(z0)) -> c(ENCARG(z0)) by ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCARG(cons_a(cons_a(b(z0)))) -> c1(ENCARG(cons_a(b(z0)))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) S tuples: A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_1, c4_1, c1_2, c4_4, c4_2, c4_3, c3_1, c_1 ---------------------------------------- (75) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_a(b(z0))) -> c1(ENCARG(b(z0))) by ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCARG(cons_a(cons_a(b(z0)))) -> c1(ENCARG(cons_a(b(z0)))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) S tuples: A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: A_1, ENCARG_1, ENCODE_A_1 Compound Symbols: c4_1, c1_2, c1_1, c4_4, c4_2, c4_3, c3_1, c_1 ---------------------------------------- (77) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A(a(a(b(b(b(b(b(b(z0))))))))) -> c4(A(a(a(b(b(b(z0))))))) by A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCARG(cons_a(cons_a(b(z0)))) -> c1(ENCARG(cons_a(b(z0)))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) S tuples: A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c1_1, c4_4, c4_2, c4_3, c4_1, c3_1, c_1 ---------------------------------------- (79) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_a(cons_a(b(z0)))) -> c1(ENCARG(cons_a(b(z0)))) by ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) S tuples: A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_4, c4_2, c4_3, c4_1, c3_1, c_1, c1_1 ---------------------------------------- (81) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(a(b(b(b(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) by A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(b(b(b(b(a(a(a(a(a(a(b(b(b(z0)))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(b(b(b(b(a(a(a(a(a(a(b(b(b(z0)))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) S tuples: A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(b(b(b(b(a(a(a(a(a(a(b(b(b(z0)))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_2, c4_3, c4_1, c3_1, c_1, c1_1, c4_4 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) S tuples: A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_2, c4_3, c4_1, c3_1, c_1, c1_1 ---------------------------------------- (85) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace A(a(a(b(b(b(a(a(b(b(b(x0))))))))))) -> c4(A(a(a(a(a(b(b(b(x0)))))))), A(a(a(a(b(b(b(x0)))))))) by A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(a(a(b(b(b(z0)))))))), A(b(b(b(b(a(a(a(a(z0)))))))))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(a(a(b(b(b(z0)))))))), A(b(b(b(b(a(a(a(a(z0)))))))))) S tuples: A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(a(a(b(b(b(z0)))))))), A(b(b(b(b(a(a(a(a(z0)))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_3, c4_1, c3_1, c_1, c1_1, c4_2 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(a(a(b(b(b(z0))))))))) S tuples: A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(a(a(b(b(b(z0))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_3, c4_1, c3_1, c_1, c1_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(a(a(a(b(b(b(z0))))))))) by A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(b(b(b(b(a(a(a(a(z0))))))))))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(b(b(b(b(a(a(a(a(z0))))))))))) S tuples: A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4(A(a(b(b(b(b(a(a(a(a(z0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_3, c4_1, c3_1, c_1, c1_1 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 S tuples: A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_3, c4_1, c3_1, c_1, c1_1, c4 ---------------------------------------- (93) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(a(b(b(b(b(b(b(z0)))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) by A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(b(b(b(b(a(a(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(b(b(b(b(a(a(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) S tuples: A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(b(b(b(b(a(a(a(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_3, c4_1, c3_1, c_1, c1_1, c4 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) S tuples: A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_3, c4_1, c3_1, c_1, c1_1, c4, c4_2 ---------------------------------------- (97) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(a(b(b(b(a(b(b(b(z0))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) by A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(b(b(b(b(a(a(a(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(b(b(b(b(a(a(a(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) S tuples: A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(b(b(b(b(a(a(a(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_1, c3_1, c_1, c1_1, c4_3, c4, c4_2 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) S tuples: A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_1, c3_1, c_1, c1_1, c4_3, c4, c4_2 ---------------------------------------- (101) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(a(a(b(b(b(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) by A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(b(b(b(b(a(a(a(a(a(a(b(b(b(z0))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(b(b(b(b(a(a(a(a(a(a(b(b(b(z0))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) S tuples: A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(b(b(b(b(a(a(a(a(a(a(b(b(b(z0))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_1, c3_1, c_1, c1_1, c4, c4_2, c4_3 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) S tuples: A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_1, c3_1, c_1, c1_1, c4, c4_2 ---------------------------------------- (105) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(a(a(b(b(b(b(b(b(z0))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) by A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(b(b(b(b(a(a(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(b(b(b(b(a(a(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) S tuples: A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(b(b(b(b(a(a(a(a(b(b(b(z0))))))))))))), A(a(a(b(b(b(b(b(b(z0)))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_1, c3_1, c_1, c1_1, c4, c4_2 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) S tuples: A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_1, c3_1, c_1, c1_1, c4, c4_2 ---------------------------------------- (109) CdtRewritingProof (BOTH BOUNDS(ID, ID)) Used rewriting to replace A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(a(a(b(b(b(a(b(b(b(z0)))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) by A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(b(b(b(b(a(a(a(a(a(b(b(b(z0)))))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(b(b(b(b(a(a(a(a(a(b(b(b(z0)))))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) S tuples: A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(b(b(b(b(a(a(a(a(a(b(b(b(z0)))))))))))))), A(a(a(b(b(b(a(b(b(b(z0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_1, c3_1, c_1, c1_1, c4, c4_2 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) S tuples: A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, A_1, ENCODE_A_1 Compound Symbols: c1_2, c4_1, c3_1, c_1, c1_1, c4, c4_2 ---------------------------------------- (113) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A(a(a(b(b(b(a(b(b(b(z0)))))))))) -> c4(A(a(a(b(b(b(z0))))))) by A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) S tuples: A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c1_2, c3_1, c_1, c1_1, c4_1, c4, c4_2 ---------------------------------------- (115) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(b(b(y0))) -> c(ENCARG(b(y0))) by ENCARG(b(b(b(y0)))) -> c(ENCARG(b(b(y0)))) ENCARG(b(b(cons_a(b(y0))))) -> c(ENCARG(b(cons_a(b(y0))))) ENCARG(b(b(cons_a(cons_a(cons_a(y0)))))) -> c(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(b(b(cons_a(cons_a(b(y0)))))) -> c(ENCARG(b(cons_a(cons_a(b(y0)))))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(b(b(b(y0)))) -> c(ENCARG(b(b(y0)))) ENCARG(b(b(cons_a(b(y0))))) -> c(ENCARG(b(cons_a(b(y0))))) ENCARG(b(b(cons_a(cons_a(cons_a(y0)))))) -> c(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(b(b(cons_a(cons_a(b(y0)))))) -> c(ENCARG(b(cons_a(cons_a(b(y0)))))) S tuples: A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c1_2, c3_1, c_1, c1_1, c4_1, c4, c4_2 ---------------------------------------- (117) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(b(cons_a(b(y0)))) -> c(ENCARG(cons_a(b(y0)))) by ENCARG(b(cons_a(b(b(y0))))) -> c(ENCARG(cons_a(b(b(y0))))) ENCARG(b(cons_a(b(cons_a(b(y0)))))) -> c(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(b(cons_a(b(cons_a(cons_a(b(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(b(b(b(y0)))) -> c(ENCARG(b(b(y0)))) ENCARG(b(b(cons_a(b(y0))))) -> c(ENCARG(b(cons_a(b(y0))))) ENCARG(b(b(cons_a(cons_a(cons_a(y0)))))) -> c(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(b(b(cons_a(cons_a(b(y0)))))) -> c(ENCARG(b(cons_a(cons_a(b(y0)))))) ENCARG(b(cons_a(b(b(y0))))) -> c(ENCARG(cons_a(b(b(y0))))) ENCARG(b(cons_a(b(cons_a(b(y0)))))) -> c(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(b(cons_a(b(cons_a(cons_a(b(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) S tuples: A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c1_2, c3_1, c_1, c1_1, c4_1, c4, c4_2 ---------------------------------------- (119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(b(cons_a(cons_a(b(y0))))) -> c(ENCARG(cons_a(cons_a(b(y0))))) by ENCARG(b(cons_a(cons_a(b(b(y0)))))) -> c(ENCARG(cons_a(cons_a(b(b(y0)))))) ENCARG(b(cons_a(cons_a(b(cons_a(b(y0))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(b(b(b(y0)))) -> c(ENCARG(b(b(y0)))) ENCARG(b(b(cons_a(b(y0))))) -> c(ENCARG(b(cons_a(b(y0))))) ENCARG(b(b(cons_a(cons_a(cons_a(y0)))))) -> c(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(b(b(cons_a(cons_a(b(y0)))))) -> c(ENCARG(b(cons_a(cons_a(b(y0)))))) ENCARG(b(cons_a(b(b(y0))))) -> c(ENCARG(cons_a(b(b(y0))))) ENCARG(b(cons_a(b(cons_a(b(y0)))))) -> c(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(b(cons_a(b(cons_a(cons_a(b(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(b(y0)))))) -> c(ENCARG(cons_a(cons_a(b(b(y0)))))) ENCARG(b(cons_a(cons_a(b(cons_a(b(y0))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) S tuples: A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c1_2, c3_1, c_1, c1_1, c4_1, c4, c4_2 ---------------------------------------- (121) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_a(b(b(y0)))) -> c1(ENCARG(b(b(y0)))) by ENCARG(cons_a(b(b(b(y0))))) -> c1(ENCARG(b(b(b(y0))))) ENCARG(cons_a(b(b(cons_a(b(y0)))))) -> c1(ENCARG(b(b(cons_a(b(y0)))))) ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(b(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(b(y0))))))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(b(b(b(y0)))) -> c(ENCARG(b(b(y0)))) ENCARG(b(b(cons_a(b(y0))))) -> c(ENCARG(b(cons_a(b(y0))))) ENCARG(b(b(cons_a(cons_a(cons_a(y0)))))) -> c(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(b(b(cons_a(cons_a(b(y0)))))) -> c(ENCARG(b(cons_a(cons_a(b(y0)))))) ENCARG(b(cons_a(b(b(y0))))) -> c(ENCARG(cons_a(b(b(y0))))) ENCARG(b(cons_a(b(cons_a(b(y0)))))) -> c(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(b(cons_a(b(cons_a(cons_a(b(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(b(y0)))))) -> c(ENCARG(cons_a(cons_a(b(b(y0)))))) ENCARG(b(cons_a(cons_a(b(cons_a(b(y0))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(b(b(y0))))) -> c1(ENCARG(b(b(b(y0))))) ENCARG(cons_a(b(b(cons_a(b(y0)))))) -> c1(ENCARG(b(b(cons_a(b(y0)))))) ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(b(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(b(y0))))))) S tuples: A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c1_2, c3_1, c_1, c1_1, c4_1, c4, c4_2 ---------------------------------------- (123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_a(b(cons_a(b(y0))))) -> c1(ENCARG(b(cons_a(b(y0))))) by ENCARG(cons_a(b(cons_a(b(b(y0)))))) -> c1(ENCARG(b(cons_a(b(b(y0)))))) ENCARG(cons_a(b(cons_a(b(cons_a(b(y0))))))) -> c1(ENCARG(b(cons_a(b(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(b(y0)))))))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(b(b(b(y0)))) -> c(ENCARG(b(b(y0)))) ENCARG(b(b(cons_a(b(y0))))) -> c(ENCARG(b(cons_a(b(y0))))) ENCARG(b(b(cons_a(cons_a(cons_a(y0)))))) -> c(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(b(b(cons_a(cons_a(b(y0)))))) -> c(ENCARG(b(cons_a(cons_a(b(y0)))))) ENCARG(b(cons_a(b(b(y0))))) -> c(ENCARG(cons_a(b(b(y0))))) ENCARG(b(cons_a(b(cons_a(b(y0)))))) -> c(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(b(cons_a(b(cons_a(cons_a(b(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(b(y0)))))) -> c(ENCARG(cons_a(cons_a(b(b(y0)))))) ENCARG(b(cons_a(cons_a(b(cons_a(b(y0))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(b(b(y0))))) -> c1(ENCARG(b(b(b(y0))))) ENCARG(cons_a(b(b(cons_a(b(y0)))))) -> c1(ENCARG(b(b(cons_a(b(y0)))))) ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(b(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(b(y0)))))) -> c1(ENCARG(b(cons_a(b(b(y0)))))) ENCARG(cons_a(b(cons_a(b(cons_a(b(y0))))))) -> c1(ENCARG(b(cons_a(b(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(b(y0)))))))) S tuples: A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c1_2, c3_1, c_1, c1_1, c4_1, c4, c4_2 ---------------------------------------- (125) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_a(b(cons_a(cons_a(b(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(b(y0)))))) by ENCARG(cons_a(b(cons_a(cons_a(b(b(y0))))))) -> c1(ENCARG(b(cons_a(cons_a(b(b(y0))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(b(b(b(y0)))) -> c(ENCARG(b(b(y0)))) ENCARG(b(b(cons_a(b(y0))))) -> c(ENCARG(b(cons_a(b(y0))))) ENCARG(b(b(cons_a(cons_a(cons_a(y0)))))) -> c(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(b(b(cons_a(cons_a(b(y0)))))) -> c(ENCARG(b(cons_a(cons_a(b(y0)))))) ENCARG(b(cons_a(b(b(y0))))) -> c(ENCARG(cons_a(b(b(y0))))) ENCARG(b(cons_a(b(cons_a(b(y0)))))) -> c(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(b(cons_a(b(cons_a(cons_a(b(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(b(y0)))))) -> c(ENCARG(cons_a(cons_a(b(b(y0)))))) ENCARG(b(cons_a(cons_a(b(cons_a(b(y0))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(b(b(y0))))) -> c1(ENCARG(b(b(b(y0))))) ENCARG(cons_a(b(b(cons_a(b(y0)))))) -> c1(ENCARG(b(b(cons_a(b(y0)))))) ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(b(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(b(y0)))))) -> c1(ENCARG(b(cons_a(b(b(y0)))))) ENCARG(cons_a(b(cons_a(b(cons_a(b(y0))))))) -> c1(ENCARG(b(cons_a(b(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(b(y0))))))) -> c1(ENCARG(b(cons_a(cons_a(b(b(y0))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) S tuples: A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c1_2, c3_1, c_1, c1_1, c4_1, c4, c4_2 ---------------------------------------- (127) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))) -> c4(A(a(a(b(b(b(b(b(b(y0)))))))))) by A(a(a(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(b(b(b(y0)))) -> c(ENCARG(b(b(y0)))) ENCARG(b(b(cons_a(b(y0))))) -> c(ENCARG(b(cons_a(b(y0))))) ENCARG(b(b(cons_a(cons_a(cons_a(y0)))))) -> c(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(b(b(cons_a(cons_a(b(y0)))))) -> c(ENCARG(b(cons_a(cons_a(b(y0)))))) ENCARG(b(cons_a(b(b(y0))))) -> c(ENCARG(cons_a(b(b(y0))))) ENCARG(b(cons_a(b(cons_a(b(y0)))))) -> c(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(b(cons_a(b(cons_a(cons_a(b(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(b(y0)))))) -> c(ENCARG(cons_a(cons_a(b(b(y0)))))) ENCARG(b(cons_a(cons_a(b(cons_a(b(y0))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(b(b(y0))))) -> c1(ENCARG(b(b(b(y0))))) ENCARG(cons_a(b(b(cons_a(b(y0)))))) -> c1(ENCARG(b(b(cons_a(b(y0)))))) ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(b(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(b(y0)))))) -> c1(ENCARG(b(cons_a(b(b(y0)))))) ENCARG(cons_a(b(cons_a(b(cons_a(b(y0))))))) -> c1(ENCARG(b(cons_a(b(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(b(y0))))))) -> c1(ENCARG(b(cons_a(cons_a(b(b(y0))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) A(a(a(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) S tuples: A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c1_2, c3_1, c_1, c1_1, c4_1, c4, c4_2 ---------------------------------------- (129) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace A(a(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) by A(a(a(b(b(b(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(b(b(b(y0)))) -> c(ENCARG(b(b(y0)))) ENCARG(b(b(cons_a(b(y0))))) -> c(ENCARG(b(cons_a(b(y0))))) ENCARG(b(b(cons_a(cons_a(cons_a(y0)))))) -> c(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(b(b(cons_a(cons_a(b(y0)))))) -> c(ENCARG(b(cons_a(cons_a(b(y0)))))) ENCARG(b(cons_a(b(b(y0))))) -> c(ENCARG(cons_a(b(b(y0))))) ENCARG(b(cons_a(b(cons_a(b(y0)))))) -> c(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(b(cons_a(b(cons_a(cons_a(b(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(b(y0)))))) -> c(ENCARG(cons_a(cons_a(b(b(y0)))))) ENCARG(b(cons_a(cons_a(b(cons_a(b(y0))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(b(b(y0))))) -> c1(ENCARG(b(b(b(y0))))) ENCARG(cons_a(b(b(cons_a(b(y0)))))) -> c1(ENCARG(b(b(cons_a(b(y0)))))) ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(b(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(b(y0)))))) -> c1(ENCARG(b(cons_a(b(b(y0)))))) ENCARG(cons_a(b(cons_a(b(cons_a(b(y0))))))) -> c1(ENCARG(b(cons_a(b(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(b(y0))))))) -> c1(ENCARG(b(cons_a(cons_a(b(b(y0))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) A(a(a(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))) S tuples: A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c1_2, c3_1, c_1, c1_1, c4_1, c4, c4_2 ---------------------------------------- (131) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_a(cons_a(b(b(y0))))) -> c1(ENCARG(cons_a(b(b(y0))))) by ENCARG(cons_a(cons_a(b(b(b(y0)))))) -> c1(ENCARG(cons_a(b(b(b(y0)))))) ENCARG(cons_a(cons_a(b(b(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(b(cons_a(b(y0))))))) ENCARG(cons_a(cons_a(b(b(cons_a(cons_a(cons_a(y0)))))))) -> c1(ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(cons_a(cons_a(b(b(cons_a(cons_a(b(y0)))))))) -> c1(ENCARG(cons_a(b(b(cons_a(cons_a(b(y0)))))))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(b(b(b(y0)))) -> c(ENCARG(b(b(y0)))) ENCARG(b(b(cons_a(b(y0))))) -> c(ENCARG(b(cons_a(b(y0))))) ENCARG(b(b(cons_a(cons_a(cons_a(y0)))))) -> c(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(b(b(cons_a(cons_a(b(y0)))))) -> c(ENCARG(b(cons_a(cons_a(b(y0)))))) ENCARG(b(cons_a(b(b(y0))))) -> c(ENCARG(cons_a(b(b(y0))))) ENCARG(b(cons_a(b(cons_a(b(y0)))))) -> c(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(b(cons_a(b(cons_a(cons_a(b(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(b(y0)))))) -> c(ENCARG(cons_a(cons_a(b(b(y0)))))) ENCARG(b(cons_a(cons_a(b(cons_a(b(y0))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(b(b(y0))))) -> c1(ENCARG(b(b(b(y0))))) ENCARG(cons_a(b(b(cons_a(b(y0)))))) -> c1(ENCARG(b(b(cons_a(b(y0)))))) ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(b(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(b(y0)))))) -> c1(ENCARG(b(cons_a(b(b(y0)))))) ENCARG(cons_a(b(cons_a(b(cons_a(b(y0))))))) -> c1(ENCARG(b(cons_a(b(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(b(y0))))))) -> c1(ENCARG(b(cons_a(cons_a(b(b(y0))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) A(a(a(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))) ENCARG(cons_a(cons_a(b(b(b(y0)))))) -> c1(ENCARG(cons_a(b(b(b(y0)))))) ENCARG(cons_a(cons_a(b(b(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(b(cons_a(b(y0))))))) ENCARG(cons_a(cons_a(b(b(cons_a(cons_a(cons_a(y0)))))))) -> c1(ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(cons_a(cons_a(b(b(cons_a(cons_a(b(y0)))))))) -> c1(ENCARG(cons_a(b(b(cons_a(cons_a(b(y0)))))))) S tuples: A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c1_2, c3_1, c_1, c1_1, c4_1, c4, c4_2 ---------------------------------------- (133) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_a(cons_a(b(cons_a(b(y0)))))) -> c1(ENCARG(cons_a(b(cons_a(b(y0)))))) by ENCARG(cons_a(cons_a(b(cons_a(b(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(b(b(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(b(cons_a(b(y0)))))))) -> c1(ENCARG(cons_a(b(cons_a(b(cons_a(b(y0)))))))) ENCARG(cons_a(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) -> c1(ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) ENCARG(cons_a(cons_a(b(cons_a(b(cons_a(cons_a(b(y0))))))))) -> c1(ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(b(y0))))))))) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(b(b(b(y0)))) -> c(ENCARG(b(b(y0)))) ENCARG(b(b(cons_a(b(y0))))) -> c(ENCARG(b(cons_a(b(y0))))) ENCARG(b(b(cons_a(cons_a(cons_a(y0)))))) -> c(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(b(b(cons_a(cons_a(b(y0)))))) -> c(ENCARG(b(cons_a(cons_a(b(y0)))))) ENCARG(b(cons_a(b(b(y0))))) -> c(ENCARG(cons_a(b(b(y0))))) ENCARG(b(cons_a(b(cons_a(b(y0)))))) -> c(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(b(cons_a(b(cons_a(cons_a(b(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(b(y0)))))) -> c(ENCARG(cons_a(cons_a(b(b(y0)))))) ENCARG(b(cons_a(cons_a(b(cons_a(b(y0))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(b(b(y0))))) -> c1(ENCARG(b(b(b(y0))))) ENCARG(cons_a(b(b(cons_a(b(y0)))))) -> c1(ENCARG(b(b(cons_a(b(y0)))))) ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(b(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(b(y0)))))) -> c1(ENCARG(b(cons_a(b(b(y0)))))) ENCARG(cons_a(b(cons_a(b(cons_a(b(y0))))))) -> c1(ENCARG(b(cons_a(b(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(b(y0))))))) -> c1(ENCARG(b(cons_a(cons_a(b(b(y0))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) A(a(a(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))) ENCARG(cons_a(cons_a(b(b(b(y0)))))) -> c1(ENCARG(cons_a(b(b(b(y0)))))) ENCARG(cons_a(cons_a(b(b(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(b(cons_a(b(y0))))))) ENCARG(cons_a(cons_a(b(b(cons_a(cons_a(cons_a(y0)))))))) -> c1(ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(cons_a(cons_a(b(b(cons_a(cons_a(b(y0)))))))) -> c1(ENCARG(cons_a(b(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(cons_a(b(cons_a(b(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(b(b(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(b(cons_a(b(y0)))))))) -> c1(ENCARG(cons_a(b(cons_a(b(cons_a(b(y0)))))))) ENCARG(cons_a(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) -> c1(ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) ENCARG(cons_a(cons_a(b(cons_a(b(cons_a(cons_a(b(y0))))))))) -> c1(ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(b(y0))))))))) S tuples: A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c1_2, c3_1, c_1, c1_1, c4_1, c4, c4_2 ---------------------------------------- (135) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) by ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(b(y0)))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(b(y0)))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(cons_a(b(y0))))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(b(y0))))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: encArg(b(z0)) -> b(encArg(z0)) encArg(cons_a(z0)) -> a(encArg(z0)) a(a(a(b(b(b(z0)))))) -> b(b(b(b(a(a(a(a(z0)))))))) Tuples: ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0)))) ENCODE_A(cons_a(cons_a(z0))) -> c3(A(a(a(encArg(z0))))) ENCARG(b(cons_a(cons_a(cons_a(y0))))) -> c(ENCARG(cons_a(cons_a(cons_a(y0))))) ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0)))))) -> c1(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) ENCARG(b(b(b(y0)))) -> c(ENCARG(b(b(y0)))) ENCARG(b(b(cons_a(b(y0))))) -> c(ENCARG(b(cons_a(b(y0))))) ENCARG(b(b(cons_a(cons_a(cons_a(y0)))))) -> c(ENCARG(b(cons_a(cons_a(cons_a(y0)))))) ENCARG(b(b(cons_a(cons_a(b(y0)))))) -> c(ENCARG(b(cons_a(cons_a(b(y0)))))) ENCARG(b(cons_a(b(b(y0))))) -> c(ENCARG(cons_a(b(b(y0))))) ENCARG(b(cons_a(b(cons_a(b(y0)))))) -> c(ENCARG(cons_a(b(cons_a(b(y0)))))) ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(b(cons_a(b(cons_a(cons_a(b(y0))))))) -> c(ENCARG(cons_a(b(cons_a(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(b(y0)))))) -> c(ENCARG(cons_a(cons_a(b(b(y0)))))) ENCARG(b(cons_a(cons_a(b(cons_a(b(y0))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(b(y0))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c(ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(b(b(y0))))) -> c1(ENCARG(b(b(b(y0))))) ENCARG(cons_a(b(b(cons_a(b(y0)))))) -> c1(ENCARG(b(b(cons_a(b(y0)))))) ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(cons_a(y0))))))) ENCARG(cons_a(b(b(cons_a(cons_a(b(y0))))))) -> c1(ENCARG(b(b(cons_a(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(b(y0)))))) -> c1(ENCARG(b(cons_a(b(b(y0)))))) ENCARG(cons_a(b(cons_a(b(cons_a(b(y0))))))) -> c1(ENCARG(b(cons_a(b(cons_a(b(y0))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(b(y0))))))) -> c1(ENCARG(b(cons_a(cons_a(b(b(y0))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(b(y0)))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(b(y0)))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) -> c1(ENCARG(b(cons_a(cons_a(b(cons_a(cons_a(b(y0))))))))) A(a(a(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))) ENCARG(cons_a(cons_a(b(b(b(y0)))))) -> c1(ENCARG(cons_a(b(b(b(y0)))))) ENCARG(cons_a(cons_a(b(b(cons_a(b(y0))))))) -> c1(ENCARG(cons_a(b(b(cons_a(b(y0))))))) ENCARG(cons_a(cons_a(b(b(cons_a(cons_a(cons_a(y0)))))))) -> c1(ENCARG(cons_a(b(b(cons_a(cons_a(cons_a(y0)))))))) ENCARG(cons_a(cons_a(b(b(cons_a(cons_a(b(y0)))))))) -> c1(ENCARG(cons_a(b(b(cons_a(cons_a(b(y0)))))))) ENCARG(cons_a(cons_a(b(cons_a(b(b(y0))))))) -> c1(ENCARG(cons_a(b(cons_a(b(b(y0))))))) ENCARG(cons_a(cons_a(b(cons_a(b(cons_a(b(y0)))))))) -> c1(ENCARG(cons_a(b(cons_a(b(cons_a(b(y0)))))))) ENCARG(cons_a(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) -> c1(ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(cons_a(y0))))))))) ENCARG(cons_a(cons_a(b(cons_a(b(cons_a(cons_a(b(y0))))))))) -> c1(ENCARG(cons_a(b(cons_a(b(cons_a(cons_a(b(y0))))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(b(y0)))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(b(y0)))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(cons_a(b(y0))))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(b(y0))))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(cons_a(y0)))))))))) ENCARG(cons_a(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))))) -> c1(ENCARG(cons_a(b(cons_a(cons_a(b(cons_a(cons_a(b(y0)))))))))) S tuples: A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(a(a(b(b(b(z0))))))))))) -> c4 A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(z0)))))))))))))))) -> c4(A(a(a(b(b(b(b(a(a(a(b(b(b(b(a(a(a(a(z0)))))))))))))))))), A(a(a(b(b(b(a(a(b(b(b(z0)))))))))))) A(a(a(b(b(b(a(a(b(b(b(b(b(b(z0)))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(z0)))))))))) A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(z0))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(z0))))))))))) A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0)))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(y0))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(y0)))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))) A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))) -> c4(A(a(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(b(b(b(y0))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(b(b(b(y0)))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(a(b(b(b(a(b(b(b(y0))))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(b(b(b(a(b(b(b(y0)))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(y0)))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(a(b(b(b(y0))))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(b(b(b(y0))))))))))))))))))) A(a(a(b(b(b(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))))) -> c4(A(a(a(b(b(b(a(b(b(b(a(a(b(b(b(a(b(b(b(y0)))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, a_1 Defined Pair Symbols: ENCARG_1, ENCODE_A_1, A_1 Compound Symbols: c1_2, c3_1, c_1, c1_1, c4_1, c4, c4_2