/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF).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), 87 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 27 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 494 ms] (14) BOUNDS(1, INF) (15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (16) CpxTRS (17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (18) CpxRelTRS (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 5517 ms] (20) CpxRelTRS (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxWeightedTrs (23) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxWeightedTrs (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CpxTypedWeightedTrs (27) CompletionProof [UPPER BOUND(ID), 2 ms] (28) CpxTypedWeightedCompleteTrs (29) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxTypedWeightedCompleteTrs (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) SimplificationProof [BOTH BOUNDS(ID, ID), 9 ms] (34) CpxRNTS (35) CompletionProof [UPPER BOUND(ID), 3 ms] (36) CpxTypedWeightedCompleteTrs (37) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) CpxTrsToCdtProof [UPPER BOUND(ID), 484 ms] (40) CdtProblem (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (42) CdtProblem (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (48) CdtProblem (49) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 2533 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 708 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 717 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12.2 s] (60) 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: 0(x1) -> 1(x1) 0(0(x1)) -> 0(x1) 3(4(5(x1))) -> 4(3(5(x1))) 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(1(0(1(1(0(1(1(0(1(0(0(0(1(0(0(0(1(1(1(1(0(1(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(1(0(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(1(0(0(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(0(0(0(1(0(1(1(1(1(1(0(1(1(1(0(0(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(1(0(1(0(0(1(0(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(1(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(0(0(1(0(1(0(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(0(0(0(0(1(0(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(1(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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(1(x_1)) -> 1(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_2(x_1) -> 2(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: 0(x1) -> 1(x1) 0(0(x1)) -> 0(x1) 3(4(5(x1))) -> 4(3(5(x1))) 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(1(0(1(1(0(1(1(0(1(0(0(0(1(0(0(0(1(1(1(1(0(1(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(1(0(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(1(0(0(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(0(0(0(1(0(1(1(1(1(1(0(1(1(1(0(0(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(1(0(1(0(0(1(0(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(1(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(0(0(1(0(1(0(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(0(0(0(0(1(0(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(1(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_2(x_1) -> 2(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: 0(x1) -> 1(x1) 0(0(x1)) -> 0(x1) 3(4(5(x1))) -> 4(3(5(x1))) 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(1(0(1(1(0(1(1(0(1(0(0(0(1(0(0(0(1(1(1(1(0(1(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(1(0(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(1(0(0(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(0(0(0(1(0(1(1(1(1(1(0(1(1(1(0(0(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(1(0(1(0(0(1(0(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(1(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(0(0(1(0(1(0(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(0(0(0(0(1(0(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(1(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(x1) -> 1(x1) 0(0(x1)) -> 0(x1) 3(4(5(x1))) -> 4(3(5(x1))) 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(1(0(1(1(0(1(1(0(1(0(0(0(1(0(0(0(1(1(1(1(0(1(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(1(0(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(1(0(0(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(0(0(0(1(0(1(1(1(1(1(0(1(1(1(0(0(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(1(0(1(0(0(1(0(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(1(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(0(0(1(0(1(0(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(0(0(0(0(1(0(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(1(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (7) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (8) 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: 0(x1) -> 1(x1) 0(0(x1)) -> 0(x1) 3(4(5(x1))) -> 4(3(5(x1))) 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(1(0(1(1(0(1(1(0(1(0(0(0(1(0(0(0(1(1(1(1(0(1(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(1(0(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(1(0(0(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(0(0(0(1(0(1(1(1(1(1(0(1(1(1(0(0(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(1(0(1(0(0(1(0(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(1(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(0(0(1(0(1(0(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(0(0(0(0(1(0(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(1(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: TRS: Rules: 0(x1) -> 1(x1) 0(0(x1)) -> 0(x1) 3(4(5(x1))) -> 4(3(5(x1))) 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(1(0(1(1(0(1(1(0(1(0(0(0(1(0(0(0(1(1(1(1(0(1(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(1(0(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(1(0(0(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(0(0(0(1(0(1(1(1(1(1(0(1(1(1(0(0(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(1(0(1(0(0(1(0(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(1(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(0(0(1(0(1(0(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(0(0(0(0(1(0(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(1(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) encArg(1(x_1)) -> 1(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) Types: 0 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 1 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 3 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 4 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 5 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 2 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encArg :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 cons_0 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 cons_3 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 cons_2 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encode_0 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encode_1 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encode_3 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encode_4 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encode_5 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encode_2 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 hole_1:5:4:cons_0:cons_3:cons_21_6 :: 1:5:4:cons_0:cons_3:cons_2 gen_1:5:4:cons_0:cons_3:cons_22_6 :: Nat -> 1:5:4:cons_0:cons_3:cons_2 ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: 0, 3, 2, encArg They will be analysed ascendingly in the following order: 0 = 2 0 < encArg 3 < encArg 2 < encArg ---------------------------------------- (12) Obligation: TRS: Rules: 0(x1) -> 1(x1) 0(0(x1)) -> 0(x1) 3(4(5(x1))) -> 4(3(5(x1))) 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(1(0(1(1(0(1(1(0(1(0(0(0(1(0(0(0(1(1(1(1(0(1(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(1(0(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(1(0(0(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(0(0(0(1(0(1(1(1(1(1(0(1(1(1(0(0(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(1(0(1(0(0(1(0(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(1(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(0(0(1(0(1(0(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(0(0(0(0(1(0(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(1(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) encArg(1(x_1)) -> 1(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) Types: 0 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 1 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 3 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 4 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 5 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 2 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encArg :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 cons_0 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 cons_3 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 cons_2 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encode_0 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encode_1 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encode_3 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encode_4 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encode_5 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 encode_2 :: 1:5:4:cons_0:cons_3:cons_2 -> 1:5:4:cons_0:cons_3:cons_2 hole_1:5:4:cons_0:cons_3:cons_21_6 :: 1:5:4:cons_0:cons_3:cons_2 gen_1:5:4:cons_0:cons_3:cons_22_6 :: Nat -> 1:5:4:cons_0:cons_3:cons_2 Generator Equations: gen_1:5:4:cons_0:cons_3:cons_22_6(0) <=> hole_1:5:4:cons_0:cons_3:cons_21_6 gen_1:5:4:cons_0:cons_3:cons_22_6(+(x, 1)) <=> 1(gen_1:5:4:cons_0:cons_3:cons_22_6(x)) The following defined symbols remain to be analysed: 3, 0, 2, encArg They will be analysed ascendingly in the following order: 0 = 2 0 < encArg 3 < encArg 2 < encArg ---------------------------------------- (13) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_1:5:4:cons_0:cons_3:cons_22_6(+(1, n23_6))) -> *3_6, rt in Omega(0) Induction Base: encArg(gen_1:5:4:cons_0:cons_3:cons_22_6(+(1, 0))) Induction Step: encArg(gen_1:5:4:cons_0:cons_3:cons_22_6(+(1, +(n23_6, 1)))) ->_R^Omega(0) 1(encArg(gen_1:5:4:cons_0:cons_3:cons_22_6(+(1, n23_6)))) ->_IH 1(*3_6) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (14) BOUNDS(1, INF) ---------------------------------------- (15) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (16) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(x1) -> 1(x1) 0(0(x1)) -> 0(x1) 3(4(5(x1))) -> 4(3(5(x1))) 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(1(0(1(1(0(1(1(0(1(0(0(0(1(0(0(0(1(1(1(1(0(1(0(1(0(1(1(0(1(1(1(1(1(0(0(1(0(1(1(0(1(0(0(1(0(1(1(0(1(0(1(1(1(0(1(1(1(0(0(0(0(1(0(0(1(1(0(0(1(1(0(0(1(0(0(1(1(1(1(1(1(1(0(1(0(0(0(1(0(1(0(0(0(1(1(0(1(0(1(1(1(1(0(0(0(0(1(0(1(1(1(1(1(0(1(1(1(0(0(1(0(1(1(1(1(0(1(1(0(0(0(1(0(0(1(0(1(0(1(1(0(0(1(1(0(1(0(0(1(1(1(0(1(0(1(0(1(1(0(1(0(1(0(0(1(0(0(0(0(1(1(1(1(0(1(0(0(0(0(0(0(0(1(1(0(1(1(0(1(0(0(1(1(1(1(0(1(0(1(0(0(0(1(0(1(0(0(1(0(1(0(0(1(1(0(1(1(1(0(1(0(1(0(0(0(1(0(0(1(0(1(0(0(1(1(1(0(1(0(1(1(0(1(0(0(0(1(1(1(1(1(0(0(0(0(1(0(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(0(0(0(0(1(0(1(0(0(0(0(1(1(1(0(0(0(0(0(1(1(1(0(1(0(1(0(0(0(0(1(1(1(0(0(1(1(1(1(0(1(0(0(1(0(1(0(1(0(1(0(0(1(1(1(1(1(0(0(0(1(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) encArg(1(x_1)) -> 1(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_2(x_1) -> 2(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: 0(x1) -> 1(x1) 3(4(5(x1))) -> 4(3(5(x1))) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(x1)) -> 0(x1) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) 0(x0) -> c_0(x0) 2(x0) -> c_2(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: 0(x1) -> 1(x1) 3(4(5(x1))) -> 4(3(5(x1))) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(x1)) -> 0(x1) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) 0(x0) -> c_0(x0) 2(x0) -> c_2(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: 0(x1) -> 1(x1) [1] 3(4(5(x1))) -> 4(3(5(x1))) [1] 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [1] 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [1] 0(c_0(x1)) -> 0(x1) [1] encArg(1(x_1)) -> 1(encArg(x_1)) [0] encArg(4(x_1)) -> 4(encArg(x_1)) [0] encArg(5(x_1)) -> 5(encArg(x_1)) [0] encArg(cons_0(x_1)) -> 0(encArg(x_1)) [0] encArg(cons_3(x_1)) -> 3(encArg(x_1)) [0] encArg(cons_2(x_1)) -> 2(encArg(x_1)) [0] encode_0(x_1) -> 0(encArg(x_1)) [0] encode_1(x_1) -> 1(encArg(x_1)) [0] encode_3(x_1) -> 3(encArg(x_1)) [0] encode_4(x_1) -> 4(encArg(x_1)) [0] encode_5(x_1) -> 5(encArg(x_1)) [0] encode_2(x_1) -> 2(encArg(x_1)) [0] 0(x0) -> c_0(x0) [0] 2(x0) -> c_2(x0) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (23) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) Renamed defined symbols to avoid conflicts with arithmetic symbols: 0 => 0' 3 => 3' 2 => 2' ---------------------------------------- (24) 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: 0'(x1) -> 1(x1) [1] 3'(4(5(x1))) -> 4(3'(5(x1))) [1] 2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0'(0'(1(0'(0'(0'(1(1(1(0'(1(1(1(1(1(0'(0'(1(0'(0'(1(0'(1(1(0'(1(0'(0'(1(1(0'(0'(0'(1(0'(1(1(0'(0'(0'(1(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(1(1(0'(0'(1(0'(1(1(1(0'(1(0'(0'(0'(1(1(0'(0'(1(1(1(1(1(0'(1(0'(0'(0'(1(0'(0'(0'(0'(0'(1(0'(1(1(0'(1(1(0'(0'(0'(1(0'(0'(0'(0'(0'(1(1(1(0'(1(1(0'(1(1(1(0'(1(0'(0'(1(0'(0'(0'(0'(0'(0'(1(0'(0'(1(0'(1(1(0'(1(0'(1(1(1(1(1(1(1(1(1(0'(1(1(1(1(1(1(0'(1(1(1(1(0'(1(0'(1(1(1(0'(1(1(0'(0'(1(1(0'(1(0'(1(0'(0'(1(0'(0'(0'(0'(0'(1(0'(0'(0'(1(1(1(0'(1(0'(1(0'(1(1(1(0'(0'(1(0'(1(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(0'(0'(0'(0'(1(0'(1(1(0'(1(1(1(0'(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(0'(0'(1(1(0'(1(0'(0'(1(0'(0'(0'(1(0'(0'(0'(1(0'(0'(1(1(0'(0'(0'(0'(1(1(1(0'(0'(0'(1(1(1(0'(1(1(1(1(1(1(1(1(1(1(1(0'(0'(0'(1(0'(0'(0'(1(1(0'(1(0'(0'(1(1(1(1(0'(1(1(1(1(1(0'(0'(0'(0'(0'(0'(1(1(0'(0'(0'(1(0'(0'(1(1(1(1(0'(0'(0'(0'(1(0'(0'(1(1(0'(1(0'(1(1(0'(0'(0'(1(1(0'(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [1] 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [1] 0'(c_0(x1)) -> 0'(x1) [1] encArg(1(x_1)) -> 1(encArg(x_1)) [0] encArg(4(x_1)) -> 4(encArg(x_1)) [0] encArg(5(x_1)) -> 5(encArg(x_1)) [0] encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0] encArg(cons_3(x_1)) -> 3'(encArg(x_1)) [0] encArg(cons_2(x_1)) -> 2'(encArg(x_1)) [0] encode_0(x_1) -> 0'(encArg(x_1)) [0] encode_1(x_1) -> 1(encArg(x_1)) [0] encode_3(x_1) -> 3'(encArg(x_1)) [0] encode_4(x_1) -> 4(encArg(x_1)) [0] encode_5(x_1) -> 5(encArg(x_1)) [0] encode_2(x_1) -> 2'(encArg(x_1)) [0] 0'(x0) -> c_0(x0) [0] 2'(x0) -> c_2(x0) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (25) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (26) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: 0'(x1) -> 1(x1) [1] 3'(4(5(x1))) -> 4(3'(5(x1))) [1] 2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0'(0'(1(0'(0'(0'(1(1(1(0'(1(1(1(1(1(0'(0'(1(0'(0'(1(0'(1(1(0'(1(0'(0'(1(1(0'(0'(0'(1(0'(1(1(0'(0'(0'(1(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(1(1(0'(0'(1(0'(1(1(1(0'(1(0'(0'(0'(1(1(0'(0'(1(1(1(1(1(0'(1(0'(0'(0'(1(0'(0'(0'(0'(0'(1(0'(1(1(0'(1(1(0'(0'(0'(1(0'(0'(0'(0'(0'(1(1(1(0'(1(1(0'(1(1(1(0'(1(0'(0'(1(0'(0'(0'(0'(0'(0'(1(0'(0'(1(0'(1(1(0'(1(0'(1(1(1(1(1(1(1(1(1(0'(1(1(1(1(1(1(0'(1(1(1(1(0'(1(0'(1(1(1(0'(1(1(0'(0'(1(1(0'(1(0'(1(0'(0'(1(0'(0'(0'(0'(0'(1(0'(0'(0'(1(1(1(0'(1(0'(1(0'(1(1(1(0'(0'(1(0'(1(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(0'(0'(0'(0'(1(0'(1(1(0'(1(1(1(0'(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(0'(0'(1(1(0'(1(0'(0'(1(0'(0'(0'(1(0'(0'(0'(1(0'(0'(1(1(0'(0'(0'(0'(1(1(1(0'(0'(0'(1(1(1(0'(1(1(1(1(1(1(1(1(1(1(1(0'(0'(0'(1(0'(0'(0'(1(1(0'(1(0'(0'(1(1(1(1(0'(1(1(1(1(1(0'(0'(0'(0'(0'(0'(1(1(0'(0'(0'(1(0'(0'(1(1(1(1(0'(0'(0'(0'(1(0'(0'(1(1(0'(1(0'(1(1(0'(0'(0'(1(1(0'(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [1] 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [1] 0'(c_0(x1)) -> 0'(x1) [1] encArg(1(x_1)) -> 1(encArg(x_1)) [0] encArg(4(x_1)) -> 4(encArg(x_1)) [0] encArg(5(x_1)) -> 5(encArg(x_1)) [0] encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0] encArg(cons_3(x_1)) -> 3'(encArg(x_1)) [0] encArg(cons_2(x_1)) -> 2'(encArg(x_1)) [0] encode_0(x_1) -> 0'(encArg(x_1)) [0] encode_1(x_1) -> 1(encArg(x_1)) [0] encode_3(x_1) -> 3'(encArg(x_1)) [0] encode_4(x_1) -> 4(encArg(x_1)) [0] encode_5(x_1) -> 5(encArg(x_1)) [0] encode_2(x_1) -> 2'(encArg(x_1)) [0] 0'(x0) -> c_0(x0) [0] 2'(x0) -> c_2(x0) [0] The TRS has the following type information: 0' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 1 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 3' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 4 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 5 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 2' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 c_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 c_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 encArg :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 cons_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 cons_3 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 cons_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 encode_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 encode_1 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 encode_3 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 encode_4 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 encode_5 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 encode_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2 Rewrite Strategy: INNERMOST ---------------------------------------- (27) 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: 3'_1 encArg_1 encode_0_1 encode_1_1 encode_3_1 encode_4_1 encode_5_1 encode_2_1 0'_1 2'_1 Due to the following rules being added: encArg(v0) -> const [0] encode_0(v0) -> const [0] encode_1(v0) -> const [0] encode_3(v0) -> const [0] encode_4(v0) -> const [0] encode_5(v0) -> const [0] encode_2(v0) -> const [0] 0'(v0) -> const [0] 2'(v0) -> const [0] 3'(v0) -> const [0] And the following fresh constants: const ---------------------------------------- (28) 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: 0'(x1) -> 1(x1) [1] 3'(4(5(x1))) -> 4(3'(5(x1))) [1] 2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0'(0'(1(0'(0'(0'(1(1(1(0'(1(1(1(1(1(0'(0'(1(0'(0'(1(0'(1(1(0'(1(0'(0'(1(1(0'(0'(0'(1(0'(1(1(0'(0'(0'(1(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(1(1(0'(0'(1(0'(1(1(1(0'(1(0'(0'(0'(1(1(0'(0'(1(1(1(1(1(0'(1(0'(0'(0'(1(0'(0'(0'(0'(0'(1(0'(1(1(0'(1(1(0'(0'(0'(1(0'(0'(0'(0'(0'(1(1(1(0'(1(1(0'(1(1(1(0'(1(0'(0'(1(0'(0'(0'(0'(0'(0'(1(0'(0'(1(0'(1(1(0'(1(0'(1(1(1(1(1(1(1(1(1(0'(1(1(1(1(1(1(0'(1(1(1(1(0'(1(0'(1(1(1(0'(1(1(0'(0'(1(1(0'(1(0'(1(0'(0'(1(0'(0'(0'(0'(0'(1(0'(0'(0'(1(1(1(0'(1(0'(1(0'(1(1(1(0'(0'(1(0'(1(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(0'(0'(0'(0'(1(0'(1(1(0'(1(1(1(0'(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(0'(0'(1(1(0'(1(0'(0'(1(0'(0'(0'(1(0'(0'(0'(1(0'(0'(1(1(0'(0'(0'(0'(1(1(1(0'(0'(0'(1(1(1(0'(1(1(1(1(1(1(1(1(1(1(1(0'(0'(0'(1(0'(0'(0'(1(1(0'(1(0'(0'(1(1(1(1(0'(1(1(1(1(1(0'(0'(0'(0'(0'(0'(1(1(0'(0'(0'(1(0'(0'(1(1(1(1(0'(0'(0'(0'(1(0'(0'(1(1(0'(1(0'(1(1(0'(0'(0'(1(1(0'(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [1] 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [1] 0'(c_0(x1)) -> 0'(x1) [1] encArg(1(x_1)) -> 1(encArg(x_1)) [0] encArg(4(x_1)) -> 4(encArg(x_1)) [0] encArg(5(x_1)) -> 5(encArg(x_1)) [0] encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0] encArg(cons_3(x_1)) -> 3'(encArg(x_1)) [0] encArg(cons_2(x_1)) -> 2'(encArg(x_1)) [0] encode_0(x_1) -> 0'(encArg(x_1)) [0] encode_1(x_1) -> 1(encArg(x_1)) [0] encode_3(x_1) -> 3'(encArg(x_1)) [0] encode_4(x_1) -> 4(encArg(x_1)) [0] encode_5(x_1) -> 5(encArg(x_1)) [0] encode_2(x_1) -> 2'(encArg(x_1)) [0] 0'(x0) -> c_0(x0) [0] 2'(x0) -> c_2(x0) [0] encArg(v0) -> const [0] encode_0(v0) -> const [0] encode_1(v0) -> const [0] encode_3(v0) -> const [0] encode_4(v0) -> const [0] encode_5(v0) -> const [0] encode_2(v0) -> const [0] 0'(v0) -> const [0] 2'(v0) -> const [0] 3'(v0) -> const [0] The TRS has the following type information: 0' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const 1 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const 3' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const 4 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const 5 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const 2' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const c_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const c_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encArg :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const cons_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const cons_3 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const cons_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encode_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encode_1 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encode_3 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encode_4 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encode_5 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encode_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const const :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const Rewrite Strategy: INNERMOST ---------------------------------------- (29) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (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: 0'(x1) -> 1(x1) [1] 3'(4(5(x1))) -> 4(3'(5(x1))) [1] 2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0'(0'(1(0'(0'(0'(1(1(1(0'(1(1(1(1(1(0'(0'(1(0'(0'(1(0'(1(1(0'(1(0'(0'(1(1(0'(0'(0'(1(0'(1(1(0'(0'(0'(1(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(1(1(0'(0'(1(0'(1(1(1(0'(1(0'(0'(0'(1(1(0'(0'(1(1(1(1(1(0'(1(0'(0'(0'(1(0'(0'(0'(0'(0'(1(0'(1(1(0'(1(1(0'(0'(0'(1(0'(0'(0'(0'(0'(1(1(1(0'(1(1(0'(1(1(1(0'(1(0'(0'(1(0'(0'(0'(0'(0'(0'(1(0'(0'(1(0'(1(1(0'(1(0'(1(1(1(1(1(1(1(1(1(0'(1(1(1(1(1(1(0'(1(1(1(1(0'(1(0'(1(1(1(0'(1(1(0'(0'(1(1(0'(1(0'(1(0'(0'(1(0'(0'(0'(0'(0'(1(0'(0'(0'(1(1(1(0'(1(0'(1(0'(1(1(1(0'(0'(1(0'(1(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(0'(0'(0'(0'(1(0'(1(1(0'(1(1(1(0'(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(0'(0'(1(1(0'(1(0'(0'(1(0'(0'(0'(1(0'(0'(0'(1(0'(0'(1(1(0'(0'(0'(0'(1(1(1(0'(0'(0'(1(1(1(0'(1(1(1(1(1(1(1(1(1(1(1(0'(0'(0'(1(0'(0'(0'(1(1(0'(1(0'(0'(1(1(1(1(0'(1(1(1(1(1(0'(0'(0'(0'(0'(0'(1(1(0'(0'(0'(1(0'(0'(1(1(1(1(0'(0'(0'(0'(1(0'(0'(1(1(0'(1(0'(1(1(0'(0'(0'(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [2] 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-> 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(0'(0'(1(0'(0'(0'(1(1(1(0'(1(1(1(1(1(0'(0'(1(0'(0'(1(0'(1(1(0'(1(0'(0'(1(1(0'(0'(0'(1(0'(1(1(0'(0'(0'(1(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(1(1(0'(0'(1(0'(1(1(1(0'(1(0'(0'(0'(1(1(0'(0'(1(1(1(1(1(0'(1(0'(0'(0'(1(0'(0'(0'(0'(0'(1(0'(1(1(0'(1(1(0'(0'(0'(1(0'(0'(0'(0'(0'(1(1(1(0'(1(1(0'(1(1(1(0'(1(0'(0'(1(0'(0'(0'(0'(0'(0'(1(0'(0'(1(0'(1(1(0'(1(0'(1(1(1(1(1(1(1(1(1(0'(1(1(1(1(1(1(0'(1(1(1(1(0'(1(0'(1(1(1(0'(1(1(0'(0'(1(1(0'(1(0'(1(0'(0'(1(0'(0'(0'(0'(0'(1(0'(0'(0'(1(1(1(0'(1(0'(1(0'(1(1(1(0'(0'(1(0'(1(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(0'(0'(0'(0'(1(0'(1(1(0'(1(1(1(0'(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(0'(0'(1(1(0'(1(0'(0'(1(0'(0'(0'(1(0'(0'(0'(1(0'(0'(1(1(0'(0'(0'(0'(1(1(1(0'(0'(0'(1(1(1(0'(1(1(1(1(1(1(1(1(1(1(1(0'(0'(0'(1(0'(0'(0'(1(1(0'(1(0'(0'(1(1(1(1(0'(1(1(1(1(1(0'(0'(0'(0'(0'(0'(1(1(0'(0'(0'(1(0'(0'(1(1(1(1(0'(0'(0'(0'(1(0'(0'(1(1(0'(1(0'(1(1(0'(0'(0'(1(1(0'(x11)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [2] 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(c_2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [1] 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(const)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [1] 0'(c_0(x1)) -> 0'(x1) [1] encArg(1(x_1)) -> 1(encArg(x_1)) [0] encArg(4(x_1)) -> 4(encArg(x_1)) [0] encArg(5(x_1)) -> 5(encArg(x_1)) [0] encArg(cons_0(1(x_1'))) -> 0'(1(encArg(x_1'))) [0] encArg(cons_0(4(x_1''))) -> 0'(4(encArg(x_1''))) [0] encArg(cons_0(5(x_11))) -> 0'(5(encArg(x_11))) [0] encArg(cons_0(cons_0(x_12))) -> 0'(0'(encArg(x_12))) [0] encArg(cons_0(cons_3(x_13))) -> 0'(3'(encArg(x_13))) [0] encArg(cons_0(cons_2(x_14))) -> 0'(2'(encArg(x_14))) [0] encArg(cons_0(x_1)) -> 0'(const) [0] encArg(cons_3(1(x_15))) -> 3'(1(encArg(x_15))) [0] encArg(cons_3(4(x_16))) -> 3'(4(encArg(x_16))) [0] encArg(cons_3(5(x_17))) -> 3'(5(encArg(x_17))) [0] encArg(cons_3(cons_0(x_18))) -> 3'(0'(encArg(x_18))) [0] encArg(cons_3(cons_3(x_19))) -> 3'(3'(encArg(x_19))) [0] encArg(cons_3(cons_2(x_110))) -> 3'(2'(encArg(x_110))) [0] encArg(cons_3(x_1)) -> 3'(const) [0] encArg(cons_2(1(x_111))) -> 2'(1(encArg(x_111))) [0] encArg(cons_2(4(x_112))) -> 2'(4(encArg(x_112))) [0] encArg(cons_2(5(x_113))) -> 2'(5(encArg(x_113))) [0] encArg(cons_2(cons_0(x_114))) -> 2'(0'(encArg(x_114))) [0] encArg(cons_2(cons_3(x_115))) -> 2'(3'(encArg(x_115))) [0] encArg(cons_2(cons_2(x_116))) -> 2'(2'(encArg(x_116))) [0] encArg(cons_2(x_1)) -> 2'(const) [0] encode_0(1(x_117)) -> 0'(1(encArg(x_117))) [0] encode_0(4(x_118)) -> 0'(4(encArg(x_118))) [0] encode_0(5(x_119)) -> 0'(5(encArg(x_119))) [0] encode_0(cons_0(x_120)) -> 0'(0'(encArg(x_120))) [0] encode_0(cons_3(x_121)) -> 0'(3'(encArg(x_121))) [0] encode_0(cons_2(x_122)) -> 0'(2'(encArg(x_122))) [0] encode_0(x_1) -> 0'(const) [0] encode_1(x_1) -> 1(encArg(x_1)) [0] encode_3(1(x_123)) -> 3'(1(encArg(x_123))) [0] encode_3(4(x_124)) -> 3'(4(encArg(x_124))) [0] encode_3(5(x_125)) -> 3'(5(encArg(x_125))) [0] encode_3(cons_0(x_126)) -> 3'(0'(encArg(x_126))) [0] encode_3(cons_3(x_127)) -> 3'(3'(encArg(x_127))) [0] encode_3(cons_2(x_128)) -> 3'(2'(encArg(x_128))) [0] encode_3(x_1) -> 3'(const) [0] encode_4(x_1) -> 4(encArg(x_1)) [0] encode_5(x_1) -> 5(encArg(x_1)) [0] encode_2(1(x_129)) -> 2'(1(encArg(x_129))) [0] encode_2(4(x_130)) -> 2'(4(encArg(x_130))) [0] encode_2(5(x_131)) -> 2'(5(encArg(x_131))) [0] encode_2(cons_0(x_132)) -> 2'(0'(encArg(x_132))) [0] encode_2(cons_3(x_133)) -> 2'(3'(encArg(x_133))) [0] encode_2(cons_2(x_134)) -> 2'(2'(encArg(x_134))) [0] encode_2(x_1) -> 2'(const) [0] 0'(x0) -> c_0(x0) [0] 2'(x0) -> c_2(x0) [0] encArg(v0) -> const [0] encode_0(v0) -> const [0] encode_1(v0) -> const [0] encode_3(v0) -> const [0] encode_4(v0) -> const [0] encode_5(v0) -> const [0] encode_2(v0) -> const [0] 0'(v0) -> const [0] 2'(v0) -> const [0] 3'(v0) -> const [0] The TRS has the following type information: 0' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const 1 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const 3' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const 4 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const 5 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const 2' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const c_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const c_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encArg :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const cons_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const cons_3 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const cons_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encode_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encode_1 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encode_3 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encode_4 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encode_5 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const encode_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const const :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:const Rewrite Strategy: INNERMOST ---------------------------------------- (31) 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 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: 0'(z) -{ 2 }-> 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(1 + (1 + (1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + 0'(1 + 0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + 0'(1 + 0'(1 + (1 + (1 + 0'(0'(1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + (1 + 0'(x11)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 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2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 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x1')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2'(z) -{ 2 }-> 0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(1 + (1 + (1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + 0'(1 + 0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + 0'(1 + 0'(1 + (1 + (1 + 0'(0'(1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + (1 + 0'(x1'')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1'')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), x1'' >= 0 2'(z) -{ 1 }-> 0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(1 + (1 + (1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + 0'(1 + 0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + 0'(1 + 0'(1 + (1 + (1 + 0'(0'(1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + (1 + 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2'(z) -{ 2 }-> 0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(1 + (1 + (1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + 0'(1 + 0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + 0'(1 + 0'(1 + (1 + (1 + 0'(0'(1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2'(z) -{ 1 }-> 0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(1 + (1 + (1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + 0'(1 + 0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + 0'(1 + 0'(1 + (1 + (1 + 0'(0'(1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 2'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 3'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 3'(z) -{ 1 }-> 1 + 3'(1 + x1) :|: z = 1 + (1 + x1), x1 >= 0 encArg(z) -{ 0 }-> 3'(3'(encArg(x_19))) :|: z = 1 + (1 + x_19), x_19 >= 0 encArg(z) -{ 0 }-> 3'(2'(encArg(x_110))) :|: z = 1 + (1 + x_110), x_110 >= 0 encArg(z) -{ 0 }-> 3'(0'(encArg(x_18))) :|: z = 1 + (1 + x_18), x_18 >= 0 encArg(z) -{ 0 }-> 3'(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 3'(1 + encArg(x_15)) :|: x_15 >= 0, z = 1 + (1 + x_15) encArg(z) -{ 0 }-> 3'(1 + encArg(x_16)) :|: x_16 >= 0, z = 1 + (1 + x_16) encArg(z) -{ 0 }-> 3'(1 + encArg(x_17)) :|: x_17 >= 0, z = 1 + (1 + x_17) encArg(z) -{ 0 }-> 2'(3'(encArg(x_115))) :|: z = 1 + (1 + x_115), x_115 >= 0 encArg(z) -{ 0 }-> 2'(2'(encArg(x_116))) :|: z = 1 + (1 + x_116), x_116 >= 0 encArg(z) -{ 0 }-> 2'(0'(encArg(x_114))) :|: z = 1 + (1 + x_114), x_114 >= 0 encArg(z) -{ 0 }-> 2'(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 2'(1 + encArg(x_111)) :|: z = 1 + (1 + x_111), x_111 >= 0 encArg(z) -{ 0 }-> 2'(1 + encArg(x_112)) :|: x_112 >= 0, z = 1 + (1 + x_112) encArg(z) -{ 0 }-> 2'(1 + encArg(x_113)) :|: x_113 >= 0, z = 1 + (1 + x_113) encArg(z) -{ 0 }-> 0'(3'(encArg(x_13))) :|: z = 1 + (1 + x_13), x_13 >= 0 encArg(z) -{ 0 }-> 0'(2'(encArg(x_14))) :|: x_14 >= 0, z = 1 + (1 + x_14) encArg(z) -{ 0 }-> 0'(0'(encArg(x_12))) :|: z = 1 + (1 + x_12), x_12 >= 0 encArg(z) -{ 0 }-> 0'(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 0'(1 + encArg(x_1')) :|: z = 1 + (1 + x_1'), x_1' >= 0 encArg(z) -{ 0 }-> 0'(1 + encArg(x_1'')) :|: z = 1 + (1 + x_1''), x_1'' >= 0 encArg(z) -{ 0 }-> 0'(1 + encArg(x_11)) :|: x_11 >= 0, z = 1 + (1 + x_11) encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0 encode_0(z) -{ 0 }-> 0'(3'(encArg(x_121))) :|: z = 1 + x_121, x_121 >= 0 encode_0(z) -{ 0 }-> 0'(2'(encArg(x_122))) :|: x_122 >= 0, z = 1 + x_122 encode_0(z) -{ 0 }-> 0'(0'(encArg(x_120))) :|: x_120 >= 0, z = 1 + x_120 encode_0(z) -{ 0 }-> 0'(0) :|: x_1 >= 0, z = x_1 encode_0(z) -{ 0 }-> 0'(1 + encArg(x_117)) :|: x_117 >= 0, z = 1 + x_117 encode_0(z) -{ 0 }-> 0'(1 + encArg(x_118)) :|: z = 1 + x_118, x_118 >= 0 encode_0(z) -{ 0 }-> 0'(1 + encArg(x_119)) :|: z = 1 + x_119, x_119 >= 0 encode_0(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_1(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_2(z) -{ 0 }-> 2'(3'(encArg(x_133))) :|: z = 1 + x_133, x_133 >= 0 encode_2(z) -{ 0 }-> 2'(2'(encArg(x_134))) :|: x_134 >= 0, z = 1 + x_134 encode_2(z) -{ 0 }-> 2'(0'(encArg(x_132))) :|: z = 1 + x_132, x_132 >= 0 encode_2(z) -{ 0 }-> 2'(0) :|: x_1 >= 0, z = x_1 encode_2(z) -{ 0 }-> 2'(1 + encArg(x_129)) :|: z = 1 + x_129, x_129 >= 0 encode_2(z) -{ 0 }-> 2'(1 + encArg(x_130)) :|: x_130 >= 0, z = 1 + x_130 encode_2(z) -{ 0 }-> 2'(1 + encArg(x_131)) :|: z = 1 + x_131, x_131 >= 0 encode_2(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_3(z) -{ 0 }-> 3'(3'(encArg(x_127))) :|: x_127 >= 0, z = 1 + x_127 encode_3(z) -{ 0 }-> 3'(2'(encArg(x_128))) :|: x_128 >= 0, z = 1 + x_128 encode_3(z) -{ 0 }-> 3'(0'(encArg(x_126))) :|: z = 1 + x_126, x_126 >= 0 encode_3(z) -{ 0 }-> 3'(0) :|: x_1 >= 0, z = x_1 encode_3(z) -{ 0 }-> 3'(1 + encArg(x_123)) :|: x_123 >= 0, z = 1 + x_123 encode_3(z) -{ 0 }-> 3'(1 + encArg(x_124)) :|: x_124 >= 0, z = 1 + x_124 encode_3(z) -{ 0 }-> 3'(1 + encArg(x_125)) :|: z = 1 + x_125, x_125 >= 0 encode_3(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_4(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_4(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_5(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_5(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 ---------------------------------------- (33) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: 0'(z) -{ 2 }-> 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(1 + (1 + (1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + 0'(1 + 0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + 0'(1 + 0'(1 + (1 + (1 + 0'(0'(1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + (1 + 0'(z - 413)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: z - 413 >= 0 0'(z) -{ 1 }-> 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: z - 347 >= 0 0'(z) -{ 1 }-> 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(1 + (z - 347))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: z - 347 >= 0 0'(z) -{ 1 }-> 0'(z - 1) :|: z - 1 >= 0 0'(z) -{ 0 }-> 0 :|: z >= 0 0'(z) -{ 1 }-> 1 + z :|: z >= 0 0'(z) -{ 0 }-> 1 + z :|: z >= 0 2'(z) -{ 2 }-> 0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(1 + (1 + (1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + 0'(1 + 0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + 0'(1 + 0'(1 + (1 + (1 + 0'(0'(1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + (1 + 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(z - 413)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: z - 413 >= 0 2'(z) -{ 2 }-> 0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(1 + (1 + (1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + 0'(1 + 0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + 0'(1 + 0'(1 + (1 + (1 + 0'(0'(1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + (1 + 0'(z - 67)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: z - 67 >= 0 2'(z) -{ 1 }-> 0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(1 + (1 + (1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + 0'(1 + 0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + 0'(1 + 0'(1 + (1 + (1 + 0'(0'(1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + (1 + 0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: z - 66 >= 0 2'(z) -{ 2 }-> 0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(1 + (1 + (1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + 0'(1 + 0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + 0'(1 + 0'(1 + (1 + (1 + 0'(0'(1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + (z - 66))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: z - 66 >= 0 2'(z) -{ 1 }-> 0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(1 + (1 + (1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + 0'(1 + 0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + 0'(1 + 0'(1 + (1 + (1 + 0'(0'(1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + (z - 66))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: z - 66 >= 0 2'(z) -{ 0 }-> 0 :|: z >= 0 2'(z) -{ 0 }-> 1 + z :|: z >= 0 3'(z) -{ 0 }-> 0 :|: z >= 0 3'(z) -{ 1 }-> 1 + 3'(1 + (z - 2)) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 3'(3'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 3'(2'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 3'(0'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 3'(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> 3'(1 + encArg(z - 2)) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 2'(3'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 2'(2'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 2'(0'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 2'(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> 2'(1 + encArg(z - 2)) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 0'(3'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 0'(2'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 0'(0'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 0'(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> 0'(1 + encArg(z - 2)) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0 encode_0(z) -{ 0 }-> 0'(3'(encArg(z - 1))) :|: z - 1 >= 0 encode_0(z) -{ 0 }-> 0'(2'(encArg(z - 1))) :|: z - 1 >= 0 encode_0(z) -{ 0 }-> 0'(0'(encArg(z - 1))) :|: z - 1 >= 0 encode_0(z) -{ 0 }-> 0'(0) :|: z >= 0 encode_0(z) -{ 0 }-> 0'(1 + encArg(z - 1)) :|: z - 1 >= 0 encode_0(z) -{ 0 }-> 0 :|: z >= 0 encode_1(z) -{ 0 }-> 0 :|: z >= 0 encode_1(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0 encode_2(z) -{ 0 }-> 2'(3'(encArg(z - 1))) :|: z - 1 >= 0 encode_2(z) -{ 0 }-> 2'(2'(encArg(z - 1))) :|: z - 1 >= 0 encode_2(z) -{ 0 }-> 2'(0'(encArg(z - 1))) :|: z - 1 >= 0 encode_2(z) -{ 0 }-> 2'(0) :|: z >= 0 encode_2(z) -{ 0 }-> 2'(1 + encArg(z - 1)) :|: z - 1 >= 0 encode_2(z) -{ 0 }-> 0 :|: z >= 0 encode_3(z) -{ 0 }-> 3'(3'(encArg(z - 1))) :|: z - 1 >= 0 encode_3(z) -{ 0 }-> 3'(2'(encArg(z - 1))) :|: z - 1 >= 0 encode_3(z) -{ 0 }-> 3'(0'(encArg(z - 1))) :|: z - 1 >= 0 encode_3(z) -{ 0 }-> 3'(0) :|: z >= 0 encode_3(z) -{ 0 }-> 3'(1 + encArg(z - 1)) :|: z - 1 >= 0 encode_3(z) -{ 0 }-> 0 :|: z >= 0 encode_4(z) -{ 0 }-> 0 :|: z >= 0 encode_4(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0 encode_5(z) -{ 0 }-> 0 :|: z >= 0 encode_5(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0 ---------------------------------------- (35) 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_0(v0) -> null_encode_0 [0] encode_1(v0) -> null_encode_1 [0] encode_3(v0) -> null_encode_3 [0] encode_4(v0) -> null_encode_4 [0] encode_5(v0) -> null_encode_5 [0] encode_2(v0) -> null_encode_2 [0] 0'(v0) -> null_0' [0] 2'(v0) -> null_2' [0] 3'(v0) -> null_3' [0] And the following fresh constants: null_encArg, null_encode_0, null_encode_1, null_encode_3, null_encode_4, null_encode_5, null_encode_2, null_0', null_2', null_3' ---------------------------------------- (36) 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: 0'(x1) -> 1(x1) [1] 3'(4(5(x1))) -> 4(3'(5(x1))) [1] 2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0'(0'(1(0'(0'(0'(1(1(1(0'(1(1(1(1(1(0'(0'(1(0'(0'(1(0'(1(1(0'(1(0'(0'(1(1(0'(0'(0'(1(0'(1(1(0'(0'(0'(1(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(1(1(0'(0'(1(0'(1(1(1(0'(1(0'(0'(0'(1(1(0'(0'(1(1(1(1(1(0'(1(0'(0'(0'(1(0'(0'(0'(0'(0'(1(0'(1(1(0'(1(1(0'(0'(0'(1(0'(0'(0'(0'(0'(1(1(1(0'(1(1(0'(1(1(1(0'(1(0'(0'(1(0'(0'(0'(0'(0'(0'(1(0'(0'(1(0'(1(1(0'(1(0'(1(1(1(1(1(1(1(1(1(0'(1(1(1(1(1(1(0'(1(1(1(1(0'(1(0'(1(1(1(0'(1(1(0'(0'(1(1(0'(1(0'(1(0'(0'(1(0'(0'(0'(0'(0'(1(0'(0'(0'(1(1(1(0'(1(0'(1(0'(1(1(1(0'(0'(1(0'(1(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(0'(0'(0'(0'(1(0'(1(1(0'(1(1(1(0'(0'(0'(0'(1(1(0'(0'(0'(1(1(1(0'(0'(0'(1(1(0'(1(0'(0'(1(0'(0'(0'(1(0'(0'(0'(1(0'(0'(1(1(0'(0'(0'(0'(1(1(1(0'(0'(0'(1(1(1(0'(1(1(1(1(1(1(1(1(1(1(1(0'(0'(0'(1(0'(0'(0'(1(1(0'(1(0'(0'(1(1(1(1(0'(1(1(1(1(1(0'(0'(0'(0'(0'(0'(1(1(0'(0'(0'(1(0'(0'(1(1(1(1(0'(0'(0'(0'(1(0'(0'(1(1(0'(1(0'(1(1(0'(0'(0'(1(1(0'(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [1] 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) [1] 0'(c_0(x1)) -> 0'(x1) [1] encArg(1(x_1)) -> 1(encArg(x_1)) [0] encArg(4(x_1)) -> 4(encArg(x_1)) [0] encArg(5(x_1)) -> 5(encArg(x_1)) [0] encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0] encArg(cons_3(x_1)) -> 3'(encArg(x_1)) [0] encArg(cons_2(x_1)) -> 2'(encArg(x_1)) [0] encode_0(x_1) -> 0'(encArg(x_1)) [0] encode_1(x_1) -> 1(encArg(x_1)) [0] encode_3(x_1) -> 3'(encArg(x_1)) [0] encode_4(x_1) -> 4(encArg(x_1)) [0] encode_5(x_1) -> 5(encArg(x_1)) [0] encode_2(x_1) -> 2'(encArg(x_1)) [0] 0'(x0) -> c_0(x0) [0] 2'(x0) -> c_2(x0) [0] encArg(v0) -> null_encArg [0] encode_0(v0) -> null_encode_0 [0] encode_1(v0) -> null_encode_1 [0] encode_3(v0) -> null_encode_3 [0] encode_4(v0) -> null_encode_4 [0] encode_5(v0) -> null_encode_5 [0] encode_2(v0) -> null_encode_2 [0] 0'(v0) -> null_0' [0] 2'(v0) -> null_2' [0] 3'(v0) -> null_3' [0] The TRS has the following type information: 0' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' 1 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' 3' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' 4 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' 5 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' 2' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' c_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' c_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' encArg :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' cons_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' cons_3 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' cons_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' encode_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' encode_1 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' encode_3 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' encode_4 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' encode_5 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' encode_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' -> 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' null_encArg :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' null_encode_0 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' null_encode_1 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' null_encode_3 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' null_encode_4 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' null_encode_5 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' null_encode_2 :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' null_0' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' null_2' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' null_3' :: 1:5:4:c_2:c_0:cons_0:cons_3:cons_2:null_encArg:null_encode_0:null_encode_1:null_encode_3:null_encode_4:null_encode_5:null_encode_2:null_0':null_2':null_3' Rewrite Strategy: INNERMOST ---------------------------------------- (37) 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_0 => 0 null_encode_1 => 0 null_encode_3 => 0 null_encode_4 => 0 null_encode_5 => 0 null_encode_2 => 0 null_0' => 0 null_2' => 0 null_3' => 0 ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: 0'(z) -{ 1 }-> 2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(2'(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 0'(x1) :|: x1 >= 0, z = 1 + x1 0'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 0'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 0'(z) -{ 1 }-> 1 + x1 :|: x1 >= 0, z = x1 2'(z) -{ 1 }-> 0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(1 + (1 + (1 + (1 + (1 + 0'(1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(0'(1 + 0'(0'(1 + 0'(1 + (1 + 0'(1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + 0'(1 + 0'(1 + (1 + (1 + 0'(1 + (1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(0'(0'(1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + 0'(1 + 0'(1 + (1 + (1 + 0'(0'(1 + 0'(1 + 0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(0'(0'(1 + 0'(1 + (1 + 0'(1 + (1 + (1 + 0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + 0'(0'(0'(1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(0'(0'(0'(1 + (1 + (1 + 0'(0'(0'(1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + 0'(0'(0'(1 + 0'(0'(0'(1 + (1 + 0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(1 + (1 + (1 + (1 + (1 + 0'(0'(0'(0'(0'(0'(1 + (1 + 0'(0'(0'(1 + 0'(0'(1 + (1 + (1 + (1 + 0'(0'(0'(0'(1 + 0'(0'(1 + (1 + 0'(1 + 0'(1 + (1 + 0'(0'(0'(1 + (1 + 0'(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 2'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 2'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 3'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 3'(z) -{ 1 }-> 1 + 3'(1 + x1) :|: z = 1 + (1 + x1), x1 >= 0 encArg(z) -{ 0 }-> 3'(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 2'(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 0'(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_0(z) -{ 0 }-> 0'(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_0(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_1(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_2(z) -{ 0 }-> 2'(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_2(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_3(z) -{ 0 }-> 3'(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_3(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_4(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_4(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 encode_5(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_5(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (39) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(1(z0)) -> 1(encArg(z0)) encArg(4(z0)) -> 4(encArg(z0)) encArg(5(z0)) -> 5(encArg(z0)) encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_3(z0)) -> 3(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_3(z0) -> 3(encArg(z0)) encode_4(z0) -> 4(encArg(z0)) encode_5(z0) -> 5(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(z0) -> c_0(z0) 0(z0) -> 1(z0) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(z0)) -> 0(z0) 2(z0) -> c_2(z0) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(4(5(z0))) -> 4(3(5(z0))) Tuples: ENCARG(1(z0)) -> c(ENCARG(z0)) ENCARG(4(z0)) -> c1(ENCARG(z0)) ENCARG(5(z0)) -> c2(ENCARG(z0)) ENCARG(cons_0(z0)) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_3(z0)) -> c4(3'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c5(2'(encArg(z0)), ENCARG(z0)) ENCODE_0(z0) -> c6(0'(encArg(z0)), ENCARG(z0)) ENCODE_1(z0) -> c7(ENCARG(z0)) ENCODE_3(z0) -> c8(3'(encArg(z0)), ENCARG(z0)) ENCODE_4(z0) -> c9(ENCARG(z0)) ENCODE_5(z0) -> c10(ENCARG(z0)) ENCODE_2(z0) -> c11(2'(encArg(z0)), ENCARG(z0)) 0'(z0) -> c12 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 2'(z0) -> c16 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0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))), 0'(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))), 0'(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))), 0'(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))), 0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18(3'(5(z0))) K tuples:none Defined Rule Symbols: 0_1, 3_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_3_1, encode_4_1, encode_5_1, encode_2_1 Defined Pair Symbols: ENCARG_1, ENCODE_0_1, ENCODE_1_1, ENCODE_3_1, ENCODE_4_1, ENCODE_5_1, ENCODE_2_1, 0'_1, 2'_1, 3'_1 Compound Symbols: c_1, c1_1, c2_1, c3_2, c4_2, c5_2, c6_2, c7_1, c8_2, c9_1, c10_1, c11_2, c12, c13, c14_67, c15_1, c16, c17_172, c18_1 ---------------------------------------- (41) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 3 leading nodes: ENCODE_1(z0) -> c7(ENCARG(z0)) ENCODE_4(z0) -> c9(ENCARG(z0)) ENCODE_5(z0) -> c10(ENCARG(z0)) Removed 2 trailing nodes: 2'(z0) -> c16 0'(z0) -> c12 ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(1(z0)) -> 1(encArg(z0)) encArg(4(z0)) -> 4(encArg(z0)) encArg(5(z0)) -> 5(encArg(z0)) encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_3(z0)) -> 3(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_3(z0) -> 3(encArg(z0)) encode_4(z0) -> 4(encArg(z0)) encode_5(z0) -> 5(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(z0) -> c_0(z0) 0(z0) -> 1(z0) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(z0)) -> 0(z0) 2(z0) -> c_2(z0) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(4(5(z0))) -> 4(3(5(z0))) Tuples: ENCARG(1(z0)) -> c(ENCARG(z0)) ENCARG(4(z0)) -> c1(ENCARG(z0)) ENCARG(5(z0)) -> c2(ENCARG(z0)) ENCARG(cons_0(z0)) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_3(z0)) -> c4(3'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c5(2'(encArg(z0)), ENCARG(z0)) ENCODE_0(z0) -> c6(0'(encArg(z0)), ENCARG(z0)) ENCODE_3(z0) -> c8(3'(encArg(z0)), ENCARG(z0)) ENCODE_2(z0) -> c11(2'(encArg(z0)), ENCARG(z0)) 0'(z0) -> c13 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-> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))), 0'(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))), 0'(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))), 0'(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))), 0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18(3'(5(z0))) K tuples:none Defined Rule Symbols: 0_1, 3_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_3_1, encode_4_1, encode_5_1, encode_2_1 Defined Pair Symbols: ENCARG_1, ENCODE_0_1, ENCODE_3_1, ENCODE_2_1, 0'_1, 2'_1, 3'_1 Compound Symbols: c_1, c1_1, c2_1, c3_2, c4_2, c5_2, c6_2, c8_2, c11_2, c13, c14_67, c15_1, c17_172, c18_1 ---------------------------------------- (43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(1(z0)) -> 1(encArg(z0)) encArg(4(z0)) -> 4(encArg(z0)) encArg(5(z0)) -> 5(encArg(z0)) encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_3(z0)) -> 3(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_3(z0) -> 3(encArg(z0)) encode_4(z0) -> 4(encArg(z0)) encode_5(z0) -> 5(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(z0) -> c_0(z0) 0(z0) -> 1(z0) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(z0)) -> 0(z0) 2(z0) -> c_2(z0) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(4(5(z0))) -> 4(3(5(z0))) Tuples: ENCARG(1(z0)) -> c(ENCARG(z0)) ENCARG(4(z0)) -> c1(ENCARG(z0)) ENCARG(5(z0)) -> c2(ENCARG(z0)) ENCARG(cons_0(z0)) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_3(z0)) -> c4(3'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c5(2'(encArg(z0)), ENCARG(z0)) ENCODE_0(z0) -> c6(0'(encArg(z0)), ENCARG(z0)) ENCODE_3(z0) -> c8(3'(encArg(z0)), ENCARG(z0)) ENCODE_2(z0) -> c11(2'(encArg(z0)), ENCARG(z0)) 0'(z0) -> c13 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 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0'(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))), 0'(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))), 0'(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))), 0'(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))), 0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 K tuples:none Defined Rule Symbols: 0_1, 3_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_3_1, encode_4_1, encode_5_1, encode_2_1 Defined Pair Symbols: ENCARG_1, ENCODE_0_1, ENCODE_3_1, ENCODE_2_1, 0'_1, 2'_1, 3'_1 Compound Symbols: c_1, c1_1, c2_1, c3_2, c4_2, c5_2, c6_2, c8_2, c11_2, c13, c14_67, c15_1, c17_172, c18 ---------------------------------------- (45) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(1(z0)) -> 1(encArg(z0)) encArg(4(z0)) -> 4(encArg(z0)) encArg(5(z0)) -> 5(encArg(z0)) encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_3(z0)) -> 3(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_3(z0) -> 3(encArg(z0)) encode_4(z0) -> 4(encArg(z0)) encode_5(z0) -> 5(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(z0) -> c_0(z0) 0(z0) -> 1(z0) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(z0)) -> 0(z0) 2(z0) -> c_2(z0) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(4(5(z0))) -> 4(3(5(z0))) Tuples: ENCARG(1(z0)) -> c(ENCARG(z0)) ENCARG(4(z0)) -> c1(ENCARG(z0)) ENCARG(5(z0)) -> c2(ENCARG(z0)) ENCARG(cons_0(z0)) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_3(z0)) -> c4(3'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c5(2'(encArg(z0)), ENCARG(z0)) 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_0(z0) -> c7(ENCARG(z0)) ENCODE_3(z0) -> c7(3'(encArg(z0))) ENCODE_3(z0) -> c7(ENCARG(z0)) ENCODE_2(z0) -> c7(2'(encArg(z0))) ENCODE_2(z0) -> c7(ENCARG(z0)) S tuples: 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))), 0'(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))), 0'(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))), 0'(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))), 0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 K tuples:none Defined Rule Symbols: 0_1, 3_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_3_1, encode_4_1, encode_5_1, encode_2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 2'_1, 3'_1, ENCODE_0_1, ENCODE_3_1, ENCODE_2_1 Compound Symbols: c_1, c1_1, c2_1, c3_2, c4_2, c5_2, c13, c14_67, c15_1, c17_172, c18, c7_1 ---------------------------------------- (47) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 3 leading nodes: ENCODE_0(z0) -> c7(ENCARG(z0)) ENCODE_3(z0) -> c7(ENCARG(z0)) ENCODE_2(z0) -> c7(ENCARG(z0)) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(1(z0)) -> 1(encArg(z0)) encArg(4(z0)) -> 4(encArg(z0)) encArg(5(z0)) -> 5(encArg(z0)) encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_3(z0)) -> 3(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_3(z0) -> 3(encArg(z0)) encode_4(z0) -> 4(encArg(z0)) encode_5(z0) -> 5(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(z0) -> c_0(z0) 0(z0) -> 1(z0) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(z0)) -> 0(z0) 2(z0) -> c_2(z0) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(4(5(z0))) -> 4(3(5(z0))) Tuples: ENCARG(1(z0)) -> c(ENCARG(z0)) ENCARG(4(z0)) -> c1(ENCARG(z0)) ENCARG(5(z0)) -> c2(ENCARG(z0)) ENCARG(cons_0(z0)) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_3(z0)) -> c4(3'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c5(2'(encArg(z0)), ENCARG(z0)) 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_3(z0) -> c7(3'(encArg(z0))) ENCODE_2(z0) -> c7(2'(encArg(z0))) S tuples: 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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0'(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))), 0'(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))), 0'(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))), 0'(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))), 0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 K tuples:none Defined Rule Symbols: 0_1, 3_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_3_1, encode_4_1, encode_5_1, encode_2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 2'_1, 3'_1, ENCODE_0_1, ENCODE_3_1, ENCODE_2_1 Compound Symbols: c_1, c1_1, c2_1, c3_2, c4_2, c5_2, c13, c14_67, c15_1, c17_172, c18, c7_1 ---------------------------------------- (49) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_3(z0) -> 3(encArg(z0)) encode_4(z0) -> 4(encArg(z0)) encode_5(z0) -> 5(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(1(z0)) -> 1(encArg(z0)) encArg(4(z0)) -> 4(encArg(z0)) encArg(5(z0)) -> 5(encArg(z0)) encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_3(z0)) -> 3(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(z0) -> c_0(z0) 0(z0) -> 1(z0) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(z0)) -> 0(z0) 3(4(5(z0))) -> 4(3(5(z0))) 2(z0) -> c_2(z0) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) Tuples: ENCARG(1(z0)) -> c(ENCARG(z0)) ENCARG(4(z0)) -> c1(ENCARG(z0)) ENCARG(5(z0)) -> c2(ENCARG(z0)) ENCARG(cons_0(z0)) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_3(z0)) -> c4(3'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c5(2'(encArg(z0)), ENCARG(z0)) 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_3(z0) -> c7(3'(encArg(z0))) ENCODE_2(z0) -> c7(2'(encArg(z0))) S tuples: 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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0'(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))), 0'(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))), 0'(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))), 0'(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))), 0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 K tuples:none Defined Rule Symbols: encArg_1, 0_1, 3_1, 2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 2'_1, 3'_1, ENCODE_0_1, ENCODE_3_1, ENCODE_2_1 Compound Symbols: c_1, c1_1, c2_1, c3_2, c4_2, c5_2, c13, c14_67, c15_1, c17_172, c18, c7_1 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_3(z0)) -> c4(3'(encArg(z0)), ENCARG(z0)) by ENCARG(cons_3(1(z0))) -> c4(3'(1(encArg(z0))), ENCARG(1(z0))) ENCARG(cons_3(4(z0))) -> c4(3'(4(encArg(z0))), ENCARG(4(z0))) ENCARG(cons_3(5(z0))) -> c4(3'(5(encArg(z0))), ENCARG(5(z0))) ENCARG(cons_3(cons_0(z0))) -> c4(3'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_3(cons_3(z0))) -> c4(3'(3(encArg(z0))), ENCARG(cons_3(z0))) ENCARG(cons_3(cons_2(z0))) -> c4(3'(2(encArg(z0))), ENCARG(cons_2(z0))) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(1(z0)) -> 1(encArg(z0)) encArg(4(z0)) -> 4(encArg(z0)) encArg(5(z0)) -> 5(encArg(z0)) encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_3(z0)) -> 3(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(z0) -> c_0(z0) 0(z0) -> 1(z0) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(z0)) -> 0(z0) 3(4(5(z0))) -> 4(3(5(z0))) 2(z0) -> c_2(z0) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) Tuples: ENCARG(1(z0)) -> c(ENCARG(z0)) ENCARG(4(z0)) -> c1(ENCARG(z0)) ENCARG(5(z0)) -> c2(ENCARG(z0)) ENCARG(cons_0(z0)) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c5(2'(encArg(z0)), ENCARG(z0)) 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_3(z0) -> c7(3'(encArg(z0))) ENCODE_2(z0) -> c7(2'(encArg(z0))) ENCARG(cons_3(1(z0))) -> c4(3'(1(encArg(z0))), ENCARG(1(z0))) ENCARG(cons_3(4(z0))) -> c4(3'(4(encArg(z0))), ENCARG(4(z0))) ENCARG(cons_3(5(z0))) -> c4(3'(5(encArg(z0))), ENCARG(5(z0))) ENCARG(cons_3(cons_0(z0))) -> c4(3'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_3(cons_3(z0))) -> c4(3'(3(encArg(z0))), ENCARG(cons_3(z0))) ENCARG(cons_3(cons_2(z0))) -> c4(3'(2(encArg(z0))), ENCARG(cons_2(z0))) S tuples: 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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0'(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))), 0'(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))), 0'(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))), 0'(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))), 0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 K tuples:none Defined Rule Symbols: encArg_1, 0_1, 3_1, 2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 2'_1, 3'_1, ENCODE_0_1, ENCODE_3_1, ENCODE_2_1 Compound Symbols: c_1, c1_1, c2_1, c3_2, c5_2, c13, c14_67, c15_1, c17_172, c18, c7_1, c4_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(1(z0)) -> 1(encArg(z0)) encArg(4(z0)) -> 4(encArg(z0)) encArg(5(z0)) -> 5(encArg(z0)) encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_3(z0)) -> 3(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(z0) -> c_0(z0) 0(z0) -> 1(z0) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(z0)) -> 0(z0) 3(4(5(z0))) -> 4(3(5(z0))) 2(z0) -> c_2(z0) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) Tuples: ENCARG(1(z0)) -> c(ENCARG(z0)) ENCARG(4(z0)) -> c1(ENCARG(z0)) ENCARG(5(z0)) -> c2(ENCARG(z0)) ENCARG(cons_0(z0)) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c5(2'(encArg(z0)), ENCARG(z0)) 0'(z0) -> c13 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_3(z0) -> c7(3'(encArg(z0))) ENCODE_2(z0) -> c7(2'(encArg(z0))) ENCARG(cons_3(4(z0))) -> c4(3'(4(encArg(z0))), ENCARG(4(z0))) ENCARG(cons_3(cons_0(z0))) -> c4(3'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_3(cons_3(z0))) -> c4(3'(3(encArg(z0))), ENCARG(cons_3(z0))) ENCARG(cons_3(cons_2(z0))) -> c4(3'(2(encArg(z0))), ENCARG(cons_2(z0))) ENCARG(cons_3(1(z0))) -> c4(ENCARG(1(z0))) ENCARG(cons_3(5(z0))) -> c4(ENCARG(5(z0))) S tuples: 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))), 0'(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))), 0'(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))), 0'(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))), 0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 K tuples:none Defined Rule Symbols: encArg_1, 0_1, 3_1, 2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 2'_1, 3'_1, ENCODE_0_1, ENCODE_3_1, ENCODE_2_1 Compound Symbols: c_1, c1_1, c2_1, c3_2, c5_2, c13, c14_67, c15_1, c17_172, c18, c7_1, c4_2, c4_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_2(z0)) -> c5(2'(encArg(z0)), ENCARG(z0)) by ENCARG(cons_2(1(z0))) -> c5(2'(1(encArg(z0))), ENCARG(1(z0))) ENCARG(cons_2(4(z0))) -> c5(2'(4(encArg(z0))), ENCARG(4(z0))) ENCARG(cons_2(5(z0))) -> c5(2'(5(encArg(z0))), ENCARG(5(z0))) ENCARG(cons_2(cons_0(z0))) -> c5(2'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_2(cons_3(z0))) -> c5(2'(3(encArg(z0))), ENCARG(cons_3(z0))) ENCARG(cons_2(cons_2(z0))) -> c5(2'(2(encArg(z0))), ENCARG(cons_2(z0))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(1(z0)) -> 1(encArg(z0)) encArg(4(z0)) -> 4(encArg(z0)) encArg(5(z0)) -> 5(encArg(z0)) encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_3(z0)) -> 3(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(z0) -> c_0(z0) 0(z0) -> 1(z0) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(z0)) -> 0(z0) 3(4(5(z0))) -> 4(3(5(z0))) 2(z0) -> c_2(z0) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) Tuples: ENCARG(1(z0)) -> c(ENCARG(z0)) ENCARG(4(z0)) -> c1(ENCARG(z0)) ENCARG(5(z0)) -> c2(ENCARG(z0)) ENCARG(cons_0(z0)) -> c3(0'(encArg(z0)), ENCARG(z0)) 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_3(z0) -> c7(3'(encArg(z0))) ENCODE_2(z0) -> c7(2'(encArg(z0))) ENCARG(cons_3(4(z0))) -> c4(3'(4(encArg(z0))), ENCARG(4(z0))) ENCARG(cons_3(cons_0(z0))) -> c4(3'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_3(cons_3(z0))) -> c4(3'(3(encArg(z0))), ENCARG(cons_3(z0))) ENCARG(cons_3(cons_2(z0))) -> c4(3'(2(encArg(z0))), ENCARG(cons_2(z0))) ENCARG(cons_3(1(z0))) -> c4(ENCARG(1(z0))) ENCARG(cons_3(5(z0))) -> c4(ENCARG(5(z0))) ENCARG(cons_2(1(z0))) -> c5(2'(1(encArg(z0))), ENCARG(1(z0))) ENCARG(cons_2(4(z0))) -> c5(2'(4(encArg(z0))), ENCARG(4(z0))) ENCARG(cons_2(5(z0))) -> c5(2'(5(encArg(z0))), ENCARG(5(z0))) ENCARG(cons_2(cons_0(z0))) -> c5(2'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_2(cons_3(z0))) -> c5(2'(3(encArg(z0))), ENCARG(cons_3(z0))) ENCARG(cons_2(cons_2(z0))) -> c5(2'(2(encArg(z0))), ENCARG(cons_2(z0))) S tuples: 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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0'(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))), 0'(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))), 0'(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))), 0'(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))), 0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 K tuples:none Defined Rule Symbols: encArg_1, 0_1, 3_1, 2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 2'_1, 3'_1, ENCODE_0_1, ENCODE_3_1, ENCODE_2_1 Compound Symbols: c_1, c1_1, c2_1, c3_2, c13, c14_67, c15_1, c17_172, c18, c7_1, c4_2, c4_1, c5_2 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(1(z0)) -> 1(encArg(z0)) encArg(4(z0)) -> 4(encArg(z0)) encArg(5(z0)) -> 5(encArg(z0)) encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_3(z0)) -> 3(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(z0) -> c_0(z0) 0(z0) -> 1(z0) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(z0)) -> 0(z0) 3(4(5(z0))) -> 4(3(5(z0))) 2(z0) -> c_2(z0) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) Tuples: ENCARG(1(z0)) -> c(ENCARG(z0)) ENCARG(4(z0)) -> c1(ENCARG(z0)) ENCARG(5(z0)) -> c2(ENCARG(z0)) ENCARG(cons_0(z0)) -> c3(0'(encArg(z0)), ENCARG(z0)) 0'(z0) -> c13 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2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 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0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_3(z0) -> c7(3'(encArg(z0))) ENCODE_2(z0) -> c7(2'(encArg(z0))) ENCARG(cons_3(4(z0))) -> c4(3'(4(encArg(z0))), ENCARG(4(z0))) ENCARG(cons_3(cons_0(z0))) -> c4(3'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_3(cons_3(z0))) -> c4(3'(3(encArg(z0))), ENCARG(cons_3(z0))) ENCARG(cons_3(cons_2(z0))) -> c4(3'(2(encArg(z0))), ENCARG(cons_2(z0))) ENCARG(cons_3(1(z0))) -> c4(ENCARG(1(z0))) ENCARG(cons_3(5(z0))) -> c4(ENCARG(5(z0))) ENCARG(cons_2(cons_0(z0))) -> c5(2'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_2(cons_3(z0))) -> c5(2'(3(encArg(z0))), ENCARG(cons_3(z0))) ENCARG(cons_2(cons_2(z0))) -> c5(2'(2(encArg(z0))), ENCARG(cons_2(z0))) ENCARG(cons_2(1(z0))) -> c5(ENCARG(1(z0))) ENCARG(cons_2(4(z0))) -> c5(ENCARG(4(z0))) ENCARG(cons_2(5(z0))) -> c5(ENCARG(5(z0))) S tuples: 0'(z0) -> c13 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(z0))))))))))), 2'(2(2(2(2(2(2(2(2(2(z0)))))))))), 2'(2(2(2(2(2(2(2(2(z0))))))))), 2'(2(2(2(2(2(2(2(z0)))))))), 2'(2(2(2(2(2(2(z0))))))), 2'(2(2(2(2(2(z0)))))), 2'(2(2(2(2(z0))))), 2'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_0(z0)) -> c15(0'(z0)) 2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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0'(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))), 0'(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))), 0'(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))))), 0'(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))), 0'(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))))))), 0'(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))), 0'(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))))))), 0'(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))))))))), 0'(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))), 0'(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))))), 0'(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))), 0'(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))))), 0'(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0))))))))))))))), 0'(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))), 0'(1(0(1(1(0(0(0(1(1(0(z0))))))))))), 0'(1(1(0(0(0(1(1(0(z0))))))))), 0'(0(0(1(1(0(z0)))))), 0'(0(1(1(0(z0))))), 0'(1(1(0(z0)))), 0'(z0)) 3'(4(5(z0))) -> c18 K tuples:none Defined Rule Symbols: encArg_1, 0_1, 3_1, 2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 2'_1, 3'_1, ENCODE_0_1, ENCODE_3_1, ENCODE_2_1 Compound Symbols: c_1, c1_1, c2_1, c3_2, c13, c14_67, c15_1, c17_172, c18, c7_1, c4_2, c4_1, c5_2, c5_1 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace 0'(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c14(2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))), 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2'(2(2(2(2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(1(z0)) -> 1(encArg(z0)) encArg(4(z0)) -> 4(encArg(z0)) encArg(5(z0)) -> 5(encArg(z0)) encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_3(z0)) -> 3(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(z0) -> c_0(z0) 0(z0) -> 1(z0) 0(1(c_0(c_0(1(1(1(1(1(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(1(1(1(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(c_0(1(c_0(1(1(c_0(1(c_0(1(1(1(c_0(1(1(1(c_0(c_0(c_0(c_0(1(c_0(c_0(1(1(c_0(c_0(1(1(c_0(c_0(1(c_0(c_0(1(1(1(1(1(1(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(1(1(c_0(1(c_0(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(1(1(1(1(c_0(1(1(1(c_0(c_0(1(c_0(1(1(1(1(c_0(1(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(1(1(c_0(c_0(1(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(1(1(c_0(1(c_0(1(c_0(c_0(1(c_0(c_0(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(c_0(c_0(c_0(c_0(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(1(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(1(c_0(1(c_0(c_0(1(1(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(c_0(1(c_0(1(c_0(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(1(c_0(c_0(c_0(c_0(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(c_0(c_0(c_0(1(1(1(c_0(1(c_0(1(c_0(c_0(c_0(c_0(1(1(1(c_0(c_0(1(1(1(1(c_0(1(c_0(c_0(1(c_0(1(c_0(1(c_0(1(c_0(c_0(1(1(1(1(1(c_0(c_0(c_0(1(c_0(c_0(c_0(c_0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(c_0(z0)) -> 0(z0) 3(4(5(z0))) -> 4(3(5(z0))) 2(z0) -> c_2(z0) 2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) Tuples: ENCARG(1(z0)) -> c(ENCARG(z0)) ENCARG(4(z0)) -> c1(ENCARG(z0)) ENCARG(5(z0)) -> c2(ENCARG(z0)) ENCARG(cons_0(z0)) -> c3(0'(encArg(z0)), ENCARG(z0)) 0'(z0) -> c13 0'(c_0(z0)) -> c15(0'(z0)) 2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> c17(0'(0(1(0(0(0(1(1(1(0(1(1(1(1(1(0(0(1(0(0(1(0(1(1(0(1(0(0(1(1(0(0(0(1(0(1(1(0(0(0(1(0(0(0(1(1(0(0(0(1(1(1(0(1(1(0(0(1(0(1(1(1(0(1(0(0(0(1(1(0(0(1(1(1(1(1(0(1(0(0(0(1(0(0(0(0(0(1(0(1(1(0(1(1(0(0(0(1(0(0(0(0(0(1(1(1(0(1(1(0(1(1(1(0(1(0(0(1(0(0(0(0(0(0(1(0(0(1(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(1(1(1(1(0(1(1(1(1(0(1(0(1(1(1(0(1(1(0(0(1(1(0(1(0(1(0(0(1(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(1(0(1(1(1(0(0(1(0(1(0(0(0(1(1(0(0(0(1(1(1(0(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(0(1(1(0(0(0(1(1(1(0(0(0(1(1(0(1(0(0(1(0(0(0(1(0(0(0(1(0(0(1(1(0(0(0(0(1(1(1(0(0(0(1(1(1(0(1(1(1(1(1(1(1(1(1(1(1(0(0(0(1(0(0(0(1(1(0(1(0(0(1(1(1(1(0(1(1(1(1(1(0(0(0(0(0(0(1(1(0(0(0(1(0(0(1(1(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(0(0(0(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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2'(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(z0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, 0_1, 3_1, 2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 2'_1, 3'_1, ENCODE_0_1, ENCODE_3_1, ENCODE_2_1 Compound Symbols: c_1, c1_1, c2_1, c3_2, c13, c15_1, c17_172, c18, c7_1, c4_2, c4_1, c5_2, c5_1, c14_67