/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF).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), 54 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 452 ms] (12) BOUNDS(1, INF) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (16) CpxTRS (17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (18) CpxRelTRS (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 22 ms] (20) CpxRelTRS (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxWeightedTrs (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxTypedWeightedTrs (25) CompletionProof [UPPER BOUND(ID), 0 ms] (26) CpxTypedWeightedCompleteTrs (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) CompletionProof [UPPER BOUND(ID), 0 ms] (30) CpxTypedWeightedCompleteTrs (31) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CpxRNTS (37) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (38) CdtProblem (39) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (40) CdtProblem (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (46) CdtProblem (47) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 12 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 57 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 102 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 98 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 168 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 101 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 94 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 85 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 100 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 201 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 107 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 158 ms] (132) CdtProblem ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: b(a(a(b(b(x1))))) -> b(a(a(a(a(b(b(x1))))))) b(a(b(b(x1)))) -> b(b(x1)) b(a(b(a(a(a(a(b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) b(a(a(b(a(a(a(a(b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) b(a(a(a(b(a(a(a(a(b(x1)))))))))) -> b(x1) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(a(x_1)) -> a(encArg(x_1)) encArg(cons_b(x_1)) -> b(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: b(a(a(b(b(x1))))) -> b(a(a(a(a(b(b(x1))))))) b(a(b(b(x1)))) -> b(b(x1)) b(a(b(a(a(a(a(b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) b(a(a(b(a(a(a(a(b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) b(a(a(a(b(a(a(a(a(b(x1)))))))))) -> b(x1) The (relative) TRS S consists of the following rules: encArg(a(x_1)) -> a(encArg(x_1)) encArg(cons_b(x_1)) -> b(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: b(a(a(b(b(x1))))) -> b(a(a(a(a(b(b(x1))))))) b(a(b(b(x1)))) -> b(b(x1)) b(a(b(a(a(a(a(b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) b(a(a(b(a(a(a(a(b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) b(a(a(a(b(a(a(a(a(b(x1)))))))))) -> b(x1) The (relative) TRS S consists of the following rules: encArg(a(x_1)) -> a(encArg(x_1)) encArg(cons_b(x_1)) -> b(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (5) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (6) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: b(a(a(b(b(x1))))) -> b(a(a(a(a(b(b(x1))))))) b(a(b(b(x1)))) -> b(b(x1)) b(a(b(a(a(a(a(b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) b(a(a(b(a(a(a(a(b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) b(a(a(a(b(a(a(a(a(b(x1)))))))))) -> b(x1) The (relative) TRS S consists of the following rules: encArg(a(x_1)) -> a(encArg(x_1)) encArg(cons_b(x_1)) -> b(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: TRS: Rules: b(a(a(b(b(x1))))) -> b(a(a(a(a(b(b(x1))))))) b(a(b(b(x1)))) -> b(b(x1)) b(a(b(a(a(a(a(b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) b(a(a(b(a(a(a(a(b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) b(a(a(a(b(a(a(a(a(b(x1)))))))))) -> b(x1) encArg(a(x_1)) -> a(encArg(x_1)) encArg(cons_b(x_1)) -> b(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) Types: b :: a:cons_b -> a:cons_b a :: a:cons_b -> a:cons_b encArg :: a:cons_b -> a:cons_b cons_b :: a:cons_b -> a:cons_b encode_b :: a:cons_b -> a:cons_b encode_a :: a:cons_b -> a:cons_b hole_a:cons_b1_0 :: a:cons_b gen_a:cons_b2_0 :: Nat -> a:cons_b ---------------------------------------- (9) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: b, encArg They will be analysed ascendingly in the following order: b < encArg ---------------------------------------- (10) Obligation: TRS: Rules: b(a(a(b(b(x1))))) -> b(a(a(a(a(b(b(x1))))))) b(a(b(b(x1)))) -> b(b(x1)) b(a(b(a(a(a(a(b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) b(a(a(b(a(a(a(a(b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) b(a(a(a(b(a(a(a(a(b(x1)))))))))) -> b(x1) encArg(a(x_1)) -> a(encArg(x_1)) encArg(cons_b(x_1)) -> b(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) Types: b :: a:cons_b -> a:cons_b a :: a:cons_b -> a:cons_b encArg :: a:cons_b -> a:cons_b cons_b :: a:cons_b -> a:cons_b encode_b :: a:cons_b -> a:cons_b encode_a :: a:cons_b -> a:cons_b hole_a:cons_b1_0 :: a:cons_b gen_a:cons_b2_0 :: Nat -> a:cons_b Generator Equations: gen_a:cons_b2_0(0) <=> hole_a:cons_b1_0 gen_a:cons_b2_0(+(x, 1)) <=> a(gen_a:cons_b2_0(x)) The following defined symbols remain to be analysed: b, encArg They will be analysed ascendingly in the following order: b < encArg ---------------------------------------- (11) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_a:cons_b2_0(+(1, n74_0))) -> *3_0, rt in Omega(0) Induction Base: encArg(gen_a:cons_b2_0(+(1, 0))) Induction Step: encArg(gen_a:cons_b2_0(+(1, +(n74_0, 1)))) ->_R^Omega(0) a(encArg(gen_a:cons_b2_0(+(1, n74_0)))) ->_IH a(*3_0) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (12) BOUNDS(1, INF) ---------------------------------------- (13) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (14) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: b(a(a(b(b(x1))))) -> b(a(a(a(a(b(b(x1))))))) b(a(b(b(x1)))) -> b(b(x1)) b(a(b(a(a(a(a(b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) b(a(a(b(a(a(a(a(b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) b(a(a(a(b(a(a(a(a(b(x1)))))))))) -> b(x1) The (relative) TRS S consists of the following rules: encArg(a(x_1)) -> a(encArg(x_1)) encArg(cons_b(x_1)) -> b(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (15) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (16) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: b(a(a(b(b(x1))))) -> b(a(a(a(a(b(b(x1))))))) b(a(b(b(x1)))) -> b(b(x1)) b(a(b(a(a(a(a(b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) b(a(a(b(a(a(a(a(b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) b(a(a(a(b(a(a(a(a(b(x1)))))))))) -> b(x1) encArg(a(x_1)) -> a(encArg(x_1)) encArg(cons_b(x_1)) -> b(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (17) NonCtorToCtorProof (UPPER BOUND(ID)) transformed non-ctor to ctor-system ---------------------------------------- (18) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: b(a(a(c_b(a(a(a(a(c_b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) b(a(c_b(a(a(a(a(c_b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) b(a(c_b(c_b(x1)))) -> b(b(x1)) b(a(a(c_b(c_b(x1))))) -> b(a(a(a(a(b(b(x1))))))) b(a(a(a(c_b(a(a(a(a(c_b(x1)))))))))) -> b(x1) The (relative) TRS S consists of the following rules: encArg(a(x_1)) -> a(encArg(x_1)) encArg(cons_b(x_1)) -> b(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) b(x0) -> c_b(x0) Rewrite Strategy: FULL ---------------------------------------- (19) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. As the TRS is a non-duplicating overlay system, we have rc = irc. ---------------------------------------- (20) 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: b(a(a(c_b(a(a(a(a(c_b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) b(a(c_b(a(a(a(a(c_b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) b(a(c_b(c_b(x1)))) -> b(b(x1)) b(a(a(c_b(c_b(x1))))) -> b(a(a(a(a(b(b(x1))))))) b(a(a(a(c_b(a(a(a(a(c_b(x1)))))))))) -> b(x1) The (relative) TRS S consists of the following rules: encArg(a(x_1)) -> a(encArg(x_1)) encArg(cons_b(x_1)) -> b(encArg(x_1)) encode_b(x_1) -> b(encArg(x_1)) encode_a(x_1) -> a(encArg(x_1)) b(x0) -> c_b(x0) Rewrite Strategy: INNERMOST ---------------------------------------- (21) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (22) 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: b(a(a(c_b(a(a(a(a(c_b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) [1] b(a(c_b(a(a(a(a(c_b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) [1] b(a(c_b(c_b(x1)))) -> b(b(x1)) [1] b(a(a(c_b(c_b(x1))))) -> b(a(a(a(a(b(b(x1))))))) [1] b(a(a(a(c_b(a(a(a(a(c_b(x1)))))))))) -> b(x1) [1] encArg(a(x_1)) -> a(encArg(x_1)) [0] encArg(cons_b(x_1)) -> b(encArg(x_1)) [0] encode_b(x_1) -> b(encArg(x_1)) [0] encode_a(x_1) -> a(encArg(x_1)) [0] b(x0) -> c_b(x0) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (23) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (24) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: b(a(a(c_b(a(a(a(a(c_b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) [1] b(a(c_b(a(a(a(a(c_b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) [1] b(a(c_b(c_b(x1)))) -> b(b(x1)) [1] b(a(a(c_b(c_b(x1))))) -> b(a(a(a(a(b(b(x1))))))) [1] b(a(a(a(c_b(a(a(a(a(c_b(x1)))))))))) -> b(x1) [1] encArg(a(x_1)) -> a(encArg(x_1)) [0] encArg(cons_b(x_1)) -> b(encArg(x_1)) [0] encode_b(x_1) -> b(encArg(x_1)) [0] encode_a(x_1) -> a(encArg(x_1)) [0] b(x0) -> c_b(x0) [0] The TRS has the following type information: b :: c_b:a:cons_b -> c_b:a:cons_b a :: c_b:a:cons_b -> c_b:a:cons_b c_b :: c_b:a:cons_b -> c_b:a:cons_b encArg :: c_b:a:cons_b -> c_b:a:cons_b cons_b :: c_b:a:cons_b -> c_b:a:cons_b encode_b :: c_b:a:cons_b -> c_b:a:cons_b encode_a :: c_b:a:cons_b -> c_b:a:cons_b Rewrite Strategy: INNERMOST ---------------------------------------- (25) 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_b(v0) -> null_encode_b [0] encode_a(v0) -> null_encode_a [0] b(v0) -> null_b [0] And the following fresh constants: null_encArg, null_encode_b, null_encode_a, null_b ---------------------------------------- (26) 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: b(a(a(c_b(a(a(a(a(c_b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) [1] b(a(c_b(a(a(a(a(c_b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) [1] b(a(c_b(c_b(x1)))) -> b(b(x1)) [1] b(a(a(c_b(c_b(x1))))) -> b(a(a(a(a(b(b(x1))))))) [1] b(a(a(a(c_b(a(a(a(a(c_b(x1)))))))))) -> b(x1) [1] encArg(a(x_1)) -> a(encArg(x_1)) [0] encArg(cons_b(x_1)) -> b(encArg(x_1)) [0] encode_b(x_1) -> b(encArg(x_1)) [0] encode_a(x_1) -> a(encArg(x_1)) [0] b(x0) -> c_b(x0) [0] encArg(v0) -> null_encArg [0] encode_b(v0) -> null_encode_b [0] encode_a(v0) -> null_encode_a [0] b(v0) -> null_b [0] The TRS has the following type information: b :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b a :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b c_b :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b encArg :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b cons_b :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b encode_b :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b encode_a :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b null_encArg :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b null_encode_b :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b null_encode_a :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b null_b :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b 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: null_encArg => 0 null_encode_b => 0 null_encode_a => 0 null_b => 0 ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: b(z) -{ 1 }-> b(x1) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))) b(z) -{ 1 }-> b(b(x1)) :|: x1 >= 0, z = 1 + (1 + (1 + x1)) b(z) -{ 1 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(x1))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))) b(z) -{ 1 }-> b(1 + (1 + (1 + (1 + b(b(x1)))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1))) b(z) -{ 1 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(x1))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))) b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 b(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 encArg(z) -{ 0 }-> b(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 }-> 0 :|: v0 >= 0, z = v0 encode_a(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_b(z) -{ 0 }-> b(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (29) 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_b_1 encode_a_1 b_1 Due to the following rules being added: encArg(v0) -> const [0] encode_b(v0) -> const [0] encode_a(v0) -> const [0] b(v0) -> const [0] And the following fresh constants: const ---------------------------------------- (30) 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: b(a(a(c_b(a(a(a(a(c_b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1))))))))))))))) [1] b(a(c_b(a(a(a(a(c_b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1)))))))))))))))))))))) [1] b(a(c_b(c_b(x1)))) -> b(b(x1)) [1] b(a(a(c_b(c_b(x1))))) -> b(a(a(a(a(b(b(x1))))))) [1] b(a(a(a(c_b(a(a(a(a(c_b(x1)))))))))) -> b(x1) [1] encArg(a(x_1)) -> a(encArg(x_1)) [0] encArg(cons_b(x_1)) -> b(encArg(x_1)) [0] encode_b(x_1) -> b(encArg(x_1)) [0] encode_a(x_1) -> a(encArg(x_1)) [0] b(x0) -> c_b(x0) [0] encArg(v0) -> const [0] encode_b(v0) -> const [0] encode_a(v0) -> const [0] b(v0) -> const [0] The TRS has the following type information: b :: c_b:a:cons_b:const -> c_b:a:cons_b:const a :: c_b:a:cons_b:const -> c_b:a:cons_b:const c_b :: c_b:a:cons_b:const -> c_b:a:cons_b:const encArg :: c_b:a:cons_b:const -> c_b:a:cons_b:const cons_b :: c_b:a:cons_b:const -> c_b:a:cons_b:const encode_b :: c_b:a:cons_b:const -> c_b:a:cons_b:const encode_a :: c_b:a:cons_b:const -> c_b:a:cons_b:const const :: c_b:a:cons_b:const Rewrite Strategy: INNERMOST ---------------------------------------- (31) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (32) 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: b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x1'))))))))))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x1'))))))))))))))))))))))))))))) [2] b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x1'')))))))))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x1'')))))))))))))))))))))))))))))))))))) [2] b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x11)))))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(x11)))))))))))))))) [2] b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x12))))))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x12))))))))))))))))))))) [2] b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x13)))))))))))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x13))))))))))))))) [2] b(a(a(c_b(a(a(a(a(c_b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(x1))))))))))))))) [1] b(a(a(c_b(a(a(a(a(c_b(x1))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(const)))))))))))))) [1] b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x14)))))))))))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x14)))))))))))))))))))))))))))))))))))) [2] b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x15))))))))))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x15))))))))))))))))))))))))))))))))))))))))))) [2] b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x16))))))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(x16))))))))))))))))))))))) [2] b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x17)))))))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x17)))))))))))))))))))))))))))) [2] b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x18))))))))))))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x18)))))))))))))))))))))) [2] b(a(c_b(a(a(a(a(c_b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(x1)))))))))))))))))))))) [1] b(a(c_b(a(a(a(a(c_b(x1)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(const))))))))))))))))))))) [1] b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x19)))))))))))) -> b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x19)))))))))))))))) [2] b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x110))))))))))) -> b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x110))))))))))))))))))))))) [2] b(a(c_b(c_b(a(c_b(c_b(x111))))))) -> b(b(b(x111))) [2] b(a(c_b(c_b(a(a(c_b(c_b(x112)))))))) -> b(b(a(a(a(a(b(b(x112)))))))) [2] b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(x113))))))))))))) -> b(b(x113)) [2] b(a(c_b(c_b(x1)))) -> b(c_b(x1)) [1] b(a(c_b(c_b(x1)))) -> b(const) [1] b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x114))))))))))))) -> b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x114))))))))))))))))))))) [2] b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x115)))))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x115)))))))))))))))))))))))))))) [2] b(a(a(c_b(c_b(a(c_b(c_b(x116)))))))) -> b(a(a(a(a(b(b(b(x116)))))))) [2] b(a(a(c_b(c_b(a(a(c_b(c_b(x117))))))))) -> b(a(a(a(a(b(b(a(a(a(a(b(b(x117))))))))))))) [2] b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(x118)))))))))))))) -> b(a(a(a(a(b(b(x118))))))) [2] b(a(a(c_b(c_b(x1))))) -> b(a(a(a(a(b(c_b(x1))))))) [1] b(a(a(c_b(c_b(x1))))) -> b(a(a(a(a(b(const)))))) [1] b(a(a(a(c_b(a(a(a(a(c_b(x1)))))))))) -> b(x1) [1] encArg(a(x_1)) -> a(encArg(x_1)) [0] encArg(cons_b(a(x_1'))) -> b(a(encArg(x_1'))) [0] encArg(cons_b(cons_b(x_1''))) -> b(b(encArg(x_1''))) [0] encArg(cons_b(x_1)) -> b(const) [0] encode_b(a(x_11)) -> b(a(encArg(x_11))) [0] encode_b(cons_b(x_12)) -> b(b(encArg(x_12))) [0] encode_b(x_1) -> b(const) [0] encode_a(x_1) -> a(encArg(x_1)) [0] b(x0) -> c_b(x0) [0] encArg(v0) -> const [0] encode_b(v0) -> const [0] encode_a(v0) -> const [0] b(v0) -> const [0] The TRS has the following type information: b :: c_b:a:cons_b:const -> c_b:a:cons_b:const a :: c_b:a:cons_b:const -> c_b:a:cons_b:const c_b :: c_b:a:cons_b:const -> c_b:a:cons_b:const encArg :: c_b:a:cons_b:const -> c_b:a:cons_b:const cons_b :: c_b:a:cons_b:const -> c_b:a:cons_b:const encode_b :: c_b:a:cons_b:const -> c_b:a:cons_b:const encode_a :: c_b:a:cons_b:const -> c_b:a:cons_b:const const :: c_b:a:cons_b:const 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: const => 0 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: b(z) -{ 1 }-> b(x1) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))) b(z) -{ 2 }-> b(b(x113)) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x113))))))))))), x113 >= 0 b(z) -{ 2 }-> b(b(b(x111))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x111))))), x111 >= 0 b(z) -{ 2 }-> b(b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(x19)))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x19)))))))))), x19 >= 0 b(z) -{ 2 }-> b(b(1 + (1 + (1 + (1 + b(b(x112))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x112)))))), x112 >= 0 b(z) -{ 2 }-> b(b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(x110)))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x110))))))))), x110 >= 0 b(z) -{ 1 }-> b(0) :|: x1 >= 0, z = 1 + (1 + (1 + x1)) b(z) -{ 1 }-> b(1 + x1) :|: x1 >= 0, z = 1 + (1 + (1 + x1)) b(z) -{ 2 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(x13))))))))))) :|: x13 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x13)))))))))))))))) b(z) -{ 2 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(b(x11)))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x11)))))))))), x11 >= 0 b(z) -{ 2 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(x1'))))))))))))))))))))) :|: x1' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1'))))))))))))))) b(z) -{ 2 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(b(x12)))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x12))))))))))), x12 >= 0 b(z) -{ 2 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(x1''))))))))))))))))))))))))))) :|: x1'' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1'')))))))))))))) b(z) -{ 1 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + 0)))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))) b(z) -{ 1 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + (1 + x1))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))) b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(b(x118)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x118)))))))))))), x118 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(b(b(x116))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x116)))))), x116 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(x114)))))))))))))))) :|: x114 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x114))))))))))) b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(b(1 + (1 + (1 + (1 + b(b(x117))))))))))) :|: x117 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x117))))))) b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(x115)))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x115)))))))))), x115 >= 0 b(z) -{ 1 }-> b(1 + (1 + (1 + (1 + b(0))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1))) b(z) -{ 1 }-> b(1 + (1 + (1 + (1 + b(1 + x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1))) b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(x18))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x18))))))))))))))), x18 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(b(x16)))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x16))))))))), x16 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(x14))))))))))))))))))))))))))) :|: x14 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x14)))))))))))))) b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(b(x17)))))))))))))))))))))) :|: x17 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x17)))))))))) b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(x15))))))))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x15))))))))))))), x15 >= 0 b(z) -{ 1 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + 0)))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))) b(z) -{ 1 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + (1 + x1))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))) b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 b(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 encArg(z) -{ 0 }-> b(b(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0 encArg(z) -{ 0 }-> b(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> b(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 }-> 0 :|: v0 >= 0, z = v0 encode_a(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_b(z) -{ 0 }-> b(b(encArg(x_12))) :|: z = 1 + x_12, x_12 >= 0 encode_b(z) -{ 0 }-> b(0) :|: x_1 >= 0, z = x_1 encode_b(z) -{ 0 }-> b(1 + encArg(x_11)) :|: x_11 >= 0, z = 1 + x_11 encode_b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 ---------------------------------------- (35) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: b(z) -{ 2 }-> b(b(b(z - 6))) :|: z - 6 >= 0 b(z) -{ 2 }-> b(b(z - 12)) :|: z - 12 >= 0 b(z) -{ 2 }-> b(b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(z - 11)))))))))))) :|: z - 11 >= 0 b(z) -{ 2 }-> b(b(1 + (1 + (1 + (1 + b(b(z - 7))))))) :|: z - 7 >= 0 b(z) -{ 2 }-> b(b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(z - 10)))))))))))))))))) :|: z - 10 >= 0 b(z) -{ 1 }-> b(0) :|: z - 3 >= 0 b(z) -{ 1 }-> b(z - 9) :|: z - 9 >= 0 b(z) -{ 2 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(b(z - 11)))))))))))) :|: z - 11 >= 0 b(z) -{ 2 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(z - 17))))))))))) :|: z - 17 >= 0 b(z) -{ 2 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(z - 16))))))))))))))))))))) :|: z - 16 >= 0 b(z) -{ 2 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(b(z - 12)))))))))))))))) :|: z - 12 >= 0 b(z) -{ 2 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(z - 15))))))))))))))))))))))))))) :|: z - 15 >= 0 b(z) -{ 1 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + 0)))))))))) :|: z - 8 >= 0 b(z) -{ 1 }-> b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + (1 + (z - 8)))))))))))) :|: z - 8 >= 0 b(z) -{ 1 }-> b(1 + (z - 3)) :|: z - 3 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(b(b(z - 7))))))) :|: z - 7 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(b(z - 13)))))) :|: z - 13 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(z - 12)))))))))))))))) :|: z - 12 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(b(1 + (1 + (1 + (1 + b(b(z - 8))))))))))) :|: z - 8 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(z - 11)))))))))))))))))))))) :|: z - 11 >= 0 b(z) -{ 1 }-> b(1 + (1 + (1 + (1 + b(0))))) :|: z - 4 >= 0 b(z) -{ 1 }-> b(1 + (1 + (1 + (1 + b(1 + (z - 4)))))) :|: z - 4 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(b(z - 10)))))))))))))))))) :|: z - 10 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(z - 16))))))))))))))))) :|: z - 16 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(z - 15))))))))))))))))))))))))))) :|: z - 15 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(b(z - 11)))))))))))))))))))))) :|: z - 11 >= 0 b(z) -{ 2 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(z - 14))))))))))))))))))))))))))))))))) :|: z - 14 >= 0 b(z) -{ 1 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + 0)))))))))))))))) :|: z - 7 >= 0 b(z) -{ 1 }-> b(1 + (1 + (1 + (1 + b(1 + (1 + (1 + (1 + b(1 + b(1 + (1 + (1 + b(1 + (1 + (1 + (1 + (1 + (z - 7)))))))))))))))))) :|: z - 7 >= 0 b(z) -{ 0 }-> 0 :|: z >= 0 b(z) -{ 0 }-> 1 + z :|: z >= 0 encArg(z) -{ 0 }-> b(b(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> b(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> b(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 }-> 0 :|: z >= 0 encode_a(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0 encode_b(z) -{ 0 }-> b(b(encArg(z - 1))) :|: z - 1 >= 0 encode_b(z) -{ 0 }-> b(0) :|: z >= 0 encode_b(z) -{ 0 }-> b(1 + encArg(z - 1)) :|: z - 1 >= 0 encode_b(z) -{ 0 }-> 0 :|: z >= 0 ---------------------------------------- (37) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) encode_b(z0) -> b(encArg(z0)) encode_a(z0) -> a(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0)) ENCODE_B(z0) -> c2(B(encArg(z0)), ENCARG(z0)) ENCODE_A(z0) -> c3(ENCARG(z0)) B(z0) -> c4 B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(a(a(a(a(b(z0)))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(a(a(a(a(b(z0)))))), B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(a(a(a(a(b(b(z0))))))), B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) S tuples: B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(a(a(a(a(b(z0)))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(a(a(a(a(b(z0)))))), B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(a(a(a(a(b(b(z0))))))), B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) K tuples:none Defined Rule Symbols: b_1, encArg_1, encode_b_1, encode_a_1 Defined Pair Symbols: ENCARG_1, ENCODE_B_1, ENCODE_A_1, B_1 Compound Symbols: c_1, c1_2, c2_2, c3_1, c4, c5_5, c6_6, c7_2, c8_3, c9_1 ---------------------------------------- (39) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: ENCODE_A(z0) -> c3(ENCARG(z0)) Removed 1 trailing nodes: B(z0) -> c4 ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) encode_b(z0) -> b(encArg(z0)) encode_a(z0) -> a(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0)) ENCODE_B(z0) -> c2(B(encArg(z0)), ENCARG(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(a(a(a(a(b(z0)))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(a(a(a(a(b(z0)))))), B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(a(a(a(a(b(b(z0))))))), B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) S tuples: B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(a(a(a(a(b(z0)))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(a(a(a(a(b(z0)))))), B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(a(a(a(a(b(b(z0))))))), B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) K tuples:none Defined Rule Symbols: b_1, encArg_1, encode_b_1, encode_a_1 Defined Pair Symbols: ENCARG_1, ENCODE_B_1, B_1 Compound Symbols: c_1, c1_2, c2_2, c5_5, c6_6, c7_2, c8_3, c9_1 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) encode_b(z0) -> b(encArg(z0)) encode_a(z0) -> a(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0)) ENCODE_B(z0) -> c2(B(encArg(z0)), ENCARG(z0)) B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) S tuples: B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) K tuples:none Defined Rule Symbols: b_1, encArg_1, encode_b_1, encode_a_1 Defined Pair Symbols: ENCARG_1, ENCODE_B_1, B_1 Compound Symbols: c_1, c1_2, c2_2, c7_2, c9_1, c5_4, c6_3, c8_2 ---------------------------------------- (43) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) encode_b(z0) -> b(encArg(z0)) encode_a(z0) -> a(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0)) B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) ENCODE_B(z0) -> c3(B(encArg(z0))) ENCODE_B(z0) -> c3(ENCARG(z0)) S tuples: B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) K tuples:none Defined Rule Symbols: b_1, encArg_1, encode_b_1, encode_a_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c1_2, c7_2, c9_1, c5_4, c6_3, c8_2, c3_1 ---------------------------------------- (45) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: ENCODE_B(z0) -> c3(ENCARG(z0)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) encode_b(z0) -> b(encArg(z0)) encode_a(z0) -> a(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0)) B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) ENCODE_B(z0) -> c3(B(encArg(z0))) S tuples: B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) K tuples:none Defined Rule Symbols: b_1, encArg_1, encode_b_1, encode_a_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c1_2, c7_2, c9_1, c5_4, c6_3, c8_2, c3_1 ---------------------------------------- (47) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_b(z0) -> b(encArg(z0)) encode_a(z0) -> a(encArg(z0)) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0)) B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) ENCODE_B(z0) -> c3(B(encArg(z0))) S tuples: B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c1_2, c7_2, c9_1, c5_4, c6_3, c8_2, c3_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0)) by ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0))) ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0))) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) ENCODE_B(z0) -> c3(B(encArg(z0))) ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0))) ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0))) S tuples: B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c7_2, c9_1, c5_4, c6_3, c8_2, c3_1, c1_2 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(c_b(z0)))) -> c7(B(b(z0)), B(z0)) by B(a(c_b(c_b(z0)))) -> c7(B(c_b(z0)), B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) ENCODE_B(z0) -> c3(B(encArg(z0))) ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0))) ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0))) B(a(c_b(c_b(z0)))) -> c7(B(c_b(z0)), B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(c_b(z0)), B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c5_4, c6_3, c8_2, c3_1, c1_2, c7_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) ENCODE_B(z0) -> c3(B(encArg(z0))) ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0))) ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c5_4, c6_3, c8_2, c3_1, c1_2, c7_2, c7_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) by B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) ENCODE_B(z0) -> c3(B(encArg(z0))) ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0))) ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c6_3, c8_2, c3_1, c1_2, c7_2, c7_1, c5_4 ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) by B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) ENCODE_B(z0) -> c3(B(encArg(z0))) ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0))) ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c8_2, c3_1, c1_2, c7_2, c7_1, c5_4, c6_3 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(a(c_b(c_b(z0))))) -> c8(B(b(z0)), B(z0)) by B(a(a(c_b(c_b(z0))))) -> c8(B(c_b(z0)), B(z0)) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) ENCODE_B(z0) -> c3(B(encArg(z0))) ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0))) ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(z0))))) -> c8(B(c_b(z0)), B(z0)) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(z0))))) -> c8(B(c_b(z0)), B(z0)) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c3_1, c1_2, c7_2, c7_1, c5_4, c6_3, c8_2 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) ENCODE_B(z0) -> c3(B(encArg(z0))) ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0))) ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c3_1, c1_2, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_B(z0) -> c3(B(encArg(z0))) by ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0))) ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c1_2, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0))) by ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c1_2, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0))) by ENCARG(cons_b(cons_b(x0))) -> c1(B(c_b(encArg(x0))), ENCARG(cons_b(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(x0))) -> c1(B(c_b(encArg(x0))), ENCARG(cons_b(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) by B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(c_b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), 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ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(c_b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) 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c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(c_b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) by B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(c_b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(c_b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> 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B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> 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B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(c_b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), 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B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) 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B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> 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c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(z0))))) by B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(c_b(b(x0))), B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> 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c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) 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B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), 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B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(c_b(b(x0))), B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1 ---------------------------------------- (81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) by B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(c_b(a(a(a(a(b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) 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c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> 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c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(c_b(a(a(a(a(b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> 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B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> 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c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_2, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) by B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(c_b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(c_b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) 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B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(c_b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> 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B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) 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B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) by B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), 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B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) 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B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> 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B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2 ---------------------------------------- (93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> 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B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> 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B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_3 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) by B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> 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B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_3, c5_1 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> 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B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> 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B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_3, c5_1 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) by B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0))))))))))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), 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B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_3, c5_1, c5_2 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) by B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(c_b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> 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B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_3, c5_1, c5_2 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) by B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), 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c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(z0))))))))))))))), 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c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> 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B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), 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B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> 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B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_3, c5_1, c5_2 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) by B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(x0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(b(x0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(b(x0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(c_b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(b(z0)))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), 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B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(b(x0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(b(x0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(c_b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(b(z0)))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_3, c5_1, c5_2 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) by B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> 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-> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(b(x0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(b(x0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(c_b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> 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B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), 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B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(b(x0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(b(x0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(c_b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(b(z0)))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_3, c5_1, c5_2 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) by B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) 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B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), 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B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c5_4, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_3, c5_1, c5_2 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) by B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(b(x0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(b(x0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(c_b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(b(z0))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> 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-> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) 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c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), 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B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(b(x0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(c_b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(b(z0))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_4, c5_3, c5_1, c5_2 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) by B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), 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B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(b(z0))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))), 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c6(B(a(c_b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), 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B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(b(z0))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_4, c5_3, c5_1, c5_2 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) 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B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(b(x0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(c_b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(b(z0))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_4, c5_3, c5_1, c5_2, c6_2 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) by B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0))))))))))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) 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B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(b(z0))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_4, c5_3, c5_1, c5_2, c6_2, c6_1 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> 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-> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(c_b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> 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c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> 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B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(b(x0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(c_b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(b(z0))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_4, c5_3, c5_1, c5_2, c6_2, c6_1 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) by B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(c_b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) 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c6(B(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) 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B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> 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B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(b(x0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(c_b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(b(z0))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_4, c5_3, c5_1, c5_2, c6_2, c6_1 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) by B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), 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B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) 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B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))) S tuples: B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) 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B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) 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B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) 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B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(b(x0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(c_b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(b(z0))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0)))))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_4, c5_3, c5_1, c5_2, c6_2, c6_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) by B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), 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c5(B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(c_b(a(a(a(a(c_b(z0)))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))))))), 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B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) 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B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) 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B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(x0)))))))) -> c6(B(a(a(a(b(a(a(a(a(b(x0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_4, c5_3, c5_1, c5_2, c6_2, c6_1 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) by B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> 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c6(B(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_4, c5_3, c5_1, c5_2, c6_2, c6_1 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) by B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(c_b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(b(z0)))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c7(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0)))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(b(a(a(c_b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) 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B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c7(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> 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c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(a(c_b(a(a(a(a(c_b(x0))))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(a(c_b(x0)))))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0))))))))))))), B(a(c_b(c_b(x0))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(c_b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(z0))))))))))))), B(a(c_b(c_b(z0))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(b(z0)))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(c_b(c_b(z0)))))))))))))))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(x0))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(c_b(c_b(x0)))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c6_3, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_4, c5_3, c5_1, c5_2, c6_2, c6_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) by B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0)))))))))))) -> c6(B(a(c_b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0)))))))))))) -> c6(B(a(b(a(a(a(c_b(a(a(a(a(b(a(a(a(a(b(b(x0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(c_b(a(a(a(a(b(b(x0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(c_b(b(x0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0)))))))))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(c_b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0)))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: encArg(a(z0)) -> a(encArg(z0)) encArg(cons_b(z0)) -> b(encArg(z0)) b(z0) -> c_b(z0) b(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))) b(a(c_b(a(a(a(a(c_b(z0)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))) b(a(c_b(c_b(z0)))) -> b(b(z0)) b(a(a(c_b(c_b(z0))))) -> b(a(a(a(a(b(b(z0))))))) b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> b(z0) Tuples: ENCARG(a(z0)) -> c(ENCARG(z0)) B(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))) -> c9(B(z0)) B(a(c_b(c_b(z0)))) -> c7(B(z0)) B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c8(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c8(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(a(c_b(c_b(a(c_b(c_b(z0)))))))) -> c8(B(b(b(z0))), B(a(c_b(c_b(z0))))) B(a(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) -> c8(B(b(a(a(a(a(b(b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c8(B(b(z0)), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(c_b(z0))))) -> c8(B(z0)) ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0)))) ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0)))) ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0)))) ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0)))) ENCARG(cons_b(cons_b(x0))) -> c1(ENCARG(cons_b(x0))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(c_b(a(a(a(b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(c_b(z0))))))) -> c7(B(b(c_b(z0))), B(a(c_b(c_b(z0))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))), B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))))) -> c7(B(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))), B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0)))))))))))) B(a(c_b(c_b(a(c_b(c_b(a(c_b(c_b(z0)))))))))) -> c7(B(b(b(b(z0)))), B(a(c_b(c_b(a(c_b(c_b(z0)))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(c_b(c_b(z0))))))))))) -> c7(B(b(b(a(a(a(a(b(b(z0))))))))), B(a(c_b(c_b(a(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(b(z0))), B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(c_b(c_b(x0))))))) -> c7(B(a(c_b(c_b(x0))))) B(a(c_b(c_b(a(a(c_b(c_b(x0)))))))) -> c7(B(b(a(a(a(a(c_b(b(x0)))))))), B(a(a(c_b(c_b(x0)))))) B(a(c_b(c_b(a(a(c_b(c_b(z0)))))))) -> c7(B(b(a(a(a(a(b(c_b(z0)))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(b(b(z0))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))) -> c7(B(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> 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B(a(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) B(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))) -> c7(B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(x0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))), B(a(a(a(b(a(a(a(a(b(x0)))))))))), B(x0)) B(a(a(c_b(a(a(a(a(c_b(z0))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))), B(a(a(a(b(a(a(a(a(b(z0)))))))))), B(z0)) B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))), B(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))), B(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))) B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) -> c5(B(a(c_b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))), 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B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(b(z0))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(c_b(c_b(z0))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c7(B(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))), B(a(a(c_b(a(a(a(a(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) B(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(x0)))))))))))) -> c7(B(a(a(c_b(a(a(a(a(c_b(x0)))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(c_b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(c_b(a(b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(c_b(a(a(a(b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(x0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(c_b(a(a(a(a(b(x0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(x0))))))))) B(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))) -> c7(B(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(c_b(a(a(a(a(c_b(z0))))))))) 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B(a(a(c_b(c_b(x0)))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(z0)))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(c_b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(z0)))))))))))))), B(a(a(c_b(c_b(z0)))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(z0)))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))))), B(a(a(c_b(c_b(a(a(a(c_b(a(a(a(a(c_b(z0))))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(z0)))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(a(a(a(a(c_b(z0)))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(z0))))))))))))))))))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))))))))))), B(a(a(c_b(c_b(a(c_b(a(a(a(a(c_b(z0))))))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(b(z0))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(c_b(c_b(z0))))))))))))))))), B(a(a(c_b(c_b(a(c_b(c_b(z0))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))) -> c6(B(a(b(a(a(a(b(a(a(a(a(b(a(a(a(a(b(b(a(a(a(a(b(b(z0)))))))))))))))))))))))), B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))))))))))), B(a(a(c_b(c_b(a(a(c_b(c_b(z0)))))))))) B(a(c_b(a(a(a(a(c_b(a(a(c_b(c_b(x0)))))))))))) -> c6(B(a(a(a(b(a(a(a(a(b(a(a(c_b(c_b(x0))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, b_1 Defined Pair Symbols: ENCARG_1, B_1, ENCODE_B_1 Compound Symbols: c_1, c9_1, c7_1, c8_2, c8_1, c3_1, c1_2, c1_1, c7_2, c5_4, c5_3, c5_1, c5_2, c6_3, c6_2, c6_1