/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 65 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), 22 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (14) CpxTRS (15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (16) CpxRelTRS (17) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxWeightedTrs (19) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 59 ms] (20) CpxWeightedTrs (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxTypedWeightedTrs (23) CompletionProof [UPPER BOUND(ID), 7 ms] (24) CpxTypedWeightedCompleteTrs (25) NarrowingProof [BOTH BOUNDS(ID, ID), 4162 ms] (26) CpxTypedWeightedCompleteTrs (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 19 ms] (28) CpxRNTS (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxRNTS (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 42 ms] (34) CpxRNTS (35) CpxTrsToCdtProof [UPPER BOUND(ID), 19.5 s] (36) CdtProblem (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 678 ms] (38) CdtProblem (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (42) CdtProblem (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 99.3 s] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 27.3 s] (46) CdtProblem ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(x1))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(x1))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(x1))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(x1))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(x1))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(x1))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(x1))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(x1))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(x1))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(x1))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(x1))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(x1))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(1(1(1(0(0(1(2(0(0(2(2(0(1(0(2(0(0(x1))))))))))))))))))))))) -> 0(1(1(1(0(1(2(0(0(2(2(2(1(2(2(2(2(2(0(1(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(2(0(1(0(2(1(0(0(0(1(1(2(2(2(0(2(2(x1))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(0(0(1(1(2(0(0(2(1(0(2(1(0(1(1(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(2(1(2(2(2(2(1(2(2(1(1(2(1(2(0(2(1(0(1(1(1(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(1(2(1(0(2(0(1(0(0(2(0(0(2(1(1(0(0(1(x1))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(0(0(1(0(2(1(2(2(0(1(0(2(2(1(0(1(2(1(x1))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(1(0(0(1(0(2(1(2(2(0(1(1(0(2(0(0(1(0(x1))))))))))))))))))))))) -> 0(1(1(0(1(1(1(1(0(2(1(2(0(1(1(2(0(1(1(1(1(1(2(2(1(1(0(x1))))))))))))))))))))))))))) 0(1(0(2(1(0(2(2(0(0(2(2(2(0(2(1(0(2(2(0(2(1(2(x1))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(1(0(2(1(1(2(0(1(0(2(1(2(0(2(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(1(1(0(0(2(0(2(2(1(1(1(1(1(1(2(2(0(1(2(0(1(0(x1))))))))))))))))))))))) -> 0(2(1(1(1(0(2(1(1(0(1(2(1(0(2(2(2(1(1(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))))))) 0(1(1(0(1(1(1(2(1(0(0(0(1(0(2(1(1(2(1(2(0(0(2(x1))))))))))))))))))))))) -> 1(0(1(1(1(1(1(0(2(2(1(1(1(0(2(1(2(1(1(0(0(1(2(1(0(0(1(x1))))))))))))))))))))))))))) 0(1(1(1(2(0(2(0(0(1(0(2(0(1(2(2(1(0(2(2(2(0(2(x1))))))))))))))))))))))) -> 1(1(1(1(2(0(1(1(1(1(1(1(0(0(1(0(0(2(2(2(0(0(2(1(0(2(0(x1))))))))))))))))))))))))))) 0(1(2(0(1(0(2(0(0(2(1(2(2(1(0(2(0(1(1(1(1(2(0(x1))))))))))))))))))))))) -> 1(0(1(0(1(1(1(0(1(1(1(2(2(1(1(2(2(1(2(1(1(2(0(2(2(2(2(x1))))))))))))))))))))))))))) 0(1(2(0(1(2(1(0(2(1(2(0(2(2(2(1(1(2(0(1(2(0(1(x1))))))))))))))))))))))) -> 2(1(0(0(0(1(0(2(2(1(1(2(2(2(1(1(2(2(1(1(2(0(1(1(0(2(1(x1))))))))))))))))))))))))))) 0(1(2(0(2(2(1(2(1(1(0(2(0(1(2(2(2(0(2(0(1(2(0(x1))))))))))))))))))))))) -> 0(2(1(2(1(2(2(1(1(0(0(2(2(1(1(1(1(0(2(2(1(1(2(0(2(2(2(x1))))))))))))))))))))))))))) 0(1(2(1(0(1(0(1(2(2(1(2(1(0(2(2(1(0(1(0(1(0(2(x1))))))))))))))))))))))) -> 0(1(1(1(2(2(2(0(1(1(2(1(1(1(1(0(1(2(2(1(2(1(1(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(2(1(1(2(1(2(0(1(1(0(0(2(0(1(1(0(0(2(0(0(1(x1))))))))))))))))))))))) -> 0(1(1(0(2(2(2(0(2(1(1(0(1(0(2(2(0(1(1(0(0(2(1(1(1(2(1(x1))))))))))))))))))))))))))) 0(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(x1))))))))))))))))))))))) -> 1(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(x1))))))))))))))))))))))))))) 0(1(2(2(1(0(2(2(1(1(1(2(0(0(2(2(0(0(1(1(2(2(1(x1))))))))))))))))))))))) -> 1(1(2(2(1(1(2(0(1(0(2(1(2(0(1(1(1(2(1(0(1(1(2(0(1(1(1(x1))))))))))))))))))))))))))) 0(1(2(2(1(1(2(0(2(1(2(0(1(2(1(2(2(2(2(0(2(0(0(x1))))))))))))))))))))))) -> 1(0(2(0(0(1(2(2(2(1(1(1(0(1(2(1(2(1(1(1(1(2(2(1(1(2(0(x1))))))))))))))))))))))))))) 0(1(2(2(2(0(0(0(0(1(0(0(2(2(0(2(0(2(2(0(1(1(0(x1))))))))))))))))))))))) -> 0(0(2(1(1(1(0(1(2(2(0(2(0(0(0(1(0(2(2(2(1(0(1(2(1(1(0(x1))))))))))))))))))))))))))) 0(2(0(1(0(0(2(1(2(1(1(2(1(2(0(1(1(0(1(0(2(0(1(x1))))))))))))))))))))))) -> 1(2(2(1(1(2(1(1(1(1(0(0(0(1(1(0(0(0(2(1(1(0(2(2(2(0(1(x1))))))))))))))))))))))))))) 0(2(0(2(0(2(0(2(1(1(0(1(2(2(1(0(1(0(0(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(1(1(2(0(2(2(2(1(0(2(0(2(2(2(2(1(0(1(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) 0(2(0(2(1(0(0(2(2(2(2(0(2(1(0(1(2(0(2(1(0(0(0(x1))))))))))))))))))))))) -> 0(2(0(2(1(1(0(1(1(1(2(1(2(0(1(0(1(2(1(1(2(1(1(1(2(2(2(x1))))))))))))))))))))))))))) 0(2(1(0(1(0(0(1(1(0(2(0(0(0(1(0(1(1(0(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(0(1(1(1(1(0(2(2(2(2(2(0(1(1(2(1(2(2(1(2(0(0(0(1(1(x1))))))))))))))))))))))))))) 0(2(1(2(0(1(0(0(1(0(0(2(2(2(2(2(1(0(2(0(2(2(1(x1))))))))))))))))))))))) -> 1(2(0(1(0(0(2(1(1(2(1(0(0(1(1(1(1(2(1(0(2(0(0(0(1(1(1(x1))))))))))))))))))))))))))) 0(2(1(2(0(2(2(2(2(2(2(2(0(1(0(1(0(2(1(1(0(0(0(x1))))))))))))))))))))))) -> 2(0(2(2(1(1(1(0(0(1(1(1(0(1(1(2(1(1(0(1(1(1(1(2(2(2(2(x1))))))))))))))))))))))))))) 0(2(2(2(1(2(0(1(1(2(1(2(0(0(2(1(0(1(2(2(2(0(1(x1))))))))))))))))))))))) -> 0(2(2(2(0(2(2(0(0(1(1(1(0(1(0(2(1(1(0(2(0(1(2(1(0(2(1(x1))))))))))))))))))))))))))) 1(0(0(0(1(1(0(2(0(1(1(2(1(1(2(2(1(2(1(0(0(0(2(x1))))))))))))))))))))))) -> 1(1(0(2(1(1(0(1(0(1(1(1(0(0(2(1(0(2(1(1(0(2(1(0(2(2(2(x1))))))))))))))))))))))))))) 1(0(0(1(1(2(0(1(1(2(2(2(0(1(0(2(0(2(0(1(1(2(1(x1))))))))))))))))))))))) -> 1(1(1(1(1(1(0(0(1(1(0(2(1(2(2(1(2(2(0(2(1(1(2(2(0(0(1(x1))))))))))))))))))))))))))) 1(0(1(1(2(2(2(1(2(2(1(0(2(2(1(0(1(2(2(2(1(0(0(x1))))))))))))))))))))))) -> 1(2(1(1(0(2(2(1(1(1(1(1(1(1(2(2(2(1(0(0(1(1(1(1(1(1(2(x1))))))))))))))))))))))))))) 1(0(1(2(0(2(0(0(2(1(0(2(0(1(2(1(0(2(0(2(0(0(1(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(2(1(1(2(2(0(2(1(0(0(1(1(1(2(0(0(1(2(1(2(1(x1))))))))))))))))))))))))))) 1(0(1(2(2(2(1(1(1(0(1(0(2(0(1(1(0(2(1(0(1(0(0(x1))))))))))))))))))))))) -> 1(1(0(0(2(0(2(2(1(0(1(1(0(1(1(1(0(2(2(1(1(0(1(1(1(1(1(x1))))))))))))))))))))))))))) 1(0(2(1(0(2(0(1(0(0(0(1(0(2(1(2(0(0(2(2(1(0(2(x1))))))))))))))))))))))) -> 1(0(1(1(1(1(0(0(0(1(1(1(0(0(2(0(0(2(0(0(2(1(1(1(1(1(1(x1))))))))))))))))))))))))))) 1(0(2(2(0(1(2(0(1(2(1(2(1(0(1(2(0(2(2(2(1(2(2(x1))))))))))))))))))))))) -> 1(1(0(1(2(0(2(0(1(0(0(2(2(2(2(0(2(2(1(2(1(1(1(1(1(2(2(x1))))))))))))))))))))))))))) 1(1(0(0(1(0(2(1(0(0(2(1(0(0(2(0(1(2(1(0(0(0(0(x1))))))))))))))))))))))) -> 1(1(1(0(0(2(1(2(1(0(0(1(1(2(2(1(1(1(1(2(1(1(1(1(0(2(2(x1))))))))))))))))))))))))))) 1(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(0(1(1(1(1(0(2(1(0(0(2(1(1(2(0(2(1(2(1(2(0(1(0(2(1(x1))))))))))))))))))))))))))) 1(1(0(2(0(1(2(2(2(2(0(2(1(2(1(2(0(2(1(0(2(2(0(x1))))))))))))))))))))))) -> 1(1(1(0(1(2(2(1(2(0(1(1(2(1(1(0(1(2(2(0(1(1(1(0(1(0(2(x1))))))))))))))))))))))))))) 1(1(0(2(1(0(2(2(0(0(1(1(0(1(0(0(2(1(2(1(0(1(2(x1))))))))))))))))))))))) -> 1(0(1(2(1(2(1(1(0(2(2(2(1(1(1(1(1(2(1(1(1(0(0(0(0(2(1(x1))))))))))))))))))))))))))) 1(1(0(2(1(2(1(0(0(1(1(2(2(2(0(2(2(2(1(0(2(0(2(x1))))))))))))))))))))))) -> 1(2(1(0(0(1(1(0(1(1(1(1(2(1(1(2(1(1(1(0(1(1(0(2(2(2(0(x1))))))))))))))))))))))))))) 1(1(0(2(1(2(2(2(0(2(1(0(0(1(2(0(2(1(1(1(2(0(0(x1))))))))))))))))))))))) -> 1(2(1(1(2(0(1(1(1(2(1(1(1(2(2(1(1(1(1(1(0(0(2(1(2(0(2(x1))))))))))))))))))))))))))) 1(1(1(1(2(2(0(0(1(1(1(2(1(2(0(2(2(0(0(1(2(1(1(x1))))))))))))))))))))))) -> 1(2(2(1(0(1(2(1(1(1(2(1(1(1(1(1(1(0(1(1(1(1(0(2(0(1(1(x1))))))))))))))))))))))))))) 1(1(1(2(2(1(1(1(2(2(0(2(0(1(2(0(0(2(2(2(0(0(0(x1))))))))))))))))))))))) -> 1(1(0(1(1(1(0(0(0(1(2(2(2(1(1(1(1(0(2(2(2(2(2(0(1(2(2(x1))))))))))))))))))))))))))) 1(1(2(0(2(1(1(2(1(1(1(1(1(0(0(1(2(2(2(1(2(0(0(x1))))))))))))))))))))))) -> 1(2(1(1(1(0(0(1(1(1(1(0(2(2(2(2(1(0(0(1(2(1(1(1(0(2(2(x1))))))))))))))))))))))))))) 1(1(2(1(0(1(1(0(0(1(2(0(0(0(0(0(2(0(1(1(0(0(2(x1))))))))))))))))))))))) -> 1(1(1(0(0(0(2(0(2(1(2(2(2(2(2(2(1(1(1(1(2(1(0(0(0(0(2(x1))))))))))))))))))))))))))) 1(1(2(2(2(0(1(1(2(0(2(2(2(2(2(0(1(1(2(2(1(2(1(x1))))))))))))))))))))))) -> 1(2(0(1(0(2(1(1(2(2(2(1(1(1(2(2(1(1(1(2(1(1(1(2(1(1(1(x1))))))))))))))))))))))))))) 1(1(2(2(2(0(1(1(2(1(0(0(1(0(0(2(1(2(2(0(1(2(2(x1))))))))))))))))))))))) -> 1(2(1(0(1(1(0(2(2(1(1(2(1(1(0(2(2(1(2(2(2(2(2(0(1(1(1(x1))))))))))))))))))))))))))) 1(1(2(2(2(2(1(2(2(1(0(2(2(1(1(2(2(0(0(0(0(0(0(x1))))))))))))))))))))))) -> 1(1(0(2(0(1(2(2(0(1(1(1(1(1(0(1(2(1(1(2(0(2(2(0(2(1(1(x1))))))))))))))))))))))))))) 1(2(0(0(0(0(1(1(0(2(2(2(2(1(0(1(0(0(0(2(1(0(1(x1))))))))))))))))))))))) -> 1(2(1(1(0(1(1(2(1(2(0(2(1(1(1(0(1(1(1(0(1(0(1(0(2(1(1(x1))))))))))))))))))))))))))) 1(2(0(0(1(1(1(1(0(2(2(0(2(2(0(2(0(2(1(1(1(1(1(x1))))))))))))))))))))))) -> 1(1(0(2(1(1(0(1(1(1(1(2(1(2(1(1(0(0(1(1(1(0(2(2(1(2(1(x1))))))))))))))))))))))))))) 1(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(x1))))))))))))))))))))))) -> 1(1(0(1(0(0(1(1(1(1(1(1(2(1(0(0(0(2(1(0(0(1(0(2(2(2(0(x1))))))))))))))))))))))))))) 1(2(0(1(1(1(2(2(2(1(1(1(1(2(0(0(0(2(1(2(0(0(0(x1))))))))))))))))))))))) -> 1(2(1(2(1(1(1(0(1(1(0(1(1(1(0(2(2(0(2(1(0(2(1(0(2(2(2(x1))))))))))))))))))))))))))) 1(2(0(2(0(0(1(2(2(1(1(2(1(1(1(2(1(1(2(1(0(0(0(x1))))))))))))))))))))))) -> 1(1(1(0(1(2(1(1(2(1(1(1(0(0(0(2(0(1(2(1(0(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 1(2(0(2(1(1(1(0(2(0(1(2(0(2(0(2(0(1(1(0(2(2(0(x1))))))))))))))))))))))) -> 1(2(2(1(1(1(0(1(2(1(1(2(1(0(0(2(1(0(2(1(1(1(0(1(0(2(0(x1))))))))))))))))))))))))))) 1(2(0(2(1(2(0(2(0(1(0(0(1(1(0(2(2(2(1(1(2(2(0(x1))))))))))))))))))))))) -> 1(1(1(1(2(1(2(1(0(1(0(2(2(1(1(0(1(2(1(1(1(1(0(2(0(2(2(x1))))))))))))))))))))))))))) 1(2(0(2(2(1(0(0(2(2(0(0(2(2(1(2(2(0(1(1(1(2(1(x1))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(2(1(1(1(1(1(1(2(0(0(2(1(0(0(1(2(2(2(1(x1))))))))))))))))))))))))))) 1(2(1(1(2(1(0(0(2(1(0(1(2(1(1(0(1(2(0(2(2(0(1(x1))))))))))))))))))))))) -> 1(2(1(1(1(0(2(0(2(0(0(2(1(0(2(1(1(1(1(1(0(0(0(1(0(1(1(x1))))))))))))))))))))))))))) 1(2(1(2(1(2(2(1(0(2(1(1(1(0(0(2(2(0(2(0(2(2(1(x1))))))))))))))))))))))) -> 1(0(2(1(0(1(0(0(1(1(1(2(0(2(2(1(1(1(1(1(2(2(1(2(1(0(1(x1))))))))))))))))))))))))))) 1(2(2(0(1(2(0(1(1(2(1(2(2(0(1(0(1(0(2(2(2(1(0(x1))))))))))))))))))))))) -> 1(1(0(0(0(1(0(2(1(0(2(2(2(1(0(0(2(1(1(0(2(2(2(2(1(1(0(x1))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(0(2(0(0(1(1(1(0(1(2(2(2(2(1(2(x1))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(0(1(0(0(0(1(1(1(2(0(2(2(2(2(1(1(1(1(2(x1))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(1(0(1(0(0(2(1(2(0(2(2(2(0(0(x1))))))))))))))))))))))) -> 1(1(1(0(2(2(0(0(2(2(2(1(2(1(1(1(1(0(2(2(2(0(1(0(2(0(2(x1))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(2(2(0(1(2(0(0(0(2(0(2(1(0(1(x1))))))))))))))))))))))) -> 1(0(1(2(1(1(2(1(0(0(1(1(0(0(2(2(0(0(2(2(0(2(1(1(1(2(1(x1))))))))))))))))))))))))))) 1(2(2(2(0(1(2(2(1(1(1(1(1(2(2(0(1(2(1(2(0(0(1(x1))))))))))))))))))))))) -> 1(1(1(1(0(1(1(1(0(0(1(0(0(0(2(1(1(1(1(1(1(1(0(1(2(0(1(x1))))))))))))))))))))))))))) 2(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(x1))))))))))))))))))))))) -> 2(0(0(0(0(1(1(2(0(1(2(2(1(0(2(0(2(2(2(0(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 2(0(0(2(1(0(1(1(1(2(0(0(1(1(1(0(1(2(1(1(0(0(0(x1))))))))))))))))))))))) -> 1(1(0(0(1(1(1(0(0(1(0(2(1(1(1(1(1(2(1(2(1(1(1(1(1(1(0(x1))))))))))))))))))))))))))) 2(0(0(2(1(1(1(1(2(2(2(1(2(1(0(2(2(1(0(0(2(0(1(x1))))))))))))))))))))))) -> 1(1(1(2(2(1(1(1(2(1(2(0(2(2(1(1(1(1(0(2(0(2(1(1(0(2(1(x1))))))))))))))))))))))))))) 2(0(1(0(1(1(1(1(2(2(2(2(0(0(1(0(1(0(0(0(2(2(0(x1))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(1(2(2(2(0(2(2(1(1(2(2(2(0(1(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(0(1(2(0(1(1(0(2(2(2(2(0(2(1(0(2(1(2(1(0(2(1(x1))))))))))))))))))))))) -> 2(1(1(0(1(1(0(2(1(1(1(0(1(0(0(2(1(1(1(0(2(0(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(0(2(0(0(1(1(1(2(0(2(2(2(0(0(1(2(2(0(0(1(0(1(x1))))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(1(1(1(1(0(1(2(2(2(1(2(0(1(2(0(1(1(1(x1))))))))))))))))))))))))))) 2(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(x1))))))))))))))))))))))) -> 2(2(2(1(0(1(1(0(2(2(0(0(1(1(1(1(1(1(0(1(1(1(2(0(2(2(0(x1))))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(1(2(2(0(2(0(1(2(1(0(0(1(0(2(1(x1))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(2(2(0(1(2(1(0(1(0(1(2(2(1(1(0(2(1(0(1(x1))))))))))))))))))))))))))) 2(0(2(1(0(1(2(2(1(2(2(0(2(0(2(0(2(2(1(2(0(2(2(x1))))))))))))))))))))))) -> 0(1(0(2(2(0(0(0(1(1(2(0(1(1(0(2(0(1(1(1(1(1(0(1(0(2(2(x1))))))))))))))))))))))))))) 2(0(2(1(1(0(2(1(0(2(1(2(2(0(0(1(0(1(0(2(0(2(0(x1))))))))))))))))))))))) -> 1(1(1(0(1(2(0(0(1(1(2(1(2(2(1(1(1(1(2(1(2(1(2(1(1(2(1(x1))))))))))))))))))))))))))) 2(1(0(1(0(2(2(2(1(2(2(0(1(2(1(1(1(1(0(0(2(0(2(x1))))))))))))))))))))))) -> 2(1(2(1(2(1(1(1(2(2(1(2(1(1(1(0(1(1(1(2(1(0(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(1(0(1(1(0(1(2(1(0(2(2(0(1(0(1(2(0(2(2(1(2(0(x1))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(0(1(1(2(2(2(0(2(1(0(0(0(2(2(2(2(2(0(0(1(1(x1))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(x1))))))))))))))))))))))))))) 2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(x1))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(x1))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(x1))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(x1))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(x1))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(x1))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(x1))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(x1))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(x1))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(x1))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(x1))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(x1))))))))))))))))))))))))))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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_2(x_1) -> 2(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(x1))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(x1))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(x1))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(x1))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(x1))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(x1))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(x1))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(x1))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(x1))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(x1))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(x1))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(x1))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(x1))))))))))))))))))))))))))) 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0(1(2(0(2(2(1(2(1(1(0(2(0(1(2(2(2(0(2(0(1(2(0(x1))))))))))))))))))))))) -> 0(2(1(2(1(2(2(1(1(0(0(2(2(1(1(1(1(0(2(2(1(1(2(0(2(2(2(x1))))))))))))))))))))))))))) 0(1(2(1(0(1(0(1(2(2(1(2(1(0(2(2(1(0(1(0(1(0(2(x1))))))))))))))))))))))) -> 0(1(1(1(2(2(2(0(1(1(2(1(1(1(1(0(1(2(2(1(2(1(1(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(2(1(1(2(1(2(0(1(1(0(0(2(0(1(1(0(0(2(0(0(1(x1))))))))))))))))))))))) -> 0(1(1(0(2(2(2(0(2(1(1(0(1(0(2(2(0(1(1(0(0(2(1(1(1(2(1(x1))))))))))))))))))))))))))) 0(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(x1))))))))))))))))))))))) -> 1(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(x1))))))))))))))))))))))))))) 0(1(2(2(1(0(2(2(1(1(1(2(0(0(2(2(0(0(1(1(2(2(1(x1))))))))))))))))))))))) -> 1(1(2(2(1(1(2(0(1(0(2(1(2(0(1(1(1(2(1(0(1(1(2(0(1(1(1(x1))))))))))))))))))))))))))) 0(1(2(2(1(1(2(0(2(1(2(0(1(2(1(2(2(2(2(0(2(0(0(x1))))))))))))))))))))))) -> 1(0(2(0(0(1(2(2(2(1(1(1(0(1(2(1(2(1(1(1(1(2(2(1(1(2(0(x1))))))))))))))))))))))))))) 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1(1(2(1(0(1(1(0(0(1(2(0(0(0(0(0(2(0(1(1(0(0(2(x1))))))))))))))))))))))) -> 1(1(1(0(0(0(2(0(2(1(2(2(2(2(2(2(1(1(1(1(2(1(0(0(0(0(2(x1))))))))))))))))))))))))))) 1(1(2(2(2(0(1(1(2(0(2(2(2(2(2(0(1(1(2(2(1(2(1(x1))))))))))))))))))))))) -> 1(2(0(1(0(2(1(1(2(2(2(1(1(1(2(2(1(1(1(2(1(1(1(2(1(1(1(x1))))))))))))))))))))))))))) 1(1(2(2(2(0(1(1(2(1(0(0(1(0(0(2(1(2(2(0(1(2(2(x1))))))))))))))))))))))) -> 1(2(1(0(1(1(0(2(2(1(1(2(1(1(0(2(2(1(2(2(2(2(2(0(1(1(1(x1))))))))))))))))))))))))))) 1(1(2(2(2(2(1(2(2(1(0(2(2(1(1(2(2(0(0(0(0(0(0(x1))))))))))))))))))))))) -> 1(1(0(2(0(1(2(2(0(1(1(1(1(1(0(1(2(1(1(2(0(2(2(0(2(1(1(x1))))))))))))))))))))))))))) 1(2(0(0(0(0(1(1(0(2(2(2(2(1(0(1(0(0(0(2(1(0(1(x1))))))))))))))))))))))) -> 1(2(1(1(0(1(1(2(1(2(0(2(1(1(1(0(1(1(1(0(1(0(1(0(2(1(1(x1))))))))))))))))))))))))))) 1(2(0(0(1(1(1(1(0(2(2(0(2(2(0(2(0(2(1(1(1(1(1(x1))))))))))))))))))))))) -> 1(1(0(2(1(1(0(1(1(1(1(2(1(2(1(1(0(0(1(1(1(0(2(2(1(2(1(x1))))))))))))))))))))))))))) 1(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(x1))))))))))))))))))))))) -> 1(1(0(1(0(0(1(1(1(1(1(1(2(1(0(0(0(2(1(0(0(1(0(2(2(2(0(x1))))))))))))))))))))))))))) 1(2(0(1(1(1(2(2(2(1(1(1(1(2(0(0(0(2(1(2(0(0(0(x1))))))))))))))))))))))) -> 1(2(1(2(1(1(1(0(1(1(0(1(1(1(0(2(2(0(2(1(0(2(1(0(2(2(2(x1))))))))))))))))))))))))))) 1(2(0(2(0(0(1(2(2(1(1(2(1(1(1(2(1(1(2(1(0(0(0(x1))))))))))))))))))))))) -> 1(1(1(0(1(2(1(1(2(1(1(1(0(0(0(2(0(1(2(1(0(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 1(2(0(2(1(1(1(0(2(0(1(2(0(2(0(2(0(1(1(0(2(2(0(x1))))))))))))))))))))))) -> 1(2(2(1(1(1(0(1(2(1(1(2(1(0(0(2(1(0(2(1(1(1(0(1(0(2(0(x1))))))))))))))))))))))))))) 1(2(0(2(1(2(0(2(0(1(0(0(1(1(0(2(2(2(1(1(2(2(0(x1))))))))))))))))))))))) -> 1(1(1(1(2(1(2(1(0(1(0(2(2(1(1(0(1(2(1(1(1(1(0(2(0(2(2(x1))))))))))))))))))))))))))) 1(2(0(2(2(1(0(0(2(2(0(0(2(2(1(2(2(0(1(1(1(2(1(x1))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(2(1(1(1(1(1(1(2(0(0(2(1(0(0(1(2(2(2(1(x1))))))))))))))))))))))))))) 1(2(1(1(2(1(0(0(2(1(0(1(2(1(1(0(1(2(0(2(2(0(1(x1))))))))))))))))))))))) -> 1(2(1(1(1(0(2(0(2(0(0(2(1(0(2(1(1(1(1(1(0(0(0(1(0(1(1(x1))))))))))))))))))))))))))) 1(2(1(2(1(2(2(1(0(2(1(1(1(0(0(2(2(0(2(0(2(2(1(x1))))))))))))))))))))))) -> 1(0(2(1(0(1(0(0(1(1(1(2(0(2(2(1(1(1(1(1(2(2(1(2(1(0(1(x1))))))))))))))))))))))))))) 1(2(2(0(1(2(0(1(1(2(1(2(2(0(1(0(1(0(2(2(2(1(0(x1))))))))))))))))))))))) -> 1(1(0(0(0(1(0(2(1(0(2(2(2(1(0(0(2(1(1(0(2(2(2(2(1(1(0(x1))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(0(2(0(0(1(1(1(0(1(2(2(2(2(1(2(x1))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(0(1(0(0(0(1(1(1(2(0(2(2(2(2(1(1(1(1(2(x1))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(1(0(1(0(0(2(1(2(0(2(2(2(0(0(x1))))))))))))))))))))))) -> 1(1(1(0(2(2(0(0(2(2(2(1(2(1(1(1(1(0(2(2(2(0(1(0(2(0(2(x1))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(2(2(0(1(2(0(0(0(2(0(2(1(0(1(x1))))))))))))))))))))))) -> 1(0(1(2(1(1(2(1(0(0(1(1(0(0(2(2(0(0(2(2(0(2(1(1(1(2(1(x1))))))))))))))))))))))))))) 1(2(2(2(0(1(2(2(1(1(1(1(1(2(2(0(1(2(1(2(0(0(1(x1))))))))))))))))))))))) -> 1(1(1(1(0(1(1(1(0(0(1(0(0(0(2(1(1(1(1(1(1(1(0(1(2(0(1(x1))))))))))))))))))))))))))) 2(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(x1))))))))))))))))))))))) -> 2(0(0(0(0(1(1(2(0(1(2(2(1(0(2(0(2(2(2(0(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 2(0(0(2(1(0(1(1(1(2(0(0(1(1(1(0(1(2(1(1(0(0(0(x1))))))))))))))))))))))) -> 1(1(0(0(1(1(1(0(0(1(0(2(1(1(1(1(1(2(1(2(1(1(1(1(1(1(0(x1))))))))))))))))))))))))))) 2(0(0(2(1(1(1(1(2(2(2(1(2(1(0(2(2(1(0(0(2(0(1(x1))))))))))))))))))))))) -> 1(1(1(2(2(1(1(1(2(1(2(0(2(2(1(1(1(1(0(2(0(2(1(1(0(2(1(x1))))))))))))))))))))))))))) 2(0(1(0(1(1(1(1(2(2(2(2(0(0(1(0(1(0(0(0(2(2(0(x1))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(1(2(2(2(0(2(2(1(1(2(2(2(0(1(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(0(1(2(0(1(1(0(2(2(2(2(0(2(1(0(2(1(2(1(0(2(1(x1))))))))))))))))))))))) -> 2(1(1(0(1(1(0(2(1(1(1(0(1(0(0(2(1(1(1(0(2(0(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(0(2(0(0(1(1(1(2(0(2(2(2(0(0(1(2(2(0(0(1(0(1(x1))))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(1(1(1(1(0(1(2(2(2(1(2(0(1(2(0(1(1(1(x1))))))))))))))))))))))))))) 2(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(x1))))))))))))))))))))))) -> 2(2(2(1(0(1(1(0(2(2(0(0(1(1(1(1(1(1(0(1(1(1(2(0(2(2(0(x1))))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(1(2(2(0(2(0(1(2(1(0(0(1(0(2(1(x1))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(2(2(0(1(2(1(0(1(0(1(2(2(1(1(0(2(1(0(1(x1))))))))))))))))))))))))))) 2(0(2(1(0(1(2(2(1(2(2(0(2(0(2(0(2(2(1(2(0(2(2(x1))))))))))))))))))))))) -> 0(1(0(2(2(0(0(0(1(1(2(0(1(1(0(2(0(1(1(1(1(1(0(1(0(2(2(x1))))))))))))))))))))))))))) 2(0(2(1(1(0(2(1(0(2(1(2(2(0(0(1(0(1(0(2(0(2(0(x1))))))))))))))))))))))) -> 1(1(1(0(1(2(0(0(1(1(2(1(2(2(1(1(1(1(2(1(2(1(2(1(1(2(1(x1))))))))))))))))))))))))))) 2(1(0(1(0(2(2(2(1(2(2(0(1(2(1(1(1(1(0(0(2(0(2(x1))))))))))))))))))))))) -> 2(1(2(1(2(1(1(1(2(2(1(2(1(1(1(0(1(1(1(2(1(0(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(1(0(1(1(0(1(2(1(0(2(2(0(1(0(1(2(0(2(2(1(2(0(x1))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(0(1(1(2(2(2(0(2(1(0(0(0(2(2(2(2(2(0(0(1(1(x1))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(x1))))))))))))))))))))))))))) 2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(x1))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(x1))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(x1))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(x1))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(x1))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(x1))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(x1))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(x1))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(x1))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(x1))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(x1))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(x1))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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_2(x_1) -> 2(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(x1))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(x1))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(x1))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(x1))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(x1))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(x1))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(x1))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(x1))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(x1))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(x1))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(x1))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(x1))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(1(1(1(0(0(1(2(0(0(2(2(0(1(0(2(0(0(x1))))))))))))))))))))))) -> 0(1(1(1(0(1(2(0(0(2(2(2(1(2(2(2(2(2(0(1(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(2(0(1(0(2(1(0(0(0(1(1(2(2(2(0(2(2(x1))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(0(0(1(1(2(0(0(2(1(0(2(1(0(1(1(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(2(1(2(2(2(2(1(2(2(1(1(2(1(2(0(2(1(0(1(1(1(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(1(2(1(0(2(0(1(0(0(2(0(0(2(1(1(0(0(1(x1))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(0(0(1(0(2(1(2(2(0(1(0(2(2(1(0(1(2(1(x1))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(1(0(0(1(0(2(1(2(2(0(1(1(0(2(0(0(1(0(x1))))))))))))))))))))))) -> 0(1(1(0(1(1(1(1(0(2(1(2(0(1(1(2(0(1(1(1(1(1(2(2(1(1(0(x1))))))))))))))))))))))))))) 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1(2(1(1(2(1(0(0(2(1(0(1(2(1(1(0(1(2(0(2(2(0(1(x1))))))))))))))))))))))) -> 1(2(1(1(1(0(2(0(2(0(0(2(1(0(2(1(1(1(1(1(0(0(0(1(0(1(1(x1))))))))))))))))))))))))))) 1(2(1(2(1(2(2(1(0(2(1(1(1(0(0(2(2(0(2(0(2(2(1(x1))))))))))))))))))))))) -> 1(0(2(1(0(1(0(0(1(1(1(2(0(2(2(1(1(1(1(1(2(2(1(2(1(0(1(x1))))))))))))))))))))))))))) 1(2(2(0(1(2(0(1(1(2(1(2(2(0(1(0(1(0(2(2(2(1(0(x1))))))))))))))))))))))) -> 1(1(0(0(0(1(0(2(1(0(2(2(2(1(0(0(2(1(1(0(2(2(2(2(1(1(0(x1))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(0(2(0(0(1(1(1(0(1(2(2(2(2(1(2(x1))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(0(1(0(0(0(1(1(1(2(0(2(2(2(2(1(1(1(1(2(x1))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(1(0(1(0(0(2(1(2(0(2(2(2(0(0(x1))))))))))))))))))))))) -> 1(1(1(0(2(2(0(0(2(2(2(1(2(1(1(1(1(0(2(2(2(0(1(0(2(0(2(x1))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(2(2(0(1(2(0(0(0(2(0(2(1(0(1(x1))))))))))))))))))))))) -> 1(0(1(2(1(1(2(1(0(0(1(1(0(0(2(2(0(0(2(2(0(2(1(1(1(2(1(x1))))))))))))))))))))))))))) 1(2(2(2(0(1(2(2(1(1(1(1(1(2(2(0(1(2(1(2(0(0(1(x1))))))))))))))))))))))) -> 1(1(1(1(0(1(1(1(0(0(1(0(0(0(2(1(1(1(1(1(1(1(0(1(2(0(1(x1))))))))))))))))))))))))))) 2(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(x1))))))))))))))))))))))) -> 2(0(0(0(0(1(1(2(0(1(2(2(1(0(2(0(2(2(2(0(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 2(0(0(2(1(0(1(1(1(2(0(0(1(1(1(0(1(2(1(1(0(0(0(x1))))))))))))))))))))))) -> 1(1(0(0(1(1(1(0(0(1(0(2(1(1(1(1(1(2(1(2(1(1(1(1(1(1(0(x1))))))))))))))))))))))))))) 2(0(0(2(1(1(1(1(2(2(2(1(2(1(0(2(2(1(0(0(2(0(1(x1))))))))))))))))))))))) -> 1(1(1(2(2(1(1(1(2(1(2(0(2(2(1(1(1(1(0(2(0(2(1(1(0(2(1(x1))))))))))))))))))))))))))) 2(0(1(0(1(1(1(1(2(2(2(2(0(0(1(0(1(0(0(0(2(2(0(x1))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(1(2(2(2(0(2(2(1(1(2(2(2(0(1(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(0(1(2(0(1(1(0(2(2(2(2(0(2(1(0(2(1(2(1(0(2(1(x1))))))))))))))))))))))) -> 2(1(1(0(1(1(0(2(1(1(1(0(1(0(0(2(1(1(1(0(2(0(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(0(2(0(0(1(1(1(2(0(2(2(2(0(0(1(2(2(0(0(1(0(1(x1))))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(1(1(1(1(0(1(2(2(2(1(2(0(1(2(0(1(1(1(x1))))))))))))))))))))))))))) 2(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(x1))))))))))))))))))))))) -> 2(2(2(1(0(1(1(0(2(2(0(0(1(1(1(1(1(1(0(1(1(1(2(0(2(2(0(x1))))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(1(2(2(0(2(0(1(2(1(0(0(1(0(2(1(x1))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(2(2(0(1(2(1(0(1(0(1(2(2(1(1(0(2(1(0(1(x1))))))))))))))))))))))))))) 2(0(2(1(0(1(2(2(1(2(2(0(2(0(2(0(2(2(1(2(0(2(2(x1))))))))))))))))))))))) -> 0(1(0(2(2(0(0(0(1(1(2(0(1(1(0(2(0(1(1(1(1(1(0(1(0(2(2(x1))))))))))))))))))))))))))) 2(0(2(1(1(0(2(1(0(2(1(2(2(0(0(1(0(1(0(2(0(2(0(x1))))))))))))))))))))))) -> 1(1(1(0(1(2(0(0(1(1(2(1(2(2(1(1(1(1(2(1(2(1(2(1(1(2(1(x1))))))))))))))))))))))))))) 2(1(0(1(0(2(2(2(1(2(2(0(1(2(1(1(1(1(0(0(2(0(2(x1))))))))))))))))))))))) -> 2(1(2(1(2(1(1(1(2(2(1(2(1(1(1(0(1(1(1(2(1(0(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(1(0(1(1(0(1(2(1(0(2(2(0(1(0(1(2(0(2(2(1(2(0(x1))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(0(1(1(2(2(2(0(2(1(0(0(0(2(2(2(2(2(0(0(1(1(x1))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(x1))))))))))))))))))))))))))) 2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(x1))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(x1))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(x1))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(x1))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(x1))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(x1))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(x1))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(x1))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(x1))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(x1))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(x1))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(x1))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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_2(x_1) -> 2(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(x1))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(x1))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(x1))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(x1))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(x1))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(x1))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(x1))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(x1))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(x1))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(x1))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(x1))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(x1))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(1(1(1(0(0(1(2(0(0(2(2(0(1(0(2(0(0(x1))))))))))))))))))))))) -> 0(1(1(1(0(1(2(0(0(2(2(2(1(2(2(2(2(2(0(1(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(2(0(1(0(2(1(0(0(0(1(1(2(2(2(0(2(2(x1))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(0(0(1(1(2(0(0(2(1(0(2(1(0(1(1(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(2(1(2(2(2(2(1(2(2(1(1(2(1(2(0(2(1(0(1(1(1(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(1(2(1(0(2(0(1(0(0(2(0(0(2(1(1(0(0(1(x1))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(0(0(1(0(2(1(2(2(0(1(0(2(2(1(0(1(2(1(x1))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(1(0(0(1(0(2(1(2(2(0(1(1(0(2(0(0(1(0(x1))))))))))))))))))))))) -> 0(1(1(0(1(1(1(1(0(2(1(2(0(1(1(2(0(1(1(1(1(1(2(2(1(1(0(x1))))))))))))))))))))))))))) 0(1(0(2(1(0(2(2(0(0(2(2(2(0(2(1(0(2(2(0(2(1(2(x1))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(1(0(2(1(1(2(0(1(0(2(1(2(0(2(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(1(1(0(0(2(0(2(2(1(1(1(1(1(1(2(2(0(1(2(0(1(0(x1))))))))))))))))))))))) -> 0(2(1(1(1(0(2(1(1(0(1(2(1(0(2(2(2(1(1(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))))))) 0(1(1(0(1(1(1(2(1(0(0(0(1(0(2(1(1(2(1(2(0(0(2(x1))))))))))))))))))))))) -> 1(0(1(1(1(1(1(0(2(2(1(1(1(0(2(1(2(1(1(0(0(1(2(1(0(0(1(x1))))))))))))))))))))))))))) 0(1(1(1(2(0(2(0(0(1(0(2(0(1(2(2(1(0(2(2(2(0(2(x1))))))))))))))))))))))) -> 1(1(1(1(2(0(1(1(1(1(1(1(0(0(1(0(0(2(2(2(0(0(2(1(0(2(0(x1))))))))))))))))))))))))))) 0(1(2(0(1(0(2(0(0(2(1(2(2(1(0(2(0(1(1(1(1(2(0(x1))))))))))))))))))))))) -> 1(0(1(0(1(1(1(0(1(1(1(2(2(1(1(2(2(1(2(1(1(2(0(2(2(2(2(x1))))))))))))))))))))))))))) 0(1(2(0(1(2(1(0(2(1(2(0(2(2(2(1(1(2(0(1(2(0(1(x1))))))))))))))))))))))) -> 2(1(0(0(0(1(0(2(2(1(1(2(2(2(1(1(2(2(1(1(2(0(1(1(0(2(1(x1))))))))))))))))))))))))))) 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1(2(1(1(2(1(0(0(2(1(0(1(2(1(1(0(1(2(0(2(2(0(1(x1))))))))))))))))))))))) -> 1(2(1(1(1(0(2(0(2(0(0(2(1(0(2(1(1(1(1(1(0(0(0(1(0(1(1(x1))))))))))))))))))))))))))) 1(2(1(2(1(2(2(1(0(2(1(1(1(0(0(2(2(0(2(0(2(2(1(x1))))))))))))))))))))))) -> 1(0(2(1(0(1(0(0(1(1(1(2(0(2(2(1(1(1(1(1(2(2(1(2(1(0(1(x1))))))))))))))))))))))))))) 1(2(2(0(1(2(0(1(1(2(1(2(2(0(1(0(1(0(2(2(2(1(0(x1))))))))))))))))))))))) -> 1(1(0(0(0(1(0(2(1(0(2(2(2(1(0(0(2(1(1(0(2(2(2(2(1(1(0(x1))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(0(2(0(0(1(1(1(0(1(2(2(2(2(1(2(x1))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(0(1(0(0(0(1(1(1(2(0(2(2(2(2(1(1(1(1(2(x1))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(1(0(1(0(0(2(1(2(0(2(2(2(0(0(x1))))))))))))))))))))))) -> 1(1(1(0(2(2(0(0(2(2(2(1(2(1(1(1(1(0(2(2(2(0(1(0(2(0(2(x1))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(2(2(0(1(2(0(0(0(2(0(2(1(0(1(x1))))))))))))))))))))))) -> 1(0(1(2(1(1(2(1(0(0(1(1(0(0(2(2(0(0(2(2(0(2(1(1(1(2(1(x1))))))))))))))))))))))))))) 1(2(2(2(0(1(2(2(1(1(1(1(1(2(2(0(1(2(1(2(0(0(1(x1))))))))))))))))))))))) -> 1(1(1(1(0(1(1(1(0(0(1(0(0(0(2(1(1(1(1(1(1(1(0(1(2(0(1(x1))))))))))))))))))))))))))) 2(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(x1))))))))))))))))))))))) -> 2(0(0(0(0(1(1(2(0(1(2(2(1(0(2(0(2(2(2(0(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 2(0(0(2(1(0(1(1(1(2(0(0(1(1(1(0(1(2(1(1(0(0(0(x1))))))))))))))))))))))) -> 1(1(0(0(1(1(1(0(0(1(0(2(1(1(1(1(1(2(1(2(1(1(1(1(1(1(0(x1))))))))))))))))))))))))))) 2(0(0(2(1(1(1(1(2(2(2(1(2(1(0(2(2(1(0(0(2(0(1(x1))))))))))))))))))))))) -> 1(1(1(2(2(1(1(1(2(1(2(0(2(2(1(1(1(1(0(2(0(2(1(1(0(2(1(x1))))))))))))))))))))))))))) 2(0(1(0(1(1(1(1(2(2(2(2(0(0(1(0(1(0(0(0(2(2(0(x1))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(1(2(2(2(0(2(2(1(1(2(2(2(0(1(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(0(1(2(0(1(1(0(2(2(2(2(0(2(1(0(2(1(2(1(0(2(1(x1))))))))))))))))))))))) -> 2(1(1(0(1(1(0(2(1(1(1(0(1(0(0(2(1(1(1(0(2(0(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(0(2(0(0(1(1(1(2(0(2(2(2(0(0(1(2(2(0(0(1(0(1(x1))))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(1(1(1(1(0(1(2(2(2(1(2(0(1(2(0(1(1(1(x1))))))))))))))))))))))))))) 2(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(x1))))))))))))))))))))))) -> 2(2(2(1(0(1(1(0(2(2(0(0(1(1(1(1(1(1(0(1(1(1(2(0(2(2(0(x1))))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(1(2(2(0(2(0(1(2(1(0(0(1(0(2(1(x1))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(2(2(0(1(2(1(0(1(0(1(2(2(1(1(0(2(1(0(1(x1))))))))))))))))))))))))))) 2(0(2(1(0(1(2(2(1(2(2(0(2(0(2(0(2(2(1(2(0(2(2(x1))))))))))))))))))))))) -> 0(1(0(2(2(0(0(0(1(1(2(0(1(1(0(2(0(1(1(1(1(1(0(1(0(2(2(x1))))))))))))))))))))))))))) 2(0(2(1(1(0(2(1(0(2(1(2(2(0(0(1(0(1(0(2(0(2(0(x1))))))))))))))))))))))) -> 1(1(1(0(1(2(0(0(1(1(2(1(2(2(1(1(1(1(2(1(2(1(2(1(1(2(1(x1))))))))))))))))))))))))))) 2(1(0(1(0(2(2(2(1(2(2(0(1(2(1(1(1(1(0(0(2(0(2(x1))))))))))))))))))))))) -> 2(1(2(1(2(1(1(1(2(2(1(2(1(1(1(0(1(1(1(2(1(0(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(1(0(1(1(0(1(2(1(0(2(2(0(1(0(1(2(0(2(2(1(2(0(x1))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(0(1(1(2(2(2(0(2(1(0(0(0(2(2(2(2(2(0(0(1(1(x1))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(x1))))))))))))))))))))))))))) 2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(x1))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(x1))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(x1))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(x1))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(x1))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(x1))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(x1))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(x1))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(x1))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(x1))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(x1))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(x1))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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_2(x_1) -> 2(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (7) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(x1))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(x1))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(x1))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(x1))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(x1))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(x1))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(x1))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(x1))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(x1))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(x1))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(x1))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(x1))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(1(1(1(0(0(1(2(0(0(2(2(0(1(0(2(0(0(x1))))))))))))))))))))))) -> 0(1(1(1(0(1(2(0(0(2(2(2(1(2(2(2(2(2(0(1(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(2(0(1(0(2(1(0(0(0(1(1(2(2(2(0(2(2(x1))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(0(0(1(1(2(0(0(2(1(0(2(1(0(1(1(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(2(1(2(2(2(2(1(2(2(1(1(2(1(2(0(2(1(0(1(1(1(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(1(2(1(0(2(0(1(0(0(2(0(0(2(1(1(0(0(1(x1))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(0(0(1(0(2(1(2(2(0(1(0(2(2(1(0(1(2(1(x1))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(1(0(0(1(0(2(1(2(2(0(1(1(0(2(0(0(1(0(x1))))))))))))))))))))))) -> 0(1(1(0(1(1(1(1(0(2(1(2(0(1(1(2(0(1(1(1(1(1(2(2(1(1(0(x1))))))))))))))))))))))))))) 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0(1(2(0(2(2(1(2(1(1(0(2(0(1(2(2(2(0(2(0(1(2(0(x1))))))))))))))))))))))) -> 0(2(1(2(1(2(2(1(1(0(0(2(2(1(1(1(1(0(2(2(1(1(2(0(2(2(2(x1))))))))))))))))))))))))))) 0(1(2(1(0(1(0(1(2(2(1(2(1(0(2(2(1(0(1(0(1(0(2(x1))))))))))))))))))))))) -> 0(1(1(1(2(2(2(0(1(1(2(1(1(1(1(0(1(2(2(1(2(1(1(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(2(1(1(2(1(2(0(1(1(0(0(2(0(1(1(0(0(2(0(0(1(x1))))))))))))))))))))))) -> 0(1(1(0(2(2(2(0(2(1(1(0(1(0(2(2(0(1(1(0(0(2(1(1(1(2(1(x1))))))))))))))))))))))))))) 0(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(x1))))))))))))))))))))))) -> 1(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(x1))))))))))))))))))))))))))) 0(1(2(2(1(0(2(2(1(1(1(2(0(0(2(2(0(0(1(1(2(2(1(x1))))))))))))))))))))))) -> 1(1(2(2(1(1(2(0(1(0(2(1(2(0(1(1(1(2(1(0(1(1(2(0(1(1(1(x1))))))))))))))))))))))))))) 0(1(2(2(1(1(2(0(2(1(2(0(1(2(1(2(2(2(2(0(2(0(0(x1))))))))))))))))))))))) -> 1(0(2(0(0(1(2(2(2(1(1(1(0(1(2(1(2(1(1(1(1(2(2(1(1(2(0(x1))))))))))))))))))))))))))) 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2(1(0(1(1(0(1(2(1(0(2(2(0(1(0(1(2(0(2(2(1(2(0(x1))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(0(1(1(2(2(2(0(2(1(0(0(0(2(2(2(2(2(0(0(1(1(x1))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(x1))))))))))))))))))))))))))) 2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(x1))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(x1))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(x1))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(x1))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(x1))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(x1))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(x1))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(x1))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(x1))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(x1))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(x1))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(x1))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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_2(x_1) -> 2(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(x1))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(x1))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(x1))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(x1))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(x1))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(x1))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(x1))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(x1))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(x1))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(x1))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(x1))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(x1))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(1(1(1(0(0(1(2(0(0(2(2(0(1(0(2(0(0(x1))))))))))))))))))))))) -> 0(1(1(1(0(1(2(0(0(2(2(2(1(2(2(2(2(2(0(1(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(2(0(1(0(2(1(0(0(0(1(1(2(2(2(0(2(2(x1))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(0(0(1(1(2(0(0(2(1(0(2(1(0(1(1(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(2(1(2(2(2(2(1(2(2(1(1(2(1(2(0(2(1(0(1(1(1(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(1(2(1(0(2(0(1(0(0(2(0(0(2(1(1(0(0(1(x1))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(0(0(1(0(2(1(2(2(0(1(0(2(2(1(0(1(2(1(x1))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(1(0(0(1(0(2(1(2(2(0(1(1(0(2(0(0(1(0(x1))))))))))))))))))))))) -> 0(1(1(0(1(1(1(1(0(2(1(2(0(1(1(2(0(1(1(1(1(1(2(2(1(1(0(x1))))))))))))))))))))))))))) 0(1(0(2(1(0(2(2(0(0(2(2(2(0(2(1(0(2(2(0(2(1(2(x1))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(1(0(2(1(1(2(0(1(0(2(1(2(0(2(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(1(1(0(0(2(0(2(2(1(1(1(1(1(1(2(2(0(1(2(0(1(0(x1))))))))))))))))))))))) -> 0(2(1(1(1(0(2(1(1(0(1(2(1(0(2(2(2(1(1(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))))))) 0(1(1(0(1(1(1(2(1(0(0(0(1(0(2(1(1(2(1(2(0(0(2(x1))))))))))))))))))))))) -> 1(0(1(1(1(1(1(0(2(2(1(1(1(0(2(1(2(1(1(0(0(1(2(1(0(0(1(x1))))))))))))))))))))))))))) 0(1(1(1(2(0(2(0(0(1(0(2(0(1(2(2(1(0(2(2(2(0(2(x1))))))))))))))))))))))) -> 1(1(1(1(2(0(1(1(1(1(1(1(0(0(1(0(0(2(2(2(0(0(2(1(0(2(0(x1))))))))))))))))))))))))))) 0(1(2(0(1(0(2(0(0(2(1(2(2(1(0(2(0(1(1(1(1(2(0(x1))))))))))))))))))))))) -> 1(0(1(0(1(1(1(0(1(1(1(2(2(1(1(2(2(1(2(1(1(2(0(2(2(2(2(x1))))))))))))))))))))))))))) 0(1(2(0(1(2(1(0(2(1(2(0(2(2(2(1(1(2(0(1(2(0(1(x1))))))))))))))))))))))) -> 2(1(0(0(0(1(0(2(2(1(1(2(2(2(1(1(2(2(1(1(2(0(1(1(0(2(1(x1))))))))))))))))))))))))))) 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2(0(2(0(0(1(1(1(2(0(2(2(2(0(0(1(2(2(0(0(1(0(1(x1))))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(1(1(1(1(0(1(2(2(2(1(2(0(1(2(0(1(1(1(x1))))))))))))))))))))))))))) 2(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(x1))))))))))))))))))))))) -> 2(2(2(1(0(1(1(0(2(2(0(0(1(1(1(1(1(1(0(1(1(1(2(0(2(2(0(x1))))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(1(2(2(0(2(0(1(2(1(0(0(1(0(2(1(x1))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(2(2(0(1(2(1(0(1(0(1(2(2(1(1(0(2(1(0(1(x1))))))))))))))))))))))))))) 2(0(2(1(0(1(2(2(1(2(2(0(2(0(2(0(2(2(1(2(0(2(2(x1))))))))))))))))))))))) -> 0(1(0(2(2(0(0(0(1(1(2(0(1(1(0(2(0(1(1(1(1(1(0(1(0(2(2(x1))))))))))))))))))))))))))) 2(0(2(1(1(0(2(1(0(2(1(2(2(0(0(1(0(1(0(2(0(2(0(x1))))))))))))))))))))))) -> 1(1(1(0(1(2(0(0(1(1(2(1(2(2(1(1(1(1(2(1(2(1(2(1(1(2(1(x1))))))))))))))))))))))))))) 2(1(0(1(0(2(2(2(1(2(2(0(1(2(1(1(1(1(0(0(2(0(2(x1))))))))))))))))))))))) -> 2(1(2(1(2(1(1(1(2(2(1(2(1(1(1(0(1(1(1(2(1(0(0(1(1(1(1(x1))))))))))))))))))))))))))) 2(1(0(1(1(0(1(2(1(0(2(2(0(1(0(1(2(0(2(2(1(2(0(x1))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(0(1(1(2(2(2(0(2(1(0(0(0(2(2(2(2(2(0(0(1(1(x1))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(x1))))))))))))))))))))))))))) 2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(x1))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(x1))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(x1))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(x1))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(x1))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(x1))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(x1))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(x1))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(x1))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(x1))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(x1))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(x1))))))))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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_2(x_1) -> 2(encArg(x_1)) Types: 0 :: 1:0:2:encArg:encode_0:encode_1:encode_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 1 :: 1:0:2:encArg:encode_0:encode_1:encode_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 2 :: 1:0:2:encArg:encode_0:encode_1:encode_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 encArg :: cons_0:cons_1:cons_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 cons_0 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 cons_1 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 cons_2 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 encode_0 :: cons_0:cons_1:cons_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 encode_1 :: cons_0:cons_1:cons_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 encode_2 :: cons_0:cons_1:cons_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 hole_1:0:2:encArg:encode_0:encode_1:encode_21_3 :: 1:0:2:encArg:encode_0:encode_1:encode_2 hole_cons_0:cons_1:cons_22_3 :: cons_0:cons_1:cons_2 gen_cons_0:cons_1:cons_23_3 :: Nat -> cons_0:cons_1:cons_2 ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: 0, 2, 1, encArg They will be analysed ascendingly in the following order: 0 = 2 0 = 1 0 < encArg 2 = 1 2 < encArg 1 < encArg ---------------------------------------- (12) Obligation: Innermost TRS: Rules: 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(x1))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(x1))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(x1))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(x1))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(x1))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(x1))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(x1))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(x1))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(x1))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(x1))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(x1))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(x1))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(1(1(1(0(0(1(2(0(0(2(2(0(1(0(2(0(0(x1))))))))))))))))))))))) -> 0(1(1(1(0(1(2(0(0(2(2(2(1(2(2(2(2(2(0(1(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(2(0(1(0(2(1(0(0(0(1(1(2(2(2(0(2(2(x1))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(0(0(1(1(2(0(0(2(1(0(2(1(0(1(1(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(2(1(2(2(2(2(1(2(2(1(1(2(1(2(0(2(1(0(1(1(1(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(1(2(1(0(2(0(1(0(0(2(0(0(2(1(1(0(0(1(x1))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(0(0(1(0(2(1(2(2(0(1(0(2(2(1(0(1(2(1(x1))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(1(0(0(1(0(2(1(2(2(0(1(1(0(2(0(0(1(0(x1))))))))))))))))))))))) -> 0(1(1(0(1(1(1(1(0(2(1(2(0(1(1(2(0(1(1(1(1(1(2(2(1(1(0(x1))))))))))))))))))))))))))) 0(1(0(2(1(0(2(2(0(0(2(2(2(0(2(1(0(2(2(0(2(1(2(x1))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(1(0(2(1(1(2(0(1(0(2(1(2(0(2(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(1(1(0(0(2(0(2(2(1(1(1(1(1(1(2(2(0(1(2(0(1(0(x1))))))))))))))))))))))) -> 0(2(1(1(1(0(2(1(1(0(1(2(1(0(2(2(2(1(1(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))))))) 0(1(1(0(1(1(1(2(1(0(0(0(1(0(2(1(1(2(1(2(0(0(2(x1))))))))))))))))))))))) -> 1(0(1(1(1(1(1(0(2(2(1(1(1(0(2(1(2(1(1(0(0(1(2(1(0(0(1(x1))))))))))))))))))))))))))) 0(1(1(1(2(0(2(0(0(1(0(2(0(1(2(2(1(0(2(2(2(0(2(x1))))))))))))))))))))))) -> 1(1(1(1(2(0(1(1(1(1(1(1(0(0(1(0(0(2(2(2(0(0(2(1(0(2(0(x1))))))))))))))))))))))))))) 0(1(2(0(1(0(2(0(0(2(1(2(2(1(0(2(0(1(1(1(1(2(0(x1))))))))))))))))))))))) -> 1(0(1(0(1(1(1(0(1(1(1(2(2(1(1(2(2(1(2(1(1(2(0(2(2(2(2(x1))))))))))))))))))))))))))) 0(1(2(0(1(2(1(0(2(1(2(0(2(2(2(1(1(2(0(1(2(0(1(x1))))))))))))))))))))))) -> 2(1(0(0(0(1(0(2(2(1(1(2(2(2(1(1(2(2(1(1(2(0(1(1(0(2(1(x1))))))))))))))))))))))))))) 0(1(2(0(2(2(1(2(1(1(0(2(0(1(2(2(2(0(2(0(1(2(0(x1))))))))))))))))))))))) -> 0(2(1(2(1(2(2(1(1(0(0(2(2(1(1(1(1(0(2(2(1(1(2(0(2(2(2(x1))))))))))))))))))))))))))) 0(1(2(1(0(1(0(1(2(2(1(2(1(0(2(2(1(0(1(0(1(0(2(x1))))))))))))))))))))))) -> 0(1(1(1(2(2(2(0(1(1(2(1(1(1(1(0(1(2(2(1(2(1(1(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(2(1(1(2(1(2(0(1(1(0(0(2(0(1(1(0(0(2(0(0(1(x1))))))))))))))))))))))) -> 0(1(1(0(2(2(2(0(2(1(1(0(1(0(2(2(0(1(1(0(0(2(1(1(1(2(1(x1))))))))))))))))))))))))))) 0(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(x1))))))))))))))))))))))) -> 1(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(x1))))))))))))))))))))))))))) 0(1(2(2(1(0(2(2(1(1(1(2(0(0(2(2(0(0(1(1(2(2(1(x1))))))))))))))))))))))) -> 1(1(2(2(1(1(2(0(1(0(2(1(2(0(1(1(1(2(1(0(1(1(2(0(1(1(1(x1))))))))))))))))))))))))))) 0(1(2(2(1(1(2(0(2(1(2(0(1(2(1(2(2(2(2(0(2(0(0(x1))))))))))))))))))))))) -> 1(0(2(0(0(1(2(2(2(1(1(1(0(1(2(1(2(1(1(1(1(2(2(1(1(2(0(x1))))))))))))))))))))))))))) 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0(2(1(2(0(2(2(2(2(2(2(2(0(1(0(1(0(2(1(1(0(0(0(x1))))))))))))))))))))))) -> 2(0(2(2(1(1(1(0(0(1(1(1(0(1(1(2(1(1(0(1(1(1(1(2(2(2(2(x1))))))))))))))))))))))))))) 0(2(2(2(1(2(0(1(1(2(1(2(0(0(2(1(0(1(2(2(2(0(1(x1))))))))))))))))))))))) -> 0(2(2(2(0(2(2(0(0(1(1(1(0(1(0(2(1(1(0(2(0(1(2(1(0(2(1(x1))))))))))))))))))))))))))) 1(0(0(0(1(1(0(2(0(1(1(2(1(1(2(2(1(2(1(0(0(0(2(x1))))))))))))))))))))))) -> 1(1(0(2(1(1(0(1(0(1(1(1(0(0(2(1(0(2(1(1(0(2(1(0(2(2(2(x1))))))))))))))))))))))))))) 1(0(0(1(1(2(0(1(1(2(2(2(0(1(0(2(0(2(0(1(1(2(1(x1))))))))))))))))))))))) -> 1(1(1(1(1(1(0(0(1(1(0(2(1(2(2(1(2(2(0(2(1(1(2(2(0(0(1(x1))))))))))))))))))))))))))) 1(0(1(1(2(2(2(1(2(2(1(0(2(2(1(0(1(2(2(2(1(0(0(x1))))))))))))))))))))))) -> 1(2(1(1(0(2(2(1(1(1(1(1(1(1(2(2(2(1(0(0(1(1(1(1(1(1(2(x1))))))))))))))))))))))))))) 1(0(1(2(0(2(0(0(2(1(0(2(0(1(2(1(0(2(0(2(0(0(1(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(2(1(1(2(2(0(2(1(0(0(1(1(1(2(0(0(1(2(1(2(1(x1))))))))))))))))))))))))))) 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2(1(0(1(1(0(1(2(1(0(2(2(0(1(0(1(2(0(2(2(1(2(0(x1))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(0(1(1(2(2(2(0(2(1(0(0(0(2(2(2(2(2(0(0(1(1(x1))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(x1))))))))))))))))))))))))))) 2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(x1))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(x1))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(x1))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(x1))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(x1))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(x1))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(x1))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(x1))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(x1))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(x1))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(x1))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(x1))))))))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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_2(x_1) -> 2(encArg(x_1)) Types: 0 :: 1:0:2:encArg:encode_0:encode_1:encode_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 1 :: 1:0:2:encArg:encode_0:encode_1:encode_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 2 :: 1:0:2:encArg:encode_0:encode_1:encode_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 encArg :: cons_0:cons_1:cons_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 cons_0 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 cons_1 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 cons_2 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 encode_0 :: cons_0:cons_1:cons_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 encode_1 :: cons_0:cons_1:cons_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 encode_2 :: cons_0:cons_1:cons_2 -> 1:0:2:encArg:encode_0:encode_1:encode_2 hole_1:0:2:encArg:encode_0:encode_1:encode_21_3 :: 1:0:2:encArg:encode_0:encode_1:encode_2 hole_cons_0:cons_1:cons_22_3 :: cons_0:cons_1:cons_2 gen_cons_0:cons_1:cons_23_3 :: Nat -> cons_0:cons_1:cons_2 Generator Equations: gen_cons_0:cons_1:cons_23_3(0) <=> hole_cons_0:cons_1:cons_22_3 gen_cons_0:cons_1:cons_23_3(+(x, 1)) <=> cons_0(gen_cons_0:cons_1:cons_23_3(x)) The following defined symbols remain to be analysed: 2, 0, 1, encArg They will be analysed ascendingly in the following order: 0 = 2 0 = 1 0 < encArg 2 = 1 2 < encArg 1 < encArg ---------------------------------------- (13) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (14) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(x1))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(x1))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(x1))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(x1))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(x1))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(x1))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(x1))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(x1))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(x1))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(x1))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(x1))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(x1))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(x1))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(x1))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(1(1(1(0(0(1(2(0(0(2(2(0(1(0(2(0(0(x1))))))))))))))))))))))) -> 0(1(1(1(0(1(2(0(0(2(2(2(1(2(2(2(2(2(0(1(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) 0(1(0(1(1(2(2(0(1(0(2(1(0(0(0(1(1(2(2(2(0(2(2(x1))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(0(0(1(1(2(0(0(2(1(0(2(1(0(1(1(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(1(2(1(2(2(2(2(1(2(2(1(1(2(1(2(0(2(1(0(1(1(1(1(2(x1))))))))))))))))))))))))))) 0(1(0(1(2(1(2(1(0(2(0(1(0(0(2(0(0(2(1(1(0(0(1(x1))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(0(0(1(0(2(1(2(2(0(1(0(2(2(1(0(1(2(1(x1))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(x1))))))))))))))))))))))))))) 0(1(0(2(0(1(0(0(1(0(2(1(2(2(0(1(1(0(2(0(0(1(0(x1))))))))))))))))))))))) -> 0(1(1(0(1(1(1(1(0(2(1(2(0(1(1(2(0(1(1(1(1(1(2(2(1(1(0(x1))))))))))))))))))))))))))) 0(1(0(2(1(0(2(2(0(0(2(2(2(0(2(1(0(2(2(0(2(1(2(x1))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(1(0(2(1(1(2(0(1(0(2(1(2(0(2(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(1(1(0(0(2(0(2(2(1(1(1(1(1(1(2(2(0(1(2(0(1(0(x1))))))))))))))))))))))) -> 0(2(1(1(1(0(2(1(1(0(1(2(1(0(2(2(2(1(1(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))))))) 0(1(1(0(1(1(1(2(1(0(0(0(1(0(2(1(1(2(1(2(0(0(2(x1))))))))))))))))))))))) -> 1(0(1(1(1(1(1(0(2(2(1(1(1(0(2(1(2(1(1(0(0(1(2(1(0(0(1(x1))))))))))))))))))))))))))) 0(1(1(1(2(0(2(0(0(1(0(2(0(1(2(2(1(0(2(2(2(0(2(x1))))))))))))))))))))))) -> 1(1(1(1(2(0(1(1(1(1(1(1(0(0(1(0(0(2(2(2(0(0(2(1(0(2(0(x1))))))))))))))))))))))))))) 0(1(2(0(1(0(2(0(0(2(1(2(2(1(0(2(0(1(1(1(1(2(0(x1))))))))))))))))))))))) -> 1(0(1(0(1(1(1(0(1(1(1(2(2(1(1(2(2(1(2(1(1(2(0(2(2(2(2(x1))))))))))))))))))))))))))) 0(1(2(0(1(2(1(0(2(1(2(0(2(2(2(1(1(2(0(1(2(0(1(x1))))))))))))))))))))))) -> 2(1(0(0(0(1(0(2(2(1(1(2(2(2(1(1(2(2(1(1(2(0(1(1(0(2(1(x1))))))))))))))))))))))))))) 0(1(2(0(2(2(1(2(1(1(0(2(0(1(2(2(2(0(2(0(1(2(0(x1))))))))))))))))))))))) -> 0(2(1(2(1(2(2(1(1(0(0(2(2(1(1(1(1(0(2(2(1(1(2(0(2(2(2(x1))))))))))))))))))))))))))) 0(1(2(1(0(1(0(1(2(2(1(2(1(0(2(2(1(0(1(0(1(0(2(x1))))))))))))))))))))))) -> 0(1(1(1(2(2(2(0(1(1(2(1(1(1(1(0(1(2(2(1(2(1(1(1(0(0(0(x1))))))))))))))))))))))))))) 0(1(2(1(1(2(1(2(0(1(1(0(0(2(0(1(1(0(0(2(0(0(1(x1))))))))))))))))))))))) -> 0(1(1(0(2(2(2(0(2(1(1(0(1(0(2(2(0(1(1(0(0(2(1(1(1(2(1(x1))))))))))))))))))))))))))) 0(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(x1))))))))))))))))))))))) -> 1(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(x1))))))))))))))))))))))))))) 0(1(2(2(1(0(2(2(1(1(1(2(0(0(2(2(0(0(1(1(2(2(1(x1))))))))))))))))))))))) -> 1(1(2(2(1(1(2(0(1(0(2(1(2(0(1(1(1(2(1(0(1(1(2(0(1(1(1(x1))))))))))))))))))))))))))) 0(1(2(2(1(1(2(0(2(1(2(0(1(2(1(2(2(2(2(0(2(0(0(x1))))))))))))))))))))))) -> 1(0(2(0(0(1(2(2(2(1(1(1(0(1(2(1(2(1(1(1(1(2(2(1(1(2(0(x1))))))))))))))))))))))))))) 0(1(2(2(2(0(0(0(0(1(0(0(2(2(0(2(0(2(2(0(1(1(0(x1))))))))))))))))))))))) -> 0(0(2(1(1(1(0(1(2(2(0(2(0(0(0(1(0(2(2(2(1(0(1(2(1(1(0(x1))))))))))))))))))))))))))) 0(2(0(1(0(0(2(1(2(1(1(2(1(2(0(1(1(0(1(0(2(0(1(x1))))))))))))))))))))))) -> 1(2(2(1(1(2(1(1(1(1(0(0(0(1(1(0(0(0(2(1(1(0(2(2(2(0(1(x1))))))))))))))))))))))))))) 0(2(0(2(0(2(0(2(1(1(0(1(2(2(1(0(1(0(0(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(1(1(2(0(2(2(2(1(0(2(0(2(2(2(2(1(0(1(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) 0(2(0(2(1(0(0(2(2(2(2(0(2(1(0(1(2(0(2(1(0(0(0(x1))))))))))))))))))))))) -> 0(2(0(2(1(1(0(1(1(1(2(1(2(0(1(0(1(2(1(1(2(1(1(1(2(2(2(x1))))))))))))))))))))))))))) 0(2(1(0(1(0(0(1(1(0(2(0(0(0(1(0(1(1(0(1(0(2(1(x1))))))))))))))))))))))) -> 1(1(0(1(1(1(1(0(2(2(2(2(2(0(1(1(2(1(2(2(1(2(0(0(0(1(1(x1))))))))))))))))))))))))))) 0(2(1(2(0(1(0(0(1(0(0(2(2(2(2(2(1(0(2(0(2(2(1(x1))))))))))))))))))))))) -> 1(2(0(1(0(0(2(1(1(2(1(0(0(1(1(1(1(2(1(0(2(0(0(0(1(1(1(x1))))))))))))))))))))))))))) 0(2(1(2(0(2(2(2(2(2(2(2(0(1(0(1(0(2(1(1(0(0(0(x1))))))))))))))))))))))) -> 2(0(2(2(1(1(1(0(0(1(1(1(0(1(1(2(1(1(0(1(1(1(1(2(2(2(2(x1))))))))))))))))))))))))))) 0(2(2(2(1(2(0(1(1(2(1(2(0(0(2(1(0(1(2(2(2(0(1(x1))))))))))))))))))))))) -> 0(2(2(2(0(2(2(0(0(1(1(1(0(1(0(2(1(1(0(2(0(1(2(1(0(2(1(x1))))))))))))))))))))))))))) 1(0(0(0(1(1(0(2(0(1(1(2(1(1(2(2(1(2(1(0(0(0(2(x1))))))))))))))))))))))) -> 1(1(0(2(1(1(0(1(0(1(1(1(0(0(2(1(0(2(1(1(0(2(1(0(2(2(2(x1))))))))))))))))))))))))))) 1(0(0(1(1(2(0(1(1(2(2(2(0(1(0(2(0(2(0(1(1(2(1(x1))))))))))))))))))))))) -> 1(1(1(1(1(1(0(0(1(1(0(2(1(2(2(1(2(2(0(2(1(1(2(2(0(0(1(x1))))))))))))))))))))))))))) 1(0(1(1(2(2(2(1(2(2(1(0(2(2(1(0(1(2(2(2(1(0(0(x1))))))))))))))))))))))) -> 1(2(1(1(0(2(2(1(1(1(1(1(1(1(2(2(2(1(0(0(1(1(1(1(1(1(2(x1))))))))))))))))))))))))))) 1(0(1(2(0(2(0(0(2(1(0(2(0(1(2(1(0(2(0(2(0(0(1(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(2(1(1(2(2(0(2(1(0(0(1(1(1(2(0(0(1(2(1(2(1(x1))))))))))))))))))))))))))) 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2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(x1))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(x1))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(x1))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(x1))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(x1))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(x1))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(x1))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(x1))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(x1))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(x1))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(x1))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(x1))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(x1))))))))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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_2(x_1) -> 2(encArg(x_1)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (15) NonCtorToCtorProof (UPPER BOUND(ID)) transformed non-ctor to ctor-system ---------------------------------------- (16) 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(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_1(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) 2(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_0(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 2(1(2(1(2(1(1(1(2(2(1(2(1(1(1(0(1(1(1(2(1(0(0(1(1(1(1(x1))))))))))))))))))))))))))) 0(c_1(c_1(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1(0(1(1(1(1(1(0(2(2(1(1(1(0(2(1(2(1(1(0(0(1(2(1(0(0(1(x1))))))))))))))))))))))))))) 1(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 1(1(0(1(1(1(1(0(2(1(0(0(2(1(1(2(0(2(1(2(1(2(0(1(0(2(1(x1))))))))))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 1(1(1(2(2(1(1(1(2(1(2(0(2(2(1(1(1(1(0(2(0(2(1(1(0(2(1(x1))))))))))))))))))))))))))) 1(c_2(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(2(1(1(1(1(1(1(2(0(0(2(1(0(0(1(2(2(2(1(x1))))))))))))))))))))))))))) 2(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_0(c_0(c_1(c_1(x1))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 1(0(1(0(1(1(1(0(1(1(1(2(2(1(1(2(2(1(2(1(1(2(0(2(2(2(2(x1))))))))))))))))))))))))))) 0(c_1(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_2(c_0(c_1(c_1(c_0(x1))))))))))))))))))))))) -> 0(0(2(1(1(1(0(1(2(2(0(2(0(0(0(1(0(2(2(2(1(0(1(2(1(1(0(x1))))))))))))))))))))))))))) 0(c_0(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(x1))))))))))))))))))))))))))) 0(c_1(c_0(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(x1))))))))))))))))))))))))))) 0(c_1(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))) -> 0(1(1(1(2(2(2(0(1(1(2(1(1(1(1(0(1(2(2(1(2(1(1(1(0(0(0(x1))))))))))))))))))))))))))) 2(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(x1))))))))))))))))))))))))))) 1(c_2(c_0(c_2(c_1(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1(2(2(1(1(1(0(1(2(1(1(2(1(0(0(2(1(0(2(1(1(1(0(1(0(2(0(x1))))))))))))))))))))))))))) 1(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(x1))))))))))))))))))))))) -> 1(1(0(0(0(1(0(2(1(0(2(2(2(1(0(0(2(1(1(0(2(2(2(2(1(1(0(x1))))))))))))))))))))))))))) 0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1(1(2(2(1(1(2(0(1(0(2(1(2(0(1(1(1(2(1(0(1(1(2(0(1(1(1(x1))))))))))))))))))))))))))) 1(c_2(c_0(c_0(c_1(c_1(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_1(c_1(c_1(c_1(c_1(x1))))))))))))))))))))))) -> 1(1(0(2(1(1(0(1(1(1(1(2(1(2(1(1(0(0(1(1(1(0(2(2(1(2(1(x1))))))))))))))))))))))))))) 0(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 0(2(0(2(1(1(0(1(1(1(2(1(2(0(1(0(1(2(1(1(2(1(1(1(2(2(2(x1))))))))))))))))))))))))))) 2(c_2(c_1(c_0(c_2(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(x1))))))))))))))))))))))))))) 1(c_0(c_2(c_1(c_0(c_2(c_0(c_1(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_2(c_1(c_0(c_2(x1))))))))))))))))))))))) -> 1(0(1(1(1(1(0(0(0(1(1(1(0(0(2(0(0(2(0(0(2(1(1(1(1(1(1(x1))))))))))))))))))))))))))) 1(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 1(2(1(0(0(1(1(0(1(1(1(1(2(1(1(2(1(1(1(0(1(1(0(2(2(2(0(x1))))))))))))))))))))))))))) 2(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(2(2(0(1(2(1(0(1(0(1(2(2(1(1(0(2(1(0(1(x1))))))))))))))))))))))))))) 1(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(x1))))))))))))))))))))))) -> 1(2(2(1(0(1(2(1(1(1(2(1(1(1(1(1(1(0(1(1(1(1(0(2(0(1(1(x1))))))))))))))))))))))))))) 2(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(x1))))))))))))))))))))))))))) 0(c_1(c_0(c_0(c_1(c_1(c_1(c_1(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) 2(c_1(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_1(x1))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(x1))))))))))))))))))))))))))) 0(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(x1))))))))))))))))))))))))))) 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1(1(0(1(1(1(0(0(0(1(2(2(2(1(1(1(1(0(2(2(2(2(2(0(1(2(2(x1))))))))))))))))))))))))))) 1(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 1(0(1(2(1(1(2(1(0(0(1(1(0(0(2(2(0(0(2(2(0(2(1(1(1(2(1(x1))))))))))))))))))))))))))) 1(c_1(c_2(c_2(c_2(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_2(x1))))))))))))))))))))))) -> 1(2(1(0(1(1(0(2(2(1(1(2(1(1(0(2(2(1(2(2(2(2(2(0(1(1(1(x1))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(1(0(2(1(1(2(0(1(0(2(1(2(0(2(1(0(1(1(1(x1))))))))))))))))))))))))))) 2(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_2(c_0(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 0(1(0(2(2(0(0(0(1(1(2(0(1(1(0(2(0(1(1(1(1(1(0(1(0(2(2(x1))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 0(2(1(2(1(2(2(1(1(0(0(2(2(1(1(1(1(0(2(2(1(1(2(0(2(2(2(x1))))))))))))))))))))))))))) 1(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_2(c_0(c_0(x1))))))))))))))))))))))) -> 1(1(1(0(2(2(0(0(2(2(2(1(2(1(1(1(1(0(2(2(2(0(1(0(2(0(2(x1))))))))))))))))))))))))))) 2(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2(1(1(0(1(1(0(2(1(1(1(0(1(0(0(2(1(1(1(0(2(0(0(1(1(1(1(x1))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(x1))))))))))))))))))))))))))) 2(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 2(2(2(1(0(1(1(0(2(2(0(0(1(1(1(1(1(1(0(1(1(1(2(0(2(2(0(x1))))))))))))))))))))))))))) 0(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(x1))))))))))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_0(c_1(c_1(c_1(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1(1(0(0(1(1(1(0(0(1(0(2(1(1(1(1(1(2(1(2(1(1(1(1(1(1(0(x1))))))))))))))))))))))))))) 0(c_2(c_1(c_2(c_0(c_1(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1(2(0(1(0(0(2(1(1(2(1(0(0(1(1(1(1(2(1(0(2(0(0(0(1(1(1(x1))))))))))))))))))))))))))) 1(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(0(1(0(0(0(1(1(1(2(0(2(2(2(2(1(1(1(1(2(x1))))))))))))))))))))))))))) 1(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_2(c_2(c_1(c_2(c_2(x1))))))))))))))))))))))) -> 1(1(0(1(2(0(2(0(1(0(0(2(2(2(2(0(2(2(1(2(1(1(1(1(1(2(2(x1))))))))))))))))))))))))))) 1(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 1(0(1(2(1(2(1(1(0(2(2(2(1(1(1(1(1(2(1(1(1(0(0(0(0(2(1(x1))))))))))))))))))))))))))) 0(c_2(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 0(2(2(2(0(2(2(0(0(1(1(1(0(1(0(2(1(1(0(2(0(1(2(1(0(2(1(x1))))))))))))))))))))))))))) 2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(x1))))))))))))))))))))))))))) 0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(x1))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(x1))))))))))))))))))))))))))) 1(c_1(c_2(c_1(c_0(c_1(c_1(c_0(c_0(c_1(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1(1(1(0(0(0(2(0(2(1(2(2(2(2(2(2(1(1(1(1(2(1(0(0(0(0(2(x1))))))))))))))))))))))))))) 2(c_1(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_1(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) 0(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 1(1(1(1(2(0(1(1(1(1(1(1(0(0(1(0(0(2(2(2(0(0(2(1(0(2(0(x1))))))))))))))))))))))))))) 1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1(1(1(1(1(1(0(0(1(1(0(2(1(2(2(1(2(2(0(2(1(1(2(2(0(0(1(x1))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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_2(x_1) -> 2(encArg(x_1)) 0(x0) -> c_0(x0) 1(x0) -> c_1(x0) 2(x0) -> c_2(x0) Rewrite Strategy: INNERMOST ---------------------------------------- (17) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (18) 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(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_1(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(x1))))))))))))))))))))))))))) [1] 2(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_0(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 2(1(2(1(2(1(1(1(2(2(1(2(1(1(1(0(1(1(1(2(1(0(0(1(1(1(1(x1))))))))))))))))))))))))))) [1] 0(c_1(c_1(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1(0(1(1(1(1(1(0(2(2(1(1(1(0(2(1(2(1(1(0(0(1(2(1(0(0(1(x1))))))))))))))))))))))))))) [1] 1(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 1(1(0(1(1(1(1(0(2(1(0(0(2(1(1(2(0(2(1(2(1(2(0(1(0(2(1(x1))))))))))))))))))))))))))) [1] 2(c_0(c_0(c_2(c_1(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 1(1(1(2(2(1(1(1(2(1(2(0(2(2(1(1(1(1(0(2(0(2(1(1(0(2(1(x1))))))))))))))))))))))))))) [1] 1(c_2(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(2(1(1(1(1(1(1(2(0(0(2(1(0(0(1(2(2(2(1(x1))))))))))))))))))))))))))) [1] 2(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_0(c_0(c_1(c_1(x1))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(x1))))))))))))))))))))))))))) [1] 0(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 1(0(1(0(1(1(1(0(1(1(1(2(2(1(1(2(2(1(2(1(1(2(0(2(2(2(2(x1))))))))))))))))))))))))))) [1] 0(c_1(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_2(c_0(c_1(c_1(c_0(x1))))))))))))))))))))))) -> 0(0(2(1(1(1(0(1(2(2(0(2(0(0(0(1(0(2(2(2(1(0(1(2(1(1(0(x1))))))))))))))))))))))))))) [1] 0(c_0(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(x1))))))))))))))))))))))))))) [1] 0(c_1(c_0(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(x1))))))))))))))))))))))))))) [1] 0(c_1(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))) -> 0(1(1(1(2(2(2(0(1(1(2(1(1(1(1(0(1(2(2(1(2(1(1(1(0(0(0(x1))))))))))))))))))))))))))) [1] 2(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(x1))))))))))))))))))))))))))) [1] 1(c_2(c_0(c_2(c_1(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1(2(2(1(1(1(0(1(2(1(1(2(1(0(0(2(1(0(2(1(1(1(0(1(0(2(0(x1))))))))))))))))))))))))))) [1] 1(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(x1))))))))))))))))))))))) -> 1(1(0(0(0(1(0(2(1(0(2(2(2(1(0(0(2(1(1(0(2(2(2(2(1(1(0(x1))))))))))))))))))))))))))) [1] 0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1(1(2(2(1(1(2(0(1(0(2(1(2(0(1(1(1(2(1(0(1(1(2(0(1(1(1(x1))))))))))))))))))))))))))) [1] 1(c_2(c_0(c_0(c_1(c_1(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_1(c_1(c_1(c_1(c_1(x1))))))))))))))))))))))) -> 1(1(0(2(1(1(0(1(1(1(1(2(1(2(1(1(0(0(1(1(1(0(2(2(1(2(1(x1))))))))))))))))))))))))))) [1] 0(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 0(2(0(2(1(1(0(1(1(1(2(1(2(0(1(0(1(2(1(1(2(1(1(1(2(2(2(x1))))))))))))))))))))))))))) [1] 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1(2(2(1(0(1(2(1(1(1(2(1(1(1(1(1(1(0(1(1(1(1(0(2(0(1(1(x1))))))))))))))))))))))))))) [1] 2(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(x1))))))))))))))))))))))))))) [1] 0(c_1(c_0(c_0(c_1(c_1(c_1(c_1(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) [1] 2(c_1(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_1(x1))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(x1))))))))))))))))))))))))))) [1] 0(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(x1))))))))))))))))))))))))))) [1] 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1(1(0(1(0(0(1(1(1(1(1(1(2(1(0(0(0(2(1(0(0(1(0(2(2(2(0(x1))))))))))))))))))))))))))) [1] 1(c_1(c_2(c_2(c_2(c_0(c_1(c_1(c_2(c_0(c_2(c_2(c_2(c_2(c_2(c_0(c_1(c_1(c_2(c_2(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1(2(0(1(0(2(1(1(2(2(2(1(1(1(2(2(1(1(1(2(1(1(1(2(1(1(1(x1))))))))))))))))))))))))))) [1] 0(c_0(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_2(x1))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(x1))))))))))))))))))))))))))) [1] 0(c_1(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_0(c_2(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 0(1(1(0(2(2(2(0(2(1(1(0(1(0(2(2(0(1(1(0(0(2(1(1(1(2(1(x1))))))))))))))))))))))))))) [1] 0(c_1(c_1(c_0(c_0(c_2(c_0(c_2(c_2(c_1(c_1(c_1(c_1(c_1(c_1(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_0(x1))))))))))))))))))))))) -> 0(2(1(1(1(0(2(1(1(0(1(2(1(0(2(2(2(1(1(0(1(1(0(1(1(1(0(x1))))))))))))))))))))))))))) [1] 0(c_0(c_0(c_0(c_1(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(x1))))))))))))))))))))))))))) [1] 1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_1(c_1(c_1(c_1(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 1(1(1(1(0(1(1(1(0(0(1(0(0(0(2(1(1(1(1(1(1(1(0(1(2(0(1(x1))))))))))))))))))))))))))) [1] 1(c_2(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1(0(2(1(0(1(0(0(1(1(1(2(0(2(2(1(1(1(1(1(2(2(1(2(1(0(1(x1))))))))))))))))))))))))))) [1] 2(c_0(c_2(c_1(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_0(c_2(c_0(x1))))))))))))))))))))))) -> 1(1(1(0(1(2(0(0(1(1(2(1(2(2(1(1(1(1(2(1(2(1(2(1(1(2(1(x1))))))))))))))))))))))))))) [1] 0(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_2(c_1(c_2(c_2(c_1(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(x1))))))))))))))))))))))))))) [1] 1(c_1(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1(1(0(2(0(1(2(2(0(1(1(1(1(1(0(1(2(1(1(2(0(2(2(0(2(1(1(x1))))))))))))))))))))))))))) [1] 2(c_0(c_2(c_0(c_0(c_1(c_1(c_1(c_2(c_0(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_2(c_0(c_0(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(1(1(1(1(0(1(2(2(2(1(2(0(1(2(0(1(1(1(x1))))))))))))))))))))))))))) [1] 0(c_2(c_1(c_2(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 2(0(2(2(1(1(1(0(0(1(1(1(0(1(1(2(1(1(0(1(1(1(1(2(2(2(2(x1))))))))))))))))))))))))))) [1] 2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_2(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(x1))))))))))))))))))))))))))) [1] 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1(2(1(1(2(0(1(1(1(2(1(1(1(2(2(1(1(1(1(1(0(0(2(1(2(0(2(x1))))))))))))))))))))))))))) [1] 2(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_1(c_2(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(x1))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(x1))))))))))))))))))))))))))) [1] 0(c_1(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_0(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(x1))))))))))))))))))))))) -> 0(1(1(1(0(1(2(0(0(2(2(2(1(2(2(2(2(2(0(1(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) [1] 2(c_0(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_1(c_2(c_2(c_1(c_1(c_0(x1))))))))))))))))))))))) -> 2(0(0(0(0(1(1(2(0(1(2(2(1(0(2(0(2(2(2(0(1(0(1(1(1(1(0(x1))))))))))))))))))))))))))) [1] 1(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_2(c_1(c_0(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1(1(0(2(1(1(0(1(0(1(1(1(0(0(2(1(0(2(1(1(0(2(1(0(2(2(2(x1))))))))))))))))))))))))))) [1] 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1(1(1(1(2(0(2(2(2(1(0(2(0(2(2(2(2(1(0(1(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) [1] 1(c_2(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 1(2(1(1(0(1(1(2(1(2(0(2(1(1(1(0(1(1(1(0(1(0(1(0(2(1(1(x1))))))))))))))))))))))))))) [1] 1(c_1(c_0(c_0(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1(1(1(0(0(2(1(2(1(0(0(1(1(2(2(1(1(1(1(2(1(1(1(1(0(2(2(x1))))))))))))))))))))))))))) [1] 1(c_2(c_0(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1(1(1(0(1(2(1(1(2(1(1(1(0(0(0(2(0(1(2(1(0(0(1(1(1(1(0(x1))))))))))))))))))))))))))) [1] 1(c_0(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_0(c_2(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(2(1(1(2(2(0(2(1(0(0(1(1(1(2(0(0(1(2(1(2(1(x1))))))))))))))))))))))))))) [1] 0(c_2(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 1(2(2(1(1(2(1(1(1(1(0(0(0(1(1(0(0(0(2(1(1(0(2(2(2(0(1(x1))))))))))))))))))))))))))) [1] 2(c_1(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_2(c_2(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(x1))))))))))))))))))))))))))) [1] 0(c_2(c_1(c_0(c_1(c_0(c_0(c_1(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_0(c_1(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 1(1(0(1(1(1(1(0(2(2(2(2(2(0(1(1(2(1(2(2(1(2(0(0(0(1(1(x1))))))))))))))))))))))))))) [1] 1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_0(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1(2(1(2(1(1(1(0(1(1(0(1(1(1(0(2(2(0(2(1(0(2(1(0(2(2(2(x1))))))))))))))))))))))))))) [1] 2(c_1(c_1(c_1(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_1(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(x1))))))))))))))))))))))))))) [1] 2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(x1))))))))))))))))))))))))))) [1] 1(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1(1(1(0(1(2(2(1(2(0(1(1(2(1(1(0(1(2(2(0(1(1(1(0(1(0(2(x1))))))))))))))))))))))))))) [1] 0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_1(c_2(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(x1))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(x1))))))))))))))))))))))))))) [1] 0(c_0(c_2(c_2(c_1(c_2(c_1(c_0(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(x1))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(x1))))))))))))))))))))))))))) [1] 0(c_1(c_0(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(x1))))))))))))))))))))))))))) [1] 1(c_0(c_1(c_2(c_2(c_2(c_1(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_1(c_0(c_1(c_0(c_0(x1))))))))))))))))))))))) -> 1(1(0(0(2(0(2(2(1(0(1(1(0(1(1(1(0(2(2(1(1(0(1(1(1(1(1(x1))))))))))))))))))))))))))) [1] 1(c_2(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1(1(1(1(2(1(2(1(0(1(0(2(2(1(1(0(1(2(1(1(1(1(0(2(0(2(2(x1))))))))))))))))))))))))))) [1] 0(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 2(1(0(0(0(1(0(2(2(1(1(2(2(2(1(1(2(2(1(1(2(0(1(1(0(2(1(x1))))))))))))))))))))))))))) [1] 1(c_1(c_1(c_2(c_2(c_1(c_1(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1(1(0(1(1(1(0(0(0(1(2(2(2(1(1(1(1(0(2(2(2(2(2(0(1(2(2(x1))))))))))))))))))))))))))) [1] 1(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 1(0(1(2(1(1(2(1(0(0(1(1(0(0(2(2(0(0(2(2(0(2(1(1(1(2(1(x1))))))))))))))))))))))))))) [1] 1(c_1(c_2(c_2(c_2(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_2(x1))))))))))))))))))))))) -> 1(2(1(0(1(1(0(2(2(1(1(2(1(1(0(2(2(1(2(2(2(2(2(0(1(1(1(x1))))))))))))))))))))))))))) [1] 0(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(1(0(2(1(1(2(0(1(0(2(1(2(0(2(1(0(1(1(1(x1))))))))))))))))))))))))))) [1] 2(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_2(c_0(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 0(1(0(2(2(0(0(0(1(1(2(0(1(1(0(2(0(1(1(1(1(1(0(1(0(2(2(x1))))))))))))))))))))))))))) [1] 0(c_1(c_2(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 0(2(1(2(1(2(2(1(1(0(0(2(2(1(1(1(1(0(2(2(1(1(2(0(2(2(2(x1))))))))))))))))))))))))))) [1] 1(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_2(c_0(c_0(x1))))))))))))))))))))))) -> 1(1(1(0(2(2(0(0(2(2(2(1(2(1(1(1(1(0(2(2(2(0(1(0(2(0(2(x1))))))))))))))))))))))))))) [1] 2(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2(1(1(0(1(1(0(2(1(1(1(0(1(0(0(2(1(1(1(0(2(0(0(1(1(1(1(x1))))))))))))))))))))))))))) [1] 0(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(x1))))))))))))))))))))))))))) [1] 2(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 2(2(2(1(0(1(1(0(2(2(0(0(1(1(1(1(1(1(0(1(1(1(2(0(2(2(0(x1))))))))))))))))))))))))))) [1] 0(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(x1))))))))))))))))))))))))))) [1] 2(c_0(c_0(c_2(c_1(c_0(c_1(c_1(c_1(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1(1(0(0(1(1(1(0(0(1(0(2(1(1(1(1(1(2(1(2(1(1(1(1(1(1(0(x1))))))))))))))))))))))))))) [1] 0(c_2(c_1(c_2(c_0(c_1(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1(2(0(1(0(0(2(1(1(2(1(0(0(1(1(1(1(2(1(0(2(0(0(0(1(1(1(x1))))))))))))))))))))))))))) [1] 1(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(0(1(0(0(0(1(1(1(2(0(2(2(2(2(1(1(1(1(2(x1))))))))))))))))))))))))))) [1] 1(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_2(c_2(c_1(c_2(c_2(x1))))))))))))))))))))))) -> 1(1(0(1(2(0(2(0(1(0(0(2(2(2(2(0(2(2(1(2(1(1(1(1(1(2(2(x1))))))))))))))))))))))))))) [1] 1(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 1(0(1(2(1(2(1(1(0(2(2(2(1(1(1(1(1(2(1(1(1(0(0(0(0(2(1(x1))))))))))))))))))))))))))) [1] 0(c_2(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 0(2(2(2(0(2(2(0(0(1(1(1(0(1(0(2(1(1(0(2(0(1(2(1(0(2(1(x1))))))))))))))))))))))))))) [1] 2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(x1))))))))))))))))))))))))))) [1] 0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(x1))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(x1))))))))))))))))))))))))))) [1] 1(c_1(c_2(c_1(c_0(c_1(c_1(c_0(c_0(c_1(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1(1(1(0(0(0(2(0(2(1(2(2(2(2(2(2(1(1(1(1(2(1(0(0(0(0(2(x1))))))))))))))))))))))))))) [1] 2(c_1(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_1(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(x1))))))))))))))))))))))))))) [1] 0(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 1(1(1(1(2(0(1(1(1(1(1(1(0(0(1(0(0(2(2(2(0(0(2(1(0(2(0(x1))))))))))))))))))))))))))) [1] 1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1(1(1(1(1(1(0(0(1(1(0(2(1(2(2(1(2(2(0(2(1(1(2(2(0(0(1(x1))))))))))))))))))))))))))) [1] encArg(cons_0(x_1)) -> 0(encArg(x_1)) [0] encArg(cons_1(x_1)) -> 1(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_2(x_1) -> 2(encArg(x_1)) [0] 0(x0) -> c_0(x0) [0] 1(x0) -> c_1(x0) [0] 2(x0) -> c_2(x0) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (19) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) Renamed defined symbols to avoid conflicts with arithmetic symbols: 0 => 0' 1 => 1' 2 => 2' ---------------------------------------- (20) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0'(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_1(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 1'(0'(2'(2'(0'(0'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(0'(1'(2'(1'(0'(1'(1'(2'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_0(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 2'(1'(2'(1'(2'(1'(1'(1'(2'(2'(1'(2'(1'(1'(1'(0'(1'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(1'(2'(1'(1'(0'(0'(1'(2'(1'(0'(0'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(1'(1'(1'(0'(2'(1'(0'(0'(2'(1'(1'(2'(0'(2'(1'(2'(1'(2'(0'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_2(c_1(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 1'(1'(1'(2'(2'(1'(1'(1'(2'(1'(2'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(2'(0'(2'(1'(1'(1'(1'(1'(1'(2'(0'(0'(2'(1'(0'(0'(1'(2'(2'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_0(c_0(c_1(c_1(x1))))))))))))))))))))))) -> 2'(2'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(1'(1'(2'(0'(0'(1'(0'(2'(2'(1'(1'(2'(0'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 1'(0'(1'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(1'(1'(2'(2'(1'(2'(1'(1'(2'(0'(2'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_2(c_0(c_1(c_1(c_0(x1))))))))))))))))))))))) -> 0'(0'(2'(1'(1'(1'(0'(1'(2'(2'(0'(2'(0'(0'(0'(1'(0'(2'(2'(2'(1'(0'(1'(2'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 0'(2'(0'(1'(2'(2'(1'(1'(0'(0'(2'(2'(2'(1'(0'(1'(2'(0'(2'(1'(0'(2'(2'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1'(2'(2'(2'(2'(1'(1'(0'(1'(1'(0'(1'(2'(1'(0'(2'(2'(1'(1'(0'(1'(1'(1'(1'(0'(1'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(1'(2'(2'(2'(0'(1'(1'(2'(1'(1'(1'(1'(0'(1'(2'(2'(1'(2'(1'(1'(1'(0'(0'(0'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 2'(2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(1'(0'(1'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_1(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(2'(2'(1'(1'(1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(2'(1'(0'(2'(1'(1'(1'(0'(1'(0'(2'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(0'(0'(1'(0'(2'(1'(0'(2'(2'(2'(1'(0'(0'(2'(1'(1'(0'(2'(2'(2'(2'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(1'(1'(1'(2'(1'(0'(1'(1'(2'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_0(c_1(c_1(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_1(c_1(c_1(c_1(c_1(x1))))))))))))))))))))))) -> 1'(1'(0'(2'(1'(1'(0'(1'(1'(1'(1'(2'(1'(2'(1'(1'(0'(0'(1'(1'(1'(0'(2'(2'(1'(2'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 0'(2'(0'(2'(1'(1'(0'(1'(1'(1'(2'(1'(2'(0'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_1(c_0(c_2(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 2'(2'(0'(1'(1'(1'(2'(0'(2'(2'(0'(1'(1'(0'(0'(1'(1'(1'(0'(1'(1'(1'(0'(1'(2'(1'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_2(c_1(c_0(c_2(c_0(c_1(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_2(c_1(c_0(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(1'(1'(1'(0'(0'(0'(1'(1'(1'(0'(0'(2'(0'(0'(2'(0'(0'(2'(1'(1'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 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2'(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 2'(2'(0'(1'(0'(1'(1'(0'(2'(2'(1'(1'(1'(1'(2'(1'(2'(0'(1'(1'(1'(2'(1'(0'(0'(1'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(1'(2'(2'(1'(2'(0'(1'(1'(2'(1'(1'(0'(1'(2'(2'(0'(1'(1'(1'(0'(1'(0'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_1(c_2(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(x1))))))))))))))))))))))) -> 0'(0'(2'(1'(0'(1'(1'(1'(1'(2'(0'(1'(0'(0'(0'(1'(0'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_2(c_1(c_2(c_1(c_0(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(x1))))))))))))))))))))))) -> 0'(0'(0'(2'(0'(0'(2'(1'(1'(1'(0'(2'(2'(2'(2'(1'(0'(1'(1'(1'(2'(1'(0'(1'(0'(0'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(2'(2'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(2'(1'(1'(1'(0'(2'(0'(2'(1'(0'(2'(2'(0'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_2(c_2(c_2(c_1(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_1(c_0(c_1(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(0'(2'(0'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(2'(1'(1'(0'(1'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(2'(1'(2'(1'(0'(1'(0'(2'(2'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(2'(0'(2'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 2'(1'(0'(0'(0'(1'(0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(2'(2'(1'(1'(2'(0'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_1(c_2(c_2(c_1(c_1(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(1'(1'(0'(0'(0'(1'(2'(2'(2'(1'(1'(1'(1'(0'(2'(2'(2'(2'(2'(0'(1'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(1'(1'(0'(0'(2'(2'(0'(0'(2'(2'(0'(2'(1'(1'(1'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_2(c_2(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_2(x1))))))))))))))))))))))) -> 1'(2'(1'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(0'(2'(2'(1'(2'(2'(2'(2'(2'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 1'(2'(1'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(2'(1'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_2(c_0(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 0'(1'(0'(2'(2'(0'(0'(0'(1'(1'(2'(0'(1'(1'(0'(2'(0'(1'(1'(1'(1'(1'(0'(1'(0'(2'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 0'(2'(1'(2'(1'(2'(2'(1'(1'(0'(0'(2'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(2'(0'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_2(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(2'(2'(0'(0'(2'(2'(2'(1'(2'(1'(1'(1'(1'(0'(2'(2'(2'(0'(1'(0'(2'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(1'(0'(1'(1'(0'(2'(1'(1'(1'(0'(1'(0'(0'(2'(1'(1'(1'(0'(2'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 0'(1'(0'(2'(2'(2'(2'(1'(0'(0'(2'(1'(1'(2'(2'(1'(0'(2'(1'(0'(2'(1'(2'(2'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 2'(2'(2'(1'(0'(1'(1'(0'(2'(2'(0'(0'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(2'(0'(2'(2'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_2(c_1(c_0(c_1(c_1(c_1(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(0'(1'(1'(1'(0'(0'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(1'(1'(1'(1'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_1(c_2(c_0(c_1(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1'(2'(0'(1'(0'(0'(2'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(2'(1'(0'(2'(0'(0'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(2'(0'(0'(1'(0'(0'(0'(1'(1'(1'(2'(0'(2'(2'(2'(2'(1'(1'(1'(1'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_2(c_2(c_1(c_2(c_2(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(2'(0'(2'(0'(1'(0'(0'(2'(2'(2'(2'(0'(2'(2'(1'(2'(1'(1'(1'(1'(1'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(2'(1'(2'(1'(1'(0'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(0'(0'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 0'(2'(2'(2'(0'(2'(2'(0'(0'(1'(1'(1'(0'(1'(0'(2'(1'(1'(0'(2'(0'(1'(2'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(0'(2'(1'(2'(2'(1'(0'(2'(1'(0'(2'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(1'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(x1))))))))))))))))))))))) -> 0'(2'(0'(2'(2'(0'(2'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_1(c_0(c_1(c_1(c_0(c_0(c_1(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(0'(0'(2'(0'(2'(1'(2'(2'(2'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(0'(0'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_1(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 2'(2'(1'(2'(2'(2'(2'(1'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(2'(2'(2'(1'(0'(0'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(0'(2'(2'(2'(0'(0'(2'(1'(0'(2'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_0(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(2'(2'(1'(2'(2'(0'(2'(1'(1'(2'(2'(0'(0'(1'(x1))))))))))))))))))))))))))) [1] encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0] encArg(cons_1(x_1)) -> 1'(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_2(x_1) -> 2'(encArg(x_1)) [0] 0'(x0) -> c_0(x0) [0] 1'(x0) -> c_1(x0) [0] 2'(x0) -> c_2(x0) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (21) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (22) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: 0'(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_1(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 1'(0'(2'(2'(0'(0'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(0'(1'(2'(1'(0'(1'(1'(2'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_0(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 2'(1'(2'(1'(2'(1'(1'(1'(2'(2'(1'(2'(1'(1'(1'(0'(1'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(1'(2'(1'(1'(0'(0'(1'(2'(1'(0'(0'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(1'(1'(1'(0'(2'(1'(0'(0'(2'(1'(1'(2'(0'(2'(1'(2'(1'(2'(0'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_2(c_1(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 1'(1'(1'(2'(2'(1'(1'(1'(2'(1'(2'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(2'(0'(2'(1'(1'(1'(1'(1'(1'(2'(0'(0'(2'(1'(0'(0'(1'(2'(2'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_0(c_0(c_1(c_1(x1))))))))))))))))))))))) -> 2'(2'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(1'(1'(2'(0'(0'(1'(0'(2'(2'(1'(1'(2'(0'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 1'(0'(1'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(1'(1'(2'(2'(1'(2'(1'(1'(2'(0'(2'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 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1'(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 1'(2'(1'(0'(0'(1'(1'(0'(1'(1'(1'(1'(2'(1'(1'(2'(1'(1'(1'(0'(1'(1'(0'(2'(2'(2'(0'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(2'(2'(2'(2'(2'(1'(1'(2'(2'(0'(1'(2'(1'(0'(1'(0'(1'(2'(2'(1'(1'(0'(2'(1'(0'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(x1))))))))))))))))))))))) -> 1'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(0'(1'(0'(2'(2'(1'(0'(1'(0'(1'(2'(1'(2'(0'(2'(2'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_0(c_1(c_1(c_1(c_1(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(0'(2'(1'(1'(1'(1'(2'(1'(2'(1'(1'(2'(1'(1'(1'(2'(1'(1'(2'(2'(2'(1'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_1(x1))))))))))))))))))))))) -> 1'(2'(0'(1'(1'(1'(0'(1'(2'(0'(2'(2'(1'(1'(0'(2'(1'(1'(1'(1'(0'(0'(1'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(1'(1'(0'(2'(1'(1'(1'(0'(1'(1'(1'(0'(2'(1'(1'(1'(0'(0'(0'(2'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_1(c_2(c_0(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 1'(2'(1'(1'(1'(0'(2'(0'(2'(0'(0'(2'(1'(0'(2'(1'(1'(1'(1'(1'(0'(0'(0'(1'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 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2'(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_2(c_0(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 0'(1'(0'(2'(2'(0'(0'(0'(1'(1'(2'(0'(1'(1'(0'(2'(0'(1'(1'(1'(1'(1'(0'(1'(0'(2'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 0'(2'(1'(2'(1'(2'(2'(1'(1'(0'(0'(2'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(2'(0'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_2(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(2'(2'(0'(0'(2'(2'(2'(1'(2'(1'(1'(1'(1'(0'(2'(2'(2'(0'(1'(0'(2'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(1'(0'(1'(1'(0'(2'(1'(1'(1'(0'(1'(0'(0'(2'(1'(1'(1'(0'(2'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 0'(1'(0'(2'(2'(2'(2'(1'(0'(0'(2'(1'(1'(2'(2'(1'(0'(2'(1'(0'(2'(1'(2'(2'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 2'(2'(2'(1'(0'(1'(1'(0'(2'(2'(0'(0'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(2'(0'(2'(2'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_2(c_1(c_0(c_1(c_1(c_1(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(0'(1'(1'(1'(0'(0'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(1'(1'(1'(1'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_1(c_2(c_0(c_1(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1'(2'(0'(1'(0'(0'(2'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(2'(1'(0'(2'(0'(0'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(2'(0'(0'(1'(0'(0'(0'(1'(1'(1'(2'(0'(2'(2'(2'(2'(1'(1'(1'(1'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_2(c_2(c_1(c_2(c_2(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(2'(0'(2'(0'(1'(0'(0'(2'(2'(2'(2'(0'(2'(2'(1'(2'(1'(1'(1'(1'(1'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(2'(1'(2'(1'(1'(0'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(0'(0'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 0'(2'(2'(2'(0'(2'(2'(0'(0'(1'(1'(1'(0'(1'(0'(2'(1'(1'(0'(2'(0'(1'(2'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(0'(2'(1'(2'(2'(1'(0'(2'(1'(0'(2'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(1'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(x1))))))))))))))))))))))) -> 0'(2'(0'(2'(2'(0'(2'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_1(c_0(c_1(c_1(c_0(c_0(c_1(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(0'(0'(2'(0'(2'(1'(2'(2'(2'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(0'(0'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_1(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 2'(2'(1'(2'(2'(2'(2'(1'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(2'(2'(2'(1'(0'(0'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(0'(2'(2'(2'(0'(0'(2'(1'(0'(2'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_0(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(2'(2'(1'(2'(2'(0'(2'(1'(1'(2'(2'(0'(0'(1'(x1))))))))))))))))))))))))))) [1] encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0] encArg(cons_1(x_1)) -> 1'(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_2(x_1) -> 2'(encArg(x_1)) [0] 0'(x0) -> c_0(x0) [0] 1'(x0) -> c_1(x0) [0] 2'(x0) -> c_2(x0) [0] The TRS has the following type information: 0' :: c_1:c_0:c_2 -> c_1:c_0:c_2 c_1 :: c_1:c_0:c_2 -> c_1:c_0:c_2 c_0 :: c_1:c_0:c_2 -> c_1:c_0:c_2 c_2 :: c_1:c_0:c_2 -> c_1:c_0:c_2 1' :: c_1:c_0:c_2 -> c_1:c_0:c_2 2' :: c_1:c_0:c_2 -> c_1:c_0:c_2 encArg :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2 cons_0 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 cons_1 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 cons_2 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 encode_0 :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2 encode_1 :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2 encode_2 :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2 Rewrite Strategy: INNERMOST ---------------------------------------- (23) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: encArg_1 encode_0_1 encode_1_1 encode_2_1 0'_1 1'_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_2(v0) -> const [0] 0'(v0) -> const [0] 1'(v0) -> const [0] 2'(v0) -> const [0] And the following fresh constants: const, const1 ---------------------------------------- (24) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: 0'(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_1(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 1'(0'(2'(2'(0'(0'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(0'(1'(2'(1'(0'(1'(1'(2'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_0(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 2'(1'(2'(1'(2'(1'(1'(1'(2'(2'(1'(2'(1'(1'(1'(0'(1'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(1'(2'(1'(1'(0'(0'(1'(2'(1'(0'(0'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(1'(1'(1'(0'(2'(1'(0'(0'(2'(1'(1'(2'(0'(2'(1'(2'(1'(2'(0'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_2(c_1(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 1'(1'(1'(2'(2'(1'(1'(1'(2'(1'(2'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(2'(0'(2'(1'(1'(1'(1'(1'(1'(2'(0'(0'(2'(1'(0'(0'(1'(2'(2'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_0(c_0(c_1(c_1(x1))))))))))))))))))))))) -> 2'(2'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(1'(1'(2'(0'(0'(1'(0'(2'(2'(1'(1'(2'(0'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 1'(0'(1'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(1'(1'(2'(2'(1'(2'(1'(1'(2'(0'(2'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_2(c_0(c_1(c_1(c_0(x1))))))))))))))))))))))) -> 0'(0'(2'(1'(1'(1'(0'(1'(2'(2'(0'(2'(0'(0'(0'(1'(0'(2'(2'(2'(1'(0'(1'(2'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 0'(2'(0'(1'(2'(2'(1'(1'(0'(0'(2'(2'(2'(1'(0'(1'(2'(0'(2'(1'(0'(2'(2'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1'(2'(2'(2'(2'(1'(1'(0'(1'(1'(0'(1'(2'(1'(0'(2'(2'(1'(1'(0'(1'(1'(1'(1'(0'(1'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(1'(2'(2'(2'(0'(1'(1'(2'(1'(1'(1'(1'(0'(1'(2'(2'(1'(2'(1'(1'(1'(0'(0'(0'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 2'(2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(1'(0'(1'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_1(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(2'(2'(1'(1'(1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(2'(1'(0'(2'(1'(1'(1'(0'(1'(0'(2'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(0'(0'(1'(0'(2'(1'(0'(2'(2'(2'(1'(0'(0'(2'(1'(1'(0'(2'(2'(2'(2'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(1'(1'(1'(2'(1'(0'(1'(1'(2'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 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2'(c_1(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_2(c_2(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 2'(1'(1'(0'(1'(2'(1'(1'(0'(1'(2'(1'(1'(0'(2'(1'(0'(1'(1'(2'(2'(2'(2'(1'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_1(c_0(c_1(c_0(c_0(c_1(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_0(c_1(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(1'(1'(1'(0'(2'(2'(2'(2'(2'(0'(1'(1'(2'(1'(2'(2'(1'(2'(0'(0'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_0(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1'(2'(1'(2'(1'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(2'(0'(2'(1'(0'(2'(1'(0'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_1(c_1(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_1(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 2'(2'(1'(1'(1'(2'(1'(1'(0'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 2'(2'(0'(1'(0'(1'(1'(0'(2'(2'(1'(1'(1'(1'(2'(1'(2'(0'(1'(1'(1'(2'(1'(0'(0'(1'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(1'(2'(2'(1'(2'(0'(1'(1'(2'(1'(1'(0'(1'(2'(2'(0'(1'(1'(1'(0'(1'(0'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_1(c_2(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(x1))))))))))))))))))))))) -> 0'(0'(2'(1'(0'(1'(1'(1'(1'(2'(0'(1'(0'(0'(0'(1'(0'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_2(c_1(c_2(c_1(c_0(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(x1))))))))))))))))))))))) -> 0'(0'(0'(2'(0'(0'(2'(1'(1'(1'(0'(2'(2'(2'(2'(1'(0'(1'(1'(1'(2'(1'(0'(1'(0'(0'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(2'(2'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(2'(1'(1'(1'(0'(2'(0'(2'(1'(0'(2'(2'(0'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_2(c_2(c_2(c_1(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_1(c_0(c_1(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(0'(2'(0'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(2'(1'(1'(0'(1'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(2'(1'(2'(1'(0'(1'(0'(2'(2'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(2'(0'(2'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 2'(1'(0'(0'(0'(1'(0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(2'(2'(1'(1'(2'(0'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_1(c_2(c_2(c_1(c_1(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(1'(1'(0'(0'(0'(1'(2'(2'(2'(1'(1'(1'(1'(0'(2'(2'(2'(2'(2'(0'(1'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(1'(1'(0'(0'(2'(2'(0'(0'(2'(2'(0'(2'(1'(1'(1'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_2(c_2(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_2(x1))))))))))))))))))))))) -> 1'(2'(1'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(0'(2'(2'(1'(2'(2'(2'(2'(2'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 1'(2'(1'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(2'(1'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_2(c_0(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 0'(1'(0'(2'(2'(0'(0'(0'(1'(1'(2'(0'(1'(1'(0'(2'(0'(1'(1'(1'(1'(1'(0'(1'(0'(2'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 0'(2'(1'(2'(1'(2'(2'(1'(1'(0'(0'(2'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(2'(0'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_2(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(2'(2'(0'(0'(2'(2'(2'(1'(2'(1'(1'(1'(1'(0'(2'(2'(2'(0'(1'(0'(2'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(1'(0'(1'(1'(0'(2'(1'(1'(1'(0'(1'(0'(0'(2'(1'(1'(1'(0'(2'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 0'(1'(0'(2'(2'(2'(2'(1'(0'(0'(2'(1'(1'(2'(2'(1'(0'(2'(1'(0'(2'(1'(2'(2'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 2'(2'(2'(1'(0'(1'(1'(0'(2'(2'(0'(0'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(2'(0'(2'(2'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_2(c_1(c_0(c_1(c_1(c_1(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(0'(1'(1'(1'(0'(0'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(1'(1'(1'(1'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_1(c_2(c_0(c_1(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1'(2'(0'(1'(0'(0'(2'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(2'(1'(0'(2'(0'(0'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(2'(0'(0'(1'(0'(0'(0'(1'(1'(1'(2'(0'(2'(2'(2'(2'(1'(1'(1'(1'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_2(c_2(c_1(c_2(c_2(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(2'(0'(2'(0'(1'(0'(0'(2'(2'(2'(2'(0'(2'(2'(1'(2'(1'(1'(1'(1'(1'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(2'(1'(2'(1'(1'(0'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(0'(0'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 0'(2'(2'(2'(0'(2'(2'(0'(0'(1'(1'(1'(0'(1'(0'(2'(1'(1'(0'(2'(0'(1'(2'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(0'(2'(1'(2'(2'(1'(0'(2'(1'(0'(2'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(1'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(x1))))))))))))))))))))))) -> 0'(2'(0'(2'(2'(0'(2'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_1(c_0(c_1(c_1(c_0(c_0(c_1(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(0'(0'(2'(0'(2'(1'(2'(2'(2'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(0'(0'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_1(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 2'(2'(1'(2'(2'(2'(2'(1'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(2'(2'(2'(1'(0'(0'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(0'(2'(2'(2'(0'(0'(2'(1'(0'(2'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_0(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(2'(2'(1'(2'(2'(0'(2'(1'(1'(2'(2'(0'(0'(1'(x1))))))))))))))))))))))))))) [1] encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0] encArg(cons_1(x_1)) -> 1'(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_2(x_1) -> 2'(encArg(x_1)) [0] 0'(x0) -> c_0(x0) [0] 1'(x0) -> c_1(x0) [0] 2'(x0) -> c_2(x0) [0] encArg(v0) -> const [0] encode_0(v0) -> const [0] encode_1(v0) -> const [0] encode_2(v0) -> const [0] 0'(v0) -> const [0] 1'(v0) -> const [0] 2'(v0) -> const [0] The TRS has the following type information: 0' :: c_1:c_0:c_2:const -> c_1:c_0:c_2:const c_1 :: c_1:c_0:c_2:const -> c_1:c_0:c_2:const c_0 :: c_1:c_0:c_2:const -> c_1:c_0:c_2:const c_2 :: c_1:c_0:c_2:const -> c_1:c_0:c_2:const 1' :: c_1:c_0:c_2:const -> c_1:c_0:c_2:const 2' :: c_1:c_0:c_2:const -> c_1:c_0:c_2:const encArg :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2:const cons_0 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 cons_1 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 cons_2 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 encode_0 :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2:const encode_1 :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2:const encode_2 :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2:const const :: c_1:c_0:c_2:const const1 :: cons_0:cons_1:cons_2 Rewrite Strategy: INNERMOST ---------------------------------------- (25) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (26) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: 0'(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_1(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 1'(0'(2'(2'(0'(0'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(0'(1'(2'(1'(0'(1'(1'(2'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_0(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 2'(1'(2'(1'(2'(1'(1'(1'(2'(2'(1'(2'(1'(1'(1'(0'(1'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(1'(2'(1'(1'(0'(0'(1'(2'(1'(0'(0'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(1'(1'(1'(0'(2'(1'(0'(0'(2'(1'(1'(2'(0'(2'(1'(2'(1'(2'(0'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_2(c_1(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 1'(1'(1'(2'(2'(1'(1'(1'(2'(1'(2'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(2'(0'(2'(1'(1'(1'(1'(1'(1'(2'(0'(0'(2'(1'(0'(0'(1'(2'(2'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_0(c_0(c_1(c_1(x1))))))))))))))))))))))) -> 2'(2'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(1'(1'(2'(0'(0'(1'(0'(2'(2'(1'(1'(2'(0'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 1'(0'(1'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(1'(1'(2'(2'(1'(2'(1'(1'(2'(0'(2'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_2(c_0(c_1(c_1(c_0(x1))))))))))))))))))))))) -> 0'(0'(2'(1'(1'(1'(0'(1'(2'(2'(0'(2'(0'(0'(0'(1'(0'(2'(2'(2'(1'(0'(1'(2'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 0'(2'(0'(1'(2'(2'(1'(1'(0'(0'(2'(2'(2'(1'(0'(1'(2'(0'(2'(1'(0'(2'(2'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1'(2'(2'(2'(2'(1'(1'(0'(1'(1'(0'(1'(2'(1'(0'(2'(2'(1'(1'(0'(1'(1'(1'(1'(0'(1'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(1'(2'(2'(2'(0'(1'(1'(2'(1'(1'(1'(1'(0'(1'(2'(2'(1'(2'(1'(1'(1'(0'(0'(0'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 2'(2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(1'(0'(1'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_1(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(2'(2'(1'(1'(1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(2'(1'(0'(2'(1'(1'(1'(0'(1'(0'(2'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(0'(0'(1'(0'(2'(1'(0'(2'(2'(2'(1'(0'(0'(2'(1'(1'(0'(2'(2'(2'(2'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(1'(1'(1'(2'(1'(0'(1'(1'(2'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_0(c_1(c_1(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_1(c_1(c_1(c_1(c_1(x1))))))))))))))))))))))) -> 1'(1'(0'(2'(1'(1'(0'(1'(1'(1'(1'(2'(1'(2'(1'(1'(0'(0'(1'(1'(1'(0'(2'(2'(1'(2'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 0'(2'(0'(2'(1'(1'(0'(1'(1'(1'(2'(1'(2'(0'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_1(c_0(c_2(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 2'(2'(0'(1'(1'(1'(2'(0'(2'(2'(0'(1'(1'(0'(0'(1'(1'(1'(0'(1'(1'(1'(0'(1'(2'(1'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_2(c_1(c_0(c_2(c_0(c_1(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_2(c_1(c_0(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(1'(1'(1'(0'(0'(0'(1'(1'(1'(0'(0'(2'(0'(0'(2'(0'(0'(2'(1'(1'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 1'(2'(1'(0'(0'(1'(1'(0'(1'(1'(1'(1'(2'(1'(1'(2'(1'(1'(1'(0'(1'(1'(0'(2'(2'(2'(0'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(2'(2'(2'(2'(2'(1'(1'(2'(2'(0'(1'(2'(1'(0'(1'(0'(1'(2'(2'(1'(1'(0'(2'(1'(0'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(x1))))))))))))))))))))))) -> 1'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(0'(1'(0'(2'(2'(1'(0'(1'(0'(1'(2'(1'(2'(0'(2'(2'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_0(c_1(c_1(c_1(c_1(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(0'(2'(1'(1'(1'(1'(2'(1'(2'(1'(1'(2'(1'(1'(1'(2'(1'(1'(2'(2'(2'(1'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_1(x1))))))))))))))))))))))) -> 1'(2'(0'(1'(1'(1'(0'(1'(2'(0'(2'(2'(1'(1'(0'(2'(1'(1'(1'(1'(0'(0'(1'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(1'(1'(0'(2'(1'(1'(1'(0'(1'(1'(1'(0'(2'(1'(1'(1'(0'(0'(0'(2'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_1(c_2(c_0(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 1'(2'(1'(1'(1'(0'(2'(0'(2'(0'(0'(2'(1'(0'(2'(1'(1'(1'(1'(1'(0'(0'(0'(1'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_0(c_1(c_1(c_1(c_1(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 2'(2'(2'(2'(2'(2'(1'(1'(1'(2'(2'(2'(0'(2'(2'(1'(1'(2'(2'(2'(0'(1'(0'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_2(c_0(c_0(c_1(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_1(c_0(c_1(c_1(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(1'(2'(1'(2'(2'(2'(2'(1'(2'(2'(1'(1'(2'(1'(2'(0'(2'(1'(0'(1'(1'(1'(1'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_0(c_2(c_2(c_1(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(0'(2'(1'(0'(0'(1'(1'(1'(0'(2'(1'(1'(1'(1'(2'(1'(1'(2'(2'(2'(1'(1'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_1(c_1(c_0(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_1(c_0(c_0(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(0'(0'(1'(1'(1'(1'(1'(1'(2'(1'(0'(0'(0'(2'(1'(0'(0'(1'(0'(2'(2'(2'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_2(c_2(c_0(c_1(c_1(c_2(c_0(c_2(c_2(c_2(c_2(c_2(c_0(c_1(c_1(c_2(c_2(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(2'(0'(1'(0'(2'(1'(1'(2'(2'(2'(1'(1'(1'(2'(2'(1'(1'(1'(2'(1'(1'(1'(2'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(2'(1'(1'(0'(0'(1'(1'(0'(1'(2'(1'(1'(1'(1'(1'(0'(1'(2'(2'(1'(1'(2'(0'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_0(c_2(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 0'(1'(1'(0'(2'(2'(2'(0'(2'(1'(1'(0'(1'(0'(2'(2'(0'(1'(1'(0'(0'(2'(1'(1'(1'(2'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_0(c_0(c_2(c_0(c_2(c_2(c_1(c_1(c_1(c_1(c_1(c_1(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_0(x1))))))))))))))))))))))) -> 0'(2'(1'(1'(1'(0'(2'(1'(1'(0'(1'(2'(1'(0'(2'(2'(2'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_0(c_0(c_1(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 0'(2'(0'(1'(1'(2'(2'(2'(1'(1'(0'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(1'(1'(2'(1'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_1(c_1(c_1(c_1(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(0'(1'(1'(1'(0'(0'(1'(0'(0'(0'(2'(1'(1'(1'(1'(1'(1'(1'(0'(1'(2'(0'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1'(0'(2'(1'(0'(1'(0'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(1'(1'(1'(2'(2'(1'(2'(1'(0'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_1(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_0(c_2(c_0(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(1'(2'(0'(0'(1'(1'(2'(1'(2'(2'(1'(1'(1'(1'(2'(1'(2'(1'(2'(1'(1'(2'(1'(x1))))))))))))))))))))))))))) [1] 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2'(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_2(c_0(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 0'(1'(0'(2'(2'(0'(0'(0'(1'(1'(2'(0'(1'(1'(0'(2'(0'(1'(1'(1'(1'(1'(0'(1'(0'(2'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 0'(2'(1'(2'(1'(2'(2'(1'(1'(0'(0'(2'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(2'(0'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_2(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(2'(2'(0'(0'(2'(2'(2'(1'(2'(1'(1'(1'(1'(0'(2'(2'(2'(0'(1'(0'(2'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(1'(0'(1'(1'(0'(2'(1'(1'(1'(0'(1'(0'(0'(2'(1'(1'(1'(0'(2'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 0'(1'(0'(2'(2'(2'(2'(1'(0'(0'(2'(1'(1'(2'(2'(1'(0'(2'(1'(0'(2'(1'(2'(2'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 2'(2'(2'(1'(0'(1'(1'(0'(2'(2'(0'(0'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(2'(0'(2'(2'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_2(c_1(c_0(c_1(c_1(c_1(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(0'(1'(1'(1'(0'(0'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(1'(1'(1'(1'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_1(c_2(c_0(c_1(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1'(2'(0'(1'(0'(0'(2'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(2'(1'(0'(2'(0'(0'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(2'(0'(0'(1'(0'(0'(0'(1'(1'(1'(2'(0'(2'(2'(2'(2'(1'(1'(1'(1'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_2(c_2(c_1(c_2(c_2(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(2'(0'(2'(0'(1'(0'(0'(2'(2'(2'(2'(0'(2'(2'(1'(2'(1'(1'(1'(1'(1'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(2'(1'(2'(1'(1'(0'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(0'(0'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 0'(2'(2'(2'(0'(2'(2'(0'(0'(1'(1'(1'(0'(1'(0'(2'(1'(1'(0'(2'(0'(1'(2'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(0'(2'(1'(2'(2'(1'(0'(2'(1'(0'(2'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(1'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(x1))))))))))))))))))))))) -> 0'(2'(0'(2'(2'(0'(2'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_1(c_0(c_1(c_1(c_0(c_0(c_1(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(0'(0'(2'(0'(2'(1'(2'(2'(2'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(0'(0'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_1(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 2'(2'(1'(2'(2'(2'(2'(1'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(2'(2'(2'(1'(0'(0'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(0'(2'(2'(2'(0'(0'(2'(1'(0'(2'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_0(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(2'(2'(1'(2'(2'(0'(2'(1'(1'(2'(2'(0'(0'(1'(x1))))))))))))))))))))))))))) [1] encArg(cons_0(cons_0(x_1'))) -> 0'(0'(encArg(x_1'))) [0] encArg(cons_0(cons_1(x_1''))) -> 0'(1'(encArg(x_1''))) [0] encArg(cons_0(cons_2(x_11))) -> 0'(2'(encArg(x_11))) [0] encArg(cons_0(x_1)) -> 0'(const) [0] encArg(cons_1(cons_0(x_12))) -> 1'(0'(encArg(x_12))) [0] encArg(cons_1(cons_1(x_13))) -> 1'(1'(encArg(x_13))) [0] encArg(cons_1(cons_2(x_14))) -> 1'(2'(encArg(x_14))) [0] encArg(cons_1(x_1)) -> 1'(const) [0] encArg(cons_2(cons_0(x_15))) -> 2'(0'(encArg(x_15))) [0] encArg(cons_2(cons_1(x_16))) -> 2'(1'(encArg(x_16))) [0] encArg(cons_2(cons_2(x_17))) -> 2'(2'(encArg(x_17))) [0] encArg(cons_2(x_1)) -> 2'(const) [0] encode_0(cons_0(x_18)) -> 0'(0'(encArg(x_18))) [0] encode_0(cons_1(x_19)) -> 0'(1'(encArg(x_19))) [0] encode_0(cons_2(x_110)) -> 0'(2'(encArg(x_110))) [0] encode_0(x_1) -> 0'(const) [0] encode_1(cons_0(x_111)) -> 1'(0'(encArg(x_111))) [0] encode_1(cons_1(x_112)) -> 1'(1'(encArg(x_112))) [0] encode_1(cons_2(x_113)) -> 1'(2'(encArg(x_113))) [0] encode_1(x_1) -> 1'(const) [0] encode_2(cons_0(x_114)) -> 2'(0'(encArg(x_114))) [0] encode_2(cons_1(x_115)) -> 2'(1'(encArg(x_115))) [0] encode_2(cons_2(x_116)) -> 2'(2'(encArg(x_116))) [0] encode_2(x_1) -> 2'(const) [0] 0'(x0) -> c_0(x0) [0] 1'(x0) -> c_1(x0) [0] 2'(x0) -> c_2(x0) [0] encArg(v0) -> const [0] encode_0(v0) -> const [0] encode_1(v0) -> const [0] encode_2(v0) -> const [0] 0'(v0) -> const [0] 1'(v0) -> const [0] 2'(v0) -> const [0] The TRS has the following type information: 0' :: c_1:c_0:c_2:const -> c_1:c_0:c_2:const c_1 :: c_1:c_0:c_2:const -> c_1:c_0:c_2:const c_0 :: c_1:c_0:c_2:const -> c_1:c_0:c_2:const c_2 :: c_1:c_0:c_2:const -> c_1:c_0:c_2:const 1' :: c_1:c_0:c_2:const -> c_1:c_0:c_2:const 2' :: c_1:c_0:c_2:const -> c_1:c_0:c_2:const encArg :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2:const cons_0 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 cons_1 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 cons_2 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 encode_0 :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2:const encode_1 :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2:const encode_2 :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2:const const :: c_1:c_0:c_2:const const1 :: cons_0:cons_1:cons_2 Rewrite Strategy: INNERMOST ---------------------------------------- (27) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: const => 0 const1 => 0 ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: 0'(z) -{ 1 }-> 2'(1'(0'(2'(1'(1'(1'(1'(2'(1'(2'(1'(1'(2'(1'(1'(1'(2'(1'(1'(2'(2'(2'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 2'(1'(0'(0'(0'(1'(0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(2'(2'(1'(1'(2'(0'(1'(1'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 2'(0'(2'(2'(1'(1'(1'(0'(0'(1'(1'(1'(0'(1'(1'(2'(1'(1'(0'(1'(1'(1'(1'(2'(2'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 2'(0'(2'(1'(0'(0'(1'(1'(1'(0'(2'(1'(1'(1'(1'(2'(1'(1'(2'(2'(2'(1'(1'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(2'(2'(2'(1'(1'(0'(1'(1'(0'(1'(2'(1'(0'(2'(2'(1'(1'(0'(1'(1'(1'(1'(0'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(2'(1'(1'(2'(1'(1'(1'(1'(0'(0'(0'(1'(1'(0'(0'(0'(2'(1'(1'(0'(2'(2'(2'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(2'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(2'(1'(1'(1'(0'(2'(0'(2'(1'(0'(2'(2'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(1'(1'(1'(2'(0'(2'(1'(2'(2'(2'(1'(1'(2'(1'(1'(0'(1'(0'(1'(2'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(1'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(2'(1'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(0'(1'(0'(0'(2'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(2'(1'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(2'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(1'(1'(1'(2'(1'(0'(1'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(1'(2'(1'(1'(0'(0'(1'(1'(0'(1'(2'(1'(1'(1'(1'(1'(0'(1'(2'(2'(1'(1'(2'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(1'(1'(2'(0'(2'(2'(2'(1'(0'(2'(0'(2'(2'(2'(2'(1'(0'(1'(2'(1'(0'(0'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(1'(1'(2'(0'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(0'(2'(2'(2'(0'(0'(2'(1'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(1'(0'(1'(0'(2'(1'(2'(2'(1'(1'(2'(0'(1'(1'(1'(2'(0'(2'(1'(1'(2'(1'(1'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(0'(1'(1'(1'(1'(0'(2'(2'(2'(2'(2'(0'(1'(1'(2'(1'(2'(2'(1'(2'(0'(0'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(0'(2'(2'(0'(0'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(0'(1'(2'(1'(0'(1'(1'(2'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(0'(2'(0'(0'(1'(2'(2'(2'(1'(1'(1'(0'(1'(2'(1'(2'(1'(1'(1'(1'(2'(2'(1'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(0'(1'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(1'(2'(1'(1'(0'(0'(1'(2'(1'(0'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(0'(1'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(1'(1'(2'(2'(1'(2'(1'(1'(2'(0'(2'(2'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(2'(0'(2'(2'(0'(0'(1'(1'(1'(0'(1'(0'(2'(1'(1'(0'(2'(0'(1'(2'(1'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(1'(2'(1'(2'(2'(1'(1'(0'(0'(2'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(2'(0'(2'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(1'(1'(1'(0'(2'(1'(1'(0'(1'(2'(1'(0'(2'(2'(2'(1'(1'(0'(1'(1'(0'(1'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(0'(2'(2'(0'(2'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(0'(0'(1'(1'(1'(1'(1'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(0'(2'(1'(1'(0'(1'(1'(1'(2'(1'(2'(0'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(2'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(0'(1'(2'(2'(1'(1'(0'(0'(2'(2'(2'(1'(0'(1'(2'(0'(2'(1'(0'(2'(2'(1'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(0'(1'(1'(2'(2'(2'(1'(1'(0'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(1'(1'(2'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(2'(2'(2'(0'(1'(1'(2'(1'(1'(1'(1'(0'(1'(2'(2'(1'(2'(1'(1'(1'(0'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(2'(1'(2'(2'(2'(2'(1'(2'(2'(1'(1'(2'(1'(2'(0'(2'(1'(0'(1'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(1'(0'(2'(1'(1'(1'(0'(1'(1'(1'(0'(2'(1'(1'(1'(0'(0'(0'(2'(1'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(0'(1'(2'(0'(0'(2'(2'(2'(1'(2'(2'(2'(2'(2'(0'(1'(1'(0'(1'(1'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(0'(2'(2'(2'(0'(2'(1'(1'(0'(1'(0'(2'(2'(0'(1'(1'(0'(0'(2'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(0'(1'(1'(1'(1'(0'(2'(1'(2'(0'(1'(1'(2'(0'(1'(1'(1'(1'(1'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(0'(2'(2'(2'(2'(1'(0'(0'(2'(1'(1'(2'(2'(1'(0'(2'(1'(0'(2'(1'(2'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(0'(2'(1'(1'(1'(0'(1'(2'(2'(0'(2'(0'(0'(0'(1'(0'(2'(2'(2'(1'(0'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(0'(2'(1'(0'(1'(1'(1'(1'(2'(0'(1'(0'(0'(0'(1'(0'(1'(1'(1'(1'(1'(1'(1'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(0'(0'(2'(0'(0'(2'(1'(1'(1'(0'(2'(2'(2'(2'(1'(0'(1'(1'(1'(2'(1'(0'(1'(0'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 0'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 1'(z) -{ 1 }-> 1'(2'(2'(1'(1'(1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(2'(1'(0'(2'(1'(1'(1'(0'(1'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(2'(1'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(2'(0'(2'(1'(0'(2'(1'(0'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(1'(2'(0'(1'(1'(1'(2'(1'(1'(1'(2'(2'(1'(1'(1'(1'(1'(0'(0'(2'(1'(2'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(1'(1'(0'(2'(0'(2'(0'(0'(2'(1'(0'(2'(1'(1'(1'(1'(1'(0'(0'(0'(1'(0'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(1'(1'(0'(0'(1'(1'(1'(1'(0'(2'(2'(2'(2'(1'(0'(0'(1'(2'(1'(1'(1'(0'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(1'(0'(2'(2'(1'(1'(1'(1'(1'(1'(1'(2'(2'(2'(1'(0'(0'(1'(1'(1'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(1'(0'(1'(1'(2'(1'(2'(0'(2'(1'(1'(1'(0'(1'(1'(1'(0'(1'(0'(1'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(0'(2'(2'(1'(2'(2'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(0'(0'(1'(1'(0'(1'(1'(1'(1'(2'(1'(1'(2'(1'(1'(1'(0'(1'(1'(0'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(0'(1'(0'(2'(1'(1'(2'(2'(2'(1'(1'(1'(2'(2'(1'(1'(1'(2'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(2'(2'(2'(1'(2'(0'(2'(1'(1'(1'(1'(1'(1'(2'(0'(0'(2'(1'(0'(0'(1'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(2'(2'(2'(1'(2'(0'(0'(1'(0'(0'(0'(1'(1'(1'(2'(0'(2'(2'(2'(2'(1'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(2'(1'(2'(1'(0'(1'(0'(2'(2'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(2'(0'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(2'(2'(1'(2'(2'(0'(2'(1'(1'(2'(2'(0'(0'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(0'(1'(1'(1'(0'(0'(1'(0'(0'(0'(2'(1'(1'(1'(1'(1'(1'(1'(0'(1'(2'(0'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(0'(2'(2'(0'(0'(2'(2'(2'(1'(2'(1'(1'(1'(1'(0'(2'(2'(2'(0'(1'(0'(2'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(0'(1'(2'(2'(1'(2'(0'(1'(1'(2'(1'(1'(0'(1'(2'(2'(0'(1'(1'(1'(0'(1'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(0'(0'(0'(2'(0'(1'(2'(1'(0'(0'(1'(1'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(0'(0'(2'(1'(2'(1'(0'(0'(1'(1'(2'(2'(1'(1'(1'(1'(2'(1'(1'(1'(1'(0'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(0'(0'(0'(2'(0'(2'(1'(2'(2'(2'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(0'(0'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(2'(1'(1'(0'(1'(1'(1'(1'(2'(1'(2'(1'(1'(0'(0'(1'(1'(1'(0'(2'(2'(1'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(2'(1'(1'(0'(1'(0'(1'(1'(1'(0'(0'(2'(1'(0'(2'(1'(1'(0'(2'(1'(0'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(2'(0'(1'(2'(2'(0'(1'(1'(1'(1'(1'(0'(1'(2'(1'(1'(2'(0'(2'(2'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(2'(1'(2'(1'(1'(2'(2'(0'(2'(1'(0'(0'(1'(1'(1'(2'(0'(0'(1'(2'(1'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(2'(0'(2'(0'(1'(0'(0'(2'(2'(2'(2'(0'(2'(2'(1'(2'(1'(1'(1'(1'(1'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(1'(1'(1'(0'(2'(1'(0'(0'(2'(1'(1'(2'(0'(2'(1'(2'(1'(2'(0'(1'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(1'(1'(0'(0'(0'(1'(2'(2'(2'(1'(1'(1'(1'(0'(2'(2'(2'(2'(2'(0'(1'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(0'(0'(1'(1'(1'(1'(1'(1'(2'(1'(0'(0'(0'(2'(1'(0'(0'(1'(0'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(0'(2'(0'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(2'(1'(1'(0'(1'(1'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(0'(0'(1'(0'(2'(1'(0'(2'(2'(2'(1'(0'(0'(2'(1'(1'(0'(2'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(2'(1'(0'(1'(0'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(1'(1'(1'(2'(2'(1'(2'(1'(0'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(1'(2'(1'(2'(1'(1'(0'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(0'(0'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(1'(1'(0'(0'(2'(2'(0'(0'(2'(2'(0'(2'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(1'(1'(1'(1'(0'(0'(0'(1'(1'(1'(0'(0'(2'(0'(0'(2'(0'(0'(2'(1'(1'(1'(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 + x1))))))))))))))))))))) 1'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 1'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 2'(z) -{ 1 }-> 2'(2'(2'(2'(2'(2'(1'(1'(2'(2'(0'(1'(2'(1'(0'(1'(0'(1'(2'(2'(1'(1'(0'(2'(1'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(2'(2'(2'(2'(1'(1'(1'(2'(2'(2'(0'(2'(2'(1'(1'(2'(2'(2'(0'(1'(0'(1'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(2'(1'(0'(1'(1'(0'(2'(2'(0'(0'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(2'(0'(2'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(1'(2'(2'(2'(2'(1'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(2'(2'(2'(1'(0'(0'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(1'(0'(1'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(1'(1'(1'(2'(1'(1'(0'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(1'(1'(1'(2'(1'(0'(2'(0'(1'(1'(2'(2'(0'(1'(1'(0'(1'(2'(0'(1'(0'(2'(1'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(1'(1'(1'(1'(1'(2'(0'(2'(1'(1'(2'(2'(1'(2'(1'(1'(1'(1'(1'(2'(1'(2'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(0'(1'(1'(1'(2'(0'(2'(2'(0'(1'(1'(0'(0'(1'(1'(1'(0'(1'(1'(1'(0'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(1'(1'(2'(0'(0'(1'(0'(2'(2'(1'(1'(2'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(0'(1'(0'(1'(1'(0'(2'(2'(1'(1'(1'(1'(2'(1'(2'(0'(1'(1'(1'(2'(1'(0'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(0'(1'(0'(2'(2'(1'(0'(1'(0'(1'(2'(1'(2'(0'(2'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(2'(1'(2'(1'(1'(1'(2'(2'(1'(2'(1'(1'(1'(0'(1'(1'(1'(2'(1'(0'(0'(1'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(1'(1'(1'(0'(1'(1'(2'(2'(2'(1'(1'(2'(1'(1'(2'(1'(0'(2'(0'(2'(0'(2'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(1'(0'(1'(2'(1'(1'(0'(1'(2'(1'(1'(0'(2'(1'(0'(1'(1'(2'(2'(2'(2'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(1'(0'(1'(1'(0'(2'(1'(1'(1'(0'(1'(0'(0'(2'(1'(1'(1'(0'(2'(0'(0'(1'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(0'(2'(1'(2'(2'(1'(0'(2'(1'(0'(2'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(0'(0'(2'(2'(1'(2'(1'(2'(1'(1'(1'(1'(0'(1'(2'(2'(2'(1'(2'(0'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(0'(0'(0'(0'(1'(1'(2'(0'(1'(2'(2'(1'(0'(2'(0'(2'(2'(2'(0'(1'(0'(1'(1'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(2'(0'(1'(1'(1'(0'(1'(2'(0'(2'(2'(1'(1'(0'(2'(1'(1'(1'(1'(0'(0'(1'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(2'(1'(0'(1'(2'(1'(2'(1'(1'(1'(2'(1'(1'(1'(1'(2'(2'(1'(0'(1'(1'(2'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(1'(2'(2'(1'(1'(1'(2'(1'(2'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(1'(0'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(1'(0'(1'(2'(0'(0'(1'(1'(2'(1'(2'(2'(1'(1'(1'(1'(2'(1'(2'(1'(2'(1'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(0'(0'(1'(1'(1'(0'(0'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(1'(1'(1'(1'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 0'(1'(0'(2'(2'(0'(0'(0'(1'(1'(2'(0'(1'(1'(0'(2'(0'(1'(1'(1'(1'(1'(0'(1'(0'(2'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 0'(0'(1'(2'(2'(2'(2'(1'(1'(2'(2'(2'(1'(1'(1'(1'(1'(1'(1'(1'(1'(0'(2'(0'(1'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 2'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 encArg(z) -{ 0 }-> 2'(2'(encArg(x_17))) :|: x_17 >= 0, z = 1 + (1 + x_17) encArg(z) -{ 0 }-> 2'(1'(encArg(x_16))) :|: x_16 >= 0, z = 1 + (1 + x_16) encArg(z) -{ 0 }-> 2'(0'(encArg(x_15))) :|: x_15 >= 0, z = 1 + (1 + x_15) encArg(z) -{ 0 }-> 2'(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 1'(2'(encArg(x_14))) :|: x_14 >= 0, z = 1 + (1 + x_14) encArg(z) -{ 0 }-> 1'(1'(encArg(x_13))) :|: z = 1 + (1 + x_13), x_13 >= 0 encArg(z) -{ 0 }-> 1'(0'(encArg(x_12))) :|: z = 1 + (1 + x_12), x_12 >= 0 encArg(z) -{ 0 }-> 1'(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 0'(2'(encArg(x_11))) :|: x_11 >= 0, z = 1 + (1 + x_11) encArg(z) -{ 0 }-> 0'(1'(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0 encArg(z) -{ 0 }-> 0'(0'(encArg(x_1'))) :|: z = 1 + (1 + x_1'), x_1' >= 0 encArg(z) -{ 0 }-> 0'(0) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_0(z) -{ 0 }-> 0'(2'(encArg(x_110))) :|: z = 1 + x_110, x_110 >= 0 encode_0(z) -{ 0 }-> 0'(1'(encArg(x_19))) :|: z = 1 + x_19, x_19 >= 0 encode_0(z) -{ 0 }-> 0'(0'(encArg(x_18))) :|: z = 1 + x_18, x_18 >= 0 encode_0(z) -{ 0 }-> 0'(0) :|: x_1 >= 0, z = x_1 encode_0(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_1(z) -{ 0 }-> 1'(2'(encArg(x_113))) :|: z = 1 + x_113, x_113 >= 0 encode_1(z) -{ 0 }-> 1'(1'(encArg(x_112))) :|: z = 1 + x_112, x_112 >= 0 encode_1(z) -{ 0 }-> 1'(0'(encArg(x_111))) :|: z = 1 + x_111, x_111 >= 0 encode_1(z) -{ 0 }-> 1'(0) :|: x_1 >= 0, z = x_1 encode_1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_2(z) -{ 0 }-> 2'(2'(encArg(x_116))) :|: x_116 >= 0, z = 1 + x_116 encode_2(z) -{ 0 }-> 2'(1'(encArg(x_115))) :|: x_115 >= 0, z = 1 + x_115 encode_2(z) -{ 0 }-> 2'(0'(encArg(x_114))) :|: x_114 >= 0, z = 1 + x_114 encode_2(z) -{ 0 }-> 2'(0) :|: x_1 >= 0, z = x_1 encode_2(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 ---------------------------------------- (29) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: 0'(z) -{ 1 }-> 2'(1'(0'(2'(1'(1'(1'(1'(2'(1'(2'(1'(1'(2'(1'(1'(1'(2'(1'(1'(2'(2'(2'(1'(2'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 2'(1'(0'(0'(0'(1'(0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(2'(2'(1'(1'(2'(0'(1'(1'(0'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 2'(0'(2'(2'(1'(1'(1'(0'(0'(1'(1'(1'(0'(1'(1'(2'(1'(1'(0'(1'(1'(1'(1'(2'(2'(2'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 2'(0'(2'(1'(0'(0'(1'(1'(1'(0'(2'(1'(1'(1'(1'(2'(1'(1'(2'(2'(2'(1'(1'(0'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(2'(2'(2'(2'(1'(1'(0'(1'(1'(0'(1'(2'(1'(0'(2'(2'(1'(1'(0'(1'(1'(1'(1'(0'(1'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(2'(2'(1'(1'(2'(1'(1'(1'(1'(0'(0'(0'(1'(1'(0'(0'(0'(2'(1'(1'(0'(2'(2'(2'(0'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(2'(2'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(2'(1'(1'(1'(0'(2'(0'(2'(1'(0'(2'(2'(0'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(2'(1'(1'(1'(2'(0'(2'(1'(2'(2'(2'(1'(1'(2'(1'(1'(0'(1'(0'(1'(2'(2'(2'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(2'(1'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(2'(1'(0'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(2'(0'(1'(0'(0'(2'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(2'(1'(0'(2'(0'(0'(0'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(1'(2'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(1'(1'(1'(2'(1'(0'(1'(1'(2'(0'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(1'(1'(2'(1'(1'(0'(0'(1'(1'(0'(1'(2'(1'(1'(1'(1'(1'(0'(1'(2'(2'(1'(1'(2'(0'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(1'(1'(1'(2'(0'(2'(2'(2'(1'(0'(2'(0'(2'(2'(2'(2'(1'(0'(1'(2'(1'(0'(0'(0'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(1'(1'(1'(2'(0'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(0'(2'(2'(2'(0'(0'(2'(1'(0'(2'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(1'(1'(0'(1'(0'(2'(1'(2'(2'(1'(1'(2'(0'(1'(1'(1'(2'(0'(2'(1'(1'(2'(1'(1'(0'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(1'(0'(1'(1'(1'(1'(0'(2'(2'(2'(2'(2'(0'(1'(1'(2'(1'(2'(2'(1'(2'(0'(0'(0'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(0'(2'(2'(0'(0'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(0'(1'(2'(1'(0'(1'(1'(2'(0'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(0'(2'(0'(0'(1'(2'(2'(2'(1'(1'(1'(0'(1'(2'(1'(2'(1'(1'(1'(1'(2'(2'(1'(1'(2'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(0'(1'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(1'(2'(1'(1'(0'(0'(1'(2'(1'(0'(0'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 1'(0'(1'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(1'(1'(2'(2'(1'(2'(1'(1'(2'(0'(2'(2'(2'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(2'(2'(2'(0'(2'(2'(0'(0'(1'(1'(1'(0'(1'(0'(2'(1'(1'(0'(2'(0'(1'(2'(1'(0'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(2'(1'(2'(1'(2'(2'(1'(1'(0'(0'(2'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(2'(0'(2'(2'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(2'(1'(1'(1'(0'(2'(1'(1'(0'(1'(2'(1'(0'(2'(2'(2'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(2'(0'(2'(2'(0'(2'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(2'(0'(2'(1'(1'(0'(1'(1'(1'(2'(1'(2'(0'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(2'(2'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(2'(0'(1'(2'(2'(1'(1'(0'(0'(2'(2'(2'(1'(0'(1'(2'(0'(2'(1'(0'(2'(2'(1'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(2'(0'(1'(1'(2'(2'(2'(1'(1'(0'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(1'(1'(2'(1'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(1'(2'(2'(2'(0'(1'(1'(2'(1'(1'(1'(1'(0'(1'(2'(2'(1'(2'(1'(1'(1'(0'(0'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(1'(2'(1'(2'(2'(2'(2'(1'(2'(2'(1'(1'(2'(1'(2'(0'(2'(1'(0'(1'(1'(1'(1'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(1'(1'(0'(2'(1'(1'(1'(0'(1'(1'(1'(0'(2'(1'(1'(1'(0'(0'(0'(2'(1'(0'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(1'(0'(1'(2'(0'(0'(2'(2'(2'(1'(2'(2'(2'(2'(2'(0'(1'(1'(0'(1'(1'(1'(1'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(0'(2'(2'(2'(0'(2'(1'(1'(0'(1'(0'(2'(2'(0'(1'(1'(0'(0'(2'(1'(1'(1'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(0'(1'(1'(1'(1'(0'(2'(1'(2'(0'(1'(1'(2'(0'(1'(1'(1'(1'(1'(2'(2'(1'(1'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(1'(0'(2'(2'(2'(2'(1'(0'(0'(2'(1'(1'(2'(2'(1'(0'(2'(1'(0'(2'(1'(2'(2'(2'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(0'(2'(1'(1'(1'(0'(1'(2'(2'(0'(2'(0'(0'(0'(1'(0'(2'(2'(2'(1'(0'(1'(2'(1'(1'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(0'(2'(1'(0'(1'(1'(1'(1'(2'(0'(1'(0'(0'(0'(1'(0'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(0'(0'(2'(0'(0'(2'(1'(1'(1'(0'(2'(2'(2'(2'(1'(0'(1'(1'(1'(2'(1'(0'(1'(0'(0'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 0 }-> 0 :|: z >= 0 0'(z) -{ 0 }-> 1 + z :|: z >= 0 1'(z) -{ 1 }-> 1'(2'(2'(1'(1'(1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(2'(1'(0'(2'(1'(1'(1'(0'(1'(0'(2'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(2'(1'(2'(1'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(2'(0'(2'(1'(0'(2'(1'(0'(2'(2'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(2'(1'(1'(2'(0'(1'(1'(1'(2'(1'(1'(1'(2'(2'(1'(1'(1'(1'(1'(0'(0'(2'(1'(2'(0'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(2'(1'(1'(1'(0'(2'(0'(2'(0'(0'(2'(1'(0'(2'(1'(1'(1'(1'(1'(0'(0'(0'(1'(0'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(2'(1'(1'(1'(0'(0'(1'(1'(1'(1'(0'(2'(2'(2'(2'(1'(0'(0'(1'(2'(1'(1'(1'(0'(2'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(2'(1'(1'(0'(2'(2'(1'(1'(1'(1'(1'(1'(1'(2'(2'(2'(1'(0'(0'(1'(1'(1'(1'(1'(1'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(2'(1'(1'(0'(1'(1'(2'(1'(2'(0'(2'(1'(1'(1'(0'(1'(1'(1'(0'(1'(0'(1'(0'(2'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(2'(1'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(0'(2'(2'(1'(2'(2'(2'(2'(2'(0'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(2'(1'(0'(0'(1'(1'(0'(1'(1'(1'(1'(2'(1'(1'(2'(1'(1'(1'(0'(1'(1'(0'(2'(2'(2'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(2'(0'(1'(0'(2'(1'(1'(2'(2'(2'(1'(1'(1'(2'(2'(1'(1'(1'(2'(1'(1'(1'(2'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(2'(2'(2'(1'(2'(0'(2'(1'(1'(1'(1'(1'(1'(2'(0'(0'(2'(1'(0'(0'(1'(2'(2'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(2'(2'(2'(1'(2'(0'(0'(1'(0'(0'(0'(1'(1'(1'(2'(0'(2'(2'(2'(2'(1'(1'(1'(1'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(1'(2'(1'(2'(1'(0'(1'(0'(2'(2'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(2'(0'(2'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(2'(2'(1'(2'(2'(0'(2'(1'(1'(2'(2'(0'(0'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(1'(0'(1'(1'(1'(0'(0'(1'(0'(0'(0'(2'(1'(1'(1'(1'(1'(1'(1'(0'(1'(2'(0'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(0'(2'(2'(0'(0'(2'(2'(2'(1'(2'(1'(1'(1'(1'(0'(2'(2'(2'(0'(1'(0'(2'(0'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(0'(1'(2'(2'(1'(2'(0'(1'(1'(2'(1'(1'(0'(1'(2'(2'(0'(1'(1'(1'(0'(1'(0'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(0'(0'(0'(2'(0'(1'(2'(1'(0'(0'(1'(1'(1'(1'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(0'(0'(2'(1'(2'(1'(0'(0'(1'(1'(2'(2'(1'(1'(1'(1'(2'(1'(1'(1'(1'(0'(2'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(0'(0'(0'(2'(0'(2'(1'(2'(2'(2'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(0'(0'(0'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(2'(1'(1'(0'(1'(1'(1'(1'(2'(1'(2'(1'(1'(0'(0'(1'(1'(1'(0'(2'(2'(1'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(2'(1'(1'(0'(1'(0'(1'(1'(1'(0'(0'(2'(1'(0'(2'(1'(1'(0'(2'(1'(0'(2'(2'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(2'(0'(1'(2'(2'(0'(1'(1'(1'(1'(1'(0'(1'(2'(1'(1'(2'(0'(2'(2'(0'(2'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(1'(2'(1'(2'(1'(1'(2'(2'(0'(2'(1'(0'(0'(1'(1'(1'(2'(0'(0'(1'(2'(1'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(1'(2'(0'(2'(0'(1'(0'(0'(2'(2'(2'(2'(0'(2'(2'(1'(2'(1'(1'(1'(1'(1'(2'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(1'(1'(1'(1'(0'(2'(1'(0'(0'(2'(1'(1'(2'(0'(2'(1'(2'(1'(2'(0'(1'(0'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(1'(1'(1'(0'(0'(0'(1'(2'(2'(2'(1'(1'(1'(1'(0'(2'(2'(2'(2'(2'(0'(1'(2'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(1'(0'(0'(1'(1'(1'(1'(1'(1'(2'(1'(0'(0'(0'(2'(1'(0'(0'(1'(0'(2'(2'(2'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(0'(2'(0'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(2'(1'(1'(0'(1'(1'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(0'(0'(1'(0'(2'(1'(0'(2'(2'(2'(1'(0'(0'(2'(1'(1'(0'(2'(2'(2'(2'(1'(1'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(0'(2'(1'(0'(1'(0'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(1'(1'(1'(2'(2'(1'(2'(1'(0'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(0'(1'(2'(1'(2'(1'(1'(0'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(0'(0'(0'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(1'(1'(0'(0'(2'(2'(0'(0'(2'(2'(0'(2'(1'(1'(1'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(0'(1'(1'(1'(1'(0'(0'(0'(1'(1'(1'(0'(0'(2'(0'(0'(2'(0'(0'(2'(1'(1'(1'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 0 }-> 0 :|: z >= 0 1'(z) -{ 0 }-> 1 + z :|: z >= 0 2'(z) -{ 1 }-> 2'(2'(2'(2'(2'(2'(1'(1'(2'(2'(0'(1'(2'(1'(0'(1'(0'(1'(2'(2'(1'(1'(0'(2'(1'(0'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(2'(2'(2'(2'(2'(1'(1'(1'(2'(2'(2'(0'(2'(2'(1'(1'(2'(2'(2'(0'(1'(0'(1'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(2'(2'(1'(0'(1'(1'(0'(2'(2'(0'(0'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(2'(0'(2'(2'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(2'(1'(2'(2'(2'(2'(1'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(2'(2'(2'(1'(0'(0'(0'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(1'(0'(1'(0'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(2'(1'(1'(1'(2'(1'(1'(0'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(2'(1'(1'(1'(2'(1'(0'(2'(0'(1'(1'(2'(2'(0'(1'(1'(0'(1'(2'(0'(1'(0'(2'(1'(1'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(2'(1'(1'(1'(1'(1'(2'(0'(2'(1'(1'(2'(2'(1'(2'(1'(1'(1'(1'(1'(2'(1'(2'(1'(2'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(2'(0'(1'(1'(1'(2'(0'(2'(2'(0'(1'(1'(0'(0'(1'(1'(1'(0'(1'(1'(1'(0'(1'(2'(1'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(2'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(1'(1'(2'(0'(0'(1'(0'(2'(2'(1'(1'(2'(0'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(2'(0'(1'(0'(1'(1'(0'(2'(2'(1'(1'(1'(1'(2'(1'(2'(0'(1'(1'(1'(2'(1'(0'(0'(1'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(0'(1'(0'(2'(2'(1'(0'(1'(0'(1'(2'(1'(2'(0'(2'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(1'(2'(1'(2'(1'(1'(1'(2'(2'(1'(2'(1'(1'(1'(0'(1'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(1'(1'(1'(1'(0'(1'(1'(2'(2'(2'(1'(1'(2'(1'(1'(2'(1'(0'(2'(0'(2'(0'(2'(2'(1'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(1'(1'(0'(1'(2'(1'(1'(0'(1'(2'(1'(1'(0'(2'(1'(0'(1'(1'(2'(2'(2'(2'(1'(2'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(1'(1'(0'(1'(1'(0'(2'(1'(1'(1'(0'(1'(0'(0'(2'(1'(1'(1'(0'(2'(0'(0'(1'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(1'(0'(2'(1'(2'(2'(1'(0'(2'(1'(0'(2'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(1'(2'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(0'(0'(2'(2'(1'(2'(1'(2'(1'(1'(1'(1'(0'(1'(2'(2'(2'(1'(2'(0'(1'(2'(0'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 2'(0'(0'(0'(0'(1'(1'(2'(0'(1'(2'(2'(1'(0'(2'(0'(2'(2'(2'(0'(1'(0'(1'(1'(1'(1'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 1'(2'(0'(1'(1'(1'(0'(1'(2'(0'(2'(2'(1'(1'(0'(2'(1'(1'(1'(1'(0'(0'(1'(0'(1'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 1'(1'(2'(1'(0'(1'(2'(1'(2'(1'(1'(1'(2'(1'(1'(1'(1'(2'(2'(1'(0'(1'(1'(2'(0'(1'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 1'(1'(1'(2'(2'(1'(1'(1'(2'(1'(2'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(1'(0'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 1'(1'(1'(0'(1'(2'(0'(0'(1'(1'(2'(1'(2'(2'(1'(1'(1'(1'(2'(1'(2'(1'(2'(1'(1'(2'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 1'(1'(0'(0'(1'(1'(1'(0'(0'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(1'(1'(1'(1'(1'(1'(0'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 0'(1'(0'(2'(2'(0'(0'(0'(1'(1'(2'(0'(1'(1'(0'(2'(0'(1'(1'(1'(1'(1'(0'(1'(0'(2'(2'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 0'(0'(1'(2'(2'(2'(2'(1'(1'(2'(2'(2'(1'(1'(1'(1'(1'(1'(1'(1'(1'(0'(2'(0'(1'(0'(1'(z - 22))))))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 0 }-> 0 :|: z >= 0 2'(z) -{ 0 }-> 1 + z :|: z >= 0 encArg(z) -{ 0 }-> 2'(2'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 2'(1'(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 }-> 1'(2'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1'(1'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1'(0'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 1'(0) :|: z - 1 >= 0 encArg(z) -{ 0 }-> 0'(2'(encArg(z - 2))) :|: z - 2 >= 0 encArg(z) -{ 0 }-> 0'(1'(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 :|: z >= 0 encode_0(z) -{ 0 }-> 0'(2'(encArg(z - 1))) :|: z - 1 >= 0 encode_0(z) -{ 0 }-> 0'(1'(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 :|: z >= 0 encode_1(z) -{ 0 }-> 1'(2'(encArg(z - 1))) :|: z - 1 >= 0 encode_1(z) -{ 0 }-> 1'(1'(encArg(z - 1))) :|: z - 1 >= 0 encode_1(z) -{ 0 }-> 1'(0'(encArg(z - 1))) :|: z - 1 >= 0 encode_1(z) -{ 0 }-> 1'(0) :|: z >= 0 encode_1(z) -{ 0 }-> 0 :|: z >= 0 encode_2(z) -{ 0 }-> 2'(2'(encArg(z - 1))) :|: z - 1 >= 0 encode_2(z) -{ 0 }-> 2'(1'(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 }-> 0 :|: z >= 0 ---------------------------------------- (31) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_0(v0) -> null_encode_0 [0] encode_1(v0) -> null_encode_1 [0] encode_2(v0) -> null_encode_2 [0] 0'(v0) -> null_0' [0] 1'(v0) -> null_1' [0] 2'(v0) -> null_2' [0] And the following fresh constants: null_encArg, null_encode_0, null_encode_1, null_encode_2, null_0', null_1', null_2', const ---------------------------------------- (32) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: 0'(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_1(c_0(c_0(c_1(x1))))))))))))))))))))))) -> 1'(0'(2'(2'(0'(0'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(0'(1'(2'(1'(0'(1'(1'(2'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_0(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 2'(1'(2'(1'(2'(1'(1'(1'(2'(2'(1'(2'(1'(1'(1'(0'(1'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(1'(2'(1'(1'(0'(0'(1'(2'(1'(0'(0'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(1'(1'(1'(0'(2'(1'(0'(0'(2'(1'(1'(2'(0'(2'(1'(2'(1'(2'(0'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_2(c_1(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 1'(1'(1'(2'(2'(1'(1'(1'(2'(1'(2'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(2'(0'(2'(1'(1'(1'(1'(1'(1'(2'(0'(0'(2'(1'(0'(0'(1'(2'(2'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_0(c_0(c_1(c_1(x1))))))))))))))))))))))) -> 2'(2'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(1'(1'(2'(0'(0'(1'(0'(2'(2'(1'(1'(2'(0'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 1'(0'(1'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(1'(1'(2'(2'(1'(2'(1'(1'(2'(0'(2'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_2(c_0(c_1(c_1(c_0(x1))))))))))))))))))))))) -> 0'(0'(2'(1'(1'(1'(0'(1'(2'(2'(0'(2'(0'(0'(0'(1'(0'(2'(2'(2'(1'(0'(1'(2'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 0'(2'(0'(1'(2'(2'(1'(1'(0'(0'(2'(2'(2'(1'(0'(1'(2'(0'(2'(1'(0'(2'(2'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1'(2'(2'(2'(2'(1'(1'(0'(1'(1'(0'(1'(2'(1'(0'(2'(2'(1'(1'(0'(1'(1'(1'(1'(0'(1'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(1'(2'(2'(2'(0'(1'(1'(2'(1'(1'(1'(1'(0'(1'(2'(2'(1'(2'(1'(1'(1'(0'(0'(0'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 2'(2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(1'(0'(1'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_1(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(2'(2'(1'(1'(1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(2'(1'(0'(2'(1'(1'(1'(0'(1'(0'(2'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(0'(0'(1'(0'(2'(1'(0'(2'(2'(2'(1'(0'(0'(2'(1'(1'(0'(2'(2'(2'(2'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(1'(1'(1'(2'(1'(0'(1'(1'(2'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_0(c_1(c_1(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_2(c_0(c_2(c_1(c_1(c_1(c_1(c_1(x1))))))))))))))))))))))) -> 1'(1'(0'(2'(1'(1'(0'(1'(1'(1'(1'(2'(1'(2'(1'(1'(0'(0'(1'(1'(1'(0'(2'(2'(1'(2'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 0'(2'(0'(2'(1'(1'(0'(1'(1'(1'(2'(1'(2'(0'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_1(c_0(c_2(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 2'(2'(0'(1'(1'(1'(2'(0'(2'(2'(0'(1'(1'(0'(0'(1'(1'(1'(0'(1'(1'(1'(0'(1'(2'(1'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_2(c_1(c_0(c_2(c_0(c_1(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_2(c_1(c_0(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(1'(1'(1'(0'(0'(0'(1'(1'(1'(0'(0'(2'(0'(0'(2'(0'(0'(2'(1'(1'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 1'(2'(1'(0'(0'(1'(1'(0'(1'(1'(1'(1'(2'(1'(1'(2'(1'(1'(1'(0'(1'(1'(0'(2'(2'(2'(0'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(2'(2'(2'(2'(2'(1'(1'(2'(2'(0'(1'(2'(1'(0'(1'(0'(1'(2'(2'(1'(1'(0'(2'(1'(0'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(x1))))))))))))))))))))))) -> 1'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(0'(1'(0'(2'(2'(1'(0'(1'(0'(1'(2'(1'(2'(0'(2'(2'(1'(x1))))))))))))))))))))))))))) [1] 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2'(c_1(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_2(c_2(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 2'(1'(1'(0'(1'(2'(1'(1'(0'(1'(2'(1'(1'(0'(2'(1'(0'(1'(1'(2'(2'(2'(2'(1'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_1(c_0(c_1(c_0(c_0(c_1(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_0(c_1(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(1'(1'(1'(0'(2'(2'(2'(2'(2'(0'(1'(1'(2'(1'(2'(2'(1'(2'(0'(0'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_0(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1'(2'(1'(2'(1'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(2'(0'(2'(1'(0'(2'(1'(0'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_1(c_1(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_1(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 2'(2'(1'(1'(1'(2'(1'(1'(0'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(2'(x1))))))))))))))))))))))))))) [1] 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0'(c_1(c_0(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_1(c_1(c_1(c_2(c_1(c_0(c_1(c_2(c_2(c_0(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(2'(2'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(2'(1'(1'(1'(0'(2'(0'(2'(1'(0'(2'(2'(0'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_2(c_2(c_2(c_1(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_1(c_0(c_1(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(0'(2'(0'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(2'(1'(1'(0'(1'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(2'(1'(2'(1'(0'(1'(0'(2'(2'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(2'(0'(2'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 2'(1'(0'(0'(0'(1'(0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(2'(2'(1'(1'(2'(0'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_1(c_2(c_2(c_1(c_1(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(1'(1'(0'(0'(0'(1'(2'(2'(2'(1'(1'(1'(1'(0'(2'(2'(2'(2'(2'(0'(1'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))) -> 1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(1'(1'(0'(0'(2'(2'(0'(0'(2'(2'(0'(2'(1'(1'(1'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_2(c_2(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_2(c_0(c_1(c_2(c_2(x1))))))))))))))))))))))) -> 1'(2'(1'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(0'(2'(2'(1'(2'(2'(2'(2'(2'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 1'(2'(1'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(2'(1'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_2(c_0(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 0'(1'(0'(2'(2'(0'(0'(0'(1'(1'(2'(0'(1'(1'(0'(2'(0'(1'(1'(1'(1'(1'(0'(1'(0'(2'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(x1))))))))))))))))))))))) -> 0'(2'(1'(2'(1'(2'(2'(1'(1'(0'(0'(2'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(2'(0'(2'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_2(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(2'(2'(0'(0'(2'(2'(2'(1'(2'(1'(1'(1'(1'(0'(2'(2'(2'(0'(1'(0'(2'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(1'(0'(1'(1'(0'(2'(1'(1'(1'(0'(1'(0'(0'(2'(1'(1'(1'(0'(2'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 0'(1'(0'(2'(2'(2'(2'(1'(0'(0'(2'(1'(1'(2'(2'(1'(0'(2'(1'(0'(2'(1'(2'(2'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 2'(2'(2'(1'(0'(1'(1'(0'(2'(2'(0'(0'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(2'(0'(2'(2'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_2(c_1(c_0(c_1(c_1(c_1(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 1'(1'(0'(0'(1'(1'(1'(0'(0'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(1'(1'(1'(1'(1'(1'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_1(c_2(c_0(c_1(c_0(c_0(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 1'(2'(0'(1'(0'(0'(2'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(2'(1'(0'(2'(0'(0'(0'(1'(1'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_1(c_1(c_1(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_2(x1))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(2'(0'(0'(1'(0'(0'(0'(1'(1'(1'(2'(0'(2'(2'(2'(2'(1'(1'(1'(1'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_1(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_2(c_2(c_1(c_2(c_2(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(2'(0'(2'(0'(1'(0'(0'(2'(2'(2'(2'(0'(2'(2'(1'(2'(1'(1'(1'(1'(1'(2'(2'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 1'(0'(1'(2'(1'(2'(1'(1'(0'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(0'(0'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 0'(2'(2'(2'(0'(2'(2'(0'(0'(1'(1'(1'(0'(1'(0'(2'(1'(1'(0'(2'(0'(1'(2'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_2(c_1(x1))))))))))))))))))))))) -> 2'(1'(0'(2'(1'(2'(2'(1'(0'(2'(1'(0'(2'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(1'(2'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(x1))))))))))))))))))))))) -> 0'(2'(0'(2'(2'(0'(2'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(x1))))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_1(c_0(c_1(c_1(c_0(c_0(c_1(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_0(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(0'(0'(0'(2'(0'(2'(1'(2'(2'(2'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(0'(0'(0'(2'(x1))))))))))))))))))))))))))) [1] 2'(c_1(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_0(c_0(c_1(c_2(c_2(c_0(c_1(x1))))))))))))))))))))))) -> 2'(2'(1'(2'(2'(2'(2'(1'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(2'(2'(2'(1'(0'(0'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_0(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(0'(2'(2'(2'(0'(0'(2'(1'(0'(2'(0'(x1))))))))))))))))))))))))))) [1] 1'(c_0(c_0(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_1(x1))))))))))))))))))))))) -> 1'(1'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(2'(2'(1'(2'(2'(0'(2'(1'(1'(2'(2'(0'(0'(1'(x1))))))))))))))))))))))))))) [1] encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0] encArg(cons_1(x_1)) -> 1'(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_2(x_1) -> 2'(encArg(x_1)) [0] 0'(x0) -> c_0(x0) [0] 1'(x0) -> c_1(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_2(v0) -> null_encode_2 [0] 0'(v0) -> null_0' [0] 1'(v0) -> null_1' [0] 2'(v0) -> null_2' [0] The TRS has the following type information: 0' :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' -> c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' c_1 :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' -> c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' c_0 :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' -> c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' c_2 :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' -> c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' 1' :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' -> c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' 2' :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' -> c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' encArg :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' cons_0 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 cons_1 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 cons_2 :: cons_0:cons_1:cons_2 -> cons_0:cons_1:cons_2 encode_0 :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' encode_1 :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' encode_2 :: cons_0:cons_1:cons_2 -> c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_encArg :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_encode_0 :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_encode_1 :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_encode_2 :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_0' :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_1' :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_2' :: c_1:c_0:c_2:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' const :: cons_0:cons_1:cons_2 Rewrite Strategy: INNERMOST ---------------------------------------- (33) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: null_encArg => 0 null_encode_0 => 0 null_encode_1 => 0 null_encode_2 => 0 null_0' => 0 null_1' => 0 null_2' => 0 const => 0 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: 0'(z) -{ 1 }-> 2'(1'(0'(2'(1'(1'(1'(1'(2'(1'(2'(1'(1'(2'(1'(1'(1'(2'(1'(1'(2'(2'(2'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 2'(1'(0'(0'(0'(1'(0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(2'(2'(1'(1'(2'(0'(1'(1'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 2'(0'(2'(2'(1'(1'(1'(0'(0'(1'(1'(1'(0'(1'(1'(2'(1'(1'(0'(1'(1'(1'(1'(2'(2'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 2'(0'(2'(1'(0'(0'(1'(1'(1'(0'(2'(1'(1'(1'(1'(2'(1'(1'(2'(2'(2'(1'(1'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(2'(2'(2'(1'(1'(0'(1'(1'(0'(1'(2'(1'(0'(2'(2'(1'(1'(0'(1'(1'(1'(1'(0'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(2'(1'(1'(2'(1'(1'(1'(1'(0'(0'(0'(1'(1'(0'(0'(0'(2'(1'(1'(0'(2'(2'(2'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(2'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(2'(1'(1'(1'(0'(2'(0'(2'(1'(0'(2'(2'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(1'(1'(1'(2'(0'(2'(1'(2'(2'(2'(1'(1'(2'(1'(1'(0'(1'(0'(1'(2'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(1'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(2'(1'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(0'(1'(0'(0'(2'(1'(1'(2'(1'(0'(0'(1'(1'(1'(1'(2'(1'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(2'(2'(1'(1'(2'(0'(1'(0'(2'(1'(2'(0'(1'(1'(1'(2'(1'(0'(1'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(1'(2'(1'(1'(0'(0'(1'(1'(0'(1'(2'(1'(1'(1'(1'(1'(0'(1'(2'(2'(1'(1'(2'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(1'(1'(2'(0'(2'(2'(2'(1'(0'(2'(0'(2'(2'(2'(2'(1'(0'(1'(2'(1'(0'(0'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(1'(1'(2'(0'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(0'(2'(2'(2'(0'(0'(2'(1'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(1'(0'(1'(0'(2'(1'(2'(2'(1'(1'(2'(0'(1'(1'(1'(2'(0'(2'(1'(1'(2'(1'(1'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(0'(1'(1'(1'(1'(0'(2'(2'(2'(2'(2'(0'(1'(1'(2'(1'(2'(2'(1'(2'(0'(0'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(0'(2'(2'(0'(0'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(0'(1'(2'(1'(0'(1'(1'(2'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(0'(2'(0'(0'(1'(2'(2'(2'(1'(1'(1'(0'(1'(2'(1'(2'(1'(1'(1'(1'(2'(2'(1'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(0'(1'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(1'(2'(1'(1'(0'(0'(1'(2'(1'(0'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(0'(1'(0'(1'(1'(1'(0'(1'(1'(1'(2'(2'(1'(1'(2'(2'(1'(2'(1'(1'(2'(0'(2'(2'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(2'(0'(2'(2'(0'(0'(1'(1'(1'(0'(1'(0'(2'(1'(1'(0'(2'(0'(1'(2'(1'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(1'(2'(1'(2'(2'(1'(1'(0'(0'(2'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(2'(0'(2'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(1'(1'(1'(0'(2'(1'(1'(0'(1'(2'(1'(0'(2'(2'(2'(1'(1'(0'(1'(1'(0'(1'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(0'(2'(2'(0'(2'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(0'(0'(1'(1'(1'(1'(1'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(0'(2'(1'(1'(0'(1'(1'(1'(2'(1'(2'(0'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(2'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(0'(1'(2'(2'(1'(1'(0'(0'(2'(2'(2'(1'(0'(1'(2'(0'(2'(1'(0'(2'(2'(1'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(0'(1'(1'(2'(2'(2'(1'(1'(0'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(1'(1'(2'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(2'(2'(2'(0'(1'(1'(2'(1'(1'(1'(1'(0'(1'(2'(2'(1'(2'(1'(1'(1'(0'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(2'(1'(2'(2'(2'(2'(1'(2'(2'(1'(1'(2'(1'(2'(0'(2'(1'(0'(1'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(1'(0'(2'(1'(1'(1'(0'(1'(1'(1'(0'(2'(1'(1'(1'(0'(0'(0'(2'(1'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(0'(1'(2'(0'(0'(2'(2'(2'(1'(2'(2'(2'(2'(2'(0'(1'(1'(0'(1'(1'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(0'(2'(2'(2'(0'(2'(1'(1'(0'(1'(0'(2'(2'(0'(1'(1'(0'(0'(2'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(0'(1'(1'(1'(1'(0'(2'(1'(2'(0'(1'(1'(2'(0'(1'(1'(1'(1'(1'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(0'(2'(2'(2'(2'(1'(0'(0'(2'(1'(1'(2'(2'(1'(0'(2'(1'(0'(2'(1'(2'(2'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(0'(2'(1'(1'(1'(0'(1'(2'(2'(0'(2'(0'(0'(0'(1'(0'(2'(2'(2'(1'(0'(1'(2'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(0'(2'(1'(0'(1'(1'(1'(1'(2'(0'(1'(0'(0'(0'(1'(0'(1'(1'(1'(1'(1'(1'(1'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(0'(0'(2'(0'(0'(2'(1'(1'(1'(0'(2'(2'(2'(2'(1'(0'(1'(1'(1'(2'(1'(0'(1'(0'(0'(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 + x1))))))))))))))))))))) 0'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 0'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 1'(z) -{ 1 }-> 1'(2'(2'(1'(1'(1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(2'(1'(0'(2'(1'(1'(1'(0'(1'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(2'(1'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(2'(0'(2'(1'(0'(2'(1'(0'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(1'(2'(0'(1'(1'(1'(2'(1'(1'(1'(2'(2'(1'(1'(1'(1'(1'(0'(0'(2'(1'(2'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(1'(1'(0'(2'(0'(2'(0'(0'(2'(1'(0'(2'(1'(1'(1'(1'(1'(0'(0'(0'(1'(0'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(1'(1'(0'(0'(1'(1'(1'(1'(0'(2'(2'(2'(2'(1'(0'(0'(1'(2'(1'(1'(1'(0'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(1'(0'(2'(2'(1'(1'(1'(1'(1'(1'(1'(2'(2'(2'(1'(0'(0'(1'(1'(1'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(1'(0'(1'(1'(2'(1'(2'(0'(2'(1'(1'(1'(0'(1'(1'(1'(0'(1'(0'(1'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(0'(2'(2'(1'(2'(2'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(1'(0'(0'(1'(1'(0'(1'(1'(1'(1'(2'(1'(1'(2'(1'(1'(1'(0'(1'(1'(0'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(2'(0'(1'(0'(2'(1'(1'(2'(2'(2'(1'(1'(1'(2'(2'(1'(1'(1'(2'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(2'(2'(2'(1'(2'(0'(2'(1'(1'(1'(1'(1'(1'(2'(0'(0'(2'(1'(0'(0'(1'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(2'(2'(2'(1'(2'(0'(0'(1'(0'(0'(0'(1'(1'(1'(2'(0'(2'(2'(2'(2'(1'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(2'(1'(2'(1'(0'(1'(0'(2'(2'(1'(1'(0'(1'(2'(1'(1'(1'(1'(0'(2'(0'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(2'(2'(1'(2'(2'(0'(2'(1'(1'(2'(2'(0'(0'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(0'(1'(1'(1'(0'(0'(1'(0'(0'(0'(2'(1'(1'(1'(1'(1'(1'(1'(0'(1'(2'(0'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(0'(2'(2'(0'(0'(2'(2'(2'(1'(2'(1'(1'(1'(1'(0'(2'(2'(2'(0'(1'(0'(2'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(0'(1'(2'(2'(1'(2'(0'(1'(1'(2'(1'(1'(0'(1'(2'(2'(0'(1'(1'(1'(0'(1'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(0'(0'(0'(2'(0'(1'(2'(1'(0'(0'(1'(1'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(0'(0'(2'(1'(2'(1'(0'(0'(1'(1'(2'(2'(1'(1'(1'(1'(2'(1'(1'(1'(1'(0'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(0'(0'(0'(2'(0'(2'(1'(2'(2'(2'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(0'(0'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(2'(1'(1'(0'(1'(1'(1'(1'(2'(1'(2'(1'(1'(0'(0'(1'(1'(1'(0'(2'(2'(1'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(2'(1'(1'(0'(1'(0'(1'(1'(1'(0'(0'(2'(1'(0'(2'(1'(1'(0'(2'(1'(0'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(2'(0'(1'(2'(2'(0'(1'(1'(1'(1'(1'(0'(1'(2'(1'(1'(2'(0'(2'(2'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(2'(1'(2'(1'(1'(2'(2'(0'(2'(1'(0'(0'(1'(1'(1'(2'(0'(0'(1'(2'(1'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(2'(0'(2'(0'(1'(0'(0'(2'(2'(2'(2'(0'(2'(2'(1'(2'(1'(1'(1'(1'(1'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(1'(1'(1'(0'(2'(1'(0'(0'(2'(1'(1'(2'(0'(2'(1'(2'(1'(2'(0'(1'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(1'(1'(0'(0'(0'(1'(2'(2'(2'(1'(1'(1'(1'(0'(2'(2'(2'(2'(2'(0'(1'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(0'(0'(1'(1'(1'(1'(1'(1'(2'(1'(0'(0'(0'(2'(1'(0'(0'(1'(0'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(0'(2'(0'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(2'(1'(1'(0'(1'(1'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(0'(0'(1'(0'(2'(1'(0'(2'(2'(2'(1'(0'(0'(2'(1'(1'(0'(2'(2'(2'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(2'(1'(0'(1'(0'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(1'(1'(1'(2'(2'(1'(2'(1'(0'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(1'(2'(1'(2'(1'(1'(0'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(0'(0'(0'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(1'(2'(1'(1'(2'(1'(0'(0'(1'(1'(0'(0'(2'(2'(0'(0'(2'(2'(0'(2'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(1'(1'(1'(1'(0'(0'(0'(1'(1'(1'(0'(0'(2'(0'(0'(2'(0'(0'(2'(1'(1'(1'(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 + x1))))))))))))))))))))) 1'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 1'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 2'(z) -{ 1 }-> 2'(2'(2'(2'(2'(2'(1'(1'(2'(2'(0'(1'(2'(1'(0'(1'(0'(1'(2'(2'(1'(1'(0'(2'(1'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(2'(2'(2'(2'(1'(1'(1'(2'(2'(2'(0'(2'(2'(1'(1'(2'(2'(2'(0'(1'(0'(1'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(2'(1'(0'(1'(1'(0'(2'(2'(0'(0'(1'(1'(1'(1'(1'(1'(0'(1'(1'(1'(2'(0'(2'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(1'(2'(2'(2'(2'(1'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(2'(2'(2'(1'(0'(0'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(1'(0'(1'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(1'(1'(1'(2'(1'(1'(0'(2'(1'(1'(1'(1'(0'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(1'(1'(1'(2'(1'(0'(2'(0'(1'(1'(2'(2'(0'(1'(1'(0'(1'(2'(0'(1'(0'(2'(1'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(1'(1'(1'(1'(1'(2'(0'(2'(1'(1'(2'(2'(1'(2'(1'(1'(1'(1'(1'(2'(1'(2'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(0'(1'(1'(1'(2'(0'(2'(2'(0'(1'(1'(0'(0'(1'(1'(1'(0'(1'(1'(1'(0'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(0'(1'(1'(0'(2'(2'(1'(1'(2'(1'(1'(1'(1'(2'(0'(0'(1'(0'(2'(2'(1'(1'(2'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(2'(0'(1'(0'(1'(1'(0'(2'(2'(1'(1'(1'(1'(2'(1'(2'(0'(1'(1'(1'(2'(1'(0'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(2'(2'(1'(0'(1'(1'(0'(1'(0'(1'(0'(2'(2'(1'(0'(1'(0'(1'(2'(1'(2'(0'(2'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(2'(1'(2'(1'(1'(1'(2'(2'(1'(2'(1'(1'(1'(0'(1'(1'(1'(2'(1'(0'(0'(1'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(1'(1'(1'(0'(1'(1'(2'(2'(2'(1'(1'(2'(1'(1'(2'(1'(0'(2'(0'(2'(0'(2'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(1'(0'(1'(2'(1'(1'(0'(1'(2'(1'(1'(0'(2'(1'(0'(1'(1'(2'(2'(2'(2'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(1'(0'(1'(1'(0'(2'(1'(1'(1'(0'(1'(0'(0'(2'(1'(1'(1'(0'(2'(0'(0'(1'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(0'(2'(1'(2'(2'(1'(0'(2'(1'(0'(2'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(0'(0'(2'(2'(1'(2'(1'(2'(1'(1'(1'(1'(0'(1'(2'(2'(2'(1'(2'(0'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(0'(0'(0'(0'(1'(1'(2'(0'(1'(2'(2'(1'(0'(2'(0'(2'(2'(2'(0'(1'(0'(1'(1'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(2'(0'(1'(1'(1'(0'(1'(2'(0'(2'(2'(1'(1'(0'(2'(1'(1'(1'(1'(0'(0'(1'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(2'(1'(0'(1'(2'(1'(2'(1'(1'(1'(2'(1'(1'(1'(1'(2'(2'(1'(0'(1'(1'(2'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(1'(2'(2'(1'(1'(1'(2'(1'(2'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(1'(0'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(1'(0'(1'(2'(0'(0'(1'(1'(2'(1'(2'(2'(1'(1'(1'(1'(2'(1'(2'(1'(2'(1'(1'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(0'(0'(1'(1'(1'(0'(0'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(1'(1'(1'(1'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 0'(1'(0'(2'(2'(0'(0'(0'(1'(1'(2'(0'(1'(1'(0'(2'(0'(1'(1'(1'(1'(1'(0'(1'(0'(2'(2'(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 + x1))))))))))))))))))))) 2'(z) -{ 1 }-> 0'(0'(1'(2'(2'(2'(2'(1'(1'(2'(2'(2'(1'(1'(1'(1'(1'(1'(1'(1'(1'(0'(2'(0'(1'(0'(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 + x1))))))))))))))))))))) 2'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 2'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 encArg(z) -{ 0 }-> 2'(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0 encArg(z) -{ 0 }-> 1'(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 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 }-> 1'(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_2(z) -{ 0 }-> 2'(encArg(x_1)) :|: x_1 >= 0, z = x_1 encode_2(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (35) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(z0))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(z0))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(z0))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(z0))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(z0))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(z0))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(z0))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(z0))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(z0))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(z0))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(z0))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(z0))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(z0))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(z0))))))))))))))))))))))))))) 0(1(0(1(1(2(1(1(1(0(0(1(2(0(0(2(2(0(1(0(2(0(0(z0))))))))))))))))))))))) -> 0(1(1(1(0(1(2(0(0(2(2(2(1(2(2(2(2(2(0(1(1(0(1(1(1(1(0(z0))))))))))))))))))))))))))) 0(1(0(1(1(2(2(0(1(0(2(1(0(0(0(1(1(2(2(2(0(2(2(z0))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(z0))))))))))))))))))))))))))) 0(1(0(1(2(0(0(1(1(2(0(0(2(1(0(2(1(0(1(1(0(1(2(z0))))))))))))))))))))))) -> 0(1(1(1(2(1(2(2(2(2(1(2(2(1(1(2(1(2(0(2(1(0(1(1(1(1(2(z0))))))))))))))))))))))))))) 0(1(0(1(2(1(2(1(0(2(0(1(0(0(2(0(0(2(1(1(0(0(1(z0))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(z0))))))))))))))))))))))))))) 0(1(0(2(0(0(0(1(0(2(1(2(2(0(1(0(2(2(1(0(1(2(1(z0))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(z0))))))))))))))))))))))))))) 0(1(0(2(0(1(0(0(1(0(2(1(2(2(0(1(1(0(2(0(0(1(0(z0))))))))))))))))))))))) -> 0(1(1(0(1(1(1(1(0(2(1(2(0(1(1(2(0(1(1(1(1(1(2(2(1(1(0(z0))))))))))))))))))))))))))) 0(1(0(2(1(0(2(2(0(0(2(2(2(0(2(1(0(2(2(0(2(1(2(z0))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(1(0(2(1(1(2(0(1(0(2(1(2(0(2(1(0(1(1(1(z0))))))))))))))))))))))))))) 0(1(1(0(0(2(0(2(2(1(1(1(1(1(1(2(2(0(1(2(0(1(0(z0))))))))))))))))))))))) -> 0(2(1(1(1(0(2(1(1(0(1(2(1(0(2(2(2(1(1(0(1(1(0(1(1(1(0(z0))))))))))))))))))))))))))) 0(1(1(0(1(1(1(2(1(0(0(0(1(0(2(1(1(2(1(2(0(0(2(z0))))))))))))))))))))))) -> 1(0(1(1(1(1(1(0(2(2(1(1(1(0(2(1(2(1(1(0(0(1(2(1(0(0(1(z0))))))))))))))))))))))))))) 0(1(1(1(2(0(2(0(0(1(0(2(0(1(2(2(1(0(2(2(2(0(2(z0))))))))))))))))))))))) -> 1(1(1(1(2(0(1(1(1(1(1(1(0(0(1(0(0(2(2(2(0(0(2(1(0(2(0(z0))))))))))))))))))))))))))) 0(1(2(0(1(0(2(0(0(2(1(2(2(1(0(2(0(1(1(1(1(2(0(z0))))))))))))))))))))))) -> 1(0(1(0(1(1(1(0(1(1(1(2(2(1(1(2(2(1(2(1(1(2(0(2(2(2(2(z0))))))))))))))))))))))))))) 0(1(2(0(1(2(1(0(2(1(2(0(2(2(2(1(1(2(0(1(2(0(1(z0))))))))))))))))))))))) -> 2(1(0(0(0(1(0(2(2(1(1(2(2(2(1(1(2(2(1(1(2(0(1(1(0(2(1(z0))))))))))))))))))))))))))) 0(1(2(0(2(2(1(2(1(1(0(2(0(1(2(2(2(0(2(0(1(2(0(z0))))))))))))))))))))))) -> 0(2(1(2(1(2(2(1(1(0(0(2(2(1(1(1(1(0(2(2(1(1(2(0(2(2(2(z0))))))))))))))))))))))))))) 0(1(2(1(0(1(0(1(2(2(1(2(1(0(2(2(1(0(1(0(1(0(2(z0))))))))))))))))))))))) -> 0(1(1(1(2(2(2(0(1(1(2(1(1(1(1(0(1(2(2(1(2(1(1(1(0(0(0(z0))))))))))))))))))))))))))) 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2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(z0))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(z0))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(z0))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(z0))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(z0))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(z0))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(z0))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(z0))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(z0))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(z0))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(z0))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(z0))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(z0))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(z0))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(z0))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))) Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(2'(encArg(z0)), ENCARG(z0)) ENCODE_0(z0) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCODE_1(z0) -> c4(1'(encArg(z0)), ENCARG(z0)) ENCODE_2(z0) -> c5(2'(encArg(z0)), ENCARG(z0)) 0'(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> c6(0'(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))), 2'(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))), 1'(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))), 2'(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))), 2'(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))), 2'(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))), 1'(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))), 0'(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))), 1'(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))), 1'(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))), 1'(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))), 1'(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))), 1'(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))), 0'(1(1(1(1(1(1(2(1(2(1(z0))))))))))), 1'(1(1(1(1(1(2(1(2(1(z0)))))))))), 1'(1(1(1(1(2(1(2(1(z0))))))))), 1'(1(1(1(2(1(2(1(z0)))))))), 1'(1(1(2(1(2(1(z0))))))), 1'(1(2(1(2(1(z0)))))), 1'(2(1(2(1(z0))))), 2'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> c7(1'(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))), 1'(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))))), 1'(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))), 2'(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))), 1'(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))), 1'(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))), 0'(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))), 0'(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))), 1'(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))), 1'(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))), 0'(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))), 1'(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))), 2'(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))), 1'(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))), 1'(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))), 1'(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))), 1'(1(0(1(2(2(1(1(2(0(0(z0))))))))))), 1'(0(1(2(2(1(1(2(0(0(z0)))))))))), 0'(1(2(2(1(1(2(0(0(z0))))))))), 1'(2(2(1(1(2(0(0(z0)))))))), 2'(2(1(1(2(0(0(z0))))))), 2'(1(1(2(0(0(z0)))))), 1'(1(2(0(0(z0))))), 1'(2(0(0(z0)))), 2'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> c8(2'(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))), 0'(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))))), 2'(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))), 1'(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))), 0'(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))), 1'(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))), 1'(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))), 1'(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))), 0'(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))), 2'(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))), 1'(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))), 1'(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))), 1'(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))), 1'(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))), 2'(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(z0))))))))))), 1'(2(2(2(1(1(0(1(1(1(z0)))))))))), 2'(2(2(1(1(0(1(1(1(z0))))))))), 2'(2(1(1(0(1(1(1(z0)))))))), 2'(1(1(0(1(1(1(z0))))))), 1'(1(0(1(1(1(z0)))))), 1'(0(1(1(1(z0))))), 0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> c9(0'(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))), 1'(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))))), 1'(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))), 1'(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))), 1'(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))), 0'(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))), 2'(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))), 1'(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))), 1'(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))), 0'(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))), 1'(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))), 1'(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))), 1'(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))), 0'(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))), 2'(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))), 1'(1(1(0(0(0(2(1(0(2(1(z0))))))))))), 1'(1(0(0(0(2(1(0(2(1(z0)))))))))), 1'(0(0(0(2(1(0(2(1(z0))))))))), 0'(0(0(2(1(0(2(1(z0)))))))), 0'(0(2(1(0(2(1(z0))))))), 0'(2(1(0(2(1(z0)))))), 2'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(z0))))))))))))))))))))))) -> c10(0'(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))))), 0'(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))))))), 2'(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))), 1'(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))))), 0'(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))), 1'(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))), 1'(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))), 1'(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))), 1'(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))), 2'(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))), 0'(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))), 1'(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))), 0'(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))), 0'(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))), 0'(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))), 1'(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))), 0'(1(1(1(1(1(1(1(0(1(0(z0))))))))))), 1'(1(1(1(1(1(1(0(1(0(z0)))))))))), 1'(1(1(1(1(1(0(1(0(z0))))))))), 1'(1(1(1(1(0(1(0(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))), 1'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(z0))))))))))))))))))))))) -> c11(1'(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))))))), 1'(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0)))))))))))))))))))))))))), 1'(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))))), 0'(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0)))))))))))))))))))))))), 1'(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))), 0'(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0)))))))))))))))))))))), 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1'(0(z0)), 0'(z0)) S tuples: 0'(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> c6(0'(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))), 2'(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))), 1'(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))), 2'(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))), 2'(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))), 2'(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))), 1'(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))), 0'(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))), 1'(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))), 1'(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))), 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2'(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))), 1'(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))), 1'(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))), 2'(1(0(2(0(2(0(2(2(1(0(z0))))))))))), 1'(0(2(0(2(0(2(2(1(0(z0)))))))))), 0'(2(0(2(0(2(2(1(0(z0))))))))), 2'(0(2(0(2(2(1(0(z0)))))))), 0'(2(0(2(2(1(0(z0))))))), 2'(0(2(2(1(0(z0)))))), 0'(2(2(1(0(z0))))), 2'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> c102(2'(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))), 2'(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))))), 1'(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))), 1'(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))), 1'(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))), 2'(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))), 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2'(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))))), 0'(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))), 1'(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))), 1'(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))), 0'(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))), 2'(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))), 2'(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))), 1'(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))), 1'(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))), 2'(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))), 1'(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))), 1'(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))), 1'(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))), 1'(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))), 2'(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))), 0'(0(1(0(2(2(1(1(2(0(1(z0))))))))))), 0'(1(0(2(2(1(1(2(0(1(z0)))))))))), 1'(0(2(2(1(1(2(0(1(z0))))))))), 0'(2(2(1(1(2(0(1(z0)))))))), 2'(2(1(1(2(0(1(z0))))))), 2'(1(1(2(0(1(z0)))))), 1'(1(2(0(1(z0))))), 1'(2(0(1(z0)))), 2'(0(1(z0))), 0'(1(z0)), 1'(z0)) 2'(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> c104(2'(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))), 2'(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))), 1'(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))), 1'(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))), 1'(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))), 2'(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))), 0'(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))), 2'(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))), 2'(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))), 0'(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))), 1'(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))), 1'(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))), 0'(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))), 0'(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))), 1'(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))), 1'(1(0(1(1(1(0(1(2(1(0(z0))))))))))), 1'(0(1(1(1(0(1(2(1(0(z0)))))))))), 0'(1(1(1(0(1(2(1(0(z0))))))))), 1'(1(1(0(1(2(1(0(z0)))))))), 1'(1(0(1(2(1(0(z0))))))), 1'(0(1(2(1(0(z0)))))), 0'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) K tuples:none Defined Rule Symbols: 0_1, 1_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_2_1 Defined Pair Symbols: ENCARG_1, ENCODE_0_1, ENCODE_1_1, ENCODE_2_1, 0'_1, 1'_1, 2'_1 Compound Symbols: c_2, c1_2, c2_2, c3_2, c4_2, c5_2, c6_27, c7_27, c8_27, c9_27, c10_27, c11_27, c12_27, c13_27, c14_27, c15_27, c16_27, c17_27, c18_27, c19_27, c20_27, c21_27, c22_27, c23_27, c24_27, c25_27, c26_27, c27_27, c28_27, c29_27, c30_27, c31_27, c32_27, c33_27, c34_27, c35_27, c36_27, c37_27, c38_27, c39_27, c40_27, c41_27, c42_27, c43_27, c44_27, c45_27, c46_27, c47_27, c48_27, c49_27, c50_27, c51_27, c52_27, c53_27, c54_27, c55_27, c56_27, c57_27, c58_27, c59_27, c60_27, c61_27, c62_27, c63_27, c64_27, c65_27, c66_27, c67_27, c68_27, c69_27, c70_27, c71_27, c72_27, c73_27, c74_27, c75_27, c76_27, c77_27, c78_27, c79_27, c80_27, c81_27, c82_27, c83_27, c84_27, c85_27, c86_27, c87_27, c88_27, c89_27, c90_27, c91_27, c92_27, c93_27, c94_27, c95_27, c96_27, c97_27, c98_27, c99_27, c100_27, c101_27, c102_27, c103_27, c104_27 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 98 trailing tuple parts ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(z0))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(z0))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(z0))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(z0))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(z0))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(z0))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(z0))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(z0))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(z0))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(z0))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(z0))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(z0))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(z0))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(z0))))))))))))))))))))))))))) 0(1(0(1(1(2(1(1(1(0(0(1(2(0(0(2(2(0(1(0(2(0(0(z0))))))))))))))))))))))) -> 0(1(1(1(0(1(2(0(0(2(2(2(1(2(2(2(2(2(0(1(1(0(1(1(1(1(0(z0))))))))))))))))))))))))))) 0(1(0(1(1(2(2(0(1(0(2(1(0(0(0(1(1(2(2(2(0(2(2(z0))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(z0))))))))))))))))))))))))))) 0(1(0(1(2(0(0(1(1(2(0(0(2(1(0(2(1(0(1(1(0(1(2(z0))))))))))))))))))))))) -> 0(1(1(1(2(1(2(2(2(2(1(2(2(1(1(2(1(2(0(2(1(0(1(1(1(1(2(z0))))))))))))))))))))))))))) 0(1(0(1(2(1(2(1(0(2(0(1(0(0(2(0(0(2(1(1(0(0(1(z0))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(z0))))))))))))))))))))))))))) 0(1(0(2(0(0(0(1(0(2(1(2(2(0(1(0(2(2(1(0(1(2(1(z0))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(z0))))))))))))))))))))))))))) 0(1(0(2(0(1(0(0(1(0(2(1(2(2(0(1(1(0(2(0(0(1(0(z0))))))))))))))))))))))) -> 0(1(1(0(1(1(1(1(0(2(1(2(0(1(1(2(0(1(1(1(1(1(2(2(1(1(0(z0))))))))))))))))))))))))))) 0(1(0(2(1(0(2(2(0(0(2(2(2(0(2(1(0(2(2(0(2(1(2(z0))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(1(0(2(1(1(2(0(1(0(2(1(2(0(2(1(0(1(1(1(z0))))))))))))))))))))))))))) 0(1(1(0(0(2(0(2(2(1(1(1(1(1(1(2(2(0(1(2(0(1(0(z0))))))))))))))))))))))) -> 0(2(1(1(1(0(2(1(1(0(1(2(1(0(2(2(2(1(1(0(1(1(0(1(1(1(0(z0))))))))))))))))))))))))))) 0(1(1(0(1(1(1(2(1(0(0(0(1(0(2(1(1(2(1(2(0(0(2(z0))))))))))))))))))))))) -> 1(0(1(1(1(1(1(0(2(2(1(1(1(0(2(1(2(1(1(0(0(1(2(1(0(0(1(z0))))))))))))))))))))))))))) 0(1(1(1(2(0(2(0(0(1(0(2(0(1(2(2(1(0(2(2(2(0(2(z0))))))))))))))))))))))) -> 1(1(1(1(2(0(1(1(1(1(1(1(0(0(1(0(0(2(2(2(0(0(2(1(0(2(0(z0))))))))))))))))))))))))))) 0(1(2(0(1(0(2(0(0(2(1(2(2(1(0(2(0(1(1(1(1(2(0(z0))))))))))))))))))))))) -> 1(0(1(0(1(1(1(0(1(1(1(2(2(1(1(2(2(1(2(1(1(2(0(2(2(2(2(z0))))))))))))))))))))))))))) 0(1(2(0(1(2(1(0(2(1(2(0(2(2(2(1(1(2(0(1(2(0(1(z0))))))))))))))))))))))) -> 2(1(0(0(0(1(0(2(2(1(1(2(2(2(1(1(2(2(1(1(2(0(1(1(0(2(1(z0))))))))))))))))))))))))))) 0(1(2(0(2(2(1(2(1(1(0(2(0(1(2(2(2(0(2(0(1(2(0(z0))))))))))))))))))))))) -> 0(2(1(2(1(2(2(1(1(0(0(2(2(1(1(1(1(0(2(2(1(1(2(0(2(2(2(z0))))))))))))))))))))))))))) 0(1(2(1(0(1(0(1(2(2(1(2(1(0(2(2(1(0(1(0(1(0(2(z0))))))))))))))))))))))) -> 0(1(1(1(2(2(2(0(1(1(2(1(1(1(1(0(1(2(2(1(2(1(1(1(0(0(0(z0))))))))))))))))))))))))))) 0(1(2(1(1(2(1(2(0(1(1(0(0(2(0(1(1(0(0(2(0(0(1(z0))))))))))))))))))))))) -> 0(1(1(0(2(2(2(0(2(1(1(0(1(0(2(2(0(1(1(0(0(2(1(1(1(2(1(z0))))))))))))))))))))))))))) 0(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(z0))))))))))))))))))))))) -> 1(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))))) 0(1(2(2(1(0(2(2(1(1(1(2(0(0(2(2(0(0(1(1(2(2(1(z0))))))))))))))))))))))) -> 1(1(2(2(1(1(2(0(1(0(2(1(2(0(1(1(1(2(1(0(1(1(2(0(1(1(1(z0))))))))))))))))))))))))))) 0(1(2(2(1(1(2(0(2(1(2(0(1(2(1(2(2(2(2(0(2(0(0(z0))))))))))))))))))))))) -> 1(0(2(0(0(1(2(2(2(1(1(1(0(1(2(1(2(1(1(1(1(2(2(1(1(2(0(z0))))))))))))))))))))))))))) 0(1(2(2(2(0(0(0(0(1(0(0(2(2(0(2(0(2(2(0(1(1(0(z0))))))))))))))))))))))) -> 0(0(2(1(1(1(0(1(2(2(0(2(0(0(0(1(0(2(2(2(1(0(1(2(1(1(0(z0))))))))))))))))))))))))))) 0(2(0(1(0(0(2(1(2(1(1(2(1(2(0(1(1(0(1(0(2(0(1(z0))))))))))))))))))))))) -> 1(2(2(1(1(2(1(1(1(1(0(0(0(1(1(0(0(0(2(1(1(0(2(2(2(0(1(z0))))))))))))))))))))))))))) 0(2(0(2(0(2(0(2(1(1(0(1(2(2(1(0(1(0(0(1(0(2(1(z0))))))))))))))))))))))) -> 1(1(1(1(2(0(2(2(2(1(0(2(0(2(2(2(2(1(0(1(2(1(0(0(0(1(1(z0))))))))))))))))))))))))))) 0(2(0(2(1(0(0(2(2(2(2(0(2(1(0(1(2(0(2(1(0(0(0(z0))))))))))))))))))))))) -> 0(2(0(2(1(1(0(1(1(1(2(1(2(0(1(0(1(2(1(1(2(1(1(1(2(2(2(z0))))))))))))))))))))))))))) 0(2(1(0(1(0(0(1(1(0(2(0(0(0(1(0(1(1(0(1(0(2(1(z0))))))))))))))))))))))) -> 1(1(0(1(1(1(1(0(2(2(2(2(2(0(1(1(2(1(2(2(1(2(0(0(0(1(1(z0))))))))))))))))))))))))))) 0(2(1(2(0(1(0(0(1(0(0(2(2(2(2(2(1(0(2(0(2(2(1(z0))))))))))))))))))))))) -> 1(2(0(1(0(0(2(1(1(2(1(0(0(1(1(1(1(2(1(0(2(0(0(0(1(1(1(z0))))))))))))))))))))))))))) 0(2(1(2(0(2(2(2(2(2(2(2(0(1(0(1(0(2(1(1(0(0(0(z0))))))))))))))))))))))) -> 2(0(2(2(1(1(1(0(0(1(1(1(0(1(1(2(1(1(0(1(1(1(1(2(2(2(2(z0))))))))))))))))))))))))))) 0(2(2(2(1(2(0(1(1(2(1(2(0(0(2(1(0(1(2(2(2(0(1(z0))))))))))))))))))))))) -> 0(2(2(2(0(2(2(0(0(1(1(1(0(1(0(2(1(1(0(2(0(1(2(1(0(2(1(z0))))))))))))))))))))))))))) 1(0(0(0(1(1(0(2(0(1(1(2(1(1(2(2(1(2(1(0(0(0(2(z0))))))))))))))))))))))) -> 1(1(0(2(1(1(0(1(0(1(1(1(0(0(2(1(0(2(1(1(0(2(1(0(2(2(2(z0))))))))))))))))))))))))))) 1(0(0(1(1(2(0(1(1(2(2(2(0(1(0(2(0(2(0(1(1(2(1(z0))))))))))))))))))))))) -> 1(1(1(1(1(1(0(0(1(1(0(2(1(2(2(1(2(2(0(2(1(1(2(2(0(0(1(z0))))))))))))))))))))))))))) 1(0(1(1(2(2(2(1(2(2(1(0(2(2(1(0(1(2(2(2(1(0(0(z0))))))))))))))))))))))) -> 1(2(1(1(0(2(2(1(1(1(1(1(1(1(2(2(2(1(0(0(1(1(1(1(1(1(2(z0))))))))))))))))))))))))))) 1(0(1(2(0(2(0(0(2(1(0(2(0(1(2(1(0(2(0(2(0(0(1(z0))))))))))))))))))))))) -> 1(1(0(1(2(1(2(1(1(2(2(0(2(1(0(0(1(1(1(2(0(0(1(2(1(2(1(z0))))))))))))))))))))))))))) 1(0(1(2(2(2(1(1(1(0(1(0(2(0(1(1(0(2(1(0(1(0(0(z0))))))))))))))))))))))) -> 1(1(0(0(2(0(2(2(1(0(1(1(0(1(1(1(0(2(2(1(1(0(1(1(1(1(1(z0))))))))))))))))))))))))))) 1(0(2(1(0(2(0(1(0(0(0(1(0(2(1(2(0(0(2(2(1(0(2(z0))))))))))))))))))))))) -> 1(0(1(1(1(1(0(0(0(1(1(1(0(0(2(0(0(2(0(0(2(1(1(1(1(1(1(z0))))))))))))))))))))))))))) 1(0(2(2(0(1(2(0(1(2(1(2(1(0(1(2(0(2(2(2(1(2(2(z0))))))))))))))))))))))) -> 1(1(0(1(2(0(2(0(1(0(0(2(2(2(2(0(2(2(1(2(1(1(1(1(1(2(2(z0))))))))))))))))))))))))))) 1(1(0(0(1(0(2(1(0(0(2(1(0(0(2(0(1(2(1(0(0(0(0(z0))))))))))))))))))))))) -> 1(1(1(0(0(2(1(2(1(0(0(1(1(2(2(1(1(1(1(2(1(1(1(1(0(2(2(z0))))))))))))))))))))))))))) 1(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(z0))))))))))))))))))))))) -> 1(1(0(1(1(1(1(0(2(1(0(0(2(1(1(2(0(2(1(2(1(2(0(1(0(2(1(z0))))))))))))))))))))))))))) 1(1(0(2(0(1(2(2(2(2(0(2(1(2(1(2(0(2(1(0(2(2(0(z0))))))))))))))))))))))) -> 1(1(1(0(1(2(2(1(2(0(1(1(2(1(1(0(1(2(2(0(1(1(1(0(1(0(2(z0))))))))))))))))))))))))))) 1(1(0(2(1(0(2(2(0(0(1(1(0(1(0(0(2(1(2(1(0(1(2(z0))))))))))))))))))))))) -> 1(0(1(2(1(2(1(1(0(2(2(2(1(1(1(1(1(2(1(1(1(0(0(0(0(2(1(z0))))))))))))))))))))))))))) 1(1(0(2(1(2(1(0(0(1(1(2(2(2(0(2(2(2(1(0(2(0(2(z0))))))))))))))))))))))) -> 1(2(1(0(0(1(1(0(1(1(1(1(2(1(1(2(1(1(1(0(1(1(0(2(2(2(0(z0))))))))))))))))))))))))))) 1(1(0(2(1(2(2(2(0(2(1(0(0(1(2(0(2(1(1(1(2(0(0(z0))))))))))))))))))))))) -> 1(2(1(1(2(0(1(1(1(2(1(1(1(2(2(1(1(1(1(1(0(0(2(1(2(0(2(z0))))))))))))))))))))))))))) 1(1(1(1(2(2(0(0(1(1(1(2(1(2(0(2(2(0(0(1(2(1(1(z0))))))))))))))))))))))) -> 1(2(2(1(0(1(2(1(1(1(2(1(1(1(1(1(1(0(1(1(1(1(0(2(0(1(1(z0))))))))))))))))))))))))))) 1(1(1(2(2(1(1(1(2(2(0(2(0(1(2(0(0(2(2(2(0(0(0(z0))))))))))))))))))))))) -> 1(1(0(1(1(1(0(0(0(1(2(2(2(1(1(1(1(0(2(2(2(2(2(0(1(2(2(z0))))))))))))))))))))))))))) 1(1(2(0(2(1(1(2(1(1(1(1(1(0(0(1(2(2(2(1(2(0(0(z0))))))))))))))))))))))) -> 1(2(1(1(1(0(0(1(1(1(1(0(2(2(2(2(1(0(0(1(2(1(1(1(0(2(2(z0))))))))))))))))))))))))))) 1(1(2(1(0(1(1(0(0(1(2(0(0(0(0(0(2(0(1(1(0(0(2(z0))))))))))))))))))))))) -> 1(1(1(0(0(0(2(0(2(1(2(2(2(2(2(2(1(1(1(1(2(1(0(0(0(0(2(z0))))))))))))))))))))))))))) 1(1(2(2(2(0(1(1(2(0(2(2(2(2(2(0(1(1(2(2(1(2(1(z0))))))))))))))))))))))) -> 1(2(0(1(0(2(1(1(2(2(2(1(1(1(2(2(1(1(1(2(1(1(1(2(1(1(1(z0))))))))))))))))))))))))))) 1(1(2(2(2(0(1(1(2(1(0(0(1(0(0(2(1(2(2(0(1(2(2(z0))))))))))))))))))))))) -> 1(2(1(0(1(1(0(2(2(1(1(2(1(1(0(2(2(1(2(2(2(2(2(0(1(1(1(z0))))))))))))))))))))))))))) 1(1(2(2(2(2(1(2(2(1(0(2(2(1(1(2(2(0(0(0(0(0(0(z0))))))))))))))))))))))) -> 1(1(0(2(0(1(2(2(0(1(1(1(1(1(0(1(2(1(1(2(0(2(2(0(2(1(1(z0))))))))))))))))))))))))))) 1(2(0(0(0(0(1(1(0(2(2(2(2(1(0(1(0(0(0(2(1(0(1(z0))))))))))))))))))))))) -> 1(2(1(1(0(1(1(2(1(2(0(2(1(1(1(0(1(1(1(0(1(0(1(0(2(1(1(z0))))))))))))))))))))))))))) 1(2(0(0(1(1(1(1(0(2(2(0(2(2(0(2(0(2(1(1(1(1(1(z0))))))))))))))))))))))) -> 1(1(0(2(1(1(0(1(1(1(1(2(1(2(1(1(0(0(1(1(1(0(2(2(1(2(1(z0))))))))))))))))))))))))))) 1(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(z0))))))))))))))))))))))) -> 1(1(0(1(0(0(1(1(1(1(1(1(2(1(0(0(0(2(1(0(0(1(0(2(2(2(0(z0))))))))))))))))))))))))))) 1(2(0(1(1(1(2(2(2(1(1(1(1(2(0(0(0(2(1(2(0(0(0(z0))))))))))))))))))))))) -> 1(2(1(2(1(1(1(0(1(1(0(1(1(1(0(2(2(0(2(1(0(2(1(0(2(2(2(z0))))))))))))))))))))))))))) 1(2(0(2(0(0(1(2(2(1(1(2(1(1(1(2(1(1(2(1(0(0(0(z0))))))))))))))))))))))) -> 1(1(1(0(1(2(1(1(2(1(1(1(0(0(0(2(0(1(2(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))) 1(2(0(2(1(1(1(0(2(0(1(2(0(2(0(2(0(1(1(0(2(2(0(z0))))))))))))))))))))))) -> 1(2(2(1(1(1(0(1(2(1(1(2(1(0(0(2(1(0(2(1(1(1(0(1(0(2(0(z0))))))))))))))))))))))))))) 1(2(0(2(1(2(0(2(0(1(0(0(1(1(0(2(2(2(1(1(2(2(0(z0))))))))))))))))))))))) -> 1(1(1(1(2(1(2(1(0(1(0(2(2(1(1(0(1(2(1(1(1(1(0(2(0(2(2(z0))))))))))))))))))))))))))) 1(2(0(2(2(1(0(0(2(2(0(0(2(2(1(2(2(0(1(1(1(2(1(z0))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(2(1(1(1(1(1(1(2(0(0(2(1(0(0(1(2(2(2(1(z0))))))))))))))))))))))))))) 1(2(1(1(2(1(0(0(2(1(0(1(2(1(1(0(1(2(0(2(2(0(1(z0))))))))))))))))))))))) -> 1(2(1(1(1(0(2(0(2(0(0(2(1(0(2(1(1(1(1(1(0(0(0(1(0(1(1(z0))))))))))))))))))))))))))) 1(2(1(2(1(2(2(1(0(2(1(1(1(0(0(2(2(0(2(0(2(2(1(z0))))))))))))))))))))))) -> 1(0(2(1(0(1(0(0(1(1(1(2(0(2(2(1(1(1(1(1(2(2(1(2(1(0(1(z0))))))))))))))))))))))))))) 1(2(2(0(1(2(0(1(1(2(1(2(2(0(1(0(1(0(2(2(2(1(0(z0))))))))))))))))))))))) -> 1(1(0(0(0(1(0(2(1(0(2(2(2(1(0(0(2(1(1(0(2(2(2(2(1(1(0(z0))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(0(2(0(0(1(1(1(0(1(2(2(2(2(1(2(z0))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(0(1(0(0(0(1(1(1(2(0(2(2(2(2(1(1(1(1(2(z0))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(1(0(1(0(0(2(1(2(0(2(2(2(0(0(z0))))))))))))))))))))))) -> 1(1(1(0(2(2(0(0(2(2(2(1(2(1(1(1(1(0(2(2(2(0(1(0(2(0(2(z0))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(2(2(0(1(2(0(0(0(2(0(2(1(0(1(z0))))))))))))))))))))))) -> 1(0(1(2(1(1(2(1(0(0(1(1(0(0(2(2(0(0(2(2(0(2(1(1(1(2(1(z0))))))))))))))))))))))))))) 1(2(2(2(0(1(2(2(1(1(1(1(1(2(2(0(1(2(1(2(0(0(1(z0))))))))))))))))))))))) -> 1(1(1(1(0(1(1(1(0(0(1(0(0(0(2(1(1(1(1(1(1(1(0(1(2(0(1(z0))))))))))))))))))))))))))) 2(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> 2(0(0(0(0(1(1(2(0(1(2(2(1(0(2(0(2(2(2(0(1(0(1(1(1(1(0(z0))))))))))))))))))))))))))) 2(0(0(2(1(0(1(1(1(2(0(0(1(1(1(0(1(2(1(1(0(0(0(z0))))))))))))))))))))))) -> 1(1(0(0(1(1(1(0(0(1(0(2(1(1(1(1(1(2(1(2(1(1(1(1(1(1(0(z0))))))))))))))))))))))))))) 2(0(0(2(1(1(1(1(2(2(2(1(2(1(0(2(2(1(0(0(2(0(1(z0))))))))))))))))))))))) -> 1(1(1(2(2(1(1(1(2(1(2(0(2(2(1(1(1(1(0(2(0(2(1(1(0(2(1(z0))))))))))))))))))))))))))) 2(0(1(0(1(1(1(1(2(2(2(2(0(0(1(0(1(0(0(0(2(2(0(z0))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(1(2(2(2(0(2(2(1(1(2(2(2(0(1(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(0(1(2(0(1(1(0(2(2(2(2(0(2(1(0(2(1(2(1(0(2(1(z0))))))))))))))))))))))) -> 2(1(1(0(1(1(0(2(1(1(1(0(1(0(0(2(1(1(1(0(2(0(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(0(2(0(0(1(1(1(2(0(2(2(2(0(0(1(2(2(0(0(1(0(1(z0))))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(1(1(1(1(0(1(2(2(2(1(2(0(1(2(0(1(1(1(z0))))))))))))))))))))))))))) 2(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> 2(2(2(1(0(1(1(0(2(2(0(0(1(1(1(1(1(1(0(1(1(1(2(0(2(2(0(z0))))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(1(2(2(0(2(0(1(2(1(0(0(1(0(2(1(z0))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(2(2(0(1(2(1(0(1(0(1(2(2(1(1(0(2(1(0(1(z0))))))))))))))))))))))))))) 2(0(2(1(0(1(2(2(1(2(2(0(2(0(2(0(2(2(1(2(0(2(2(z0))))))))))))))))))))))) -> 0(1(0(2(2(0(0(0(1(1(2(0(1(1(0(2(0(1(1(1(1(1(0(1(0(2(2(z0))))))))))))))))))))))))))) 2(0(2(1(1(0(2(1(0(2(1(2(2(0(0(1(0(1(0(2(0(2(0(z0))))))))))))))))))))))) -> 1(1(1(0(1(2(0(0(1(1(2(1(2(2(1(1(1(1(2(1(2(1(2(1(1(2(1(z0))))))))))))))))))))))))))) 2(1(0(1(0(2(2(2(1(2(2(0(1(2(1(1(1(1(0(0(2(0(2(z0))))))))))))))))))))))) -> 2(1(2(1(2(1(1(1(2(2(1(2(1(1(1(0(1(1(1(2(1(0(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(1(0(1(1(0(1(2(1(0(2(2(0(1(0(1(2(0(2(2(1(2(0(z0))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(z0))))))))))))))))))))))))))) 2(1(0(1(1(2(2(2(0(2(1(0(0(0(2(2(2(2(2(0(0(1(1(z0))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(z0))))))))))))))))))))))))))) 2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(z0))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(z0))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(z0))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(z0))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(z0))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(z0))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(z0))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(z0))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(z0))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(z0))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(z0))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(z0))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(z0))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(z0))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(z0))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))) Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(2'(encArg(z0)), ENCARG(z0)) ENCODE_0(z0) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCODE_1(z0) -> c4(1'(encArg(z0)), ENCARG(z0)) ENCODE_2(z0) -> c5(2'(encArg(z0)), ENCARG(z0)) 0'(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> c6(0'(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))), 2'(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))), 1'(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))), 2'(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))), 2'(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))), 2'(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))), 1'(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))), 0'(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))), 1'(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))), 1'(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))), 1'(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))), 1'(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))), 1'(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))), 0'(1(1(1(1(1(1(2(1(2(1(z0))))))))))), 1'(1(1(1(1(1(2(1(2(1(z0)))))))))), 1'(1(1(1(1(2(1(2(1(z0))))))))), 1'(1(1(1(2(1(2(1(z0)))))))), 1'(1(1(2(1(2(1(z0))))))), 1'(1(2(1(2(1(z0)))))), 1'(2(1(2(1(z0))))), 2'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> c7(1'(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))), 1'(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))))), 1'(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))), 2'(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))), 1'(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))), 1'(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))), 0'(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))), 0'(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))), 1'(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))), 1'(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))), 0'(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))), 1'(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))), 2'(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))), 1'(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))), 1'(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))), 1'(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))), 1'(1(0(1(2(2(1(1(2(0(0(z0))))))))))), 1'(0(1(2(2(1(1(2(0(0(z0)))))))))), 0'(1(2(2(1(1(2(0(0(z0))))))))), 1'(2(2(1(1(2(0(0(z0)))))))), 2'(2(1(1(2(0(0(z0))))))), 2'(1(1(2(0(0(z0)))))), 1'(1(2(0(0(z0))))), 1'(2(0(0(z0)))), 2'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> c8(2'(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))), 0'(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))))), 2'(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))), 1'(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))), 0'(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))), 1'(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))), 1'(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))), 1'(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))), 0'(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))), 2'(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))), 1'(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))), 1'(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))), 1'(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))), 1'(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))), 2'(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(z0))))))))))), 1'(2(2(2(1(1(0(1(1(1(z0)))))))))), 2'(2(2(1(1(0(1(1(1(z0))))))))), 2'(2(1(1(0(1(1(1(z0)))))))), 2'(1(1(0(1(1(1(z0))))))), 1'(1(0(1(1(1(z0)))))), 1'(0(1(1(1(z0))))), 0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> c9(0'(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))), 1'(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))))), 1'(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))), 1'(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))), 1'(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))), 0'(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))), 2'(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))), 1'(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))), 1'(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))), 0'(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))), 1'(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))), 1'(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))), 1'(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))), 0'(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))), 2'(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))), 1'(1(1(0(0(0(2(1(0(2(1(z0))))))))))), 1'(1(0(0(0(2(1(0(2(1(z0)))))))))), 1'(0(0(0(2(1(0(2(1(z0))))))))), 0'(0(0(2(1(0(2(1(z0)))))))), 0'(0(2(1(0(2(1(z0))))))), 0'(2(1(0(2(1(z0)))))), 2'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(z0))))))))))))))))))))))) -> c10(0'(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))))), 0'(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))))))), 2'(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))), 1'(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))))), 0'(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))), 1'(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))), 1'(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))), 1'(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))), 1'(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))), 2'(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))), 0'(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))), 1'(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))), 0'(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))), 0'(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))), 0'(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))), 1'(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))), 0'(1(1(1(1(1(1(1(0(1(0(z0))))))))))), 1'(1(1(1(1(1(1(0(1(0(z0)))))))))), 1'(1(1(1(1(1(0(1(0(z0))))))))), 1'(1(1(1(1(0(1(0(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))), 1'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(z0))))))))))))))))))))))) -> c11(1'(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))))))), 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1'(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))))))), 1'(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))), 1'(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))))), 1'(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))), 1'(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))), 2'(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))), 2'(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))), 2'(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))), 1'(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))), 1'(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))), 2'(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))), 1'(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))), 1'(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))), 2'(1(0(2(0(2(0(2(2(1(0(z0))))))))))), 1'(0(2(0(2(0(2(2(1(0(z0)))))))))), 0'(2(0(2(0(2(2(1(0(z0))))))))), 2'(0(2(0(2(2(1(0(z0)))))))), 0'(2(0(2(2(1(0(z0))))))), 2'(0(2(2(1(0(z0)))))), 0'(2(2(1(0(z0))))), 2'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> c102(2'(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))), 2'(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))))), 1'(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))), 1'(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))), 1'(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))), 2'(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))), 1'(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))), 0'(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))), 2'(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))), 1'(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))), 1'(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))), 2'(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))), 2'(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))), 0'(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))), 1'(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))), 1'(0(1(2(0(1(0(2(1(1(2(z0))))))))))), 0'(1(2(0(1(0(2(1(1(2(z0)))))))))), 1'(2(0(1(0(2(1(1(2(z0))))))))), 2'(0(1(0(2(1(1(2(z0)))))))), 0'(1(0(2(1(1(2(z0))))))), 1'(0(2(1(1(2(z0)))))), 0'(2(1(1(2(z0))))), 2'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) 2'(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> c103(2'(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))), 2'(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))))), 0'(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))), 1'(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))), 1'(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))), 0'(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))), 2'(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))), 2'(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))), 1'(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))), 1'(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))), 2'(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))), 1'(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))), 1'(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))), 1'(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))), 1'(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))), 2'(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))), 0'(0(1(0(2(2(1(1(2(0(1(z0))))))))))), 0'(1(0(2(2(1(1(2(0(1(z0)))))))))), 1'(0(2(2(1(1(2(0(1(z0))))))))), 0'(2(2(1(1(2(0(1(z0)))))))), 2'(2(1(1(2(0(1(z0))))))), 2'(1(1(2(0(1(z0)))))), 1'(1(2(0(1(z0))))), 1'(2(0(1(z0)))), 2'(0(1(z0))), 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0'(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))), 0'(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))), 1'(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))), 1'(1(0(1(1(1(0(1(2(1(0(z0))))))))))), 1'(0(1(1(1(0(1(2(1(0(z0)))))))))), 0'(1(1(1(0(1(2(1(0(z0))))))))), 1'(1(1(0(1(2(1(0(z0)))))))), 1'(1(0(1(2(1(0(z0))))))), 1'(0(1(2(1(0(z0)))))), 0'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(z0))))))))))))))))))))))) -> c33(1'(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))))), 2'(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))))), 1'(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))), 1'(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))), 1'(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))), 2'(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))), 0'(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))), 2'(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))), 2'(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))), 2'(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))), 2'(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))), 1'(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))), 2'(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))), 1'(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))), 1'(0(1(0(1(2(2(2(1(1(1(z0))))))))))), 0'(1(0(1(2(2(2(1(1(1(z0)))))))))), 1'(0(1(2(2(2(1(1(1(z0))))))))), 2'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 1'(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(z0))))))))))))))))))))))) -> c52(0'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c66(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> c79(1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c85(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) S tuples: 0'(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> c6(0'(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))), 2'(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))), 1'(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))), 2'(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))), 2'(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))), 2'(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))), 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1'(0(1(2(1(2(0(2(2(1(z0)))))))))), 0'(1(2(1(2(0(2(2(1(z0))))))))), 1'(2(1(2(0(2(2(1(z0)))))))), 2'(1(2(0(2(2(1(z0))))))), 1'(2(0(2(2(1(z0)))))), 2'(0(2(2(1(z0))))), 0'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(z0))))))))))))))))))))))) -> c101(2'(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))))), 1'(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))))))), 1'(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))), 1'(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))))), 1'(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))), 1'(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))), 2'(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))), 2'(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))), 2'(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))), 1'(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))), 1'(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))), 2'(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))), 1'(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))), 1'(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))), 2'(1(0(2(0(2(0(2(2(1(0(z0))))))))))), 1'(0(2(0(2(0(2(2(1(0(z0)))))))))), 0'(2(0(2(0(2(2(1(0(z0))))))))), 2'(0(2(0(2(2(1(0(z0)))))))), 0'(2(0(2(2(1(0(z0))))))), 2'(0(2(2(1(0(z0)))))), 0'(2(2(1(0(z0))))), 2'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> c102(2'(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))), 2'(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))))), 1'(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))), 1'(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))), 1'(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))), 2'(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))), 1'(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))), 0'(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))), 2'(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))), 1'(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))), 1'(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))), 2'(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))), 2'(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))), 0'(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))), 1'(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))), 1'(0(1(2(0(1(0(2(1(1(2(z0))))))))))), 0'(1(2(0(1(0(2(1(1(2(z0)))))))))), 1'(2(0(1(0(2(1(1(2(z0))))))))), 2'(0(1(0(2(1(1(2(z0)))))))), 0'(1(0(2(1(1(2(z0))))))), 1'(0(2(1(1(2(z0)))))), 0'(2(1(1(2(z0))))), 2'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) 2'(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> c103(2'(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))), 2'(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))))), 0'(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))), 1'(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))), 1'(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))), 0'(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))), 2'(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))), 2'(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))), 1'(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))), 1'(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))), 2'(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))), 1'(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))), 1'(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))), 1'(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))), 1'(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))), 2'(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))), 0'(0(1(0(2(2(1(1(2(0(1(z0))))))))))), 0'(1(0(2(2(1(1(2(0(1(z0)))))))))), 1'(0(2(2(1(1(2(0(1(z0))))))))), 0'(2(2(1(1(2(0(1(z0)))))))), 2'(2(1(1(2(0(1(z0))))))), 2'(1(1(2(0(1(z0)))))), 1'(1(2(0(1(z0))))), 1'(2(0(1(z0)))), 2'(0(1(z0))), 0'(1(z0)), 1'(z0)) 2'(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> c104(2'(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))), 2'(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))), 1'(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))), 1'(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))), 1'(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))), 2'(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))), 0'(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))), 2'(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))), 2'(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))), 0'(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))), 1'(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))), 1'(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))), 0'(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))), 0'(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))), 1'(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))), 1'(1(0(1(1(1(0(1(2(1(0(z0))))))))))), 1'(0(1(1(1(0(1(2(1(0(z0)))))))))), 0'(1(1(1(0(1(2(1(0(z0))))))))), 1'(1(1(0(1(2(1(0(z0)))))))), 1'(1(0(1(2(1(0(z0))))))), 1'(0(1(2(1(0(z0)))))), 0'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(z0))))))))))))))))))))))) -> c33(1'(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))))), 2'(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))))), 1'(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))), 1'(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))), 1'(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))), 2'(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))), 0'(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))), 2'(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))), 2'(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))), 2'(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))), 2'(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))), 1'(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))), 2'(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))), 1'(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))), 1'(0(1(0(1(2(2(2(1(1(1(z0))))))))))), 0'(1(0(1(2(2(2(1(1(1(z0)))))))))), 1'(0(1(2(2(2(1(1(1(z0))))))))), 2'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 1'(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(z0))))))))))))))))))))))) -> c52(0'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c66(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> c79(1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c85(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) K tuples:none Defined Rule Symbols: 0_1, 1_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_2_1 Defined Pair Symbols: ENCARG_1, ENCODE_0_1, ENCODE_1_1, ENCODE_2_1, 0'_1, 1'_1, 2'_1 Compound Symbols: c_2, c1_2, c2_2, c3_2, c4_2, c5_2, c6_27, c7_27, c8_27, c9_27, c10_27, c11_27, c12_27, c13_27, c14_27, c15_27, c16_27, c17_27, c18_27, c19_27, c20_27, c21_27, c22_27, c23_27, c24_27, c25_27, c26_27, c27_27, c28_27, c29_27, c30_27, c31_27, c32_27, c34_27, c35_27, c36_27, c37_27, c38_27, c39_27, c40_27, c41_27, c42_27, c43_27, c44_27, c45_27, c46_27, c47_27, c48_27, c49_27, c50_27, c51_27, c53_27, c54_27, c55_27, c56_27, c57_27, c58_27, c59_27, c60_27, c61_27, c62_27, c63_27, c64_27, c65_27, c67_27, c68_27, c69_27, c70_27, c71_27, c72_27, c73_27, c74_27, c75_27, c76_27, c77_27, c78_27, c80_27, c81_27, c82_27, c83_27, c84_27, c86_27, c87_27, c88_27, c89_27, c90_27, c91_27, c92_27, c93_27, c94_27, c95_27, c96_27, c97_27, c98_27, c99_27, c100_27, c101_27, c102_27, c103_27, c104_27, c33_23, c52_5, c66_3, c79_3, c85_3 ---------------------------------------- (39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(z0))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(z0))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(z0))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(z0))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(z0))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(z0))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(z0))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(z0))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(z0))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(z0))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(z0))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(z0))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(z0))))))))))))))))))))))) -> 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1(1(2(2(2(1(2(0(2(1(1(1(1(1(1(2(0(0(2(1(0(0(1(2(2(2(1(z0))))))))))))))))))))))))))) 1(2(1(1(2(1(0(0(2(1(0(1(2(1(1(0(1(2(0(2(2(0(1(z0))))))))))))))))))))))) -> 1(2(1(1(1(0(2(0(2(0(0(2(1(0(2(1(1(1(1(1(0(0(0(1(0(1(1(z0))))))))))))))))))))))))))) 1(2(1(2(1(2(2(1(0(2(1(1(1(0(0(2(2(0(2(0(2(2(1(z0))))))))))))))))))))))) -> 1(0(2(1(0(1(0(0(1(1(1(2(0(2(2(1(1(1(1(1(2(2(1(2(1(0(1(z0))))))))))))))))))))))))))) 1(2(2(0(1(2(0(1(1(2(1(2(2(0(1(0(1(0(2(2(2(1(0(z0))))))))))))))))))))))) -> 1(1(0(0(0(1(0(2(1(0(2(2(2(1(0(0(2(1(1(0(2(2(2(2(1(1(0(z0))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(0(2(0(0(1(1(1(0(1(2(2(2(2(1(2(z0))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(0(1(0(0(0(1(1(1(2(0(2(2(2(2(1(1(1(1(2(z0))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(1(0(1(0(0(2(1(2(0(2(2(2(0(0(z0))))))))))))))))))))))) -> 1(1(1(0(2(2(0(0(2(2(2(1(2(1(1(1(1(0(2(2(2(0(1(0(2(0(2(z0))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(2(2(0(1(2(0(0(0(2(0(2(1(0(1(z0))))))))))))))))))))))) -> 1(0(1(2(1(1(2(1(0(0(1(1(0(0(2(2(0(0(2(2(0(2(1(1(1(2(1(z0))))))))))))))))))))))))))) 1(2(2(2(0(1(2(2(1(1(1(1(1(2(2(0(1(2(1(2(0(0(1(z0))))))))))))))))))))))) -> 1(1(1(1(0(1(1(1(0(0(1(0(0(0(2(1(1(1(1(1(1(1(0(1(2(0(1(z0))))))))))))))))))))))))))) 2(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> 2(0(0(0(0(1(1(2(0(1(2(2(1(0(2(0(2(2(2(0(1(0(1(1(1(1(0(z0))))))))))))))))))))))))))) 2(0(0(2(1(0(1(1(1(2(0(0(1(1(1(0(1(2(1(1(0(0(0(z0))))))))))))))))))))))) -> 1(1(0(0(1(1(1(0(0(1(0(2(1(1(1(1(1(2(1(2(1(1(1(1(1(1(0(z0))))))))))))))))))))))))))) 2(0(0(2(1(1(1(1(2(2(2(1(2(1(0(2(2(1(0(0(2(0(1(z0))))))))))))))))))))))) -> 1(1(1(2(2(1(1(1(2(1(2(0(2(2(1(1(1(1(0(2(0(2(1(1(0(2(1(z0))))))))))))))))))))))))))) 2(0(1(0(1(1(1(1(2(2(2(2(0(0(1(0(1(0(0(0(2(2(0(z0))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(1(2(2(2(0(2(2(1(1(2(2(2(0(1(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(0(1(2(0(1(1(0(2(2(2(2(0(2(1(0(2(1(2(1(0(2(1(z0))))))))))))))))))))))) -> 2(1(1(0(1(1(0(2(1(1(1(0(1(0(0(2(1(1(1(0(2(0(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(0(2(0(0(1(1(1(2(0(2(2(2(0(0(1(2(2(0(0(1(0(1(z0))))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(1(1(1(1(0(1(2(2(2(1(2(0(1(2(0(1(1(1(z0))))))))))))))))))))))))))) 2(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> 2(2(2(1(0(1(1(0(2(2(0(0(1(1(1(1(1(1(0(1(1(1(2(0(2(2(0(z0))))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(1(2(2(0(2(0(1(2(1(0(0(1(0(2(1(z0))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(2(2(0(1(2(1(0(1(0(1(2(2(1(1(0(2(1(0(1(z0))))))))))))))))))))))))))) 2(0(2(1(0(1(2(2(1(2(2(0(2(0(2(0(2(2(1(2(0(2(2(z0))))))))))))))))))))))) -> 0(1(0(2(2(0(0(0(1(1(2(0(1(1(0(2(0(1(1(1(1(1(0(1(0(2(2(z0))))))))))))))))))))))))))) 2(0(2(1(1(0(2(1(0(2(1(2(2(0(0(1(0(1(0(2(0(2(0(z0))))))))))))))))))))))) -> 1(1(1(0(1(2(0(0(1(1(2(1(2(2(1(1(1(1(2(1(2(1(2(1(1(2(1(z0))))))))))))))))))))))))))) 2(1(0(1(0(2(2(2(1(2(2(0(1(2(1(1(1(1(0(0(2(0(2(z0))))))))))))))))))))))) -> 2(1(2(1(2(1(1(1(2(2(1(2(1(1(1(0(1(1(1(2(1(0(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(1(0(1(1(0(1(2(1(0(2(2(0(1(0(1(2(0(2(2(1(2(0(z0))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(z0))))))))))))))))))))))))))) 2(1(0(1(1(2(2(2(0(2(1(0(0(0(2(2(2(2(2(0(0(1(1(z0))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(z0))))))))))))))))))))))))))) 2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(z0))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(z0))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(z0))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(z0))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(z0))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(z0))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(z0))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(z0))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(z0))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(z0))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(z0))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(z0))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(z0))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(z0))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(z0))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))) Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(2'(encArg(z0)), ENCARG(z0)) 0'(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> c6(0'(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))), 2'(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))), 1'(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))), 2'(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))), 2'(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))), 2'(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))), 1'(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))), 0'(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))), 1'(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))), 1'(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))), 1'(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))), 1'(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))), 1'(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))), 0'(1(1(1(1(1(1(2(1(2(1(z0))))))))))), 1'(1(1(1(1(1(2(1(2(1(z0)))))))))), 1'(1(1(1(1(2(1(2(1(z0))))))))), 1'(1(1(1(2(1(2(1(z0)))))))), 1'(1(1(2(1(2(1(z0))))))), 1'(1(2(1(2(1(z0)))))), 1'(2(1(2(1(z0))))), 2'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> c7(1'(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))), 1'(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))))), 1'(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))), 2'(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))), 1'(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))), 1'(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))), 0'(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))), 0'(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))), 1'(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))), 1'(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))), 0'(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))), 1'(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))), 2'(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))), 1'(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))), 1'(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))), 1'(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))), 1'(1(0(1(2(2(1(1(2(0(0(z0))))))))))), 1'(0(1(2(2(1(1(2(0(0(z0)))))))))), 0'(1(2(2(1(1(2(0(0(z0))))))))), 1'(2(2(1(1(2(0(0(z0)))))))), 2'(2(1(1(2(0(0(z0))))))), 2'(1(1(2(0(0(z0)))))), 1'(1(2(0(0(z0))))), 1'(2(0(0(z0)))), 2'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> c8(2'(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))), 0'(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))))), 2'(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))), 1'(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))), 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1'(0(z0)), 0'(z0)) 2'(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> c102(2'(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))), 2'(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))))), 1'(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))), 1'(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))), 1'(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))), 2'(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))), 1'(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))), 0'(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))), 2'(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))), 1'(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))), 1'(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))), 2'(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))), 2'(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))), 0'(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))), 1'(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))), 1'(0(1(2(0(1(0(2(1(1(2(z0))))))))))), 0'(1(2(0(1(0(2(1(1(2(z0)))))))))), 1'(2(0(1(0(2(1(1(2(z0))))))))), 2'(0(1(0(2(1(1(2(z0)))))))), 0'(1(0(2(1(1(2(z0))))))), 1'(0(2(1(1(2(z0)))))), 0'(2(1(1(2(z0))))), 2'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) 2'(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> c103(2'(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))), 2'(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))))), 0'(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))), 1'(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))), 1'(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))), 0'(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))), 2'(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))), 2'(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))), 1'(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))), 1'(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))), 2'(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))), 1'(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))), 1'(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))), 1'(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))), 1'(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))), 2'(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))), 0'(0(1(0(2(2(1(1(2(0(1(z0))))))))))), 0'(1(0(2(2(1(1(2(0(1(z0)))))))))), 1'(0(2(2(1(1(2(0(1(z0))))))))), 0'(2(2(1(1(2(0(1(z0)))))))), 2'(2(1(1(2(0(1(z0))))))), 2'(1(1(2(0(1(z0)))))), 1'(1(2(0(1(z0))))), 1'(2(0(1(z0)))), 2'(0(1(z0))), 0'(1(z0)), 1'(z0)) 2'(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> c104(2'(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))), 2'(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))), 1'(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))), 1'(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))), 1'(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))), 2'(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))), 0'(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))), 2'(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))), 2'(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))), 0'(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))), 1'(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))), 1'(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))), 0'(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))), 0'(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))), 1'(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))), 1'(1(0(1(1(1(0(1(2(1(0(z0))))))))))), 1'(0(1(1(1(0(1(2(1(0(z0)))))))))), 0'(1(1(1(0(1(2(1(0(z0))))))))), 1'(1(1(0(1(2(1(0(z0)))))))), 1'(1(0(1(2(1(0(z0))))))), 1'(0(1(2(1(0(z0)))))), 0'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(z0))))))))))))))))))))))) -> c33(1'(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))))), 2'(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))))), 1'(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))), 1'(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))), 1'(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))), 2'(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))), 0'(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))), 2'(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))), 2'(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))), 2'(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))), 2'(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))), 1'(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))), 2'(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))), 1'(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))), 1'(0(1(0(1(2(2(2(1(1(1(z0))))))))))), 0'(1(0(1(2(2(2(1(1(1(z0)))))))))), 1'(0(1(2(2(2(1(1(1(z0))))))))), 2'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 1'(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(z0))))))))))))))))))))))) -> c52(0'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c66(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> c79(1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c85(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) ENCODE_0(z0) -> c105(0'(encArg(z0))) ENCODE_0(z0) -> c105(ENCARG(z0)) ENCODE_1(z0) -> c105(1'(encArg(z0))) ENCODE_1(z0) -> c105(ENCARG(z0)) ENCODE_2(z0) -> c105(2'(encArg(z0))) ENCODE_2(z0) -> c105(ENCARG(z0)) S tuples: 0'(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> c6(0'(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))), 2'(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))), 1'(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))), 2'(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))), 2'(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))), 2'(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))), 1'(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))), 0'(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))), 1'(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))), 1'(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))), 1'(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))), 1'(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))), 1'(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))), 0'(1(1(1(1(1(1(2(1(2(1(z0))))))))))), 1'(1(1(1(1(1(2(1(2(1(z0)))))))))), 1'(1(1(1(1(2(1(2(1(z0))))))))), 1'(1(1(1(2(1(2(1(z0)))))))), 1'(1(1(2(1(2(1(z0))))))), 1'(1(2(1(2(1(z0)))))), 1'(2(1(2(1(z0))))), 2'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> c7(1'(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))), 1'(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))))), 1'(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))), 2'(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))), 1'(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))), 1'(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))), 0'(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))), 0'(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))), 1'(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))), 1'(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))), 0'(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))), 1'(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))), 2'(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))), 1'(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))), 1'(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))), 1'(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))), 1'(1(0(1(2(2(1(1(2(0(0(z0))))))))))), 1'(0(1(2(2(1(1(2(0(0(z0)))))))))), 0'(1(2(2(1(1(2(0(0(z0))))))))), 1'(2(2(1(1(2(0(0(z0)))))))), 2'(2(1(1(2(0(0(z0))))))), 2'(1(1(2(0(0(z0)))))), 1'(1(2(0(0(z0))))), 1'(2(0(0(z0)))), 2'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> c8(2'(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))), 0'(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))))), 2'(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))), 1'(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))), 0'(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))), 1'(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))), 1'(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))), 1'(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))), 0'(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))), 2'(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))), 1'(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))), 1'(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))), 1'(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))), 1'(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))), 2'(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(z0))))))))))), 1'(2(2(2(1(1(0(1(1(1(z0)))))))))), 2'(2(2(1(1(0(1(1(1(z0))))))))), 2'(2(1(1(0(1(1(1(z0)))))))), 2'(1(1(0(1(1(1(z0))))))), 1'(1(0(1(1(1(z0)))))), 1'(0(1(1(1(z0))))), 0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> c9(0'(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))), 1'(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))))), 1'(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))), 1'(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))), 1'(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))), 0'(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))), 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1'(2(z0)), 2'(z0)) 2'(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> c103(2'(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))), 2'(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))))), 0'(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))), 1'(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))), 1'(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))), 0'(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))), 2'(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))), 2'(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))), 1'(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))), 1'(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))), 2'(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))), 1'(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))), 1'(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))), 1'(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))), 1'(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))), 2'(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))), 0'(0(1(0(2(2(1(1(2(0(1(z0))))))))))), 0'(1(0(2(2(1(1(2(0(1(z0)))))))))), 1'(0(2(2(1(1(2(0(1(z0))))))))), 0'(2(2(1(1(2(0(1(z0)))))))), 2'(2(1(1(2(0(1(z0))))))), 2'(1(1(2(0(1(z0)))))), 1'(1(2(0(1(z0))))), 1'(2(0(1(z0)))), 2'(0(1(z0))), 0'(1(z0)), 1'(z0)) 2'(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> c104(2'(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))), 2'(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))), 1'(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))), 1'(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))), 1'(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))), 2'(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))), 0'(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))), 2'(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))), 2'(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))), 0'(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))), 1'(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))), 1'(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))), 0'(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))), 0'(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))), 1'(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))), 1'(1(0(1(1(1(0(1(2(1(0(z0))))))))))), 1'(0(1(1(1(0(1(2(1(0(z0)))))))))), 0'(1(1(1(0(1(2(1(0(z0))))))))), 1'(1(1(0(1(2(1(0(z0)))))))), 1'(1(0(1(2(1(0(z0))))))), 1'(0(1(2(1(0(z0)))))), 0'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(z0))))))))))))))))))))))) -> c33(1'(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))))), 2'(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))))), 1'(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))), 1'(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))), 1'(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))), 2'(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))), 0'(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))), 2'(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))), 2'(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))), 2'(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))), 2'(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))), 1'(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))), 2'(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))), 1'(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))), 1'(0(1(0(1(2(2(2(1(1(1(z0))))))))))), 0'(1(0(1(2(2(2(1(1(1(z0)))))))))), 1'(0(1(2(2(2(1(1(1(z0))))))))), 2'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 1'(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(z0))))))))))))))))))))))) -> c52(0'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c66(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> c79(1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c85(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) K tuples:none Defined Rule Symbols: 0_1, 1_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, 2'_1, ENCODE_0_1, ENCODE_1_1, ENCODE_2_1 Compound Symbols: c_2, c1_2, c2_2, c6_27, c7_27, c8_27, c9_27, c10_27, c11_27, c12_27, c13_27, c14_27, c15_27, c16_27, c17_27, c18_27, c19_27, c20_27, c21_27, c22_27, c23_27, c24_27, c25_27, c26_27, c27_27, c28_27, c29_27, c30_27, c31_27, c32_27, c34_27, c35_27, c36_27, c37_27, c38_27, c39_27, c40_27, c41_27, c42_27, c43_27, c44_27, c45_27, c46_27, c47_27, c48_27, c49_27, c50_27, c51_27, c53_27, c54_27, c55_27, c56_27, c57_27, c58_27, c59_27, c60_27, c61_27, c62_27, c63_27, c64_27, c65_27, c67_27, c68_27, c69_27, c70_27, c71_27, c72_27, c73_27, c74_27, c75_27, c76_27, c77_27, c78_27, c80_27, c81_27, c82_27, c83_27, c84_27, c86_27, c87_27, c88_27, c89_27, c90_27, c91_27, c92_27, c93_27, c94_27, c95_27, c96_27, c97_27, c98_27, c99_27, c100_27, c101_27, c102_27, c103_27, c104_27, c33_23, c52_5, c66_3, c79_3, c85_3, c105_1 ---------------------------------------- (41) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 3 leading nodes: ENCODE_0(z0) -> c105(ENCARG(z0)) ENCODE_1(z0) -> c105(ENCARG(z0)) ENCODE_2(z0) -> c105(ENCARG(z0)) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(z0))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(z0))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(z0))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(z0))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(z0))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(z0))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(z0))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(z0))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(z0))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(z0))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(z0))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(z0))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(z0))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(z0))))))))))))))))))))))))))) 0(1(0(1(1(2(1(1(1(0(0(1(2(0(0(2(2(0(1(0(2(0(0(z0))))))))))))))))))))))) -> 0(1(1(1(0(1(2(0(0(2(2(2(1(2(2(2(2(2(0(1(1(0(1(1(1(1(0(z0))))))))))))))))))))))))))) 0(1(0(1(1(2(2(0(1(0(2(1(0(0(0(1(1(2(2(2(0(2(2(z0))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(z0))))))))))))))))))))))))))) 0(1(0(1(2(0(0(1(1(2(0(0(2(1(0(2(1(0(1(1(0(1(2(z0))))))))))))))))))))))) -> 0(1(1(1(2(1(2(2(2(2(1(2(2(1(1(2(1(2(0(2(1(0(1(1(1(1(2(z0))))))))))))))))))))))))))) 0(1(0(1(2(1(2(1(0(2(0(1(0(0(2(0(0(2(1(1(0(0(1(z0))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(z0))))))))))))))))))))))))))) 0(1(0(2(0(0(0(1(0(2(1(2(2(0(1(0(2(2(1(0(1(2(1(z0))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(z0))))))))))))))))))))))))))) 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2(1(0(1(0(2(2(2(1(2(2(0(1(2(1(1(1(1(0(0(2(0(2(z0))))))))))))))))))))))) -> 2(1(2(1(2(1(1(1(2(2(1(2(1(1(1(0(1(1(1(2(1(0(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(1(0(1(1(0(1(2(1(0(2(2(0(1(0(1(2(0(2(2(1(2(0(z0))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(z0))))))))))))))))))))))))))) 2(1(0(1(1(2(2(2(0(2(1(0(0(0(2(2(2(2(2(0(0(1(1(z0))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(z0))))))))))))))))))))))))))) 2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(z0))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(z0))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(z0))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(z0))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(z0))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(z0))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(z0))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(z0))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(z0))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(z0))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(z0))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(z0))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(z0))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(z0))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(z0))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))) Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(2'(encArg(z0)), ENCARG(z0)) 0'(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> c6(0'(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))), 2'(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))), 1'(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))), 2'(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))), 2'(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))), 2'(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))), 1'(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))), 0'(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))), 1'(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))), 1'(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))), 1'(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))), 1'(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))), 1'(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))), 0'(1(1(1(1(1(1(2(1(2(1(z0))))))))))), 1'(1(1(1(1(1(2(1(2(1(z0)))))))))), 1'(1(1(1(1(2(1(2(1(z0))))))))), 1'(1(1(1(2(1(2(1(z0)))))))), 1'(1(1(2(1(2(1(z0))))))), 1'(1(2(1(2(1(z0)))))), 1'(2(1(2(1(z0))))), 2'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> c7(1'(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))), 1'(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))))), 1'(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))), 2'(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))), 1'(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))), 1'(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))), 0'(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))), 0'(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))), 1'(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))), 1'(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))), 0'(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))), 1'(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))), 2'(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))), 1'(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))), 1'(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))), 1'(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))), 1'(1(0(1(2(2(1(1(2(0(0(z0))))))))))), 1'(0(1(2(2(1(1(2(0(0(z0)))))))))), 0'(1(2(2(1(1(2(0(0(z0))))))))), 1'(2(2(1(1(2(0(0(z0)))))))), 2'(2(1(1(2(0(0(z0))))))), 2'(1(1(2(0(0(z0)))))), 1'(1(2(0(0(z0))))), 1'(2(0(0(z0)))), 2'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> c8(2'(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))), 0'(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))))), 2'(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))), 1'(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))), 0'(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))), 1'(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))), 1'(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))), 1'(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))), 0'(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))), 2'(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))), 1'(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))), 1'(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))), 1'(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))), 1'(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))), 2'(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(z0))))))))))), 1'(2(2(2(1(1(0(1(1(1(z0)))))))))), 2'(2(2(1(1(0(1(1(1(z0))))))))), 2'(2(1(1(0(1(1(1(z0)))))))), 2'(1(1(0(1(1(1(z0))))))), 1'(1(0(1(1(1(z0)))))), 1'(0(1(1(1(z0))))), 0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> c9(0'(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))), 1'(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))))), 1'(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))), 1'(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))), 1'(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))), 0'(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))), 2'(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))), 1'(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))), 1'(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))), 0'(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))), 1'(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))), 1'(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))), 1'(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))), 0'(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))), 2'(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))), 1'(1(1(0(0(0(2(1(0(2(1(z0))))))))))), 1'(1(0(0(0(2(1(0(2(1(z0)))))))))), 1'(0(0(0(2(1(0(2(1(z0))))))))), 0'(0(0(2(1(0(2(1(z0)))))))), 0'(0(2(1(0(2(1(z0))))))), 0'(2(1(0(2(1(z0)))))), 2'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(z0))))))))))))))))))))))) -> c10(0'(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))))), 0'(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))))))), 2'(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))), 1'(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))))), 0'(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))), 1'(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))), 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0'(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))), 0'(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))), 1'(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))), 1'(1(0(1(1(1(0(1(2(1(0(z0))))))))))), 1'(0(1(1(1(0(1(2(1(0(z0)))))))))), 0'(1(1(1(0(1(2(1(0(z0))))))))), 1'(1(1(0(1(2(1(0(z0)))))))), 1'(1(0(1(2(1(0(z0))))))), 1'(0(1(2(1(0(z0)))))), 0'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(z0))))))))))))))))))))))) -> c33(1'(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))))), 2'(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))))), 1'(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))), 1'(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))), 1'(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))), 2'(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))), 0'(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))), 2'(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))), 2'(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))), 2'(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))), 2'(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))), 1'(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))), 2'(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))), 1'(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))), 1'(0(1(0(1(2(2(2(1(1(1(z0))))))))))), 0'(1(0(1(2(2(2(1(1(1(z0)))))))))), 1'(0(1(2(2(2(1(1(1(z0))))))))), 2'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 1'(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(z0))))))))))))))))))))))) -> c52(0'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c66(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> c79(1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c85(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) ENCODE_0(z0) -> c105(0'(encArg(z0))) ENCODE_1(z0) -> c105(1'(encArg(z0))) ENCODE_2(z0) -> c105(2'(encArg(z0))) S tuples: 0'(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> c6(0'(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))), 2'(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))), 1'(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))), 2'(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))), 2'(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))), 2'(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))), 1'(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))), 0'(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))), 1'(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))), 1'(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))), 1'(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))), 1'(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))), 1'(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))), 0'(1(1(1(1(1(1(2(1(2(1(z0))))))))))), 1'(1(1(1(1(1(2(1(2(1(z0)))))))))), 1'(1(1(1(1(2(1(2(1(z0))))))))), 1'(1(1(1(2(1(2(1(z0)))))))), 1'(1(1(2(1(2(1(z0))))))), 1'(1(2(1(2(1(z0)))))), 1'(2(1(2(1(z0))))), 2'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> c7(1'(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))), 1'(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))))), 1'(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))), 2'(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))), 1'(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))), 1'(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))), 0'(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))), 0'(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))), 1'(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))), 1'(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))), 0'(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))), 1'(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))), 2'(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))), 1'(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))), 1'(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))), 1'(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))), 1'(1(0(1(2(2(1(1(2(0(0(z0))))))))))), 1'(0(1(2(2(1(1(2(0(0(z0)))))))))), 0'(1(2(2(1(1(2(0(0(z0))))))))), 1'(2(2(1(1(2(0(0(z0)))))))), 2'(2(1(1(2(0(0(z0))))))), 2'(1(1(2(0(0(z0)))))), 1'(1(2(0(0(z0))))), 1'(2(0(0(z0)))), 2'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> c8(2'(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))), 0'(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))))), 2'(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))), 1'(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))), 0'(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))), 1'(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))), 1'(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))), 1'(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))), 0'(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))), 2'(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))), 1'(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))), 1'(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))), 1'(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))), 1'(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))), 2'(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(z0))))))))))), 1'(2(2(2(1(1(0(1(1(1(z0)))))))))), 2'(2(2(1(1(0(1(1(1(z0))))))))), 2'(2(1(1(0(1(1(1(z0)))))))), 2'(1(1(0(1(1(1(z0))))))), 1'(1(0(1(1(1(z0)))))), 1'(0(1(1(1(z0))))), 0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> c9(0'(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))), 1'(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))))), 1'(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))), 1'(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))), 1'(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))), 0'(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))), 2'(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))), 1'(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))), 1'(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))), 0'(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))), 1'(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))), 1'(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))), 1'(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))), 0'(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))), 2'(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))), 1'(1(1(0(0(0(2(1(0(2(1(z0))))))))))), 1'(1(0(0(0(2(1(0(2(1(z0)))))))))), 1'(0(0(0(2(1(0(2(1(z0))))))))), 0'(0(0(2(1(0(2(1(z0)))))))), 0'(0(2(1(0(2(1(z0))))))), 0'(2(1(0(2(1(z0)))))), 2'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(z0))))))))))))))))))))))) -> 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1'(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0)))))))))))))))))))))))))), 2'(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))))))))))))))), 2'(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0)))))))))))))))))))))))), 1'(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))))))))))))), 0'(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0)))))))))))))))))))))), 1'(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))))))))))), 1'(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0)))))))))))))))))))), 0'(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))))))))), 1'(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0)))))))))))))))))), 0'(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))))))), 1'(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0)))))))))))))))), 0'(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))))), 2'(2(1(0(1(0(1(2(1(2(0(2(2(1(z0)))))))))))))), 2'(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))), 1'(0(1(0(1(2(1(2(0(2(2(1(z0)))))))))))), 0'(1(0(1(2(1(2(0(2(2(1(z0))))))))))), 1'(0(1(2(1(2(0(2(2(1(z0)))))))))), 0'(1(2(1(2(0(2(2(1(z0))))))))), 1'(2(1(2(0(2(2(1(z0)))))))), 2'(1(2(0(2(2(1(z0))))))), 1'(2(0(2(2(1(z0)))))), 2'(0(2(2(1(z0))))), 0'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(z0))))))))))))))))))))))) -> c101(2'(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))))), 1'(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))))))), 1'(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))), 1'(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))))), 1'(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))), 1'(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))), 2'(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))), 2'(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))), 2'(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))), 1'(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))), 1'(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))), 2'(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))), 1'(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))), 1'(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))), 2'(1(0(2(0(2(0(2(2(1(0(z0))))))))))), 1'(0(2(0(2(0(2(2(1(0(z0)))))))))), 0'(2(0(2(0(2(2(1(0(z0))))))))), 2'(0(2(0(2(2(1(0(z0)))))))), 0'(2(0(2(2(1(0(z0))))))), 2'(0(2(2(1(0(z0)))))), 0'(2(2(1(0(z0))))), 2'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> c102(2'(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))), 2'(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))))), 1'(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))), 1'(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))), 1'(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))), 2'(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))), 1'(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))), 0'(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))), 2'(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))), 1'(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))), 1'(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))), 2'(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))), 2'(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))), 0'(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))), 1'(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))), 1'(0(1(2(0(1(0(2(1(1(2(z0))))))))))), 0'(1(2(0(1(0(2(1(1(2(z0)))))))))), 1'(2(0(1(0(2(1(1(2(z0))))))))), 2'(0(1(0(2(1(1(2(z0)))))))), 0'(1(0(2(1(1(2(z0))))))), 1'(0(2(1(1(2(z0)))))), 0'(2(1(1(2(z0))))), 2'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) 2'(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> c103(2'(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))), 2'(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))))), 0'(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))), 1'(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))), 1'(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))), 0'(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))), 2'(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))), 2'(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))), 1'(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))), 1'(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))), 2'(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))), 1'(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))), 1'(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))), 1'(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))), 1'(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))), 2'(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))), 0'(0(1(0(2(2(1(1(2(0(1(z0))))))))))), 0'(1(0(2(2(1(1(2(0(1(z0)))))))))), 1'(0(2(2(1(1(2(0(1(z0))))))))), 0'(2(2(1(1(2(0(1(z0)))))))), 2'(2(1(1(2(0(1(z0))))))), 2'(1(1(2(0(1(z0)))))), 1'(1(2(0(1(z0))))), 1'(2(0(1(z0)))), 2'(0(1(z0))), 0'(1(z0)), 1'(z0)) 2'(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> c104(2'(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))), 2'(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))), 1'(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))), 1'(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))), 1'(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))), 2'(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))), 0'(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))), 2'(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))), 2'(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))), 0'(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))), 1'(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))), 1'(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))), 0'(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))), 0'(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))), 1'(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))), 1'(1(0(1(1(1(0(1(2(1(0(z0))))))))))), 1'(0(1(1(1(0(1(2(1(0(z0)))))))))), 0'(1(1(1(0(1(2(1(0(z0))))))))), 1'(1(1(0(1(2(1(0(z0)))))))), 1'(1(0(1(2(1(0(z0))))))), 1'(0(1(2(1(0(z0)))))), 0'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(z0))))))))))))))))))))))) -> c33(1'(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))))), 2'(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))))), 1'(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))), 1'(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))), 1'(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))), 2'(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))), 0'(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))), 2'(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))), 2'(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))), 2'(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))), 2'(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))), 1'(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))), 2'(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))), 1'(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))), 1'(0(1(0(1(2(2(2(1(1(1(z0))))))))))), 0'(1(0(1(2(2(2(1(1(1(z0)))))))))), 1'(0(1(2(2(2(1(1(1(z0))))))))), 2'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 1'(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(z0))))))))))))))))))))))) -> c52(0'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c66(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> c79(1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c85(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) K tuples:none Defined Rule Symbols: 0_1, 1_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, 2'_1, ENCODE_0_1, ENCODE_1_1, ENCODE_2_1 Compound Symbols: c_2, c1_2, c2_2, c6_27, c7_27, c8_27, c9_27, c10_27, c11_27, c12_27, c13_27, c14_27, c15_27, c16_27, c17_27, c18_27, c19_27, c20_27, c21_27, c22_27, c23_27, c24_27, c25_27, c26_27, c27_27, c28_27, c29_27, c30_27, c31_27, c32_27, c34_27, c35_27, c36_27, c37_27, c38_27, c39_27, c40_27, c41_27, c42_27, c43_27, c44_27, c45_27, c46_27, c47_27, c48_27, c49_27, c50_27, c51_27, c53_27, c54_27, c55_27, c56_27, c57_27, c58_27, c59_27, c60_27, c61_27, c62_27, c63_27, c64_27, c65_27, c67_27, c68_27, c69_27, c70_27, c71_27, c72_27, c73_27, c74_27, c75_27, c76_27, c77_27, c78_27, c80_27, c81_27, c82_27, c83_27, c84_27, c86_27, c87_27, c88_27, c89_27, c90_27, c91_27, c92_27, c93_27, c94_27, c95_27, c96_27, c97_27, c98_27, c99_27, c100_27, c101_27, c102_27, c103_27, c104_27, c33_23, c52_5, c66_3, c79_3, c85_3, c105_1 ---------------------------------------- (43) 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_2(z0) -> 2(encArg(z0)) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> 0(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))) 0(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> 1(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))) 0(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> 2(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))) 0(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> 0(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))) 0(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(z0))))))))))))))))))))))) -> 0(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))))) 0(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(z0))))))))))))))))))))))) -> 1(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))))))) 0(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(z0))))))))))))))))))))))) -> 0(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(z0))))))))))))))))))))))))))) 0(0(2(1(2(1(1(2(2(0(1(0(0(0(1(2(2(2(1(2(2(2(1(z0))))))))))))))))))))))) -> 0(2(0(1(2(2(1(1(0(0(2(2(2(1(0(1(2(0(2(1(0(2(2(1(1(1(1(z0))))))))))))))))))))))))))) 0(0(2(2(1(2(1(0(1(1(2(2(1(0(2(2(0(0(2(0(2(0(0(z0))))))))))))))))))))))) -> 0(0(0(2(0(0(2(1(1(1(0(2(2(2(2(1(0(1(1(1(2(1(0(1(0(0(0(z0))))))))))))))))))))))))))) 0(1(0(0(1(1(1(1(1(2(1(2(2(1(1(2(1(0(0(0(0(2(1(z0))))))))))))))))))))))) -> 2(1(0(2(1(1(1(1(2(1(2(1(1(2(1(1(1(2(1(1(2(2(2(1(2(1(1(z0))))))))))))))))))))))))))) 0(1(0(0(2(1(2(2(1(0(1(1(1(2(1(0(1(2(2(0(1(2(1(z0))))))))))))))))))))))) -> 1(2(2(0(1(1(1(0(1(1(1(2(2(2(1(1(1(0(2(0(2(1(0(2(2(0(1(z0))))))))))))))))))))))))))) 0(1(0(1(0(1(2(2(0(2(2(2(0(1(2(1(1(2(0(1(2(1(2(z0))))))))))))))))))))))) -> 0(1(1(0(1(2(1(1(1(1(0(0(1(0(1(2(1(1(0(1(1(1(1(0(2(0(2(z0))))))))))))))))))))))))))) 0(1(0(1(1(2(1(1(1(0(0(1(2(0(0(2(2(0(1(0(2(0(0(z0))))))))))))))))))))))) -> 0(1(1(1(0(1(2(0(0(2(2(2(1(2(2(2(2(2(0(1(1(0(1(1(1(1(0(z0))))))))))))))))))))))))))) 0(1(0(1(1(2(2(0(1(0(2(1(0(0(0(1(1(2(2(2(0(2(2(z0))))))))))))))))))))))) -> 1(2(2(2(2(1(1(0(1(1(0(1(2(1(0(2(2(1(1(0(1(1(1(1(0(1(2(z0))))))))))))))))))))))))))) 0(1(0(1(2(0(0(1(1(2(0(0(2(1(0(2(1(0(1(1(0(1(2(z0))))))))))))))))))))))) -> 0(1(1(1(2(1(2(2(2(2(1(2(2(1(1(2(1(2(0(2(1(0(1(1(1(1(2(z0))))))))))))))))))))))))))) 0(1(0(1(2(1(2(1(0(2(0(1(0(0(2(0(0(2(1(1(0(0(1(z0))))))))))))))))))))))) -> 1(0(2(2(0(0(2(2(0(1(1(1(0(1(1(0(0(1(2(1(0(1(1(2(0(1(1(z0))))))))))))))))))))))))))) 0(1(0(2(0(0(0(1(0(2(1(2(2(0(1(0(2(2(1(0(1(2(1(z0))))))))))))))))))))))) -> 0(1(0(2(2(2(2(1(0(0(2(1(1(2(2(1(0(2(1(0(2(1(2(2(2(1(1(z0))))))))))))))))))))))))))) 0(1(0(2(0(1(0(0(1(0(2(1(2(2(0(1(1(0(2(0(0(1(0(z0))))))))))))))))))))))) -> 0(1(1(0(1(1(1(1(0(2(1(2(0(1(1(2(0(1(1(1(1(1(2(2(1(1(0(z0))))))))))))))))))))))))))) 0(1(0(2(1(0(2(2(0(0(2(2(2(0(2(1(0(2(2(0(2(1(2(z0))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(1(0(2(1(1(2(0(1(0(2(1(2(0(2(1(0(1(1(1(z0))))))))))))))))))))))))))) 0(1(1(0(0(2(0(2(2(1(1(1(1(1(1(2(2(0(1(2(0(1(0(z0))))))))))))))))))))))) -> 0(2(1(1(1(0(2(1(1(0(1(2(1(0(2(2(2(1(1(0(1(1(0(1(1(1(0(z0))))))))))))))))))))))))))) 0(1(1(0(1(1(1(2(1(0(0(0(1(0(2(1(1(2(1(2(0(0(2(z0))))))))))))))))))))))) -> 1(0(1(1(1(1(1(0(2(2(1(1(1(0(2(1(2(1(1(0(0(1(2(1(0(0(1(z0))))))))))))))))))))))))))) 0(1(1(1(2(0(2(0(0(1(0(2(0(1(2(2(1(0(2(2(2(0(2(z0))))))))))))))))))))))) -> 1(1(1(1(2(0(1(1(1(1(1(1(0(0(1(0(0(2(2(2(0(0(2(1(0(2(0(z0))))))))))))))))))))))))))) 0(1(2(0(1(0(2(0(0(2(1(2(2(1(0(2(0(1(1(1(1(2(0(z0))))))))))))))))))))))) -> 1(0(1(0(1(1(1(0(1(1(1(2(2(1(1(2(2(1(2(1(1(2(0(2(2(2(2(z0))))))))))))))))))))))))))) 0(1(2(0(1(2(1(0(2(1(2(0(2(2(2(1(1(2(0(1(2(0(1(z0))))))))))))))))))))))) -> 2(1(0(0(0(1(0(2(2(1(1(2(2(2(1(1(2(2(1(1(2(0(1(1(0(2(1(z0))))))))))))))))))))))))))) 0(1(2(0(2(2(1(2(1(1(0(2(0(1(2(2(2(0(2(0(1(2(0(z0))))))))))))))))))))))) -> 0(2(1(2(1(2(2(1(1(0(0(2(2(1(1(1(1(0(2(2(1(1(2(0(2(2(2(z0))))))))))))))))))))))))))) 0(1(2(1(0(1(0(1(2(2(1(2(1(0(2(2(1(0(1(0(1(0(2(z0))))))))))))))))))))))) -> 0(1(1(1(2(2(2(0(1(1(2(1(1(1(1(0(1(2(2(1(2(1(1(1(0(0(0(z0))))))))))))))))))))))))))) 0(1(2(1(1(2(1(2(0(1(1(0(0(2(0(1(1(0(0(2(0(0(1(z0))))))))))))))))))))))) -> 0(1(1(0(2(2(2(0(2(1(1(0(1(0(2(2(0(1(1(0(0(2(1(1(1(2(1(z0))))))))))))))))))))))))))) 0(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(z0))))))))))))))))))))))) -> 1(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))))) 0(1(2(2(1(0(2(2(1(1(1(2(0(0(2(2(0(0(1(1(2(2(1(z0))))))))))))))))))))))) -> 1(1(2(2(1(1(2(0(1(0(2(1(2(0(1(1(1(2(1(0(1(1(2(0(1(1(1(z0))))))))))))))))))))))))))) 0(1(2(2(1(1(2(0(2(1(2(0(1(2(1(2(2(2(2(0(2(0(0(z0))))))))))))))))))))))) -> 1(0(2(0(0(1(2(2(2(1(1(1(0(1(2(1(2(1(1(1(1(2(2(1(1(2(0(z0))))))))))))))))))))))))))) 0(1(2(2(2(0(0(0(0(1(0(0(2(2(0(2(0(2(2(0(1(1(0(z0))))))))))))))))))))))) -> 0(0(2(1(1(1(0(1(2(2(0(2(0(0(0(1(0(2(2(2(1(0(1(2(1(1(0(z0))))))))))))))))))))))))))) 0(2(0(1(0(0(2(1(2(1(1(2(1(2(0(1(1(0(1(0(2(0(1(z0))))))))))))))))))))))) -> 1(2(2(1(1(2(1(1(1(1(0(0(0(1(1(0(0(0(2(1(1(0(2(2(2(0(1(z0))))))))))))))))))))))))))) 0(2(0(2(0(2(0(2(1(1(0(1(2(2(1(0(1(0(0(1(0(2(1(z0))))))))))))))))))))))) -> 1(1(1(1(2(0(2(2(2(1(0(2(0(2(2(2(2(1(0(1(2(1(0(0(0(1(1(z0))))))))))))))))))))))))))) 0(2(0(2(1(0(0(2(2(2(2(0(2(1(0(1(2(0(2(1(0(0(0(z0))))))))))))))))))))))) -> 0(2(0(2(1(1(0(1(1(1(2(1(2(0(1(0(1(2(1(1(2(1(1(1(2(2(2(z0))))))))))))))))))))))))))) 0(2(1(0(1(0(0(1(1(0(2(0(0(0(1(0(1(1(0(1(0(2(1(z0))))))))))))))))))))))) -> 1(1(0(1(1(1(1(0(2(2(2(2(2(0(1(1(2(1(2(2(1(2(0(0(0(1(1(z0))))))))))))))))))))))))))) 0(2(1(2(0(1(0(0(1(0(0(2(2(2(2(2(1(0(2(0(2(2(1(z0))))))))))))))))))))))) -> 1(2(0(1(0(0(2(1(1(2(1(0(0(1(1(1(1(2(1(0(2(0(0(0(1(1(1(z0))))))))))))))))))))))))))) 0(2(1(2(0(2(2(2(2(2(2(2(0(1(0(1(0(2(1(1(0(0(0(z0))))))))))))))))))))))) -> 2(0(2(2(1(1(1(0(0(1(1(1(0(1(1(2(1(1(0(1(1(1(1(2(2(2(2(z0))))))))))))))))))))))))))) 0(2(2(2(1(2(0(1(1(2(1(2(0(0(2(1(0(1(2(2(2(0(1(z0))))))))))))))))))))))) -> 0(2(2(2(0(2(2(0(0(1(1(1(0(1(0(2(1(1(0(2(0(1(2(1(0(2(1(z0))))))))))))))))))))))))))) 1(0(0(0(1(1(0(2(0(1(1(2(1(1(2(2(1(2(1(0(0(0(2(z0))))))))))))))))))))))) -> 1(1(0(2(1(1(0(1(0(1(1(1(0(0(2(1(0(2(1(1(0(2(1(0(2(2(2(z0))))))))))))))))))))))))))) 1(0(0(1(1(2(0(1(1(2(2(2(0(1(0(2(0(2(0(1(1(2(1(z0))))))))))))))))))))))) -> 1(1(1(1(1(1(0(0(1(1(0(2(1(2(2(1(2(2(0(2(1(1(2(2(0(0(1(z0))))))))))))))))))))))))))) 1(0(1(1(2(2(2(1(2(2(1(0(2(2(1(0(1(2(2(2(1(0(0(z0))))))))))))))))))))))) -> 1(2(1(1(0(2(2(1(1(1(1(1(1(1(2(2(2(1(0(0(1(1(1(1(1(1(2(z0))))))))))))))))))))))))))) 1(0(1(2(0(2(0(0(2(1(0(2(0(1(2(1(0(2(0(2(0(0(1(z0))))))))))))))))))))))) -> 1(1(0(1(2(1(2(1(1(2(2(0(2(1(0(0(1(1(1(2(0(0(1(2(1(2(1(z0))))))))))))))))))))))))))) 1(0(1(2(2(2(1(1(1(0(1(0(2(0(1(1(0(2(1(0(1(0(0(z0))))))))))))))))))))))) -> 1(1(0(0(2(0(2(2(1(0(1(1(0(1(1(1(0(2(2(1(1(0(1(1(1(1(1(z0))))))))))))))))))))))))))) 1(0(2(1(0(2(0(1(0(0(0(1(0(2(1(2(0(0(2(2(1(0(2(z0))))))))))))))))))))))) -> 1(0(1(1(1(1(0(0(0(1(1(1(0(0(2(0(0(2(0(0(2(1(1(1(1(1(1(z0))))))))))))))))))))))))))) 1(0(2(2(0(1(2(0(1(2(1(2(1(0(1(2(0(2(2(2(1(2(2(z0))))))))))))))))))))))) -> 1(1(0(1(2(0(2(0(1(0(0(2(2(2(2(0(2(2(1(2(1(1(1(1(1(2(2(z0))))))))))))))))))))))))))) 1(1(0(0(1(0(2(1(0(0(2(1(0(0(2(0(1(2(1(0(0(0(0(z0))))))))))))))))))))))) -> 1(1(1(0(0(2(1(2(1(0(0(1(1(2(2(1(1(1(1(2(1(1(1(1(0(2(2(z0))))))))))))))))))))))))))) 1(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(z0))))))))))))))))))))))) -> 1(1(0(1(1(1(1(0(2(1(0(0(2(1(1(2(0(2(1(2(1(2(0(1(0(2(1(z0))))))))))))))))))))))))))) 1(1(0(2(0(1(2(2(2(2(0(2(1(2(1(2(0(2(1(0(2(2(0(z0))))))))))))))))))))))) -> 1(1(1(0(1(2(2(1(2(0(1(1(2(1(1(0(1(2(2(0(1(1(1(0(1(0(2(z0))))))))))))))))))))))))))) 1(1(0(2(1(0(2(2(0(0(1(1(0(1(0(0(2(1(2(1(0(1(2(z0))))))))))))))))))))))) -> 1(0(1(2(1(2(1(1(0(2(2(2(1(1(1(1(1(2(1(1(1(0(0(0(0(2(1(z0))))))))))))))))))))))))))) 1(1(0(2(1(2(1(0(0(1(1(2(2(2(0(2(2(2(1(0(2(0(2(z0))))))))))))))))))))))) -> 1(2(1(0(0(1(1(0(1(1(1(1(2(1(1(2(1(1(1(0(1(1(0(2(2(2(0(z0))))))))))))))))))))))))))) 1(1(0(2(1(2(2(2(0(2(1(0(0(1(2(0(2(1(1(1(2(0(0(z0))))))))))))))))))))))) -> 1(2(1(1(2(0(1(1(1(2(1(1(1(2(2(1(1(1(1(1(0(0(2(1(2(0(2(z0))))))))))))))))))))))))))) 1(1(1(1(2(2(0(0(1(1(1(2(1(2(0(2(2(0(0(1(2(1(1(z0))))))))))))))))))))))) -> 1(2(2(1(0(1(2(1(1(1(2(1(1(1(1(1(1(0(1(1(1(1(0(2(0(1(1(z0))))))))))))))))))))))))))) 1(1(1(2(2(1(1(1(2(2(0(2(0(1(2(0(0(2(2(2(0(0(0(z0))))))))))))))))))))))) -> 1(1(0(1(1(1(0(0(0(1(2(2(2(1(1(1(1(0(2(2(2(2(2(0(1(2(2(z0))))))))))))))))))))))))))) 1(1(2(0(2(1(1(2(1(1(1(1(1(0(0(1(2(2(2(1(2(0(0(z0))))))))))))))))))))))) -> 1(2(1(1(1(0(0(1(1(1(1(0(2(2(2(2(1(0(0(1(2(1(1(1(0(2(2(z0))))))))))))))))))))))))))) 1(1(2(1(0(1(1(0(0(1(2(0(0(0(0(0(2(0(1(1(0(0(2(z0))))))))))))))))))))))) -> 1(1(1(0(0(0(2(0(2(1(2(2(2(2(2(2(1(1(1(1(2(1(0(0(0(0(2(z0))))))))))))))))))))))))))) 1(1(2(2(2(0(1(1(2(0(2(2(2(2(2(0(1(1(2(2(1(2(1(z0))))))))))))))))))))))) -> 1(2(0(1(0(2(1(1(2(2(2(1(1(1(2(2(1(1(1(2(1(1(1(2(1(1(1(z0))))))))))))))))))))))))))) 1(1(2(2(2(0(1(1(2(1(0(0(1(0(0(2(1(2(2(0(1(2(2(z0))))))))))))))))))))))) -> 1(2(1(0(1(1(0(2(2(1(1(2(1(1(0(2(2(1(2(2(2(2(2(0(1(1(1(z0))))))))))))))))))))))))))) 1(1(2(2(2(2(1(2(2(1(0(2(2(1(1(2(2(0(0(0(0(0(0(z0))))))))))))))))))))))) -> 1(1(0(2(0(1(2(2(0(1(1(1(1(1(0(1(2(1(1(2(0(2(2(0(2(1(1(z0))))))))))))))))))))))))))) 1(2(0(0(0(0(1(1(0(2(2(2(2(1(0(1(0(0(0(2(1(0(1(z0))))))))))))))))))))))) -> 1(2(1(1(0(1(1(2(1(2(0(2(1(1(1(0(1(1(1(0(1(0(1(0(2(1(1(z0))))))))))))))))))))))))))) 1(2(0(0(1(1(1(1(0(2(2(0(2(2(0(2(0(2(1(1(1(1(1(z0))))))))))))))))))))))) -> 1(1(0(2(1(1(0(1(1(1(1(2(1(2(1(1(0(0(1(1(1(0(2(2(1(2(1(z0))))))))))))))))))))))))))) 1(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(z0))))))))))))))))))))))) -> 1(1(0(1(0(0(1(1(1(1(1(1(2(1(0(0(0(2(1(0(0(1(0(2(2(2(0(z0))))))))))))))))))))))))))) 1(2(0(1(1(1(2(2(2(1(1(1(1(2(0(0(0(2(1(2(0(0(0(z0))))))))))))))))))))))) -> 1(2(1(2(1(1(1(0(1(1(0(1(1(1(0(2(2(0(2(1(0(2(1(0(2(2(2(z0))))))))))))))))))))))))))) 1(2(0(2(0(0(1(2(2(1(1(2(1(1(1(2(1(1(2(1(0(0(0(z0))))))))))))))))))))))) -> 1(1(1(0(1(2(1(1(2(1(1(1(0(0(0(2(0(1(2(1(0(0(1(1(1(1(0(z0))))))))))))))))))))))))))) 1(2(0(2(1(1(1(0(2(0(1(2(0(2(0(2(0(1(1(0(2(2(0(z0))))))))))))))))))))))) -> 1(2(2(1(1(1(0(1(2(1(1(2(1(0(0(2(1(0(2(1(1(1(0(1(0(2(0(z0))))))))))))))))))))))))))) 1(2(0(2(1(2(0(2(0(1(0(0(1(1(0(2(2(2(1(1(2(2(0(z0))))))))))))))))))))))) -> 1(1(1(1(2(1(2(1(0(1(0(2(2(1(1(0(1(2(1(1(1(1(0(2(0(2(2(z0))))))))))))))))))))))))))) 1(2(0(2(2(1(0(0(2(2(0(0(2(2(1(2(2(0(1(1(1(2(1(z0))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(2(1(1(1(1(1(1(2(0(0(2(1(0(0(1(2(2(2(1(z0))))))))))))))))))))))))))) 1(2(1(1(2(1(0(0(2(1(0(1(2(1(1(0(1(2(0(2(2(0(1(z0))))))))))))))))))))))) -> 1(2(1(1(1(0(2(0(2(0(0(2(1(0(2(1(1(1(1(1(0(0(0(1(0(1(1(z0))))))))))))))))))))))))))) 1(2(1(2(1(2(2(1(0(2(1(1(1(0(0(2(2(0(2(0(2(2(1(z0))))))))))))))))))))))) -> 1(0(2(1(0(1(0(0(1(1(1(2(0(2(2(1(1(1(1(1(2(2(1(2(1(0(1(z0))))))))))))))))))))))))))) 1(2(2(0(1(2(0(1(1(2(1(2(2(0(1(0(1(0(2(2(2(1(0(z0))))))))))))))))))))))) -> 1(1(0(0(0(1(0(2(1(0(2(2(2(1(0(0(2(1(1(0(2(2(2(2(1(1(0(z0))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(0(2(0(0(1(1(1(0(1(2(2(2(2(1(2(z0))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(0(1(0(0(0(1(1(1(2(0(2(2(2(2(1(1(1(1(2(z0))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(1(0(1(0(0(2(1(2(0(2(2(2(0(0(z0))))))))))))))))))))))) -> 1(1(1(0(2(2(0(0(2(2(2(1(2(1(1(1(1(0(2(2(2(0(1(0(2(0(2(z0))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(2(2(0(1(2(0(0(0(2(0(2(1(0(1(z0))))))))))))))))))))))) -> 1(0(1(2(1(1(2(1(0(0(1(1(0(0(2(2(0(0(2(2(0(2(1(1(1(2(1(z0))))))))))))))))))))))))))) 1(2(2(2(0(1(2(2(1(1(1(1(1(2(2(0(1(2(1(2(0(0(1(z0))))))))))))))))))))))) -> 1(1(1(1(0(1(1(1(0(0(1(0(0(0(2(1(1(1(1(1(1(1(0(1(2(0(1(z0))))))))))))))))))))))))))) 2(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> 2(0(0(0(0(1(1(2(0(1(2(2(1(0(2(0(2(2(2(0(1(0(1(1(1(1(0(z0))))))))))))))))))))))))))) 2(0(0(2(1(0(1(1(1(2(0(0(1(1(1(0(1(2(1(1(0(0(0(z0))))))))))))))))))))))) -> 1(1(0(0(1(1(1(0(0(1(0(2(1(1(1(1(1(2(1(2(1(1(1(1(1(1(0(z0))))))))))))))))))))))))))) 2(0(0(2(1(1(1(1(2(2(2(1(2(1(0(2(2(1(0(0(2(0(1(z0))))))))))))))))))))))) -> 1(1(1(2(2(1(1(1(2(1(2(0(2(2(1(1(1(1(0(2(0(2(1(1(0(2(1(z0))))))))))))))))))))))))))) 2(0(1(0(1(1(1(1(2(2(2(2(0(0(1(0(1(0(0(0(2(2(0(z0))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(1(2(2(2(0(2(2(1(1(2(2(2(0(1(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(0(1(2(0(1(1(0(2(2(2(2(0(2(1(0(2(1(2(1(0(2(1(z0))))))))))))))))))))))) -> 2(1(1(0(1(1(0(2(1(1(1(0(1(0(0(2(1(1(1(0(2(0(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(0(2(0(0(1(1(1(2(0(2(2(2(0(0(1(2(2(0(0(1(0(1(z0))))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(1(1(1(1(0(1(2(2(2(1(2(0(1(2(0(1(1(1(z0))))))))))))))))))))))))))) 2(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> 2(2(2(1(0(1(1(0(2(2(0(0(1(1(1(1(1(1(0(1(1(1(2(0(2(2(0(z0))))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(1(2(2(0(2(0(1(2(1(0(0(1(0(2(1(z0))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(2(2(0(1(2(1(0(1(0(1(2(2(1(1(0(2(1(0(1(z0))))))))))))))))))))))))))) 2(0(2(1(0(1(2(2(1(2(2(0(2(0(2(0(2(2(1(2(0(2(2(z0))))))))))))))))))))))) -> 0(1(0(2(2(0(0(0(1(1(2(0(1(1(0(2(0(1(1(1(1(1(0(1(0(2(2(z0))))))))))))))))))))))))))) 2(0(2(1(1(0(2(1(0(2(1(2(2(0(0(1(0(1(0(2(0(2(0(z0))))))))))))))))))))))) -> 1(1(1(0(1(2(0(0(1(1(2(1(2(2(1(1(1(1(2(1(2(1(2(1(1(2(1(z0))))))))))))))))))))))))))) 2(1(0(1(0(2(2(2(1(2(2(0(1(2(1(1(1(1(0(0(2(0(2(z0))))))))))))))))))))))) -> 2(1(2(1(2(1(1(1(2(2(1(2(1(1(1(0(1(1(1(2(1(0(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(1(0(1(1(0(1(2(1(0(2(2(0(1(0(1(2(0(2(2(1(2(0(z0))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(z0))))))))))))))))))))))))))) 2(1(0(1(1(2(2(2(0(2(1(0(0(0(2(2(2(2(2(0(0(1(1(z0))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(z0))))))))))))))))))))))))))) 2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(z0))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(z0))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(z0))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(z0))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(z0))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(z0))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(z0))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(z0))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(z0))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(z0))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(z0))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(z0))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(z0))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(z0))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(z0))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))) Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(2'(encArg(z0)), ENCARG(z0)) 0'(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> c6(0'(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))), 2'(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))), 1'(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))), 2'(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))), 2'(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))), 2'(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))), 1'(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))), 0'(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))), 1'(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))), 1'(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))), 1'(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))), 1'(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))), 1'(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))), 0'(1(1(1(1(1(1(2(1(2(1(z0))))))))))), 1'(1(1(1(1(1(2(1(2(1(z0)))))))))), 1'(1(1(1(1(2(1(2(1(z0))))))))), 1'(1(1(1(2(1(2(1(z0)))))))), 1'(1(1(2(1(2(1(z0))))))), 1'(1(2(1(2(1(z0)))))), 1'(2(1(2(1(z0))))), 2'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> c7(1'(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))), 1'(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))))), 1'(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))), 2'(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))), 1'(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))), 1'(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))), 0'(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))), 0'(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))), 1'(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))), 1'(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))), 0'(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))), 1'(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))), 2'(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))), 1'(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))), 1'(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))), 1'(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))), 1'(1(0(1(2(2(1(1(2(0(0(z0))))))))))), 1'(0(1(2(2(1(1(2(0(0(z0)))))))))), 0'(1(2(2(1(1(2(0(0(z0))))))))), 1'(2(2(1(1(2(0(0(z0)))))))), 2'(2(1(1(2(0(0(z0))))))), 2'(1(1(2(0(0(z0)))))), 1'(1(2(0(0(z0))))), 1'(2(0(0(z0)))), 2'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> c8(2'(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))), 0'(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))))), 2'(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))), 1'(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))), 0'(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))), 1'(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))), 1'(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))), 1'(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))), 0'(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))), 2'(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))), 1'(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))), 1'(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))), 1'(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))), 1'(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))), 2'(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(z0))))))))))), 1'(2(2(2(1(1(0(1(1(1(z0)))))))))), 2'(2(2(1(1(0(1(1(1(z0))))))))), 2'(2(1(1(0(1(1(1(z0)))))))), 2'(1(1(0(1(1(1(z0))))))), 1'(1(0(1(1(1(z0)))))), 1'(0(1(1(1(z0))))), 0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> c9(0'(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))), 1'(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))))), 1'(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))), 1'(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))), 1'(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))), 0'(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))), 2'(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))), 1'(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))), 1'(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))), 0'(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))), 1'(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))), 1'(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))), 1'(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))), 0'(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))), 2'(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))), 1'(1(1(0(0(0(2(1(0(2(1(z0))))))))))), 1'(1(0(0(0(2(1(0(2(1(z0)))))))))), 1'(0(0(0(2(1(0(2(1(z0))))))))), 0'(0(0(2(1(0(2(1(z0)))))))), 0'(0(2(1(0(2(1(z0))))))), 0'(2(1(0(2(1(z0)))))), 2'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(z0))))))))))))))))))))))) -> c10(0'(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))))), 0'(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))))))), 2'(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))), 1'(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))))), 0'(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))), 1'(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))), 1'(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))), 1'(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))), 1'(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))), 2'(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))), 0'(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))), 1'(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))), 0'(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))), 0'(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))), 0'(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))), 1'(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))), 0'(1(1(1(1(1(1(1(0(1(0(z0))))))))))), 1'(1(1(1(1(1(1(0(1(0(z0)))))))))), 1'(1(1(1(1(1(0(1(0(z0))))))))), 1'(1(1(1(1(0(1(0(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))), 1'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(z0))))))))))))))))))))))) -> c11(1'(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))))))), 1'(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0)))))))))))))))))))))))))), 1'(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))))), 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1'(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))))), 1'(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))), 1'(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))), 2'(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))), 2'(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))), 2'(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))), 1'(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))), 1'(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))), 2'(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))), 1'(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))), 1'(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))), 2'(1(0(2(0(2(0(2(2(1(0(z0))))))))))), 1'(0(2(0(2(0(2(2(1(0(z0)))))))))), 0'(2(0(2(0(2(2(1(0(z0))))))))), 2'(0(2(0(2(2(1(0(z0)))))))), 0'(2(0(2(2(1(0(z0))))))), 2'(0(2(2(1(0(z0)))))), 0'(2(2(1(0(z0))))), 2'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> c102(2'(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))), 2'(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))))), 1'(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))), 1'(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))), 1'(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))), 2'(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))), 1'(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))), 0'(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))), 2'(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))), 1'(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))), 1'(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))), 2'(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))), 2'(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))), 0'(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))), 1'(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))), 1'(0(1(2(0(1(0(2(1(1(2(z0))))))))))), 0'(1(2(0(1(0(2(1(1(2(z0)))))))))), 1'(2(0(1(0(2(1(1(2(z0))))))))), 2'(0(1(0(2(1(1(2(z0)))))))), 0'(1(0(2(1(1(2(z0))))))), 1'(0(2(1(1(2(z0)))))), 0'(2(1(1(2(z0))))), 2'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) 2'(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> c103(2'(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))), 2'(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))))), 0'(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))), 1'(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))), 1'(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))), 0'(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))), 2'(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))), 2'(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))), 1'(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))), 1'(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))), 2'(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))), 1'(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))), 1'(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))), 1'(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))), 1'(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))), 2'(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))), 0'(0(1(0(2(2(1(1(2(0(1(z0))))))))))), 0'(1(0(2(2(1(1(2(0(1(z0)))))))))), 1'(0(2(2(1(1(2(0(1(z0))))))))), 0'(2(2(1(1(2(0(1(z0)))))))), 2'(2(1(1(2(0(1(z0))))))), 2'(1(1(2(0(1(z0)))))), 1'(1(2(0(1(z0))))), 1'(2(0(1(z0)))), 2'(0(1(z0))), 0'(1(z0)), 1'(z0)) 2'(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> c104(2'(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))), 2'(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))), 1'(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))), 1'(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))), 1'(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))), 2'(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))), 0'(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))), 2'(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))), 2'(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))), 0'(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))), 1'(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))), 1'(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))), 0'(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))), 0'(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))), 1'(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))), 1'(1(0(1(1(1(0(1(2(1(0(z0))))))))))), 1'(0(1(1(1(0(1(2(1(0(z0)))))))))), 0'(1(1(1(0(1(2(1(0(z0))))))))), 1'(1(1(0(1(2(1(0(z0)))))))), 1'(1(0(1(2(1(0(z0))))))), 1'(0(1(2(1(0(z0)))))), 0'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(z0))))))))))))))))))))))) -> c33(1'(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))))), 2'(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))))), 1'(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))), 1'(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))), 1'(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))), 2'(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))), 0'(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))), 2'(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))), 2'(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))), 2'(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))), 2'(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))), 1'(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))), 2'(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))), 1'(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))), 1'(0(1(0(1(2(2(2(1(1(1(z0))))))))))), 0'(1(0(1(2(2(2(1(1(1(z0)))))))))), 1'(0(1(2(2(2(1(1(1(z0))))))))), 2'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 1'(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(z0))))))))))))))))))))))) -> c52(0'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c66(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> c79(1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c85(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) ENCODE_0(z0) -> c105(0'(encArg(z0))) ENCODE_1(z0) -> c105(1'(encArg(z0))) ENCODE_2(z0) -> c105(2'(encArg(z0))) S tuples: 0'(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> c6(0'(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))), 2'(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))), 1'(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))), 2'(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))), 2'(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))), 2'(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))), 1'(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))), 0'(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))), 1'(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))), 1'(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))), 1'(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))), 1'(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))), 1'(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))), 0'(1(1(1(1(1(1(2(1(2(1(z0))))))))))), 1'(1(1(1(1(1(2(1(2(1(z0)))))))))), 1'(1(1(1(1(2(1(2(1(z0))))))))), 1'(1(1(1(2(1(2(1(z0)))))))), 1'(1(1(2(1(2(1(z0))))))), 1'(1(2(1(2(1(z0)))))), 1'(2(1(2(1(z0))))), 2'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> c7(1'(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))), 1'(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))))), 1'(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))), 2'(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))), 1'(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))), 1'(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))), 0'(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))), 0'(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))), 1'(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))), 1'(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))), 0'(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))), 1'(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))), 2'(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))), 1'(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))), 1'(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))), 1'(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))), 1'(1(0(1(2(2(1(1(2(0(0(z0))))))))))), 1'(0(1(2(2(1(1(2(0(0(z0)))))))))), 0'(1(2(2(1(1(2(0(0(z0))))))))), 1'(2(2(1(1(2(0(0(z0)))))))), 2'(2(1(1(2(0(0(z0))))))), 2'(1(1(2(0(0(z0)))))), 1'(1(2(0(0(z0))))), 1'(2(0(0(z0)))), 2'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> c8(2'(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))), 0'(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))))), 2'(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))), 1'(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))), 0'(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))), 1'(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))), 1'(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))), 1'(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))), 0'(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))), 2'(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))), 1'(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))), 1'(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))), 1'(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))), 1'(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))), 2'(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(z0))))))))))), 1'(2(2(2(1(1(0(1(1(1(z0)))))))))), 2'(2(2(1(1(0(1(1(1(z0))))))))), 2'(2(1(1(0(1(1(1(z0)))))))), 2'(1(1(0(1(1(1(z0))))))), 1'(1(0(1(1(1(z0)))))), 1'(0(1(1(1(z0))))), 0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> c9(0'(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))), 1'(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))))), 1'(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))), 1'(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))), 1'(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))), 0'(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))), 2'(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))), 1'(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))), 1'(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))), 0'(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))), 1'(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))), 1'(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))), 1'(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))), 0'(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))), 2'(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))), 1'(1(1(0(0(0(2(1(0(2(1(z0))))))))))), 1'(1(0(0(0(2(1(0(2(1(z0)))))))))), 1'(0(0(0(2(1(0(2(1(z0))))))))), 0'(0(0(2(1(0(2(1(z0)))))))), 0'(0(2(1(0(2(1(z0))))))), 0'(2(1(0(2(1(z0)))))), 2'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(1(1(0(0(1(1(2(1(2(2(2(2(2(0(0(2(1(1(2(1(0(z0))))))))))))))))))))))) -> c10(0'(0(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))))), 0'(2(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))))))), 2'(1(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))))), 1'(0(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))))), 0'(1(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))))), 1'(1(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))))), 1'(1(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))))), 1'(1(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))))), 1'(2(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))))), 2'(0(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))))), 0'(1(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))))), 1'(0(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))))), 0'(0(0(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))))), 0'(0(1(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))))), 0'(1(0(1(1(1(1(1(1(1(0(1(0(z0))))))))))))), 1'(0(1(1(1(1(1(1(1(0(1(0(z0)))))))))))), 0'(1(1(1(1(1(1(1(0(1(0(z0))))))))))), 1'(1(1(1(1(1(1(0(1(0(z0)))))))))), 1'(1(1(1(1(1(0(1(0(z0))))))))), 1'(1(1(1(1(0(1(0(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))), 1'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(0(2(1(0(2(2(1(1(2(2(1(2(0(2(1(2(2(1(1(0(2(1(z0))))))))))))))))))))))) -> c11(1'(1(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))))))), 1'(1(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0)))))))))))))))))))))))))), 1'(0(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))))), 0'(1(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0)))))))))))))))))))))))), 1'(0(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))))), 0'(2(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0)))))))))))))))))))))), 2'(1(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))))), 1'(2(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0)))))))))))))))))))), 2'(2(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))))), 2'(1(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0)))))))))))))))))), 1'(1(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))))), 1'(2(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0)))))))))))))))), 2'(0(1(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))))), 0'(1(1(1(2(0(2(1(1(2(1(1(0(1(z0)))))))))))))), 1'(1(1(2(0(2(1(1(2(1(1(0(1(z0))))))))))))), 1'(1(2(0(2(1(1(2(1(1(0(1(z0)))))))))))), 1'(2(0(2(1(1(2(1(1(0(1(z0))))))))))), 2'(0(2(1(1(2(1(1(0(1(z0)))))))))), 0'(2(1(1(2(1(1(0(1(z0))))))))), 2'(1(1(2(1(1(0(1(z0)))))))), 1'(1(2(1(1(0(1(z0))))))), 1'(2(1(1(0(1(z0)))))), 2'(1(1(0(1(z0))))), 1'(1(0(1(z0)))), 1'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(0(2(1(1(2(1(0(0(2(1(2(0(2(0(2(1(2(2(2(2(1(1(z0))))))))))))))))))))))) -> c12(0'(2(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(z0))))))))))))))))))))))))))), 2'(0(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(z0)))))))))))))))))))))))))), 0'(2(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(z0))))))))))))))))))))))))), 2'(2(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(z0)))))))))))))))))))))))), 2'(0(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(z0))))))))))))))))))))))), 0'(2(1(1(1(1(0(0(2(0(1(1(0(0(1(1(1(1(1(0(2(1(z0)))))))))))))))))))))), 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2'(1(z0)), 1'(z0)) 2'(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(z0))))))))))))))))))))))) -> c101(2'(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))))), 1'(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))))))), 1'(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))), 1'(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))))), 1'(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))))), 1'(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))))), 2'(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))), 2'(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))))), 2'(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))), 1'(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))))), 1'(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))), 2'(1(1(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))))), 1'(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))), 1'(2(1(0(2(0(2(0(2(2(1(0(z0)))))))))))), 2'(1(0(2(0(2(0(2(2(1(0(z0))))))))))), 1'(0(2(0(2(0(2(2(1(0(z0)))))))))), 0'(2(0(2(0(2(2(1(0(z0))))))))), 2'(0(2(0(2(2(1(0(z0)))))))), 0'(2(0(2(2(1(0(z0))))))), 2'(0(2(2(1(0(z0)))))), 0'(2(2(1(0(z0))))), 2'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> c102(2'(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))), 2'(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))))), 1'(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))), 1'(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))))), 1'(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))), 2'(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))))), 1'(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))), 0'(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))))), 2'(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))))), 1'(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))), 1'(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))))), 2'(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))), 2'(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))), 0'(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))), 1'(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))), 1'(0(1(2(0(1(0(2(1(1(2(z0))))))))))), 0'(1(2(0(1(0(2(1(1(2(z0)))))))))), 1'(2(0(1(0(2(1(1(2(z0))))))))), 2'(0(1(0(2(1(1(2(z0)))))))), 0'(1(0(2(1(1(2(z0))))))), 1'(0(2(1(1(2(z0)))))), 0'(2(1(1(2(z0))))), 2'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) 2'(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> c103(2'(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))), 2'(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))))), 0'(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))), 1'(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))), 1'(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))), 0'(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))), 2'(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))), 2'(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))), 1'(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))), 1'(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))), 2'(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))), 1'(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))), 1'(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))), 1'(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))), 1'(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))), 2'(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))), 0'(0(1(0(2(2(1(1(2(0(1(z0))))))))))), 0'(1(0(2(2(1(1(2(0(1(z0)))))))))), 1'(0(2(2(1(1(2(0(1(z0))))))))), 0'(2(2(1(1(2(0(1(z0)))))))), 2'(2(1(1(2(0(1(z0))))))), 2'(1(1(2(0(1(z0)))))), 1'(1(2(0(1(z0))))), 1'(2(0(1(z0)))), 2'(0(1(z0))), 0'(1(z0)), 1'(z0)) 2'(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> c104(2'(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))), 2'(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))), 1'(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))), 1'(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))), 1'(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))), 2'(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))), 0'(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))), 2'(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))), 2'(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))), 0'(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))), 1'(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))), 1'(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))), 0'(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))), 0'(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))), 1'(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))), 1'(1(0(1(1(1(0(1(2(1(0(z0))))))))))), 1'(0(1(1(1(0(1(2(1(0(z0)))))))))), 0'(1(1(1(0(1(2(1(0(z0))))))))), 1'(1(1(0(1(2(1(0(z0)))))))), 1'(1(0(1(2(1(0(z0))))))), 1'(0(1(2(1(0(z0)))))), 0'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(z0))))))))))))))))))))))) -> c33(1'(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))))), 2'(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))))), 1'(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))), 1'(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))), 1'(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))), 2'(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))), 0'(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))), 2'(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))), 2'(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))), 2'(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))), 2'(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))), 1'(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))), 2'(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))), 1'(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))), 1'(0(1(0(1(2(2(2(1(1(1(z0))))))))))), 0'(1(0(1(2(2(2(1(1(1(z0)))))))))), 1'(0(1(2(2(2(1(1(1(z0))))))))), 2'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 1'(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(z0))))))))))))))))))))))) -> c52(0'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c66(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> c79(1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c85(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) K tuples:none Defined Rule Symbols: encArg_1, 0_1, 1_1, 2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, 2'_1, ENCODE_0_1, ENCODE_1_1, ENCODE_2_1 Compound Symbols: c_2, c1_2, c2_2, c6_27, c7_27, c8_27, c9_27, c10_27, c11_27, c12_27, c13_27, c14_27, c15_27, c16_27, c17_27, c18_27, c19_27, c20_27, c21_27, c22_27, c23_27, c24_27, c25_27, c26_27, c27_27, c28_27, c29_27, c30_27, c31_27, c32_27, c34_27, c35_27, c36_27, c37_27, c38_27, c39_27, c40_27, c41_27, c42_27, c43_27, c44_27, c45_27, c46_27, c47_27, c48_27, c49_27, c50_27, c51_27, c53_27, c54_27, c55_27, c56_27, c57_27, c58_27, c59_27, c60_27, c61_27, c62_27, c63_27, c64_27, c65_27, c67_27, c68_27, c69_27, c70_27, c71_27, c72_27, c73_27, c74_27, c75_27, c76_27, c77_27, c78_27, c80_27, c81_27, c82_27, c83_27, c84_27, c86_27, c87_27, c88_27, c89_27, c90_27, c91_27, c92_27, c93_27, c94_27, c95_27, c96_27, c97_27, c98_27, c99_27, c100_27, c101_27, c102_27, c103_27, c104_27, c33_23, c52_5, c66_3, c79_3, c85_3, c105_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) by ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(0'(2(encArg(z0))), ENCARG(cons_2(z0))) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 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1(2(1(1(2(1(0(0(2(1(0(1(2(1(1(0(1(2(0(2(2(0(1(z0))))))))))))))))))))))) -> 1(2(1(1(1(0(2(0(2(0(0(2(1(0(2(1(1(1(1(1(0(0(0(1(0(1(1(z0))))))))))))))))))))))))))) 1(2(1(2(1(2(2(1(0(2(1(1(1(0(0(2(2(0(2(0(2(2(1(z0))))))))))))))))))))))) -> 1(0(2(1(0(1(0(0(1(1(1(2(0(2(2(1(1(1(1(1(2(2(1(2(1(0(1(z0))))))))))))))))))))))))))) 1(2(2(0(1(2(0(1(1(2(1(2(2(0(1(0(1(0(2(2(2(1(0(z0))))))))))))))))))))))) -> 1(1(0(0(0(1(0(2(1(0(2(2(2(1(0(0(2(1(1(0(2(2(2(2(1(1(0(z0))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(0(2(0(0(1(1(1(0(1(2(2(2(2(1(2(z0))))))))))))))))))))))) -> 1(1(2(2(2(1(2(0(0(1(0(0(0(1(1(1(2(0(2(2(2(2(1(1(1(1(2(z0))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(1(0(1(0(0(2(1(2(0(2(2(2(0(0(z0))))))))))))))))))))))) -> 1(1(1(0(2(2(0(0(2(2(2(1(2(1(1(1(1(0(2(2(2(0(1(0(2(0(2(z0))))))))))))))))))))))))))) 1(2(2(1(1(0(1(2(1(2(2(0(1(2(0(0(0(2(0(2(1(0(1(z0))))))))))))))))))))))) -> 1(0(1(2(1(1(2(1(0(0(1(1(0(0(2(2(0(0(2(2(0(2(1(1(1(2(1(z0))))))))))))))))))))))))))) 1(2(2(2(0(1(2(2(1(1(1(1(1(2(2(0(1(2(1(2(0(0(1(z0))))))))))))))))))))))) -> 1(1(1(1(0(1(1(1(0(0(1(0(0(0(2(1(1(1(1(1(1(1(0(1(2(0(1(z0))))))))))))))))))))))))))) 2(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> 2(0(0(0(0(1(1(2(0(1(2(2(1(0(2(0(2(2(2(0(1(0(1(1(1(1(0(z0))))))))))))))))))))))))))) 2(0(0(2(1(0(1(1(1(2(0(0(1(1(1(0(1(2(1(1(0(0(0(z0))))))))))))))))))))))) -> 1(1(0(0(1(1(1(0(0(1(0(2(1(1(1(1(1(2(1(2(1(1(1(1(1(1(0(z0))))))))))))))))))))))))))) 2(0(0(2(1(1(1(1(2(2(2(1(2(1(0(2(2(1(0(0(2(0(1(z0))))))))))))))))))))))) -> 1(1(1(2(2(1(1(1(2(1(2(0(2(2(1(1(1(1(0(2(0(2(1(1(0(2(1(z0))))))))))))))))))))))))))) 2(0(1(0(1(1(1(1(2(2(2(2(0(0(1(0(1(0(0(0(2(2(0(z0))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(1(2(2(2(0(2(2(1(1(2(2(2(0(1(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(0(1(2(0(1(1(0(2(2(2(2(0(2(1(0(2(1(2(1(0(2(1(z0))))))))))))))))))))))) -> 2(1(1(0(1(1(0(2(1(1(1(0(1(0(0(2(1(1(1(0(2(0(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(0(2(0(0(1(1(1(2(0(2(2(2(0(0(1(2(2(0(0(1(0(1(z0))))))))))))))))))))))) -> 2(0(0(2(2(1(2(1(2(1(1(1(1(0(1(2(2(2(1(2(0(1(2(0(1(1(1(z0))))))))))))))))))))))))))) 2(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> 2(2(2(1(0(1(1(0(2(2(0(0(1(1(1(1(1(1(0(1(1(1(2(0(2(2(0(z0))))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(1(2(2(0(2(0(1(2(1(0(0(1(0(2(1(z0))))))))))))))))))))))) -> 2(2(2(2(2(2(1(1(2(2(0(1(2(1(0(1(0(1(2(2(1(1(0(2(1(0(1(z0))))))))))))))))))))))))))) 2(0(2(1(0(1(2(2(1(2(2(0(2(0(2(0(2(2(1(2(0(2(2(z0))))))))))))))))))))))) -> 0(1(0(2(2(0(0(0(1(1(2(0(1(1(0(2(0(1(1(1(1(1(0(1(0(2(2(z0))))))))))))))))))))))))))) 2(0(2(1(1(0(2(1(0(2(1(2(2(0(0(1(0(1(0(2(0(2(0(z0))))))))))))))))))))))) -> 1(1(1(0(1(2(0(0(1(1(2(1(2(2(1(1(1(1(2(1(2(1(2(1(1(2(1(z0))))))))))))))))))))))))))) 2(1(0(1(0(2(2(2(1(2(2(0(1(2(1(1(1(1(0(0(2(0(2(z0))))))))))))))))))))))) -> 2(1(2(1(2(1(1(1(2(2(1(2(1(1(1(0(1(1(1(2(1(0(0(1(1(1(1(z0))))))))))))))))))))))))))) 2(1(0(1(1(0(1(2(1(0(2(2(0(1(0(1(2(0(2(2(1(2(0(z0))))))))))))))))))))))) -> 2(1(1(0(1(2(1(1(0(1(2(1(1(0(2(1(0(1(1(2(2(2(2(1(2(1(1(z0))))))))))))))))))))))))))) 2(1(0(1(1(2(2(2(0(2(1(0(0(0(2(2(2(2(2(0(0(1(1(z0))))))))))))))))))))))) -> 1(2(0(1(1(1(0(1(2(0(2(2(1(1(0(2(1(1(1(1(0(0(1(0(1(1(1(z0))))))))))))))))))))))))))) 2(1(1(0(0(2(2(2(1(0(1(0(1(0(1(0(1(2(2(1(0(0(0(z0))))))))))))))))))))))) -> 2(2(0(1(0(1(1(0(2(2(1(1(1(1(2(1(2(0(1(1(1(2(1(0(0(1(0(z0))))))))))))))))))))))))))) 2(1(1(0(1(0(0(2(0(1(2(0(2(2(1(1(0(2(0(2(2(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(1(1(2(0(2(1(1(2(2(1(2(1(1(1(1(1(2(1(2(1(2(0(z0))))))))))))))))))))))))))) 2(1(1(1(1(1(0(1(0(0(0(2(1(0(1(0(2(2(0(1(0(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(2(1(1(0(2(1(1(1(1(0(2(2(1(1(1(0(2(0(1(2(1(2(z0))))))))))))))))))))))))))) 2(1(1(1(2(2(2(1(1(0(2(0(2(0(2(1(2(1(2(2(1(0(1(z0))))))))))))))))))))))) -> 2(2(1(2(2(1(0(1(1(0(1(1(1(1(1(1(1(1(0(1(0(1(0(1(0(1(1(z0))))))))))))))))))))))))))) 2(1(1(2(0(1(1(1(0(0(0(2(1(2(2(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))) -> 1(1(2(1(0(1(2(1(2(1(1(1(2(1(1(1(1(2(2(1(0(1(1(2(0(1(1(z0))))))))))))))))))))))))))) 2(1(1(2(1(2(1(0(0(0(0(0(1(1(0(1(0(0(1(2(2(0(1(z0))))))))))))))))))))))) -> 2(2(1(2(2(2(2(1(1(1(0(1(0(1(2(2(2(2(2(2(2(1(0(0(0(1(1(z0))))))))))))))))))))))))))) 2(1(2(0(0(1(2(1(0(2(0(1(1(1(0(1(1(2(0(1(0(0(1(z0))))))))))))))))))))))) -> 0(0(1(2(2(2(2(1(1(2(2(2(1(1(1(1(1(1(1(1(1(0(2(0(1(0(1(z0))))))))))))))))))))))))))) 2(1(2(0(0(2(1(1(2(1(0(0(1(0(1(0(2(1(0(2(2(2(1(z0))))))))))))))))))))))) -> 2(1(0(2(1(2(2(1(0(2(1(0(2(0(1(1(1(2(0(2(2(1(1(1(2(1(1(z0))))))))))))))))))))))))))) 2(1(2(1(0(0(2(1(2(0(2(0(0(1(2(0(1(1(2(0(0(2(1(z0))))))))))))))))))))))) -> 2(1(2(2(1(0(1(1(0(1(0(1(0(2(2(1(0(1(0(1(2(1(2(0(2(2(1(z0))))))))))))))))))))))))))) 2(1(2(1(1(2(0(2(0(1(2(1(2(1(1(1(2(2(0(2(2(0(0(z0))))))))))))))))))))))) -> 2(1(1(1(1(0(1(1(2(2(2(1(1(2(1(1(2(1(0(2(0(2(0(2(2(1(0(z0))))))))))))))))))))))))))) 2(2(0(1(1(2(2(2(0(2(1(2(2(2(1(2(0(1(0(0(1(1(2(z0))))))))))))))))))))))) -> 2(2(1(1(1(2(1(0(2(0(1(1(2(2(0(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))))))))))))))))) 2(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> 2(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))) 2(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> 2(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))) Tuples: ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(2'(encArg(z0)), ENCARG(z0)) 0'(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> c6(0'(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))), 2'(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))), 1'(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))), 2'(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))), 2'(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))), 2'(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))), 1'(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))), 0'(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))), 1'(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))), 1'(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))), 1'(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))), 1'(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))), 1'(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))), 0'(1(1(1(1(1(1(2(1(2(1(z0))))))))))), 1'(1(1(1(1(1(2(1(2(1(z0)))))))))), 1'(1(1(1(1(2(1(2(1(z0))))))))), 1'(1(1(1(2(1(2(1(z0)))))))), 1'(1(1(2(1(2(1(z0))))))), 1'(1(2(1(2(1(z0)))))), 1'(2(1(2(1(z0))))), 2'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> c7(1'(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))), 1'(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))))), 1'(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))), 2'(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))), 1'(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))), 1'(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))), 0'(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))), 0'(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))), 1'(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))), 1'(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))), 0'(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))), 1'(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))), 2'(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))), 1'(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))), 1'(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))), 1'(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))), 1'(1(0(1(2(2(1(1(2(0(0(z0))))))))))), 1'(0(1(2(2(1(1(2(0(0(z0)))))))))), 0'(1(2(2(1(1(2(0(0(z0))))))))), 1'(2(2(1(1(2(0(0(z0)))))))), 2'(2(1(1(2(0(0(z0))))))), 2'(1(1(2(0(0(z0)))))), 1'(1(2(0(0(z0))))), 1'(2(0(0(z0)))), 2'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> c8(2'(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))), 0'(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))))), 2'(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))), 1'(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))), 0'(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))), 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2'(0(1(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))))), 0'(1(1(0(1(2(0(1(0(2(1(1(2(z0))))))))))))), 1'(1(0(1(2(0(1(0(2(1(1(2(z0)))))))))))), 1'(0(1(2(0(1(0(2(1(1(2(z0))))))))))), 0'(1(2(0(1(0(2(1(1(2(z0)))))))))), 1'(2(0(1(0(2(1(1(2(z0))))))))), 2'(0(1(0(2(1(1(2(z0)))))))), 0'(1(0(2(1(1(2(z0))))))), 1'(0(2(1(1(2(z0)))))), 0'(2(1(1(2(z0))))), 2'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) 2'(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> c103(2'(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))), 2'(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))))), 0'(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))), 1'(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))), 1'(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))), 0'(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))), 2'(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))), 2'(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))), 1'(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))), 1'(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))), 2'(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))), 1'(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))), 1'(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))), 1'(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))), 1'(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))), 2'(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))), 0'(0(1(0(2(2(1(1(2(0(1(z0))))))))))), 0'(1(0(2(2(1(1(2(0(1(z0)))))))))), 1'(0(2(2(1(1(2(0(1(z0))))))))), 0'(2(2(1(1(2(0(1(z0)))))))), 2'(2(1(1(2(0(1(z0))))))), 2'(1(1(2(0(1(z0)))))), 1'(1(2(0(1(z0))))), 1'(2(0(1(z0)))), 2'(0(1(z0))), 0'(1(z0)), 1'(z0)) 2'(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> c104(2'(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))), 2'(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))), 1'(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))), 1'(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))), 1'(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))), 2'(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))), 0'(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))), 2'(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))), 2'(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))), 0'(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))), 1'(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))), 1'(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))), 0'(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))), 0'(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))), 1'(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))), 1'(1(0(1(1(1(0(1(2(1(0(z0))))))))))), 1'(0(1(1(1(0(1(2(1(0(z0)))))))))), 0'(1(1(1(0(1(2(1(0(z0))))))))), 1'(1(1(0(1(2(1(0(z0)))))))), 1'(1(0(1(2(1(0(z0))))))), 1'(0(1(2(1(0(z0)))))), 0'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(z0))))))))))))))))))))))) -> c33(1'(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))))), 2'(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))))), 1'(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))), 1'(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))), 1'(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))), 2'(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))), 0'(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))), 2'(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))), 2'(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))), 2'(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))), 2'(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))), 1'(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))), 2'(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))), 1'(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))), 1'(0(1(0(1(2(2(2(1(1(1(z0))))))))))), 0'(1(0(1(2(2(2(1(1(1(z0)))))))))), 1'(0(1(2(2(2(1(1(1(z0))))))))), 2'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 1'(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(z0))))))))))))))))))))))) -> c52(0'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c66(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> c79(1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c85(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) ENCODE_0(z0) -> c105(0'(encArg(z0))) ENCODE_1(z0) -> c105(1'(encArg(z0))) ENCODE_2(z0) -> c105(2'(encArg(z0))) ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(0'(2(encArg(z0))), ENCARG(cons_2(z0))) S tuples: 0'(0(0(0(1(1(2(0(1(1(1(2(1(0(2(0(2(1(1(2(0(0(1(z0))))))))))))))))))))))) -> c6(0'(2(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))))), 2'(0(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))))), 0'(1(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))))), 1'(2(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))))), 2'(2(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))))), 2'(2(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))))), 2'(1(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))))), 1'(1(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))))), 1'(0(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))))), 0'(1(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))))), 1'(1(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))))), 1'(1(1(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))))), 1'(1(1(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))))), 1'(1(0(1(1(1(1(1(1(2(1(2(1(z0))))))))))))), 1'(0(1(1(1(1(1(1(2(1(2(1(z0)))))))))))), 0'(1(1(1(1(1(1(2(1(2(1(z0))))))))))), 1'(1(1(1(1(1(2(1(2(1(z0)))))))))), 1'(1(1(1(1(2(1(2(1(z0))))))))), 1'(1(1(1(2(1(2(1(z0)))))))), 1'(1(1(2(1(2(1(z0))))))), 1'(1(2(1(2(1(z0)))))), 1'(2(1(2(1(z0))))), 2'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(0(2(2(2(2(1(2(0(1(0(2(2(1(2(2(2(2(1(1(1(2(z0))))))))))))))))))))))) -> c7(1'(1(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))))), 1'(1(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))))), 1'(2(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))))), 2'(1(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))))), 1'(1(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))))), 1'(0(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))))), 0'(0(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))))), 0'(1(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))))), 1'(1(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))))), 1'(0(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))))), 0'(1(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))))), 1'(2(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))))), 2'(1(1(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))))), 1'(1(1(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))))), 1'(1(1(1(0(1(2(2(1(1(2(0(0(z0))))))))))))), 1'(1(1(0(1(2(2(1(1(2(0(0(z0)))))))))))), 1'(1(0(1(2(2(1(1(2(0(0(z0))))))))))), 1'(0(1(2(2(1(1(2(0(0(z0)))))))))), 0'(1(2(2(1(1(2(0(0(z0))))))))), 1'(2(2(1(1(2(0(0(z0)))))))), 2'(2(1(1(2(0(0(z0))))))), 2'(1(1(2(0(0(z0)))))), 1'(1(2(0(0(z0))))), 1'(2(0(0(z0)))), 2'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(0(1(0(1(0(2(1(1(0(1(0(2(0(0(2(2(1(0(0(0(2(1(z0))))))))))))))))))))))) -> c8(2'(0(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))))), 0'(2(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))))), 2'(1(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))))), 1'(0(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))))), 0'(0(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))))), 0'(1(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))))), 1'(1(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))))), 1'(1(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))))), 1'(0(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))))), 0'(2(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))))), 2'(1(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))))), 1'(1(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))))), 1'(1(1(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))))), 1'(1(2(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))))), 1'(2(1(1(2(2(2(1(1(0(1(1(1(z0))))))))))))), 2'(1(1(2(2(2(1(1(0(1(1(1(z0)))))))))))), 1'(1(2(2(2(1(1(0(1(1(1(z0))))))))))), 1'(2(2(2(1(1(0(1(1(1(z0)))))))))), 2'(2(2(1(1(0(1(1(1(z0))))))))), 2'(2(1(1(0(1(1(1(z0)))))))), 2'(1(1(0(1(1(1(z0))))))), 1'(1(0(1(1(1(z0)))))), 1'(0(1(1(1(z0))))), 0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(0(1(0(1(2(1(1(2(1(1(1(1(0(2(1(0(0(2(2(2(1(2(z0))))))))))))))))))))))) -> c9(0'(1(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))))), 1'(1(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))))), 1'(1(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))))), 1'(1(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0)))))))))))))))))))))))), 1'(0(2(1(1(1(0(1(1(1(0(2(1(1(1(0(0(0(2(1(0(2(1(z0))))))))))))))))))))))), 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1'(2(z0)), 2'(z0)) 2'(2(1(0(1(2(2(0(0(2(2(2(2(2(2(1(0(1(0(0(0(1(1(z0))))))))))))))))))))))) -> c103(2'(2(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))))), 2'(0(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))))), 0'(1(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))))), 1'(1(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))))), 1'(0(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))))), 0'(2(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))))), 2'(2(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))))), 2'(1(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))))), 1'(1(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))))), 1'(2(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))))), 2'(1(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))))), 1'(1(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))))), 1'(1(1(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))))), 1'(1(2(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))))), 1'(2(0(0(1(0(2(2(1(1(2(0(1(z0))))))))))))), 2'(0(0(1(0(2(2(1(1(2(0(1(z0)))))))))))), 0'(0(1(0(2(2(1(1(2(0(1(z0))))))))))), 0'(1(0(2(2(1(1(2(0(1(z0)))))))))), 1'(0(2(2(1(1(2(0(1(z0))))))))), 0'(2(2(1(1(2(0(1(z0)))))))), 2'(2(1(1(2(0(1(z0))))))), 2'(1(1(2(0(1(z0)))))), 1'(1(2(0(1(z0))))), 1'(2(0(1(z0)))), 2'(0(1(z0))), 0'(1(z0)), 1'(z0)) 2'(2(1(0(2(1(2(2(1(2(2(0(1(2(2(0(1(2(1(1(2(1(2(z0))))))))))))))))))))))) -> c104(2'(2(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))))), 2'(0(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))))), 0'(1(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))))), 1'(1(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))))), 1'(1(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))))), 1'(2(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))))), 2'(0(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))))), 0'(2(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))))), 2'(2(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))))), 2'(0(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))))), 0'(1(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))))), 1'(1(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))))), 1'(0(0(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))))), 0'(0(1(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))))), 0'(1(1(1(0(1(1(1(0(1(2(1(0(z0))))))))))))), 1'(1(1(0(1(1(1(0(1(2(1(0(z0)))))))))))), 1'(1(0(1(1(1(0(1(2(1(0(z0))))))))))), 1'(0(1(1(1(0(1(2(1(0(z0)))))))))), 0'(1(1(1(0(1(2(1(0(z0))))))))), 1'(1(1(0(1(2(1(0(z0)))))))), 1'(1(0(1(2(1(0(z0))))))), 1'(0(1(2(1(0(z0)))))), 0'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(1(2(2(0(2(0(1(0(1(1(2(0(0(2(2(1(0(1(2(1(1(1(z0))))))))))))))))))))))) -> c33(1'(2(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))))), 2'(1(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))))), 1'(1(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))))), 1'(1(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))))), 1'(2(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))))), 2'(0(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))))), 0'(2(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))))), 2'(1(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))))), 1'(2(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))))), 2'(2(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))))), 2'(2(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))))), 2'(1(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))))), 1'(1(2(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))))), 2'(1(1(0(1(0(1(2(2(2(1(1(1(z0))))))))))))), 1'(1(0(1(0(1(2(2(2(1(1(1(z0)))))))))))), 1'(0(1(0(1(2(2(2(1(1(1(z0))))))))))), 0'(1(0(1(2(2(2(1(1(1(z0)))))))))), 1'(0(1(2(2(2(1(1(1(z0))))))))), 2'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 1'(1(0(0(2(0(1(2(2(2(1(2(1(2(1(0(0(1(0(1(0(2(1(z0))))))))))))))))))))))) -> c52(0'(1(0(2(1(z0))))), 1'(0(2(1(z0)))), 0'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(2(0(1(1(0(1(2(0(2(1(1(2(0(1(1(0(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c66(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(0(0(1(2(2(0(0(2(0(0(1(0(0(0(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))) -> c79(1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(0(2(0(1(2(2(2(1(1(0(0(1(1(1(1(2(0(1(0(2(2(0(z0))))))))))))))))))))))) -> c85(2'(2(0(z0))), 2'(0(z0)), 0'(z0)) K tuples:none Defined Rule Symbols: encArg_1, 0_1, 1_1, 2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, 2'_1, ENCODE_0_1, ENCODE_1_1, ENCODE_2_1 Compound Symbols: c1_2, c2_2, c6_27, c7_27, c8_27, c9_27, c10_27, c11_27, c12_27, c13_27, c14_27, c15_27, c16_27, c17_27, c18_27, c19_27, c20_27, c21_27, c22_27, c23_27, c24_27, c25_27, c26_27, c27_27, c28_27, c29_27, c30_27, c31_27, c32_27, c34_27, c35_27, c36_27, c37_27, c38_27, c39_27, c40_27, c41_27, c42_27, c43_27, c44_27, c45_27, c46_27, c47_27, c48_27, c49_27, c50_27, c51_27, c53_27, c54_27, c55_27, c56_27, c57_27, c58_27, c59_27, c60_27, c61_27, c62_27, c63_27, c64_27, c65_27, c67_27, c68_27, c69_27, c70_27, c71_27, c72_27, c73_27, c74_27, c75_27, c76_27, c77_27, c78_27, c80_27, c81_27, c82_27, c83_27, c84_27, c86_27, c87_27, c88_27, c89_27, c90_27, c91_27, c92_27, c93_27, c94_27, c95_27, c96_27, c97_27, c98_27, c99_27, c100_27, c101_27, c102_27, c103_27, c104_27, c33_23, c52_5, c66_3, c79_3, c85_3, c105_1, c_2