/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 49 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), 17 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) RcToIrcProof [BOTH BOUNDS(ID, ID), 3004 ms] (18) CpxRelTRS (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxWeightedTrs (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 53 ms] (22) CpxWeightedTrs (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxTypedWeightedTrs (25) CompletionProof [UPPER BOUND(ID), 14 ms] (26) CpxTypedWeightedCompleteTrs (27) NarrowingProof [BOTH BOUNDS(ID, ID), 5456 ms] (28) CpxTypedWeightedCompleteTrs (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 15 ms] (30) CpxRNTS (31) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CpxRNTS (33) CompletionProof [UPPER BOUND(ID), 16 ms] (34) CpxTypedWeightedCompleteTrs (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 28 ms] (36) CpxRNTS (37) CpxTrsToCdtProof [UPPER BOUND(ID), 2548 ms] (38) CdtProblem (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (44) CdtProblem (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 20.4 s] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6343 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6351 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6308 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20.0 s] (54) CdtProblem ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(0(1(0(0(x1))))) -> 0(1(0(1(1(1(1(x1))))))) 1(2(2(0(1(2(x1)))))) -> 1(1(1(1(1(0(1(1(0(x1))))))))) 2(0(2(0(1(0(x1)))))) -> 1(1(0(1(1(1(1(0(x1)))))))) 2(0(2(2(1(2(x1)))))) -> 1(1(0(0(1(1(2(x1))))))) 1(0(1(1(2(1(2(x1))))))) -> 0(1(1(1(1(1(2(2(x1)))))))) 1(1(2(1(2(1(2(x1))))))) -> 1(0(2(1(1(1(1(1(x1)))))))) 2(0(2(0(0(0(0(x1))))))) -> 0(1(1(1(1(2(1(0(x1)))))))) 0(0(0(1(2(2(0(0(x1)))))))) -> 0(1(1(1(1(0(0(2(2(x1))))))))) 0(0(1(2(2(0(1(0(2(x1))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(x1)))))))))))) 0(1(0(2(2(1(0(1(0(0(x1)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(x1))))))))))) 1(1(0(2(2(2(0(2(2(2(x1)))))))))) -> 1(0(0(2(0(1(1(1(0(1(1(x1))))))))))) 0(0(2(1(1(1(0(1(1(2(1(x1))))))))))) -> 0(1(1(1(1(1(1(1(0(1(0(0(0(x1))))))))))))) 2(0(1(1(2(1(0(2(0(0(1(x1))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(x1)))))))))))) 1(1(2(2(2(0(1(0(2(2(1(2(x1)))))))))))) -> 1(1(0(1(1(0(0(0(1(2(0(2(1(x1))))))))))))) 2(2(2(0(0(1(2(1(1(2(2(2(x1)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(x1))))))))))))) 0(1(1(1(0(1(2(2(1(0(0(0(0(x1))))))))))))) -> 0(1(1(1(2(1(2(0(1(1(1(1(1(1(x1)))))))))))))) 1(0(2(2(0(2(1(0(2(1(2(1(2(x1))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(x1)))))))))))))))))) 2(1(0(1(0(0(0(2(0(0(2(1(2(x1))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(x1))))))))))))))) 2(2(0(0(0(0(0(2(2(1(0(2(2(x1))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(x1)))))))))))))) 0(0(1(1(2(0(1(0(2(0(2(1(1(0(x1)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(x1)))))))))))))))) 0(2(2(0(2(1(2(0(2(0(0(2(2(1(x1)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(x1)))))))))))))))) 0(2(2(1(1(2(0(1(1(2(1(0(0(2(x1)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(x1)))))))))))))))) 1(0(1(0(1(0(1(0(2(1(2(2(2(0(x1)))))))))))))) -> 1(0(2(2(0(0(1(1(1(2(0(2(1(0(x1)))))))))))))) 2(0(1(2(0(1(0(0(0(2(0(1(0(2(x1)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(x1))))))))))))))) 2(2(0(0(2(1(2(1(0(2(0(0(2(2(x1)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(x1))))))))))))))) 0(0(2(1(2(0(2(1(0(0(0(2(2(2(0(x1))))))))))))))) -> 1(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(x1)))))))))))))))) 0(1(0(2(1(1(2(2(2(0(0(2(2(0(0(x1))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(x1))))))))))))))))) 0(1(0(2(2(1(1(0(1(0(2(0(0(0(0(x1))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(x1)))))))))))))))) 0(1(2(1(2(2(1(0(0(2(2(1(2(1(2(x1))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) 1(2(0(2(0(0(0(2(1(0(1(2(0(0(0(x1))))))))))))))) -> 1(1(0(1(1(0(2(2(0(1(2(2(0(0(0(2(x1)))))))))))))))) 2(0(0(2(1(1(2(1(0(1(0(0(2(2(0(x1))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(x1))))))))))))))))) 2(2(2(0(0(1(2(1(0(2(2(1(2(2(1(x1))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(x1)))))))))))))))))))) 0(0(0(0(1(2(0(2(0(1(1(2(2(0(0(2(x1)))))))))))))))) -> 0(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(x1))))))))))))))))) 0(1(0(1(2(0(0(0(1(1(0(2(2(0(2(2(x1)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(x1))))))))))))))))) 2(0(2(2(0(2(2(2(2(1(1(1(1(2(1(2(x1)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(x1)))))))))))))))))) 2(1(1(2(0(1(2(0(2(1(0(0(2(2(2(1(x1)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) 2(2(0(2(1(1(2(2(0(2(2(0(0(0(2(1(x1)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(x1))))))))))))))))) 0(1(0(1(2(2(2(0(0(0(2(0(0(0(2(0(2(x1))))))))))))))))) -> 1(1(0(1(2(1(1(2(2(1(0(2(1(0(1(1(1(0(x1)))))))))))))))))) 0(0(0(0(0(1(1(0(2(2(1(2(0(2(0(0(2(0(x1)))))))))))))))))) -> 0(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(x1)))))))))))))))))))) 0(0(0(2(0(1(2(0(0(1(0(2(0(1(1(2(0(2(x1)))))))))))))))))) -> 0(1(0(2(1(1(2(2(2(2(1(1(1(0(2(0(1(2(1(x1))))))))))))))))))) 1(2(2(2(0(0(0(0(0(1(0(1(2(1(1(0(2(0(x1)))))))))))))))))) -> 2(1(0(1(2(1(1(2(1(1(1(1(0(2(0(1(0(1(1(1(0(x1))))))))))))))))))))) 2(2(0(1(0(2(0(0(1(0(2(0(1(0(2(0(1(0(x1)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(x1))))))))))))))))))))) 2(2(1(2(2(2(0(1(0(0(0(0(0(2(2(2(1(0(x1)))))))))))))))))) -> 1(2(1(0(1(1(2(1(1(0(2(2(1(1(1(1(0(2(0(2(1(x1))))))))))))))))))))) 0(0(1(2(0(1(1(2(1(2(1(1(2(2(0(1(0(2(2(x1))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(x1))))))))))))))))))))) 0(1(0(1(2(0(1(1(1(0(2(1(1(2(1(0(2(2(1(x1))))))))))))))))))) -> 1(1(2(2(1(2(2(1(1(1(2(2(0(1(0(1(0(2(1(1(x1)))))))))))))))))))) 0(1(2(0(2(2(0(0(0(1(2(0(0(1(0(1(0(2(1(x1))))))))))))))))))) -> 0(0(1(2(1(1(1(1(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(x1))))))))))))))))))))))) 1(0(1(2(1(0(1(2(1(2(1(1(2(1(0(2(2(0(2(x1))))))))))))))))))) -> 1(1(1(1(2(0(1(2(0(2(2(2(0(0(2(0(1(2(2(0(x1)))))))))))))))))))) 2(0(2(2(0(2(2(0(0(2(2(1(2(0(1(2(1(0(1(x1))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(2(0(1(1(1(1(1(0(0(2(0(1(1(x1)))))))))))))))))))))) 2(1(2(1(2(1(1(2(1(0(1(0(2(0(1(0(2(2(2(x1))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(x1))))))))))))))))))))) 2(2(0(2(0(1(0(2(2(1(1(0(1(0(1(1(1(0(1(x1))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(x1))))))))))))))))))) 0(2(0(2(2(0(2(1(1(1(0(2(1(2(1(0(0(1(0(2(x1)))))))))))))))))))) -> 2(1(1(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(x1)))))))))))))))))))))) 0(2(2(1(2(2(2(0(1(2(2(2(2(1(1(0(0(0(1(0(x1)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(x1)))))))))))))))))))))))) 1(1(1(2(0(0(0(2(0(1(2(0(0(2(2(2(1(1(0(0(x1)))))))))))))))))))) -> 1(1(0(2(1(2(2(2(2(2(0(2(1(1(1(0(0(0(0(1(1(x1))))))))))))))))))))) 1(1(1(2(0(2(1(1(2(2(0(0(1(2(0(0(0(0(2(0(x1)))))))))))))))))))) -> 1(1(1(1(1(2(0(2(0(2(1(0(0(0(2(1(2(0(1(2(2(x1))))))))))))))))))))) 2(2(2(1(2(2(2(1(2(2(2(1(1(2(0(0(2(1(0(2(x1)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(x1))))))))))))))))))))))))))) 1(1(2(0(0(0(0(1(1(0(0(1(1(0(0(0(0(0(0(2(1(x1))))))))))))))))))))) -> 1(1(0(0(2(0(0(0(2(0(0(0(1(0(0(0(0(1(1(1(1(x1))))))))))))))))))))) 1(1(2(1(1(1(1(0(0(0(2(2(1(1(2(0(1(2(2(0(1(x1))))))))))))))))))))) -> 1(0(2(1(2(1(2(1(0(0(2(2(2(0(1(0(1(1(1(1(1(x1))))))))))))))))))))) 2(1(0(0(2(1(0(1(0(2(2(0(0(2(2(0(0(0(1(0(2(x1))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(x1))))))))))))))))))))))) 2(2(0(2(2(1(2(0(0(2(1(1(2(0(1(2(0(1(0(0(0(x1))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(x1)))))))))))))))))))))) 2(2(1(2(1(1(2(2(0(0(2(0(2(0(0(2(0(1(2(2(0(x1))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(x1))))))))))))))))))))))) 0(1(1(0(2(1(0(1(2(0(0(1(1(2(0(0(2(0(0(2(2(2(x1)))))))))))))))))))))) -> 0(2(2(1(2(2(1(2(1(1(1(1(2(0(1(0(0(1(1(1(0(1(1(x1))))))))))))))))))))))) 0(2(0(0(0(2(0(1(2(0(1(1(1(1(2(0(2(0(0(1(0(2(x1)))))))))))))))))))))) -> 0(2(2(1(1(0(0(2(2(1(1(0(1(1(1(2(0(1(2(1(0(1(1(x1))))))))))))))))))))))) 0(2(0(0(2(2(0(0(2(0(2(1(0(1(2(1(1(2(0(2(1(2(x1)))))))))))))))))))))) -> 2(0(0(2(1(2(1(0(1(2(2(1(2(2(2(1(1(1(1(0(2(0(1(x1))))))))))))))))))))))) 1(1(2(0(2(2(0(2(2(1(0(0(0(0(0(2(2(0(2(2(2(2(x1)))))))))))))))))))))) -> 2(1(1(1(0(1(1(1(1(2(2(1(1(2(2(0(0(0(1(2(1(0(0(x1))))))))))))))))))))))) 1(2(0(1(0(2(1(0(0(0(0(2(1(0(2(0(0(2(1(1(2(1(x1)))))))))))))))))))))) -> 1(0(0(2(2(1(2(1(1(0(1(1(1(0(1(0(1(1(1(2(1(0(2(2(1(x1))))))))))))))))))))))))) 1(2(0(2(0(1(2(1(0(0(2(2(1(0(0(0(2(1(1(2(1(2(x1)))))))))))))))))))))) -> 1(1(1(2(2(2(1(0(1(1(0(2(0(1(0(1(2(0(0(0(1(1(1(0(x1)))))))))))))))))))))))) 1(2(1(0(1(0(2(2(2(1(0(0(2(0(1(1(0(2(2(2(0(0(x1)))))))))))))))))))))) -> 1(0(1(1(1(0(2(1(2(0(0(0(0(2(1(2(2(0(2(2(2(0(x1)))))))))))))))))))))) 1(2(2(2(2(2(2(1(1(0(1(0(2(2(2(1(1(2(1(2(1(1(x1)))))))))))))))))))))) -> 0(2(0(2(0(0(0(1(2(0(2(1(2(0(2(1(1(0(0(0(1(1(1(1(x1)))))))))))))))))))))))) 2(0(0(0(2(0(0(2(2(2(0(0(2(1(0(0(1(0(0(1(2(1(x1)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(x1)))))))))))))))))))))))) 2(0(0(2(1(2(0(2(1(0(2(2(1(2(1(1(2(0(2(0(0(2(x1)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(x1)))))))))))))))))))))))) 2(0(1(2(1(1(0(2(0(2(2(2(2(1(1(2(1(1(1(2(2(1(x1)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(x1))))))))))))))))))))))) 0(0(0(1(0(1(2(2(0(0(2(0(1(0(1(2(0(1(1(2(0(0(0(x1))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(x1))))))))))))))))))))))) 1(0(2(1(2(2(2(1(0(2(1(2(1(2(2(2(1(0(0(0(0(2(2(x1))))))))))))))))))))))) -> 1(1(1(2(2(2(1(2(2(2(1(0(1(0(1(1(1(0(0(1(2(0(0(2(0(2(x1)))))))))))))))))))))))))) 1(1(2(2(2(0(1(0(2(1(2(0(2(1(1(2(0(1(2(0(2(2(0(x1))))))))))))))))))))))) -> 1(0(2(2(0(2(1(1(1(1(1(0(1(1(1(1(0(2(0(2(2(2(1(1(2(x1))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(1(1(0(0(2(2(2(2(0(2(0(0(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(x1)))))))))))))))))))))))) 2(0(2(2(0(1(0(2(0(0(1(2(1(2(0(0(2(0(0(2(2(2(2(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(x1)))))))))))))))))))))))) 0(0(1(1(2(1(1(1(2(2(1(2(2(0(1(1(1(2(1(2(0(2(1(2(x1)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(x1))))))))))))))))))))))))) 0(2(0(0(1(0(2(2(2(2(1(2(2(0(1(0(2(2(1(2(1(2(1(2(x1)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(2(0(1(0(2(0(1(2(0(1(2(2(1(0(2(2(2(1(1(2(0(0(0(x1)))))))))))))))))))))))) -> 0(1(1(1(1(0(0(1(1(1(1(0(1(0(0(2(0(1(1(1(0(1(2(0(1(1(x1)))))))))))))))))))))))))) 2(1(2(1(2(1(0(0(1(2(1(0(2(0(1(1(0(2(1(0(1(0(1(0(x1)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(x1)))))))))))))))))))))))) 0(2(2(1(2(0(0(1(0(2(2(0(0(1(0(0(0(2(2(2(0(2(1(0(0(x1))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(x1)))))))))))))))))))))))))) 1(1(1(0(0(1(2(2(1(0(2(1(2(1(0(2(2(2(1(1(0(0(2(1(2(x1))))))))))))))))))))))))) -> 1(1(2(2(2(1(1(1(1(1(0(0(1(1(2(0(1(2(1(0(1(2(1(1(0(1(x1)))))))))))))))))))))))))) 1(2(0(1(0(2(0(0(0(1(1(2(1(0(0(1(0(1(0(2(0(1(0(2(2(x1))))))))))))))))))))))))) -> 1(1(0(1(0(2(0(0(1(2(1(1(1(1(1(0(0(2(2(1(0(2(2(1(2(2(x1)))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(2(2(1(0(2(2(1(0(2(2(1(1(2(0(0(0(1(x1))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(x1)))))))))))))))))))))))))))) 2(1(2(1(2(0(0(1(0(2(1(2(0(1(2(0(0(2(1(0(2(0(2(2(2(x1))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(x1)))))))))))))))))))))))))) 2(1(2(2(2(2(1(1(0(0(2(1(2(0(0(0(1(1(0(0(1(1(2(0(1(x1))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(x1))))))))))))))))))))))))) 2(2(0(2(2(0(0(1(2(0(1(1(0(1(2(1(0(2(1(0(2(2(1(0(1(x1))))))))))))))))))))))))) -> 1(0(0(1(2(1(1(0(1(0(1(1(1(0(1(2(2(2(1(2(2(2(2(1(2(1(1(1(x1)))))))))))))))))))))))))))) 2(2(2(2(1(1(0(1(0(0(0(2(1(0(2(1(2(0(0(2(0(0(2(2(2(x1))))))))))))))))))))))))) -> 1(0(0(0(2(1(1(1(1(1(1(0(0(1(0(1(2(0(2(1(2(1(1(0(1(2(0(x1))))))))))))))))))))))))))) 0(1(2(1(1(0(2(1(1(2(1(1(2(0(2(0(2(2(2(2(0(0(2(1(1(2(x1)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(x1))))))))))))))))))))))))))) 1(1(2(2(1(1(2(1(0(1(2(1(1(1(0(0(1(1(0(1(1(1(1(2(0(2(x1)))))))))))))))))))))))))) -> 0(1(1(2(1(2(2(2(2(1(1(1(1(1(0(1(0(2(1(0(0(1(1(1(1(1(x1)))))))))))))))))))))))))) 1(2(1(2(1(0(0(2(2(0(2(0(2(2(0(1(1(0(0(1(2(2(0(0(2(2(x1)))))))))))))))))))))))))) -> 1(0(2(0(0(1(1(0(1(2(2(0(1(1(0(0(0(1(1(1(2(2(1(2(2(0(1(2(x1)))))))))))))))))))))))))))) 0(1(2(0(0(1(2(2(1(1(0(1(0(0(2(2(0(2(2(0(0(0(0(1(0(2(0(x1))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(x1)))))))))))))))))))))))))))) 0(1(2(1(0(2(2(2(2(0(0(1(2(1(0(0(0(0(2(0(0(0(2(0(1(0(2(x1))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x1)))))))))))))))))))))))))))) 0(2(0(1(0(2(2(1(1(0(0(0(2(0(2(0(1(0(0(1(2(1(2(2(1(1(0(x1))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(x1)))))))))))))))))))))))))))) 0(2(1(2(1(2(2(0(2(1(0(1(2(1(1(1(2(2(1(2(0(1(1(1(0(0(2(x1))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(x1)))))))))))))))))))))))))))) 1(0(1(0(1(2(2(0(2(0(1(2(0(0(1(0(0(0(2(0(1(0(0(2(0(2(1(x1))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(x1)))))))))))))))))))))))))))) 0(0(2(2(0(2(1(2(2(0(0(0(2(2(0(2(2(2(1(0(1(0(1(2(2(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(x1))))))))))))))))))))))))))))) 0(1(1(1(2(0(0(0(1(2(1(0(0(0(1(1(0(1(2(2(0(2(2(0(1(2(0(1(x1)))))))))))))))))))))))))))) -> 1(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(x1)))))))))))))))))))))))))))) 0(1(2(0(0(2(1(1(2(1(1(2(2(1(0(2(2(2(2(2(2(2(2(1(2(2(0(2(x1)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(2(1(0(1(2(1(2(0(0(1(1(0(0(2(2(0(0(0(1(1(0(1(2(0(0(x1)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(x1))))))))))))))))))))))))))))) 0(2(0(2(2(1(0(2(1(1(1(2(1(1(2(2(1(2(0(1(1(0(2(2(0(0(1(2(x1)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(x1))))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(2(0(2(2(0(2(1(2(2(1(2(1(1(2(1(2(0(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(0(1(1(0(0(0(2(0(2(0(1(1(1(1(1(0(2(0(2(1(0(1(2(2(2(2(0(2(x1)))))))))))))))))))))))))))))) 2(0(0(1(0(2(2(1(0(1(0(2(0(1(0(2(0(2(2(0(2(1(1(2(2(2(2(0(x1)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(x1))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(0(2(1(0(2(1(0(0(2(0(1(2(1(0(2(0(2(x1)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(x1))))))))))))))))))))))))))))) 0(1(1(2(1(1(0(2(0(2(2(0(1(1(0(0(2(1(1(1(2(0(0(2(0(2(0(1(2(x1))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(1(2(2(1(2(0(1(1(1(2(2(0(0(0(2(2(2(1(0(2(0(0(1(2(1(2(x1))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(x1))))))))))))))))))))))))))))) 0(2(0(0(2(1(2(0(2(2(1(1(2(1(1(2(0(1(0(2(2(2(1(1(1(2(0(2(1(x1))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(x1))))))))))))))))))))))))))))) 1(0(2(1(2(2(1(0(0(1(1(1(0(0(2(1(1(0(2(0(2(1(0(2(0(0(2(1(2(x1))))))))))))))))))))))))))))) -> 1(1(1(1(0(0(1(0(1(1(0(1(1(2(1(1(2(0(1(2(1(0(0(1(2(1(2(2(2(2(x1)))))))))))))))))))))))))))))) 2(0(0(0(1(2(0(0(1(2(2(2(0(2(1(0(2(0(0(1(1(0(0(2(2(0(2(1(2(x1))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(x1)))))))))))))))))))))))))))))) 0(1(2(2(2(1(1(0(1(2(0(2(1(1(1(2(2(1(2(0(2(2(0(2(2(2(0(0(2(0(x1)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(1(2(2(0(2(2(1(1(1(1(2(1(2(0(2(2(0(2(2(0(0(0(1(0(x1)))))))))))))))))))))))))))))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(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 (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(0(1(0(0(x1))))) -> 0(1(0(1(1(1(1(x1))))))) 1(2(2(0(1(2(x1)))))) -> 1(1(1(1(1(0(1(1(0(x1))))))))) 2(0(2(0(1(0(x1)))))) -> 1(1(0(1(1(1(1(0(x1)))))))) 2(0(2(2(1(2(x1)))))) -> 1(1(0(0(1(1(2(x1))))))) 1(0(1(1(2(1(2(x1))))))) -> 0(1(1(1(1(1(2(2(x1)))))))) 1(1(2(1(2(1(2(x1))))))) -> 1(0(2(1(1(1(1(1(x1)))))))) 2(0(2(0(0(0(0(x1))))))) -> 0(1(1(1(1(2(1(0(x1)))))))) 0(0(0(1(2(2(0(0(x1)))))))) -> 0(1(1(1(1(0(0(2(2(x1))))))))) 0(0(1(2(2(0(1(0(2(x1))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(x1)))))))))))) 0(1(0(2(2(1(0(1(0(0(x1)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(x1))))))))))) 1(1(0(2(2(2(0(2(2(2(x1)))))))))) -> 1(0(0(2(0(1(1(1(0(1(1(x1))))))))))) 0(0(2(1(1(1(0(1(1(2(1(x1))))))))))) -> 0(1(1(1(1(1(1(1(0(1(0(0(0(x1))))))))))))) 2(0(1(1(2(1(0(2(0(0(1(x1))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(x1)))))))))))) 1(1(2(2(2(0(1(0(2(2(1(2(x1)))))))))))) -> 1(1(0(1(1(0(0(0(1(2(0(2(1(x1))))))))))))) 2(2(2(0(0(1(2(1(1(2(2(2(x1)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(x1))))))))))))) 0(1(1(1(0(1(2(2(1(0(0(0(0(x1))))))))))))) -> 0(1(1(1(2(1(2(0(1(1(1(1(1(1(x1)))))))))))))) 1(0(2(2(0(2(1(0(2(1(2(1(2(x1))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(x1)))))))))))))))))) 2(1(0(1(0(0(0(2(0(0(2(1(2(x1))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(x1))))))))))))))) 2(2(0(0(0(0(0(2(2(1(0(2(2(x1))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(x1)))))))))))))) 0(0(1(1(2(0(1(0(2(0(2(1(1(0(x1)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(x1)))))))))))))))) 0(2(2(0(2(1(2(0(2(0(0(2(2(1(x1)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(x1)))))))))))))))) 0(2(2(1(1(2(0(1(1(2(1(0(0(2(x1)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(x1)))))))))))))))) 1(0(1(0(1(0(1(0(2(1(2(2(2(0(x1)))))))))))))) -> 1(0(2(2(0(0(1(1(1(2(0(2(1(0(x1)))))))))))))) 2(0(1(2(0(1(0(0(0(2(0(1(0(2(x1)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(x1))))))))))))))) 2(2(0(0(2(1(2(1(0(2(0(0(2(2(x1)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(x1))))))))))))))) 0(0(2(1(2(0(2(1(0(0(0(2(2(2(0(x1))))))))))))))) -> 1(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(x1)))))))))))))))) 0(1(0(2(1(1(2(2(2(0(0(2(2(0(0(x1))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(x1))))))))))))))))) 0(1(0(2(2(1(1(0(1(0(2(0(0(0(0(x1))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(x1)))))))))))))))) 0(1(2(1(2(2(1(0(0(2(2(1(2(1(2(x1))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) 1(2(0(2(0(0(0(2(1(0(1(2(0(0(0(x1))))))))))))))) -> 1(1(0(1(1(0(2(2(0(1(2(2(0(0(0(2(x1)))))))))))))))) 2(0(0(2(1(1(2(1(0(1(0(0(2(2(0(x1))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(x1))))))))))))))))) 2(2(2(0(0(1(2(1(0(2(2(1(2(2(1(x1))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(x1)))))))))))))))))))) 0(0(0(0(1(2(0(2(0(1(1(2(2(0(0(2(x1)))))))))))))))) -> 0(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(x1))))))))))))))))) 0(1(0(1(2(0(0(0(1(1(0(2(2(0(2(2(x1)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(x1))))))))))))))))) 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1(1(0(1(0(2(0(0(1(2(1(1(1(1(1(0(0(2(2(1(0(2(2(1(2(2(x1)))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(2(2(1(0(2(2(1(0(2(2(1(1(2(0(0(0(1(x1))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(x1)))))))))))))))))))))))))))) 2(1(2(1(2(0(0(1(0(2(1(2(0(1(2(0(0(2(1(0(2(0(2(2(2(x1))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(x1)))))))))))))))))))))))))) 2(1(2(2(2(2(1(1(0(0(2(1(2(0(0(0(1(1(0(0(1(1(2(0(1(x1))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(x1))))))))))))))))))))))))) 2(2(0(2(2(0(0(1(2(0(1(1(0(1(2(1(0(2(1(0(2(2(1(0(1(x1))))))))))))))))))))))))) -> 1(0(0(1(2(1(1(0(1(0(1(1(1(0(1(2(2(2(1(2(2(2(2(1(2(1(1(1(x1)))))))))))))))))))))))))))) 2(2(2(2(1(1(0(1(0(0(0(2(1(0(2(1(2(0(0(2(0(0(2(2(2(x1))))))))))))))))))))))))) -> 1(0(0(0(2(1(1(1(1(1(1(0(0(1(0(1(2(0(2(1(2(1(1(0(1(2(0(x1))))))))))))))))))))))))))) 0(1(2(1(1(0(2(1(1(2(1(1(2(0(2(0(2(2(2(2(0(0(2(1(1(2(x1)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(x1))))))))))))))))))))))))))) 1(1(2(2(1(1(2(1(0(1(2(1(1(1(0(0(1(1(0(1(1(1(1(2(0(2(x1)))))))))))))))))))))))))) -> 0(1(1(2(1(2(2(2(2(1(1(1(1(1(0(1(0(2(1(0(0(1(1(1(1(1(x1)))))))))))))))))))))))))) 1(2(1(2(1(0(0(2(2(0(2(0(2(2(0(1(1(0(0(1(2(2(0(0(2(2(x1)))))))))))))))))))))))))) -> 1(0(2(0(0(1(1(0(1(2(2(0(1(1(0(0(0(1(1(1(2(2(1(2(2(0(1(2(x1)))))))))))))))))))))))))))) 0(1(2(0(0(1(2(2(1(1(0(1(0(0(2(2(0(2(2(0(0(0(0(1(0(2(0(x1))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(x1)))))))))))))))))))))))))))) 0(1(2(1(0(2(2(2(2(0(0(1(2(1(0(0(0(0(2(0(0(0(2(0(1(0(2(x1))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x1)))))))))))))))))))))))))))) 0(2(0(1(0(2(2(1(1(0(0(0(2(0(2(0(1(0(0(1(2(1(2(2(1(1(0(x1))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(x1)))))))))))))))))))))))))))) 0(2(1(2(1(2(2(0(2(1(0(1(2(1(1(1(2(2(1(2(0(1(1(1(0(0(2(x1))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(x1)))))))))))))))))))))))))))) 1(0(1(0(1(2(2(0(2(0(1(2(0(0(1(0(0(0(2(0(1(0(0(2(0(2(1(x1))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(x1)))))))))))))))))))))))))))) 0(0(2(2(0(2(1(2(2(0(0(0(2(2(0(2(2(2(1(0(1(0(1(2(2(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(x1))))))))))))))))))))))))))))) 0(1(1(1(2(0(0(0(1(2(1(0(0(0(1(1(0(1(2(2(0(2(2(0(1(2(0(1(x1)))))))))))))))))))))))))))) -> 1(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(x1)))))))))))))))))))))))))))) 0(1(2(0(0(2(1(1(2(1(1(2(2(1(0(2(2(2(2(2(2(2(2(1(2(2(0(2(x1)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(2(1(0(1(2(1(2(0(0(1(1(0(0(2(2(0(0(0(1(1(0(1(2(0(0(x1)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(x1))))))))))))))))))))))))))))) 0(2(0(2(2(1(0(2(1(1(1(2(1(1(2(2(1(2(0(1(1(0(2(2(0(0(1(2(x1)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(x1))))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(2(0(2(2(0(2(1(2(2(1(2(1(1(2(1(2(0(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(0(1(1(0(0(0(2(0(2(0(1(1(1(1(1(0(2(0(2(1(0(1(2(2(2(2(0(2(x1)))))))))))))))))))))))))))))) 2(0(0(1(0(2(2(1(0(1(0(2(0(1(0(2(0(2(2(0(2(1(1(2(2(2(2(0(x1)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(x1))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(0(2(1(0(2(1(0(0(2(0(1(2(1(0(2(0(2(x1)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(x1))))))))))))))))))))))))))))) 0(1(1(2(1(1(0(2(0(2(2(0(1(1(0(0(2(1(1(1(2(0(0(2(0(2(0(1(2(x1))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(1(2(2(1(2(0(1(1(1(2(2(0(0(0(2(2(2(1(0(2(0(0(1(2(1(2(x1))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(x1))))))))))))))))))))))))))))) 0(2(0(0(2(1(2(0(2(2(1(1(2(1(1(2(0(1(0(2(2(2(1(1(1(2(0(2(1(x1))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(x1))))))))))))))))))))))))))))) 1(0(2(1(2(2(1(0(0(1(1(1(0(0(2(1(1(0(2(0(2(1(0(2(0(0(2(1(2(x1))))))))))))))))))))))))))))) -> 1(1(1(1(0(0(1(0(1(1(0(1(1(2(1(1(2(0(1(2(1(0(0(1(2(1(2(2(2(2(x1)))))))))))))))))))))))))))))) 2(0(0(0(1(2(0(0(1(2(2(2(0(2(1(0(2(0(0(1(1(0(0(2(2(0(2(1(2(x1))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(x1)))))))))))))))))))))))))))))) 0(1(2(2(2(1(1(0(1(2(0(2(1(1(1(2(2(1(2(0(2(2(0(2(2(2(0(0(2(0(x1)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(1(2(2(0(2(2(1(1(1(1(2(1(2(0(2(2(0(2(2(0(0(0(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: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(0(1(0(0(x1))))) -> 0(1(0(1(1(1(1(x1))))))) 1(2(2(0(1(2(x1)))))) -> 1(1(1(1(1(0(1(1(0(x1))))))))) 2(0(2(0(1(0(x1)))))) -> 1(1(0(1(1(1(1(0(x1)))))))) 2(0(2(2(1(2(x1)))))) -> 1(1(0(0(1(1(2(x1))))))) 1(0(1(1(2(1(2(x1))))))) -> 0(1(1(1(1(1(2(2(x1)))))))) 1(1(2(1(2(1(2(x1))))))) -> 1(0(2(1(1(1(1(1(x1)))))))) 2(0(2(0(0(0(0(x1))))))) -> 0(1(1(1(1(2(1(0(x1)))))))) 0(0(0(1(2(2(0(0(x1)))))))) -> 0(1(1(1(1(0(0(2(2(x1))))))))) 0(0(1(2(2(0(1(0(2(x1))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(x1)))))))))))) 0(1(0(2(2(1(0(1(0(0(x1)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(x1))))))))))) 1(1(0(2(2(2(0(2(2(2(x1)))))))))) -> 1(0(0(2(0(1(1(1(0(1(1(x1))))))))))) 0(0(2(1(1(1(0(1(1(2(1(x1))))))))))) -> 0(1(1(1(1(1(1(1(0(1(0(0(0(x1))))))))))))) 2(0(1(1(2(1(0(2(0(0(1(x1))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(x1)))))))))))) 1(1(2(2(2(0(1(0(2(2(1(2(x1)))))))))))) -> 1(1(0(1(1(0(0(0(1(2(0(2(1(x1))))))))))))) 2(2(2(0(0(1(2(1(1(2(2(2(x1)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(x1))))))))))))) 0(1(1(1(0(1(2(2(1(0(0(0(0(x1))))))))))))) -> 0(1(1(1(2(1(2(0(1(1(1(1(1(1(x1)))))))))))))) 1(0(2(2(0(2(1(0(2(1(2(1(2(x1))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(x1)))))))))))))))))) 2(1(0(1(0(0(0(2(0(0(2(1(2(x1))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(x1))))))))))))))) 2(2(0(0(0(0(0(2(2(1(0(2(2(x1))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(x1)))))))))))))) 0(0(1(1(2(0(1(0(2(0(2(1(1(0(x1)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(x1)))))))))))))))) 0(2(2(0(2(1(2(0(2(0(0(2(2(1(x1)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(x1)))))))))))))))) 0(2(2(1(1(2(0(1(1(2(1(0(0(2(x1)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(x1)))))))))))))))) 1(0(1(0(1(0(1(0(2(1(2(2(2(0(x1)))))))))))))) -> 1(0(2(2(0(0(1(1(1(2(0(2(1(0(x1)))))))))))))) 2(0(1(2(0(1(0(0(0(2(0(1(0(2(x1)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(x1))))))))))))))) 2(2(0(0(2(1(2(1(0(2(0(0(2(2(x1)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(x1))))))))))))))) 0(0(2(1(2(0(2(1(0(0(0(2(2(2(0(x1))))))))))))))) -> 1(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(x1)))))))))))))))) 0(1(0(2(1(1(2(2(2(0(0(2(2(0(0(x1))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(x1))))))))))))))))) 0(1(0(2(2(1(1(0(1(0(2(0(0(0(0(x1))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(x1)))))))))))))))) 0(1(2(1(2(2(1(0(0(2(2(1(2(1(2(x1))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) 1(2(0(2(0(0(0(2(1(0(1(2(0(0(0(x1))))))))))))))) -> 1(1(0(1(1(0(2(2(0(1(2(2(0(0(0(2(x1)))))))))))))))) 2(0(0(2(1(1(2(1(0(1(0(0(2(2(0(x1))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(x1))))))))))))))))) 2(2(2(0(0(1(2(1(0(2(2(1(2(2(1(x1))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(x1)))))))))))))))))))) 0(0(0(0(1(2(0(2(0(1(1(2(2(0(0(2(x1)))))))))))))))) -> 0(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(x1))))))))))))))))) 0(1(0(1(2(0(0(0(1(1(0(2(2(0(2(2(x1)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(x1))))))))))))))))) 2(0(2(2(0(2(2(2(2(1(1(1(1(2(1(2(x1)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(x1)))))))))))))))))) 2(1(1(2(0(1(2(0(2(1(0(0(2(2(2(1(x1)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) 2(2(0(2(1(1(2(2(0(2(2(0(0(0(2(1(x1)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(x1))))))))))))))))) 0(1(0(1(2(2(2(0(0(0(2(0(0(0(2(0(2(x1))))))))))))))))) -> 1(1(0(1(2(1(1(2(2(1(0(2(1(0(1(1(1(0(x1)))))))))))))))))) 0(0(0(0(0(1(1(0(2(2(1(2(0(2(0(0(2(0(x1)))))))))))))))))) -> 0(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(x1)))))))))))))))))))) 0(0(0(2(0(1(2(0(0(1(0(2(0(1(1(2(0(2(x1)))))))))))))))))) -> 0(1(0(2(1(1(2(2(2(2(1(1(1(0(2(0(1(2(1(x1))))))))))))))))))) 1(2(2(2(0(0(0(0(0(1(0(1(2(1(1(0(2(0(x1)))))))))))))))))) -> 2(1(0(1(2(1(1(2(1(1(1(1(0(2(0(1(0(1(1(1(0(x1))))))))))))))))))))) 2(2(0(1(0(2(0(0(1(0(2(0(1(0(2(0(1(0(x1)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(x1))))))))))))))))))))) 2(2(1(2(2(2(0(1(0(0(0(0(0(2(2(2(1(0(x1)))))))))))))))))) -> 1(2(1(0(1(1(2(1(1(0(2(2(1(1(1(1(0(2(0(2(1(x1))))))))))))))))))))) 0(0(1(2(0(1(1(2(1(2(1(1(2(2(0(1(0(2(2(x1))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(x1))))))))))))))))))))) 0(1(0(1(2(0(1(1(1(0(2(1(1(2(1(0(2(2(1(x1))))))))))))))))))) -> 1(1(2(2(1(2(2(1(1(1(2(2(0(1(0(1(0(2(1(1(x1)))))))))))))))))))) 0(1(2(0(2(2(0(0(0(1(2(0(0(1(0(1(0(2(1(x1))))))))))))))))))) -> 0(0(1(2(1(1(1(1(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(x1))))))))))))))))))))))) 1(0(1(2(1(0(1(2(1(2(1(1(2(1(0(2(2(0(2(x1))))))))))))))))))) -> 1(1(1(1(2(0(1(2(0(2(2(2(0(0(2(0(1(2(2(0(x1)))))))))))))))))))) 2(0(2(2(0(2(2(0(0(2(2(1(2(0(1(2(1(0(1(x1))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(2(0(1(1(1(1(1(0(0(2(0(1(1(x1)))))))))))))))))))))) 2(1(2(1(2(1(1(2(1(0(1(0(2(0(1(0(2(2(2(x1))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(x1))))))))))))))))))))) 2(2(0(2(0(1(0(2(2(1(1(0(1(0(1(1(1(0(1(x1))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(x1))))))))))))))))))) 0(2(0(2(2(0(2(1(1(1(0(2(1(2(1(0(0(1(0(2(x1)))))))))))))))))))) -> 2(1(1(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(x1)))))))))))))))))))))) 0(2(2(1(2(2(2(0(1(2(2(2(2(1(1(0(0(0(1(0(x1)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(x1)))))))))))))))))))))))) 1(1(1(2(0(0(0(2(0(1(2(0(0(2(2(2(1(1(0(0(x1)))))))))))))))))))) -> 1(1(0(2(1(2(2(2(2(2(0(2(1(1(1(0(0(0(0(1(1(x1))))))))))))))))))))) 1(1(1(2(0(2(1(1(2(2(0(0(1(2(0(0(0(0(2(0(x1)))))))))))))))))))) -> 1(1(1(1(1(2(0(2(0(2(1(0(0(0(2(1(2(0(1(2(2(x1))))))))))))))))))))) 2(2(2(1(2(2(2(1(2(2(2(1(1(2(0(0(2(1(0(2(x1)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(x1))))))))))))))))))))))))))) 1(1(2(0(0(0(0(1(1(0(0(1(1(0(0(0(0(0(0(2(1(x1))))))))))))))))))))) -> 1(1(0(0(2(0(0(0(2(0(0(0(1(0(0(0(0(1(1(1(1(x1))))))))))))))))))))) 1(1(2(1(1(1(1(0(0(0(2(2(1(1(2(0(1(2(2(0(1(x1))))))))))))))))))))) -> 1(0(2(1(2(1(2(1(0(0(2(2(2(0(1(0(1(1(1(1(1(x1))))))))))))))))))))) 2(1(0(0(2(1(0(1(0(2(2(0(0(2(2(0(0(0(1(0(2(x1))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(x1))))))))))))))))))))))) 2(2(0(2(2(1(2(0(0(2(1(1(2(0(1(2(0(1(0(0(0(x1))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(x1)))))))))))))))))))))) 2(2(1(2(1(1(2(2(0(0(2(0(2(0(0(2(0(1(2(2(0(x1))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(x1))))))))))))))))))))))) 0(1(1(0(2(1(0(1(2(0(0(1(1(2(0(0(2(0(0(2(2(2(x1)))))))))))))))))))))) -> 0(2(2(1(2(2(1(2(1(1(1(1(2(0(1(0(0(1(1(1(0(1(1(x1))))))))))))))))))))))) 0(2(0(0(0(2(0(1(2(0(1(1(1(1(2(0(2(0(0(1(0(2(x1)))))))))))))))))))))) -> 0(2(2(1(1(0(0(2(2(1(1(0(1(1(1(2(0(1(2(1(0(1(1(x1))))))))))))))))))))))) 0(2(0(0(2(2(0(0(2(0(2(1(0(1(2(1(1(2(0(2(1(2(x1)))))))))))))))))))))) -> 2(0(0(2(1(2(1(0(1(2(2(1(2(2(2(1(1(1(1(0(2(0(1(x1))))))))))))))))))))))) 1(1(2(0(2(2(0(2(2(1(0(0(0(0(0(2(2(0(2(2(2(2(x1)))))))))))))))))))))) -> 2(1(1(1(0(1(1(1(1(2(2(1(1(2(2(0(0(0(1(2(1(0(0(x1))))))))))))))))))))))) 1(2(0(1(0(2(1(0(0(0(0(2(1(0(2(0(0(2(1(1(2(1(x1)))))))))))))))))))))) -> 1(0(0(2(2(1(2(1(1(0(1(1(1(0(1(0(1(1(1(2(1(0(2(2(1(x1))))))))))))))))))))))))) 1(2(0(2(0(1(2(1(0(0(2(2(1(0(0(0(2(1(1(2(1(2(x1)))))))))))))))))))))) -> 1(1(1(2(2(2(1(0(1(1(0(2(0(1(0(1(2(0(0(0(1(1(1(0(x1)))))))))))))))))))))))) 1(2(1(0(1(0(2(2(2(1(0(0(2(0(1(1(0(2(2(2(0(0(x1)))))))))))))))))))))) -> 1(0(1(1(1(0(2(1(2(0(0(0(0(2(1(2(2(0(2(2(2(0(x1)))))))))))))))))))))) 1(2(2(2(2(2(2(1(1(0(1(0(2(2(2(1(1(2(1(2(1(1(x1)))))))))))))))))))))) -> 0(2(0(2(0(0(0(1(2(0(2(1(2(0(2(1(1(0(0(0(1(1(1(1(x1)))))))))))))))))))))))) 2(0(0(0(2(0(0(2(2(2(0(0(2(1(0(0(1(0(0(1(2(1(x1)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(x1)))))))))))))))))))))))) 2(0(0(2(1(2(0(2(1(0(2(2(1(2(1(1(2(0(2(0(0(2(x1)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(x1)))))))))))))))))))))))) 2(0(1(2(1(1(0(2(0(2(2(2(2(1(1(2(1(1(1(2(2(1(x1)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(x1))))))))))))))))))))))) 0(0(0(1(0(1(2(2(0(0(2(0(1(0(1(2(0(1(1(2(0(0(0(x1))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(x1))))))))))))))))))))))) 1(0(2(1(2(2(2(1(0(2(1(2(1(2(2(2(1(0(0(0(0(2(2(x1))))))))))))))))))))))) -> 1(1(1(2(2(2(1(2(2(2(1(0(1(0(1(1(1(0(0(1(2(0(0(2(0(2(x1)))))))))))))))))))))))))) 1(1(2(2(2(0(1(0(2(1(2(0(2(1(1(2(0(1(2(0(2(2(0(x1))))))))))))))))))))))) -> 1(0(2(2(0(2(1(1(1(1(1(0(1(1(1(1(0(2(0(2(2(2(1(1(2(x1))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(1(1(0(0(2(2(2(2(0(2(0(0(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(x1)))))))))))))))))))))))) 2(0(2(2(0(1(0(2(0(0(1(2(1(2(0(0(2(0(0(2(2(2(2(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(x1)))))))))))))))))))))))) 0(0(1(1(2(1(1(1(2(2(1(2(2(0(1(1(1(2(1(2(0(2(1(2(x1)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(x1))))))))))))))))))))))))) 0(2(0(0(1(0(2(2(2(2(1(2(2(0(1(0(2(2(1(2(1(2(1(2(x1)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(2(0(1(0(2(0(1(2(0(1(2(2(1(0(2(2(2(1(1(2(0(0(0(x1)))))))))))))))))))))))) -> 0(1(1(1(1(0(0(1(1(1(1(0(1(0(0(2(0(1(1(1(0(1(2(0(1(1(x1)))))))))))))))))))))))))) 2(1(2(1(2(1(0(0(1(2(1(0(2(0(1(1(0(2(1(0(1(0(1(0(x1)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(x1)))))))))))))))))))))))) 0(2(2(1(2(0(0(1(0(2(2(0(0(1(0(0(0(2(2(2(0(2(1(0(0(x1))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(x1)))))))))))))))))))))))))) 1(1(1(0(0(1(2(2(1(0(2(1(2(1(0(2(2(2(1(1(0(0(2(1(2(x1))))))))))))))))))))))))) -> 1(1(2(2(2(1(1(1(1(1(0(0(1(1(2(0(1(2(1(0(1(2(1(1(0(1(x1)))))))))))))))))))))))))) 1(2(0(1(0(2(0(0(0(1(1(2(1(0(0(1(0(1(0(2(0(1(0(2(2(x1))))))))))))))))))))))))) -> 1(1(0(1(0(2(0(0(1(2(1(1(1(1(1(0(0(2(2(1(0(2(2(1(2(2(x1)))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(2(2(1(0(2(2(1(0(2(2(1(1(2(0(0(0(1(x1))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(x1)))))))))))))))))))))))))))) 2(1(2(1(2(0(0(1(0(2(1(2(0(1(2(0(0(2(1(0(2(0(2(2(2(x1))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(x1)))))))))))))))))))))))))) 2(1(2(2(2(2(1(1(0(0(2(1(2(0(0(0(1(1(0(0(1(1(2(0(1(x1))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(x1))))))))))))))))))))))))) 2(2(0(2(2(0(0(1(2(0(1(1(0(1(2(1(0(2(1(0(2(2(1(0(1(x1))))))))))))))))))))))))) -> 1(0(0(1(2(1(1(0(1(0(1(1(1(0(1(2(2(2(1(2(2(2(2(1(2(1(1(1(x1)))))))))))))))))))))))))))) 2(2(2(2(1(1(0(1(0(0(0(2(1(0(2(1(2(0(0(2(0(0(2(2(2(x1))))))))))))))))))))))))) -> 1(0(0(0(2(1(1(1(1(1(1(0(0(1(0(1(2(0(2(1(2(1(1(0(1(2(0(x1))))))))))))))))))))))))))) 0(1(2(1(1(0(2(1(1(2(1(1(2(0(2(0(2(2(2(2(0(0(2(1(1(2(x1)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(x1))))))))))))))))))))))))))) 1(1(2(2(1(1(2(1(0(1(2(1(1(1(0(0(1(1(0(1(1(1(1(2(0(2(x1)))))))))))))))))))))))))) -> 0(1(1(2(1(2(2(2(2(1(1(1(1(1(0(1(0(2(1(0(0(1(1(1(1(1(x1)))))))))))))))))))))))))) 1(2(1(2(1(0(0(2(2(0(2(0(2(2(0(1(1(0(0(1(2(2(0(0(2(2(x1)))))))))))))))))))))))))) -> 1(0(2(0(0(1(1(0(1(2(2(0(1(1(0(0(0(1(1(1(2(2(1(2(2(0(1(2(x1)))))))))))))))))))))))))))) 0(1(2(0(0(1(2(2(1(1(0(1(0(0(2(2(0(2(2(0(0(0(0(1(0(2(0(x1))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(x1)))))))))))))))))))))))))))) 0(1(2(1(0(2(2(2(2(0(0(1(2(1(0(0(0(0(2(0(0(0(2(0(1(0(2(x1))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x1)))))))))))))))))))))))))))) 0(2(0(1(0(2(2(1(1(0(0(0(2(0(2(0(1(0(0(1(2(1(2(2(1(1(0(x1))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(x1)))))))))))))))))))))))))))) 0(2(1(2(1(2(2(0(2(1(0(1(2(1(1(1(2(2(1(2(0(1(1(1(0(0(2(x1))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(x1)))))))))))))))))))))))))))) 1(0(1(0(1(2(2(0(2(0(1(2(0(0(1(0(0(0(2(0(1(0(0(2(0(2(1(x1))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(x1)))))))))))))))))))))))))))) 0(0(2(2(0(2(1(2(2(0(0(0(2(2(0(2(2(2(1(0(1(0(1(2(2(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(x1))))))))))))))))))))))))))))) 0(1(1(1(2(0(0(0(1(2(1(0(0(0(1(1(0(1(2(2(0(2(2(0(1(2(0(1(x1)))))))))))))))))))))))))))) -> 1(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(x1)))))))))))))))))))))))))))) 0(1(2(0(0(2(1(1(2(1(1(2(2(1(0(2(2(2(2(2(2(2(2(1(2(2(0(2(x1)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(2(1(0(1(2(1(2(0(0(1(1(0(0(2(2(0(0(0(1(1(0(1(2(0(0(x1)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(x1))))))))))))))))))))))))))))) 0(2(0(2(2(1(0(2(1(1(1(2(1(1(2(2(1(2(0(1(1(0(2(2(0(0(1(2(x1)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(x1))))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(2(0(2(2(0(2(1(2(2(1(2(1(1(2(1(2(0(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(0(1(1(0(0(0(2(0(2(0(1(1(1(1(1(0(2(0(2(1(0(1(2(2(2(2(0(2(x1)))))))))))))))))))))))))))))) 2(0(0(1(0(2(2(1(0(1(0(2(0(1(0(2(0(2(2(0(2(1(1(2(2(2(2(0(x1)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(x1))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(0(2(1(0(2(1(0(0(2(0(1(2(1(0(2(0(2(x1)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(x1))))))))))))))))))))))))))))) 0(1(1(2(1(1(0(2(0(2(2(0(1(1(0(0(2(1(1(1(2(0(0(2(0(2(0(1(2(x1))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(1(2(2(1(2(0(1(1(1(2(2(0(0(0(2(2(2(1(0(2(0(0(1(2(1(2(x1))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(x1))))))))))))))))))))))))))))) 0(2(0(0(2(1(2(0(2(2(1(1(2(1(1(2(0(1(0(2(2(2(1(1(1(2(0(2(1(x1))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(x1))))))))))))))))))))))))))))) 1(0(2(1(2(2(1(0(0(1(1(1(0(0(2(1(1(0(2(0(2(1(0(2(0(0(2(1(2(x1))))))))))))))))))))))))))))) -> 1(1(1(1(0(0(1(0(1(1(0(1(1(2(1(1(2(0(1(2(1(0(0(1(2(1(2(2(2(2(x1)))))))))))))))))))))))))))))) 2(0(0(0(1(2(0(0(1(2(2(2(0(2(1(0(2(0(0(1(1(0(0(2(2(0(2(1(2(x1))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(x1)))))))))))))))))))))))))))))) 0(1(2(2(2(1(1(0(1(2(0(2(1(1(1(2(2(1(2(0(2(2(0(2(2(2(0(0(2(0(x1)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(1(2(2(0(2(2(1(1(1(1(2(1(2(0(2(2(0(2(2(0(0(0(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: FULL ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(0(1(0(0(x1))))) -> 0(1(0(1(1(1(1(x1))))))) 1(2(2(0(1(2(x1)))))) -> 1(1(1(1(1(0(1(1(0(x1))))))))) 2(0(2(0(1(0(x1)))))) -> 1(1(0(1(1(1(1(0(x1)))))))) 2(0(2(2(1(2(x1)))))) -> 1(1(0(0(1(1(2(x1))))))) 1(0(1(1(2(1(2(x1))))))) -> 0(1(1(1(1(1(2(2(x1)))))))) 1(1(2(1(2(1(2(x1))))))) -> 1(0(2(1(1(1(1(1(x1)))))))) 2(0(2(0(0(0(0(x1))))))) -> 0(1(1(1(1(2(1(0(x1)))))))) 0(0(0(1(2(2(0(0(x1)))))))) -> 0(1(1(1(1(0(0(2(2(x1))))))))) 0(0(1(2(2(0(1(0(2(x1))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(x1)))))))))))) 0(1(0(2(2(1(0(1(0(0(x1)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(x1))))))))))) 1(1(0(2(2(2(0(2(2(2(x1)))))))))) -> 1(0(0(2(0(1(1(1(0(1(1(x1))))))))))) 0(0(2(1(1(1(0(1(1(2(1(x1))))))))))) -> 0(1(1(1(1(1(1(1(0(1(0(0(0(x1))))))))))))) 2(0(1(1(2(1(0(2(0(0(1(x1))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(x1)))))))))))) 1(1(2(2(2(0(1(0(2(2(1(2(x1)))))))))))) -> 1(1(0(1(1(0(0(0(1(2(0(2(1(x1))))))))))))) 2(2(2(0(0(1(2(1(1(2(2(2(x1)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(x1))))))))))))) 0(1(1(1(0(1(2(2(1(0(0(0(0(x1))))))))))))) -> 0(1(1(1(2(1(2(0(1(1(1(1(1(1(x1)))))))))))))) 1(0(2(2(0(2(1(0(2(1(2(1(2(x1))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(x1)))))))))))))))))) 2(1(0(1(0(0(0(2(0(0(2(1(2(x1))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(x1))))))))))))))) 2(2(0(0(0(0(0(2(2(1(0(2(2(x1))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(x1)))))))))))))) 0(0(1(1(2(0(1(0(2(0(2(1(1(0(x1)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(x1)))))))))))))))) 0(2(2(0(2(1(2(0(2(0(0(2(2(1(x1)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(x1)))))))))))))))) 0(2(2(1(1(2(0(1(1(2(1(0(0(2(x1)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(x1)))))))))))))))) 1(0(1(0(1(0(1(0(2(1(2(2(2(0(x1)))))))))))))) -> 1(0(2(2(0(0(1(1(1(2(0(2(1(0(x1)))))))))))))) 2(0(1(2(0(1(0(0(0(2(0(1(0(2(x1)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(x1))))))))))))))) 2(2(0(0(2(1(2(1(0(2(0(0(2(2(x1)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(x1))))))))))))))) 0(0(2(1(2(0(2(1(0(0(0(2(2(2(0(x1))))))))))))))) -> 1(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(x1)))))))))))))))) 0(1(0(2(1(1(2(2(2(0(0(2(2(0(0(x1))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(x1))))))))))))))))) 0(1(0(2(2(1(1(0(1(0(2(0(0(0(0(x1))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(x1)))))))))))))))) 0(1(2(1(2(2(1(0(0(2(2(1(2(1(2(x1))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) 1(2(0(2(0(0(0(2(1(0(1(2(0(0(0(x1))))))))))))))) -> 1(1(0(1(1(0(2(2(0(1(2(2(0(0(0(2(x1)))))))))))))))) 2(0(0(2(1(1(2(1(0(1(0(0(2(2(0(x1))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(x1))))))))))))))))) 2(2(2(0(0(1(2(1(0(2(2(1(2(2(1(x1))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(x1)))))))))))))))))))) 0(0(0(0(1(2(0(2(0(1(1(2(2(0(0(2(x1)))))))))))))))) -> 0(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(x1))))))))))))))))) 0(1(0(1(2(0(0(0(1(1(0(2(2(0(2(2(x1)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(x1))))))))))))))))) 2(0(2(2(0(2(2(2(2(1(1(1(1(2(1(2(x1)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(x1)))))))))))))))))) 2(1(1(2(0(1(2(0(2(1(0(0(2(2(2(1(x1)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) 2(2(0(2(1(1(2(2(0(2(2(0(0(0(2(1(x1)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(x1))))))))))))))))) 0(1(0(1(2(2(2(0(0(0(2(0(0(0(2(0(2(x1))))))))))))))))) -> 1(1(0(1(2(1(1(2(2(1(0(2(1(0(1(1(1(0(x1)))))))))))))))))) 0(0(0(0(0(1(1(0(2(2(1(2(0(2(0(0(2(0(x1)))))))))))))))))) -> 0(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(x1)))))))))))))))))))) 0(0(0(2(0(1(2(0(0(1(0(2(0(1(1(2(0(2(x1)))))))))))))))))) -> 0(1(0(2(1(1(2(2(2(2(1(1(1(0(2(0(1(2(1(x1))))))))))))))))))) 1(2(2(2(0(0(0(0(0(1(0(1(2(1(1(0(2(0(x1)))))))))))))))))) -> 2(1(0(1(2(1(1(2(1(1(1(1(0(2(0(1(0(1(1(1(0(x1))))))))))))))))))))) 2(2(0(1(0(2(0(0(1(0(2(0(1(0(2(0(1(0(x1)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(x1))))))))))))))))))))) 2(2(1(2(2(2(0(1(0(0(0(0(0(2(2(2(1(0(x1)))))))))))))))))) -> 1(2(1(0(1(1(2(1(1(0(2(2(1(1(1(1(0(2(0(2(1(x1))))))))))))))))))))) 0(0(1(2(0(1(1(2(1(2(1(1(2(2(0(1(0(2(2(x1))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(x1))))))))))))))))))))) 0(1(0(1(2(0(1(1(1(0(2(1(1(2(1(0(2(2(1(x1))))))))))))))))))) -> 1(1(2(2(1(2(2(1(1(1(2(2(0(1(0(1(0(2(1(1(x1)))))))))))))))))))) 0(1(2(0(2(2(0(0(0(1(2(0(0(1(0(1(0(2(1(x1))))))))))))))))))) -> 0(0(1(2(1(1(1(1(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(x1))))))))))))))))))))))) 1(0(1(2(1(0(1(2(1(2(1(1(2(1(0(2(2(0(2(x1))))))))))))))))))) -> 1(1(1(1(2(0(1(2(0(2(2(2(0(0(2(0(1(2(2(0(x1)))))))))))))))))))) 2(0(2(2(0(2(2(0(0(2(2(1(2(0(1(2(1(0(1(x1))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(2(0(1(1(1(1(1(0(0(2(0(1(1(x1)))))))))))))))))))))) 2(1(2(1(2(1(1(2(1(0(1(0(2(0(1(0(2(2(2(x1))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(x1))))))))))))))))))))) 2(2(0(2(0(1(0(2(2(1(1(0(1(0(1(1(1(0(1(x1))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(x1))))))))))))))))))) 0(2(0(2(2(0(2(1(1(1(0(2(1(2(1(0(0(1(0(2(x1)))))))))))))))))))) -> 2(1(1(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(x1)))))))))))))))))))))) 0(2(2(1(2(2(2(0(1(2(2(2(2(1(1(0(0(0(1(0(x1)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(x1)))))))))))))))))))))))) 1(1(1(2(0(0(0(2(0(1(2(0(0(2(2(2(1(1(0(0(x1)))))))))))))))))))) -> 1(1(0(2(1(2(2(2(2(2(0(2(1(1(1(0(0(0(0(1(1(x1))))))))))))))))))))) 1(1(1(2(0(2(1(1(2(2(0(0(1(2(0(0(0(0(2(0(x1)))))))))))))))))))) -> 1(1(1(1(1(2(0(2(0(2(1(0(0(0(2(1(2(0(1(2(2(x1))))))))))))))))))))) 2(2(2(1(2(2(2(1(2(2(2(1(1(2(0(0(2(1(0(2(x1)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(x1))))))))))))))))))))))))))) 1(1(2(0(0(0(0(1(1(0(0(1(1(0(0(0(0(0(0(2(1(x1))))))))))))))))))))) -> 1(1(0(0(2(0(0(0(2(0(0(0(1(0(0(0(0(1(1(1(1(x1))))))))))))))))))))) 1(1(2(1(1(1(1(0(0(0(2(2(1(1(2(0(1(2(2(0(1(x1))))))))))))))))))))) -> 1(0(2(1(2(1(2(1(0(0(2(2(2(0(1(0(1(1(1(1(1(x1))))))))))))))))))))) 2(1(0(0(2(1(0(1(0(2(2(0(0(2(2(0(0(0(1(0(2(x1))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(x1))))))))))))))))))))))) 2(2(0(2(2(1(2(0(0(2(1(1(2(0(1(2(0(1(0(0(0(x1))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(x1)))))))))))))))))))))) 2(2(1(2(1(1(2(2(0(0(2(0(2(0(0(2(0(1(2(2(0(x1))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(x1))))))))))))))))))))))) 0(1(1(0(2(1(0(1(2(0(0(1(1(2(0(0(2(0(0(2(2(2(x1)))))))))))))))))))))) -> 0(2(2(1(2(2(1(2(1(1(1(1(2(0(1(0(0(1(1(1(0(1(1(x1))))))))))))))))))))))) 0(2(0(0(0(2(0(1(2(0(1(1(1(1(2(0(2(0(0(1(0(2(x1)))))))))))))))))))))) -> 0(2(2(1(1(0(0(2(2(1(1(0(1(1(1(2(0(1(2(1(0(1(1(x1))))))))))))))))))))))) 0(2(0(0(2(2(0(0(2(0(2(1(0(1(2(1(1(2(0(2(1(2(x1)))))))))))))))))))))) -> 2(0(0(2(1(2(1(0(1(2(2(1(2(2(2(1(1(1(1(0(2(0(1(x1))))))))))))))))))))))) 1(1(2(0(2(2(0(2(2(1(0(0(0(0(0(2(2(0(2(2(2(2(x1)))))))))))))))))))))) -> 2(1(1(1(0(1(1(1(1(2(2(1(1(2(2(0(0(0(1(2(1(0(0(x1))))))))))))))))))))))) 1(2(0(1(0(2(1(0(0(0(0(2(1(0(2(0(0(2(1(1(2(1(x1)))))))))))))))))))))) -> 1(0(0(2(2(1(2(1(1(0(1(1(1(0(1(0(1(1(1(2(1(0(2(2(1(x1))))))))))))))))))))))))) 1(2(0(2(0(1(2(1(0(0(2(2(1(0(0(0(2(1(1(2(1(2(x1)))))))))))))))))))))) -> 1(1(1(2(2(2(1(0(1(1(0(2(0(1(0(1(2(0(0(0(1(1(1(0(x1)))))))))))))))))))))))) 1(2(1(0(1(0(2(2(2(1(0(0(2(0(1(1(0(2(2(2(0(0(x1)))))))))))))))))))))) -> 1(0(1(1(1(0(2(1(2(0(0(0(0(2(1(2(2(0(2(2(2(0(x1)))))))))))))))))))))) 1(2(2(2(2(2(2(1(1(0(1(0(2(2(2(1(1(2(1(2(1(1(x1)))))))))))))))))))))) -> 0(2(0(2(0(0(0(1(2(0(2(1(2(0(2(1(1(0(0(0(1(1(1(1(x1)))))))))))))))))))))))) 2(0(0(0(2(0(0(2(2(2(0(0(2(1(0(0(1(0(0(1(2(1(x1)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(x1)))))))))))))))))))))))) 2(0(0(2(1(2(0(2(1(0(2(2(1(2(1(1(2(0(2(0(0(2(x1)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(x1)))))))))))))))))))))))) 2(0(1(2(1(1(0(2(0(2(2(2(2(1(1(2(1(1(1(2(2(1(x1)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(x1))))))))))))))))))))))) 0(0(0(1(0(1(2(2(0(0(2(0(1(0(1(2(0(1(1(2(0(0(0(x1))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(x1))))))))))))))))))))))) 1(0(2(1(2(2(2(1(0(2(1(2(1(2(2(2(1(0(0(0(0(2(2(x1))))))))))))))))))))))) -> 1(1(1(2(2(2(1(2(2(2(1(0(1(0(1(1(1(0(0(1(2(0(0(2(0(2(x1)))))))))))))))))))))))))) 1(1(2(2(2(0(1(0(2(1(2(0(2(1(1(2(0(1(2(0(2(2(0(x1))))))))))))))))))))))) -> 1(0(2(2(0(2(1(1(1(1(1(0(1(1(1(1(0(2(0(2(2(2(1(1(2(x1))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(1(1(0(0(2(2(2(2(0(2(0(0(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(x1)))))))))))))))))))))))) 2(0(2(2(0(1(0(2(0(0(1(2(1(2(0(0(2(0(0(2(2(2(2(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(x1)))))))))))))))))))))))) 0(0(1(1(2(1(1(1(2(2(1(2(2(0(1(1(1(2(1(2(0(2(1(2(x1)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(x1))))))))))))))))))))))))) 0(2(0(0(1(0(2(2(2(2(1(2(2(0(1(0(2(2(1(2(1(2(1(2(x1)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(2(0(1(0(2(0(1(2(0(1(2(2(1(0(2(2(2(1(1(2(0(0(0(x1)))))))))))))))))))))))) -> 0(1(1(1(1(0(0(1(1(1(1(0(1(0(0(2(0(1(1(1(0(1(2(0(1(1(x1)))))))))))))))))))))))))) 2(1(2(1(2(1(0(0(1(2(1(0(2(0(1(1(0(2(1(0(1(0(1(0(x1)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(x1)))))))))))))))))))))))) 0(2(2(1(2(0(0(1(0(2(2(0(0(1(0(0(0(2(2(2(0(2(1(0(0(x1))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(x1)))))))))))))))))))))))))) 1(1(1(0(0(1(2(2(1(0(2(1(2(1(0(2(2(2(1(1(0(0(2(1(2(x1))))))))))))))))))))))))) -> 1(1(2(2(2(1(1(1(1(1(0(0(1(1(2(0(1(2(1(0(1(2(1(1(0(1(x1)))))))))))))))))))))))))) 1(2(0(1(0(2(0(0(0(1(1(2(1(0(0(1(0(1(0(2(0(1(0(2(2(x1))))))))))))))))))))))))) -> 1(1(0(1(0(2(0(0(1(2(1(1(1(1(1(0(0(2(2(1(0(2(2(1(2(2(x1)))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(2(2(1(0(2(2(1(0(2(2(1(1(2(0(0(0(1(x1))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(x1)))))))))))))))))))))))))))) 2(1(2(1(2(0(0(1(0(2(1(2(0(1(2(0(0(2(1(0(2(0(2(2(2(x1))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(x1)))))))))))))))))))))))))) 2(1(2(2(2(2(1(1(0(0(2(1(2(0(0(0(1(1(0(0(1(1(2(0(1(x1))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(x1))))))))))))))))))))))))) 2(2(0(2(2(0(0(1(2(0(1(1(0(1(2(1(0(2(1(0(2(2(1(0(1(x1))))))))))))))))))))))))) -> 1(0(0(1(2(1(1(0(1(0(1(1(1(0(1(2(2(2(1(2(2(2(2(1(2(1(1(1(x1)))))))))))))))))))))))))))) 2(2(2(2(1(1(0(1(0(0(0(2(1(0(2(1(2(0(0(2(0(0(2(2(2(x1))))))))))))))))))))))))) -> 1(0(0(0(2(1(1(1(1(1(1(0(0(1(0(1(2(0(2(1(2(1(1(0(1(2(0(x1))))))))))))))))))))))))))) 0(1(2(1(1(0(2(1(1(2(1(1(2(0(2(0(2(2(2(2(0(0(2(1(1(2(x1)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(x1))))))))))))))))))))))))))) 1(1(2(2(1(1(2(1(0(1(2(1(1(1(0(0(1(1(0(1(1(1(1(2(0(2(x1)))))))))))))))))))))))))) -> 0(1(1(2(1(2(2(2(2(1(1(1(1(1(0(1(0(2(1(0(0(1(1(1(1(1(x1)))))))))))))))))))))))))) 1(2(1(2(1(0(0(2(2(0(2(0(2(2(0(1(1(0(0(1(2(2(0(0(2(2(x1)))))))))))))))))))))))))) -> 1(0(2(0(0(1(1(0(1(2(2(0(1(1(0(0(0(1(1(1(2(2(1(2(2(0(1(2(x1)))))))))))))))))))))))))))) 0(1(2(0(0(1(2(2(1(1(0(1(0(0(2(2(0(2(2(0(0(0(0(1(0(2(0(x1))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(x1)))))))))))))))))))))))))))) 0(1(2(1(0(2(2(2(2(0(0(1(2(1(0(0(0(0(2(0(0(0(2(0(1(0(2(x1))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x1)))))))))))))))))))))))))))) 0(2(0(1(0(2(2(1(1(0(0(0(2(0(2(0(1(0(0(1(2(1(2(2(1(1(0(x1))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(x1)))))))))))))))))))))))))))) 0(2(1(2(1(2(2(0(2(1(0(1(2(1(1(1(2(2(1(2(0(1(1(1(0(0(2(x1))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(x1)))))))))))))))))))))))))))) 1(0(1(0(1(2(2(0(2(0(1(2(0(0(1(0(0(0(2(0(1(0(0(2(0(2(1(x1))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(x1)))))))))))))))))))))))))))) 0(0(2(2(0(2(1(2(2(0(0(0(2(2(0(2(2(2(1(0(1(0(1(2(2(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(x1))))))))))))))))))))))))))))) 0(1(1(1(2(0(0(0(1(2(1(0(0(0(1(1(0(1(2(2(0(2(2(0(1(2(0(1(x1)))))))))))))))))))))))))))) -> 1(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(x1)))))))))))))))))))))))))))) 0(1(2(0(0(2(1(1(2(1(1(2(2(1(0(2(2(2(2(2(2(2(2(1(2(2(0(2(x1)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(2(1(0(1(2(1(2(0(0(1(1(0(0(2(2(0(0(0(1(1(0(1(2(0(0(x1)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(x1))))))))))))))))))))))))))))) 0(2(0(2(2(1(0(2(1(1(1(2(1(1(2(2(1(2(0(1(1(0(2(2(0(0(1(2(x1)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(x1))))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(2(0(2(2(0(2(1(2(2(1(2(1(1(2(1(2(0(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(0(1(1(0(0(0(2(0(2(0(1(1(1(1(1(0(2(0(2(1(0(1(2(2(2(2(0(2(x1)))))))))))))))))))))))))))))) 2(0(0(1(0(2(2(1(0(1(0(2(0(1(0(2(0(2(2(0(2(1(1(2(2(2(2(0(x1)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(x1))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(0(2(1(0(2(1(0(0(2(0(1(2(1(0(2(0(2(x1)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(x1))))))))))))))))))))))))))))) 0(1(1(2(1(1(0(2(0(2(2(0(1(1(0(0(2(1(1(1(2(0(0(2(0(2(0(1(2(x1))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(1(2(2(1(2(0(1(1(1(2(2(0(0(0(2(2(2(1(0(2(0(0(1(2(1(2(x1))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(x1))))))))))))))))))))))))))))) 0(2(0(0(2(1(2(0(2(2(1(1(2(1(1(2(0(1(0(2(2(2(1(1(1(2(0(2(1(x1))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(x1))))))))))))))))))))))))))))) 1(0(2(1(2(2(1(0(0(1(1(1(0(0(2(1(1(0(2(0(2(1(0(2(0(0(2(1(2(x1))))))))))))))))))))))))))))) -> 1(1(1(1(0(0(1(0(1(1(0(1(1(2(1(1(2(0(1(2(1(0(0(1(2(1(2(2(2(2(x1)))))))))))))))))))))))))))))) 2(0(0(0(1(2(0(0(1(2(2(2(0(2(1(0(2(0(0(1(1(0(0(2(2(0(2(1(2(x1))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(x1)))))))))))))))))))))))))))))) 0(1(2(2(2(1(1(0(1(2(0(2(1(1(1(2(2(1(2(0(2(2(0(2(2(2(0(0(2(0(x1)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(1(2(2(0(2(2(1(1(1(1(2(1(2(0(2(2(0(2(2(0(0(0(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: FULL ---------------------------------------- (7) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (8) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(0(1(0(0(x1))))) -> 0(1(0(1(1(1(1(x1))))))) 1(2(2(0(1(2(x1)))))) -> 1(1(1(1(1(0(1(1(0(x1))))))))) 2(0(2(0(1(0(x1)))))) -> 1(1(0(1(1(1(1(0(x1)))))))) 2(0(2(2(1(2(x1)))))) -> 1(1(0(0(1(1(2(x1))))))) 1(0(1(1(2(1(2(x1))))))) -> 0(1(1(1(1(1(2(2(x1)))))))) 1(1(2(1(2(1(2(x1))))))) -> 1(0(2(1(1(1(1(1(x1)))))))) 2(0(2(0(0(0(0(x1))))))) -> 0(1(1(1(1(2(1(0(x1)))))))) 0(0(0(1(2(2(0(0(x1)))))))) -> 0(1(1(1(1(0(0(2(2(x1))))))))) 0(0(1(2(2(0(1(0(2(x1))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(x1)))))))))))) 0(1(0(2(2(1(0(1(0(0(x1)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(x1))))))))))) 1(1(0(2(2(2(0(2(2(2(x1)))))))))) -> 1(0(0(2(0(1(1(1(0(1(1(x1))))))))))) 0(0(2(1(1(1(0(1(1(2(1(x1))))))))))) -> 0(1(1(1(1(1(1(1(0(1(0(0(0(x1))))))))))))) 2(0(1(1(2(1(0(2(0(0(1(x1))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(x1)))))))))))) 1(1(2(2(2(0(1(0(2(2(1(2(x1)))))))))))) -> 1(1(0(1(1(0(0(0(1(2(0(2(1(x1))))))))))))) 2(2(2(0(0(1(2(1(1(2(2(2(x1)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(x1))))))))))))) 0(1(1(1(0(1(2(2(1(0(0(0(0(x1))))))))))))) -> 0(1(1(1(2(1(2(0(1(1(1(1(1(1(x1)))))))))))))) 1(0(2(2(0(2(1(0(2(1(2(1(2(x1))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(x1)))))))))))))))))) 2(1(0(1(0(0(0(2(0(0(2(1(2(x1))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(x1))))))))))))))) 2(2(0(0(0(0(0(2(2(1(0(2(2(x1))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(x1)))))))))))))) 0(0(1(1(2(0(1(0(2(0(2(1(1(0(x1)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(x1)))))))))))))))) 0(2(2(0(2(1(2(0(2(0(0(2(2(1(x1)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(x1)))))))))))))))) 0(2(2(1(1(2(0(1(1(2(1(0(0(2(x1)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(x1)))))))))))))))) 1(0(1(0(1(0(1(0(2(1(2(2(2(0(x1)))))))))))))) -> 1(0(2(2(0(0(1(1(1(2(0(2(1(0(x1)))))))))))))) 2(0(1(2(0(1(0(0(0(2(0(1(0(2(x1)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(x1))))))))))))))) 2(2(0(0(2(1(2(1(0(2(0(0(2(2(x1)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(x1))))))))))))))) 0(0(2(1(2(0(2(1(0(0(0(2(2(2(0(x1))))))))))))))) -> 1(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(x1)))))))))))))))) 0(1(0(2(1(1(2(2(2(0(0(2(2(0(0(x1))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(x1))))))))))))))))) 0(1(0(2(2(1(1(0(1(0(2(0(0(0(0(x1))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(x1)))))))))))))))) 0(1(2(1(2(2(1(0(0(2(2(1(2(1(2(x1))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) 1(2(0(2(0(0(0(2(1(0(1(2(0(0(0(x1))))))))))))))) -> 1(1(0(1(1(0(2(2(0(1(2(2(0(0(0(2(x1)))))))))))))))) 2(0(0(2(1(1(2(1(0(1(0(0(2(2(0(x1))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(x1))))))))))))))))) 2(2(2(0(0(1(2(1(0(2(2(1(2(2(1(x1))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(x1)))))))))))))))))))) 0(0(0(0(1(2(0(2(0(1(1(2(2(0(0(2(x1)))))))))))))))) -> 0(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(x1))))))))))))))))) 0(1(0(1(2(0(0(0(1(1(0(2(2(0(2(2(x1)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(x1))))))))))))))))) 2(0(2(2(0(2(2(2(2(1(1(1(1(2(1(2(x1)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(x1)))))))))))))))))) 2(1(1(2(0(1(2(0(2(1(0(0(2(2(2(1(x1)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) 2(2(0(2(1(1(2(2(0(2(2(0(0(0(2(1(x1)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(x1))))))))))))))))) 0(1(0(1(2(2(2(0(0(0(2(0(0(0(2(0(2(x1))))))))))))))))) -> 1(1(0(1(2(1(1(2(2(1(0(2(1(0(1(1(1(0(x1)))))))))))))))))) 0(0(0(0(0(1(1(0(2(2(1(2(0(2(0(0(2(0(x1)))))))))))))))))) -> 0(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(x1)))))))))))))))))))) 0(0(0(2(0(1(2(0(0(1(0(2(0(1(1(2(0(2(x1)))))))))))))))))) -> 0(1(0(2(1(1(2(2(2(2(1(1(1(0(2(0(1(2(1(x1))))))))))))))))))) 1(2(2(2(0(0(0(0(0(1(0(1(2(1(1(0(2(0(x1)))))))))))))))))) -> 2(1(0(1(2(1(1(2(1(1(1(1(0(2(0(1(0(1(1(1(0(x1))))))))))))))))))))) 2(2(0(1(0(2(0(0(1(0(2(0(1(0(2(0(1(0(x1)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(x1))))))))))))))))))))) 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1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(x1))))))))))))))))))))))))))) 1(1(2(2(1(1(2(1(0(1(2(1(1(1(0(0(1(1(0(1(1(1(1(2(0(2(x1)))))))))))))))))))))))))) -> 0(1(1(2(1(2(2(2(2(1(1(1(1(1(0(1(0(2(1(0(0(1(1(1(1(1(x1)))))))))))))))))))))))))) 1(2(1(2(1(0(0(2(2(0(2(0(2(2(0(1(1(0(0(1(2(2(0(0(2(2(x1)))))))))))))))))))))))))) -> 1(0(2(0(0(1(1(0(1(2(2(0(1(1(0(0(0(1(1(1(2(2(1(2(2(0(1(2(x1)))))))))))))))))))))))))))) 0(1(2(0(0(1(2(2(1(1(0(1(0(0(2(2(0(2(2(0(0(0(0(1(0(2(0(x1))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(x1)))))))))))))))))))))))))))) 0(1(2(1(0(2(2(2(2(0(0(1(2(1(0(0(0(0(2(0(0(0(2(0(1(0(2(x1))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x1)))))))))))))))))))))))))))) 0(2(0(1(0(2(2(1(1(0(0(0(2(0(2(0(1(0(0(1(2(1(2(2(1(1(0(x1))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(x1)))))))))))))))))))))))))))) 0(2(1(2(1(2(2(0(2(1(0(1(2(1(1(1(2(2(1(2(0(1(1(1(0(0(2(x1))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(x1)))))))))))))))))))))))))))) 1(0(1(0(1(2(2(0(2(0(1(2(0(0(1(0(0(0(2(0(1(0(0(2(0(2(1(x1))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(x1)))))))))))))))))))))))))))) 0(0(2(2(0(2(1(2(2(0(0(0(2(2(0(2(2(2(1(0(1(0(1(2(2(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(x1))))))))))))))))))))))))))))) 0(1(1(1(2(0(0(0(1(2(1(0(0(0(1(1(0(1(2(2(0(2(2(0(1(2(0(1(x1)))))))))))))))))))))))))))) -> 1(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(x1)))))))))))))))))))))))))))) 0(1(2(0(0(2(1(1(2(1(1(2(2(1(0(2(2(2(2(2(2(2(2(1(2(2(0(2(x1)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(2(1(0(1(2(1(2(0(0(1(1(0(0(2(2(0(0(0(1(1(0(1(2(0(0(x1)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(x1))))))))))))))))))))))))))))) 0(2(0(2(2(1(0(2(1(1(1(2(1(1(2(2(1(2(0(1(1(0(2(2(0(0(1(2(x1)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(x1))))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(2(0(2(2(0(2(1(2(2(1(2(1(1(2(1(2(0(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(0(1(1(0(0(0(2(0(2(0(1(1(1(1(1(0(2(0(2(1(0(1(2(2(2(2(0(2(x1)))))))))))))))))))))))))))))) 2(0(0(1(0(2(2(1(0(1(0(2(0(1(0(2(0(2(2(0(2(1(1(2(2(2(2(0(x1)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(x1))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(0(2(1(0(2(1(0(0(2(0(1(2(1(0(2(0(2(x1)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(x1))))))))))))))))))))))))))))) 0(1(1(2(1(1(0(2(0(2(2(0(1(1(0(0(2(1(1(1(2(0(0(2(0(2(0(1(2(x1))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(1(2(2(1(2(0(1(1(1(2(2(0(0(0(2(2(2(1(0(2(0(0(1(2(1(2(x1))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(x1))))))))))))))))))))))))))))) 0(2(0(0(2(1(2(0(2(2(1(1(2(1(1(2(0(1(0(2(2(2(1(1(1(2(0(2(1(x1))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(x1))))))))))))))))))))))))))))) 1(0(2(1(2(2(1(0(0(1(1(1(0(0(2(1(1(0(2(0(2(1(0(2(0(0(2(1(2(x1))))))))))))))))))))))))))))) -> 1(1(1(1(0(0(1(0(1(1(0(1(1(2(1(1(2(0(1(2(1(0(0(1(2(1(2(2(2(2(x1)))))))))))))))))))))))))))))) 2(0(0(0(1(2(0(0(1(2(2(2(0(2(1(0(2(0(0(1(1(0(0(2(2(0(2(1(2(x1))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(x1)))))))))))))))))))))))))))))) 0(1(2(2(2(1(1(0(1(2(0(2(1(1(1(2(2(1(2(0(2(2(0(2(2(2(0(0(2(0(x1)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(1(2(2(0(2(2(1(1(1(1(2(1(2(0(2(2(0(2(2(0(0(0(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: FULL ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: TRS: Rules: 0(0(1(0(0(x1))))) -> 0(1(0(1(1(1(1(x1))))))) 1(2(2(0(1(2(x1)))))) -> 1(1(1(1(1(0(1(1(0(x1))))))))) 2(0(2(0(1(0(x1)))))) -> 1(1(0(1(1(1(1(0(x1)))))))) 2(0(2(2(1(2(x1)))))) -> 1(1(0(0(1(1(2(x1))))))) 1(0(1(1(2(1(2(x1))))))) -> 0(1(1(1(1(1(2(2(x1)))))))) 1(1(2(1(2(1(2(x1))))))) -> 1(0(2(1(1(1(1(1(x1)))))))) 2(0(2(0(0(0(0(x1))))))) -> 0(1(1(1(1(2(1(0(x1)))))))) 0(0(0(1(2(2(0(0(x1)))))))) -> 0(1(1(1(1(0(0(2(2(x1))))))))) 0(0(1(2(2(0(1(0(2(x1))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(x1)))))))))))) 0(1(0(2(2(1(0(1(0(0(x1)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(x1))))))))))) 1(1(0(2(2(2(0(2(2(2(x1)))))))))) -> 1(0(0(2(0(1(1(1(0(1(1(x1))))))))))) 0(0(2(1(1(1(0(1(1(2(1(x1))))))))))) -> 0(1(1(1(1(1(1(1(0(1(0(0(0(x1))))))))))))) 2(0(1(1(2(1(0(2(0(0(1(x1))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(x1)))))))))))) 1(1(2(2(2(0(1(0(2(2(1(2(x1)))))))))))) -> 1(1(0(1(1(0(0(0(1(2(0(2(1(x1))))))))))))) 2(2(2(0(0(1(2(1(1(2(2(2(x1)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(x1))))))))))))) 0(1(1(1(0(1(2(2(1(0(0(0(0(x1))))))))))))) -> 0(1(1(1(2(1(2(0(1(1(1(1(1(1(x1)))))))))))))) 1(0(2(2(0(2(1(0(2(1(2(1(2(x1))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(x1)))))))))))))))))) 2(1(0(1(0(0(0(2(0(0(2(1(2(x1))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(x1))))))))))))))) 2(2(0(0(0(0(0(2(2(1(0(2(2(x1))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(x1)))))))))))))) 0(0(1(1(2(0(1(0(2(0(2(1(1(0(x1)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(x1)))))))))))))))) 0(2(2(0(2(1(2(0(2(0(0(2(2(1(x1)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(x1)))))))))))))))) 0(2(2(1(1(2(0(1(1(2(1(0(0(2(x1)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(x1)))))))))))))))) 1(0(1(0(1(0(1(0(2(1(2(2(2(0(x1)))))))))))))) -> 1(0(2(2(0(0(1(1(1(2(0(2(1(0(x1)))))))))))))) 2(0(1(2(0(1(0(0(0(2(0(1(0(2(x1)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(x1))))))))))))))) 2(2(0(0(2(1(2(1(0(2(0(0(2(2(x1)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(x1))))))))))))))) 0(0(2(1(2(0(2(1(0(0(0(2(2(2(0(x1))))))))))))))) -> 1(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(x1)))))))))))))))) 0(1(0(2(1(1(2(2(2(0(0(2(2(0(0(x1))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(x1))))))))))))))))) 0(1(0(2(2(1(1(0(1(0(2(0(0(0(0(x1))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(x1)))))))))))))))) 0(1(2(1(2(2(1(0(0(2(2(1(2(1(2(x1))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) 1(2(0(2(0(0(0(2(1(0(1(2(0(0(0(x1))))))))))))))) -> 1(1(0(1(1(0(2(2(0(1(2(2(0(0(0(2(x1)))))))))))))))) 2(0(0(2(1(1(2(1(0(1(0(0(2(2(0(x1))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(x1))))))))))))))))) 2(2(2(0(0(1(2(1(0(2(2(1(2(2(1(x1))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(x1)))))))))))))))))))) 0(0(0(0(1(2(0(2(0(1(1(2(2(0(0(2(x1)))))))))))))))) -> 0(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(x1))))))))))))))))) 0(1(0(1(2(0(0(0(1(1(0(2(2(0(2(2(x1)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(x1))))))))))))))))) 2(0(2(2(0(2(2(2(2(1(1(1(1(2(1(2(x1)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(x1)))))))))))))))))) 2(1(1(2(0(1(2(0(2(1(0(0(2(2(2(1(x1)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) 2(2(0(2(1(1(2(2(0(2(2(0(0(0(2(1(x1)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(x1))))))))))))))))) 0(1(0(1(2(2(2(0(0(0(2(0(0(0(2(0(2(x1))))))))))))))))) -> 1(1(0(1(2(1(1(2(2(1(0(2(1(0(1(1(1(0(x1)))))))))))))))))) 0(0(0(0(0(1(1(0(2(2(1(2(0(2(0(0(2(0(x1)))))))))))))))))) -> 0(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(x1)))))))))))))))))))) 0(0(0(2(0(1(2(0(0(1(0(2(0(1(1(2(0(2(x1)))))))))))))))))) -> 0(1(0(2(1(1(2(2(2(2(1(1(1(0(2(0(1(2(1(x1))))))))))))))))))) 1(2(2(2(0(0(0(0(0(1(0(1(2(1(1(0(2(0(x1)))))))))))))))))) -> 2(1(0(1(2(1(1(2(1(1(1(1(0(2(0(1(0(1(1(1(0(x1))))))))))))))))))))) 2(2(0(1(0(2(0(0(1(0(2(0(1(0(2(0(1(0(x1)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(x1))))))))))))))))))))) 2(2(1(2(2(2(0(1(0(0(0(0(0(2(2(2(1(0(x1)))))))))))))))))) -> 1(2(1(0(1(1(2(1(1(0(2(2(1(1(1(1(0(2(0(2(1(x1))))))))))))))))))))) 0(0(1(2(0(1(1(2(1(2(1(1(2(2(0(1(0(2(2(x1))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(x1))))))))))))))))))))) 0(1(0(1(2(0(1(1(1(0(2(1(1(2(1(0(2(2(1(x1))))))))))))))))))) -> 1(1(2(2(1(2(2(1(1(1(2(2(0(1(0(1(0(2(1(1(x1)))))))))))))))))))) 0(1(2(0(2(2(0(0(0(1(2(0(0(1(0(1(0(2(1(x1))))))))))))))))))) -> 0(0(1(2(1(1(1(1(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(x1))))))))))))))))))))))) 1(0(1(2(1(0(1(2(1(2(1(1(2(1(0(2(2(0(2(x1))))))))))))))))))) -> 1(1(1(1(2(0(1(2(0(2(2(2(0(0(2(0(1(2(2(0(x1)))))))))))))))))))) 2(0(2(2(0(2(2(0(0(2(2(1(2(0(1(2(1(0(1(x1))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(2(0(1(1(1(1(1(0(0(2(0(1(1(x1)))))))))))))))))))))) 2(1(2(1(2(1(1(2(1(0(1(0(2(0(1(0(2(2(2(x1))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(x1))))))))))))))))))))) 2(2(0(2(0(1(0(2(2(1(1(0(1(0(1(1(1(0(1(x1))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(x1))))))))))))))))))) 0(2(0(2(2(0(2(1(1(1(0(2(1(2(1(0(0(1(0(2(x1)))))))))))))))))))) -> 2(1(1(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(x1)))))))))))))))))))))) 0(2(2(1(2(2(2(0(1(2(2(2(2(1(1(0(0(0(1(0(x1)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(x1)))))))))))))))))))))))) 1(1(1(2(0(0(0(2(0(1(2(0(0(2(2(2(1(1(0(0(x1)))))))))))))))))))) -> 1(1(0(2(1(2(2(2(2(2(0(2(1(1(1(0(0(0(0(1(1(x1))))))))))))))))))))) 1(1(1(2(0(2(1(1(2(2(0(0(1(2(0(0(0(0(2(0(x1)))))))))))))))))))) -> 1(1(1(1(1(2(0(2(0(2(1(0(0(0(2(1(2(0(1(2(2(x1))))))))))))))))))))) 2(2(2(1(2(2(2(1(2(2(2(1(1(2(0(0(2(1(0(2(x1)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(x1))))))))))))))))))))))))))) 1(1(2(0(0(0(0(1(1(0(0(1(1(0(0(0(0(0(0(2(1(x1))))))))))))))))))))) -> 1(1(0(0(2(0(0(0(2(0(0(0(1(0(0(0(0(1(1(1(1(x1))))))))))))))))))))) 1(1(2(1(1(1(1(0(0(0(2(2(1(1(2(0(1(2(2(0(1(x1))))))))))))))))))))) -> 1(0(2(1(2(1(2(1(0(0(2(2(2(0(1(0(1(1(1(1(1(x1))))))))))))))))))))) 2(1(0(0(2(1(0(1(0(2(2(0(0(2(2(0(0(0(1(0(2(x1))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(x1))))))))))))))))))))))) 2(2(0(2(2(1(2(0(0(2(1(1(2(0(1(2(0(1(0(0(0(x1))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(x1)))))))))))))))))))))) 2(2(1(2(1(1(2(2(0(0(2(0(2(0(0(2(0(1(2(2(0(x1))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(x1))))))))))))))))))))))) 0(1(1(0(2(1(0(1(2(0(0(1(1(2(0(0(2(0(0(2(2(2(x1)))))))))))))))))))))) -> 0(2(2(1(2(2(1(2(1(1(1(1(2(0(1(0(0(1(1(1(0(1(1(x1))))))))))))))))))))))) 0(2(0(0(0(2(0(1(2(0(1(1(1(1(2(0(2(0(0(1(0(2(x1)))))))))))))))))))))) -> 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2(0(0(0(2(0(0(2(2(2(0(0(2(1(0(0(1(0(0(1(2(1(x1)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(x1)))))))))))))))))))))))) 2(0(0(2(1(2(0(2(1(0(2(2(1(2(1(1(2(0(2(0(0(2(x1)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(x1)))))))))))))))))))))))) 2(0(1(2(1(1(0(2(0(2(2(2(2(1(1(2(1(1(1(2(2(1(x1)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(x1))))))))))))))))))))))) 0(0(0(1(0(1(2(2(0(0(2(0(1(0(1(2(0(1(1(2(0(0(0(x1))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(x1))))))))))))))))))))))) 1(0(2(1(2(2(2(1(0(2(1(2(1(2(2(2(1(0(0(0(0(2(2(x1))))))))))))))))))))))) -> 1(1(1(2(2(2(1(2(2(2(1(0(1(0(1(1(1(0(0(1(2(0(0(2(0(2(x1)))))))))))))))))))))))))) 1(1(2(2(2(0(1(0(2(1(2(0(2(1(1(2(0(1(2(0(2(2(0(x1))))))))))))))))))))))) -> 1(0(2(2(0(2(1(1(1(1(1(0(1(1(1(1(0(2(0(2(2(2(1(1(2(x1))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(1(1(0(0(2(2(2(2(0(2(0(0(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(x1)))))))))))))))))))))))) 2(0(2(2(0(1(0(2(0(0(1(2(1(2(0(0(2(0(0(2(2(2(2(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(x1)))))))))))))))))))))))) 0(0(1(1(2(1(1(1(2(2(1(2(2(0(1(1(1(2(1(2(0(2(1(2(x1)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(x1))))))))))))))))))))))))) 0(2(0(0(1(0(2(2(2(2(1(2(2(0(1(0(2(2(1(2(1(2(1(2(x1)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(2(0(1(0(2(0(1(2(0(1(2(2(1(0(2(2(2(1(1(2(0(0(0(x1)))))))))))))))))))))))) -> 0(1(1(1(1(0(0(1(1(1(1(0(1(0(0(2(0(1(1(1(0(1(2(0(1(1(x1)))))))))))))))))))))))))) 2(1(2(1(2(1(0(0(1(2(1(0(2(0(1(1(0(2(1(0(1(0(1(0(x1)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(x1)))))))))))))))))))))))) 0(2(2(1(2(0(0(1(0(2(2(0(0(1(0(0(0(2(2(2(0(2(1(0(0(x1))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(x1)))))))))))))))))))))))))) 1(1(1(0(0(1(2(2(1(0(2(1(2(1(0(2(2(2(1(1(0(0(2(1(2(x1))))))))))))))))))))))))) -> 1(1(2(2(2(1(1(1(1(1(0(0(1(1(2(0(1(2(1(0(1(2(1(1(0(1(x1)))))))))))))))))))))))))) 1(2(0(1(0(2(0(0(0(1(1(2(1(0(0(1(0(1(0(2(0(1(0(2(2(x1))))))))))))))))))))))))) -> 1(1(0(1(0(2(0(0(1(2(1(1(1(1(1(0(0(2(2(1(0(2(2(1(2(2(x1)))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(2(2(1(0(2(2(1(0(2(2(1(1(2(0(0(0(1(x1))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(x1)))))))))))))))))))))))))))) 2(1(2(1(2(0(0(1(0(2(1(2(0(1(2(0(0(2(1(0(2(0(2(2(2(x1))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(x1)))))))))))))))))))))))))) 2(1(2(2(2(2(1(1(0(0(2(1(2(0(0(0(1(1(0(0(1(1(2(0(1(x1))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(x1))))))))))))))))))))))))) 2(2(0(2(2(0(0(1(2(0(1(1(0(1(2(1(0(2(1(0(2(2(1(0(1(x1))))))))))))))))))))))))) -> 1(0(0(1(2(1(1(0(1(0(1(1(1(0(1(2(2(2(1(2(2(2(2(1(2(1(1(1(x1)))))))))))))))))))))))))))) 2(2(2(2(1(1(0(1(0(0(0(2(1(0(2(1(2(0(0(2(0(0(2(2(2(x1))))))))))))))))))))))))) -> 1(0(0(0(2(1(1(1(1(1(1(0(0(1(0(1(2(0(2(1(2(1(1(0(1(2(0(x1))))))))))))))))))))))))))) 0(1(2(1(1(0(2(1(1(2(1(1(2(0(2(0(2(2(2(2(0(0(2(1(1(2(x1)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(x1))))))))))))))))))))))))))) 1(1(2(2(1(1(2(1(0(1(2(1(1(1(0(0(1(1(0(1(1(1(1(2(0(2(x1)))))))))))))))))))))))))) -> 0(1(1(2(1(2(2(2(2(1(1(1(1(1(0(1(0(2(1(0(0(1(1(1(1(1(x1)))))))))))))))))))))))))) 1(2(1(2(1(0(0(2(2(0(2(0(2(2(0(1(1(0(0(1(2(2(0(0(2(2(x1)))))))))))))))))))))))))) -> 1(0(2(0(0(1(1(0(1(2(2(0(1(1(0(0(0(1(1(1(2(2(1(2(2(0(1(2(x1)))))))))))))))))))))))))))) 0(1(2(0(0(1(2(2(1(1(0(1(0(0(2(2(0(2(2(0(0(0(0(1(0(2(0(x1))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(x1)))))))))))))))))))))))))))) 0(1(2(1(0(2(2(2(2(0(0(1(2(1(0(0(0(0(2(0(0(0(2(0(1(0(2(x1))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x1)))))))))))))))))))))))))))) 0(2(0(1(0(2(2(1(1(0(0(0(2(0(2(0(1(0(0(1(2(1(2(2(1(1(0(x1))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(x1)))))))))))))))))))))))))))) 0(2(1(2(1(2(2(0(2(1(0(1(2(1(1(1(2(2(1(2(0(1(1(1(0(0(2(x1))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(x1)))))))))))))))))))))))))))) 1(0(1(0(1(2(2(0(2(0(1(2(0(0(1(0(0(0(2(0(1(0(0(2(0(2(1(x1))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(x1)))))))))))))))))))))))))))) 0(0(2(2(0(2(1(2(2(0(0(0(2(2(0(2(2(2(1(0(1(0(1(2(2(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(x1))))))))))))))))))))))))))))) 0(1(1(1(2(0(0(0(1(2(1(0(0(0(1(1(0(1(2(2(0(2(2(0(1(2(0(1(x1)))))))))))))))))))))))))))) -> 1(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(x1)))))))))))))))))))))))))))) 0(1(2(0(0(2(1(1(2(1(1(2(2(1(0(2(2(2(2(2(2(2(2(1(2(2(0(2(x1)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(2(1(0(1(2(1(2(0(0(1(1(0(0(2(2(0(0(0(1(1(0(1(2(0(0(x1)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(x1))))))))))))))))))))))))))))) 0(2(0(2(2(1(0(2(1(1(1(2(1(1(2(2(1(2(0(1(1(0(2(2(0(0(1(2(x1)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(x1))))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(2(0(2(2(0(2(1(2(2(1(2(1(1(2(1(2(0(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(0(1(1(0(0(0(2(0(2(0(1(1(1(1(1(0(2(0(2(1(0(1(2(2(2(2(0(2(x1)))))))))))))))))))))))))))))) 2(0(0(1(0(2(2(1(0(1(0(2(0(1(0(2(0(2(2(0(2(1(1(2(2(2(2(0(x1)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(x1))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(0(2(1(0(2(1(0(0(2(0(1(2(1(0(2(0(2(x1)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(x1))))))))))))))))))))))))))))) 0(1(1(2(1(1(0(2(0(2(2(0(1(1(0(0(2(1(1(1(2(0(0(2(0(2(0(1(2(x1))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(1(2(2(1(2(0(1(1(1(2(2(0(0(0(2(2(2(1(0(2(0(0(1(2(1(2(x1))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(x1))))))))))))))))))))))))))))) 0(2(0(0(2(1(2(0(2(2(1(1(2(1(1(2(0(1(0(2(2(2(1(1(1(2(0(2(1(x1))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(x1))))))))))))))))))))))))))))) 1(0(2(1(2(2(1(0(0(1(1(1(0(0(2(1(1(0(2(0(2(1(0(2(0(0(2(1(2(x1))))))))))))))))))))))))))))) -> 1(1(1(1(0(0(1(0(1(1(0(1(1(2(1(1(2(0(1(2(1(0(0(1(2(1(2(2(2(2(x1)))))))))))))))))))))))))))))) 2(0(0(0(1(2(0(0(1(2(2(2(0(2(1(0(2(0(0(1(1(0(0(2(2(0(2(1(2(x1))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(x1)))))))))))))))))))))))))))))) 0(1(2(2(2(1(1(0(1(2(0(2(1(1(1(2(2(1(2(0(2(2(0(2(2(2(0(0(2(0(x1)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(1(2(2(0(2(2(1(1(1(1(2(1(2(0(2(2(0(2(2(0(0(0(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 :: 0:1:2:encArg:encode_0:encode_1:encode_2 -> 0:1:2:encArg:encode_0:encode_1:encode_2 1 :: 0:1:2:encArg:encode_0:encode_1:encode_2 -> 0:1:2:encArg:encode_0:encode_1:encode_2 2 :: 0:1:2:encArg:encode_0:encode_1:encode_2 -> 0:1:2:encArg:encode_0:encode_1:encode_2 encArg :: cons_0:cons_1:cons_2 -> 0:1:2: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 -> 0:1:2:encArg:encode_0:encode_1:encode_2 encode_1 :: cons_0:cons_1:cons_2 -> 0:1:2:encArg:encode_0:encode_1:encode_2 encode_2 :: cons_0:cons_1:cons_2 -> 0:1:2:encArg:encode_0:encode_1:encode_2 hole_0:1:2:encArg:encode_0:encode_1:encode_21_3 :: 0:1:2: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, 1, 2, encArg They will be analysed ascendingly in the following order: 0 = 1 0 = 2 0 < encArg 1 = 2 1 < encArg 2 < encArg ---------------------------------------- (12) Obligation: TRS: Rules: 0(0(1(0(0(x1))))) -> 0(1(0(1(1(1(1(x1))))))) 1(2(2(0(1(2(x1)))))) -> 1(1(1(1(1(0(1(1(0(x1))))))))) 2(0(2(0(1(0(x1)))))) -> 1(1(0(1(1(1(1(0(x1)))))))) 2(0(2(2(1(2(x1)))))) -> 1(1(0(0(1(1(2(x1))))))) 1(0(1(1(2(1(2(x1))))))) -> 0(1(1(1(1(1(2(2(x1)))))))) 1(1(2(1(2(1(2(x1))))))) -> 1(0(2(1(1(1(1(1(x1)))))))) 2(0(2(0(0(0(0(x1))))))) -> 0(1(1(1(1(2(1(0(x1)))))))) 0(0(0(1(2(2(0(0(x1)))))))) -> 0(1(1(1(1(0(0(2(2(x1))))))))) 0(0(1(2(2(0(1(0(2(x1))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(x1)))))))))))) 0(1(0(2(2(1(0(1(0(0(x1)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(x1))))))))))) 1(1(0(2(2(2(0(2(2(2(x1)))))))))) -> 1(0(0(2(0(1(1(1(0(1(1(x1))))))))))) 0(0(2(1(1(1(0(1(1(2(1(x1))))))))))) -> 0(1(1(1(1(1(1(1(0(1(0(0(0(x1))))))))))))) 2(0(1(1(2(1(0(2(0(0(1(x1))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(x1)))))))))))) 1(1(2(2(2(0(1(0(2(2(1(2(x1)))))))))))) -> 1(1(0(1(1(0(0(0(1(2(0(2(1(x1))))))))))))) 2(2(2(0(0(1(2(1(1(2(2(2(x1)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(x1))))))))))))) 0(1(1(1(0(1(2(2(1(0(0(0(0(x1))))))))))))) -> 0(1(1(1(2(1(2(0(1(1(1(1(1(1(x1)))))))))))))) 1(0(2(2(0(2(1(0(2(1(2(1(2(x1))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(x1)))))))))))))))))) 2(1(0(1(0(0(0(2(0(0(2(1(2(x1))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(x1))))))))))))))) 2(2(0(0(0(0(0(2(2(1(0(2(2(x1))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(x1)))))))))))))) 0(0(1(1(2(0(1(0(2(0(2(1(1(0(x1)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(x1)))))))))))))))) 0(2(2(0(2(1(2(0(2(0(0(2(2(1(x1)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(x1)))))))))))))))) 0(2(2(1(1(2(0(1(1(2(1(0(0(2(x1)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(x1)))))))))))))))) 1(0(1(0(1(0(1(0(2(1(2(2(2(0(x1)))))))))))))) -> 1(0(2(2(0(0(1(1(1(2(0(2(1(0(x1)))))))))))))) 2(0(1(2(0(1(0(0(0(2(0(1(0(2(x1)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(x1))))))))))))))) 2(2(0(0(2(1(2(1(0(2(0(0(2(2(x1)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(x1))))))))))))))) 0(0(2(1(2(0(2(1(0(0(0(2(2(2(0(x1))))))))))))))) -> 1(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(x1)))))))))))))))) 0(1(0(2(1(1(2(2(2(0(0(2(2(0(0(x1))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(x1))))))))))))))))) 0(1(0(2(2(1(1(0(1(0(2(0(0(0(0(x1))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(x1)))))))))))))))) 0(1(2(1(2(2(1(0(0(2(2(1(2(1(2(x1))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) 1(2(0(2(0(0(0(2(1(0(1(2(0(0(0(x1))))))))))))))) -> 1(1(0(1(1(0(2(2(0(1(2(2(0(0(0(2(x1)))))))))))))))) 2(0(0(2(1(1(2(1(0(1(0(0(2(2(0(x1))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(x1))))))))))))))))) 2(2(2(0(0(1(2(1(0(2(2(1(2(2(1(x1))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(x1)))))))))))))))))))) 0(0(0(0(1(2(0(2(0(1(1(2(2(0(0(2(x1)))))))))))))))) -> 0(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(x1))))))))))))))))) 0(1(0(1(2(0(0(0(1(1(0(2(2(0(2(2(x1)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(x1))))))))))))))))) 2(0(2(2(0(2(2(2(2(1(1(1(1(2(1(2(x1)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(x1)))))))))))))))))) 2(1(1(2(0(1(2(0(2(1(0(0(2(2(2(1(x1)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) 2(2(0(2(1(1(2(2(0(2(2(0(0(0(2(1(x1)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(x1))))))))))))))))) 0(1(0(1(2(2(2(0(0(0(2(0(0(0(2(0(2(x1))))))))))))))))) -> 1(1(0(1(2(1(1(2(2(1(0(2(1(0(1(1(1(0(x1)))))))))))))))))) 0(0(0(0(0(1(1(0(2(2(1(2(0(2(0(0(2(0(x1)))))))))))))))))) -> 0(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(x1)))))))))))))))))))) 0(0(0(2(0(1(2(0(0(1(0(2(0(1(1(2(0(2(x1)))))))))))))))))) -> 0(1(0(2(1(1(2(2(2(2(1(1(1(0(2(0(1(2(1(x1))))))))))))))))))) 1(2(2(2(0(0(0(0(0(1(0(1(2(1(1(0(2(0(x1)))))))))))))))))) -> 2(1(0(1(2(1(1(2(1(1(1(1(0(2(0(1(0(1(1(1(0(x1))))))))))))))))))))) 2(2(0(1(0(2(0(0(1(0(2(0(1(0(2(0(1(0(x1)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(x1))))))))))))))))))))) 2(2(1(2(2(2(0(1(0(0(0(0(0(2(2(2(1(0(x1)))))))))))))))))) -> 1(2(1(0(1(1(2(1(1(0(2(2(1(1(1(1(0(2(0(2(1(x1))))))))))))))))))))) 0(0(1(2(0(1(1(2(1(2(1(1(2(2(0(1(0(2(2(x1))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(x1))))))))))))))))))))) 0(1(0(1(2(0(1(1(1(0(2(1(1(2(1(0(2(2(1(x1))))))))))))))))))) -> 1(1(2(2(1(2(2(1(1(1(2(2(0(1(0(1(0(2(1(1(x1)))))))))))))))))))) 0(1(2(0(2(2(0(0(0(1(2(0(0(1(0(1(0(2(1(x1))))))))))))))))))) -> 0(0(1(2(1(1(1(1(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(x1))))))))))))))))))))))) 1(0(1(2(1(0(1(2(1(2(1(1(2(1(0(2(2(0(2(x1))))))))))))))))))) -> 1(1(1(1(2(0(1(2(0(2(2(2(0(0(2(0(1(2(2(0(x1)))))))))))))))))))) 2(0(2(2(0(2(2(0(0(2(2(1(2(0(1(2(1(0(1(x1))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(2(0(1(1(1(1(1(0(0(2(0(1(1(x1)))))))))))))))))))))) 2(1(2(1(2(1(1(2(1(0(1(0(2(0(1(0(2(2(2(x1))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(x1))))))))))))))))))))) 2(2(0(2(0(1(0(2(2(1(1(0(1(0(1(1(1(0(1(x1))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(x1))))))))))))))))))) 0(2(0(2(2(0(2(1(1(1(0(2(1(2(1(0(0(1(0(2(x1)))))))))))))))))))) -> 2(1(1(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(x1)))))))))))))))))))))) 0(2(2(1(2(2(2(0(1(2(2(2(2(1(1(0(0(0(1(0(x1)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(x1)))))))))))))))))))))))) 1(1(1(2(0(0(0(2(0(1(2(0(0(2(2(2(1(1(0(0(x1)))))))))))))))))))) -> 1(1(0(2(1(2(2(2(2(2(0(2(1(1(1(0(0(0(0(1(1(x1))))))))))))))))))))) 1(1(1(2(0(2(1(1(2(2(0(0(1(2(0(0(0(0(2(0(x1)))))))))))))))))))) -> 1(1(1(1(1(2(0(2(0(2(1(0(0(0(2(1(2(0(1(2(2(x1))))))))))))))))))))) 2(2(2(1(2(2(2(1(2(2(2(1(1(2(0(0(2(1(0(2(x1)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(x1))))))))))))))))))))))))))) 1(1(2(0(0(0(0(1(1(0(0(1(1(0(0(0(0(0(0(2(1(x1))))))))))))))))))))) -> 1(1(0(0(2(0(0(0(2(0(0(0(1(0(0(0(0(1(1(1(1(x1))))))))))))))))))))) 1(1(2(1(1(1(1(0(0(0(2(2(1(1(2(0(1(2(2(0(1(x1))))))))))))))))))))) -> 1(0(2(1(2(1(2(1(0(0(2(2(2(0(1(0(1(1(1(1(1(x1))))))))))))))))))))) 2(1(0(0(2(1(0(1(0(2(2(0(0(2(2(0(0(0(1(0(2(x1))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(x1))))))))))))))))))))))) 2(2(0(2(2(1(2(0(0(2(1(1(2(0(1(2(0(1(0(0(0(x1))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(x1)))))))))))))))))))))) 2(2(1(2(1(1(2(2(0(0(2(0(2(0(0(2(0(1(2(2(0(x1))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(x1))))))))))))))))))))))) 0(1(1(0(2(1(0(1(2(0(0(1(1(2(0(0(2(0(0(2(2(2(x1)))))))))))))))))))))) -> 0(2(2(1(2(2(1(2(1(1(1(1(2(0(1(0(0(1(1(1(0(1(1(x1))))))))))))))))))))))) 0(2(0(0(0(2(0(1(2(0(1(1(1(1(2(0(2(0(0(1(0(2(x1)))))))))))))))))))))) -> 0(2(2(1(1(0(0(2(2(1(1(0(1(1(1(2(0(1(2(1(0(1(1(x1))))))))))))))))))))))) 0(2(0(0(2(2(0(0(2(0(2(1(0(1(2(1(1(2(0(2(1(2(x1)))))))))))))))))))))) -> 2(0(0(2(1(2(1(0(1(2(2(1(2(2(2(1(1(1(1(0(2(0(1(x1))))))))))))))))))))))) 1(1(2(0(2(2(0(2(2(1(0(0(0(0(0(2(2(0(2(2(2(2(x1)))))))))))))))))))))) -> 2(1(1(1(0(1(1(1(1(2(2(1(1(2(2(0(0(0(1(2(1(0(0(x1))))))))))))))))))))))) 1(2(0(1(0(2(1(0(0(0(0(2(1(0(2(0(0(2(1(1(2(1(x1)))))))))))))))))))))) -> 1(0(0(2(2(1(2(1(1(0(1(1(1(0(1(0(1(1(1(2(1(0(2(2(1(x1))))))))))))))))))))))))) 1(2(0(2(0(1(2(1(0(0(2(2(1(0(0(0(2(1(1(2(1(2(x1)))))))))))))))))))))) -> 1(1(1(2(2(2(1(0(1(1(0(2(0(1(0(1(2(0(0(0(1(1(1(0(x1)))))))))))))))))))))))) 1(2(1(0(1(0(2(2(2(1(0(0(2(0(1(1(0(2(2(2(0(0(x1)))))))))))))))))))))) -> 1(0(1(1(1(0(2(1(2(0(0(0(0(2(1(2(2(0(2(2(2(0(x1)))))))))))))))))))))) 1(2(2(2(2(2(2(1(1(0(1(0(2(2(2(1(1(2(1(2(1(1(x1)))))))))))))))))))))) -> 0(2(0(2(0(0(0(1(2(0(2(1(2(0(2(1(1(0(0(0(1(1(1(1(x1)))))))))))))))))))))))) 2(0(0(0(2(0(0(2(2(2(0(0(2(1(0(0(1(0(0(1(2(1(x1)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(x1)))))))))))))))))))))))) 2(0(0(2(1(2(0(2(1(0(2(2(1(2(1(1(2(0(2(0(0(2(x1)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(x1)))))))))))))))))))))))) 2(0(1(2(1(1(0(2(0(2(2(2(2(1(1(2(1(1(1(2(2(1(x1)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(x1))))))))))))))))))))))) 0(0(0(1(0(1(2(2(0(0(2(0(1(0(1(2(0(1(1(2(0(0(0(x1))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(x1))))))))))))))))))))))) 1(0(2(1(2(2(2(1(0(2(1(2(1(2(2(2(1(0(0(0(0(2(2(x1))))))))))))))))))))))) -> 1(1(1(2(2(2(1(2(2(2(1(0(1(0(1(1(1(0(0(1(2(0(0(2(0(2(x1)))))))))))))))))))))))))) 1(1(2(2(2(0(1(0(2(1(2(0(2(1(1(2(0(1(2(0(2(2(0(x1))))))))))))))))))))))) -> 1(0(2(2(0(2(1(1(1(1(1(0(1(1(1(1(0(2(0(2(2(2(1(1(2(x1))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(1(1(0(0(2(2(2(2(0(2(0(0(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(x1)))))))))))))))))))))))) 2(0(2(2(0(1(0(2(0(0(1(2(1(2(0(0(2(0(0(2(2(2(2(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(x1)))))))))))))))))))))))) 0(0(1(1(2(1(1(1(2(2(1(2(2(0(1(1(1(2(1(2(0(2(1(2(x1)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(x1))))))))))))))))))))))))) 0(2(0(0(1(0(2(2(2(2(1(2(2(0(1(0(2(2(1(2(1(2(1(2(x1)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(2(0(1(0(2(0(1(2(0(1(2(2(1(0(2(2(2(1(1(2(0(0(0(x1)))))))))))))))))))))))) -> 0(1(1(1(1(0(0(1(1(1(1(0(1(0(0(2(0(1(1(1(0(1(2(0(1(1(x1)))))))))))))))))))))))))) 2(1(2(1(2(1(0(0(1(2(1(0(2(0(1(1(0(2(1(0(1(0(1(0(x1)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(x1)))))))))))))))))))))))) 0(2(2(1(2(0(0(1(0(2(2(0(0(1(0(0(0(2(2(2(0(2(1(0(0(x1))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(x1)))))))))))))))))))))))))) 1(1(1(0(0(1(2(2(1(0(2(1(2(1(0(2(2(2(1(1(0(0(2(1(2(x1))))))))))))))))))))))))) -> 1(1(2(2(2(1(1(1(1(1(0(0(1(1(2(0(1(2(1(0(1(2(1(1(0(1(x1)))))))))))))))))))))))))) 1(2(0(1(0(2(0(0(0(1(1(2(1(0(0(1(0(1(0(2(0(1(0(2(2(x1))))))))))))))))))))))))) -> 1(1(0(1(0(2(0(0(1(2(1(1(1(1(1(0(0(2(2(1(0(2(2(1(2(2(x1)))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(2(2(1(0(2(2(1(0(2(2(1(1(2(0(0(0(1(x1))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(x1)))))))))))))))))))))))))))) 2(1(2(1(2(0(0(1(0(2(1(2(0(1(2(0(0(2(1(0(2(0(2(2(2(x1))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(x1)))))))))))))))))))))))))) 2(1(2(2(2(2(1(1(0(0(2(1(2(0(0(0(1(1(0(0(1(1(2(0(1(x1))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(x1))))))))))))))))))))))))) 2(2(0(2(2(0(0(1(2(0(1(1(0(1(2(1(0(2(1(0(2(2(1(0(1(x1))))))))))))))))))))))))) -> 1(0(0(1(2(1(1(0(1(0(1(1(1(0(1(2(2(2(1(2(2(2(2(1(2(1(1(1(x1)))))))))))))))))))))))))))) 2(2(2(2(1(1(0(1(0(0(0(2(1(0(2(1(2(0(0(2(0(0(2(2(2(x1))))))))))))))))))))))))) -> 1(0(0(0(2(1(1(1(1(1(1(0(0(1(0(1(2(0(2(1(2(1(1(0(1(2(0(x1))))))))))))))))))))))))))) 0(1(2(1(1(0(2(1(1(2(1(1(2(0(2(0(2(2(2(2(0(0(2(1(1(2(x1)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(x1))))))))))))))))))))))))))) 1(1(2(2(1(1(2(1(0(1(2(1(1(1(0(0(1(1(0(1(1(1(1(2(0(2(x1)))))))))))))))))))))))))) -> 0(1(1(2(1(2(2(2(2(1(1(1(1(1(0(1(0(2(1(0(0(1(1(1(1(1(x1)))))))))))))))))))))))))) 1(2(1(2(1(0(0(2(2(0(2(0(2(2(0(1(1(0(0(1(2(2(0(0(2(2(x1)))))))))))))))))))))))))) -> 1(0(2(0(0(1(1(0(1(2(2(0(1(1(0(0(0(1(1(1(2(2(1(2(2(0(1(2(x1)))))))))))))))))))))))))))) 0(1(2(0(0(1(2(2(1(1(0(1(0(0(2(2(0(2(2(0(0(0(0(1(0(2(0(x1))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(x1)))))))))))))))))))))))))))) 0(1(2(1(0(2(2(2(2(0(0(1(2(1(0(0(0(0(2(0(0(0(2(0(1(0(2(x1))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x1)))))))))))))))))))))))))))) 0(2(0(1(0(2(2(1(1(0(0(0(2(0(2(0(1(0(0(1(2(1(2(2(1(1(0(x1))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(x1)))))))))))))))))))))))))))) 0(2(1(2(1(2(2(0(2(1(0(1(2(1(1(1(2(2(1(2(0(1(1(1(0(0(2(x1))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(x1)))))))))))))))))))))))))))) 1(0(1(0(1(2(2(0(2(0(1(2(0(0(1(0(0(0(2(0(1(0(0(2(0(2(1(x1))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(x1)))))))))))))))))))))))))))) 0(0(2(2(0(2(1(2(2(0(0(0(2(2(0(2(2(2(1(0(1(0(1(2(2(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(x1))))))))))))))))))))))))))))) 0(1(1(1(2(0(0(0(1(2(1(0(0(0(1(1(0(1(2(2(0(2(2(0(1(2(0(1(x1)))))))))))))))))))))))))))) -> 1(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(x1)))))))))))))))))))))))))))) 0(1(2(0(0(2(1(1(2(1(1(2(2(1(0(2(2(2(2(2(2(2(2(1(2(2(0(2(x1)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(2(1(0(1(2(1(2(0(0(1(1(0(0(2(2(0(0(0(1(1(0(1(2(0(0(x1)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(x1))))))))))))))))))))))))))))) 0(2(0(2(2(1(0(2(1(1(1(2(1(1(2(2(1(2(0(1(1(0(2(2(0(0(1(2(x1)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(x1))))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(2(0(2(2(0(2(1(2(2(1(2(1(1(2(1(2(0(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(0(1(1(0(0(0(2(0(2(0(1(1(1(1(1(0(2(0(2(1(0(1(2(2(2(2(0(2(x1)))))))))))))))))))))))))))))) 2(0(0(1(0(2(2(1(0(1(0(2(0(1(0(2(0(2(2(0(2(1(1(2(2(2(2(0(x1)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(x1))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(0(2(1(0(2(1(0(0(2(0(1(2(1(0(2(0(2(x1)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(x1))))))))))))))))))))))))))))) 0(1(1(2(1(1(0(2(0(2(2(0(1(1(0(0(2(1(1(1(2(0(0(2(0(2(0(1(2(x1))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(1(2(2(1(2(0(1(1(1(2(2(0(0(0(2(2(2(1(0(2(0(0(1(2(1(2(x1))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(x1))))))))))))))))))))))))))))) 0(2(0(0(2(1(2(0(2(2(1(1(2(1(1(2(0(1(0(2(2(2(1(1(1(2(0(2(1(x1))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(x1))))))))))))))))))))))))))))) 1(0(2(1(2(2(1(0(0(1(1(1(0(0(2(1(1(0(2(0(2(1(0(2(0(0(2(1(2(x1))))))))))))))))))))))))))))) -> 1(1(1(1(0(0(1(0(1(1(0(1(1(2(1(1(2(0(1(2(1(0(0(1(2(1(2(2(2(2(x1)))))))))))))))))))))))))))))) 2(0(0(0(1(2(0(0(1(2(2(2(0(2(1(0(2(0(0(1(1(0(0(2(2(0(2(1(2(x1))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(x1)))))))))))))))))))))))))))))) 0(1(2(2(2(1(1(0(1(2(0(2(1(1(1(2(2(1(2(0(2(2(0(2(2(2(0(0(2(0(x1)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(1(2(2(0(2(2(1(1(1(1(2(1(2(0(2(2(0(2(2(0(0(0(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 :: 0:1:2:encArg:encode_0:encode_1:encode_2 -> 0:1:2:encArg:encode_0:encode_1:encode_2 1 :: 0:1:2:encArg:encode_0:encode_1:encode_2 -> 0:1:2:encArg:encode_0:encode_1:encode_2 2 :: 0:1:2:encArg:encode_0:encode_1:encode_2 -> 0:1:2:encArg:encode_0:encode_1:encode_2 encArg :: cons_0:cons_1:cons_2 -> 0:1:2: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 -> 0:1:2:encArg:encode_0:encode_1:encode_2 encode_1 :: cons_0:cons_1:cons_2 -> 0:1:2:encArg:encode_0:encode_1:encode_2 encode_2 :: cons_0:cons_1:cons_2 -> 0:1:2:encArg:encode_0:encode_1:encode_2 hole_0:1:2:encArg:encode_0:encode_1:encode_21_3 :: 0:1:2: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: 1, 0, 2, encArg They will be analysed ascendingly in the following order: 0 = 1 0 = 2 0 < encArg 1 = 2 1 < encArg 2 < encArg ---------------------------------------- (13) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (14) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(0(1(0(0(x1))))) -> 0(1(0(1(1(1(1(x1))))))) 1(2(2(0(1(2(x1)))))) -> 1(1(1(1(1(0(1(1(0(x1))))))))) 2(0(2(0(1(0(x1)))))) -> 1(1(0(1(1(1(1(0(x1)))))))) 2(0(2(2(1(2(x1)))))) -> 1(1(0(0(1(1(2(x1))))))) 1(0(1(1(2(1(2(x1))))))) -> 0(1(1(1(1(1(2(2(x1)))))))) 1(1(2(1(2(1(2(x1))))))) -> 1(0(2(1(1(1(1(1(x1)))))))) 2(0(2(0(0(0(0(x1))))))) -> 0(1(1(1(1(2(1(0(x1)))))))) 0(0(0(1(2(2(0(0(x1)))))))) -> 0(1(1(1(1(0(0(2(2(x1))))))))) 0(0(1(2(2(0(1(0(2(x1))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(x1)))))))))))) 0(1(0(2(2(1(0(1(0(0(x1)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(x1))))))))))) 1(1(0(2(2(2(0(2(2(2(x1)))))))))) -> 1(0(0(2(0(1(1(1(0(1(1(x1))))))))))) 0(0(2(1(1(1(0(1(1(2(1(x1))))))))))) -> 0(1(1(1(1(1(1(1(0(1(0(0(0(x1))))))))))))) 2(0(1(1(2(1(0(2(0(0(1(x1))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(x1)))))))))))) 1(1(2(2(2(0(1(0(2(2(1(2(x1)))))))))))) -> 1(1(0(1(1(0(0(0(1(2(0(2(1(x1))))))))))))) 2(2(2(0(0(1(2(1(1(2(2(2(x1)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(x1))))))))))))) 0(1(1(1(0(1(2(2(1(0(0(0(0(x1))))))))))))) -> 0(1(1(1(2(1(2(0(1(1(1(1(1(1(x1)))))))))))))) 1(0(2(2(0(2(1(0(2(1(2(1(2(x1))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(x1)))))))))))))))))) 2(1(0(1(0(0(0(2(0(0(2(1(2(x1))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(x1))))))))))))))) 2(2(0(0(0(0(0(2(2(1(0(2(2(x1))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(x1)))))))))))))) 0(0(1(1(2(0(1(0(2(0(2(1(1(0(x1)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(x1)))))))))))))))) 0(2(2(0(2(1(2(0(2(0(0(2(2(1(x1)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(x1)))))))))))))))) 0(2(2(1(1(2(0(1(1(2(1(0(0(2(x1)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(x1)))))))))))))))) 1(0(1(0(1(0(1(0(2(1(2(2(2(0(x1)))))))))))))) -> 1(0(2(2(0(0(1(1(1(2(0(2(1(0(x1)))))))))))))) 2(0(1(2(0(1(0(0(0(2(0(1(0(2(x1)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(x1))))))))))))))) 2(2(0(0(2(1(2(1(0(2(0(0(2(2(x1)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(x1))))))))))))))) 0(0(2(1(2(0(2(1(0(0(0(2(2(2(0(x1))))))))))))))) -> 1(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(x1)))))))))))))))) 0(1(0(2(1(1(2(2(2(0(0(2(2(0(0(x1))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(x1))))))))))))))))) 0(1(0(2(2(1(1(0(1(0(2(0(0(0(0(x1))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(x1)))))))))))))))) 0(1(2(1(2(2(1(0(0(2(2(1(2(1(2(x1))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) 1(2(0(2(0(0(0(2(1(0(1(2(0(0(0(x1))))))))))))))) -> 1(1(0(1(1(0(2(2(0(1(2(2(0(0(0(2(x1)))))))))))))))) 2(0(0(2(1(1(2(1(0(1(0(0(2(2(0(x1))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(x1))))))))))))))))) 2(2(2(0(0(1(2(1(0(2(2(1(2(2(1(x1))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(x1)))))))))))))))))))) 0(0(0(0(1(2(0(2(0(1(1(2(2(0(0(2(x1)))))))))))))))) -> 0(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(x1))))))))))))))))) 0(1(0(1(2(0(0(0(1(1(0(2(2(0(2(2(x1)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(x1))))))))))))))))) 2(0(2(2(0(2(2(2(2(1(1(1(1(2(1(2(x1)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(x1)))))))))))))))))) 2(1(1(2(0(1(2(0(2(1(0(0(2(2(2(1(x1)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) 2(2(0(2(1(1(2(2(0(2(2(0(0(0(2(1(x1)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(x1))))))))))))))))) 0(1(0(1(2(2(2(0(0(0(2(0(0(0(2(0(2(x1))))))))))))))))) -> 1(1(0(1(2(1(1(2(2(1(0(2(1(0(1(1(1(0(x1)))))))))))))))))) 0(0(0(0(0(1(1(0(2(2(1(2(0(2(0(0(2(0(x1)))))))))))))))))) -> 0(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(x1)))))))))))))))))))) 0(0(0(2(0(1(2(0(0(1(0(2(0(1(1(2(0(2(x1)))))))))))))))))) -> 0(1(0(2(1(1(2(2(2(2(1(1(1(0(2(0(1(2(1(x1))))))))))))))))))) 1(2(2(2(0(0(0(0(0(1(0(1(2(1(1(0(2(0(x1)))))))))))))))))) -> 2(1(0(1(2(1(1(2(1(1(1(1(0(2(0(1(0(1(1(1(0(x1))))))))))))))))))))) 2(2(0(1(0(2(0(0(1(0(2(0(1(0(2(0(1(0(x1)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(x1))))))))))))))))))))) 2(2(1(2(2(2(0(1(0(0(0(0(0(2(2(2(1(0(x1)))))))))))))))))) -> 1(2(1(0(1(1(2(1(1(0(2(2(1(1(1(1(0(2(0(2(1(x1))))))))))))))))))))) 0(0(1(2(0(1(1(2(1(2(1(1(2(2(0(1(0(2(2(x1))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(x1))))))))))))))))))))) 0(1(0(1(2(0(1(1(1(0(2(1(1(2(1(0(2(2(1(x1))))))))))))))))))) -> 1(1(2(2(1(2(2(1(1(1(2(2(0(1(0(1(0(2(1(1(x1)))))))))))))))))))) 0(1(2(0(2(2(0(0(0(1(2(0(0(1(0(1(0(2(1(x1))))))))))))))))))) -> 0(0(1(2(1(1(1(1(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(x1))))))))))))))))))))))) 1(0(1(2(1(0(1(2(1(2(1(1(2(1(0(2(2(0(2(x1))))))))))))))))))) -> 1(1(1(1(2(0(1(2(0(2(2(2(0(0(2(0(1(2(2(0(x1)))))))))))))))))))) 2(0(2(2(0(2(2(0(0(2(2(1(2(0(1(2(1(0(1(x1))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(2(0(1(1(1(1(1(0(0(2(0(1(1(x1)))))))))))))))))))))) 2(1(2(1(2(1(1(2(1(0(1(0(2(0(1(0(2(2(2(x1))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(x1))))))))))))))))))))) 2(2(0(2(0(1(0(2(2(1(1(0(1(0(1(1(1(0(1(x1))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(x1))))))))))))))))))) 0(2(0(2(2(0(2(1(1(1(0(2(1(2(1(0(0(1(0(2(x1)))))))))))))))))))) -> 2(1(1(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(x1)))))))))))))))))))))) 0(2(2(1(2(2(2(0(1(2(2(2(2(1(1(0(0(0(1(0(x1)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(x1)))))))))))))))))))))))) 1(1(1(2(0(0(0(2(0(1(2(0(0(2(2(2(1(1(0(0(x1)))))))))))))))))))) -> 1(1(0(2(1(2(2(2(2(2(0(2(1(1(1(0(0(0(0(1(1(x1))))))))))))))))))))) 1(1(1(2(0(2(1(1(2(2(0(0(1(2(0(0(0(0(2(0(x1)))))))))))))))))))) -> 1(1(1(1(1(2(0(2(0(2(1(0(0(0(2(1(2(0(1(2(2(x1))))))))))))))))))))) 2(2(2(1(2(2(2(1(2(2(2(1(1(2(0(0(2(1(0(2(x1)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(x1))))))))))))))))))))))))))) 1(1(2(0(0(0(0(1(1(0(0(1(1(0(0(0(0(0(0(2(1(x1))))))))))))))))))))) -> 1(1(0(0(2(0(0(0(2(0(0(0(1(0(0(0(0(1(1(1(1(x1))))))))))))))))))))) 1(1(2(1(1(1(1(0(0(0(2(2(1(1(2(0(1(2(2(0(1(x1))))))))))))))))))))) -> 1(0(2(1(2(1(2(1(0(0(2(2(2(0(1(0(1(1(1(1(1(x1))))))))))))))))))))) 2(1(0(0(2(1(0(1(0(2(2(0(0(2(2(0(0(0(1(0(2(x1))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(x1))))))))))))))))))))))) 2(2(0(2(2(1(2(0(0(2(1(1(2(0(1(2(0(1(0(0(0(x1))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(x1)))))))))))))))))))))) 2(2(1(2(1(1(2(2(0(0(2(0(2(0(0(2(0(1(2(2(0(x1))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(x1))))))))))))))))))))))) 0(1(1(0(2(1(0(1(2(0(0(1(1(2(0(0(2(0(0(2(2(2(x1)))))))))))))))))))))) -> 0(2(2(1(2(2(1(2(1(1(1(1(2(0(1(0(0(1(1(1(0(1(1(x1))))))))))))))))))))))) 0(2(0(0(0(2(0(1(2(0(1(1(1(1(2(0(2(0(0(1(0(2(x1)))))))))))))))))))))) -> 0(2(2(1(1(0(0(2(2(1(1(0(1(1(1(2(0(1(2(1(0(1(1(x1))))))))))))))))))))))) 0(2(0(0(2(2(0(0(2(0(2(1(0(1(2(1(1(2(0(2(1(2(x1)))))))))))))))))))))) -> 2(0(0(2(1(2(1(0(1(2(2(1(2(2(2(1(1(1(1(0(2(0(1(x1))))))))))))))))))))))) 1(1(2(0(2(2(0(2(2(1(0(0(0(0(0(2(2(0(2(2(2(2(x1)))))))))))))))))))))) -> 2(1(1(1(0(1(1(1(1(2(2(1(1(2(2(0(0(0(1(2(1(0(0(x1))))))))))))))))))))))) 1(2(0(1(0(2(1(0(0(0(0(2(1(0(2(0(0(2(1(1(2(1(x1)))))))))))))))))))))) -> 1(0(0(2(2(1(2(1(1(0(1(1(1(0(1(0(1(1(1(2(1(0(2(2(1(x1))))))))))))))))))))))))) 1(2(0(2(0(1(2(1(0(0(2(2(1(0(0(0(2(1(1(2(1(2(x1)))))))))))))))))))))) -> 1(1(1(2(2(2(1(0(1(1(0(2(0(1(0(1(2(0(0(0(1(1(1(0(x1)))))))))))))))))))))))) 1(2(1(0(1(0(2(2(2(1(0(0(2(0(1(1(0(2(2(2(0(0(x1)))))))))))))))))))))) -> 1(0(1(1(1(0(2(1(2(0(0(0(0(2(1(2(2(0(2(2(2(0(x1)))))))))))))))))))))) 1(2(2(2(2(2(2(1(1(0(1(0(2(2(2(1(1(2(1(2(1(1(x1)))))))))))))))))))))) -> 0(2(0(2(0(0(0(1(2(0(2(1(2(0(2(1(1(0(0(0(1(1(1(1(x1)))))))))))))))))))))))) 2(0(0(0(2(0(0(2(2(2(0(0(2(1(0(0(1(0(0(1(2(1(x1)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(x1)))))))))))))))))))))))) 2(0(0(2(1(2(0(2(1(0(2(2(1(2(1(1(2(0(2(0(0(2(x1)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(x1)))))))))))))))))))))))) 2(0(1(2(1(1(0(2(0(2(2(2(2(1(1(2(1(1(1(2(2(1(x1)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(x1))))))))))))))))))))))) 0(0(0(1(0(1(2(2(0(0(2(0(1(0(1(2(0(1(1(2(0(0(0(x1))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(x1))))))))))))))))))))))) 1(0(2(1(2(2(2(1(0(2(1(2(1(2(2(2(1(0(0(0(0(2(2(x1))))))))))))))))))))))) -> 1(1(1(2(2(2(1(2(2(2(1(0(1(0(1(1(1(0(0(1(2(0(0(2(0(2(x1)))))))))))))))))))))))))) 1(1(2(2(2(0(1(0(2(1(2(0(2(1(1(2(0(1(2(0(2(2(0(x1))))))))))))))))))))))) -> 1(0(2(2(0(2(1(1(1(1(1(0(1(1(1(1(0(2(0(2(2(2(1(1(2(x1))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(1(1(0(0(2(2(2(2(0(2(0(0(0(1(2(x1))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(x1)))))))))))))))))))))))) 2(0(2(2(0(1(0(2(0(0(1(2(1(2(0(0(2(0(0(2(2(2(2(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(x1)))))))))))))))))))))))) 0(0(1(1(2(1(1(1(2(2(1(2(2(0(1(1(1(2(1(2(0(2(1(2(x1)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(x1))))))))))))))))))))))))) 0(2(0(0(1(0(2(2(2(2(1(2(2(0(1(0(2(2(1(2(1(2(1(2(x1)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(2(0(1(0(2(0(1(2(0(1(2(2(1(0(2(2(2(1(1(2(0(0(0(x1)))))))))))))))))))))))) -> 0(1(1(1(1(0(0(1(1(1(1(0(1(0(0(2(0(1(1(1(0(1(2(0(1(1(x1)))))))))))))))))))))))))) 2(1(2(1(2(1(0(0(1(2(1(0(2(0(1(1(0(2(1(0(1(0(1(0(x1)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(x1)))))))))))))))))))))))) 0(2(2(1(2(0(0(1(0(2(2(0(0(1(0(0(0(2(2(2(0(2(1(0(0(x1))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(x1)))))))))))))))))))))))))) 1(1(1(0(0(1(2(2(1(0(2(1(2(1(0(2(2(2(1(1(0(0(2(1(2(x1))))))))))))))))))))))))) -> 1(1(2(2(2(1(1(1(1(1(0(0(1(1(2(0(1(2(1(0(1(2(1(1(0(1(x1)))))))))))))))))))))))))) 1(2(0(1(0(2(0(0(0(1(1(2(1(0(0(1(0(1(0(2(0(1(0(2(2(x1))))))))))))))))))))))))) -> 1(1(0(1(0(2(0(0(1(2(1(1(1(1(1(0(0(2(2(1(0(2(2(1(2(2(x1)))))))))))))))))))))))))) 2(0(2(0(2(2(1(0(2(2(1(0(2(2(1(0(2(2(1(1(2(0(0(0(1(x1))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(x1)))))))))))))))))))))))))))) 2(1(2(1(2(0(0(1(0(2(1(2(0(1(2(0(0(2(1(0(2(0(2(2(2(x1))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(x1)))))))))))))))))))))))))) 2(1(2(2(2(2(1(1(0(0(2(1(2(0(0(0(1(1(0(0(1(1(2(0(1(x1))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(x1))))))))))))))))))))))))) 2(2(0(2(2(0(0(1(2(0(1(1(0(1(2(1(0(2(1(0(2(2(1(0(1(x1))))))))))))))))))))))))) -> 1(0(0(1(2(1(1(0(1(0(1(1(1(0(1(2(2(2(1(2(2(2(2(1(2(1(1(1(x1)))))))))))))))))))))))))))) 2(2(2(2(1(1(0(1(0(0(0(2(1(0(2(1(2(0(0(2(0(0(2(2(2(x1))))))))))))))))))))))))) -> 1(0(0(0(2(1(1(1(1(1(1(0(0(1(0(1(2(0(2(1(2(1(1(0(1(2(0(x1))))))))))))))))))))))))))) 0(1(2(1(1(0(2(1(1(2(1(1(2(0(2(0(2(2(2(2(0(0(2(1(1(2(x1)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(x1))))))))))))))))))))))))))) 1(1(2(2(1(1(2(1(0(1(2(1(1(1(0(0(1(1(0(1(1(1(1(2(0(2(x1)))))))))))))))))))))))))) -> 0(1(1(2(1(2(2(2(2(1(1(1(1(1(0(1(0(2(1(0(0(1(1(1(1(1(x1)))))))))))))))))))))))))) 1(2(1(2(1(0(0(2(2(0(2(0(2(2(0(1(1(0(0(1(2(2(0(0(2(2(x1)))))))))))))))))))))))))) -> 1(0(2(0(0(1(1(0(1(2(2(0(1(1(0(0(0(1(1(1(2(2(1(2(2(0(1(2(x1)))))))))))))))))))))))))))) 0(1(2(0(0(1(2(2(1(1(0(1(0(0(2(2(0(2(2(0(0(0(0(1(0(2(0(x1))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(x1)))))))))))))))))))))))))))) 0(1(2(1(0(2(2(2(2(0(0(1(2(1(0(0(0(0(2(0(0(0(2(0(1(0(2(x1))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x1)))))))))))))))))))))))))))) 0(2(0(1(0(2(2(1(1(0(0(0(2(0(2(0(1(0(0(1(2(1(2(2(1(1(0(x1))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(x1)))))))))))))))))))))))))))) 0(2(1(2(1(2(2(0(2(1(0(1(2(1(1(1(2(2(1(2(0(1(1(1(0(0(2(x1))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(x1)))))))))))))))))))))))))))) 1(0(1(0(1(2(2(0(2(0(1(2(0(0(1(0(0(0(2(0(1(0(0(2(0(2(1(x1))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(x1)))))))))))))))))))))))))))) 0(0(2(2(0(2(1(2(2(0(0(0(2(2(0(2(2(2(1(0(1(0(1(2(2(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(x1))))))))))))))))))))))))))))) 0(1(1(1(2(0(0(0(1(2(1(0(0(0(1(1(0(1(2(2(0(2(2(0(1(2(0(1(x1)))))))))))))))))))))))))))) -> 1(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(x1)))))))))))))))))))))))))))) 0(1(2(0(0(2(1(1(2(1(1(2(2(1(0(2(2(2(2(2(2(2(2(1(2(2(0(2(x1)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(2(1(0(1(2(1(2(0(0(1(1(0(0(2(2(0(0(0(1(1(0(1(2(0(0(x1)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(x1))))))))))))))))))))))))))))) 0(2(0(2(2(1(0(2(1(1(1(2(1(1(2(2(1(2(0(1(1(0(2(2(0(0(1(2(x1)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(x1))))))))))))))))))))))))))))) 1(2(2(1(0(1(2(0(2(0(2(2(0(2(1(2(2(1(2(1(1(2(1(2(0(0(0(0(x1)))))))))))))))))))))))))))) -> 0(2(0(1(1(0(0(0(2(0(2(0(1(1(1(1(1(0(2(0(2(1(0(1(2(2(2(2(0(2(x1)))))))))))))))))))))))))))))) 2(0(0(1(0(2(2(1(0(1(0(2(0(1(0(2(0(2(2(0(2(1(1(2(2(2(2(0(x1)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(x1))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(0(2(1(0(2(1(0(0(2(0(1(2(1(0(2(0(2(x1)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(x1))))))))))))))))))))))))))))) 0(1(1(2(1(1(0(2(0(2(2(0(1(1(0(0(2(1(1(1(2(0(0(2(0(2(0(1(2(x1))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(x1)))))))))))))))))))))))))))))) 0(1(2(1(2(2(1(2(0(1(1(1(2(2(0(0(0(2(2(2(1(0(2(0(0(1(2(1(2(x1))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(x1))))))))))))))))))))))))))))) 0(2(0(0(2(1(2(0(2(2(1(1(2(1(1(2(0(1(0(2(2(2(1(1(1(2(0(2(1(x1))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(x1))))))))))))))))))))))))))))) 1(0(2(1(2(2(1(0(0(1(1(1(0(0(2(1(1(0(2(0(2(1(0(2(0(0(2(1(2(x1))))))))))))))))))))))))))))) -> 1(1(1(1(0(0(1(0(1(1(0(1(1(2(1(1(2(0(1(2(1(0(0(1(2(1(2(2(2(2(x1)))))))))))))))))))))))))))))) 2(0(0(0(1(2(0(0(1(2(2(2(0(2(1(0(2(0(0(1(1(0(0(2(2(0(2(1(2(x1))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(x1)))))))))))))))))))))))))))))) 0(1(2(2(2(1(1(0(1(2(0(2(1(1(1(2(2(1(2(0(2(2(0(2(2(2(0(0(2(0(x1)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(1(2(2(0(2(2(1(1(1(1(2(1(2(0(2(2(0(2(2(0(0(0(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: FULL ---------------------------------------- (15) NonCtorToCtorProof (UPPER BOUND(ID)) transformed non-ctor to ctor-system ---------------------------------------- (16) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x1)))))))))))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(x1))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) 1(c_1(c_2(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_0(c_0(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))) -> 1(1(0(0(2(0(0(0(2(0(0(0(1(0(0(0(0(1(1(1(1(x1))))))))))))))))))))) 1(c_2(c_1(c_2(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(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(x1)))))))))))))))))))))))))) -> 1(0(2(0(0(1(1(0(1(2(2(0(1(1(0(0(0(1(1(1(2(2(1(2(2(0(1(2(x1)))))))))))))))))))))))))))) 2(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))))) -> 1(0(0(1(2(1(1(0(1(0(1(1(1(0(1(2(2(2(1(2(2(2(2(1(2(1(1(1(x1)))))))))))))))))))))))))))) 2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 1(0(0(0(2(1(1(1(1(1(1(0(0(1(0(1(2(0(2(1(2(1(1(0(1(2(0(x1))))))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(x1))))))))))))))))))))))))))))) 1(c_1(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(x1)))))))))))))))))))) -> 1(1(0(2(1(2(2(2(2(2(0(2(1(1(1(0(0(0(0(1(1(x1))))))))))))))))))))) 1(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_2(c_1(c_1(x1)))))))))))))))))))))) -> 0(2(0(2(0(0(0(1(2(0(2(1(2(0(2(1(1(0(0(0(1(1(1(1(x1)))))))))))))))))))))))) 1(c_2(c_0(c_2(c_0(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))) -> 1(1(0(1(1(0(2(2(0(1(2(2(0(0(0(2(x1)))))))))))))))) 2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(x1))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(x1))))))))))))))))))))))))))))) 1(c_0(c_1(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_0(c_2(x1))))))))))))))))))) -> 1(1(1(1(2(0(1(2(0(2(2(2(0(0(2(0(1(2(2(0(x1)))))))))))))))))))) 2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(x1)))))))))))))))))) -> 1(2(1(0(1(1(2(1(1(0(2(2(1(1(1(1(0(2(0(2(1(x1))))))))))))))))))))) 1(c_0(c_1(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_2(c_0(x1)))))))))))))) -> 1(0(2(2(0(0(1(1(1(2(0(2(1(0(x1)))))))))))))) 0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(x1))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(x1)))))))))))))))))))))))))))) 2(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(x1)))))))))))))))))))))))))))))) 1(c_0(c_1(c_1(c_2(c_1(c_2(x1))))))) -> 0(1(1(1(1(1(2(2(x1)))))))) 0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(x1))))))))))))))))))))))))))))) 0(c_0(c_1(c_0(c_0(x1))))) -> 0(1(0(1(1(1(1(x1))))))) 0(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(x1))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(x1)))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_1(x1))))))))))))))))))) -> 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2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(c_2(c_2(c_2(x1)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(x1))))))))))))) 1(c_1(c_2(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_2(x1)))))))))))))))))))))))))) -> 0(1(1(2(1(2(2(2(2(1(1(1(1(1(0(1(0(2(1(0(0(1(1(1(1(1(x1)))))))))))))))))))))))))) 2(c_2(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_2(x1)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(x1))))))))))))))) 1(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_0(c_0(c_0(c_2(c_0(x1)))))))))))))))))))) -> 1(1(1(1(1(2(0(2(0(2(1(0(0(0(2(1(2(0(1(2(2(x1))))))))))))))))))))) 0(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_2(x1))))))))))))))))) -> 1(1(0(1(2(1(1(2(2(1(0(2(1(0(1(1(1(0(x1)))))))))))))))))) 0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(x1)))))))))))))))))))))) -> 0(2(2(1(1(0(0(2(2(1(1(0(1(1(1(2(0(1(2(1(0(1(1(x1))))))))))))))))))))))) 0(c_1(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_1(c_1(c_0(c_0(c_2(c_1(c_1(c_1(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_2(x1))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(x1)))))))))))))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_2(x1))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(x1))))))))))))))))))))) 0(c_1(c_2(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_0(c_0(x1)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(x1))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))) -> 0(0(1(2(1(1(1(1(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(x1))))))))))))))))))))))) 0(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_0(x1)))))))))))))))))) -> 0(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(x1)))))))))))))))))))) 2(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(x1))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(x1)))))))))))))))))))))))))))) 1(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_0(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_2(c_0(c_1(x1))))))))))))))))))))) -> 1(0(2(1(2(1(2(1(0(0(2(2(2(0(1(0(1(1(1(1(1(x1))))))))))))))))))))) 0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_2(x1)))))))))))))))))))) -> 2(1(1(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(x1)))))))))))))))))))))) 2(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(x1)))))))))))))))))))))))) 0(c_1(c_1(c_1(c_2(c_0(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(x1)))))))))))))))))))))))))))) -> 1(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(x1)))))))))))))))))))))))))))) 0(c_2(c_2(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_2(c_1(x1)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(x1)))))))))))))))) 1(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_1(c_1(c_1(c_0(c_0(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 1(1(1(1(0(0(1(0(1(1(0(1(1(2(1(1(2(0(1(2(1(0(0(1(2(1(2(2(2(2(x1)))))))))))))))))))))))))))))) 1(c_2(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_0(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 1(1(1(2(2(2(1(0(1(1(0(2(0(1(0(1(2(0(0(0(1(1(1(0(x1)))))))))))))))))))))))) 1(c_2(c_2(c_0(c_1(c_2(x1)))))) -> 1(1(1(1(1(0(1(1(0(x1))))))))) 0(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_2(x1)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(x1)))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))) -> 0(1(1(1(1(0(0(1(1(1(1(0(1(0(0(2(0(1(1(1(0(1(2(0(1(1(x1)))))))))))))))))))))))))) 2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(x1)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(x1))))))))))))))))) 2(c_0(c_2(c_0(c_0(c_0(c_0(x1))))))) -> 0(1(1(1(1(2(1(0(x1)))))))) 2(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(x1)))))))))))))))))))))))) 0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_0(x1))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(x1)))))))))))))))) 2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(x1)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(x1))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(x1))))))))))))))))) 2(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(x1))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(x1))))))))))))))))))) 1(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_0(c_0(x1)))))))))))))))))))))) -> 1(0(1(1(1(0(2(1(2(0(0(0(0(2(1(2(2(0(2(2(2(0(x1)))))))))))))))))))))) 1(c_0(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1(1(1(2(2(2(1(2(2(2(1(0(1(0(1(1(1(0(0(1(2(0(0(2(0(2(x1)))))))))))))))))))))))))) 0(c_1(c_0(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(x1)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(x1))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(x1)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(x1)))))))))))))))))))))))) 2(c_0(c_2(c_0(c_1(c_0(x1)))))) -> 1(1(0(1(1(1(1(0(x1)))))))) 1(c_0(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(x1))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(x1)))))))))))))))))) 1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(x1)))))))))))))))))))))))))))) 2(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(x1))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(x1)))))))))))) 0(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 2(0(0(2(1(2(1(0(1(2(2(1(2(2(2(1(1(1(1(0(2(0(1(x1))))))))))))))))))))))) 1(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))))))))) -> 1(1(0(1(0(2(0(0(1(2(1(1(1(1(1(0(0(2(2(1(0(2(2(1(2(2(x1)))))))))))))))))))))))))) 1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1(0(2(2(0(2(1(1(1(1(1(0(1(1(1(1(0(2(0(2(2(2(1(1(2(x1))))))))))))))))))))))))) 0(c_0(c_2(c_1(c_1(c_1(c_0(c_1(c_1(c_2(c_1(x1))))))))))) -> 0(1(1(1(1(1(1(1(0(1(0(0(0(x1))))))))))))) 0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(x1)))))))))))))))))) -> 0(1(0(2(1(1(2(2(2(2(1(1(1(0(2(0(1(2(1(x1))))))))))))))))))) 2(c_0(c_2(c_2(c_1(c_2(x1)))))) -> 1(1(0(0(1(1(2(x1))))))) 1(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(x1)))))))))))))))))) -> 2(1(0(1(2(1(1(2(1(1(1(1(0(2(0(1(0(1(1(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)) 0(x0) -> c_0(x0) 1(x0) -> c_1(x0) 2(x0) -> c_2(x0) Rewrite Strategy: FULL ---------------------------------------- (17) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. As the TRS is a non-duplicating overlay system, we have rc = irc. ---------------------------------------- (18) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x1)))))))))))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(x1))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) 1(c_1(c_2(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_0(c_0(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))) -> 1(1(0(0(2(0(0(0(2(0(0(0(1(0(0(0(0(1(1(1(1(x1))))))))))))))))))))) 1(c_2(c_1(c_2(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(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(x1)))))))))))))))))))))))))) -> 1(0(2(0(0(1(1(0(1(2(2(0(1(1(0(0(0(1(1(1(2(2(1(2(2(0(1(2(x1)))))))))))))))))))))))))))) 2(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))))) -> 1(0(0(1(2(1(1(0(1(0(1(1(1(0(1(2(2(2(1(2(2(2(2(1(2(1(1(1(x1)))))))))))))))))))))))))))) 2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 1(0(0(0(2(1(1(1(1(1(1(0(0(1(0(1(2(0(2(1(2(1(1(0(1(2(0(x1))))))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(x1))))))))))))))))))))))))))))) 1(c_1(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(x1)))))))))))))))))))) -> 1(1(0(2(1(2(2(2(2(2(0(2(1(1(1(0(0(0(0(1(1(x1))))))))))))))))))))) 1(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_2(c_1(c_1(x1)))))))))))))))))))))) -> 0(2(0(2(0(0(0(1(2(0(2(1(2(0(2(1(1(0(0(0(1(1(1(1(x1)))))))))))))))))))))))) 1(c_2(c_0(c_2(c_0(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))) -> 1(1(0(1(1(0(2(2(0(1(2(2(0(0(0(2(x1)))))))))))))))) 2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(x1))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(x1))))))))))))))))))))))))))))) 1(c_0(c_1(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_0(c_2(x1))))))))))))))))))) -> 1(1(1(1(2(0(1(2(0(2(2(2(0(0(2(0(1(2(2(0(x1)))))))))))))))))))) 2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(x1)))))))))))))))))) -> 1(2(1(0(1(1(2(1(1(0(2(2(1(1(1(1(0(2(0(2(1(x1))))))))))))))))))))) 1(c_0(c_1(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_2(c_0(x1)))))))))))))) -> 1(0(2(2(0(0(1(1(1(2(0(2(1(0(x1)))))))))))))) 0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(x1))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(x1)))))))))))))))))))))))))))) 2(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(x1)))))))))))))))))))))))))))))) 1(c_0(c_1(c_1(c_2(c_1(c_2(x1))))))) -> 0(1(1(1(1(1(2(2(x1)))))))) 0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(x1))))))))))))))))))))))))))))) 0(c_0(c_1(c_0(c_0(x1))))) -> 0(1(0(1(1(1(1(x1))))))) 0(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(x1))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(x1)))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_1(x1))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(2(0(1(1(1(1(1(0(0(2(0(1(1(x1)))))))))))))))))))))) 1(c_1(c_1(c_0(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))) -> 1(1(2(2(2(1(1(1(1(1(0(0(1(1(2(0(1(2(1(0(1(2(1(1(0(1(x1)))))))))))))))))))))))))) 2(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(x1)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(x1))))))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(x1)))))))))))))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(x1))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(x1)))))))))))))))))))))))))))) 0(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(x1)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(x1)))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(x1))))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(x1)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(x1)))))))))))))))) 2(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(x1))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(x1))))))))))))))) 0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(x1))))))))))))))))))))) 2(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(x1))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(x1))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(x1))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(x1)))))))))))))) 0(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(x1))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(x1)))))))))))) 1(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0(2(0(1(1(0(0(0(2(0(2(0(1(1(1(1(1(0(2(0(2(1(0(1(2(2(2(2(0(2(x1)))))))))))))))))))))))))))))) 2(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(x1))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(x1)))))))))))))))))))))) 0(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(x1))))))))))))))))))))))) 0(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(x1)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(x1))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_0(x1)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(x1))))))))))) 2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(x1))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(x1))))))))))))))))))))))))) 0(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_2(x1)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(x1))))))))))))))))))))))))))) 0(c_2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(x1))))))))))))))))))))))))))))) 0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_1(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_2(x1)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(x1))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(x1)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(x1)))))))))))))))))) 2(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(x1))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(x1))))))))))))))))))))))) 0(c_1(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(x1))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(x1))))))))))))))))) 1(c_1(c_0(c_2(c_2(c_2(c_0(c_2(c_2(c_2(x1)))))))))) -> 1(0(0(2(0(1(1(1(0(1(1(x1))))))))))) 1(c_1(c_2(c_0(c_2(c_2(c_0(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(x1)))))))))))))))))))))) -> 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0(c_2(c_2(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_2(c_1(x1)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(x1)))))))))))))))) 1(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_1(c_1(c_1(c_0(c_0(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 1(1(1(1(0(0(1(0(1(1(0(1(1(2(1(1(2(0(1(2(1(0(0(1(2(1(2(2(2(2(x1)))))))))))))))))))))))))))))) 1(c_2(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_0(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 1(1(1(2(2(2(1(0(1(1(0(2(0(1(0(1(2(0(0(0(1(1(1(0(x1)))))))))))))))))))))))) 1(c_2(c_2(c_0(c_1(c_2(x1)))))) -> 1(1(1(1(1(0(1(1(0(x1))))))))) 0(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_2(x1)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(x1)))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))) -> 0(1(1(1(1(0(0(1(1(1(1(0(1(0(0(2(0(1(1(1(0(1(2(0(1(1(x1)))))))))))))))))))))))))) 2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(x1)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(x1))))))))))))))))) 2(c_0(c_2(c_0(c_0(c_0(c_0(x1))))))) -> 0(1(1(1(1(2(1(0(x1)))))))) 2(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(x1)))))))))))))))))))))))) 0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_0(x1))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(x1)))))))))))))))) 2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(x1)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(x1))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(x1))))))))))))))))) 2(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(x1))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(x1))))))))))))))))))) 1(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_0(c_0(x1)))))))))))))))))))))) -> 1(0(1(1(1(0(2(1(2(0(0(0(0(2(1(2(2(0(2(2(2(0(x1)))))))))))))))))))))) 1(c_0(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1(1(1(2(2(2(1(2(2(2(1(0(1(0(1(1(1(0(0(1(2(0(0(2(0(2(x1)))))))))))))))))))))))))) 0(c_1(c_0(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(x1)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(x1))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(x1)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(x1)))))))))))))))))))))))) 2(c_0(c_2(c_0(c_1(c_0(x1)))))) -> 1(1(0(1(1(1(1(0(x1)))))))) 1(c_0(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(x1))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(x1)))))))))))))))))) 1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(x1)))))))))))))))))))))))))))) 2(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(x1))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(x1)))))))))))) 0(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 2(0(0(2(1(2(1(0(1(2(2(1(2(2(2(1(1(1(1(0(2(0(1(x1))))))))))))))))))))))) 1(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))))))))) -> 1(1(0(1(0(2(0(0(1(2(1(1(1(1(1(0(0(2(2(1(0(2(2(1(2(2(x1)))))))))))))))))))))))))) 1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1(0(2(2(0(2(1(1(1(1(1(0(1(1(1(1(0(2(0(2(2(2(1(1(2(x1))))))))))))))))))))))))) 0(c_0(c_2(c_1(c_1(c_1(c_0(c_1(c_1(c_2(c_1(x1))))))))))) -> 0(1(1(1(1(1(1(1(0(1(0(0(0(x1))))))))))))) 0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(x1)))))))))))))))))) -> 0(1(0(2(1(1(2(2(2(2(1(1(1(0(2(0(1(2(1(x1))))))))))))))))))) 2(c_0(c_2(c_2(c_1(c_2(x1)))))) -> 1(1(0(0(1(1(2(x1))))))) 1(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(x1)))))))))))))))))) -> 2(1(0(1(2(1(1(2(1(1(1(1(0(2(0(1(0(1(1(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)) 0(x0) -> c_0(x0) 1(x0) -> c_1(x0) 2(x0) -> c_2(x0) Rewrite Strategy: INNERMOST ---------------------------------------- (19) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (20) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x1)))))))))))))))))))))))))))) [1] 0(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(x1))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(x1))))))))))))))))))) [1] 1(c_1(c_2(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_0(c_0(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))) -> 1(1(0(0(2(0(0(0(2(0(0(0(1(0(0(0(0(1(1(1(1(x1))))))))))))))))))))) [1] 1(c_2(c_1(c_2(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(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(x1)))))))))))))))))))))))))) -> 1(0(2(0(0(1(1(0(1(2(2(0(1(1(0(0(0(1(1(1(2(2(1(2(2(0(1(2(x1)))))))))))))))))))))))))))) [1] 2(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))))) -> 1(0(0(1(2(1(1(0(1(0(1(1(1(0(1(2(2(2(1(2(2(2(2(1(2(1(1(1(x1)))))))))))))))))))))))))))) [1] 2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 1(0(0(0(2(1(1(1(1(1(1(0(0(1(0(1(2(0(2(1(2(1(1(0(1(2(0(x1))))))))))))))))))))))))))) [1] 2(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(x1))))))))))))))))))))))))))))) [1] 1(c_1(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(x1)))))))))))))))))))) -> 1(1(0(2(1(2(2(2(2(2(0(2(1(1(1(0(0(0(0(1(1(x1))))))))))))))))))))) [1] 1(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_2(c_1(c_1(x1)))))))))))))))))))))) -> 0(2(0(2(0(0(0(1(2(0(2(1(2(0(2(1(1(0(0(0(1(1(1(1(x1)))))))))))))))))))))))) [1] 1(c_2(c_0(c_2(c_0(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))) -> 1(1(0(1(1(0(2(2(0(1(2(2(0(0(0(2(x1)))))))))))))))) [1] 2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(x1))))))))))))))) [1] 0(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(x1))))))))))))))))))))))))))))) [1] 1(c_0(c_1(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_0(c_2(x1))))))))))))))))))) -> 1(1(1(1(2(0(1(2(0(2(2(2(0(0(2(0(1(2(2(0(x1)))))))))))))))))))) [1] 2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(x1)))))))))))))))))) -> 1(2(1(0(1(1(2(1(1(0(2(2(1(1(1(1(0(2(0(2(1(x1))))))))))))))))))))) [1] 1(c_0(c_1(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_2(c_0(x1)))))))))))))) -> 1(0(2(2(0(0(1(1(1(2(0(2(1(0(x1)))))))))))))) [1] 0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(x1))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(x1)))))))))))))))))))))))))))) [1] 2(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(x1)))))))))))))))))))))))))))))) [1] 1(c_0(c_1(c_1(c_2(c_1(c_2(x1))))))) -> 0(1(1(1(1(1(2(2(x1)))))))) [1] 0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(x1))))))))))))))))))))))))))))) [1] 0(c_0(c_1(c_0(c_0(x1))))) -> 0(1(0(1(1(1(1(x1))))))) [1] 0(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(x1))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(x1)))))))))))))))))))))))))) [1] 2(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_1(x1))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(2(0(1(1(1(1(1(0(0(2(0(1(1(x1)))))))))))))))))))))) [1] 1(c_1(c_1(c_0(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))) -> 1(1(2(2(2(1(1(1(1(1(0(0(1(1(2(0(1(2(1(0(1(2(1(1(0(1(x1)))))))))))))))))))))))))) [1] 2(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(x1)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(x1))))))))))))))))))))))) [1] 2(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(x1)))))))))))))))))))))))))) [1] 0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(x1))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(x1)))))))))))))))))))))))))))) [1] 0(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(x1)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(x1)))))))))))))))))))))))) [1] 0(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(x1))))))))))))))))))))))))) [1] 0(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(x1)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(x1)))))))))))))))) [1] 2(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(x1))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(x1))))))))))))))) [1] 0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(x1))))))))))))))))))))) [1] 2(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(x1))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(x1))))))))))))))))))))))) [1] 2(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(x1))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(x1)))))))))))))) [1] 0(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(x1))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(x1)))))))))))) [1] 1(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0(2(0(1(1(0(0(0(2(0(2(0(1(1(1(1(1(0(2(0(2(1(0(1(2(2(2(2(0(2(x1)))))))))))))))))))))))))))))) [1] 2(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(x1))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(x1)))))))))))))))))))))) [1] 0(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(x1))))))))))))))))))))))) [1] 0(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(x1)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(x1))))))))))))))))))))))))))) [1] 0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_0(x1)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(x1))))))))))) [1] 2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(x1))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(x1))))))))))))))))))))))))) [1] 0(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_2(x1)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(x1))))))))))))))))))))))))))) [1] 0(c_2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(x1))))))))))))))))))))))))))))) [1] 0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_1(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_2(x1)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(x1))))))))))))))))))))))))))))) [1] 0(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(x1)))))))))))))))))))))))))))))) [1] 2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(x1)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(x1)))))))))))))))))) [1] 2(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(x1))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(x1))))))))))))))))))))))) [1] 0(c_1(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(x1))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(x1))))))))))))))))) [1] 1(c_1(c_0(c_2(c_2(c_2(c_0(c_2(c_2(c_2(x1)))))))))) -> 1(0(0(2(0(1(1(1(0(1(1(x1))))))))))) [1] 1(c_1(c_2(c_0(c_2(c_2(c_0(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(x1)))))))))))))))))))))) -> 2(1(1(1(0(1(1(1(1(2(2(1(1(2(2(0(0(0(1(2(1(0(0(x1))))))))))))))))))))))) [1] 0(c_2(c_1(c_2(c_1(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_0(c_2(x1))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(x1)))))))))))))))))))))))))))) [1] 0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_1(x1))))))))))))))))))) -> 1(1(2(2(1(2(2(1(1(1(2(2(0(1(0(1(0(2(1(1(x1)))))))))))))))))))) [1] 2(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_1(c_2(c_1(x1)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(x1)))))))))))))))))))))))) [1] 1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(x1)))))))))))) -> 1(1(0(1(1(0(0(0(1(2(0(2(1(x1))))))))))))) [1] 2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(x1)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(x1))))))))))))))))))))))))))) [1] 0(c_1(c_1(c_0(c_2(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_0(c_0(c_2(c_2(c_2(x1)))))))))))))))))))))) -> 0(2(2(1(2(2(1(2(1(1(1(1(2(0(1(0(0(1(1(1(0(1(1(x1))))))))))))))))))))))) [1] 0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_0(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_0(x1)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(1(2(2(0(2(2(1(1(1(1(2(1(2(0(2(2(0(2(2(0(0(0(1(0(x1)))))))))))))))))))))))))))))) [1] 0(c_0(c_0(c_1(c_2(c_2(c_0(c_0(x1)))))))) -> 0(1(1(1(1(0(0(2(2(x1))))))))) [1] 0(c_1(c_1(c_1(c_0(c_1(c_2(c_2(c_1(c_0(c_0(c_0(c_0(x1))))))))))))) -> 0(1(1(1(2(1(2(0(1(1(1(1(1(1(x1)))))))))))))) [1] 0(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(x1))))))))))))))) -> 1(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(x1)))))))))))))))) [1] 2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_0(x1)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(x1))))))))))))))))))))) [1] 2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_2(x1)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(x1)))))))))))))))))))))))) [1] 1(c_2(c_0(c_1(c_0(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(x1)))))))))))))))))))))) -> 1(0(0(2(2(1(2(1(1(0(1(1(1(0(1(0(1(1(1(2(1(0(2(2(1(x1))))))))))))))))))))))))) [1] 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_2(c_1(x1))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(x1)))))))))))))))))))) [1] 0(c_0(c_0(c_0(c_1(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_2(c_0(c_0(c_2(x1)))))))))))))))) -> 0(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(x1))))))))))))))))) [1] 1(c_1(c_2(c_1(c_2(c_1(c_2(x1))))))) -> 1(0(2(1(1(1(1(1(x1)))))))) [1] 2(c_0(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_2(c_0(x1)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(x1))))))))))))))))))))))))))))) [1] 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(c_2(c_2(c_2(x1)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(x1))))))))))))) [1] 1(c_1(c_2(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_2(x1)))))))))))))))))))))))))) -> 0(1(1(2(1(2(2(2(2(1(1(1(1(1(0(1(0(2(1(0(0(1(1(1(1(1(x1)))))))))))))))))))))))))) [1] 2(c_2(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_2(x1)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(x1))))))))))))))) [1] 1(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_0(c_0(c_0(c_2(c_0(x1)))))))))))))))))))) -> 1(1(1(1(1(2(0(2(0(2(1(0(0(0(2(1(2(0(1(2(2(x1))))))))))))))))))))) [1] 0(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_2(x1))))))))))))))))) -> 1(1(0(1(2(1(1(2(2(1(0(2(1(0(1(1(1(0(x1)))))))))))))))))) [1] 0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(x1)))))))))))))))))))))) -> 0(2(2(1(1(0(0(2(2(1(1(0(1(1(1(2(0(1(2(1(0(1(1(x1))))))))))))))))))))))) [1] 0(c_1(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_1(c_1(c_0(c_0(c_2(c_1(c_1(c_1(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_2(x1))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(x1)))))))))))))))))))))))))))))) [1] 2(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_2(x1))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(x1))))))))))))))))))))) [1] 0(c_1(c_2(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_0(c_0(x1)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(x1))))))))))))))))))))))))))))) [1] 0(c_1(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))) -> 0(0(1(2(1(1(1(1(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(x1))))))))))))))))))))))) [1] 0(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_0(x1)))))))))))))))))) -> 0(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(x1)))))))))))))))))))) [1] 2(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(x1))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(x1)))))))))))))))))))))))))))) [1] 1(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_0(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_2(c_0(c_1(x1))))))))))))))))))))) -> 1(0(2(1(2(1(2(1(0(0(2(2(2(0(1(0(1(1(1(1(1(x1))))))))))))))))))))) [1] 0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_2(x1)))))))))))))))))))) -> 2(1(1(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(x1)))))))))))))))))))))) [1] 2(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(x1)))))))))))))))))))))))) [1] 0(c_1(c_1(c_1(c_2(c_0(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(x1)))))))))))))))))))))))))))) -> 1(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(x1)))))))))))))))))))))))))))) [1] 0(c_2(c_2(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_2(c_1(x1)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(x1)))))))))))))))) [1] 1(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_1(c_1(c_1(c_0(c_0(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 1(1(1(1(0(0(1(0(1(1(0(1(1(2(1(1(2(0(1(2(1(0(0(1(2(1(2(2(2(2(x1)))))))))))))))))))))))))))))) [1] 1(c_2(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_0(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 1(1(1(2(2(2(1(0(1(1(0(2(0(1(0(1(2(0(0(0(1(1(1(0(x1)))))))))))))))))))))))) [1] 1(c_2(c_2(c_0(c_1(c_2(x1)))))) -> 1(1(1(1(1(0(1(1(0(x1))))))))) [1] 0(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_2(x1)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(x1)))))))))))))))) [1] 0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))) -> 0(1(1(1(1(0(0(1(1(1(1(0(1(0(0(2(0(1(1(1(0(1(2(0(1(1(x1)))))))))))))))))))))))))) [1] 2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(x1)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(x1))))))))))))))))) [1] 2(c_0(c_2(c_0(c_0(c_0(c_0(x1))))))) -> 0(1(1(1(1(2(1(0(x1)))))))) [1] 2(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(x1)))))))))))))))))))))))) [1] 0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_0(x1))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(x1)))))))))))))))) [1] 2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(x1)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(x1)))))))))))))))))))) [1] 2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(x1))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(x1))))))))))))))))) [1] 2(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(x1))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(x1))))))))))))))))))) [1] 1(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_0(c_0(x1)))))))))))))))))))))) -> 1(0(1(1(1(0(2(1(2(0(0(0(0(2(1(2(2(0(2(2(2(0(x1)))))))))))))))))))))) [1] 1(c_0(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1(1(1(2(2(2(1(2(2(2(1(0(1(0(1(1(1(0(0(1(2(0(0(2(0(2(x1)))))))))))))))))))))))))) [1] 0(c_1(c_0(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(x1)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(x1))))))))))))))))) [1] 2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(x1)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(x1)))))))))))))))))))))))) [1] 2(c_0(c_2(c_0(c_1(c_0(x1)))))) -> 1(1(0(1(1(1(1(0(x1)))))))) [1] 1(c_0(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(x1))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(x1)))))))))))))))))) [1] 1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(x1)))))))))))))))))))))))))))) [1] 2(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(x1))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(x1)))))))))))) [1] 0(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 2(0(0(2(1(2(1(0(1(2(2(1(2(2(2(1(1(1(1(0(2(0(1(x1))))))))))))))))))))))) [1] 1(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))))))))) -> 1(1(0(1(0(2(0(0(1(2(1(1(1(1(1(0(0(2(2(1(0(2(2(1(2(2(x1)))))))))))))))))))))))))) [1] 1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1(0(2(2(0(2(1(1(1(1(1(0(1(1(1(1(0(2(0(2(2(2(1(1(2(x1))))))))))))))))))))))))) [1] 0(c_0(c_2(c_1(c_1(c_1(c_0(c_1(c_1(c_2(c_1(x1))))))))))) -> 0(1(1(1(1(1(1(1(0(1(0(0(0(x1))))))))))))) [1] 0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(x1)))))))))))))))))) -> 0(1(0(2(1(1(2(2(2(2(1(1(1(0(2(0(1(2(1(x1))))))))))))))))))) [1] 2(c_0(c_2(c_2(c_1(c_2(x1)))))) -> 1(1(0(0(1(1(2(x1))))))) [1] 1(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(x1)))))))))))))))))) -> 2(1(0(1(2(1(1(2(1(1(1(1(0(2(0(1(0(1(1(1(0(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) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) Renamed defined symbols to avoid conflicts with arithmetic symbols: 0 => 0' 1 => 1' 2 => 2' ---------------------------------------- (22) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))))))) -> 1'(2'(1'(2'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(0'(2'(2'(0'(1'(2'(2'(0'(1'(0'(1'(1'(0'(0'(x1)))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(x1))))))))))))))) -> 1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(1'(x1))))))))))))))))))) [1] 1'(c_1(c_2(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_0(c_0(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))) -> 1'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(0'(1'(0'(0'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))) [1] 1'(c_2(c_1(c_2(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(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(x1)))))))))))))))))))))))))) -> 1'(0'(2'(0'(0'(1'(1'(0'(1'(2'(2'(0'(1'(1'(0'(0'(0'(1'(1'(1'(2'(2'(1'(2'(2'(0'(1'(2'(x1)))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))))) -> 1'(0'(0'(1'(2'(1'(1'(0'(1'(0'(1'(1'(1'(0'(1'(2'(2'(2'(1'(2'(2'(2'(2'(1'(2'(1'(1'(1'(x1)))))))))))))))))))))))))))) [1] 2'(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 1'(0'(0'(0'(2'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(2'(0'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0'(2'(2'(2'(0'(0'(0'(1'(0'(1'(1'(2'(2'(0'(0'(0'(1'(2'(2'(2'(2'(0'(2'(2'(1'(2'(2'(1'(2'(x1))))))))))))))))))))))))))))) [1] 1'(c_1(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(x1)))))))))))))))))))) -> 1'(1'(0'(2'(1'(2'(2'(2'(2'(2'(0'(2'(1'(1'(1'(0'(0'(0'(0'(1'(1'(x1))))))))))))))))))))) [1] 1'(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_2(c_1(c_1(x1)))))))))))))))))))))) -> 0'(2'(0'(2'(0'(0'(0'(1'(2'(0'(2'(1'(2'(0'(2'(1'(1'(0'(0'(0'(1'(1'(1'(1'(x1)))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_0(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))) -> 1'(1'(0'(1'(1'(0'(2'(2'(0'(1'(2'(2'(0'(0'(0'(2'(x1)))))))))))))))) [1] 2'(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1)))))))))))))) -> 1'(2'(2'(0'(0'(2'(2'(1'(0'(1'(1'(1'(1'(2'(0'(x1))))))))))))))) [1] 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 0'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(2'(2'(2'(0'(0'(0'(2'(2'(1'(1'(1'(2'(0'(0'(0'(2'(1'(2'(x1))))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_0(c_2(x1))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(1'(2'(0'(2'(2'(2'(0'(0'(2'(0'(1'(2'(2'(0'(x1)))))))))))))))))))) [1] 2'(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(x1)))))))))))))))))) -> 1'(2'(1'(0'(1'(1'(2'(1'(1'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(x1))))))))))))))))))))) [1] 1'(c_0(c_1(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_2(c_0(x1)))))))))))))) -> 1'(0'(2'(2'(0'(0'(1'(1'(1'(2'(0'(2'(1'(0'(x1)))))))))))))) [1] 0'(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(x1))))))))))))))))))))))))))) -> 1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(1'(2'(0'(2'(0'(0'(0'(1'(0'(1'(0'(1'(1'(0'(2'(1'(2'(0'(x1)))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 2'(2'(2'(0'(1'(2'(2'(2'(2'(1'(1'(2'(2'(0'(0'(2'(2'(2'(1'(1'(1'(2'(0'(1'(0'(1'(1'(2'(2'(0'(x1)))))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_1(c_2(c_1(c_2(x1))))))) -> 0'(1'(1'(1'(1'(1'(2'(2'(x1)))))))) [1] 0'(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(1'(0'(0'(1'(2'(1'(2'(2'(1'(1'(1'(2'(0'(2'(1'(2'(2'(1'(1'(x1))))))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_0(c_0(x1))))) -> 0'(1'(0'(1'(1'(1'(1'(x1))))))) [1] 0'(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(x1))))))))))))))))))))))))) -> 1'(0'(1'(2'(2'(0'(0'(0'(1'(2'(0'(0'(1'(0'(1'(1'(1'(0'(0'(1'(1'(2'(1'(0'(0'(1'(x1)))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_1(x1))))))))))))))))))) -> 2'(0'(1'(0'(0'(1'(2'(0'(2'(2'(0'(1'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(x1)))))))))))))))))))))) [1] 1'(c_1(c_1(c_0(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(1'(1'(1'(1'(0'(0'(1'(1'(2'(0'(1'(2'(1'(0'(1'(2'(1'(1'(0'(1'(x1)))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(x1)))))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(2'(1'(0'(0'(2'(2'(1'(1'(0'(2'(2'(1'(2'(1'(1'(1'(0'(x1))))))))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 2'(1'(1'(1'(0'(2'(2'(0'(2'(0'(0'(2'(0'(2'(1'(0'(2'(1'(2'(1'(1'(2'(2'(2'(1'(2'(x1)))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(x1))))))))))))))))))))))))))) -> 2'(2'(1'(1'(0'(2'(1'(1'(1'(2'(1'(2'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(x1)))))))))))))))))))))))))))) [1] 0'(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(x1)))))))))))))))))))) -> 0'(1'(2'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(1'(1'(1'(1'(1'(0'(1'(x1)))))))))))))))))))))))) [1] 0'(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))))) -> 0'(1'(1'(0'(1'(1'(2'(0'(1'(2'(1'(2'(0'(1'(1'(1'(1'(2'(2'(0'(0'(0'(1'(1'(1'(x1))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(x1)))))))))))))) -> 2'(1'(0'(1'(1'(1'(2'(0'(1'(1'(1'(2'(2'(1'(1'(0'(x1)))))))))))))))) [1] 2'(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(x1))))))))))))) -> 1'(1'(1'(1'(0'(2'(2'(0'(1'(2'(1'(1'(1'(0'(1'(x1))))))))))))))) [1] 0'(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))) -> 2'(0'(0'(1'(2'(2'(1'(0'(2'(2'(1'(2'(1'(1'(1'(0'(0'(1'(1'(1'(0'(x1))))))))))))))))))))) [1] 2'(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(x1))))))))))))))))))))) -> 1'(2'(2'(0'(2'(2'(1'(1'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(1'(0'(2'(2'(x1))))))))))))))))))))))) [1] 2'(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(x1))))))))))))) -> 2'(0'(1'(0'(1'(2'(2'(0'(1'(0'(0'(1'(1'(1'(x1)))))))))))))) [1] 0'(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(x1))))))))) -> 2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(2'(x1)))))))))))) [1] 1'(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0'(2'(0'(1'(1'(0'(0'(0'(2'(0'(2'(0'(1'(1'(1'(1'(1'(0'(2'(0'(2'(1'(0'(1'(2'(2'(2'(2'(0'(2'(x1)))))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(x1))))))))))))))))))))) -> 2'(1'(0'(1'(2'(0'(0'(2'(2'(1'(1'(1'(1'(0'(1'(2'(0'(2'(0'(0'(1'(1'(x1)))))))))))))))))))))) [1] 0'(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 0'(1'(0'(1'(0'(0'(2'(2'(0'(0'(2'(1'(1'(0'(0'(2'(0'(2'(0'(1'(1'(0'(0'(x1))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(x1)))))))))))))))))))))))))) -> 1'(1'(2'(2'(0'(1'(0'(1'(1'(2'(1'(0'(2'(1'(1'(2'(2'(1'(2'(1'(1'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_0(x1)))))))))) -> 1'(1'(1'(1'(0'(0'(2'(1'(0'(2'(1'(x1))))))))))) [1] 2'(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(x1))))))))))))))))))))))))) -> 2'(1'(0'(2'(0'(0'(2'(1'(0'(1'(1'(2'(0'(0'(2'(0'(1'(2'(2'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_2(x1)))))))))))))))))))))))) -> 2'(0'(0'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(1'(0'(2'(2'(2'(2'(2'(2'(0'(1'(0'(0'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))))) -> 0'(2'(2'(0'(2'(1'(1'(1'(1'(2'(0'(0'(2'(1'(2'(2'(1'(0'(0'(1'(2'(2'(1'(1'(0'(2'(2'(2'(1'(x1))))))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_1(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_2(x1)))))))))))))))))))))))))))) -> 1'(2'(0'(0'(0'(1'(2'(0'(1'(1'(1'(1'(1'(0'(0'(2'(1'(2'(2'(2'(2'(0'(0'(0'(0'(0'(2'(2'(1'(x1))))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0'(1'(1'(0'(0'(2'(1'(0'(2'(1'(0'(1'(2'(1'(2'(0'(2'(0'(2'(1'(0'(1'(2'(0'(1'(1'(1'(1'(1'(1'(x1)))))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(x1)))))))))))))))) -> 1'(0'(1'(1'(1'(1'(2'(2'(0'(1'(1'(1'(0'(2'(1'(0'(2'(2'(x1)))))))))))))))))) [1] 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1'(0'(1'(1'(1'(0'(2'(1'(2'(0'(0'(0'(0'(2'(1'(2'(2'(0'(2'(2'(2'(0'(x1)))))))))))))))))))))) [1] 1'(c_0(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(2'(2'(2'(1'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(0'(0'(1'(2'(0'(0'(2'(0'(2'(x1)))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(x1)))))))))))))))) -> 1'(2'(1'(1'(0'(1'(1'(0'(0'(1'(0'(0'(0'(1'(1'(1'(0'(x1))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(x1)))))))))))))))))))))))) -> 2'(0'(1'(1'(0'(0'(2'(0'(1'(2'(1'(1'(2'(0'(0'(1'(0'(2'(1'(2'(1'(1'(1'(0'(x1)))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_1(c_0(x1)))))) -> 1'(1'(0'(1'(1'(1'(1'(0'(x1)))))))) [1] 1'(c_0(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(x1))))))))))))) -> 1'(1'(1'(1'(1'(0'(1'(2'(1'(2'(1'(0'(1'(1'(0'(0'(1'(1'(x1)))))))))))))))))) [1] 1'(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))) -> 1'(0'(1'(2'(2'(1'(2'(0'(2'(0'(0'(0'(1'(1'(2'(2'(1'(1'(1'(1'(1'(1'(0'(0'(2'(1'(1'(0'(x1)))))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(x1))))))))))) -> 0'(1'(0'(0'(2'(1'(0'(1'(1'(1'(1'(0'(x1)))))))))))) [1] 0'(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 2'(0'(0'(2'(1'(2'(1'(0'(1'(2'(2'(1'(2'(2'(2'(1'(1'(1'(1'(0'(2'(0'(1'(x1))))))))))))))))))))))) [1] 1'(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))))))))) -> 1'(1'(0'(1'(0'(2'(0'(0'(1'(2'(1'(1'(1'(1'(1'(0'(0'(2'(2'(1'(0'(2'(2'(1'(2'(2'(x1)))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(0'(2'(2'(0'(2'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(2'(2'(1'(1'(2'(x1))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_1(c_1(c_0(c_1(c_1(c_2(c_1(x1))))))))))) -> 0'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(0'(x1))))))))))))) [1] 0'(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(x1)))))))))))))))))) -> 0'(1'(0'(2'(1'(1'(2'(2'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(x1))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_1(c_2(x1)))))) -> 1'(1'(0'(0'(1'(1'(2'(x1))))))) [1] 1'(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(x1)))))))))))))))))) -> 2'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(1'(0'(2'(0'(1'(0'(1'(1'(1'(0'(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 ---------------------------------------- (23) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (24) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))))))) -> 1'(2'(1'(2'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(0'(2'(2'(0'(1'(2'(2'(0'(1'(0'(1'(1'(0'(0'(x1)))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(x1))))))))))))))) -> 1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(1'(x1))))))))))))))))))) [1] 1'(c_1(c_2(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_0(c_0(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))) -> 1'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(0'(1'(0'(0'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))) [1] 1'(c_2(c_1(c_2(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(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(x1)))))))))))))))))))))))))) -> 1'(0'(2'(0'(0'(1'(1'(0'(1'(2'(2'(0'(1'(1'(0'(0'(0'(1'(1'(1'(2'(2'(1'(2'(2'(0'(1'(2'(x1)))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))))) -> 1'(0'(0'(1'(2'(1'(1'(0'(1'(0'(1'(1'(1'(0'(1'(2'(2'(2'(1'(2'(2'(2'(2'(1'(2'(1'(1'(1'(x1)))))))))))))))))))))))))))) [1] 2'(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 1'(0'(0'(0'(2'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(2'(0'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0'(2'(2'(2'(0'(0'(0'(1'(0'(1'(1'(2'(2'(0'(0'(0'(1'(2'(2'(2'(2'(0'(2'(2'(1'(2'(2'(1'(2'(x1))))))))))))))))))))))))))))) [1] 1'(c_1(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(x1)))))))))))))))))))) -> 1'(1'(0'(2'(1'(2'(2'(2'(2'(2'(0'(2'(1'(1'(1'(0'(0'(0'(0'(1'(1'(x1))))))))))))))))))))) [1] 1'(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_2(c_1(c_1(x1)))))))))))))))))))))) -> 0'(2'(0'(2'(0'(0'(0'(1'(2'(0'(2'(1'(2'(0'(2'(1'(1'(0'(0'(0'(1'(1'(1'(1'(x1)))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_0(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))) -> 1'(1'(0'(1'(1'(0'(2'(2'(0'(1'(2'(2'(0'(0'(0'(2'(x1)))))))))))))))) [1] 2'(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1)))))))))))))) -> 1'(2'(2'(0'(0'(2'(2'(1'(0'(1'(1'(1'(1'(2'(0'(x1))))))))))))))) [1] 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 0'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(2'(2'(2'(0'(0'(0'(2'(2'(1'(1'(1'(2'(0'(0'(0'(2'(1'(2'(x1))))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_0(c_2(x1))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(1'(2'(0'(2'(2'(2'(0'(0'(2'(0'(1'(2'(2'(0'(x1)))))))))))))))))))) [1] 2'(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(x1)))))))))))))))))) -> 1'(2'(1'(0'(1'(1'(2'(1'(1'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(x1))))))))))))))))))))) [1] 1'(c_0(c_1(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_2(c_0(x1)))))))))))))) -> 1'(0'(2'(2'(0'(0'(1'(1'(1'(2'(0'(2'(1'(0'(x1)))))))))))))) [1] 0'(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(x1))))))))))))))))))))))))))) -> 1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(1'(2'(0'(2'(0'(0'(0'(1'(0'(1'(0'(1'(1'(0'(2'(1'(2'(0'(x1)))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 2'(2'(2'(0'(1'(2'(2'(2'(2'(1'(1'(2'(2'(0'(0'(2'(2'(2'(1'(1'(1'(2'(0'(1'(0'(1'(1'(2'(2'(0'(x1)))))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_1(c_2(c_1(c_2(x1))))))) -> 0'(1'(1'(1'(1'(1'(2'(2'(x1)))))))) [1] 0'(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(1'(0'(0'(1'(2'(1'(2'(2'(1'(1'(1'(2'(0'(2'(1'(2'(2'(1'(1'(x1))))))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_0(c_0(x1))))) -> 0'(1'(0'(1'(1'(1'(1'(x1))))))) [1] 0'(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(x1))))))))))))))))))))))))) -> 1'(0'(1'(2'(2'(0'(0'(0'(1'(2'(0'(0'(1'(0'(1'(1'(1'(0'(0'(1'(1'(2'(1'(0'(0'(1'(x1)))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_1(x1))))))))))))))))))) -> 2'(0'(1'(0'(0'(1'(2'(0'(2'(2'(0'(1'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(x1)))))))))))))))))))))) [1] 1'(c_1(c_1(c_0(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(1'(1'(1'(1'(0'(0'(1'(1'(2'(0'(1'(2'(1'(0'(1'(2'(1'(1'(0'(1'(x1)))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(x1)))))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(2'(1'(0'(0'(2'(2'(1'(1'(0'(2'(2'(1'(2'(1'(1'(1'(0'(x1))))))))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 2'(1'(1'(1'(0'(2'(2'(0'(2'(0'(0'(2'(0'(2'(1'(0'(2'(1'(2'(1'(1'(2'(2'(2'(1'(2'(x1)))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(x1))))))))))))))))))))))))))) -> 2'(2'(1'(1'(0'(2'(1'(1'(1'(2'(1'(2'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(x1)))))))))))))))))))))))))))) [1] 0'(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(x1)))))))))))))))))))) -> 0'(1'(2'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(1'(1'(1'(1'(1'(0'(1'(x1)))))))))))))))))))))))) [1] 0'(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))))) -> 0'(1'(1'(0'(1'(1'(2'(0'(1'(2'(1'(2'(0'(1'(1'(1'(1'(2'(2'(0'(0'(0'(1'(1'(1'(x1))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(x1)))))))))))))) -> 2'(1'(0'(1'(1'(1'(2'(0'(1'(1'(1'(2'(2'(1'(1'(0'(x1)))))))))))))))) [1] 2'(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(x1))))))))))))) -> 1'(1'(1'(1'(0'(2'(2'(0'(1'(2'(1'(1'(1'(0'(1'(x1))))))))))))))) [1] 0'(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))) -> 2'(0'(0'(1'(2'(2'(1'(0'(2'(2'(1'(2'(1'(1'(1'(0'(0'(1'(1'(1'(0'(x1))))))))))))))))))))) [1] 2'(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(x1))))))))))))))))))))) -> 1'(2'(2'(0'(2'(2'(1'(1'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(1'(0'(2'(2'(x1))))))))))))))))))))))) [1] 2'(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(x1))))))))))))) -> 2'(0'(1'(0'(1'(2'(2'(0'(1'(0'(0'(1'(1'(1'(x1)))))))))))))) [1] 0'(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(x1))))))))) -> 2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(2'(x1)))))))))))) [1] 1'(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0'(2'(0'(1'(1'(0'(0'(0'(2'(0'(2'(0'(1'(1'(1'(1'(1'(0'(2'(0'(2'(1'(0'(1'(2'(2'(2'(2'(0'(2'(x1)))))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(x1))))))))))))))))))))) -> 2'(1'(0'(1'(2'(0'(0'(2'(2'(1'(1'(1'(1'(0'(1'(2'(0'(2'(0'(0'(1'(1'(x1)))))))))))))))))))))) [1] 0'(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 0'(1'(0'(1'(0'(0'(2'(2'(0'(0'(2'(1'(1'(0'(0'(2'(0'(2'(0'(1'(1'(0'(0'(x1))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(x1)))))))))))))))))))))))))) -> 1'(1'(2'(2'(0'(1'(0'(1'(1'(2'(1'(0'(2'(1'(1'(2'(2'(1'(2'(1'(1'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_0(x1)))))))))) -> 1'(1'(1'(1'(0'(0'(2'(1'(0'(2'(1'(x1))))))))))) [1] 2'(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(x1))))))))))))))))))))))))) -> 2'(1'(0'(2'(0'(0'(2'(1'(0'(1'(1'(2'(0'(0'(2'(0'(1'(2'(2'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_2(x1)))))))))))))))))))))))) -> 2'(0'(0'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(1'(0'(2'(2'(2'(2'(2'(2'(0'(1'(0'(0'(0'(x1))))))))))))))))))))))))))) [1] 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2'(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(2'(1'(0'(0'(0'(0'(1'(1'(2'(2'(0'(1'(1'(0'(1'(0'(0'(0'(2'(2'(1'(x1)))))))))))))))))))))))) [1] 0'(c_1(c_1(c_1(c_2(c_0(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(x1)))))))))))))))))))))))))))) -> 1'(0'(0'(0'(0'(0'(0'(2'(1'(2'(1'(2'(0'(2'(0'(2'(0'(1'(1'(1'(1'(0'(1'(1'(2'(2'(0'(1'(x1)))))))))))))))))))))))))))) [1] 0'(c_2(c_2(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_2(c_1(x1)))))))))))))) -> 2'(2'(1'(0'(1'(1'(2'(0'(0'(1'(1'(1'(1'(2'(1'(1'(x1)))))))))))))))) [1] 1'(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_1(c_1(c_1(c_0(c_0(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 1'(1'(1'(1'(0'(0'(1'(0'(1'(1'(0'(1'(1'(2'(1'(1'(2'(0'(1'(2'(1'(0'(0'(1'(2'(1'(2'(2'(2'(2'(x1)))))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_0(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 1'(1'(1'(2'(2'(2'(1'(0'(1'(1'(0'(2'(0'(1'(0'(1'(2'(0'(0'(0'(1'(1'(1'(0'(x1)))))))))))))))))))))))) [1] 1'(c_2(c_2(c_0(c_1(c_2(x1)))))) -> 1'(1'(1'(1'(1'(0'(1'(1'(0'(x1))))))))) [1] 0'(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_2(x1)))))))))))))) -> 2'(2'(1'(1'(1'(1'(0'(1'(0'(2'(2'(1'(2'(0'(2'(1'(x1)))))))))))))))) [1] 0'(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))) -> 0'(1'(1'(1'(1'(0'(0'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(1'(1'(1'(0'(1'(2'(0'(1'(1'(x1)))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(x1)))))))))))))))) -> 1'(0'(0'(2'(1'(2'(1'(1'(2'(2'(1'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_0(c_0(c_0(x1))))))) -> 0'(1'(1'(1'(1'(2'(1'(0'(x1)))))))) [1] 2'(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(2'(1'(0'(1'(1'(2'(1'(0'(0'(2'(2'(2'(0'(1'(0'(1'(1'(0'(2'(0'(x1)))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_0(x1))))))))))))))) -> 1'(2'(1'(0'(0'(0'(1'(2'(1'(1'(1'(2'(2'(1'(1'(1'(x1)))))))))))))))) [1] 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(x1)))))))))))))))) -> 1'(2'(2'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(1'(1'(1'(0'(0'(1'(0'(x1)))))))))))))))))))) [1] 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(x1))))))))))))))) -> 1'(1'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(2'(0'(0'(0'(0'(x1))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(x1))))))))))))))))))) -> 2'(0'(0'(0'(0'(2'(1'(1'(1'(1'(1'(0'(1'(0'(2'(2'(2'(1'(1'(x1))))))))))))))))))) [1] 1'(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_0(c_0(x1)))))))))))))))))))))) -> 1'(0'(1'(1'(1'(0'(2'(1'(2'(0'(0'(0'(0'(2'(1'(2'(2'(0'(2'(2'(2'(0'(x1)))))))))))))))))))))) [1] 1'(c_0(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(2'(2'(2'(1'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(0'(0'(1'(2'(0'(0'(2'(0'(2'(x1)))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(x1)))))))))))))))) -> 1'(2'(1'(1'(0'(1'(1'(0'(0'(1'(0'(0'(0'(1'(1'(1'(0'(x1))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(x1)))))))))))))))))))))))) -> 2'(0'(1'(1'(0'(0'(2'(0'(1'(2'(1'(1'(2'(0'(0'(1'(0'(2'(1'(2'(1'(1'(1'(0'(x1)))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_1(c_0(x1)))))) -> 1'(1'(0'(1'(1'(1'(1'(0'(x1)))))))) [1] 1'(c_0(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(x1))))))))))))) -> 1'(1'(1'(1'(1'(0'(1'(2'(1'(2'(1'(0'(1'(1'(0'(0'(1'(1'(x1)))))))))))))))))) [1] 1'(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))) -> 1'(0'(1'(2'(2'(1'(2'(0'(2'(0'(0'(0'(1'(1'(2'(2'(1'(1'(1'(1'(1'(1'(0'(0'(2'(1'(1'(0'(x1)))))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(x1))))))))))) -> 0'(1'(0'(0'(2'(1'(0'(1'(1'(1'(1'(0'(x1)))))))))))) [1] 0'(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 2'(0'(0'(2'(1'(2'(1'(0'(1'(2'(2'(1'(2'(2'(2'(1'(1'(1'(1'(0'(2'(0'(1'(x1))))))))))))))))))))))) [1] 1'(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))))))))) -> 1'(1'(0'(1'(0'(2'(0'(0'(1'(2'(1'(1'(1'(1'(1'(0'(0'(2'(2'(1'(0'(2'(2'(1'(2'(2'(x1)))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(0'(2'(2'(0'(2'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(2'(2'(1'(1'(2'(x1))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_1(c_1(c_0(c_1(c_1(c_2(c_1(x1))))))))))) -> 0'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(0'(x1))))))))))))) [1] 0'(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(x1)))))))))))))))))) -> 0'(1'(0'(2'(1'(1'(2'(2'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(x1))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_1(c_2(x1)))))) -> 1'(1'(0'(0'(1'(1'(2'(x1))))))) [1] 1'(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(x1)))))))))))))))))) -> 2'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(1'(0'(2'(0'(1'(0'(1'(1'(1'(0'(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_2:c_0:c_1 -> c_2:c_0:c_1 c_1 :: c_2:c_0:c_1 -> c_2:c_0:c_1 c_2 :: c_2:c_0:c_1 -> c_2:c_0:c_1 c_0 :: c_2:c_0:c_1 -> c_2:c_0:c_1 1' :: c_2:c_0:c_1 -> c_2:c_0:c_1 2' :: c_2:c_0:c_1 -> c_2:c_0:c_1 encArg :: cons_0:cons_1:cons_2 -> c_2:c_0:c_1 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_2:c_0:c_1 encode_1 :: cons_0:cons_1:cons_2 -> c_2:c_0:c_1 encode_2 :: cons_0:cons_1:cons_2 -> c_2:c_0:c_1 Rewrite Strategy: INNERMOST ---------------------------------------- (25) 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 ---------------------------------------- (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_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))))))) -> 1'(2'(1'(2'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(0'(2'(2'(0'(1'(2'(2'(0'(1'(0'(1'(1'(0'(0'(x1)))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(x1))))))))))))))) -> 1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(1'(x1))))))))))))))))))) [1] 1'(c_1(c_2(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_0(c_0(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))) -> 1'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(0'(1'(0'(0'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))) [1] 1'(c_2(c_1(c_2(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(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(x1)))))))))))))))))))))))))) -> 1'(0'(2'(0'(0'(1'(1'(0'(1'(2'(2'(0'(1'(1'(0'(0'(0'(1'(1'(1'(2'(2'(1'(2'(2'(0'(1'(2'(x1)))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))))) -> 1'(0'(0'(1'(2'(1'(1'(0'(1'(0'(1'(1'(1'(0'(1'(2'(2'(2'(1'(2'(2'(2'(2'(1'(2'(1'(1'(1'(x1)))))))))))))))))))))))))))) [1] 2'(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 1'(0'(0'(0'(2'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(2'(0'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0'(2'(2'(2'(0'(0'(0'(1'(0'(1'(1'(2'(2'(0'(0'(0'(1'(2'(2'(2'(2'(0'(2'(2'(1'(2'(2'(1'(2'(x1))))))))))))))))))))))))))))) [1] 1'(c_1(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(x1)))))))))))))))))))) -> 1'(1'(0'(2'(1'(2'(2'(2'(2'(2'(0'(2'(1'(1'(1'(0'(0'(0'(0'(1'(1'(x1))))))))))))))))))))) [1] 1'(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_2(c_1(c_1(x1)))))))))))))))))))))) -> 0'(2'(0'(2'(0'(0'(0'(1'(2'(0'(2'(1'(2'(0'(2'(1'(1'(0'(0'(0'(1'(1'(1'(1'(x1)))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_0(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))) -> 1'(1'(0'(1'(1'(0'(2'(2'(0'(1'(2'(2'(0'(0'(0'(2'(x1)))))))))))))))) [1] 2'(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1)))))))))))))) -> 1'(2'(2'(0'(0'(2'(2'(1'(0'(1'(1'(1'(1'(2'(0'(x1))))))))))))))) [1] 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 0'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(2'(2'(2'(0'(0'(0'(2'(2'(1'(1'(1'(2'(0'(0'(0'(2'(1'(2'(x1))))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_0(c_2(x1))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(1'(2'(0'(2'(2'(2'(0'(0'(2'(0'(1'(2'(2'(0'(x1)))))))))))))))))))) [1] 2'(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(x1)))))))))))))))))) -> 1'(2'(1'(0'(1'(1'(2'(1'(1'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(x1))))))))))))))))))))) [1] 1'(c_0(c_1(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_2(c_0(x1)))))))))))))) -> 1'(0'(2'(2'(0'(0'(1'(1'(1'(2'(0'(2'(1'(0'(x1)))))))))))))) [1] 0'(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(x1))))))))))))))))))))))))))) -> 1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(1'(2'(0'(2'(0'(0'(0'(1'(0'(1'(0'(1'(1'(0'(2'(1'(2'(0'(x1)))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 2'(2'(2'(0'(1'(2'(2'(2'(2'(1'(1'(2'(2'(0'(0'(2'(2'(2'(1'(1'(1'(2'(0'(1'(0'(1'(1'(2'(2'(0'(x1)))))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_1(c_2(c_1(c_2(x1))))))) -> 0'(1'(1'(1'(1'(1'(2'(2'(x1)))))))) [1] 0'(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(1'(0'(0'(1'(2'(1'(2'(2'(1'(1'(1'(2'(0'(2'(1'(2'(2'(1'(1'(x1))))))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_0(c_0(x1))))) -> 0'(1'(0'(1'(1'(1'(1'(x1))))))) [1] 0'(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(x1))))))))))))))))))))))))) -> 1'(0'(1'(2'(2'(0'(0'(0'(1'(2'(0'(0'(1'(0'(1'(1'(1'(0'(0'(1'(1'(2'(1'(0'(0'(1'(x1)))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_1(x1))))))))))))))))))) -> 2'(0'(1'(0'(0'(1'(2'(0'(2'(2'(0'(1'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(x1)))))))))))))))))))))) [1] 1'(c_1(c_1(c_0(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))) -> 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0'(2'(1'(2'(1'(0'(0'(1'(2'(2'(1'(1'(1'(1'(2'(2'(2'(2'(0'(0'(1'(2'(1'(2'(x1)))))))))))))))))))))))) [1] 1'(c_2(c_0(c_1(c_0(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(x1)))))))))))))))))))))) -> 1'(0'(0'(2'(2'(1'(2'(1'(1'(0'(1'(1'(1'(0'(1'(0'(1'(1'(1'(2'(1'(0'(2'(2'(1'(x1))))))))))))))))))))))))) [1] 2'(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_2(c_1(x1))))))))))))))) -> 2'(1'(0'(1'(1'(1'(0'(1'(1'(1'(0'(0'(1'(1'(1'(0'(1'(2'(0'(1'(x1)))))))))))))))))))) [1] 0'(c_0(c_0(c_0(c_1(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_2(c_0(c_0(c_2(x1)))))))))))))))) -> 0'(2'(1'(2'(2'(0'(1'(1'(1'(1'(2'(1'(1'(0'(0'(2'(1'(x1))))))))))))))))) [1] 1'(c_1(c_2(c_1(c_2(c_1(c_2(x1))))))) -> 1'(0'(2'(1'(1'(1'(1'(1'(x1)))))))) [1] 2'(c_0(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_2(c_0(x1)))))))))))))))))))))))))))) -> 1'(2'(0'(2'(0'(2'(0'(2'(2'(2'(0'(1'(2'(0'(2'(2'(1'(0'(1'(1'(1'(1'(2'(1'(2'(0'(2'(2'(2'(x1))))))))))))))))))))))))))))) [1] 2'(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(c_2(c_2(c_2(x1)))))))))))) -> 1'(1'(2'(0'(1'(1'(1'(1'(1'(0'(1'(1'(0'(x1))))))))))))) [1] 1'(c_1(c_2(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_2(x1)))))))))))))))))))))))))) -> 0'(1'(1'(2'(1'(2'(2'(2'(2'(1'(1'(1'(1'(1'(0'(1'(0'(2'(1'(0'(0'(1'(1'(1'(1'(1'(x1)))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_2(x1)))))))))))))) -> 0'(0'(1'(1'(1'(1'(2'(0'(1'(0'(1'(0'(2'(1'(2'(x1))))))))))))))) [1] 1'(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_0(c_0(c_0(c_2(c_0(x1)))))))))))))))))))) -> 1'(1'(1'(1'(1'(2'(0'(2'(0'(2'(1'(0'(0'(0'(2'(1'(2'(0'(1'(2'(2'(x1))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_2(x1))))))))))))))))) -> 1'(1'(0'(1'(2'(1'(1'(2'(2'(1'(0'(2'(1'(0'(1'(1'(1'(0'(x1)))))))))))))))))) [1] 0'(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(x1)))))))))))))))))))))) -> 0'(2'(2'(1'(1'(0'(0'(2'(2'(1'(1'(0'(1'(1'(1'(2'(0'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))))))))) [1] 0'(c_1(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_1(c_1(c_0(c_0(c_2(c_1(c_1(c_1(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_2(x1))))))))))))))))))))))))))))) -> 1'(1'(2'(0'(0'(2'(1'(2'(2'(1'(0'(0'(0'(2'(0'(1'(1'(1'(2'(1'(1'(0'(0'(0'(1'(2'(2'(1'(1'(1'(x1)))))))))))))))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_2(x1))))))))))))))))))) -> 1'(2'(1'(1'(1'(1'(0'(0'(0'(1'(1'(2'(2'(2'(2'(2'(0'(1'(2'(2'(2'(x1))))))))))))))))))))) [1] 0'(c_1(c_2(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_0(c_0(x1)))))))))))))))))))))))))))) -> 2'(1'(2'(2'(1'(0'(1'(0'(0'(1'(1'(2'(2'(2'(2'(2'(2'(2'(1'(2'(1'(1'(1'(2'(1'(1'(1'(1'(1'(x1))))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(x1))))))))))))))))))) -> 0'(0'(1'(2'(1'(1'(1'(1'(1'(2'(1'(0'(1'(2'(0'(1'(0'(2'(0'(1'(0'(1'(1'(x1))))))))))))))))))))))) [1] 0'(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_0(x1)))))))))))))))))) -> 0'(1'(1'(1'(2'(1'(2'(1'(1'(0'(0'(1'(1'(0'(0'(0'(1'(0'(2'(2'(x1)))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(x1))))))))))))))))))))))))) -> 2'(0'(0'(0'(1'(0'(1'(1'(1'(2'(1'(1'(1'(1'(2'(1'(2'(0'(0'(2'(2'(2'(1'(2'(2'(1'(1'(0'(x1)))))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_0(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_2(c_0(c_1(x1))))))))))))))))))))) -> 1'(0'(2'(1'(2'(1'(2'(1'(0'(0'(2'(2'(2'(0'(1'(0'(1'(1'(1'(1'(1'(x1))))))))))))))))))))) [1] 0'(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_2(x1)))))))))))))))))))) -> 2'(1'(1'(1'(2'(1'(0'(1'(1'(1'(2'(2'(1'(1'(1'(0'(1'(0'(1'(1'(2'(0'(x1)))))))))))))))))))))) [1] 2'(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(x1))))))))))))))))))))))) -> 0'(1'(1'(2'(1'(0'(0'(0'(0'(1'(1'(2'(2'(0'(1'(1'(0'(1'(0'(0'(0'(2'(2'(1'(x1)))))))))))))))))))))))) [1] 0'(c_1(c_1(c_1(c_2(c_0(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(x1)))))))))))))))))))))))))))) -> 1'(0'(0'(0'(0'(0'(0'(2'(1'(2'(1'(2'(0'(2'(0'(2'(0'(1'(1'(1'(1'(0'(1'(1'(2'(2'(0'(1'(x1)))))))))))))))))))))))))))) [1] 0'(c_2(c_2(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_2(c_1(x1)))))))))))))) -> 2'(2'(1'(0'(1'(1'(2'(0'(0'(1'(1'(1'(1'(2'(1'(1'(x1)))))))))))))))) [1] 1'(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_1(c_1(c_1(c_0(c_0(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 1'(1'(1'(1'(0'(0'(1'(0'(1'(1'(0'(1'(1'(2'(1'(1'(2'(0'(1'(2'(1'(0'(0'(1'(2'(1'(2'(2'(2'(2'(x1)))))))))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_0(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 1'(1'(1'(2'(2'(2'(1'(0'(1'(1'(0'(2'(0'(1'(0'(1'(2'(0'(0'(0'(1'(1'(1'(0'(x1)))))))))))))))))))))))) [1] 1'(c_2(c_2(c_0(c_1(c_2(x1)))))) -> 1'(1'(1'(1'(1'(0'(1'(1'(0'(x1))))))))) [1] 0'(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_2(x1)))))))))))))) -> 2'(2'(1'(1'(1'(1'(0'(1'(0'(2'(2'(1'(2'(0'(2'(1'(x1)))))))))))))))) [1] 0'(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))) -> 0'(1'(1'(1'(1'(0'(0'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(1'(1'(1'(0'(1'(2'(0'(1'(1'(x1)))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(x1)))))))))))))))) -> 1'(0'(0'(2'(1'(2'(1'(1'(2'(2'(1'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_0(c_0(c_0(x1))))))) -> 0'(1'(1'(1'(1'(2'(1'(0'(x1)))))))) [1] 2'(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(x1))))))))))))))))))))))) -> 1'(1'(0'(1'(2'(1'(0'(1'(1'(2'(1'(0'(0'(2'(2'(2'(0'(1'(0'(1'(1'(0'(2'(0'(x1)))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_0(x1))))))))))))))) -> 1'(2'(1'(0'(0'(0'(1'(2'(1'(1'(1'(2'(2'(1'(1'(1'(x1)))))))))))))))) [1] 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(x1)))))))))))))))) -> 1'(2'(2'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(1'(1'(1'(0'(0'(1'(0'(x1)))))))))))))))))))) [1] 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(x1))))))))))))))) -> 1'(1'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(2'(0'(0'(0'(0'(x1))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(x1))))))))))))))))))) -> 2'(0'(0'(0'(0'(2'(1'(1'(1'(1'(1'(0'(1'(0'(2'(2'(2'(1'(1'(x1))))))))))))))))))) [1] 1'(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_0(c_0(x1)))))))))))))))))))))) -> 1'(0'(1'(1'(1'(0'(2'(1'(2'(0'(0'(0'(0'(2'(1'(2'(2'(0'(2'(2'(2'(0'(x1)))))))))))))))))))))) [1] 1'(c_0(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(2'(2'(2'(1'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(0'(0'(1'(2'(0'(0'(2'(0'(2'(x1)))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(x1)))))))))))))))) -> 1'(2'(1'(1'(0'(1'(1'(0'(0'(1'(0'(0'(0'(1'(1'(1'(0'(x1))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(x1)))))))))))))))))))))))) -> 2'(0'(1'(1'(0'(0'(2'(0'(1'(2'(1'(1'(2'(0'(0'(1'(0'(2'(1'(2'(1'(1'(1'(0'(x1)))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_1(c_0(x1)))))) -> 1'(1'(0'(1'(1'(1'(1'(0'(x1)))))))) [1] 1'(c_0(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(x1))))))))))))) -> 1'(1'(1'(1'(1'(0'(1'(2'(1'(2'(1'(0'(1'(1'(0'(0'(1'(1'(x1)))))))))))))))))) [1] 1'(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))) -> 1'(0'(1'(2'(2'(1'(2'(0'(2'(0'(0'(0'(1'(1'(2'(2'(1'(1'(1'(1'(1'(1'(0'(0'(2'(1'(1'(0'(x1)))))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(x1))))))))))) -> 0'(1'(0'(0'(2'(1'(0'(1'(1'(1'(1'(0'(x1)))))))))))) [1] 0'(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 2'(0'(0'(2'(1'(2'(1'(0'(1'(2'(2'(1'(2'(2'(2'(1'(1'(1'(1'(0'(2'(0'(1'(x1))))))))))))))))))))))) [1] 1'(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))))))))) -> 1'(1'(0'(1'(0'(2'(0'(0'(1'(2'(1'(1'(1'(1'(1'(0'(0'(2'(2'(1'(0'(2'(2'(1'(2'(2'(x1)))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(0'(2'(2'(0'(2'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(2'(2'(1'(1'(2'(x1))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_1(c_1(c_0(c_1(c_1(c_2(c_1(x1))))))))))) -> 0'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(0'(x1))))))))))))) [1] 0'(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(x1)))))))))))))))))) -> 0'(1'(0'(2'(1'(1'(2'(2'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(x1))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_1(c_2(x1)))))) -> 1'(1'(0'(0'(1'(1'(2'(x1))))))) [1] 1'(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(x1)))))))))))))))))) -> 2'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(1'(0'(2'(0'(1'(0'(1'(1'(1'(0'(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_2:c_0:c_1:const -> c_2:c_0:c_1:const c_1 :: c_2:c_0:c_1:const -> c_2:c_0:c_1:const c_2 :: c_2:c_0:c_1:const -> c_2:c_0:c_1:const c_0 :: c_2:c_0:c_1:const -> c_2:c_0:c_1:const 1' :: c_2:c_0:c_1:const -> c_2:c_0:c_1:const 2' :: c_2:c_0:c_1:const -> c_2:c_0:c_1:const encArg :: cons_0:cons_1:cons_2 -> c_2:c_0:c_1: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_2:c_0:c_1:const encode_1 :: cons_0:cons_1:cons_2 -> c_2:c_0:c_1:const encode_2 :: cons_0:cons_1:cons_2 -> c_2:c_0:c_1:const const :: c_2:c_0:c_1:const const1 :: cons_0:cons_1:cons_2 Rewrite Strategy: INNERMOST ---------------------------------------- (27) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (28) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))))))) -> 1'(2'(1'(2'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(0'(2'(2'(0'(1'(2'(2'(0'(1'(0'(1'(1'(0'(0'(x1)))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(x1))))))))))))))) -> 1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(1'(x1))))))))))))))))))) [1] 1'(c_1(c_2(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_0(c_0(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))) -> 1'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(0'(1'(0'(0'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))) [1] 1'(c_2(c_1(c_2(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(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(x1)))))))))))))))))))))))))) -> 1'(0'(2'(0'(0'(1'(1'(0'(1'(2'(2'(0'(1'(1'(0'(0'(0'(1'(1'(1'(2'(2'(1'(2'(2'(0'(1'(2'(x1)))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))))) -> 1'(0'(0'(1'(2'(1'(1'(0'(1'(0'(1'(1'(1'(0'(1'(2'(2'(2'(1'(2'(2'(2'(2'(1'(2'(1'(1'(1'(x1)))))))))))))))))))))))))))) [1] 2'(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 1'(0'(0'(0'(2'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(2'(0'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0'(2'(2'(2'(0'(0'(0'(1'(0'(1'(1'(2'(2'(0'(0'(0'(1'(2'(2'(2'(2'(0'(2'(2'(1'(2'(2'(1'(2'(x1))))))))))))))))))))))))))))) [1] 1'(c_1(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(x1)))))))))))))))))))) -> 1'(1'(0'(2'(1'(2'(2'(2'(2'(2'(0'(2'(1'(1'(1'(0'(0'(0'(0'(1'(1'(x1))))))))))))))))))))) [1] 1'(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_2(c_1(c_1(x1)))))))))))))))))))))) -> 0'(2'(0'(2'(0'(0'(0'(1'(2'(0'(2'(1'(2'(0'(2'(1'(1'(0'(0'(0'(1'(1'(1'(1'(x1)))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_0(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))) -> 1'(1'(0'(1'(1'(0'(2'(2'(0'(1'(2'(2'(0'(0'(0'(2'(x1)))))))))))))))) [1] 2'(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1)))))))))))))) -> 1'(2'(2'(0'(0'(2'(2'(1'(0'(1'(1'(1'(1'(2'(0'(x1))))))))))))))) [1] 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 0'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(2'(2'(2'(0'(0'(0'(2'(2'(1'(1'(1'(2'(0'(0'(0'(2'(1'(2'(x1))))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_0(c_2(x1))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(1'(2'(0'(2'(2'(2'(0'(0'(2'(0'(1'(2'(2'(0'(x1)))))))))))))))))))) [1] 2'(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(x1)))))))))))))))))) -> 1'(2'(1'(0'(1'(1'(2'(1'(1'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(x1))))))))))))))))))))) [1] 1'(c_0(c_1(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_2(c_0(x1)))))))))))))) -> 1'(0'(2'(2'(0'(0'(1'(1'(1'(2'(0'(2'(1'(0'(x1)))))))))))))) [1] 0'(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(x1))))))))))))))))))))))))))) -> 1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(1'(2'(0'(2'(0'(0'(0'(1'(0'(1'(0'(1'(1'(0'(2'(1'(2'(0'(x1)))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 2'(2'(2'(0'(1'(2'(2'(2'(2'(1'(1'(2'(2'(0'(0'(2'(2'(2'(1'(1'(1'(2'(0'(1'(0'(1'(1'(2'(2'(0'(x1)))))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_1(c_2(c_1(c_2(x1))))))) -> 0'(1'(1'(1'(1'(1'(2'(2'(x1)))))))) [1] 0'(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(1'(0'(0'(1'(2'(1'(2'(2'(1'(1'(1'(2'(0'(2'(1'(2'(2'(1'(1'(x1))))))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_0(c_0(x1))))) -> 0'(1'(0'(1'(1'(1'(1'(x1))))))) [1] 0'(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(x1))))))))))))))))))))))))) -> 1'(0'(1'(2'(2'(0'(0'(0'(1'(2'(0'(0'(1'(0'(1'(1'(1'(0'(0'(1'(1'(2'(1'(0'(0'(1'(x1)))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_1(x1))))))))))))))))))) -> 2'(0'(1'(0'(0'(1'(2'(0'(2'(2'(0'(1'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(x1)))))))))))))))))))))) [1] 1'(c_1(c_1(c_0(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(1'(1'(1'(1'(0'(0'(1'(1'(2'(0'(1'(2'(1'(0'(1'(2'(1'(1'(0'(1'(x1)))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(x1)))))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(2'(1'(0'(0'(2'(2'(1'(1'(0'(2'(2'(1'(2'(1'(1'(1'(0'(x1))))))))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 2'(1'(1'(1'(0'(2'(2'(0'(2'(0'(0'(2'(0'(2'(1'(0'(2'(1'(2'(1'(1'(2'(2'(2'(1'(2'(x1)))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(x1))))))))))))))))))))))))))) -> 2'(2'(1'(1'(0'(2'(1'(1'(1'(2'(1'(2'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(x1)))))))))))))))))))))))))))) [1] 0'(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(x1)))))))))))))))))))) -> 0'(1'(2'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(1'(1'(1'(1'(1'(0'(1'(x1)))))))))))))))))))))))) [1] 0'(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))))) -> 0'(1'(1'(0'(1'(1'(2'(0'(1'(2'(1'(2'(0'(1'(1'(1'(1'(2'(2'(0'(0'(0'(1'(1'(1'(x1))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(x1)))))))))))))) -> 2'(1'(0'(1'(1'(1'(2'(0'(1'(1'(1'(2'(2'(1'(1'(0'(x1)))))))))))))))) [1] 2'(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(x1))))))))))))) -> 1'(1'(1'(1'(0'(2'(2'(0'(1'(2'(1'(1'(1'(0'(1'(x1))))))))))))))) [1] 0'(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))) -> 2'(0'(0'(1'(2'(2'(1'(0'(2'(2'(1'(2'(1'(1'(1'(0'(0'(1'(1'(1'(0'(x1))))))))))))))))))))) [1] 2'(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(x1))))))))))))))))))))) -> 1'(2'(2'(0'(2'(2'(1'(1'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(1'(0'(2'(2'(x1))))))))))))))))))))))) [1] 2'(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(x1))))))))))))) -> 2'(0'(1'(0'(1'(2'(2'(0'(1'(0'(0'(1'(1'(1'(x1)))))))))))))) [1] 0'(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(x1))))))))) -> 2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(2'(x1)))))))))))) [1] 1'(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0'(2'(0'(1'(1'(0'(0'(0'(2'(0'(2'(0'(1'(1'(1'(1'(1'(0'(2'(0'(2'(1'(0'(1'(2'(2'(2'(2'(0'(2'(x1)))))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(x1))))))))))))))))))))) -> 2'(1'(0'(1'(2'(0'(0'(2'(2'(1'(1'(1'(1'(0'(1'(2'(0'(2'(0'(0'(1'(1'(x1)))))))))))))))))))))) [1] 0'(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 0'(1'(0'(1'(0'(0'(2'(2'(0'(0'(2'(1'(1'(0'(0'(2'(0'(2'(0'(1'(1'(0'(0'(x1))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(x1)))))))))))))))))))))))))) -> 1'(1'(2'(2'(0'(1'(0'(1'(1'(2'(1'(0'(2'(1'(1'(2'(2'(1'(2'(1'(1'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_0(x1)))))))))) -> 1'(1'(1'(1'(0'(0'(2'(1'(0'(2'(1'(x1))))))))))) [1] 2'(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(x1))))))))))))))))))))))))) -> 2'(1'(0'(2'(0'(0'(2'(1'(0'(1'(1'(2'(0'(0'(2'(0'(1'(2'(2'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_2(x1)))))))))))))))))))))))) -> 2'(0'(0'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(1'(0'(2'(2'(2'(2'(2'(2'(0'(1'(0'(0'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))))) -> 0'(2'(2'(0'(2'(1'(1'(1'(1'(2'(0'(0'(2'(1'(2'(2'(1'(0'(0'(1'(2'(2'(1'(1'(0'(2'(2'(2'(1'(x1))))))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_1(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_2(x1)))))))))))))))))))))))))))) -> 1'(2'(0'(0'(0'(1'(2'(0'(1'(1'(1'(1'(1'(0'(0'(2'(1'(2'(2'(2'(2'(0'(0'(0'(0'(0'(2'(2'(1'(x1))))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0'(1'(1'(0'(0'(2'(1'(0'(2'(1'(0'(1'(2'(1'(2'(0'(2'(0'(2'(1'(0'(1'(2'(0'(1'(1'(1'(1'(1'(1'(x1)))))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(x1)))))))))))))))) -> 1'(0'(1'(1'(1'(1'(2'(2'(0'(1'(1'(1'(0'(2'(1'(0'(2'(2'(x1)))))))))))))))))) [1] 2'(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(x1))))))))))))))))))))) -> 2'(1'(2'(2'(1'(1'(2'(2'(2'(2'(1'(0'(1'(1'(1'(2'(1'(0'(1'(2'(0'(2'(1'(x1))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(x1))))))))))))))) -> 0'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(2'(0'(1'(1'(1'(0'(x1))))))))))))))))) [1] 1'(c_1(c_0(c_2(c_2(c_2(c_0(c_2(c_2(c_2(x1)))))))))) -> 1'(0'(0'(2'(0'(1'(1'(1'(0'(1'(1'(x1))))))))))) [1] 1'(c_1(c_2(c_0(c_2(c_2(c_0(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(x1)))))))))))))))))))))) -> 2'(1'(1'(1'(0'(1'(1'(1'(1'(2'(2'(1'(1'(2'(2'(0'(0'(0'(1'(2'(1'(0'(0'(x1))))))))))))))))))))))) [1] 0'(c_2(c_1(c_2(c_1(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_0(c_2(x1))))))))))))))))))))))))))) -> 0'(1'(2'(1'(1'(2'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(0'(1'(0'(1'(1'(0'(2'(1'(0'(1'(0'(x1)))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_1(x1))))))))))))))))))) -> 1'(1'(2'(2'(1'(2'(2'(1'(1'(1'(2'(2'(0'(1'(0'(1'(0'(2'(1'(1'(x1)))))))))))))))))))) [1] 2'(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_1(c_2(c_1(x1)))))))))))))))))))))) -> 2'(0'(0'(0'(2'(1'(2'(0'(2'(2'(0'(2'(0'(0'(0'(1'(1'(0'(1'(1'(1'(1'(2'(1'(x1)))))))))))))))))))))))) [1] 1'(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(x1)))))))))))) -> 1'(1'(0'(1'(1'(0'(0'(0'(1'(2'(0'(2'(1'(x1))))))))))))) [1] 2'(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(x1)))))))))))))))))))) -> 2'(1'(2'(1'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(0'(0'(1'(1'(1'(0'(0'(1'(1'(1'(2'(0'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_0(c_2(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_0(c_0(c_2(c_2(c_2(x1)))))))))))))))))))))) -> 0'(2'(2'(1'(2'(2'(1'(2'(1'(1'(1'(1'(2'(0'(1'(0'(0'(1'(1'(1'(0'(1'(1'(x1))))))))))))))))))))))) [1] 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1'(0'(1'(1'(1'(0'(2'(1'(2'(0'(0'(0'(0'(2'(1'(2'(2'(0'(2'(2'(2'(0'(x1)))))))))))))))))))))) [1] 1'(c_0(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(2'(2'(2'(1'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(0'(0'(1'(2'(0'(0'(2'(0'(2'(x1)))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(x1)))))))))))))))) -> 1'(2'(1'(1'(0'(1'(1'(0'(0'(1'(0'(0'(0'(1'(1'(1'(0'(x1))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(x1)))))))))))))))))))))))) -> 2'(0'(1'(1'(0'(0'(2'(0'(1'(2'(1'(1'(2'(0'(0'(1'(0'(2'(1'(2'(1'(1'(1'(0'(x1)))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_1(c_0(x1)))))) -> 1'(1'(0'(1'(1'(1'(1'(0'(x1)))))))) [1] 1'(c_0(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(x1))))))))))))) -> 1'(1'(1'(1'(1'(0'(1'(2'(1'(2'(1'(0'(1'(1'(0'(0'(1'(1'(x1)))))))))))))))))) [1] 1'(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))) -> 1'(0'(1'(2'(2'(1'(2'(0'(2'(0'(0'(0'(1'(1'(2'(2'(1'(1'(1'(1'(1'(1'(0'(0'(2'(1'(1'(0'(x1)))))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(x1))))))))))) -> 0'(1'(0'(0'(2'(1'(0'(1'(1'(1'(1'(0'(x1)))))))))))) [1] 0'(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 2'(0'(0'(2'(1'(2'(1'(0'(1'(2'(2'(1'(2'(2'(2'(1'(1'(1'(1'(0'(2'(0'(1'(x1))))))))))))))))))))))) [1] 1'(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))))))))) -> 1'(1'(0'(1'(0'(2'(0'(0'(1'(2'(1'(1'(1'(1'(1'(0'(0'(2'(2'(1'(0'(2'(2'(1'(2'(2'(x1)))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(0'(2'(2'(0'(2'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(2'(2'(1'(1'(2'(x1))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_1(c_1(c_0(c_1(c_1(c_2(c_1(x1))))))))))) -> 0'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(0'(x1))))))))))))) [1] 0'(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(x1)))))))))))))))))) -> 0'(1'(0'(2'(1'(1'(2'(2'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(x1))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_1(c_2(x1)))))) -> 1'(1'(0'(0'(1'(1'(2'(x1))))))) [1] 1'(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(x1)))))))))))))))))) -> 2'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(1'(0'(2'(0'(1'(0'(1'(1'(1'(0'(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_2:c_0:c_1:const -> c_2:c_0:c_1:const c_1 :: c_2:c_0:c_1:const -> c_2:c_0:c_1:const c_2 :: c_2:c_0:c_1:const -> c_2:c_0:c_1:const c_0 :: c_2:c_0:c_1:const -> c_2:c_0:c_1:const 1' :: c_2:c_0:c_1:const -> c_2:c_0:c_1:const 2' :: c_2:c_0:c_1:const -> c_2:c_0:c_1:const encArg :: cons_0:cons_1:cons_2 -> c_2:c_0:c_1: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_2:c_0:c_1:const encode_1 :: cons_0:cons_1:cons_2 -> c_2:c_0:c_1:const encode_2 :: cons_0:cons_1:cons_2 -> c_2:c_0:c_1:const const :: c_2:c_0:c_1:const const1 :: cons_0:cons_1:cons_2 Rewrite Strategy: INNERMOST ---------------------------------------- (29) 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 ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: 0'(z) -{ 1 }-> 2'(2'(1'(1'(1'(1'(0'(1'(0'(2'(2'(1'(2'(0'(2'(1'(x1)))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))) 0'(z) -{ 1 }-> 2'(2'(1'(1'(0'(2'(1'(1'(1'(2'(1'(2'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(2'(0'(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 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))) 0'(z) -{ 1 }-> 2'(2'(1'(0'(1'(1'(2'(0'(0'(1'(1'(1'(1'(2'(1'(1'(x1)))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))) 0'(z) -{ 1 }-> 2'(1'(2'(2'(1'(0'(1'(0'(0'(1'(1'(2'(2'(2'(2'(2'(2'(2'(1'(2'(1'(1'(1'(2'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 0'(z) -{ 1 }-> 2'(1'(1'(1'(2'(1'(0'(1'(1'(1'(2'(2'(1'(1'(1'(0'(1'(0'(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 + x1)))))))))))))))))) 0'(z) -{ 1 }-> 2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(2'(x1)))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))) 0'(z) -{ 1 }-> 2'(1'(0'(2'(2'(2'(1'(2'(2'(0'(2'(2'(1'(1'(1'(1'(2'(1'(2'(0'(2'(2'(0'(2'(2'(0'(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 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))))) 0'(z) -{ 1 }-> 2'(1'(0'(1'(1'(1'(2'(0'(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 + x1)))))))))))) 0'(z) -{ 1 }-> 2'(0'(0'(2'(1'(2'(1'(0'(1'(2'(2'(1'(2'(2'(2'(1'(1'(1'(1'(0'(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 + x1)))))))))))))))))))) 0'(z) -{ 1 }-> 2'(0'(0'(1'(2'(2'(1'(0'(2'(2'(1'(2'(1'(1'(1'(0'(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 + x1))))))))))))))))) 0'(z) -{ 1 }-> 2'(0'(0'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(1'(0'(2'(2'(2'(2'(2'(2'(0'(1'(0'(0'(0'(x1))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 1'(2'(2'(2'(2'(1'(0'(0'(1'(0'(0'(1'(1'(2'(1'(0'(x1)))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))) 0'(z) -{ 1 }-> 1'(2'(1'(2'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(0'(2'(2'(0'(1'(2'(2'(0'(1'(0'(1'(1'(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 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(1'(1'(0'(1'(1'(0'(0'(1'(0'(0'(0'(1'(1'(1'(0'(x1))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))) 0'(z) -{ 1 }-> 1'(2'(1'(0'(0'(0'(1'(2'(1'(1'(1'(2'(2'(1'(1'(1'(x1)))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))) 0'(z) -{ 1 }-> 1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(1'(2'(0'(2'(0'(0'(0'(1'(0'(1'(0'(1'(1'(0'(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 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(0'(0'(0'(1'(2'(0'(1'(1'(1'(1'(1'(0'(0'(2'(1'(2'(2'(2'(2'(0'(0'(0'(0'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(2'(2'(1'(2'(2'(1'(1'(1'(2'(2'(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 + x1))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(2'(2'(0'(1'(0'(1'(1'(2'(1'(0'(2'(1'(1'(2'(2'(1'(2'(1'(1'(1'(2'(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 + (1 + (1 + (1 + x1)))))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(2'(0'(0'(2'(1'(2'(2'(1'(0'(0'(0'(2'(0'(1'(1'(1'(2'(1'(1'(0'(0'(0'(1'(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 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(1'(x1))))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))) 0'(z) -{ 1 }-> 1'(1'(1'(1'(0'(0'(2'(1'(0'(2'(1'(x1))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))) 0'(z) -{ 1 }-> 1'(1'(0'(1'(2'(1'(1'(2'(2'(1'(0'(2'(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 + x1))))))))))))))) 0'(z) -{ 1 }-> 1'(0'(1'(2'(2'(0'(0'(0'(1'(2'(0'(0'(1'(0'(1'(1'(1'(0'(0'(1'(1'(2'(1'(0'(0'(1'(x1)))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 1'(0'(0'(0'(0'(0'(0'(2'(1'(2'(1'(2'(0'(2'(0'(2'(0'(1'(1'(1'(1'(0'(1'(1'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(2'(0'(1'(1'(1'(0'(x1))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(1'(2'(2'(1'(2'(1'(1'(1'(1'(2'(0'(1'(0'(0'(1'(1'(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 + x1)))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(1'(0'(0'(1'(2'(1'(2'(2'(1'(1'(1'(2'(0'(2'(1'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(1'(1'(0'(0'(2'(2'(1'(1'(0'(1'(1'(1'(2'(0'(1'(2'(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 + x1)))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(2'(2'(2'(0'(0'(0'(2'(2'(1'(1'(1'(2'(0'(0'(0'(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 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(0'(2'(1'(1'(1'(1'(2'(0'(0'(2'(1'(2'(2'(1'(0'(0'(1'(2'(2'(1'(1'(0'(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 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(1'(2'(2'(0'(1'(1'(1'(1'(2'(1'(1'(0'(0'(2'(1'(x1))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))) 0'(z) -{ 1 }-> 0'(1'(2'(1'(1'(2'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(0'(1'(0'(1'(1'(0'(2'(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 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(2'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(1'(1'(1'(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 + x1)))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(2'(1'(2'(1'(1'(0'(0'(1'(1'(0'(0'(0'(1'(0'(2'(2'(x1)))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(1'(2'(1'(2'(0'(1'(1'(1'(1'(1'(1'(x1)))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(0'(x1))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(1'(0'(0'(2'(2'(x1))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(1'(0'(0'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(1'(1'(1'(0'(1'(2'(0'(1'(1'(x1)))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(0'(1'(1'(2'(0'(1'(2'(1'(2'(0'(1'(1'(1'(1'(2'(2'(0'(0'(0'(1'(1'(1'(x1))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(0'(0'(2'(1'(0'(2'(1'(0'(1'(2'(1'(2'(0'(2'(0'(2'(1'(0'(1'(2'(0'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(0'(2'(1'(1'(2'(2'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(x1))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 0'(1'(0'(1'(1'(1'(1'(x1))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1))) 0'(z) -{ 1 }-> 0'(1'(0'(1'(0'(0'(2'(2'(0'(0'(2'(1'(1'(0'(0'(2'(0'(2'(0'(1'(1'(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'(0'(1'(2'(1'(1'(1'(1'(1'(2'(1'(0'(1'(2'(0'(1'(0'(2'(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 + x1))))))))))))))))) 0'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 0'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 1'(z) -{ 1 }-> 2'(1'(1'(1'(0'(1'(1'(1'(1'(2'(2'(1'(1'(2'(2'(0'(0'(0'(1'(2'(1'(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 + x1)))))))))))))))))))) 1'(z) -{ 1 }-> 2'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(1'(0'(2'(0'(1'(0'(1'(1'(1'(0'(x1))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))), x1 >= 0 1'(z) -{ 1 }-> 1'(1'(2'(2'(2'(1'(1'(1'(1'(1'(0'(0'(1'(1'(2'(0'(1'(2'(1'(0'(1'(2'(1'(1'(0'(1'(x1)))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(2'(2'(2'(1'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(0'(0'(1'(2'(0'(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'(2'(2'(2'(1'(0'(1'(1'(0'(2'(0'(1'(0'(1'(2'(0'(0'(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 + x1)))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(2'(0'(1'(2'(0'(2'(2'(2'(0'(0'(2'(0'(1'(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 + x1))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(1'(2'(0'(2'(0'(2'(1'(0'(0'(0'(2'(1'(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 + x1)))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(1'(0'(1'(2'(1'(2'(1'(0'(1'(1'(0'(0'(1'(1'(x1)))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(1'(0'(1'(1'(0'(x1))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1)))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(0'(0'(1'(0'(1'(1'(0'(1'(1'(2'(1'(1'(2'(0'(1'(2'(1'(0'(0'(1'(2'(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 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(2'(1'(2'(2'(2'(2'(2'(0'(2'(1'(1'(1'(0'(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 + x1)))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(1'(0'(2'(2'(0'(1'(2'(2'(0'(0'(0'(2'(x1)))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(1'(0'(0'(0'(1'(2'(0'(2'(1'(x1))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(0'(2'(0'(0'(1'(2'(1'(1'(1'(1'(1'(0'(0'(2'(2'(1'(0'(2'(2'(1'(2'(2'(x1)))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(0'(1'(0'(0'(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 + x1))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(2'(2'(0'(2'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(2'(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))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(2'(2'(0'(0'(1'(1'(1'(2'(0'(2'(1'(0'(x1)))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))) 1'(z) -{ 1 }-> 1'(0'(2'(1'(2'(1'(2'(1'(0'(0'(2'(2'(2'(0'(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 + x1))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(2'(1'(1'(1'(1'(1'(x1)))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1))))) 1'(z) -{ 1 }-> 1'(0'(2'(0'(0'(1'(1'(0'(1'(2'(2'(0'(1'(1'(0'(0'(0'(1'(1'(1'(2'(2'(1'(2'(2'(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 + (1 + (1 + (1 + x1)))))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(1'(2'(2'(1'(2'(0'(2'(0'(0'(0'(1'(1'(2'(2'(1'(1'(1'(1'(1'(1'(0'(0'(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 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(1'(1'(1'(0'(2'(1'(2'(0'(0'(0'(0'(2'(1'(2'(2'(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 + x1)))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(0'(2'(2'(1'(2'(1'(1'(0'(1'(1'(1'(0'(1'(0'(1'(1'(1'(2'(1'(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 + x1)))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(0'(2'(0'(1'(1'(1'(0'(1'(1'(x1))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))) 1'(z) -{ 1 }-> 0'(2'(0'(2'(0'(0'(0'(1'(2'(0'(2'(1'(2'(0'(2'(1'(1'(0'(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 + x1)))))))))))))))))))) 1'(z) -{ 1 }-> 0'(2'(0'(1'(1'(0'(0'(0'(2'(0'(2'(0'(1'(1'(1'(1'(1'(0'(2'(0'(2'(1'(0'(1'(2'(2'(2'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 1'(z) -{ 1 }-> 0'(1'(1'(2'(1'(2'(2'(2'(2'(1'(1'(1'(1'(1'(0'(1'(0'(2'(1'(0'(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 + (1 + (1 + (1 + x1)))))))))))))))))))))))) 1'(z) -{ 1 }-> 0'(1'(1'(1'(1'(1'(2'(2'(x1)))))))) :|: x1 >= 0, z = 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'(0'(1'(2'(2'(2'(2'(1'(1'(2'(2'(0'(0'(2'(2'(2'(1'(1'(1'(2'(0'(1'(0'(1'(1'(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 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(2'(2'(1'(1'(2'(2'(2'(2'(1'(0'(1'(1'(1'(2'(1'(0'(1'(2'(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 + x1))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(2'(1'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(0'(0'(1'(1'(1'(0'(0'(1'(1'(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 + x1)))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(1'(1'(0'(2'(2'(0'(2'(0'(0'(2'(0'(2'(1'(0'(2'(1'(2'(1'(1'(2'(2'(2'(1'(2'(x1)))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 2'(1'(0'(2'(0'(0'(2'(1'(0'(1'(1'(2'(0'(0'(2'(0'(1'(2'(2'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 2'(1'(0'(1'(2'(0'(0'(2'(2'(1'(1'(1'(1'(0'(1'(2'(0'(2'(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 + x1))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(0'(1'(1'(1'(0'(1'(1'(1'(0'(0'(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 + x1))))))))))))) 2'(z) -{ 1 }-> 2'(0'(1'(1'(0'(0'(2'(0'(1'(2'(1'(1'(2'(0'(0'(1'(0'(2'(1'(2'(1'(1'(1'(0'(x1)))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 2'(0'(1'(0'(1'(2'(2'(0'(1'(0'(0'(1'(1'(1'(x1)))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))) 2'(z) -{ 1 }-> 2'(0'(1'(0'(1'(1'(0'(0'(1'(1'(1'(2'(0'(1'(1'(1'(2'(0'(0'(2'(1'(x1))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 2'(0'(1'(0'(0'(1'(2'(0'(2'(2'(0'(1'(1'(1'(1'(1'(0'(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 + x1))))))))))))))))) 2'(z) -{ 1 }-> 2'(0'(0'(0'(2'(1'(2'(0'(2'(2'(0'(2'(0'(0'(0'(1'(1'(0'(1'(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 + x1)))))))))))))))))))) 2'(z) -{ 1 }-> 2'(0'(0'(0'(1'(0'(1'(1'(1'(2'(1'(1'(1'(1'(2'(1'(2'(0'(0'(2'(2'(2'(1'(2'(2'(1'(1'(0'(x1)))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 2'(0'(0'(0'(0'(2'(1'(1'(1'(1'(1'(0'(1'(0'(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 + x1))))))))))))))))) 2'(z) -{ 1 }-> 1'(2'(2'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(1'(1'(1'(0'(0'(1'(0'(x1)))))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))) 2'(z) -{ 1 }-> 1'(2'(2'(0'(2'(2'(1'(1'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(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 + x1))))))))))))))))))) 2'(z) -{ 1 }-> 1'(2'(2'(0'(0'(2'(2'(1'(0'(1'(1'(1'(1'(2'(0'(x1))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))) 2'(z) -{ 1 }-> 1'(2'(1'(1'(1'(1'(0'(0'(0'(1'(1'(2'(2'(2'(2'(2'(0'(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 + x1))))))))))))))))) 2'(z) -{ 1 }-> 1'(2'(1'(0'(1'(1'(2'(1'(1'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(x1))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 1'(2'(0'(2'(0'(2'(0'(2'(2'(2'(0'(1'(2'(0'(2'(2'(1'(0'(1'(1'(1'(1'(2'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(2'(0'(0'(0'(0'(x1))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))) 2'(z) -{ 1 }-> 1'(1'(2'(0'(1'(1'(1'(1'(1'(0'(1'(1'(0'(x1))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))) 2'(z) -{ 1 }-> 1'(1'(1'(1'(2'(0'(2'(1'(0'(0'(2'(2'(1'(1'(0'(2'(2'(1'(2'(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 + x1)))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(1'(1'(0'(2'(2'(0'(1'(2'(1'(1'(1'(0'(1'(x1))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))) 2'(z) -{ 1 }-> 1'(1'(0'(1'(2'(1'(0'(1'(1'(2'(1'(0'(0'(2'(2'(2'(0'(1'(0'(1'(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))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(0'(1'(1'(1'(1'(0'(x1)))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1)))) 2'(z) -{ 1 }-> 1'(1'(0'(0'(1'(1'(2'(x1))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1)))) 2'(z) -{ 1 }-> 1'(0'(1'(1'(1'(1'(2'(2'(0'(1'(1'(1'(0'(2'(1'(0'(2'(2'(x1)))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))) 2'(z) -{ 1 }-> 1'(0'(0'(2'(1'(2'(1'(1'(2'(2'(1'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))) 2'(z) -{ 1 }-> 1'(0'(0'(1'(2'(1'(1'(0'(1'(0'(1'(1'(1'(0'(1'(2'(2'(2'(1'(2'(2'(2'(2'(1'(2'(1'(1'(1'(x1)))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 1'(0'(0'(0'(2'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(2'(0'(x1))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 0'(2'(2'(2'(0'(0'(0'(1'(0'(1'(1'(2'(2'(0'(0'(0'(1'(2'(2'(2'(2'(0'(2'(2'(1'(2'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 2'(z) -{ 1 }-> 0'(2'(1'(2'(1'(0'(0'(1'(2'(2'(1'(1'(1'(1'(2'(2'(2'(2'(0'(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 + x1)))))))))))))))))))) 2'(z) -{ 1 }-> 0'(1'(1'(2'(1'(0'(0'(0'(0'(1'(1'(2'(2'(0'(1'(1'(0'(1'(0'(0'(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 }-> 0'(1'(1'(1'(1'(2'(1'(0'(x1)))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1))))) 2'(z) -{ 1 }-> 0'(1'(0'(0'(2'(1'(0'(1'(1'(1'(1'(0'(x1)))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))) 2'(z) -{ 1 }-> 0'(0'(1'(1'(1'(1'(2'(0'(1'(0'(1'(0'(2'(1'(2'(x1))))))))))))))) :|: x1 >= 0, z = 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 ---------------------------------------- (31) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: 0'(z) -{ 1 }-> 2'(2'(1'(1'(1'(1'(0'(1'(0'(2'(2'(1'(2'(0'(2'(1'(z - 13)))))))))))))))) :|: z - 13 >= 0 0'(z) -{ 1 }-> 2'(2'(1'(1'(0'(2'(1'(1'(1'(2'(1'(2'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(z - 26)))))))))))))))))))))))))))) :|: z - 26 >= 0 0'(z) -{ 1 }-> 2'(2'(1'(0'(1'(1'(2'(0'(0'(1'(1'(1'(1'(2'(1'(1'(z - 13)))))))))))))))) :|: z - 13 >= 0 0'(z) -{ 1 }-> 2'(1'(2'(2'(1'(0'(1'(0'(0'(1'(1'(2'(2'(2'(2'(2'(2'(2'(1'(2'(1'(1'(1'(2'(1'(1'(1'(1'(1'(z - 27))))))))))))))))))))))))))))) :|: z - 27 >= 0 0'(z) -{ 1 }-> 2'(1'(1'(1'(2'(1'(0'(1'(1'(1'(2'(2'(1'(1'(1'(0'(1'(0'(1'(1'(2'(0'(z - 19)))))))))))))))))))))) :|: z - 19 >= 0 0'(z) -{ 1 }-> 2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(2'(z - 8)))))))))))) :|: z - 8 >= 0 0'(z) -{ 1 }-> 2'(1'(0'(2'(2'(2'(1'(2'(2'(0'(2'(2'(1'(1'(1'(1'(2'(1'(2'(0'(2'(2'(0'(2'(2'(0'(0'(0'(1'(0'(z - 29)))))))))))))))))))))))))))))) :|: z - 29 >= 0 0'(z) -{ 1 }-> 2'(1'(0'(1'(1'(1'(2'(0'(1'(1'(1'(2'(2'(1'(1'(0'(z - 13)))))))))))))))) :|: z - 13 >= 0 0'(z) -{ 1 }-> 2'(0'(0'(2'(1'(2'(1'(0'(1'(2'(2'(1'(2'(2'(2'(1'(1'(1'(1'(0'(2'(0'(1'(z - 21))))))))))))))))))))))) :|: z - 21 >= 0 0'(z) -{ 1 }-> 2'(0'(0'(1'(2'(2'(1'(0'(2'(2'(1'(2'(1'(1'(1'(0'(0'(1'(1'(1'(0'(z - 18))))))))))))))))))))) :|: z - 18 >= 0 0'(z) -{ 1 }-> 2'(0'(0'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(1'(0'(2'(2'(2'(2'(2'(2'(0'(1'(0'(0'(0'(z - 23))))))))))))))))))))))))))) :|: z - 23 >= 0 0'(z) -{ 1 }-> 1'(2'(2'(2'(2'(1'(0'(0'(1'(0'(0'(1'(1'(2'(1'(0'(z - 14)))))))))))))))) :|: z - 14 >= 0 0'(z) -{ 1 }-> 1'(2'(1'(2'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(0'(2'(2'(0'(1'(2'(2'(0'(1'(0'(1'(1'(0'(0'(z - 26)))))))))))))))))))))))))))) :|: z - 26 >= 0 0'(z) -{ 1 }-> 1'(2'(1'(1'(0'(1'(1'(0'(0'(1'(0'(0'(0'(1'(1'(1'(0'(z - 15))))))))))))))))) :|: z - 15 >= 0 0'(z) -{ 1 }-> 1'(2'(1'(0'(0'(0'(1'(2'(1'(1'(1'(2'(2'(1'(1'(1'(z - 14)))))))))))))))) :|: z - 14 >= 0 0'(z) -{ 1 }-> 1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(1'(2'(0'(2'(0'(0'(0'(1'(0'(1'(0'(1'(1'(0'(2'(1'(2'(0'(z - 26)))))))))))))))))))))))))))) :|: z - 26 >= 0 0'(z) -{ 1 }-> 1'(2'(0'(0'(0'(1'(2'(0'(1'(1'(1'(1'(1'(0'(0'(2'(1'(2'(2'(2'(2'(0'(0'(0'(0'(0'(2'(2'(1'(z - 27))))))))))))))))))))))))))))) :|: z - 27 >= 0 0'(z) -{ 1 }-> 1'(1'(2'(2'(1'(2'(2'(1'(1'(1'(2'(2'(0'(1'(0'(1'(0'(2'(1'(1'(z - 18)))))))))))))))))))) :|: z - 18 >= 0 0'(z) -{ 1 }-> 1'(1'(2'(2'(0'(1'(0'(1'(1'(2'(1'(0'(2'(1'(1'(2'(2'(1'(2'(1'(1'(1'(2'(1'(0'(1'(1'(z - 25))))))))))))))))))))))))))) :|: z - 25 >= 0 0'(z) -{ 1 }-> 1'(1'(2'(0'(0'(2'(1'(2'(2'(1'(0'(0'(0'(2'(0'(1'(1'(1'(2'(1'(1'(0'(0'(0'(1'(2'(2'(1'(1'(1'(z - 28)))))))))))))))))))))))))))))) :|: z - 28 >= 0 0'(z) -{ 1 }-> 1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(1'(z - 14))))))))))))))))))) :|: z - 14 >= 0 0'(z) -{ 1 }-> 1'(1'(1'(1'(0'(0'(2'(1'(0'(2'(1'(z - 9))))))))))) :|: z - 9 >= 0 0'(z) -{ 1 }-> 1'(1'(0'(1'(2'(1'(1'(2'(2'(1'(0'(2'(1'(0'(1'(1'(1'(0'(z - 16)))))))))))))))))) :|: z - 16 >= 0 0'(z) -{ 1 }-> 1'(0'(1'(2'(2'(0'(0'(0'(1'(2'(0'(0'(1'(0'(1'(1'(1'(0'(0'(1'(1'(2'(1'(0'(0'(1'(z - 24)))))))))))))))))))))))))) :|: z - 24 >= 0 0'(z) -{ 1 }-> 1'(0'(0'(0'(0'(0'(0'(2'(1'(2'(1'(2'(0'(2'(0'(2'(0'(1'(1'(1'(1'(0'(1'(1'(2'(2'(0'(1'(z - 27)))))))))))))))))))))))))))) :|: z - 27 >= 0 0'(z) -{ 1 }-> 0'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(2'(0'(1'(1'(1'(0'(z - 14))))))))))))))))) :|: z - 14 >= 0 0'(z) -{ 1 }-> 0'(2'(2'(1'(2'(2'(1'(2'(1'(1'(1'(1'(2'(0'(1'(0'(0'(1'(1'(1'(0'(1'(1'(z - 21))))))))))))))))))))))) :|: z - 21 >= 0 0'(z) -{ 1 }-> 0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(1'(0'(0'(1'(2'(1'(2'(2'(1'(1'(1'(2'(0'(2'(1'(2'(2'(1'(1'(z - 27))))))))))))))))))))))))))))) :|: z - 27 >= 0 0'(z) -{ 1 }-> 0'(2'(2'(1'(1'(0'(0'(2'(2'(1'(1'(0'(1'(1'(1'(2'(0'(1'(2'(1'(0'(1'(1'(z - 21))))))))))))))))))))))) :|: z - 21 >= 0 0'(z) -{ 1 }-> 0'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(2'(2'(2'(0'(0'(0'(2'(2'(1'(1'(1'(2'(0'(0'(0'(2'(1'(2'(z - 28))))))))))))))))))))))))))))) :|: z - 28 >= 0 0'(z) -{ 1 }-> 0'(2'(2'(0'(2'(1'(1'(1'(1'(2'(0'(0'(2'(1'(2'(2'(1'(0'(0'(1'(2'(2'(1'(1'(0'(2'(2'(2'(1'(z - 28))))))))))))))))))))))))))))) :|: z - 28 >= 0 0'(z) -{ 1 }-> 0'(2'(1'(2'(2'(0'(1'(1'(1'(1'(2'(1'(1'(0'(0'(2'(1'(z - 15))))))))))))))))) :|: z - 15 >= 0 0'(z) -{ 1 }-> 0'(1'(2'(1'(1'(2'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(0'(1'(0'(1'(1'(0'(2'(1'(0'(1'(0'(z - 26)))))))))))))))))))))))))))) :|: z - 26 >= 0 0'(z) -{ 1 }-> 0'(1'(2'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(1'(1'(1'(1'(1'(0'(1'(z - 19)))))))))))))))))))))))) :|: z - 19 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(1'(2'(1'(2'(1'(1'(0'(0'(1'(1'(0'(0'(0'(1'(0'(2'(2'(z - 17)))))))))))))))))))) :|: z - 17 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(1'(2'(1'(2'(0'(1'(1'(1'(1'(1'(1'(z - 12)))))))))))))) :|: z - 12 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(0'(z - 10))))))))))))) :|: z - 10 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(1'(1'(0'(0'(2'(2'(z - 7))))))))) :|: z - 7 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(1'(1'(0'(0'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(1'(1'(1'(0'(1'(2'(0'(1'(1'(z - 23)))))))))))))))))))))))))) :|: z - 23 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(0'(1'(1'(2'(0'(1'(2'(1'(2'(0'(1'(1'(1'(1'(2'(2'(0'(0'(0'(1'(1'(1'(z - 23))))))))))))))))))))))))) :|: z - 23 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(0'(0'(2'(1'(0'(2'(1'(0'(1'(2'(1'(2'(0'(2'(0'(2'(1'(0'(1'(2'(0'(1'(1'(1'(1'(1'(1'(z - 27)))))))))))))))))))))))))))))) :|: z - 27 >= 0 0'(z) -{ 1 }-> 0'(1'(0'(2'(1'(1'(2'(2'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(z - 17))))))))))))))))))) :|: z - 17 >= 0 0'(z) -{ 1 }-> 0'(1'(0'(1'(1'(1'(1'(z - 4))))))) :|: z - 4 >= 0 0'(z) -{ 1 }-> 0'(1'(0'(1'(0'(0'(2'(2'(0'(0'(2'(1'(1'(0'(0'(2'(0'(2'(0'(1'(1'(0'(0'(z - 22))))))))))))))))))))))) :|: z - 22 >= 0 0'(z) -{ 1 }-> 0'(0'(1'(2'(1'(1'(1'(1'(1'(2'(1'(0'(1'(2'(0'(1'(0'(2'(0'(1'(0'(1'(1'(z - 18))))))))))))))))))))))) :|: z - 18 >= 0 0'(z) -{ 0 }-> 0 :|: z >= 0 0'(z) -{ 0 }-> 1 + z :|: z >= 0 1'(z) -{ 1 }-> 2'(1'(1'(1'(0'(1'(1'(1'(1'(2'(2'(1'(1'(2'(2'(0'(0'(0'(1'(2'(1'(0'(0'(z - 21))))))))))))))))))))))) :|: z - 21 >= 0 1'(z) -{ 1 }-> 2'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(1'(0'(2'(0'(1'(0'(1'(1'(1'(0'(z - 17))))))))))))))))))))) :|: z - 17 >= 0 1'(z) -{ 1 }-> 1'(1'(2'(2'(2'(1'(1'(1'(1'(1'(0'(0'(1'(1'(2'(0'(1'(2'(1'(0'(1'(2'(1'(1'(0'(1'(z - 24)))))))))))))))))))))))))) :|: z - 24 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(2'(2'(2'(1'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(0'(0'(1'(2'(0'(0'(2'(0'(2'(z - 22)))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(2'(2'(2'(1'(0'(1'(1'(0'(2'(0'(1'(0'(1'(2'(0'(0'(0'(1'(1'(1'(0'(z - 21)))))))))))))))))))))))) :|: z - 21 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(1'(2'(0'(1'(2'(0'(2'(2'(2'(0'(0'(2'(0'(1'(2'(2'(0'(z - 18)))))))))))))))))))) :|: z - 18 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(1'(1'(2'(0'(2'(0'(2'(1'(0'(0'(0'(2'(1'(2'(0'(1'(2'(2'(z - 19))))))))))))))))))))) :|: z - 19 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(1'(1'(0'(1'(2'(1'(2'(1'(0'(1'(1'(0'(0'(1'(1'(z - 12)))))))))))))))))) :|: z - 12 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(1'(1'(0'(1'(1'(0'(z - 5))))))))) :|: z - 5 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(1'(0'(0'(1'(0'(1'(1'(0'(1'(1'(2'(1'(1'(2'(0'(1'(2'(1'(0'(0'(1'(2'(1'(2'(2'(2'(2'(z - 28)))))))))))))))))))))))))))))) :|: z - 28 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(2'(1'(2'(2'(2'(2'(2'(0'(2'(1'(1'(1'(0'(0'(0'(0'(1'(1'(z - 19))))))))))))))))))))) :|: z - 19 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(1'(1'(0'(2'(2'(0'(1'(2'(2'(0'(0'(0'(2'(z - 14)))))))))))))))) :|: z - 14 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(1'(1'(0'(0'(0'(1'(2'(0'(2'(1'(z - 11))))))))))))) :|: z - 11 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(1'(0'(2'(0'(0'(1'(2'(1'(1'(1'(1'(1'(0'(0'(2'(2'(1'(0'(2'(2'(1'(2'(2'(z - 24)))))))))))))))))))))))))) :|: z - 24 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(0'(1'(0'(0'(0'(0'(1'(1'(1'(1'(z - 20))))))))))))))))))))) :|: z - 20 >= 0 1'(z) -{ 1 }-> 1'(0'(2'(2'(0'(2'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(2'(2'(1'(1'(2'(z - 22))))))))))))))))))))))))) :|: z - 22 >= 0 1'(z) -{ 1 }-> 1'(0'(2'(2'(0'(0'(1'(1'(1'(2'(0'(2'(1'(0'(z - 13)))))))))))))) :|: z - 13 >= 0 1'(z) -{ 1 }-> 1'(0'(2'(1'(2'(1'(2'(1'(0'(0'(2'(2'(2'(0'(1'(0'(1'(1'(1'(1'(1'(z - 20))))))))))))))))))))) :|: z - 20 >= 0 1'(z) -{ 1 }-> 1'(0'(2'(1'(1'(1'(1'(1'(z - 6)))))))) :|: z - 6 >= 0 1'(z) -{ 1 }-> 1'(0'(2'(0'(0'(1'(1'(0'(1'(2'(2'(0'(1'(1'(0'(0'(0'(1'(1'(1'(2'(2'(1'(2'(2'(0'(1'(2'(z - 25)))))))))))))))))))))))))))) :|: z - 25 >= 0 1'(z) -{ 1 }-> 1'(0'(1'(2'(2'(1'(2'(0'(2'(0'(0'(0'(1'(1'(2'(2'(1'(1'(1'(1'(1'(1'(0'(0'(2'(1'(1'(0'(z - 26)))))))))))))))))))))))))))) :|: z - 26 >= 0 1'(z) -{ 1 }-> 1'(0'(1'(1'(1'(0'(2'(1'(2'(0'(0'(0'(0'(2'(1'(2'(2'(0'(2'(2'(2'(0'(z - 21)))))))))))))))))))))) :|: z - 21 >= 0 1'(z) -{ 1 }-> 1'(0'(0'(2'(2'(1'(2'(1'(1'(0'(1'(1'(1'(0'(1'(0'(1'(1'(1'(2'(1'(0'(2'(2'(1'(z - 21))))))))))))))))))))))))) :|: z - 21 >= 0 1'(z) -{ 1 }-> 1'(0'(0'(2'(0'(1'(1'(1'(0'(1'(1'(z - 9))))))))))) :|: z - 9 >= 0 1'(z) -{ 1 }-> 0'(2'(0'(2'(0'(0'(0'(1'(2'(0'(2'(1'(2'(0'(2'(1'(1'(0'(0'(0'(1'(1'(1'(1'(z - 21)))))))))))))))))))))))) :|: z - 21 >= 0 1'(z) -{ 1 }-> 0'(2'(0'(1'(1'(0'(0'(0'(2'(0'(2'(0'(1'(1'(1'(1'(1'(0'(2'(0'(2'(1'(0'(1'(2'(2'(2'(2'(0'(2'(z - 27)))))))))))))))))))))))))))))) :|: z - 27 >= 0 1'(z) -{ 1 }-> 0'(1'(1'(2'(1'(2'(2'(2'(2'(1'(1'(1'(1'(1'(0'(1'(0'(2'(1'(0'(0'(1'(1'(1'(1'(1'(z - 25)))))))))))))))))))))))))) :|: z - 25 >= 0 1'(z) -{ 1 }-> 0'(1'(1'(1'(1'(1'(2'(2'(z - 6)))))))) :|: z - 6 >= 0 1'(z) -{ 0 }-> 0 :|: z >= 0 1'(z) -{ 0 }-> 1 + z :|: z >= 0 2'(z) -{ 1 }-> 2'(2'(2'(0'(1'(2'(2'(2'(2'(1'(1'(2'(2'(0'(0'(2'(2'(2'(1'(1'(1'(2'(0'(1'(0'(1'(1'(2'(2'(0'(z - 28)))))))))))))))))))))))))))))) :|: z - 28 >= 0 2'(z) -{ 1 }-> 2'(1'(2'(2'(1'(1'(2'(2'(2'(2'(1'(0'(1'(1'(1'(2'(1'(0'(1'(2'(0'(2'(1'(z - 20))))))))))))))))))))))) :|: z - 20 >= 0 2'(z) -{ 1 }-> 2'(1'(2'(1'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(0'(0'(1'(1'(1'(0'(0'(1'(1'(1'(2'(0'(2'(z - 19))))))))))))))))))))))))))) :|: z - 19 >= 0 2'(z) -{ 1 }-> 2'(1'(1'(1'(0'(2'(2'(0'(2'(0'(0'(2'(0'(2'(1'(0'(2'(1'(2'(1'(1'(2'(2'(2'(1'(2'(z - 24)))))))))))))))))))))))))) :|: z - 24 >= 0 2'(z) -{ 1 }-> 2'(1'(0'(2'(0'(0'(2'(1'(0'(1'(1'(2'(0'(0'(2'(0'(1'(2'(2'(1'(2'(1'(0'(1'(1'(z - 24))))))))))))))))))))))))) :|: z - 24 >= 0 2'(z) -{ 1 }-> 2'(1'(0'(1'(2'(0'(0'(2'(2'(1'(1'(1'(1'(0'(1'(2'(0'(2'(0'(0'(1'(1'(z - 20)))))))))))))))))))))) :|: z - 20 >= 0 2'(z) -{ 1 }-> 2'(1'(0'(1'(1'(1'(0'(1'(1'(1'(0'(0'(1'(1'(1'(0'(1'(2'(0'(1'(z - 14)))))))))))))))))))) :|: z - 14 >= 0 2'(z) -{ 1 }-> 2'(0'(1'(1'(0'(0'(2'(0'(1'(2'(1'(1'(2'(0'(0'(1'(0'(2'(1'(2'(1'(1'(1'(0'(z - 23)))))))))))))))))))))))) :|: z - 23 >= 0 2'(z) -{ 1 }-> 2'(0'(1'(0'(1'(2'(2'(0'(1'(0'(0'(1'(1'(1'(z - 12)))))))))))))) :|: z - 12 >= 0 2'(z) -{ 1 }-> 2'(0'(1'(0'(1'(1'(0'(0'(1'(1'(1'(2'(0'(1'(1'(1'(2'(0'(0'(2'(1'(z - 17))))))))))))))))))))) :|: z - 17 >= 0 2'(z) -{ 1 }-> 2'(0'(1'(0'(0'(1'(2'(0'(2'(2'(0'(1'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(z - 18)))))))))))))))))))))) :|: z - 18 >= 0 2'(z) -{ 1 }-> 2'(0'(0'(0'(2'(1'(2'(0'(2'(2'(0'(2'(0'(0'(0'(1'(1'(0'(1'(1'(1'(1'(2'(1'(z - 21)))))))))))))))))))))))) :|: z - 21 >= 0 2'(z) -{ 1 }-> 2'(0'(0'(0'(1'(0'(1'(1'(1'(2'(1'(1'(1'(1'(2'(1'(2'(0'(0'(2'(2'(2'(1'(2'(2'(1'(1'(0'(z - 24)))))))))))))))))))))))))))) :|: z - 24 >= 0 2'(z) -{ 1 }-> 2'(0'(0'(0'(0'(2'(1'(1'(1'(1'(1'(0'(1'(0'(2'(2'(2'(1'(1'(z - 18))))))))))))))))))) :|: z - 18 >= 0 2'(z) -{ 1 }-> 1'(2'(2'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(1'(1'(1'(0'(0'(1'(0'(z - 15)))))))))))))))))))) :|: z - 15 >= 0 2'(z) -{ 1 }-> 1'(2'(2'(0'(2'(2'(1'(1'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(1'(0'(2'(2'(z - 20))))))))))))))))))))))) :|: z - 20 >= 0 2'(z) -{ 1 }-> 1'(2'(2'(0'(0'(2'(2'(1'(0'(1'(1'(1'(1'(2'(0'(z - 13))))))))))))))) :|: z - 13 >= 0 2'(z) -{ 1 }-> 1'(2'(1'(1'(1'(1'(0'(0'(0'(1'(1'(2'(2'(2'(2'(2'(0'(1'(2'(2'(2'(z - 18))))))))))))))))))))) :|: z - 18 >= 0 2'(z) -{ 1 }-> 1'(2'(1'(0'(1'(1'(2'(1'(1'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(z - 17))))))))))))))))))))) :|: z - 17 >= 0 2'(z) -{ 1 }-> 1'(2'(0'(2'(0'(2'(0'(2'(2'(2'(0'(1'(2'(0'(2'(2'(1'(0'(1'(1'(1'(1'(2'(1'(2'(0'(2'(2'(2'(z - 27))))))))))))))))))))))))))))) :|: z - 27 >= 0 2'(z) -{ 1 }-> 1'(1'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(2'(0'(0'(0'(0'(z - 14))))))))))))))))) :|: z - 14 >= 0 2'(z) -{ 1 }-> 1'(1'(2'(0'(1'(1'(1'(1'(1'(0'(1'(1'(0'(z - 11))))))))))))) :|: z - 11 >= 0 2'(z) -{ 1 }-> 1'(1'(1'(1'(2'(0'(2'(1'(0'(0'(2'(2'(1'(1'(0'(2'(2'(1'(2'(1'(1'(1'(0'(z - 21))))))))))))))))))))))) :|: z - 21 >= 0 2'(z) -{ 1 }-> 1'(1'(1'(1'(0'(2'(2'(0'(1'(2'(1'(1'(1'(0'(1'(z - 12))))))))))))))) :|: z - 12 >= 0 2'(z) -{ 1 }-> 1'(1'(0'(1'(2'(1'(0'(1'(1'(2'(1'(0'(0'(2'(2'(2'(0'(1'(0'(1'(1'(0'(2'(0'(z - 22)))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 1'(1'(0'(1'(1'(1'(1'(0'(z - 5)))))))) :|: z - 5 >= 0 2'(z) -{ 1 }-> 1'(1'(0'(0'(1'(1'(2'(z - 5))))))) :|: z - 5 >= 0 2'(z) -{ 1 }-> 1'(0'(1'(1'(1'(1'(2'(2'(0'(1'(1'(1'(0'(2'(1'(0'(2'(2'(z - 15)))))))))))))))))) :|: z - 15 >= 0 2'(z) -{ 1 }-> 1'(0'(0'(2'(1'(2'(1'(1'(2'(2'(1'(1'(2'(1'(0'(1'(1'(z - 15))))))))))))))))) :|: z - 15 >= 0 2'(z) -{ 1 }-> 1'(0'(0'(1'(2'(1'(1'(0'(1'(0'(1'(1'(1'(0'(1'(2'(2'(2'(1'(2'(2'(2'(2'(1'(2'(1'(1'(1'(z - 24)))))))))))))))))))))))))))) :|: z - 24 >= 0 2'(z) -{ 1 }-> 1'(0'(0'(0'(2'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(2'(0'(z - 24))))))))))))))))))))))))))) :|: z - 24 >= 0 2'(z) -{ 1 }-> 0'(2'(2'(2'(0'(0'(0'(1'(0'(1'(1'(2'(2'(0'(0'(0'(1'(2'(2'(2'(2'(0'(2'(2'(1'(2'(2'(1'(2'(z - 27))))))))))))))))))))))))))))) :|: z - 27 >= 0 2'(z) -{ 1 }-> 0'(2'(1'(2'(1'(0'(0'(1'(2'(2'(1'(1'(1'(1'(2'(2'(2'(2'(0'(0'(1'(2'(1'(2'(z - 21)))))))))))))))))))))))) :|: z - 21 >= 0 2'(z) -{ 1 }-> 0'(1'(1'(2'(1'(0'(0'(0'(0'(1'(1'(2'(2'(0'(1'(1'(0'(1'(0'(0'(0'(2'(2'(1'(z - 22)))))))))))))))))))))))) :|: z - 22 >= 0 2'(z) -{ 1 }-> 0'(1'(1'(1'(1'(2'(1'(0'(z - 6)))))))) :|: z - 6 >= 0 2'(z) -{ 1 }-> 0'(1'(0'(0'(2'(1'(0'(1'(1'(1'(1'(0'(z - 10)))))))))))) :|: z - 10 >= 0 2'(z) -{ 1 }-> 0'(0'(1'(1'(1'(1'(2'(0'(1'(0'(1'(0'(2'(1'(2'(z - 13))))))))))))))) :|: z - 13 >= 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 ---------------------------------------- (33) 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 ---------------------------------------- (34) 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_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1))))))))))))))))))))))))))) -> 1'(2'(1'(2'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(0'(2'(2'(0'(1'(2'(2'(0'(1'(0'(1'(1'(0'(0'(x1)))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(x1))))))))))))))) -> 1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(1'(x1))))))))))))))))))) [1] 1'(c_1(c_2(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_0(c_0(c_0(c_0(c_0(c_2(c_1(x1))))))))))))))))))))) -> 1'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(0'(1'(0'(0'(0'(0'(1'(1'(1'(1'(x1))))))))))))))))))))) [1] 1'(c_2(c_1(c_2(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(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(x1)))))))))))))))))))))))))) -> 1'(0'(2'(0'(0'(1'(1'(0'(1'(2'(2'(0'(1'(1'(0'(0'(0'(1'(1'(1'(2'(2'(1'(2'(2'(0'(1'(2'(x1)))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(x1))))))))))))))))))))))))) -> 1'(0'(0'(1'(2'(1'(1'(0'(1'(0'(1'(1'(1'(0'(1'(2'(2'(2'(1'(2'(2'(2'(2'(1'(2'(1'(1'(1'(x1)))))))))))))))))))))))))))) [1] 2'(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 1'(0'(0'(0'(2'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(2'(0'(x1))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0'(2'(2'(2'(0'(0'(0'(1'(0'(1'(1'(2'(2'(0'(0'(0'(1'(2'(2'(2'(2'(0'(2'(2'(1'(2'(2'(1'(2'(x1))))))))))))))))))))))))))))) [1] 1'(c_1(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(x1)))))))))))))))))))) -> 1'(1'(0'(2'(1'(2'(2'(2'(2'(2'(0'(2'(1'(1'(1'(0'(0'(0'(0'(1'(1'(x1))))))))))))))))))))) [1] 1'(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_2(c_1(c_1(x1)))))))))))))))))))))) -> 0'(2'(0'(2'(0'(0'(0'(1'(2'(0'(2'(1'(2'(0'(2'(1'(1'(0'(0'(0'(1'(1'(1'(1'(x1)))))))))))))))))))))))) [1] 1'(c_2(c_0(c_2(c_0(c_0(c_0(c_2(c_1(c_0(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))) -> 1'(1'(0'(1'(1'(0'(2'(2'(0'(1'(2'(2'(0'(0'(0'(2'(x1)))))))))))))))) [1] 2'(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x1)))))))))))))) -> 1'(2'(2'(0'(0'(2'(2'(1'(0'(1'(1'(1'(1'(2'(0'(x1))))))))))))))) [1] 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 0'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(2'(2'(2'(0'(0'(0'(2'(2'(1'(1'(1'(2'(0'(0'(0'(2'(1'(2'(x1))))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_0(c_2(x1))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(1'(2'(0'(2'(2'(2'(0'(0'(2'(0'(1'(2'(2'(0'(x1)))))))))))))))))))) [1] 2'(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(x1)))))))))))))))))) -> 1'(2'(1'(0'(1'(1'(2'(1'(1'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(x1))))))))))))))))))))) [1] 1'(c_0(c_1(c_0(c_1(c_0(c_1(c_0(c_2(c_1(c_2(c_2(c_2(c_0(x1)))))))))))))) -> 1'(0'(2'(2'(0'(0'(1'(1'(1'(2'(0'(2'(1'(0'(x1)))))))))))))) [1] 0'(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(x1))))))))))))))))))))))))))) -> 1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(1'(2'(0'(2'(0'(0'(0'(1'(0'(1'(0'(1'(1'(0'(2'(1'(2'(0'(x1)))))))))))))))))))))))))))) [1] 2'(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))))))) -> 2'(2'(2'(0'(1'(2'(2'(2'(2'(1'(1'(2'(2'(0'(0'(2'(2'(2'(1'(1'(1'(2'(0'(1'(0'(1'(1'(2'(2'(0'(x1)))))))))))))))))))))))))))))) [1] 1'(c_0(c_1(c_1(c_2(c_1(c_2(x1))))))) -> 0'(1'(1'(1'(1'(1'(2'(2'(x1)))))))) [1] 0'(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(1'(0'(0'(1'(2'(1'(2'(2'(1'(1'(1'(2'(0'(2'(1'(2'(2'(1'(1'(x1))))))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_0(c_0(x1))))) -> 0'(1'(0'(1'(1'(1'(1'(x1))))))) [1] 0'(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(x1))))))))))))))))))))))))) -> 1'(0'(1'(2'(2'(0'(0'(0'(1'(2'(0'(0'(1'(0'(1'(1'(1'(0'(0'(1'(1'(2'(1'(0'(0'(1'(x1)))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_1(x1))))))))))))))))))) -> 2'(0'(1'(0'(0'(1'(2'(0'(2'(2'(0'(1'(1'(1'(1'(1'(0'(0'(2'(0'(1'(1'(x1)))))))))))))))))))))) [1] 1'(c_1(c_1(c_0(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(x1))))))))))))))))))))))))) -> 1'(1'(2'(2'(2'(1'(1'(1'(1'(1'(0'(0'(1'(1'(2'(0'(1'(2'(1'(0'(1'(2'(1'(1'(0'(1'(x1)))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(x1)))))))))))))))))))))) -> 1'(1'(1'(1'(2'(0'(2'(1'(0'(0'(2'(2'(1'(1'(0'(2'(2'(1'(2'(1'(1'(1'(0'(x1))))))))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(x1))))))))))))))))))))))))) -> 2'(1'(1'(1'(0'(2'(2'(0'(2'(0'(0'(2'(0'(2'(1'(0'(2'(1'(2'(1'(1'(2'(2'(2'(1'(2'(x1)))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(x1))))))))))))))))))))))))))) -> 2'(2'(1'(1'(0'(2'(1'(1'(1'(2'(1'(2'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(2'(0'(2'(2'(1'(1'(x1)))))))))))))))))))))))))))) [1] 0'(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(x1)))))))))))))))))))) -> 0'(1'(2'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(1'(1'(1'(1'(1'(0'(1'(x1)))))))))))))))))))))))) [1] 0'(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))))) -> 0'(1'(1'(0'(1'(1'(2'(0'(1'(2'(1'(2'(0'(1'(1'(1'(1'(2'(2'(0'(0'(0'(1'(1'(1'(x1))))))))))))))))))))))))) [1] 0'(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(x1)))))))))))))) -> 2'(1'(0'(1'(1'(1'(2'(0'(1'(1'(1'(2'(2'(1'(1'(0'(x1)))))))))))))))) [1] 2'(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(x1))))))))))))) -> 1'(1'(1'(1'(0'(2'(2'(0'(1'(2'(1'(1'(1'(0'(1'(x1))))))))))))))) [1] 0'(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))) -> 2'(0'(0'(1'(2'(2'(1'(0'(2'(2'(1'(2'(1'(1'(1'(0'(0'(1'(1'(1'(0'(x1))))))))))))))))))))) [1] 2'(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(x1))))))))))))))))))))) -> 1'(2'(2'(0'(2'(2'(1'(1'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(1'(0'(2'(2'(x1))))))))))))))))))))))) [1] 2'(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(x1))))))))))))) -> 2'(0'(1'(0'(1'(2'(2'(0'(1'(0'(0'(1'(1'(1'(x1)))))))))))))) [1] 0'(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(x1))))))))) -> 2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(2'(x1)))))))))))) [1] 1'(c_2(c_2(c_1(c_0(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_2(c_0(c_0(c_0(c_0(x1)))))))))))))))))))))))))))) -> 0'(2'(0'(1'(1'(0'(0'(0'(2'(0'(2'(0'(1'(1'(1'(1'(1'(0'(2'(0'(2'(1'(0'(1'(2'(2'(2'(2'(0'(2'(x1)))))))))))))))))))))))))))))) [1] 2'(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(x1))))))))))))))))))))) -> 2'(1'(0'(1'(2'(0'(0'(2'(2'(1'(1'(1'(1'(0'(1'(2'(0'(2'(0'(0'(1'(1'(x1)))))))))))))))))))))) [1] 0'(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(x1))))))))))))))))))))))) -> 0'(1'(0'(1'(0'(0'(2'(2'(0'(0'(2'(1'(1'(0'(0'(2'(0'(2'(0'(1'(1'(0'(0'(x1))))))))))))))))))))))) [1] 0'(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(x1)))))))))))))))))))))))))) -> 1'(1'(2'(2'(0'(1'(0'(1'(1'(2'(1'(0'(2'(1'(1'(2'(2'(1'(2'(1'(1'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_0(x1)))))))))) -> 1'(1'(1'(1'(0'(0'(2'(1'(0'(2'(1'(x1))))))))))) [1] 2'(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(x1))))))))))))))))))))))))) -> 2'(1'(0'(2'(0'(0'(2'(1'(0'(1'(1'(2'(0'(0'(2'(0'(1'(2'(2'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_2(x1)))))))))))))))))))))))) -> 2'(0'(0'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(1'(0'(2'(2'(2'(2'(2'(2'(0'(1'(0'(0'(0'(x1))))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))))) -> 0'(2'(2'(0'(2'(1'(1'(1'(1'(2'(0'(0'(2'(1'(2'(2'(1'(0'(0'(1'(2'(2'(1'(1'(0'(2'(2'(2'(1'(x1))))))))))))))))))))))))))))) [1] 0'(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_1(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_2(x1)))))))))))))))))))))))))))) -> 1'(2'(0'(0'(0'(1'(2'(0'(1'(1'(1'(1'(1'(0'(0'(2'(1'(2'(2'(2'(2'(0'(0'(0'(0'(0'(2'(2'(1'(x1))))))))))))))))))))))))))))) [1] 0'(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_2(x1)))))))))))))))))))))))))))) -> 0'(1'(1'(0'(0'(2'(1'(0'(2'(1'(0'(1'(2'(1'(2'(0'(2'(0'(2'(1'(0'(1'(2'(0'(1'(1'(1'(1'(1'(1'(x1)))))))))))))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(x1)))))))))))))))) -> 1'(0'(1'(1'(1'(1'(2'(2'(0'(1'(1'(1'(0'(2'(1'(0'(2'(2'(x1)))))))))))))))))) [1] 2'(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(x1))))))))))))))))))))) -> 2'(1'(2'(2'(1'(1'(2'(2'(2'(2'(1'(0'(1'(1'(1'(2'(1'(0'(1'(2'(0'(2'(1'(x1))))))))))))))))))))))) [1] 0'(c_1(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(x1))))))))))))))) -> 0'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(2'(0'(1'(1'(1'(0'(x1))))))))))))))))) [1] 1'(c_1(c_0(c_2(c_2(c_2(c_0(c_2(c_2(c_2(x1)))))))))) -> 1'(0'(0'(2'(0'(1'(1'(1'(0'(1'(1'(x1))))))))))) [1] 1'(c_1(c_2(c_0(c_2(c_2(c_0(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(x1)))))))))))))))))))))) -> 2'(1'(1'(1'(0'(1'(1'(1'(1'(2'(2'(1'(1'(2'(2'(0'(0'(0'(1'(2'(1'(0'(0'(x1))))))))))))))))))))))) [1] 0'(c_2(c_1(c_2(c_1(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_0(c_2(x1))))))))))))))))))))))))))) -> 0'(1'(2'(1'(1'(2'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(0'(1'(0'(1'(1'(0'(2'(1'(0'(1'(0'(x1)))))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_1(x1))))))))))))))))))) -> 1'(1'(2'(2'(1'(2'(2'(1'(1'(1'(2'(2'(0'(1'(0'(1'(0'(2'(1'(1'(x1)))))))))))))))))))) [1] 2'(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_1(c_2(c_1(x1)))))))))))))))))))))) -> 2'(0'(0'(0'(2'(1'(2'(0'(2'(2'(0'(2'(0'(0'(0'(1'(1'(0'(1'(1'(1'(1'(2'(1'(x1)))))))))))))))))))))))) [1] 1'(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(x1)))))))))))) -> 1'(1'(0'(1'(1'(0'(0'(0'(1'(2'(0'(2'(1'(x1))))))))))))) [1] 2'(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(x1)))))))))))))))))))) -> 2'(1'(2'(1'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(0'(0'(1'(1'(1'(0'(0'(1'(1'(1'(2'(0'(2'(x1))))))))))))))))))))))))))) [1] 0'(c_1(c_1(c_0(c_2(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_0(c_0(c_2(c_2(c_2(x1)))))))))))))))))))))) -> 0'(2'(2'(1'(2'(2'(1'(2'(1'(1'(1'(1'(2'(0'(1'(0'(0'(1'(1'(1'(0'(1'(1'(x1))))))))))))))))))))))) [1] 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1'(0'(1'(1'(1'(0'(2'(1'(2'(0'(0'(0'(0'(2'(1'(2'(2'(0'(2'(2'(2'(0'(x1)))))))))))))))))))))) [1] 1'(c_0(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_2(x1))))))))))))))))))))))) -> 1'(1'(1'(2'(2'(2'(1'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(0'(0'(1'(2'(0'(0'(2'(0'(2'(x1)))))))))))))))))))))))))) [1] 0'(c_1(c_0(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(x1)))))))))))))))) -> 1'(2'(1'(1'(0'(1'(1'(0'(0'(1'(0'(0'(0'(1'(1'(1'(0'(x1))))))))))))))))) [1] 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(x1)))))))))))))))))))))))) -> 2'(0'(1'(1'(0'(0'(2'(0'(1'(2'(1'(1'(2'(0'(0'(1'(0'(2'(1'(2'(1'(1'(1'(0'(x1)))))))))))))))))))))))) [1] 2'(c_0(c_2(c_0(c_1(c_0(x1)))))) -> 1'(1'(0'(1'(1'(1'(1'(0'(x1)))))))) [1] 1'(c_0(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(x1))))))))))))) -> 1'(1'(1'(1'(1'(0'(1'(2'(1'(2'(1'(0'(1'(1'(0'(0'(1'(1'(x1)))))))))))))))))) [1] 1'(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_2(c_1(x1))))))))))))))))))))))))))) -> 1'(0'(1'(2'(2'(1'(2'(0'(2'(0'(0'(0'(1'(1'(2'(2'(1'(1'(1'(1'(1'(1'(0'(0'(2'(1'(1'(0'(x1)))))))))))))))))))))))))))) [1] 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(x1))))))))))) -> 0'(1'(0'(0'(2'(1'(0'(1'(1'(1'(1'(0'(x1)))))))))))) [1] 0'(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_2(x1)))))))))))))))))))))) -> 2'(0'(0'(2'(1'(2'(1'(0'(1'(2'(2'(1'(2'(2'(2'(1'(1'(1'(1'(0'(2'(0'(1'(x1))))))))))))))))))))))) [1] 1'(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(x1))))))))))))))))))))))))) -> 1'(1'(0'(1'(0'(2'(0'(0'(1'(2'(1'(1'(1'(1'(1'(0'(0'(2'(2'(1'(0'(2'(2'(1'(2'(2'(x1)))))))))))))))))))))))))) [1] 1'(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_2(c_0(x1))))))))))))))))))))))) -> 1'(0'(2'(2'(0'(2'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(2'(2'(1'(1'(2'(x1))))))))))))))))))))))))) [1] 0'(c_0(c_2(c_1(c_1(c_1(c_0(c_1(c_1(c_2(c_1(x1))))))))))) -> 0'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(0'(x1))))))))))))) [1] 0'(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(x1)))))))))))))))))) -> 0'(1'(0'(2'(1'(1'(2'(2'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(x1))))))))))))))))))) [1] 2'(c_0(c_2(c_2(c_1(c_2(x1)))))) -> 1'(1'(0'(0'(1'(1'(2'(x1))))))) [1] 1'(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(x1)))))))))))))))))) -> 2'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(1'(0'(2'(0'(1'(0'(1'(1'(1'(0'(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_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' -> c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' c_1 :: c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' -> c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' c_2 :: c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' -> c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' c_0 :: c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' -> c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' 1' :: c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' -> c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' 2' :: c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' -> c_2:c_0:c_1: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_2:c_0:c_1: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_2:c_0:c_1: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_2:c_0:c_1: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_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_encArg :: c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_encode_0 :: c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_encode_1 :: c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_encode_2 :: c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_0' :: c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_1' :: c_2:c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_encode_2:null_0':null_1':null_2' null_2' :: c_2:c_0:c_1: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 ---------------------------------------- (35) 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 ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: 0'(z) -{ 1 }-> 2'(2'(1'(1'(1'(1'(0'(1'(0'(2'(2'(1'(2'(0'(2'(1'(x1)))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))) 0'(z) -{ 1 }-> 2'(2'(1'(1'(0'(2'(1'(1'(1'(2'(1'(2'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(2'(0'(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 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))) 0'(z) -{ 1 }-> 2'(2'(1'(0'(1'(1'(2'(0'(0'(1'(1'(1'(1'(2'(1'(1'(x1)))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))) 0'(z) -{ 1 }-> 2'(1'(2'(2'(1'(0'(1'(0'(0'(1'(1'(2'(2'(2'(2'(2'(2'(2'(1'(2'(1'(1'(1'(2'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 0'(z) -{ 1 }-> 2'(1'(1'(1'(2'(1'(0'(1'(1'(1'(2'(2'(1'(1'(1'(0'(1'(0'(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 + x1)))))))))))))))))) 0'(z) -{ 1 }-> 2'(1'(1'(1'(1'(1'(2'(1'(1'(1'(0'(2'(x1)))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))) 0'(z) -{ 1 }-> 2'(1'(0'(2'(2'(2'(1'(2'(2'(0'(2'(2'(1'(1'(1'(1'(2'(1'(2'(0'(2'(2'(0'(2'(2'(0'(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 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))))) 0'(z) -{ 1 }-> 2'(1'(0'(1'(1'(1'(2'(0'(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 + x1)))))))))))) 0'(z) -{ 1 }-> 2'(0'(0'(2'(1'(2'(1'(0'(1'(2'(2'(1'(2'(2'(2'(1'(1'(1'(1'(0'(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 + x1)))))))))))))))))))) 0'(z) -{ 1 }-> 2'(0'(0'(1'(2'(2'(1'(0'(2'(2'(1'(2'(1'(1'(1'(0'(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 + x1))))))))))))))))) 0'(z) -{ 1 }-> 2'(0'(0'(0'(0'(1'(1'(1'(1'(1'(0'(2'(1'(1'(1'(0'(2'(2'(2'(2'(2'(2'(0'(1'(0'(0'(0'(x1))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 1'(2'(2'(2'(2'(1'(0'(0'(1'(0'(0'(1'(1'(2'(1'(0'(x1)))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))) 0'(z) -{ 1 }-> 1'(2'(1'(2'(1'(1'(0'(1'(0'(1'(2'(2'(2'(2'(0'(2'(2'(0'(1'(2'(2'(0'(1'(0'(1'(1'(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 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(1'(1'(0'(1'(1'(0'(0'(1'(0'(0'(0'(1'(1'(1'(0'(x1))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))) 0'(z) -{ 1 }-> 1'(2'(1'(0'(0'(0'(1'(2'(1'(1'(1'(2'(2'(1'(1'(1'(x1)))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))) 0'(z) -{ 1 }-> 1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(1'(2'(0'(2'(0'(0'(0'(1'(0'(1'(0'(1'(1'(0'(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 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(2'(0'(0'(0'(1'(2'(0'(1'(1'(1'(1'(1'(0'(0'(2'(1'(2'(2'(2'(2'(0'(0'(0'(0'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(2'(2'(1'(2'(2'(1'(1'(1'(2'(2'(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 + x1))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(2'(2'(0'(1'(0'(1'(1'(2'(1'(0'(2'(1'(1'(2'(2'(1'(2'(1'(1'(1'(2'(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 + (1 + (1 + (1 + x1)))))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(2'(0'(0'(2'(1'(2'(2'(1'(0'(0'(0'(2'(0'(1'(1'(1'(2'(1'(1'(0'(0'(0'(1'(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 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))) 0'(z) -{ 1 }-> 1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(1'(x1))))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))) 0'(z) -{ 1 }-> 1'(1'(1'(1'(0'(0'(2'(1'(0'(2'(1'(x1))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))) 0'(z) -{ 1 }-> 1'(1'(0'(1'(2'(1'(1'(2'(2'(1'(0'(2'(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 + x1))))))))))))))) 0'(z) -{ 1 }-> 1'(0'(1'(2'(2'(0'(0'(0'(1'(2'(0'(0'(1'(0'(1'(1'(1'(0'(0'(1'(1'(2'(1'(0'(0'(1'(x1)))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 1'(0'(0'(0'(0'(0'(0'(2'(1'(2'(1'(2'(0'(2'(0'(2'(0'(1'(1'(1'(1'(0'(1'(1'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(2'(1'(1'(1'(1'(2'(1'(0'(2'(0'(1'(1'(1'(0'(x1))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(1'(2'(2'(1'(2'(1'(1'(1'(1'(2'(0'(1'(0'(0'(1'(1'(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 + x1)))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(1'(1'(2'(2'(2'(1'(1'(1'(0'(0'(1'(2'(1'(2'(2'(1'(1'(1'(2'(0'(2'(1'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(1'(1'(0'(0'(2'(2'(1'(1'(0'(1'(1'(1'(2'(0'(1'(2'(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 + x1)))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(1'(0'(1'(2'(1'(1'(1'(2'(2'(2'(2'(0'(0'(0'(2'(2'(1'(1'(1'(2'(0'(0'(0'(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 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(2'(0'(2'(1'(1'(1'(1'(2'(0'(0'(2'(1'(2'(2'(1'(0'(0'(1'(2'(2'(1'(1'(0'(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 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(2'(1'(2'(2'(0'(1'(1'(1'(1'(2'(1'(1'(0'(0'(2'(1'(x1))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))) 0'(z) -{ 1 }-> 0'(1'(2'(1'(1'(2'(1'(0'(2'(1'(1'(1'(1'(1'(2'(1'(2'(0'(1'(0'(1'(1'(0'(2'(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 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(2'(0'(1'(2'(1'(1'(1'(1'(0'(0'(1'(1'(0'(2'(1'(1'(1'(1'(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 + x1)))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(2'(1'(2'(1'(1'(0'(0'(1'(1'(0'(0'(0'(1'(0'(2'(2'(x1)))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(1'(2'(1'(2'(0'(1'(1'(1'(1'(1'(1'(x1)))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(1'(1'(1'(1'(0'(1'(0'(0'(0'(x1))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(1'(0'(0'(2'(2'(x1))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))) 0'(z) -{ 1 }-> 0'(1'(1'(1'(1'(0'(0'(1'(1'(1'(1'(0'(1'(0'(0'(2'(0'(1'(1'(1'(0'(1'(2'(0'(1'(1'(x1)))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(0'(1'(1'(2'(0'(1'(2'(1'(2'(0'(1'(1'(1'(1'(2'(2'(0'(0'(0'(1'(1'(1'(x1))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 0'(1'(1'(0'(0'(2'(1'(0'(2'(1'(0'(1'(2'(1'(2'(0'(2'(0'(2'(1'(0'(1'(2'(0'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 0'(z) -{ 1 }-> 0'(1'(0'(2'(1'(1'(2'(2'(2'(2'(1'(1'(1'(0'(2'(0'(1'(2'(1'(x1))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))), x1 >= 0 0'(z) -{ 1 }-> 0'(1'(0'(1'(1'(1'(1'(x1))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1))) 0'(z) -{ 1 }-> 0'(1'(0'(1'(0'(0'(2'(2'(0'(0'(2'(1'(1'(0'(0'(2'(0'(2'(0'(1'(1'(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'(0'(1'(2'(1'(1'(1'(1'(1'(2'(1'(0'(1'(2'(0'(1'(0'(2'(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 + x1))))))))))))))))) 0'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 0'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0 1'(z) -{ 1 }-> 2'(1'(1'(1'(0'(1'(1'(1'(1'(2'(2'(1'(1'(2'(2'(0'(0'(0'(1'(2'(1'(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 + x1)))))))))))))))))))) 1'(z) -{ 1 }-> 2'(1'(0'(1'(2'(1'(1'(2'(1'(1'(1'(1'(0'(2'(0'(1'(0'(1'(1'(1'(0'(x1))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))), x1 >= 0 1'(z) -{ 1 }-> 1'(1'(2'(2'(2'(1'(1'(1'(1'(1'(0'(0'(1'(1'(2'(0'(1'(2'(1'(0'(1'(2'(1'(1'(0'(1'(x1)))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 1'(z) -{ 1 }-> 1'(1'(1'(2'(2'(2'(1'(2'(2'(2'(1'(0'(1'(0'(1'(1'(1'(0'(0'(1'(2'(0'(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'(2'(2'(2'(1'(0'(1'(1'(0'(2'(0'(1'(0'(1'(2'(0'(0'(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 + x1)))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(2'(0'(1'(2'(0'(2'(2'(2'(0'(0'(2'(0'(1'(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 + x1))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(1'(2'(0'(2'(0'(2'(1'(0'(0'(0'(2'(1'(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 + x1)))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(1'(0'(1'(2'(1'(2'(1'(0'(1'(1'(0'(0'(1'(1'(x1)))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(1'(0'(1'(1'(0'(x1))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1)))) 1'(z) -{ 1 }-> 1'(1'(1'(1'(0'(0'(1'(0'(1'(1'(0'(1'(1'(2'(1'(1'(2'(0'(1'(2'(1'(0'(0'(1'(2'(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 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(2'(1'(2'(2'(2'(2'(2'(0'(2'(1'(1'(1'(0'(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 + x1)))))))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(1'(0'(2'(2'(0'(1'(2'(2'(0'(0'(0'(2'(x1)))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(1'(0'(0'(0'(1'(2'(0'(2'(1'(x1))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))) 1'(z) -{ 1 }-> 1'(1'(0'(1'(0'(2'(0'(0'(1'(2'(1'(1'(1'(1'(1'(0'(0'(2'(2'(1'(0'(2'(2'(1'(2'(2'(x1)))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 1'(z) -{ 1 }-> 1'(1'(0'(0'(2'(0'(0'(0'(2'(0'(0'(0'(1'(0'(0'(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 + x1))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(2'(2'(0'(2'(1'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(2'(0'(2'(2'(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))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(2'(2'(0'(0'(1'(1'(1'(2'(0'(2'(1'(0'(x1)))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))) 1'(z) -{ 1 }-> 1'(0'(2'(1'(2'(1'(2'(1'(0'(0'(2'(2'(2'(0'(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 + x1))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(2'(1'(1'(1'(1'(1'(x1)))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1))))) 1'(z) -{ 1 }-> 1'(0'(2'(0'(0'(1'(1'(0'(1'(2'(2'(0'(1'(1'(0'(0'(0'(1'(1'(1'(2'(2'(1'(2'(2'(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 + (1 + (1 + (1 + x1)))))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(1'(2'(2'(1'(2'(0'(2'(0'(0'(0'(1'(1'(2'(2'(1'(1'(1'(1'(1'(1'(0'(0'(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 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(1'(1'(1'(0'(2'(1'(2'(0'(0'(0'(0'(2'(1'(2'(2'(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 + x1)))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(0'(2'(2'(1'(2'(1'(1'(0'(1'(1'(1'(0'(1'(0'(1'(1'(1'(2'(1'(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 + x1)))))))))))))))))))) 1'(z) -{ 1 }-> 1'(0'(0'(2'(0'(1'(1'(1'(0'(1'(1'(x1))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))) 1'(z) -{ 1 }-> 0'(2'(0'(2'(0'(0'(0'(1'(2'(0'(2'(1'(2'(0'(2'(1'(1'(0'(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 + x1)))))))))))))))))))) 1'(z) -{ 1 }-> 0'(2'(0'(1'(1'(0'(0'(0'(2'(0'(2'(0'(1'(1'(1'(1'(1'(0'(2'(0'(2'(1'(0'(1'(2'(2'(2'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 1'(z) -{ 1 }-> 0'(1'(1'(2'(1'(2'(2'(2'(2'(1'(1'(1'(1'(1'(0'(1'(0'(2'(1'(0'(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 + (1 + (1 + (1 + x1)))))))))))))))))))))))) 1'(z) -{ 1 }-> 0'(1'(1'(1'(1'(1'(2'(2'(x1)))))))) :|: x1 >= 0, z = 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'(0'(1'(2'(2'(2'(2'(1'(1'(2'(2'(0'(0'(2'(2'(2'(1'(1'(1'(2'(0'(1'(0'(1'(1'(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 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(2'(2'(1'(1'(2'(2'(2'(2'(1'(0'(1'(1'(1'(2'(1'(0'(1'(2'(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 + x1))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(2'(1'(2'(2'(2'(1'(1'(1'(1'(1'(2'(1'(0'(0'(1'(1'(1'(0'(0'(1'(1'(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 + x1)))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(1'(1'(0'(2'(2'(0'(2'(0'(0'(2'(0'(2'(1'(0'(2'(1'(2'(1'(1'(2'(2'(2'(1'(2'(x1)))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 2'(1'(0'(2'(0'(0'(2'(1'(0'(1'(1'(2'(0'(0'(2'(0'(1'(2'(2'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 2'(1'(0'(1'(2'(0'(0'(2'(2'(1'(1'(1'(1'(0'(1'(2'(0'(2'(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 + x1))))))))))))))))))) 2'(z) -{ 1 }-> 2'(1'(0'(1'(1'(1'(0'(1'(1'(1'(0'(0'(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 + x1))))))))))))) 2'(z) -{ 1 }-> 2'(0'(1'(1'(0'(0'(2'(0'(1'(2'(1'(1'(2'(0'(0'(1'(0'(2'(1'(2'(1'(1'(1'(0'(x1)))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 2'(0'(1'(0'(1'(2'(2'(0'(1'(0'(0'(1'(1'(1'(x1)))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))) 2'(z) -{ 1 }-> 2'(0'(1'(0'(1'(1'(0'(0'(1'(1'(1'(2'(0'(1'(1'(1'(2'(0'(0'(2'(1'(x1))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 2'(0'(1'(0'(0'(1'(2'(0'(2'(2'(0'(1'(1'(1'(1'(1'(0'(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 + x1))))))))))))))))) 2'(z) -{ 1 }-> 2'(0'(0'(0'(2'(1'(2'(0'(2'(2'(0'(2'(0'(0'(0'(1'(1'(0'(1'(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 + x1)))))))))))))))))))) 2'(z) -{ 1 }-> 2'(0'(0'(0'(1'(0'(1'(1'(1'(2'(1'(1'(1'(1'(2'(1'(2'(0'(0'(2'(2'(2'(1'(2'(2'(1'(1'(0'(x1)))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 2'(0'(0'(0'(0'(2'(1'(1'(1'(1'(1'(0'(1'(0'(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 + x1))))))))))))))))) 2'(z) -{ 1 }-> 1'(2'(2'(1'(1'(1'(1'(0'(1'(1'(1'(1'(0'(1'(1'(1'(0'(0'(1'(0'(x1)))))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))) 2'(z) -{ 1 }-> 1'(2'(2'(0'(2'(2'(1'(1'(1'(1'(0'(1'(1'(0'(1'(1'(1'(0'(2'(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 + x1))))))))))))))))))) 2'(z) -{ 1 }-> 1'(2'(2'(0'(0'(2'(2'(1'(0'(1'(1'(1'(1'(2'(0'(x1))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))) 2'(z) -{ 1 }-> 1'(2'(1'(1'(1'(1'(0'(0'(0'(1'(1'(2'(2'(2'(2'(2'(0'(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 + x1))))))))))))))))) 2'(z) -{ 1 }-> 1'(2'(1'(0'(1'(1'(2'(1'(1'(0'(2'(2'(1'(1'(1'(1'(0'(2'(0'(2'(1'(x1))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 1'(2'(0'(2'(0'(2'(0'(2'(2'(2'(0'(1'(2'(0'(2'(2'(1'(0'(1'(1'(1'(1'(2'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(2'(2'(0'(1'(1'(1'(0'(1'(1'(0'(2'(0'(0'(0'(0'(x1))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))) 2'(z) -{ 1 }-> 1'(1'(2'(0'(1'(1'(1'(1'(1'(0'(1'(1'(0'(x1))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))) 2'(z) -{ 1 }-> 1'(1'(1'(1'(2'(0'(2'(1'(0'(0'(2'(2'(1'(1'(0'(2'(2'(1'(2'(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 + x1)))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(1'(1'(0'(2'(2'(0'(1'(2'(1'(1'(1'(0'(1'(x1))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))) 2'(z) -{ 1 }-> 1'(1'(0'(1'(2'(1'(0'(1'(1'(2'(1'(0'(0'(2'(2'(2'(0'(1'(0'(1'(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))))))))))))))))))))) 2'(z) -{ 1 }-> 1'(1'(0'(1'(1'(1'(1'(0'(x1)))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1)))) 2'(z) -{ 1 }-> 1'(1'(0'(0'(1'(1'(2'(x1))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1)))) 2'(z) -{ 1 }-> 1'(0'(1'(1'(1'(1'(2'(2'(0'(1'(1'(1'(0'(2'(1'(0'(2'(2'(x1)))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))) 2'(z) -{ 1 }-> 1'(0'(0'(2'(1'(2'(1'(1'(2'(2'(1'(1'(2'(1'(0'(1'(1'(x1))))))))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))) 2'(z) -{ 1 }-> 1'(0'(0'(1'(2'(1'(1'(0'(1'(0'(1'(1'(1'(0'(1'(2'(2'(2'(1'(2'(2'(2'(2'(1'(2'(1'(1'(1'(x1)))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 1'(0'(0'(0'(2'(1'(1'(1'(1'(1'(1'(0'(0'(1'(0'(1'(2'(0'(2'(1'(2'(1'(1'(0'(1'(2'(0'(x1))))))))))))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))))))))))))))))), x1 >= 0 2'(z) -{ 1 }-> 0'(2'(2'(2'(0'(0'(0'(1'(0'(1'(1'(2'(2'(0'(0'(0'(1'(2'(2'(2'(2'(0'(2'(2'(1'(2'(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 + (1 + (1 + (1 + (1 + (1 + x1)))))))))))))))))))))))))) 2'(z) -{ 1 }-> 0'(2'(1'(2'(1'(0'(0'(1'(2'(2'(1'(1'(1'(1'(2'(2'(2'(2'(0'(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 + x1)))))))))))))))))))) 2'(z) -{ 1 }-> 0'(1'(1'(2'(1'(0'(0'(0'(0'(1'(1'(2'(2'(0'(1'(1'(0'(1'(0'(0'(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 }-> 0'(1'(1'(1'(1'(2'(1'(0'(x1)))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1))))) 2'(z) -{ 1 }-> 0'(1'(0'(0'(2'(1'(0'(1'(1'(1'(1'(0'(x1)))))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))))) 2'(z) -{ 1 }-> 0'(0'(1'(1'(1'(1'(2'(0'(1'(0'(1'(0'(2'(1'(2'(x1))))))))))))))) :|: x1 >= 0, z = 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. ---------------------------------------- (37) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (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(z0) -> c_0(z0) 0(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))) 0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))) 0(c_0(c_1(c_0(c_0(z0))))) -> 0(1(0(1(1(1(1(z0))))))) 0(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(z0))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(z0))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(z0)))))))))))))))))))))))))))) 0(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(z0)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(z0)))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(z0))))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(z0)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(z0)))))))))))))))) 0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(z0))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))))))) 0(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(z0))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(z0)))))))))))) 0(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(z0))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(z0))))))))))))))))))))))) 0(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(z0)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(z0))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_0(z0)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(z0))))))))))) 0(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(z0))))))))))))))))))))))))))) 0(c_2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_2(c_1(z0))))))))))))))))))))))))))))) -> 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2(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(z0))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(z0)))))))))))))) 2(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(z0))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(z0)))))))))))))))))))))) 2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(z0))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(z0))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(z0)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(z0)))))))))))))))))) 2(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(z0))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(z0))))))))))))))))))))))) 2(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_1(c_2(c_1(z0)))))))))))))))))))))) -> 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2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(c_2(c_2(c_2(z0)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(z0))))))))))))) 2(c_2(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_2(z0)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(z0))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_2(z0))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))))))))) 2(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(z0))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))))) 2(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))) 2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))) 2(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> 0(1(1(1(1(2(1(0(z0)))))))) 2(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))) 2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))) 2(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))) 2(c_0(c_2(c_0(c_1(c_0(z0)))))) -> 1(1(0(1(1(1(1(0(z0)))))))) 2(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))) 2(c_0(c_2(c_2(c_1(c_2(z0)))))) -> 1(1(0(0(1(1(2(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'(z0) -> c6 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(z0))))))))))), 1'(2(2(0(1(0(1(1(0(0(z0)))))))))), 2'(2(0(1(0(1(1(0(0(z0))))))))), 2'(0(1(0(1(1(0(0(z0)))))))), 0'(1(0(1(1(0(0(z0))))))), 1'(0(1(1(0(0(z0)))))), 0'(1(1(0(0(z0))))), 1'(1(0(0(z0)))), 1'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> c8(1'(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))), 1'(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))))), 1'(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))), 1'(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))), 1'(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))), 1'(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))), 1'(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))), 0'(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))), 1'(0(0(2(0(0(0(2(0(0(1(z0))))))))))), 0'(0(2(0(0(0(2(0(0(1(z0)))))))))), 0'(2(0(0(0(2(0(0(1(z0))))))))), 2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> c9(0'(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))))), 2'(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))), 1'(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))), 0'(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))), 1'(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))), 2'(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))), 1'(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))), 1'(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))), 1'(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))), 2'(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))), 2'(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))), 2'(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))), 2'(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))), 0'(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))), 0'(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))), 0'(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))), 2'(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))), 2'(1(1(1(2(0(0(0(2(1(2(z0))))))))))), 1'(1(1(2(0(0(0(2(1(2(z0)))))))))), 1'(1(2(0(0(0(2(1(2(z0))))))))), 1'(2(0(0(0(2(1(2(z0)))))))), 2'(0(0(0(2(1(2(z0))))))), 0'(0(0(2(1(2(z0)))))), 0'(0(2(1(2(z0))))), 0'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) 0'(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> c10(1'(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))), 2'(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))))))), 0'(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))), 2'(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))))), 1'(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))), 2'(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))), 1'(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))), 1'(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))), 0'(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))), 1'(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))), 1'(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))), 2'(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))), 0'(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))), 2'(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))), 0'(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))), 0'(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))), 0'(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))), 1'(0(1(0(1(1(0(2(1(2(0(z0))))))))))), 0'(1(0(1(1(0(2(1(2(0(z0)))))))))), 1'(0(1(1(0(2(1(2(0(z0))))))))), 0'(1(1(0(2(1(2(0(z0)))))))), 1'(1(0(2(1(2(0(z0))))))), 1'(0(2(1(2(0(z0)))))), 0'(2(1(2(0(z0))))), 2'(1(2(0(z0)))), 1'(2(0(z0))), 2'(0(z0)), 0'(z0)) 0'(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> c11(0'(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))), 2'(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))))), 2'(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))), 1'(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))), 1'(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))), 2'(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))), 2'(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))), 2'(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))), 1'(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))), 1'(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))), 1'(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))), 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0'(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(z0))))))))))))))) -> c34(1'(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(z0)))))))))))))))), 2'(2(2(2(1(0(0(1(0(0(1(1(2(1(0(z0))))))))))))))), 2'(2(2(1(0(0(1(0(0(1(1(2(1(0(z0)))))))))))))), 2'(2(1(0(0(1(0(0(1(1(2(1(0(z0))))))))))))), 2'(1(0(0(1(0(0(1(1(2(1(0(z0)))))))))))), 1'(0(0(1(0(0(1(1(2(1(0(z0))))))))))), 0'(0(1(0(0(1(1(2(1(0(z0)))))))))), 0'(1(0(0(1(1(2(1(0(z0))))))))), 1'(0(0(1(1(2(1(0(z0)))))))), 0'(0(1(1(2(1(0(z0))))))), 0'(1(1(2(1(0(z0)))))), 1'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(c_0(c_0(c_0(c_1(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_2(c_0(c_0(c_2(z0)))))))))))))))) -> c35(0'(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(z0))))))))))))))))), 2'(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(z0)))))))))))))))), 1'(2(2(0(1(1(1(1(2(1(1(0(0(2(1(z0))))))))))))))), 2'(2(0(1(1(1(1(2(1(1(0(0(2(1(z0)))))))))))))), 2'(0(1(1(1(1(2(1(1(0(0(2(1(z0))))))))))))), 0'(1(1(1(1(2(1(1(0(0(2(1(z0)))))))))))), 1'(1(1(1(2(1(1(0(0(2(1(z0))))))))))), 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1'(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))), 2'(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))), 1'(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))), 1'(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))), 1'(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))), 1'(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))), 2'(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))), 1'(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))), 2'(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))), 0'(0(2(2(2(1(2(2(1(1(0(z0))))))))))), 0'(2(2(2(1(2(2(1(1(0(z0)))))))))), 2'(2(2(1(2(2(1(1(0(z0))))))))), 2'(2(1(2(2(1(1(0(z0)))))))), 2'(1(2(2(1(1(0(z0))))))), 1'(2(2(1(1(0(z0)))))), 2'(2(1(1(0(z0))))), 2'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> c108(0'(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))), 1'(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))))), 1'(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))), 2'(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))), 1'(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))), 0'(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))), 0'(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))), 0'(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))), 1'(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))), 1'(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))), 2'(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))), 2'(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))), 0'(1(1(0(1(0(0(0(2(2(1(z0))))))))))), 1'(1(0(1(0(0(0(2(2(1(z0)))))))))), 1'(0(1(0(0(0(2(2(1(z0))))))))), 0'(1(0(0(0(2(2(1(z0)))))))), 1'(0(0(0(2(2(1(z0))))))), 0'(0(0(2(2(1(z0)))))), 0'(0(2(2(1(z0))))), 0'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> c109(1'(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))), 0'(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))))), 0'(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))), 2'(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))), 1'(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))), 2'(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))), 1'(1(2(2(1(1(2(1(0(1(1(z0))))))))))), 1'(2(2(1(1(2(1(0(1(1(z0)))))))))), 2'(2(1(1(2(1(0(1(1(z0))))))))), 2'(1(1(2(1(0(1(1(z0)))))))), 1'(1(2(1(0(1(1(z0))))))), 1'(2(1(0(1(1(z0)))))), 2'(1(0(1(1(z0))))), 1'(0(1(1(z0)))), 0'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> c110(0'(1(1(1(1(2(1(0(z0)))))))), 1'(1(1(1(2(1(0(z0))))))), 1'(1(1(2(1(0(z0)))))), 1'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> 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1'(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(z0))))))))))))))))), 1'(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(z0)))))))))))))))), 1'(0(0(1(1(0(2(1(1(1(1(1(1(0(1(z0))))))))))))))), 0'(0(1(1(0(2(1(1(1(1(1(1(0(1(z0)))))))))))))), 0'(1(1(0(2(1(1(1(1(1(1(0(1(z0))))))))))))), 1'(1(0(2(1(1(1(1(1(1(0(1(z0)))))))))))), 1'(0(2(1(1(1(1(1(1(0(1(z0))))))))))), 0'(2(1(1(1(1(1(1(0(1(z0)))))))))), 2'(1(1(1(1(1(1(0(1(z0))))))))), 1'(1(1(1(1(1(0(1(z0)))))))), 1'(1(1(1(1(0(1(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))), 1'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> c16(0'(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(z0))))))))))))))))))))))))), 1'(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(z0)))))))))))))))))))))))), 1'(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(z0))))))))))))))))))))))), 0'(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(z0)))))))))))))))))))))), 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2'(1(2(2(1(1(0(z0))))))), 1'(2(2(1(1(0(z0)))))), 2'(2(1(1(0(z0))))), 2'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> c108(0'(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))), 1'(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))))), 1'(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))), 2'(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))), 1'(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))), 0'(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))), 0'(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))), 0'(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))), 1'(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))), 1'(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))), 2'(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))), 2'(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))), 0'(1(1(0(1(0(0(0(2(2(1(z0))))))))))), 1'(1(0(1(0(0(0(2(2(1(z0)))))))))), 1'(0(1(0(0(0(2(2(1(z0))))))))), 0'(1(0(0(0(2(2(1(z0)))))))), 1'(0(0(0(2(2(1(z0))))))), 0'(0(0(2(2(1(z0)))))), 0'(0(2(2(1(z0))))), 0'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> c109(1'(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))), 0'(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))))), 0'(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))), 2'(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))), 1'(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))), 2'(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))), 1'(1(2(2(1(1(2(1(0(1(1(z0))))))))))), 1'(2(2(1(1(2(1(0(1(1(z0)))))))))), 2'(2(1(1(2(1(0(1(1(z0))))))))), 2'(1(1(2(1(0(1(1(z0)))))))), 1'(1(2(1(0(1(1(z0))))))), 1'(2(1(0(1(1(z0)))))), 2'(1(0(1(1(z0))))), 1'(0(1(1(z0)))), 0'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> c110(0'(1(1(1(1(2(1(0(z0)))))))), 1'(1(1(1(2(1(0(z0))))))), 1'(1(1(2(1(0(z0)))))), 1'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> c111(1'(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))), 1'(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))))), 0'(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))), 1'(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))), 2'(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))), 1'(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))), 0'(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))), 1'(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))), 1'(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))), 2'(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))), 1'(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))), 0'(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))), 0'(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))), 2'(2(2(0(1(0(1(1(0(2(0(z0))))))))))), 2'(2(0(1(0(1(1(0(2(0(z0)))))))))), 2'(0(1(0(1(1(0(2(0(z0))))))))), 0'(1(0(1(1(0(2(0(z0)))))))), 1'(0(1(1(0(2(0(z0))))))), 0'(1(1(0(2(0(z0)))))), 1'(1(0(2(0(z0))))), 1'(0(2(0(z0)))), 0'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> c112(1'(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))), 2'(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))))), 2'(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))), 1'(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))), 1'(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))), 1'(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))), 1'(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))), 0'(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))), 1'(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))), 1'(1(1(0(1(1(1(0(0(1(0(z0))))))))))), 1'(1(0(1(1(1(0(0(1(0(z0)))))))))), 1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(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, c7_28, c8_19, c9_29, c10_28, c11_29, c12_7, c13_26, c14_28, c15_24, c16_25, c17_16, c18_21, c19_12, c20_23, c21_27, c22_11, c23_27, c24_29, c25_29, c26_30, c27_17, c28_28, c29_20, c30_23, c31_30, c32_9, c33_14, c34_16, c35_17, c36_18, c37_23, c38_30, c39_29, c40_23, c41_20, c42_22, c43_28, c44_16, c45_16, c46_26, c47_16, c48_17, c49_23, c50_13, c51_19, c52, c53_21, c54_28, c55_21, c56_24, c57_16, c58_20, c59_14, c60_8, c61_26, c62_30, c63_11, c64_23, c65_13, c66_25, c67_8, c68_26, c69_21, c70_21, c71_30, c72_24, c73_9, c74_22, c75_26, c76_18, c77_28, c78_26, c79_25, c80_21, c81, c82_28, c83_27, c84_29, c85_15, c86_21, c87_30, c88_22, c89_23, c90_26, c91_15, c92_23, c93_14, c94_22, c95_25, c96_18, c97_23, c98_24, c99_27, c100_21, c101_24, c102_20, c103_29, c104_13, c105_15, c106_21, c107_28, c108_24, c109_17, c110_8, c111_24, c112_20, c113_17, c114_19, c115_24, c116_8, c117_12, c118_7 ---------------------------------------- (39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: 2'(z0) -> c81 0'(z0) -> c6 1'(z0) -> c52 ---------------------------------------- (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(z0) -> c_0(z0) 0(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))) 0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))) 0(c_0(c_1(c_0(c_0(z0))))) -> 0(1(0(1(1(1(1(z0))))))) 0(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(z0))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(z0))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(z0)))))))))))))))))))))))))))) 0(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(z0)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(z0)))))))))))))))))))))))) 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2(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(z0)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(z0))))))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(z0))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(z0)))))))))))))))))))))))))) 2(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(z0))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(z0))))))))))))))) 2(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(z0))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(z0))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(z0))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(z0)))))))))))))) 2(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(z0))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(z0)))))))))))))))))))))) 2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(z0))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(z0))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(z0)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(z0)))))))))))))))))) 2(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(z0))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(z0))))))))))))))))))))))) 2(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_1(c_2(c_1(z0)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(z0)))))))))))))))))))))))) 2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(z0)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(z0))))))))))))))))))))))))))) 2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_0(z0)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(z0))))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_2(z0)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(z0)))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_2(c_1(z0))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(z0)))))))))))))))))))) 2(c_0(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_2(c_0(z0)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(z0))))))))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(c_2(c_2(c_2(z0)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(z0))))))))))))) 2(c_2(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_2(z0)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(z0))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_2(z0))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))))))))) 2(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(z0))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))))) 2(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))) 2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))) 2(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> 0(1(1(1(1(2(1(0(z0)))))))) 2(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))) 2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))) 2(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))) 2(c_0(c_2(c_0(c_1(c_0(z0)))))) -> 1(1(0(1(1(1(1(0(z0)))))))) 2(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))) 2(c_0(c_2(c_2(c_1(c_2(z0)))))) -> 1(1(0(0(1(1(2(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'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(z0))))))))))), 1'(2(2(0(1(0(1(1(0(0(z0)))))))))), 2'(2(0(1(0(1(1(0(0(z0))))))))), 2'(0(1(0(1(1(0(0(z0)))))))), 0'(1(0(1(1(0(0(z0))))))), 1'(0(1(1(0(0(z0)))))), 0'(1(1(0(0(z0))))), 1'(1(0(0(z0)))), 1'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> c8(1'(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))), 1'(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))))), 1'(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))), 1'(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))), 1'(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))), 1'(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))), 1'(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))), 0'(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))), 1'(0(0(2(0(0(0(2(0(0(1(z0))))))))))), 0'(0(2(0(0(0(2(0(0(1(z0)))))))))), 0'(2(0(0(0(2(0(0(1(z0))))))))), 2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> c9(0'(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))))), 2'(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))), 1'(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))), 0'(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))), 1'(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))), 2'(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))), 1'(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))), 1'(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))), 1'(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))), 2'(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))), 2'(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))), 2'(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))), 2'(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))), 0'(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))), 0'(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))), 0'(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))), 2'(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))), 2'(1(1(1(2(0(0(0(2(1(2(z0))))))))))), 1'(1(1(2(0(0(0(2(1(2(z0)))))))))), 1'(1(2(0(0(0(2(1(2(z0))))))))), 1'(2(0(0(0(2(1(2(z0)))))))), 2'(0(0(0(2(1(2(z0))))))), 0'(0(0(2(1(2(z0)))))), 0'(0(2(1(2(z0))))), 0'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) 0'(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> c10(1'(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))), 2'(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))))))), 0'(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))), 2'(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))))), 1'(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))), 2'(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))), 1'(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))), 1'(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))), 0'(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))), 1'(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))), 1'(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))), 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1'(2(0(1(1(1(2(2(1(1(0(z0))))))))))), 2'(0(1(1(1(2(2(1(1(0(z0)))))))))), 0'(1(1(1(2(2(1(1(0(z0))))))))), 1'(1(1(2(2(1(1(0(z0)))))))), 1'(1(2(2(1(1(0(z0))))))), 1'(2(2(1(1(0(z0)))))), 2'(2(1(1(0(z0))))), 2'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(z0))))))))))))))))))) -> c18(2'(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))))))), 0'(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0)))))))))))))))))))), 0'(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))))), 1'(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0)))))))))))))))))), 2'(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))), 2'(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0)))))))))))))))), 1'(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))), 0'(2(2(1(2(1(1(1(0(0(1(1(1(0(z0)))))))))))))), 2'(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))), 2'(1(2(1(1(1(0(0(1(1(1(0(z0)))))))))))), 1'(2(1(1(1(0(0(1(1(1(0(z0))))))))))), 2'(1(1(1(0(0(1(1(1(0(z0)))))))))), 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0'(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))), 0'(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))), 2'(2(2(0(1(0(1(1(0(2(0(z0))))))))))), 2'(2(0(1(0(1(1(0(2(0(z0)))))))))), 2'(0(1(0(1(1(0(2(0(z0))))))))), 0'(1(0(1(1(0(2(0(z0)))))))), 1'(0(1(1(0(2(0(z0))))))), 0'(1(1(0(2(0(z0)))))), 1'(1(0(2(0(z0))))), 1'(0(2(0(z0)))), 0'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> c112(1'(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))), 2'(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))))), 2'(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))), 1'(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))), 1'(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))), 1'(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))), 1'(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))), 0'(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))), 1'(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))), 1'(1(1(0(1(1(1(0(0(1(0(z0))))))))))), 1'(1(0(1(1(1(0(0(1(0(z0)))))))))), 1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 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2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) S tuples: 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 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1'(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0)))))))))))))))))), 1'(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))))), 1'(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0)))))))))))))))), 0'(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))), 0'(0(1(1(2(2(2(2(2(0(1(2(2(2(z0)))))))))))))), 0'(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))), 1'(1(2(2(2(2(2(0(1(2(2(2(z0)))))))))))), 1'(2(2(2(2(2(0(1(2(2(2(z0))))))))))), 2'(2(2(2(2(0(1(2(2(2(z0)))))))))), 2'(2(2(2(0(1(2(2(2(z0))))))))), 2'(2(2(0(1(2(2(2(z0)))))))), 2'(2(0(1(2(2(2(z0))))))), 2'(0(1(2(2(2(z0)))))), 0'(1(2(2(2(z0))))), 1'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 2'(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(z0))))))))))))))))))))))))) -> c107(2'(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))))))), 0'(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))), 0'(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))))), 1'(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))), 1'(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))), 1'(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))), 1'(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))), 2'(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))), 1'(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))), 1'(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))), 1'(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))), 1'(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))), 2'(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))), 1'(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))), 2'(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))), 0'(0(2(2(2(1(2(2(1(1(0(z0))))))))))), 0'(2(2(2(1(2(2(1(1(0(z0)))))))))), 2'(2(2(1(2(2(1(1(0(z0))))))))), 2'(2(1(2(2(1(1(0(z0)))))))), 2'(1(2(2(1(1(0(z0))))))), 1'(2(2(1(1(0(z0)))))), 2'(2(1(1(0(z0))))), 2'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> c108(0'(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))), 1'(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))))), 1'(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))), 2'(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))), 1'(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))), 0'(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))), 0'(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))), 0'(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))), 1'(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))), 1'(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))), 2'(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))), 2'(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))), 0'(1(1(0(1(0(0(0(2(2(1(z0))))))))))), 1'(1(0(1(0(0(0(2(2(1(z0)))))))))), 1'(0(1(0(0(0(2(2(1(z0))))))))), 0'(1(0(0(0(2(2(1(z0)))))))), 1'(0(0(0(2(2(1(z0))))))), 0'(0(0(2(2(1(z0)))))), 0'(0(2(2(1(z0))))), 0'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> c109(1'(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))), 0'(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))))), 0'(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))), 2'(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))), 1'(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))), 2'(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))), 1'(1(2(2(1(1(2(1(0(1(1(z0))))))))))), 1'(2(2(1(1(2(1(0(1(1(z0)))))))))), 2'(2(1(1(2(1(0(1(1(z0))))))))), 2'(1(1(2(1(0(1(1(z0)))))))), 1'(1(2(1(0(1(1(z0))))))), 1'(2(1(0(1(1(z0)))))), 2'(1(0(1(1(z0))))), 1'(0(1(1(z0)))), 0'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> c110(0'(1(1(1(1(2(1(0(z0)))))))), 1'(1(1(1(2(1(0(z0))))))), 1'(1(1(2(1(0(z0)))))), 1'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> c111(1'(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))), 1'(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))))), 0'(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))), 1'(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))), 2'(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))), 1'(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))), 0'(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))), 1'(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))), 1'(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))), 2'(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))), 1'(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))), 0'(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))), 0'(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))), 2'(2(2(0(1(0(1(1(0(2(0(z0))))))))))), 2'(2(0(1(0(1(1(0(2(0(z0)))))))))), 2'(0(1(0(1(1(0(2(0(z0))))))))), 0'(1(0(1(1(0(2(0(z0)))))))), 1'(0(1(1(0(2(0(z0))))))), 0'(1(1(0(2(0(z0)))))), 1'(1(0(2(0(z0))))), 1'(0(2(0(z0)))), 0'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> c112(1'(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))), 2'(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))))), 2'(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))), 1'(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))), 1'(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))), 1'(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))), 1'(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))), 0'(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))), 1'(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))), 1'(1(1(0(1(1(1(0(0(1(0(z0))))))))))), 1'(1(0(1(1(1(0(0(1(0(z0)))))))))), 1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(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, c7_28, c8_19, c9_29, c10_28, c11_29, c12_7, c13_26, c14_28, c15_24, c16_25, c17_16, c18_21, c19_12, c20_23, c21_27, c22_11, c23_27, c24_29, c25_29, c26_30, c27_17, c28_28, c29_20, c30_23, c31_30, c32_9, c33_14, c34_16, c35_17, c36_18, c37_23, c38_30, c39_29, c40_23, c41_20, c42_22, c43_28, c44_16, c45_16, c46_26, c47_16, c48_17, c49_23, c50_13, c51_19, c53_21, c54_28, c55_21, c56_24, c57_16, c58_20, c59_14, c60_8, c61_26, c62_30, c63_11, c64_23, c65_13, c66_25, c67_8, c68_26, c69_21, c70_21, c71_30, c72_24, c73_9, c74_22, c75_26, c76_18, c77_28, c78_26, c79_25, c80_21, c82_28, c83_27, c84_29, c85_15, c86_21, c87_30, c88_22, c89_23, c90_26, c91_15, c92_23, c93_14, c94_22, c95_25, c96_18, c97_23, c98_24, c99_27, c100_21, c101_24, c102_20, c103_29, c104_13, c105_15, c106_21, c107_28, c108_24, c109_17, c110_8, c111_24, c112_20, c113_17, c114_19, c115_24, c116_8, c117_12, c118_7 ---------------------------------------- (41) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (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(z0) -> c_0(z0) 0(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))) 0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))) 0(c_0(c_1(c_0(c_0(z0))))) -> 0(1(0(1(1(1(1(z0))))))) 0(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(z0))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(z0))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(z0)))))))))))))))))))))))))))) 0(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(z0)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(z0)))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(z0))))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(z0)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(z0)))))))))))))))) 0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(z0))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))))))) 0(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(z0))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(z0)))))))))))) 0(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(z0))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(z0))))))))))))))))))))))) 0(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(z0)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(z0))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_0(z0)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(z0))))))))))) 0(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(z0))))))))))))))))))))))))))) 0(c_2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_2(c_1(z0))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(z0))))))))))))))))))))))))))))) 0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_1(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_2(z0)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_2(z0)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(z0)))))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(z0))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(z0))))))))))))))))) 0(c_2(c_1(c_2(c_1(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_0(c_2(z0))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(z0)))))))))))))))))))))))))))) 0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_1(z0))))))))))))))))))) -> 1(1(2(2(1(2(2(1(1(1(2(2(0(1(0(1(0(2(1(1(z0)))))))))))))))))))) 0(c_1(c_1(c_0(c_2(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_0(c_0(c_2(c_2(c_2(z0)))))))))))))))))))))) -> 0(2(2(1(2(2(1(2(1(1(1(1(2(0(1(0(0(1(1(1(0(1(1(z0))))))))))))))))))))))) 0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_0(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_0(z0)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(1(2(2(0(2(2(1(1(1(1(2(1(2(0(2(2(0(2(2(0(0(0(1(0(z0)))))))))))))))))))))))))))))) 0(c_0(c_0(c_1(c_2(c_2(c_0(c_0(z0)))))))) -> 0(1(1(1(1(0(0(2(2(z0))))))))) 0(c_1(c_1(c_1(c_0(c_1(c_2(c_2(c_1(c_0(c_0(c_0(c_0(z0))))))))))))) -> 0(1(1(1(2(1(2(0(1(1(1(1(1(1(z0)))))))))))))) 0(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(z0))))))))))))))) -> 1(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(z0)))))))))))))))) 0(c_0(c_0(c_0(c_1(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_2(c_0(c_0(c_2(z0)))))))))))))))) -> 0(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(z0))))))))))))))))) 0(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_2(z0))))))))))))))))) -> 1(1(0(1(2(1(1(2(2(1(0(2(1(0(1(1(1(0(z0)))))))))))))))))) 0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(z0)))))))))))))))))))))) -> 0(2(2(1(1(0(0(2(2(1(1(0(1(1(1(2(0(1(2(1(0(1(1(z0))))))))))))))))))))))) 0(c_1(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_1(c_1(c_0(c_0(c_2(c_1(c_1(c_1(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_2(z0))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(z0)))))))))))))))))))))))))))))) 0(c_1(c_2(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_0(c_0(z0)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(z0))))))))))))))))))) -> 0(0(1(2(1(1(1(1(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(z0))))))))))))))))))))))) 0(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_0(z0)))))))))))))))))) -> 0(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(z0)))))))))))))))))))) 0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_2(z0)))))))))))))))))))) -> 2(1(1(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(z0)))))))))))))))))))))) 0(c_1(c_1(c_1(c_2(c_0(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(z0)))))))))))))))))))))))))))) -> 1(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(z0)))))))))))))))))))))))))))) 0(c_2(c_2(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_2(c_1(z0)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(z0)))))))))))))))) 0(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_2(z0)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(z0)))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))) -> 0(1(1(1(1(0(0(1(1(1(1(0(1(0(0(2(0(1(1(1(0(1(2(0(1(1(z0)))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(z0)))))))))))))))) 0(c_1(c_0(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(z0)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(z0))))))))))))))))) 0(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_2(z0)))))))))))))))))))))) -> 2(0(0(2(1(2(1(0(1(2(2(1(2(2(2(1(1(1(1(0(2(0(1(z0))))))))))))))))))))))) 0(c_0(c_2(c_1(c_1(c_1(c_0(c_1(c_1(c_2(c_1(z0))))))))))) -> 0(1(1(1(1(1(1(1(0(1(0(0(0(z0))))))))))))) 0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0)))))))))))))))))) -> 0(1(0(2(1(1(2(2(2(2(1(1(1(0(2(0(1(2(1(z0))))))))))))))))))) 1(z0) -> c_1(z0) 1(c_1(c_2(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_0(c_0(c_0(c_0(c_0(c_2(c_1(z0))))))))))))))))))))) -> 1(1(0(0(2(0(0(0(2(0(0(0(1(0(0(0(0(1(1(1(1(z0))))))))))))))))))))) 1(c_2(c_1(c_2(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(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_2(z0)))))))))))))))))))))))))) -> 1(0(2(0(0(1(1(0(1(2(2(0(1(1(0(0(0(1(1(1(2(2(1(2(2(0(1(2(z0)))))))))))))))))))))))))))) 1(c_1(c_1(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_2(c_2(c_1(c_1(c_0(c_0(z0)))))))))))))))))))) -> 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2(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(z0)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(z0))))))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(z0))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(z0)))))))))))))))))))))))))) 2(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(z0))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(z0))))))))))))))) 2(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(z0))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(z0))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(z0))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(z0)))))))))))))) 2(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(z0))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(z0)))))))))))))))))))))) 2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(z0))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(z0))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(z0)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(z0)))))))))))))))))) 2(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(z0))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(z0))))))))))))))))))))))) 2(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_1(c_2(c_1(z0)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(z0)))))))))))))))))))))))) 2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(z0)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(z0))))))))))))))))))))))))))) 2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_0(z0)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(z0))))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_2(z0)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(z0)))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_2(c_1(z0))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(z0)))))))))))))))))))) 2(c_0(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_2(c_0(z0)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(z0))))))))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(c_2(c_2(c_2(z0)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(z0))))))))))))) 2(c_2(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_2(z0)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(z0))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_2(z0))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))))))))) 2(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(z0))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))))) 2(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))) 2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))) 2(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> 0(1(1(1(1(2(1(0(z0)))))))) 2(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))) 2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))) 2(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))) 2(c_0(c_2(c_0(c_1(c_0(z0)))))) -> 1(1(0(1(1(1(1(0(z0)))))))) 2(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))) 2(c_0(c_2(c_2(c_1(c_2(z0)))))) -> 1(1(0(0(1(1(2(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'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(z0))))))))))), 1'(2(2(0(1(0(1(1(0(0(z0)))))))))), 2'(2(0(1(0(1(1(0(0(z0))))))))), 2'(0(1(0(1(1(0(0(z0)))))))), 0'(1(0(1(1(0(0(z0))))))), 1'(0(1(1(0(0(z0)))))), 0'(1(1(0(0(z0))))), 1'(1(0(0(z0)))), 1'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> c8(1'(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))), 1'(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))))), 1'(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))), 1'(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))), 1'(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))), 1'(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))), 1'(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))), 0'(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))), 1'(0(0(2(0(0(0(2(0(0(1(z0))))))))))), 0'(0(2(0(0(0(2(0(0(1(z0)))))))))), 0'(2(0(0(0(2(0(0(1(z0))))))))), 2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> c9(0'(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))))), 2'(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))), 1'(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))), 0'(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))), 1'(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))), 2'(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))), 1'(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))), 1'(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))), 1'(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))), 2'(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))), 2'(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))), 2'(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))), 2'(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))), 0'(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))), 0'(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))), 0'(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))), 2'(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))), 2'(1(1(1(2(0(0(0(2(1(2(z0))))))))))), 1'(1(1(2(0(0(0(2(1(2(z0)))))))))), 1'(1(2(0(0(0(2(1(2(z0))))))))), 1'(2(0(0(0(2(1(2(z0)))))))), 2'(0(0(0(2(1(2(z0))))))), 0'(0(0(2(1(2(z0)))))), 0'(0(2(1(2(z0))))), 0'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) 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2'(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))), 0'(1(1(0(1(0(0(0(2(2(1(z0))))))))))), 1'(1(0(1(0(0(0(2(2(1(z0)))))))))), 1'(0(1(0(0(0(2(2(1(z0))))))))), 0'(1(0(0(0(2(2(1(z0)))))))), 1'(0(0(0(2(2(1(z0))))))), 0'(0(0(2(2(1(z0)))))), 0'(0(2(2(1(z0))))), 0'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> c109(1'(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))), 0'(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))))), 0'(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))), 2'(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))), 1'(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))), 2'(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))), 1'(1(2(2(1(1(2(1(0(1(1(z0))))))))))), 1'(2(2(1(1(2(1(0(1(1(z0)))))))))), 2'(2(1(1(2(1(0(1(1(z0))))))))), 2'(1(1(2(1(0(1(1(z0)))))))), 1'(1(2(1(0(1(1(z0))))))), 1'(2(1(0(1(1(z0)))))), 2'(1(0(1(1(z0))))), 1'(0(1(1(z0)))), 0'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> c110(0'(1(1(1(1(2(1(0(z0)))))))), 1'(1(1(1(2(1(0(z0))))))), 1'(1(1(2(1(0(z0)))))), 1'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> c111(1'(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))), 1'(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))))), 0'(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))), 1'(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))), 2'(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))), 1'(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))), 0'(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))), 1'(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))), 1'(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))), 2'(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))), 1'(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))), 0'(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))), 0'(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))), 2'(2(2(0(1(0(1(1(0(2(0(z0))))))))))), 2'(2(0(1(0(1(1(0(2(0(z0)))))))))), 2'(0(1(0(1(1(0(2(0(z0))))))))), 0'(1(0(1(1(0(2(0(z0)))))))), 1'(0(1(1(0(2(0(z0))))))), 0'(1(1(0(2(0(z0)))))), 1'(1(0(2(0(z0))))), 1'(0(2(0(z0)))), 0'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> c112(1'(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))), 2'(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))))), 2'(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))), 1'(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))), 1'(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))), 1'(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))), 1'(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))), 0'(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))), 1'(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))), 1'(1(1(0(1(1(1(0(0(1(0(z0))))))))))), 1'(1(0(1(1(1(0(0(1(0(z0)))))))))), 1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) ENCODE_0(z0) -> c6(0'(encArg(z0))) ENCODE_0(z0) -> c6(ENCARG(z0)) ENCODE_1(z0) -> c6(1'(encArg(z0))) ENCODE_1(z0) -> c6(ENCARG(z0)) ENCODE_2(z0) -> c6(2'(encArg(z0))) ENCODE_2(z0) -> c6(ENCARG(z0)) S tuples: 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))), 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0'(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))), 0'(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))), 2'(2(2(0(1(0(1(1(0(2(0(z0))))))))))), 2'(2(0(1(0(1(1(0(2(0(z0)))))))))), 2'(0(1(0(1(1(0(2(0(z0))))))))), 0'(1(0(1(1(0(2(0(z0)))))))), 1'(0(1(1(0(2(0(z0))))))), 0'(1(1(0(2(0(z0)))))), 1'(1(0(2(0(z0))))), 1'(0(2(0(z0)))), 0'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> c112(1'(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))), 2'(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))))), 2'(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))), 1'(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))), 1'(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))), 1'(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))), 1'(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))), 0'(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))), 1'(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))), 1'(1(1(0(1(1(1(0(0(1(0(z0))))))))))), 1'(1(0(1(1(1(0(0(1(0(z0)))))))))), 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1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(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, c7_28, c8_19, c9_29, c10_28, c11_29, c12_7, c13_26, c14_28, c15_24, c16_25, c17_16, c18_21, c19_12, c20_23, c21_27, c22_11, c23_27, c24_29, c25_29, c26_30, c27_17, c28_28, c29_20, c30_23, c31_30, c32_9, c33_14, c34_16, c35_17, c36_18, c37_23, c38_30, c39_29, c40_23, c41_20, c42_22, c43_28, c44_16, c45_16, c46_26, c47_16, c48_17, c49_23, c50_13, c51_19, c53_21, c54_28, c55_21, c56_24, c57_16, c58_20, c59_14, c60_8, c61_26, c62_30, c63_11, c64_23, c65_13, c66_25, c67_8, c68_26, c69_21, c70_21, c71_30, c72_24, c73_9, c74_22, c75_26, c76_18, c77_28, c78_26, c79_25, c80_21, c82_28, c83_27, c84_29, c85_15, c86_21, c87_30, c88_22, c89_23, c90_26, c91_15, c92_23, c93_14, c94_22, c95_25, c96_18, c97_23, c98_24, c99_27, c100_21, c101_24, c102_20, c103_29, c104_13, c105_15, c106_21, c107_28, c108_24, c109_17, c110_8, c111_24, c112_20, c113_17, c114_19, c115_24, c116_8, c117_12, c118_7, c6_1 ---------------------------------------- (43) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 3 leading nodes: ENCODE_0(z0) -> c6(ENCARG(z0)) ENCODE_1(z0) -> c6(ENCARG(z0)) ENCODE_2(z0) -> c6(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)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(z0) -> c_0(z0) 0(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))) 0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))) 0(c_0(c_1(c_0(c_0(z0))))) -> 0(1(0(1(1(1(1(z0))))))) 0(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(z0))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(z0))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(z0)))))))))))))))))))))))))))) 0(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(z0)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(z0)))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(z0))))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(z0)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(z0)))))))))))))))) 0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(z0))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))))))) 0(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(z0))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(z0)))))))))))) 0(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(z0))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(z0))))))))))))))))))))))) 0(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(z0)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(z0))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_0(z0)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(z0))))))))))) 0(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(z0))))))))))))))))))))))))))) 0(c_2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_2(c_1(z0))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(z0))))))))))))))))))))))))))))) 0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_1(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_2(z0)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_2(z0)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(z0)))))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(z0))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(z0))))))))))))))))) 0(c_2(c_1(c_2(c_1(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_0(c_2(z0))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(z0)))))))))))))))))))))))))))) 0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_1(z0))))))))))))))))))) -> 1(1(2(2(1(2(2(1(1(1(2(2(0(1(0(1(0(2(1(1(z0)))))))))))))))))))) 0(c_1(c_1(c_0(c_2(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_0(c_0(c_2(c_2(c_2(z0)))))))))))))))))))))) -> 0(2(2(1(2(2(1(2(1(1(1(1(2(0(1(0(0(1(1(1(0(1(1(z0))))))))))))))))))))))) 0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_0(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_0(z0)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(1(2(2(0(2(2(1(1(1(1(2(1(2(0(2(2(0(2(2(0(0(0(1(0(z0)))))))))))))))))))))))))))))) 0(c_0(c_0(c_1(c_2(c_2(c_0(c_0(z0)))))))) -> 0(1(1(1(1(0(0(2(2(z0))))))))) 0(c_1(c_1(c_1(c_0(c_1(c_2(c_2(c_1(c_0(c_0(c_0(c_0(z0))))))))))))) -> 0(1(1(1(2(1(2(0(1(1(1(1(1(1(z0)))))))))))))) 0(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(z0))))))))))))))) -> 1(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(z0)))))))))))))))) 0(c_0(c_0(c_0(c_1(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_2(c_0(c_0(c_2(z0)))))))))))))))) -> 0(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(z0))))))))))))))))) 0(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_2(z0))))))))))))))))) -> 1(1(0(1(2(1(1(2(2(1(0(2(1(0(1(1(1(0(z0)))))))))))))))))) 0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(z0)))))))))))))))))))))) -> 0(2(2(1(1(0(0(2(2(1(1(0(1(1(1(2(0(1(2(1(0(1(1(z0))))))))))))))))))))))) 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0(c_1(c_1(c_1(c_2(c_0(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(z0)))))))))))))))))))))))))))) -> 1(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(z0)))))))))))))))))))))))))))) 0(c_2(c_2(c_0(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_2(c_1(z0)))))))))))))) -> 2(2(1(0(1(1(2(0(0(1(1(1(1(2(1(1(z0)))))))))))))))) 0(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_2(z0)))))))))))))) -> 2(2(1(1(1(1(0(1(0(2(2(1(2(0(2(1(z0)))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))) -> 0(1(1(1(1(0(0(1(1(1(1(0(1(0(0(2(0(1(1(1(0(1(2(0(1(1(z0)))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))))))))))) -> 1(2(1(0(0(0(1(2(1(1(1(2(2(1(1(1(z0)))))))))))))))) 0(c_1(c_0(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_2(c_2(z0)))))))))))))))) -> 1(2(1(1(0(1(1(0(0(1(0(0(0(1(1(1(0(z0))))))))))))))))) 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2(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(z0)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(z0))))))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(z0))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(z0)))))))))))))))))))))))))) 2(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(z0))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(z0))))))))))))))) 2(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(z0))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(z0))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(z0))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(z0)))))))))))))) 2(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(z0))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(z0)))))))))))))))))))))) 2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(z0))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(z0))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(z0)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(z0)))))))))))))))))) 2(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(z0))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(z0))))))))))))))))))))))) 2(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_1(c_2(c_1(z0)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(z0)))))))))))))))))))))))) 2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(z0)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(z0))))))))))))))))))))))))))) 2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_0(z0)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(z0))))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_2(z0)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(z0)))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_2(c_1(z0))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(z0)))))))))))))))))))) 2(c_0(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_2(c_0(z0)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(z0))))))))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(c_2(c_2(c_2(z0)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(z0))))))))))))) 2(c_2(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_2(z0)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(z0))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_2(z0))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))))))))) 2(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(z0))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))))) 2(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))) 2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))) 2(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> 0(1(1(1(1(2(1(0(z0)))))))) 2(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))) 2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))) 2(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))) 2(c_0(c_2(c_0(c_1(c_0(z0)))))) -> 1(1(0(1(1(1(1(0(z0)))))))) 2(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))) 2(c_0(c_2(c_2(c_1(c_2(z0)))))) -> 1(1(0(0(1(1(2(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'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(z0))))))))))), 1'(2(2(0(1(0(1(1(0(0(z0)))))))))), 2'(2(0(1(0(1(1(0(0(z0))))))))), 2'(0(1(0(1(1(0(0(z0)))))))), 0'(1(0(1(1(0(0(z0))))))), 1'(0(1(1(0(0(z0)))))), 0'(1(1(0(0(z0))))), 1'(1(0(0(z0)))), 1'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> c8(1'(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))), 1'(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))))), 1'(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))), 1'(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))), 1'(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))), 1'(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))), 1'(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))), 0'(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))), 1'(0(0(2(0(0(0(2(0(0(1(z0))))))))))), 0'(0(2(0(0(0(2(0(0(1(z0)))))))))), 0'(2(0(0(0(2(0(0(1(z0))))))))), 2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> c9(0'(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))))), 2'(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))), 1'(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))), 0'(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))), 1'(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))), 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2'(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))), 0'(1(1(0(1(0(0(0(2(2(1(z0))))))))))), 1'(1(0(1(0(0(0(2(2(1(z0)))))))))), 1'(0(1(0(0(0(2(2(1(z0))))))))), 0'(1(0(0(0(2(2(1(z0)))))))), 1'(0(0(0(2(2(1(z0))))))), 0'(0(0(2(2(1(z0)))))), 0'(0(2(2(1(z0))))), 0'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> c109(1'(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))), 0'(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))))), 0'(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))), 2'(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))), 1'(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))), 2'(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))), 1'(1(2(2(1(1(2(1(0(1(1(z0))))))))))), 1'(2(2(1(1(2(1(0(1(1(z0)))))))))), 2'(2(1(1(2(1(0(1(1(z0))))))))), 2'(1(1(2(1(0(1(1(z0)))))))), 1'(1(2(1(0(1(1(z0))))))), 1'(2(1(0(1(1(z0)))))), 2'(1(0(1(1(z0))))), 1'(0(1(1(z0)))), 0'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> c110(0'(1(1(1(1(2(1(0(z0)))))))), 1'(1(1(1(2(1(0(z0))))))), 1'(1(1(2(1(0(z0)))))), 1'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> c111(1'(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))), 1'(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))))), 0'(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))), 1'(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))), 2'(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))), 1'(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))), 0'(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))), 1'(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))), 1'(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))), 2'(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))), 1'(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))), 0'(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))), 0'(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))), 2'(2(2(0(1(0(1(1(0(2(0(z0))))))))))), 2'(2(0(1(0(1(1(0(2(0(z0)))))))))), 2'(0(1(0(1(1(0(2(0(z0))))))))), 0'(1(0(1(1(0(2(0(z0)))))))), 1'(0(1(1(0(2(0(z0))))))), 0'(1(1(0(2(0(z0)))))), 1'(1(0(2(0(z0))))), 1'(0(2(0(z0)))), 0'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> c112(1'(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))), 2'(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))))), 2'(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))), 1'(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))), 1'(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))), 1'(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))), 1'(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))), 0'(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))), 1'(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))), 1'(1(1(0(1(1(1(0(0(1(0(z0))))))))))), 1'(1(0(1(1(1(0(0(1(0(z0)))))))))), 1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) ENCODE_0(z0) -> c6(0'(encArg(z0))) ENCODE_1(z0) -> c6(1'(encArg(z0))) ENCODE_2(z0) -> c6(2'(encArg(z0))) S tuples: 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 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0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(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, c7_28, c8_19, c9_29, c10_28, c11_29, c12_7, c13_26, c14_28, c15_24, c16_25, c17_16, c18_21, c19_12, c20_23, c21_27, c22_11, c23_27, c24_29, c25_29, c26_30, c27_17, c28_28, c29_20, c30_23, c31_30, c32_9, c33_14, c34_16, c35_17, c36_18, c37_23, c38_30, c39_29, c40_23, c41_20, c42_22, c43_28, c44_16, c45_16, c46_26, c47_16, c48_17, c49_23, c50_13, c51_19, c53_21, c54_28, c55_21, c56_24, c57_16, c58_20, c59_14, c60_8, c61_26, c62_30, c63_11, c64_23, c65_13, c66_25, c67_8, c68_26, c69_21, c70_21, c71_30, c72_24, c73_9, c74_22, c75_26, c76_18, c77_28, c78_26, c79_25, c80_21, c82_28, c83_27, c84_29, c85_15, c86_21, c87_30, c88_22, c89_23, c90_26, c91_15, c92_23, c93_14, c94_22, c95_25, c96_18, c97_23, c98_24, c99_27, c100_21, c101_24, c102_20, c103_29, c104_13, c105_15, c106_21, c107_28, c108_24, c109_17, c110_8, c111_24, c112_20, c113_17, c114_19, c115_24, c116_8, c117_12, c118_7, c6_1 ---------------------------------------- (45) 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)) ---------------------------------------- (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)) 0(z0) -> c_0(z0) 0(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))) 0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))) 0(c_0(c_1(c_0(c_0(z0))))) -> 0(1(0(1(1(1(1(z0))))))) 0(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(z0))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(z0))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(z0)))))))))))))))))))))))))))) 0(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(z0)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(z0)))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(z0))))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(z0)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(z0)))))))))))))))) 0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(z0))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))))))) 0(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(z0))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(z0)))))))))))) 0(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(z0))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(z0))))))))))))))))))))))) 0(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(z0)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(z0))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_0(z0)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(z0))))))))))) 0(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(z0))))))))))))))))))))))))))) 0(c_2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_2(c_1(z0))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(z0))))))))))))))))))))))))))))) 0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_1(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_2(z0)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_2(z0)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(z0)))))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(z0))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(z0))))))))))))))))) 0(c_2(c_1(c_2(c_1(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_0(c_2(z0))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(z0)))))))))))))))))))))))))))) 0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_1(z0))))))))))))))))))) -> 1(1(2(2(1(2(2(1(1(1(2(2(0(1(0(1(0(2(1(1(z0)))))))))))))))))))) 0(c_1(c_1(c_0(c_2(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_0(c_0(c_2(c_2(c_2(z0)))))))))))))))))))))) -> 0(2(2(1(2(2(1(2(1(1(1(1(2(0(1(0(0(1(1(1(0(1(1(z0))))))))))))))))))))))) 0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_0(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_0(z0)))))))))))))))))))))))))))))) -> 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0(c_1(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_1(c_1(c_0(c_0(c_2(c_1(c_1(c_1(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_2(z0))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(z0)))))))))))))))))))))))))))))) 0(c_1(c_2(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_0(c_0(z0)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(z0))))))))))))))))))) -> 0(0(1(2(1(1(1(1(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(z0))))))))))))))))))))))) 0(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_0(z0)))))))))))))))))) -> 0(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(z0)))))))))))))))))))) 0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_2(z0)))))))))))))))))))) -> 2(1(1(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(z0)))))))))))))))))))))) 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2(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_0(c_2(z0)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(z0))))))))))))))))))))))))))))) 2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(z0))))))))))))))) 2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(z0)))))))))))))))))) -> 1(2(1(0(1(1(2(1(1(0(2(2(1(1(1(1(0(2(0(2(1(z0))))))))))))))))))))) 2(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(z0)))))))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_1(z0))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(2(0(1(1(1(1(1(0(0(2(0(1(1(z0)))))))))))))))))))))) 2(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(z0)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(z0))))))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(z0))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(z0)))))))))))))))))))))))))) 2(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(z0))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(z0))))))))))))))) 2(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(z0))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(z0))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(z0))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(z0)))))))))))))) 2(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(z0))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(z0)))))))))))))))))))))) 2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(z0))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(z0))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(z0)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(z0)))))))))))))))))) 2(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(z0))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(z0))))))))))))))))))))))) 2(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_1(c_2(c_1(z0)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(z0)))))))))))))))))))))))) 2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(z0)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(z0))))))))))))))))))))))))))) 2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_0(z0)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(z0))))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_2(z0)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(z0)))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_2(c_1(z0))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(z0)))))))))))))))))))) 2(c_0(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_2(c_0(z0)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(z0))))))))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(c_2(c_2(c_2(z0)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(z0))))))))))))) 2(c_2(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_2(z0)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(z0))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_2(z0))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))))))))) 2(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(z0))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))))) 2(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))) 2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))) 2(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> 0(1(1(1(1(2(1(0(z0)))))))) 2(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))) 2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))) 2(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))) 2(c_0(c_2(c_0(c_1(c_0(z0)))))) -> 1(1(0(1(1(1(1(0(z0)))))))) 2(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))) 2(c_0(c_2(c_2(c_1(c_2(z0)))))) -> 1(1(0(0(1(1(2(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'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(z0))))))))))), 1'(2(2(0(1(0(1(1(0(0(z0)))))))))), 2'(2(0(1(0(1(1(0(0(z0))))))))), 2'(0(1(0(1(1(0(0(z0)))))))), 0'(1(0(1(1(0(0(z0))))))), 1'(0(1(1(0(0(z0)))))), 0'(1(1(0(0(z0))))), 1'(1(0(0(z0)))), 1'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> c8(1'(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))), 1'(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))))), 1'(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))), 1'(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))), 1'(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))), 1'(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))), 1'(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))), 0'(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))), 1'(0(0(2(0(0(0(2(0(0(1(z0))))))))))), 0'(0(2(0(0(0(2(0(0(1(z0)))))))))), 0'(2(0(0(0(2(0(0(1(z0))))))))), 2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> c9(0'(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))))), 2'(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))), 1'(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))), 0'(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))), 1'(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))), 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2'(1(2(2(1(1(0(z0))))))), 1'(2(2(1(1(0(z0)))))), 2'(2(1(1(0(z0))))), 2'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> c108(0'(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))), 1'(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))))), 1'(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))), 2'(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))), 1'(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))), 0'(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))), 0'(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))), 0'(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))), 1'(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))), 1'(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))), 2'(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))), 2'(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))), 0'(1(1(0(1(0(0(0(2(2(1(z0))))))))))), 1'(1(0(1(0(0(0(2(2(1(z0)))))))))), 1'(0(1(0(0(0(2(2(1(z0))))))))), 0'(1(0(0(0(2(2(1(z0)))))))), 1'(0(0(0(2(2(1(z0))))))), 0'(0(0(2(2(1(z0)))))), 0'(0(2(2(1(z0))))), 0'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> c109(1'(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))), 0'(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))))), 0'(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))), 2'(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))), 1'(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))), 2'(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))), 1'(1(2(2(1(1(2(1(0(1(1(z0))))))))))), 1'(2(2(1(1(2(1(0(1(1(z0)))))))))), 2'(2(1(1(2(1(0(1(1(z0))))))))), 2'(1(1(2(1(0(1(1(z0)))))))), 1'(1(2(1(0(1(1(z0))))))), 1'(2(1(0(1(1(z0)))))), 2'(1(0(1(1(z0))))), 1'(0(1(1(z0)))), 0'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> c110(0'(1(1(1(1(2(1(0(z0)))))))), 1'(1(1(1(2(1(0(z0))))))), 1'(1(1(2(1(0(z0)))))), 1'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> c111(1'(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))), 1'(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))))), 0'(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))), 1'(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))), 2'(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))), 1'(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))), 0'(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))), 1'(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))), 1'(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))), 2'(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))), 1'(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))), 0'(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))), 0'(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))), 2'(2(2(0(1(0(1(1(0(2(0(z0))))))))))), 2'(2(0(1(0(1(1(0(2(0(z0)))))))))), 2'(0(1(0(1(1(0(2(0(z0))))))))), 0'(1(0(1(1(0(2(0(z0)))))))), 1'(0(1(1(0(2(0(z0))))))), 0'(1(1(0(2(0(z0)))))), 1'(1(0(2(0(z0))))), 1'(0(2(0(z0)))), 0'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> c112(1'(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))), 2'(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))))), 2'(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))), 1'(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))), 1'(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))), 1'(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))), 1'(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))), 0'(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))), 1'(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))), 1'(1(1(0(1(1(1(0(0(1(0(z0))))))))))), 1'(1(0(1(1(1(0(0(1(0(z0)))))))))), 1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) ENCODE_0(z0) -> c6(0'(encArg(z0))) ENCODE_1(z0) -> c6(1'(encArg(z0))) ENCODE_2(z0) -> c6(2'(encArg(z0))) S tuples: 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(z0))))))))))), 1'(2(2(0(1(0(1(1(0(0(z0)))))))))), 2'(2(0(1(0(1(1(0(0(z0))))))))), 2'(0(1(0(1(1(0(0(z0)))))))), 0'(1(0(1(1(0(0(z0))))))), 1'(0(1(1(0(0(z0)))))), 0'(1(1(0(0(z0))))), 1'(1(0(0(z0)))), 1'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> c8(1'(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))), 1'(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))))), 1'(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))), 1'(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))), 1'(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))), 1'(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))), 1'(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))), 0'(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))), 1'(0(0(2(0(0(0(2(0(0(1(z0))))))))))), 0'(0(2(0(0(0(2(0(0(1(z0)))))))))), 0'(2(0(0(0(2(0(0(1(z0))))))))), 2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 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0'(1(0(1(1(0(2(1(2(0(z0)))))))))), 1'(0(1(1(0(2(1(2(0(z0))))))))), 0'(1(1(0(2(1(2(0(z0)))))))), 1'(1(0(2(1(2(0(z0))))))), 1'(0(2(1(2(0(z0)))))), 0'(2(1(2(0(z0))))), 2'(1(2(0(z0)))), 1'(2(0(z0))), 2'(0(z0)), 0'(z0)) 0'(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> c11(0'(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))), 2'(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))))), 2'(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))), 1'(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))), 1'(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))), 2'(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))), 2'(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))), 2'(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))), 1'(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))), 1'(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))), 1'(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))), 0'(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))), 0'(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))), 1'(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))), 2'(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))), 1'(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))), 2'(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))), 2'(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))), 1'(1(1(2(0(2(1(2(2(1(1(z0))))))))))), 1'(1(2(0(2(1(2(2(1(1(z0)))))))))), 1'(2(0(2(1(2(2(1(1(z0))))))))), 2'(0(2(1(2(2(1(1(z0)))))))), 0'(2(1(2(2(1(1(z0))))))), 2'(1(2(2(1(1(z0)))))), 1'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(c_0(c_1(c_0(c_0(z0))))) -> c12(0'(1(0(1(1(1(1(z0))))))), 1'(0(1(1(1(1(z0)))))), 0'(1(1(1(1(z0))))), 1'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(z0))))))))))))))))))))))))) -> c13(1'(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))))))), 0'(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0))))))))))))))))))))))))), 1'(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))))), 2'(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0))))))))))))))))))))))), 2'(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))), 0'(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0))))))))))))))))))))), 0'(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))), 0'(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0))))))))))))))))))), 1'(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))), 2'(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0))))))))))))))))), 0'(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))), 0'(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0))))))))))))))), 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1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(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, c7_28, c8_19, c9_29, c10_28, c11_29, c12_7, c13_26, c14_28, c15_24, c16_25, c17_16, c18_21, c19_12, c20_23, c21_27, c22_11, c23_27, c24_29, c25_29, c26_30, c27_17, c28_28, c29_20, c30_23, c31_30, c32_9, c33_14, c34_16, c35_17, c36_18, c37_23, c38_30, c39_29, c40_23, c41_20, c42_22, c43_28, c44_16, c45_16, c46_26, c47_16, c48_17, c49_23, c50_13, c51_19, c53_21, c54_28, c55_21, c56_24, c57_16, c58_20, c59_14, c60_8, c61_26, c62_30, c63_11, c64_23, c65_13, c66_25, c67_8, c68_26, c69_21, c70_21, c71_30, c72_24, c73_9, c74_22, c75_26, c76_18, c77_28, c78_26, c79_25, c80_21, c82_28, c83_27, c84_29, c85_15, c86_21, c87_30, c88_22, c89_23, c90_26, c91_15, c92_23, c93_14, c94_22, c95_25, c96_18, c97_23, c98_24, c99_27, c100_21, c101_24, c102_20, c103_29, c104_13, c105_15, c106_21, c107_28, c108_24, c109_17, c110_8, c111_24, c112_20, c113_17, c114_19, c115_24, c116_8, c117_12, c118_7, c6_1 ---------------------------------------- (47) 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))) ---------------------------------------- (48) 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(z0) -> c_0(z0) 0(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))) 0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))) 0(c_0(c_1(c_0(c_0(z0))))) -> 0(1(0(1(1(1(1(z0))))))) 0(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(z0))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(z0))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(z0)))))))))))))))))))))))))))) 0(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(z0)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(z0)))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(z0))))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(z0)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(z0)))))))))))))))) 0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(z0))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))))))) 0(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(z0))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(z0)))))))))))) 0(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(z0))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(z0))))))))))))))))))))))) 0(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(z0)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(z0))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_0(z0)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(z0))))))))))) 0(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(z0))))))))))))))))))))))))))) 0(c_2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_2(c_1(z0))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(z0))))))))))))))))))))))))))))) 0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_1(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_2(z0)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_2(z0)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(z0)))))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(z0))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(z0))))))))))))))))) 0(c_2(c_1(c_2(c_1(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_0(c_2(z0))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(z0)))))))))))))))))))))))))))) 0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_1(z0))))))))))))))))))) -> 1(1(2(2(1(2(2(1(1(1(2(2(0(1(0(1(0(2(1(1(z0)))))))))))))))))))) 0(c_1(c_1(c_0(c_2(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_0(c_0(c_2(c_2(c_2(z0)))))))))))))))))))))) -> 0(2(2(1(2(2(1(2(1(1(1(1(2(0(1(0(0(1(1(1(0(1(1(z0))))))))))))))))))))))) 0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_0(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_0(z0)))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(1(2(2(0(2(2(1(1(1(1(2(1(2(0(2(2(0(2(2(0(0(0(1(0(z0)))))))))))))))))))))))))))))) 0(c_0(c_0(c_1(c_2(c_2(c_0(c_0(z0)))))))) -> 0(1(1(1(1(0(0(2(2(z0))))))))) 0(c_1(c_1(c_1(c_0(c_1(c_2(c_2(c_1(c_0(c_0(c_0(c_0(z0))))))))))))) -> 0(1(1(1(2(1(2(0(1(1(1(1(1(1(z0)))))))))))))) 0(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(z0))))))))))))))) -> 1(2(2(2(2(1(0(0(1(0(0(1(1(2(1(0(z0)))))))))))))))) 0(c_0(c_0(c_0(c_1(c_2(c_0(c_2(c_0(c_1(c_1(c_2(c_2(c_0(c_0(c_2(z0)))))))))))))))) -> 0(2(1(2(2(0(1(1(1(1(2(1(1(0(0(2(1(z0))))))))))))))))) 0(c_1(c_0(c_1(c_2(c_2(c_2(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_2(z0))))))))))))))))) -> 1(1(0(1(2(1(1(2(2(1(0(2(1(0(1(1(1(0(z0)))))))))))))))))) 0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(z0)))))))))))))))))))))) -> 0(2(2(1(1(0(0(2(2(1(1(0(1(1(1(2(0(1(2(1(0(1(1(z0))))))))))))))))))))))) 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1(c_1(c_2(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_1(c_0(c_0(c_1(c_1(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_2(z0)))))))))))))))))))))))))) -> 0(1(1(2(1(2(2(2(2(1(1(1(1(1(0(1(0(2(1(0(0(1(1(1(1(1(z0)))))))))))))))))))))))))) 1(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_0(c_0(c_0(c_2(c_0(z0)))))))))))))))))))) -> 1(1(1(1(1(2(0(2(0(2(1(0(0(0(2(1(2(0(1(2(2(z0))))))))))))))))))))) 1(c_1(c_2(c_1(c_1(c_1(c_1(c_0(c_0(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_2(c_0(c_1(z0))))))))))))))))))))) -> 1(0(2(1(2(1(2(1(0(0(2(2(2(0(1(0(1(1(1(1(1(z0))))))))))))))))))))) 1(c_0(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_1(c_1(c_1(c_0(c_0(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 1(1(1(1(0(0(1(0(1(1(0(1(1(2(1(1(2(0(1(2(1(0(0(1(2(1(2(2(2(2(z0)))))))))))))))))))))))))))))) 1(c_2(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_0(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_2(z0)))))))))))))))))))))) -> 1(1(1(2(2(2(1(0(1(1(0(2(0(1(0(1(2(0(0(0(1(1(1(0(z0)))))))))))))))))))))))) 1(c_2(c_2(c_0(c_1(c_2(z0)))))) -> 1(1(1(1(1(0(1(1(0(z0))))))))) 1(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_0(c_0(z0)))))))))))))))))))))) -> 1(0(1(1(1(0(2(1(2(0(0(0(0(2(1(2(2(0(2(2(2(0(z0)))))))))))))))))))))) 1(c_0(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_2(z0))))))))))))))))))))))) -> 1(1(1(2(2(2(1(2(2(2(1(0(1(0(1(1(1(0(0(1(2(0(0(2(0(2(z0)))))))))))))))))))))))))) 1(c_0(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(z0))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(z0)))))))))))))))))) 1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_2(c_1(z0))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(z0)))))))))))))))))))))))))))) 1(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(z0))))))))))))))))))))))))) -> 1(1(0(1(0(2(0(0(1(2(1(1(1(1(1(0(0(2(2(1(0(2(2(1(2(2(z0)))))))))))))))))))))))))) 1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_2(c_0(z0))))))))))))))))))))))) -> 1(0(2(2(0(2(1(1(1(1(1(0(1(1(1(1(0(2(0(2(2(2(1(1(2(z0))))))))))))))))))))))))) 1(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(z0)))))))))))))))))) -> 2(1(0(1(2(1(1(2(1(1(1(1(0(2(0(1(0(1(1(1(0(z0))))))))))))))))))))) 2(z0) -> c_2(z0) 2(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(z0))))))))))))))))))))))))) -> 1(0(0(1(2(1(1(0(1(0(1(1(1(0(1(2(2(2(1(2(2(2(2(1(2(1(1(1(z0)))))))))))))))))))))))))))) 2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(z0))))))))))))))))))))))))) -> 1(0(0(0(2(1(1(1(1(1(1(0(0(1(0(1(2(0(2(1(2(1(1(0(1(2(0(z0))))))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_0(c_2(z0)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(z0))))))))))))))))))))))))))))) 2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(z0))))))))))))))) 2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(z0)))))))))))))))))) -> 1(2(1(0(1(1(2(1(1(0(2(2(1(1(1(1(0(2(0(2(1(z0))))))))))))))))))))) 2(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(z0)))))))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_1(z0))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(2(0(1(1(1(1(1(0(0(2(0(1(1(z0)))))))))))))))))))))) 2(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(z0)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(z0))))))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(z0))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(z0)))))))))))))))))))))))))) 2(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(z0))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(z0))))))))))))))) 2(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(z0))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(z0))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(z0))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(z0)))))))))))))) 2(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(z0))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(z0)))))))))))))))))))))) 2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(z0))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(z0))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(z0)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(z0)))))))))))))))))) 2(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(z0))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(z0))))))))))))))))))))))) 2(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_1(c_2(c_1(z0)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(z0)))))))))))))))))))))))) 2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(z0)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(z0))))))))))))))))))))))))))) 2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_0(z0)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(z0))))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_2(z0)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(z0)))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_2(c_1(z0))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(z0)))))))))))))))))))) 2(c_0(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_2(c_0(z0)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(z0))))))))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(c_2(c_2(c_2(z0)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(z0))))))))))))) 2(c_2(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_2(z0)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(z0))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_2(z0))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))))))))) 2(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(z0))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))))) 2(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))) 2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))) 2(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> 0(1(1(1(1(2(1(0(z0)))))))) 2(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))) 2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))) 2(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))) 2(c_0(c_2(c_0(c_1(c_0(z0)))))) -> 1(1(0(1(1(1(1(0(z0)))))))) 2(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))) 2(c_0(c_2(c_2(c_1(c_2(z0)))))) -> 1(1(0(0(1(1(2(z0))))))) Tuples: ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(2'(encArg(z0)), ENCARG(z0)) 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 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0'(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))), 1'(0(0(2(0(0(0(2(0(0(1(z0))))))))))), 0'(0(2(0(0(0(2(0(0(1(z0)))))))))), 0'(2(0(0(0(2(0(0(1(z0))))))))), 2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> c9(0'(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))))), 2'(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))), 1'(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))), 0'(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))), 1'(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))), 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0'(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))))), 1'(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))), 1'(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))), 1'(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))), 1'(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))), 2'(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))), 1'(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))), 1'(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))), 1'(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))), 1'(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))), 2'(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))), 1'(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))), 2'(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))), 0'(0(2(2(2(1(2(2(1(1(0(z0))))))))))), 0'(2(2(2(1(2(2(1(1(0(z0)))))))))), 2'(2(2(1(2(2(1(1(0(z0))))))))), 2'(2(1(2(2(1(1(0(z0)))))))), 2'(1(2(2(1(1(0(z0))))))), 1'(2(2(1(1(0(z0)))))), 2'(2(1(1(0(z0))))), 2'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> c108(0'(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))), 1'(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))))), 1'(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))), 2'(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))), 1'(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))), 0'(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))), 0'(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))), 0'(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))), 1'(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))), 1'(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))), 2'(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))), 2'(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))), 0'(1(1(0(1(0(0(0(2(2(1(z0))))))))))), 1'(1(0(1(0(0(0(2(2(1(z0)))))))))), 1'(0(1(0(0(0(2(2(1(z0))))))))), 0'(1(0(0(0(2(2(1(z0)))))))), 1'(0(0(0(2(2(1(z0))))))), 0'(0(0(2(2(1(z0)))))), 0'(0(2(2(1(z0))))), 0'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> c109(1'(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))), 0'(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))))), 0'(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))), 2'(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))), 1'(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))), 2'(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))), 1'(1(2(2(1(1(2(1(0(1(1(z0))))))))))), 1'(2(2(1(1(2(1(0(1(1(z0)))))))))), 2'(2(1(1(2(1(0(1(1(z0))))))))), 2'(1(1(2(1(0(1(1(z0)))))))), 1'(1(2(1(0(1(1(z0))))))), 1'(2(1(0(1(1(z0)))))), 2'(1(0(1(1(z0))))), 1'(0(1(1(z0)))), 0'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> c110(0'(1(1(1(1(2(1(0(z0)))))))), 1'(1(1(1(2(1(0(z0))))))), 1'(1(1(2(1(0(z0)))))), 1'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> c111(1'(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))), 1'(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))))), 0'(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))), 1'(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))), 2'(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))), 1'(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))), 0'(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))), 1'(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))), 1'(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))), 2'(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))), 1'(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))), 0'(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))), 0'(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))), 2'(2(2(0(1(0(1(1(0(2(0(z0))))))))))), 2'(2(0(1(0(1(1(0(2(0(z0)))))))))), 2'(0(1(0(1(1(0(2(0(z0))))))))), 0'(1(0(1(1(0(2(0(z0)))))))), 1'(0(1(1(0(2(0(z0))))))), 0'(1(1(0(2(0(z0)))))), 1'(1(0(2(0(z0))))), 1'(0(2(0(z0)))), 0'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> c112(1'(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))), 2'(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))))), 2'(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))), 1'(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))), 1'(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))), 1'(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))), 1'(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))), 0'(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))), 1'(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))), 1'(1(1(0(1(1(1(0(0(1(0(z0))))))))))), 1'(1(0(1(1(1(0(0(1(0(z0)))))))))), 1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) ENCODE_0(z0) -> c6(0'(encArg(z0))) ENCODE_1(z0) -> c6(1'(encArg(z0))) ENCODE_2(z0) -> c6(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'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(z0))))))))))), 1'(2(2(0(1(0(1(1(0(0(z0)))))))))), 2'(2(0(1(0(1(1(0(0(z0))))))))), 2'(0(1(0(1(1(0(0(z0)))))))), 0'(1(0(1(1(0(0(z0))))))), 1'(0(1(1(0(0(z0)))))), 0'(1(1(0(0(z0))))), 1'(1(0(0(z0)))), 1'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> c8(1'(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))), 1'(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))))), 1'(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))), 1'(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))), 1'(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))), 1'(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))), 1'(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))), 0'(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))), 1'(0(0(2(0(0(0(2(0(0(1(z0))))))))))), 0'(0(2(0(0(0(2(0(0(1(z0)))))))))), 0'(2(0(0(0(2(0(0(1(z0))))))))), 2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> c9(0'(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))))), 2'(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))), 1'(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))), 0'(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))), 1'(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))), 2'(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))), 1'(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))), 1'(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))), 1'(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))), 2'(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))), 2'(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))), 2'(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))), 2'(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))), 0'(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))), 0'(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))), 0'(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))), 2'(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))), 2'(1(1(1(2(0(0(0(2(1(2(z0))))))))))), 1'(1(1(2(0(0(0(2(1(2(z0)))))))))), 1'(1(2(0(0(0(2(1(2(z0))))))))), 1'(2(0(0(0(2(1(2(z0)))))))), 2'(0(0(0(2(1(2(z0))))))), 0'(0(0(2(1(2(z0)))))), 0'(0(2(1(2(z0))))), 0'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) 0'(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> c10(1'(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))), 2'(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))))))), 0'(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))), 2'(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))))), 1'(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))), 2'(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))), 1'(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))), 1'(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))), 0'(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))), 1'(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))), 1'(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))), 2'(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))), 0'(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))), 2'(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))), 0'(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))), 0'(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))), 0'(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))), 1'(0(1(0(1(1(0(2(1(2(0(z0))))))))))), 0'(1(0(1(1(0(2(1(2(0(z0)))))))))), 1'(0(1(1(0(2(1(2(0(z0))))))))), 0'(1(1(0(2(1(2(0(z0)))))))), 1'(1(0(2(1(2(0(z0))))))), 1'(0(2(1(2(0(z0)))))), 0'(2(1(2(0(z0))))), 2'(1(2(0(z0)))), 1'(2(0(z0))), 2'(0(z0)), 0'(z0)) 0'(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> c11(0'(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))), 2'(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))))), 2'(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))), 1'(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))), 1'(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))), 2'(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))), 2'(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))), 2'(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))), 1'(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))), 1'(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))), 1'(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))), 0'(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))), 0'(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))), 1'(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))), 2'(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))), 1'(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))), 2'(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))), 2'(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))), 1'(1(1(2(0(2(1(2(2(1(1(z0))))))))))), 1'(1(2(0(2(1(2(2(1(1(z0)))))))))), 1'(2(0(2(1(2(2(1(1(z0))))))))), 2'(0(2(1(2(2(1(1(z0)))))))), 0'(2(1(2(2(1(1(z0))))))), 2'(1(2(2(1(1(z0)))))), 1'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 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0'(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))), 0'(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))), 2'(2(2(0(1(0(1(1(0(2(0(z0))))))))))), 2'(2(0(1(0(1(1(0(2(0(z0)))))))))), 2'(0(1(0(1(1(0(2(0(z0))))))))), 0'(1(0(1(1(0(2(0(z0)))))))), 1'(0(1(1(0(2(0(z0))))))), 0'(1(1(0(2(0(z0)))))), 1'(1(0(2(0(z0))))), 1'(0(2(0(z0)))), 0'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> c112(1'(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))), 2'(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))))), 2'(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))), 1'(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))), 1'(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))), 1'(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))), 1'(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))), 0'(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))), 1'(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))), 1'(1(1(0(1(1(1(0(0(1(0(z0))))))))))), 1'(1(0(1(1(1(0(0(1(0(z0)))))))))), 1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(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, c7_28, c8_19, c9_29, c10_28, c11_29, c12_7, c13_26, c14_28, c15_24, c16_25, c17_16, c18_21, c19_12, c20_23, c21_27, c22_11, c23_27, c24_29, c25_29, c26_30, c27_17, c28_28, c29_20, c30_23, c31_30, c32_9, c33_14, c34_16, c35_17, c36_18, c37_23, c38_30, c39_29, c40_23, c41_20, c42_22, c43_28, c44_16, c45_16, c46_26, c47_16, c48_17, c49_23, c50_13, c51_19, c53_21, c54_28, c55_21, c56_24, c57_16, c58_20, c59_14, c60_8, c61_26, c62_30, c63_11, c64_23, c65_13, c66_25, c67_8, c68_26, c69_21, c70_21, c71_30, c72_24, c73_9, c74_22, c75_26, c76_18, c77_28, c78_26, c79_25, c80_21, c82_28, c83_27, c84_29, c85_15, c86_21, c87_30, c88_22, c89_23, c90_26, c91_15, c92_23, c93_14, c94_22, c95_25, c96_18, c97_23, c98_24, c99_27, c100_21, c101_24, c102_20, c103_29, c104_13, c105_15, c106_21, c107_28, c108_24, c109_17, c110_8, c111_24, c112_20, c113_17, c114_19, c115_24, c116_8, c117_12, c118_7, c6_1, c_2 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) by ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(1'(2(encArg(z0))), ENCARG(cons_2(z0))) ---------------------------------------- (50) 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(z0) -> c_0(z0) 0(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))) 0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))) 0(c_0(c_1(c_0(c_0(z0))))) -> 0(1(0(1(1(1(1(z0))))))) 0(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(z0))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(z0))))))))))))))))))))))))))) -> 2(2(1(1(0(2(1(1(1(2(1(2(2(2(2(1(0(1(0(1(1(1(2(0(2(2(1(1(z0)))))))))))))))))))))))))))) 0(c_2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_1(c_0(z0)))))))))))))))))))) -> 0(1(2(0(1(2(1(1(1(1(0(0(1(1(0(2(1(1(1(1(1(1(0(1(z0)))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(z0))))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(z0)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(z0)))))))))))))))) 0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(z0))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))))))) 0(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(z0))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(z0)))))))))))) 0(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(z0))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(z0))))))))))))))))))))))) 0(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(z0)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(z0))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_0(z0)))))))))) -> 1(1(1(1(0(0(2(1(0(2(1(z0))))))))))) 0(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 2(0(0(0(0(1(1(1(1(1(0(2(1(1(1(0(2(2(2(2(2(2(0(1(0(0(0(z0))))))))))))))))))))))))))) 0(c_2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_1(c_1(c_2(c_0(c_2(c_1(z0))))))))))))))))))))))))))))) -> 0(2(2(0(2(1(1(1(1(2(0(0(2(1(2(2(1(0(0(1(2(2(1(1(0(2(2(2(1(z0))))))))))))))))))))))))))))) 0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_1(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_2(z0)))))))))))))))))))))))))))) -> 1(2(0(0(0(1(2(0(1(1(1(1(1(0(0(2(1(2(2(2(2(0(0(0(0(0(2(2(1(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_2(c_1(c_2(c_2(c_0(c_2(z0)))))))))))))))))))))))))))) -> 0(1(1(0(0(2(1(0(2(1(0(1(2(1(2(0(2(0(2(1(0(1(2(0(1(1(1(1(1(1(z0)))))))))))))))))))))))))))))) 0(c_1(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(z0))))))))))))))) -> 0(2(2(2(1(1(1(1(2(1(0(2(0(1(1(1(0(z0))))))))))))))))) 0(c_2(c_1(c_2(c_1(c_2(c_2(c_0(c_2(c_1(c_0(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_0(c_2(z0))))))))))))))))))))))))))) -> 0(1(2(1(1(2(1(0(2(1(1(1(1(1(2(1(2(0(1(0(1(1(0(2(1(0(1(0(z0)))))))))))))))))))))))))))) 0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_2(c_2(c_1(z0))))))))))))))))))) -> 1(1(2(2(1(2(2(1(1(1(2(2(0(1(0(1(0(2(1(1(z0)))))))))))))))))))) 0(c_1(c_1(c_0(c_2(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_0(c_0(c_2(c_2(c_2(z0)))))))))))))))))))))) -> 0(2(2(1(2(2(1(2(1(1(1(1(2(0(1(0(0(1(1(1(0(1(1(z0))))))))))))))))))))))) 0(c_1(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_2(c_0(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_0(z0)))))))))))))))))))))))))))))) -> 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1(c_2(c_2(c_0(c_1(c_2(z0)))))) -> 1(1(1(1(1(0(1(1(0(z0))))))))) 1(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_1(c_0(c_2(c_2(c_2(c_0(c_0(z0)))))))))))))))))))))) -> 1(0(1(1(1(0(2(1(2(0(0(0(0(2(1(2(2(0(2(2(2(0(z0)))))))))))))))))))))) 1(c_0(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(c_2(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_2(z0))))))))))))))))))))))) -> 1(1(1(2(2(2(1(2(2(2(1(0(1(0(1(1(1(0(0(1(2(0(0(2(0(2(z0)))))))))))))))))))))))))) 1(c_0(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_1(c_2(z0))))))))))))) -> 1(1(1(1(1(0(1(2(1(2(1(0(1(1(0(0(1(1(z0)))))))))))))))))) 1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_0(c_2(c_0(c_2(c_1(z0))))))))))))))))))))))))))) -> 1(0(1(2(2(1(2(0(2(0(0(0(1(1(2(2(1(1(1(1(1(1(0(0(2(1(1(0(z0)))))))))))))))))))))))))))) 1(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_0(c_1(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(z0))))))))))))))))))))))))) -> 1(1(0(1(0(2(0(0(1(2(1(1(1(1(1(0(0(2(2(1(0(2(2(1(2(2(z0)))))))))))))))))))))))))) 1(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_2(c_0(z0))))))))))))))))))))))) -> 1(0(2(2(0(2(1(1(1(1(1(0(1(1(1(1(0(2(0(2(2(2(1(1(2(z0))))))))))))))))))))))))) 1(c_2(c_2(c_2(c_0(c_0(c_0(c_0(c_0(c_1(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(z0)))))))))))))))))) -> 2(1(0(1(2(1(1(2(1(1(1(1(0(2(0(1(0(1(1(1(0(z0))))))))))))))))))))) 2(z0) -> c_2(z0) 2(c_2(c_0(c_2(c_2(c_0(c_0(c_1(c_2(c_0(c_1(c_1(c_0(c_1(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_1(z0))))))))))))))))))))))))) -> 1(0(0(1(2(1(1(0(1(0(1(1(1(0(1(2(2(2(1(2(2(2(2(1(2(1(1(1(z0)))))))))))))))))))))))))))) 2(c_2(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_1(c_0(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(z0))))))))))))))))))))))))) -> 1(0(0(0(2(1(1(1(1(1(1(0(0(1(0(1(2(0(2(1(2(1(1(0(1(2(0(z0))))))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_1(c_0(c_2(c_1(c_0(c_2(c_1(c_0(c_0(c_2(c_0(c_1(c_2(c_1(c_0(c_2(c_0(c_2(z0)))))))))))))))))))))))))))) -> 0(2(2(2(0(0(0(1(0(1(1(2(2(0(0(0(1(2(2(2(2(0(2(2(1(2(2(1(2(z0))))))))))))))))))))))))))))) 2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0)))))))))))))) -> 1(2(2(0(0(2(2(1(0(1(1(1(1(2(0(z0))))))))))))))) 2(c_2(c_1(c_2(c_2(c_2(c_0(c_1(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(z0)))))))))))))))))) -> 1(2(1(0(1(1(2(1(1(0(2(2(1(1(1(1(0(2(0(2(1(z0))))))))))))))))))))) 2(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 2(2(2(0(1(2(2(2(2(1(1(2(2(0(0(2(2(2(1(1(1(2(0(1(0(1(1(2(2(0(z0)))))))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_1(c_2(c_0(c_1(c_2(c_1(c_0(c_1(z0))))))))))))))))))) -> 2(0(1(0(0(1(2(0(2(2(0(1(1(1(1(1(0(0(2(0(1(1(z0)))))))))))))))))))))) 2(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(z0)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(z0))))))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(z0))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(z0)))))))))))))))))))))))))) 2(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(z0))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(z0))))))))))))))) 2(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(z0))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(z0))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(z0))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(z0)))))))))))))) 2(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(z0))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(z0)))))))))))))))))))))) 2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(z0))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(z0))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(z0)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(z0)))))))))))))))))) 2(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(z0))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(z0))))))))))))))))))))))) 2(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_1(c_2(c_1(z0)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(z0)))))))))))))))))))))))) 2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(z0)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(z0))))))))))))))))))))))))))) 2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_0(z0)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(z0))))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_2(z0)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(z0)))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_2(c_1(z0))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(z0)))))))))))))))))))) 2(c_0(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_2(c_0(z0)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(z0))))))))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(c_2(c_2(c_2(z0)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(z0))))))))))))) 2(c_2(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_2(z0)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(z0))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_2(z0))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))))))))) 2(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(z0))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))))) 2(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))) 2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))) 2(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> 0(1(1(1(1(2(1(0(z0)))))))) 2(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))) 2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))) 2(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))) 2(c_0(c_2(c_0(c_1(c_0(z0)))))) -> 1(1(0(1(1(1(1(0(z0)))))))) 2(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))) 2(c_0(c_2(c_2(c_1(c_2(z0)))))) -> 1(1(0(0(1(1(2(z0))))))) Tuples: ENCARG(cons_2(z0)) -> c2(2'(encArg(z0)), ENCARG(z0)) 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(z0))))))))))), 1'(2(2(0(1(0(1(1(0(0(z0)))))))))), 2'(2(0(1(0(1(1(0(0(z0))))))))), 2'(0(1(0(1(1(0(0(z0)))))))), 0'(1(0(1(1(0(0(z0))))))), 1'(0(1(1(0(0(z0)))))), 0'(1(1(0(0(z0))))), 1'(1(0(0(z0)))), 1'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> c8(1'(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))), 1'(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))))), 1'(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))), 1'(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))), 1'(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))), 1'(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))), 1'(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))), 0'(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))), 1'(0(0(2(0(0(0(2(0(0(1(z0))))))))))), 0'(0(2(0(0(0(2(0(0(1(z0)))))))))), 0'(2(0(0(0(2(0(0(1(z0))))))))), 2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> c9(0'(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))))), 2'(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))), 1'(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))), 0'(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))), 1'(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))), 2'(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))), 1'(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))), 1'(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))), 1'(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))), 2'(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))), 2'(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))), 2'(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))), 2'(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))), 0'(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))), 0'(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))), 0'(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))), 2'(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))), 2'(1(1(1(2(0(0(0(2(1(2(z0))))))))))), 1'(1(1(2(0(0(0(2(1(2(z0)))))))))), 1'(1(2(0(0(0(2(1(2(z0))))))))), 1'(2(0(0(0(2(1(2(z0)))))))), 2'(0(0(0(2(1(2(z0))))))), 0'(0(0(2(1(2(z0)))))), 0'(0(2(1(2(z0))))), 0'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) 0'(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> c10(1'(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))), 2'(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))))))), 0'(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))), 2'(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))))), 1'(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))), 2'(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))), 1'(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))), 1'(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))), 0'(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))), 1'(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))), 1'(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))), 2'(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))), 0'(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))), 2'(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))), 0'(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))), 0'(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))), 0'(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))), 1'(0(1(0(1(1(0(2(1(2(0(z0))))))))))), 0'(1(0(1(1(0(2(1(2(0(z0)))))))))), 1'(0(1(1(0(2(1(2(0(z0))))))))), 0'(1(1(0(2(1(2(0(z0)))))))), 1'(1(0(2(1(2(0(z0))))))), 1'(0(2(1(2(0(z0)))))), 0'(2(1(2(0(z0))))), 2'(1(2(0(z0)))), 1'(2(0(z0))), 2'(0(z0)), 0'(z0)) 0'(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> c11(0'(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))), 2'(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))))), 2'(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))), 1'(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))), 1'(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))), 2'(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))), 2'(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))), 2'(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))), 1'(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))), 1'(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))), 1'(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))), 0'(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))), 0'(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))), 1'(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))), 2'(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))), 1'(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))), 2'(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))), 2'(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))), 1'(1(1(2(0(2(1(2(2(1(1(z0))))))))))), 1'(1(2(0(2(1(2(2(1(1(z0)))))))))), 1'(2(0(2(1(2(2(1(1(z0))))))))), 2'(0(2(1(2(2(1(1(z0)))))))), 0'(2(1(2(2(1(1(z0))))))), 2'(1(2(2(1(1(z0)))))), 1'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(c_0(c_1(c_0(c_0(z0))))) -> c12(0'(1(0(1(1(1(1(z0))))))), 1'(0(1(1(1(1(z0)))))), 0'(1(1(1(1(z0))))), 1'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(z0))))))))))))))))))))))))) -> c13(1'(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))))))), 0'(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0))))))))))))))))))))))))), 1'(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))))), 2'(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0))))))))))))))))))))))), 2'(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))), 0'(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0))))))))))))))))))))), 0'(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))), 0'(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0))))))))))))))))))), 1'(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))), 2'(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0))))))))))))))))), 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1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) ENCODE_0(z0) -> c6(0'(encArg(z0))) ENCODE_1(z0) -> c6(1'(encArg(z0))) ENCODE_2(z0) -> c6(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))) ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(1'(2(encArg(z0))), ENCARG(cons_2(z0))) S tuples: 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(z0))))))))))), 1'(2(2(0(1(0(1(1(0(0(z0)))))))))), 2'(2(0(1(0(1(1(0(0(z0))))))))), 2'(0(1(0(1(1(0(0(z0)))))))), 0'(1(0(1(1(0(0(z0))))))), 1'(0(1(1(0(0(z0)))))), 0'(1(1(0(0(z0))))), 1'(1(0(0(z0)))), 1'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> c8(1'(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))), 1'(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))))), 1'(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))), 1'(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))), 1'(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))), 1'(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))), 1'(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))), 0'(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))), 1'(0(0(2(0(0(0(2(0(0(1(z0))))))))))), 0'(0(2(0(0(0(2(0(0(1(z0)))))))))), 0'(2(0(0(0(2(0(0(1(z0))))))))), 2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> c9(0'(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))))), 2'(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))), 1'(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))), 0'(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))), 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1'(2(0(1(1(1(2(2(1(1(0(z0))))))))))), 2'(0(1(1(1(2(2(1(1(0(z0)))))))))), 0'(1(1(1(2(2(1(1(0(z0))))))))), 1'(1(1(2(2(1(1(0(z0)))))))), 1'(1(2(2(1(1(0(z0))))))), 1'(2(2(1(1(0(z0)))))), 2'(2(1(1(0(z0))))), 2'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 0'(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(z0))))))))))))))))))) -> c18(2'(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))))))), 0'(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0)))))))))))))))))))), 0'(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))))), 1'(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0)))))))))))))))))), 2'(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))), 2'(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0)))))))))))))))), 1'(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))), 0'(2(2(1(2(1(1(1(0(0(1(1(1(0(z0)))))))))))))), 2'(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))), 2'(1(2(1(1(1(0(0(1(1(1(0(z0)))))))))))), 1'(2(1(1(1(0(0(1(1(1(0(z0))))))))))), 2'(1(1(1(0(0(1(1(1(0(z0)))))))))), 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2'(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))), 0'(1(1(0(1(0(0(0(2(2(1(z0))))))))))), 1'(1(0(1(0(0(0(2(2(1(z0)))))))))), 1'(0(1(0(0(0(2(2(1(z0))))))))), 0'(1(0(0(0(2(2(1(z0)))))))), 1'(0(0(0(2(2(1(z0))))))), 0'(0(0(2(2(1(z0)))))), 0'(0(2(2(1(z0))))), 0'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> c109(1'(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))), 0'(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))))), 0'(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))), 2'(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))), 1'(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))), 2'(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))), 1'(1(2(2(1(1(2(1(0(1(1(z0))))))))))), 1'(2(2(1(1(2(1(0(1(1(z0)))))))))), 2'(2(1(1(2(1(0(1(1(z0))))))))), 2'(1(1(2(1(0(1(1(z0)))))))), 1'(1(2(1(0(1(1(z0))))))), 1'(2(1(0(1(1(z0)))))), 2'(1(0(1(1(z0))))), 1'(0(1(1(z0)))), 0'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> c110(0'(1(1(1(1(2(1(0(z0)))))))), 1'(1(1(1(2(1(0(z0))))))), 1'(1(1(2(1(0(z0)))))), 1'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> c111(1'(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))), 1'(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))))), 0'(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))), 1'(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))), 2'(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))), 1'(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))), 0'(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))), 1'(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))), 1'(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))), 2'(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))), 1'(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))), 0'(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))), 0'(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))), 2'(2(2(0(1(0(1(1(0(2(0(z0))))))))))), 2'(2(0(1(0(1(1(0(2(0(z0)))))))))), 2'(0(1(0(1(1(0(2(0(z0))))))))), 0'(1(0(1(1(0(2(0(z0)))))))), 1'(0(1(1(0(2(0(z0))))))), 0'(1(1(0(2(0(z0)))))), 1'(1(0(2(0(z0))))), 1'(0(2(0(z0)))), 0'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> c112(1'(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))), 2'(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))))), 2'(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))), 1'(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))), 1'(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))), 1'(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))), 1'(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))), 0'(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))), 1'(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))), 1'(1(1(0(1(1(1(0(0(1(0(z0))))))))))), 1'(1(0(1(1(1(0(0(1(0(z0)))))))))), 1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(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: c2_2, c7_28, c8_19, c9_29, c10_28, c11_29, c12_7, c13_26, c14_28, c15_24, c16_25, c17_16, c18_21, c19_12, c20_23, c21_27, c22_11, c23_27, c24_29, c25_29, c26_30, c27_17, c28_28, c29_20, c30_23, c31_30, c32_9, c33_14, c34_16, c35_17, c36_18, c37_23, c38_30, c39_29, c40_23, c41_20, c42_22, c43_28, c44_16, c45_16, c46_26, c47_16, c48_17, c49_23, c50_13, c51_19, c53_21, c54_28, c55_21, c56_24, c57_16, c58_20, c59_14, c60_8, c61_26, c62_30, c63_11, c64_23, c65_13, c66_25, c67_8, c68_26, c69_21, c70_21, c71_30, c72_24, c73_9, c74_22, c75_26, c76_18, c77_28, c78_26, c79_25, c80_21, c82_28, c83_27, c84_29, c85_15, c86_21, c87_30, c88_22, c89_23, c90_26, c91_15, c92_23, c93_14, c94_22, c95_25, c96_18, c97_23, c98_24, c99_27, c100_21, c101_24, c102_20, c103_29, c104_13, c105_15, c106_21, c107_28, c108_24, c109_17, c110_8, c111_24, c112_20, c113_17, c114_19, c115_24, c116_8, c117_12, c118_7, c6_1, c_2, c1_2 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_2(z0)) -> c2(2'(encArg(z0)), ENCARG(z0)) by ENCARG(cons_2(cons_0(z0))) -> c2(2'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_2(cons_1(z0))) -> c2(2'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_2(cons_2(z0))) -> c2(2'(2(encArg(z0))), ENCARG(cons_2(z0))) ---------------------------------------- (52) 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(z0) -> c_0(z0) 0(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> 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0(c_0(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(c_2(c_2(c_0(c_1(c_1(c_1(c_2(c_1(c_2(c_0(c_2(c_1(c_2(z0)))))))))))))))))))))))) -> 0(1(1(0(1(1(2(0(1(2(1(2(0(1(1(1(1(2(2(0(0(0(1(1(1(z0))))))))))))))))))))))))) 0(c_0(c_1(c_1(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_1(c_1(c_0(z0)))))))))))))) -> 2(1(0(1(1(1(2(0(1(1(1(2(2(1(1(0(z0)))))))))))))))) 0(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_1(c_0(c_2(c_2(z0))))))))))))))))))) -> 2(0(0(1(2(2(1(0(2(2(1(2(1(1(1(0(0(1(1(1(0(z0))))))))))))))))))))) 0(c_0(c_1(c_2(c_2(c_0(c_1(c_0(c_2(z0))))))))) -> 2(1(1(1(1(1(2(1(1(1(0(2(z0)))))))))))) 0(c_0(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_1(c_0(c_1(c_2(c_0(c_1(c_1(c_2(c_0(c_0(c_0(z0))))))))))))))))))))))) -> 0(1(0(1(0(0(2(2(0(0(2(1(1(0(0(2(0(2(0(1(1(0(0(z0))))))))))))))))))))))) 0(c_1(c_2(c_1(c_1(c_0(c_2(c_1(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_1(c_2(z0)))))))))))))))))))))))))) -> 1(1(2(2(0(1(0(1(1(2(1(0(2(1(1(2(2(1(2(1(1(1(2(1(0(1(1(z0))))))))))))))))))))))))))) 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2(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(z0)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(z0))))))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(z0))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(z0)))))))))))))))))))))))))) 2(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(z0))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(z0))))))))))))))) 2(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(z0))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(z0))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(z0))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(z0)))))))))))))) 2(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(z0))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(z0)))))))))))))))))))))) 2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(z0))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(z0))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(z0)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(z0)))))))))))))))))) 2(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(z0))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(z0))))))))))))))))))))))) 2(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_1(c_2(c_1(z0)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(z0)))))))))))))))))))))))) 2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(z0)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(z0))))))))))))))))))))))))))) 2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_0(z0)))))))))))))))))) -> 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1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))) 2(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))) 2(c_0(c_2(c_0(c_1(c_0(z0)))))) -> 1(1(0(1(1(1(1(0(z0)))))))) 2(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))) 2(c_0(c_2(c_2(c_1(c_2(z0)))))) -> 1(1(0(0(1(1(2(z0))))))) Tuples: 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> 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2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> c9(0'(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))))), 2'(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))), 1'(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))), 0'(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))), 1'(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))), 2'(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))), 1'(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))), 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0'(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))), 0'(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))), 0'(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))), 1'(0(1(0(1(1(0(2(1(2(0(z0))))))))))), 0'(1(0(1(1(0(2(1(2(0(z0)))))))))), 1'(0(1(1(0(2(1(2(0(z0))))))))), 0'(1(1(0(2(1(2(0(z0)))))))), 1'(1(0(2(1(2(0(z0))))))), 1'(0(2(1(2(0(z0)))))), 0'(2(1(2(0(z0))))), 2'(1(2(0(z0)))), 1'(2(0(z0))), 2'(0(z0)), 0'(z0)) 0'(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> c11(0'(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))), 2'(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))))), 2'(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))), 1'(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))), 1'(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))), 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1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) ENCODE_0(z0) -> c6(0'(encArg(z0))) ENCODE_1(z0) -> c6(1'(encArg(z0))) ENCODE_2(z0) -> c6(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))) ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(1'(2(encArg(z0))), ENCARG(cons_2(z0))) ENCARG(cons_2(cons_0(z0))) -> c2(2'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_2(cons_1(z0))) -> c2(2'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_2(cons_2(z0))) -> c2(2'(2(encArg(z0))), ENCARG(cons_2(z0))) S tuples: 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(z0))))))))))), 1'(2(2(0(1(0(1(1(0(0(z0)))))))))), 2'(2(0(1(0(1(1(0(0(z0))))))))), 2'(0(1(0(1(1(0(0(z0)))))))), 0'(1(0(1(1(0(0(z0))))))), 1'(0(1(1(0(0(z0)))))), 0'(1(1(0(0(z0))))), 1'(1(0(0(z0)))), 1'(0(0(z0))), 0'(0(z0)), 0'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> c8(1'(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))), 1'(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))))), 1'(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))), 1'(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))), 1'(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))), 1'(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))), 1'(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))), 0'(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))), 1'(0(0(2(0(0(0(2(0(0(1(z0))))))))))), 0'(0(2(0(0(0(2(0(0(1(z0)))))))))), 0'(2(0(0(0(2(0(0(1(z0))))))))), 2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> c9(0'(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))))), 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1'(1(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(z0))))))))))))))))), 1'(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(z0)))))))))))))))), 1'(2(1(0(1(2(0(1(0(2(0(1(0(1(1(z0))))))))))))))), 2'(1(0(1(2(0(1(0(2(0(1(0(1(1(z0)))))))))))))), 1'(0(1(2(0(1(0(2(0(1(0(1(1(z0))))))))))))), 0'(1(2(0(1(0(2(0(1(0(1(1(z0)))))))))))), 1'(2(0(1(0(2(0(1(0(1(1(z0))))))))))), 2'(0(1(0(2(0(1(0(1(1(z0)))))))))), 0'(1(0(2(0(1(0(1(1(z0))))))))), 1'(0(2(0(1(0(1(1(z0)))))))), 0'(2(0(1(0(1(1(z0))))))), 2'(0(1(0(1(1(z0)))))), 0'(1(0(1(1(z0))))), 1'(0(1(1(z0)))), 0'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_0(z0)))))))))))))))))) -> c41(0'(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(z0)))))))))))))))))))), 1'(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(z0))))))))))))))))))), 1'(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(z0)))))))))))))))))), 1'(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(z0))))))))))))))))), 2'(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(z0)))))))))))))))), 1'(2(1(1(0(0(1(1(0(0(0(1(0(2(2(z0))))))))))))))), 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2'(2(2(2(0(1(2(2(2(z0))))))))), 2'(2(2(0(1(2(2(2(z0)))))))), 2'(2(0(1(2(2(2(z0))))))), 2'(0(1(2(2(2(z0)))))), 0'(1(2(2(2(z0))))), 1'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 2'(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(z0))))))))))))))))))))))))) -> c107(2'(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))))))), 0'(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))), 0'(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))))), 1'(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))), 1'(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))), 1'(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))), 1'(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))), 2'(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))), 1'(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))), 1'(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))), 1'(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))), 1'(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))), 2'(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))), 1'(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))), 2'(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))), 0'(0(2(2(2(1(2(2(1(1(0(z0))))))))))), 0'(2(2(2(1(2(2(1(1(0(z0)))))))))), 2'(2(2(1(2(2(1(1(0(z0))))))))), 2'(2(1(2(2(1(1(0(z0)))))))), 2'(1(2(2(1(1(0(z0))))))), 1'(2(2(1(1(0(z0)))))), 2'(2(1(1(0(z0))))), 2'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> c108(0'(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))), 1'(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))))), 1'(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))), 2'(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))), 1'(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))), 0'(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))), 0'(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))), 0'(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))), 1'(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))), 1'(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))), 2'(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))), 2'(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))), 0'(1(1(0(1(0(0(0(2(2(1(z0))))))))))), 1'(1(0(1(0(0(0(2(2(1(z0)))))))))), 1'(0(1(0(0(0(2(2(1(z0))))))))), 0'(1(0(0(0(2(2(1(z0)))))))), 1'(0(0(0(2(2(1(z0))))))), 0'(0(0(2(2(1(z0)))))), 0'(0(2(2(1(z0))))), 0'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> c109(1'(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))), 0'(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))))), 0'(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))), 2'(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))), 1'(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))), 2'(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))), 1'(1(2(2(1(1(2(1(0(1(1(z0))))))))))), 1'(2(2(1(1(2(1(0(1(1(z0)))))))))), 2'(2(1(1(2(1(0(1(1(z0))))))))), 2'(1(1(2(1(0(1(1(z0)))))))), 1'(1(2(1(0(1(1(z0))))))), 1'(2(1(0(1(1(z0)))))), 2'(1(0(1(1(z0))))), 1'(0(1(1(z0)))), 0'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> c110(0'(1(1(1(1(2(1(0(z0)))))))), 1'(1(1(1(2(1(0(z0))))))), 1'(1(1(2(1(0(z0)))))), 1'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> c111(1'(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))), 1'(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))))), 0'(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))), 1'(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))), 2'(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))), 1'(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))), 0'(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))), 1'(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))), 1'(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))), 2'(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))), 1'(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))), 0'(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))), 0'(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))), 2'(2(2(0(1(0(1(1(0(2(0(z0))))))))))), 2'(2(0(1(0(1(1(0(2(0(z0)))))))))), 2'(0(1(0(1(1(0(2(0(z0))))))))), 0'(1(0(1(1(0(2(0(z0)))))))), 1'(0(1(1(0(2(0(z0))))))), 0'(1(1(0(2(0(z0)))))), 1'(1(0(2(0(z0))))), 1'(0(2(0(z0)))), 0'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> c112(1'(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))), 2'(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))))), 2'(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))), 1'(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))), 1'(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))), 1'(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))), 1'(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))), 0'(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))), 1'(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))), 1'(1(1(0(1(1(1(0(0(1(0(z0))))))))))), 1'(1(0(1(1(1(0(0(1(0(z0)))))))))), 1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) K tuples:none Defined Rule Symbols: encArg_1, 0_1, 1_1, 2_1 Defined Pair Symbols: 0'_1, 1'_1, 2'_1, ENCODE_0_1, ENCODE_1_1, ENCODE_2_1, ENCARG_1 Compound Symbols: c7_28, c8_19, c9_29, c10_28, c11_29, c12_7, c13_26, c14_28, c15_24, c16_25, c17_16, c18_21, c19_12, c20_23, c21_27, c22_11, c23_27, c24_29, c25_29, c26_30, c27_17, c28_28, c29_20, c30_23, c31_30, c32_9, c33_14, c34_16, c35_17, c36_18, c37_23, c38_30, c39_29, c40_23, c41_20, c42_22, c43_28, c44_16, c45_16, c46_26, c47_16, c48_17, c49_23, c50_13, c51_19, c53_21, c54_28, c55_21, c56_24, c57_16, c58_20, c59_14, c60_8, c61_26, c62_30, c63_11, c64_23, c65_13, c66_25, c67_8, c68_26, c69_21, c70_21, c71_30, c72_24, c73_9, c74_22, c75_26, c76_18, c77_28, c78_26, c79_25, c80_21, c82_28, c83_27, c84_29, c85_15, c86_21, c87_30, c88_22, c89_23, c90_26, c91_15, c92_23, c93_14, c94_22, c95_25, c96_18, c97_23, c98_24, c99_27, c100_21, c101_24, c102_20, c103_29, c104_13, c105_15, c106_21, c107_28, c108_24, c109_17, c110_8, c111_24, c112_20, c113_17, c114_19, c115_24, c116_8, c117_12, c118_7, c6_1, c_2, c1_2, c2_2 ---------------------------------------- (53) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(z0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(z0))))))))))), 1'(2(2(0(1(0(1(1(0(0(z0)))))))))), 2'(2(0(1(0(1(1(0(0(z0))))))))), 2'(0(1(0(1(1(0(0(z0)))))))), 0'(1(0(1(1(0(0(z0))))))), 1'(0(1(1(0(0(z0)))))), 0'(1(1(0(0(z0))))), 1'(1(0(0(z0)))), 1'(0(0(z0))), 0'(0(z0)), 0'(z0)) by 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x0))))))))))))))))))))))))))) -> c7(1'(c_2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(x0))))))))))), 1'(2(2(0(1(0(1(1(0(0(x0)))))))))), 2'(2(0(1(0(1(1(0(0(x0))))))))), 2'(0(1(0(1(1(0(0(x0)))))))), 0'(1(0(1(1(0(0(x0))))))), 1'(0(1(1(0(0(x0)))))), 0'(1(1(0(0(x0))))), 1'(1(0(0(x0)))), 1'(0(0(x0))), 0'(0(x0)), 0'(x0)) 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x0))))))))))))))))))))))))))) -> c7(1'(2(c_1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(x0))))))))))), 1'(2(2(0(1(0(1(1(0(0(x0)))))))))), 2'(2(0(1(0(1(1(0(0(x0))))))))), 2'(0(1(0(1(1(0(0(x0)))))))), 0'(1(0(1(1(0(0(x0))))))), 1'(0(1(1(0(0(x0)))))), 0'(1(1(0(0(x0))))), 1'(1(0(0(x0)))), 1'(0(0(x0))), 0'(0(x0)), 0'(x0)) 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x0))))))))))))))))))))))))))) -> c7(1'(2(1(c_2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(x0))))))))))), 1'(2(2(0(1(0(1(1(0(0(x0)))))))))), 2'(2(0(1(0(1(1(0(0(x0))))))))), 2'(0(1(0(1(1(0(0(x0)))))))), 0'(1(0(1(1(0(0(x0))))))), 1'(0(1(1(0(0(x0)))))), 0'(1(1(0(0(x0))))), 1'(1(0(0(x0)))), 1'(0(0(x0))), 0'(0(x0)), 0'(x0)) 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x0))))))))))))))))))))))))))) -> c7(1'(2(1(2(c_1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(x0))))))))))), 1'(2(2(0(1(0(1(1(0(0(x0)))))))))), 2'(2(0(1(0(1(1(0(0(x0))))))))), 2'(0(1(0(1(1(0(0(x0)))))))), 0'(1(0(1(1(0(0(x0))))))), 1'(0(1(1(0(0(x0)))))), 0'(1(1(0(0(x0))))), 1'(1(0(0(x0)))), 1'(0(0(x0))), 0'(0(x0)), 0'(x0)) 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(c_1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))), 2'(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))), 2'(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))), 2'(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))), 0'(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))), 2'(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))), 2'(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))), 0'(1(2(2(0(1(0(1(1(0(0(x0))))))))))), 1'(2(2(0(1(0(1(1(0(0(x0)))))))))), 2'(2(0(1(0(1(1(0(0(x0))))))))), 2'(0(1(0(1(1(0(0(x0)))))))), 0'(1(0(1(1(0(0(x0))))))), 1'(0(1(1(0(0(x0)))))), 0'(1(1(0(0(x0))))), 1'(1(0(0(x0)))), 1'(0(0(x0))), 0'(0(x0)), 0'(x0)) 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x0))))))))))))))))))))))))))) -> c7(1'(2(1(2(1(1(c_0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))))), 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0'(1(2(2(0(1(0(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0)))))))))))))))))))))))))))), 1'(2(2(0(1(0(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0))))))))))))))))))))))))))), 2'(2(0(1(0(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0)))))))))))))))))))))))))), 2'(0(1(0(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0))))))))))))))))))))))))), 0'(1(0(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0)))))))))))))))))))))))), 1'(0(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0))))))))))))))))))))))), 0'(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0)))))))))))))))))))))), 1'(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0))))))))))))))))))))), 1'(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0)))))))))))))))))))), 0'(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0))))))))))))))))))), 0'(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0))))))))))))))))))) ---------------------------------------- (54) 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(z0) -> c_0(z0) 0(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(z0))))))))))))))))))))))))))) -> 1(2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(z0)))))))))))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> 1(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))) 0(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> 0(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> 1(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))) 0(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> 0(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))) 0(c_0(c_1(c_0(c_0(z0))))) -> 0(1(0(1(1(1(1(z0))))))) 0(c_2(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_1(c_0(c_0(c_0(c_2(c_2(c_2(c_0(c_2(c_1(c_0(c_0(z0))))))))))))))))))))))))) -> 1(0(1(2(2(0(0(0(1(2(0(0(1(0(1(1(1(0(0(1(1(2(1(0(0(1(z0)))))))))))))))))))))))))) 0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_0(c_0(c_1(c_2(c_1(c_2(c_2(c_1(c_1(c_0(z0))))))))))))))))))))))))))) -> 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0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_1(c_1(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_1(c_0(c_2(z0)))))))))))))))))))))) -> 0(2(2(1(1(0(0(2(2(1(1(0(1(1(1(2(0(1(2(1(0(1(1(z0))))))))))))))))))))))) 0(c_1(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_1(c_1(c_0(c_0(c_2(c_1(c_1(c_1(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_1(c_2(z0))))))))))))))))))))))))))))) -> 1(1(2(0(0(2(1(2(2(1(0(0(0(2(0(1(1(1(2(1(1(0(0(0(1(2(2(1(1(1(z0)))))))))))))))))))))))))))))) 0(c_1(c_2(c_2(c_1(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_1(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_0(c_0(z0)))))))))))))))))))))))))))) -> 2(1(2(2(1(0(1(0(0(1(1(2(2(2(2(2(2(2(1(2(1(1(1(2(1(1(1(1(1(z0))))))))))))))))))))))))))))) 0(c_1(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_1(c_0(c_2(c_1(z0))))))))))))))))))) -> 0(0(1(2(1(1(1(1(1(2(1(0(1(2(0(1(0(2(0(1(0(1(1(z0))))))))))))))))))))))) 0(c_0(c_0(c_0(c_0(c_1(c_1(c_0(c_2(c_2(c_1(c_2(c_0(c_2(c_0(c_0(c_2(c_0(z0)))))))))))))))))) -> 0(1(1(1(2(1(2(1(1(0(0(1(1(0(0(0(1(0(2(2(z0)))))))))))))))))))) 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2(c_0(c_1(c_2(c_1(c_1(c_0(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_2(c_1(c_1(c_1(c_2(c_2(c_1(z0)))))))))))))))))))))) -> 1(1(1(1(2(0(2(1(0(0(2(2(1(1(0(2(2(1(2(1(1(1(0(z0))))))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_1(c_2(c_0(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(c_0(c_2(c_2(c_2(z0))))))))))))))))))))))))) -> 2(1(1(1(0(2(2(0(2(0(0(2(0(2(1(0(2(1(2(1(1(2(2(2(1(2(z0)))))))))))))))))))))))))) 2(c_1(c_0(c_1(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_1(c_2(z0))))))))))))) -> 1(1(1(1(0(2(2(0(1(2(1(1(1(0(1(z0))))))))))))))) 2(c_1(c_0(c_0(c_2(c_1(c_0(c_1(c_0(c_2(c_2(c_0(c_0(c_2(c_2(c_0(c_0(c_0(c_1(c_0(c_2(z0))))))))))))))))))))) -> 1(2(2(0(2(2(1(1(1(1(0(1(1(0(1(1(1(0(2(1(0(2(2(z0))))))))))))))))))))))) 2(c_2(c_0(c_0(c_0(c_0(c_0(c_2(c_2(c_1(c_0(c_2(c_2(z0))))))))))))) -> 2(0(1(0(1(2(2(0(1(0(0(1(1(1(z0)))))))))))))) 2(c_2(c_0(c_2(c_2(c_1(c_2(c_0(c_0(c_2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_1(c_0(c_0(c_0(z0))))))))))))))))))))) -> 2(1(0(1(2(0(0(2(2(1(1(1(1(0(1(2(0(2(0(0(1(1(z0)))))))))))))))))))))) 2(c_1(c_2(c_2(c_2(c_2(c_1(c_1(c_0(c_0(c_2(c_1(c_2(c_0(c_0(c_0(c_1(c_1(c_0(c_0(c_1(c_1(c_2(c_0(c_1(z0))))))))))))))))))))))))) -> 2(1(0(2(0(0(2(1(0(1(1(2(0(0(2(0(1(2(2(1(2(1(0(1(1(z0))))))))))))))))))))))))) 2(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_2(c_1(c_1(c_1(c_1(c_2(c_1(c_2(z0)))))))))))))))) -> 1(0(1(1(1(1(2(2(0(1(1(1(0(2(1(0(2(2(z0)))))))))))))))))) 2(c_2(c_1(c_2(c_1(c_1(c_2(c_2(c_0(c_0(c_2(c_0(c_2(c_0(c_0(c_2(c_0(c_1(c_2(c_2(c_0(z0))))))))))))))))))))) -> 2(1(2(2(1(1(2(2(2(2(1(0(1(1(1(2(1(0(1(2(0(2(1(z0))))))))))))))))))))))) 2(c_0(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_0(c_0(c_2(c_1(c_0(c_0(c_1(c_0(c_0(c_1(c_2(c_1(z0)))))))))))))))))))))) -> 2(0(0(0(2(1(2(0(2(2(0(2(0(0(0(1(1(0(1(1(1(1(2(1(z0)))))))))))))))))))))))) 2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_2(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_2(c_1(c_0(c_2(z0)))))))))))))))))))) -> 2(1(2(1(2(2(2(1(1(1(1(1(2(1(0(0(1(1(1(0(0(1(1(1(2(0(2(z0))))))))))))))))))))))))))) 2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_1(c_0(z0)))))))))))))))))) -> 2(0(1(0(1(1(0(0(1(1(1(2(0(1(1(1(2(0(0(2(1(z0))))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_2(c_0(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_1(c_1(c_2(c_0(c_2(c_0(c_0(c_2(z0)))))))))))))))))))))) -> 0(2(1(2(1(0(0(1(2(2(1(1(1(1(2(2(2(2(0(0(1(2(1(2(z0)))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_2(c_2(c_1(c_2(c_2(c_1(z0))))))))))))))) -> 2(1(0(1(1(1(0(1(1(1(0(0(1(1(1(0(1(2(0(1(z0)))))))))))))))))))) 2(c_0(c_0(c_1(c_0(c_2(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_2(c_2(c_0(z0)))))))))))))))))))))))))))) -> 1(2(0(2(0(2(0(2(2(2(0(1(2(0(2(2(1(0(1(1(1(1(2(1(2(0(2(2(2(z0))))))))))))))))))))))))))))) 2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_1(c_2(c_2(c_2(z0)))))))))))) -> 1(1(2(0(1(1(1(1(1(0(1(1(0(z0))))))))))))) 2(c_2(c_0(c_0(c_2(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_2(c_2(z0)))))))))))))) -> 0(0(1(1(1(1(2(0(1(0(1(0(2(1(2(z0))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_2(z0))))))))))))))))))) -> 1(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))))))))) 2(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(z0))))))))))))))))))))))))) -> 2(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))))) 2(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> 0(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))) 2(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> 1(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))) 2(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> 0(1(1(1(1(2(1(0(z0)))))))) 2(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> 1(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))) 2(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> 1(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))) 2(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> 1(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))) 2(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> 2(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))) 2(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> 2(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))) 2(c_0(c_2(c_0(c_1(c_0(z0)))))) -> 1(1(0(1(1(1(1(0(z0)))))))) 2(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> 0(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))) 2(c_0(c_2(c_2(c_1(c_2(z0)))))) -> 1(1(0(0(1(1(2(z0))))))) Tuples: 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_0(c_0(c_2(c_2(c_1(c_2(c_1(c_2(z0))))))))))))))) -> c8(1'(1(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))))), 1'(1(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))))), 1'(1(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))))), 1'(1(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))))), 1'(1(1(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))))), 1'(1(0(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))))), 1'(0(1(0(0(2(0(0(0(2(0(0(1(z0))))))))))))), 0'(1(0(0(2(0(0(0(2(0(0(1(z0)))))))))))), 1'(0(0(2(0(0(0(2(0(0(1(z0))))))))))), 0'(0(2(0(0(0(2(0(0(1(z0)))))))))), 0'(2(0(0(0(2(0(0(1(z0))))))))), 2'(0(0(0(2(0(0(1(z0)))))))), 0'(0(0(2(0(0(1(z0))))))), 0'(0(2(0(0(1(z0)))))), 0'(2(0(0(1(z0))))), 2'(0(0(1(z0)))), 0'(0(1(z0))), 0'(1(z0)), 1'(z0)) 0'(c_1(c_2(c_1(c_2(c_2(c_1(c_2(c_0(c_1(c_1(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_2(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(z0))))))))))))))))))))))))))))) -> c9(0'(2(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))))), 2'(1(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))))), 1'(0(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))))), 0'(1(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))))), 1'(2(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))))), 2'(1(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))))), 1'(1(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))))), 1'(1(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))))), 1'(2(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))))), 2'(2(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))))), 2'(2(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))))), 2'(2(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))))), 2'(0(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))))), 0'(0(0(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))))), 0'(0(2(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))))), 0'(2(2(1(1(1(2(0(0(0(2(1(2(z0))))))))))))), 2'(2(1(1(1(2(0(0(0(2(1(2(z0)))))))))))), 2'(1(1(1(2(0(0(0(2(1(2(z0))))))))))), 1'(1(1(2(0(0(0(2(1(2(z0)))))))))), 1'(1(2(0(0(0(2(1(2(z0))))))))), 1'(2(0(0(0(2(1(2(z0)))))))), 2'(0(0(0(2(1(2(z0))))))), 0'(0(0(2(1(2(z0)))))), 0'(0(2(1(2(z0))))), 0'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) 0'(c_1(c_2(c_0(c_0(c_1(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_0(c_1(c_0(c_2(c_0(z0))))))))))))))))))))))))))) -> c10(1'(2(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))))), 2'(0(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))))))), 0'(2(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))))), 2'(1(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))))), 1'(2(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))))), 2'(1(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))))), 1'(1(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0)))))))))))))))))))))), 1'(0(1(1(2(0(2(0(0(0(1(0(1(0(1(1(0(2(1(2(0(z0))))))))))))))))))))), 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2'(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))))), 2'(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))), 1'(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))), 1'(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))), 2'(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))), 2'(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))), 2'(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))), 1'(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))), 1'(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))), 1'(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))), 0'(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))), 0'(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))), 1'(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))), 2'(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))), 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2'(1(1(0(0(1(1(0(0(0(1(0(2(2(z0)))))))))))))), 1'(1(0(0(1(1(0(0(0(1(0(2(2(z0))))))))))))), 1'(0(0(1(1(0(0(0(1(0(2(2(z0)))))))))))), 0'(0(1(1(0(0(0(1(0(2(2(z0))))))))))), 0'(1(1(0(0(0(1(0(2(2(z0)))))))))), 1'(1(0(0(0(1(0(2(2(z0))))))))), 1'(0(0(0(1(0(2(2(z0)))))))), 0'(0(0(1(0(2(2(z0))))))), 0'(0(1(0(2(2(z0)))))), 0'(1(0(2(2(z0))))), 1'(0(2(2(z0)))), 0'(2(2(z0))), 2'(2(z0)), 2'(z0)) 0'(c_2(c_0(c_2(c_2(c_0(c_2(c_1(c_1(c_1(c_0(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_0(c_2(z0)))))))))))))))))))) -> c42(2'(1(1(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(z0)))))))))))))))))))))), 1'(1(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(z0))))))))))))))))))))), 1'(1(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(z0)))))))))))))))))))), 1'(2(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(z0))))))))))))))))))), 2'(1(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(z0)))))))))))))))))), 1'(0(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(z0))))))))))))))))), 0'(1(1(1(2(2(1(1(1(0(1(0(1(1(2(0(z0)))))))))))))))), 1'(1(1(2(2(1(1(1(0(1(0(1(1(2(0(z0))))))))))))))), 1'(1(2(2(1(1(1(0(1(0(1(1(2(0(z0)))))))))))))), 1'(2(2(1(1(1(0(1(0(1(1(2(0(z0))))))))))))), 2'(2(1(1(1(0(1(0(1(1(2(0(z0)))))))))))), 2'(1(1(1(0(1(0(1(1(2(0(z0))))))))))), 1'(1(1(0(1(0(1(1(2(0(z0)))))))))), 1'(1(0(1(0(1(1(2(0(z0))))))))), 1'(0(1(0(1(1(2(0(z0)))))))), 0'(1(0(1(1(2(0(z0))))))), 1'(0(1(1(2(0(z0)))))), 0'(1(1(2(0(z0))))), 1'(1(2(0(z0)))), 1'(2(0(z0))), 2'(0(z0)), 0'(z0)) 0'(c_1(c_1(c_1(c_2(c_0(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_1(c_1(c_0(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_1(c_2(c_0(c_1(z0)))))))))))))))))))))))))))) -> c43(1'(0(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(z0)))))))))))))))))))))))))))), 0'(0(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(z0))))))))))))))))))))))))))), 0'(0(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(z0)))))))))))))))))))))))))), 0'(0(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(z0))))))))))))))))))))))))), 0'(0(0(2(1(2(1(2(0(2(0(2(0(1(1(1(1(0(1(1(2(2(0(1(z0)))))))))))))))))))))))), 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1'(1(2(0(1(0(1(0(2(1(2(z0))))))))))), 1'(2(0(1(0(1(0(2(1(2(z0)))))))))), 2'(0(1(0(1(0(2(1(2(z0))))))))), 0'(1(0(1(0(2(1(2(z0)))))))), 1'(0(1(0(2(1(2(z0))))))), 0'(1(0(2(1(2(z0)))))), 1'(0(2(1(2(z0))))), 0'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_2(z0))))))))))))))))))) -> c106(1'(2(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))))))))), 2'(1(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0)))))))))))))))))))), 1'(1(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))))))), 1'(1(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0)))))))))))))))))), 1'(1(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))))), 1'(0(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0)))))))))))))))), 0'(0(0(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))))), 0'(0(1(1(2(2(2(2(2(0(1(2(2(2(z0)))))))))))))), 0'(1(1(2(2(2(2(2(0(1(2(2(2(z0))))))))))))), 1'(1(2(2(2(2(2(0(1(2(2(2(z0)))))))))))), 1'(2(2(2(2(2(0(1(2(2(2(z0))))))))))), 2'(2(2(2(2(0(1(2(2(2(z0)))))))))), 2'(2(2(2(0(1(2(2(2(z0))))))))), 2'(2(2(0(1(2(2(2(z0)))))))), 2'(2(0(1(2(2(2(z0))))))), 2'(0(1(2(2(2(z0)))))), 0'(1(2(2(2(z0))))), 1'(2(2(2(z0)))), 2'(2(2(z0))), 2'(2(z0)), 2'(z0)) 2'(c_0(c_2(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_0(c_2(c_2(c_1(c_1(c_2(c_0(c_0(c_0(c_1(z0))))))))))))))))))))))))) -> c107(2'(0(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))))), 0'(0(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))))))), 0'(0(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))))), 0'(1(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))))), 1'(0(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))))), 1'(1(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))))), 1'(1(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))))), 1'(2(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))))), 2'(1(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))))), 1'(1(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))))), 1'(1(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))))), 1'(1(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))))), 1'(2(1(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))))), 2'(1(2(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))))), 1'(2(0(0(2(2(2(1(2(2(1(1(0(z0))))))))))))), 2'(0(0(2(2(2(1(2(2(1(1(0(z0)))))))))))), 0'(0(2(2(2(1(2(2(1(1(0(z0))))))))))), 0'(2(2(2(1(2(2(1(1(0(z0)))))))))), 2'(2(2(1(2(2(1(1(0(z0))))))))), 2'(2(1(2(2(1(1(0(z0)))))))), 2'(1(2(2(1(1(0(z0))))))), 1'(2(2(1(1(0(z0)))))), 2'(2(1(1(0(z0))))), 2'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_1(c_1(c_2(c_0(c_2(c_1(c_1(c_0(c_0(c_2(c_2(c_2(c_2(c_0(c_2(c_0(c_0(c_0(c_1(c_2(z0))))))))))))))))))))))) -> c108(0'(1(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))))), 1'(1(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))))), 1'(2(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))))), 2'(1(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))), 1'(0(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))))), 0'(0(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))), 0'(0(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))))), 0'(0(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))))), 0'(1(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))))), 1'(1(2(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))))), 1'(2(2(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))))), 2'(2(0(1(1(0(1(0(0(0(2(2(1(z0))))))))))))), 2'(0(1(1(0(1(0(0(0(2(2(1(z0)))))))))))), 0'(1(1(0(1(0(0(0(2(2(1(z0))))))))))), 1'(1(0(1(0(0(0(2(2(1(z0)))))))))), 1'(0(1(0(0(0(2(2(1(z0))))))))), 0'(1(0(0(0(2(2(1(z0)))))))), 1'(0(0(0(2(2(1(z0))))))), 0'(0(0(2(2(1(z0)))))), 0'(0(2(2(1(z0))))), 0'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(c_2(c_0(c_2(c_1(c_1(c_2(c_2(c_0(c_2(c_2(c_0(c_0(c_0(c_2(c_1(z0)))))))))))))))) -> c109(1'(0(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))))), 0'(0(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))))), 0'(2(1(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))))), 2'(1(2(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))))), 1'(2(1(1(2(2(1(1(2(1(0(1(1(z0))))))))))))), 2'(1(1(2(2(1(1(2(1(0(1(1(z0)))))))))))), 1'(1(2(2(1(1(2(1(0(1(1(z0))))))))))), 1'(2(2(1(1(2(1(0(1(1(z0)))))))))), 2'(2(1(1(2(1(0(1(1(z0))))))))), 2'(1(1(2(1(0(1(1(z0)))))))), 1'(1(2(1(0(1(1(z0))))))), 1'(2(1(0(1(1(z0)))))), 2'(1(0(1(1(z0))))), 1'(0(1(1(z0)))), 0'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_0(c_2(c_0(c_0(c_0(c_0(z0))))))) -> c110(0'(1(1(1(1(2(1(0(z0)))))))), 1'(1(1(1(2(1(0(z0))))))), 1'(1(1(2(1(0(z0)))))), 1'(1(2(1(0(z0))))), 1'(2(1(0(z0)))), 2'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_0(c_1(c_0(c_2(c_0(c_0(c_1(c_2(c_1(c_2(c_0(c_0(c_2(c_0(c_0(c_2(c_2(c_2(c_2(z0))))))))))))))))))))))) -> c111(1'(1(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))))), 1'(0(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))))), 0'(1(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))))), 1'(2(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))))), 2'(1(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))))), 1'(0(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))))), 0'(1(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))))), 1'(1(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))))), 1'(2(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))))), 2'(1(0(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))))), 1'(0(0(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))))), 0'(0(2(2(2(0(1(0(1(1(0(2(0(z0))))))))))))), 0'(2(2(2(0(1(0(1(1(0(2(0(z0)))))))))))), 2'(2(2(0(1(0(1(1(0(2(0(z0))))))))))), 2'(2(0(1(0(1(1(0(2(0(z0)))))))))), 2'(0(1(0(1(1(0(2(0(z0))))))))), 0'(1(0(1(1(0(2(0(z0)))))))), 1'(0(1(1(0(2(0(z0))))))), 0'(1(1(0(2(0(z0)))))), 1'(1(0(2(0(z0))))), 1'(0(2(0(z0)))), 0'(2(0(z0))), 2'(0(z0)), 0'(z0)) 2'(c_1(c_1(c_2(c_0(c_1(c_2(c_0(c_2(c_1(c_0(c_0(c_2(c_2(c_2(c_1(z0)))))))))))))))) -> c112(1'(2(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))))), 2'(2(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))))), 2'(1(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))))), 1'(1(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))))), 1'(1(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))))), 1'(1(0(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))))), 1'(0(1(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))))), 0'(1(1(1(1(0(1(1(1(0(0(1(0(z0))))))))))))), 1'(1(1(1(0(1(1(1(0(0(1(0(z0)))))))))))), 1'(1(1(0(1(1(1(0(0(1(0(z0))))))))))), 1'(1(0(1(1(1(0(0(1(0(z0)))))))))), 1'(0(1(1(1(0(0(1(0(z0))))))))), 0'(1(1(1(0(0(1(0(z0)))))))), 1'(1(1(0(0(1(0(z0))))))), 1'(1(0(0(1(0(z0)))))), 1'(0(0(1(0(z0))))), 0'(0(1(0(z0)))), 0'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_0(c_2(c_1(c_1(c_2(c_1(c_0(c_1(c_0(c_0(c_2(c_2(c_0(z0))))))))))))))) -> c113(1'(1(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))))), 1'(2(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))))), 2'(2(0(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))))), 2'(0(1(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))))), 0'(1(1(1(0(1(1(0(2(0(0(0(0(z0))))))))))))), 1'(1(1(0(1(1(0(2(0(0(0(0(z0)))))))))))), 1'(1(0(1(1(0(2(0(0(0(0(z0))))))))))), 1'(0(1(1(0(2(0(0(0(0(z0)))))))))), 0'(1(1(0(2(0(0(0(0(z0))))))))), 1'(1(0(2(0(0(0(0(z0)))))))), 1'(0(2(0(0(0(0(z0))))))), 0'(2(0(0(0(0(z0)))))), 2'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) 2'(c_2(c_0(c_2(c_0(c_1(c_0(c_2(c_2(c_1(c_1(c_0(c_1(c_0(c_1(c_1(c_1(c_0(c_1(z0))))))))))))))))))) -> c114(2'(0(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))))), 0'(0(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))))), 0'(0(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))))), 0'(0(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))))), 0'(2(1(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))))), 2'(1(1(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))))), 1'(1(1(1(1(0(1(0(2(2(2(1(1(z0))))))))))))), 1'(1(1(1(0(1(0(2(2(2(1(1(z0)))))))))))), 1'(1(1(0(1(0(2(2(2(1(1(z0))))))))))), 1'(1(0(1(0(2(2(2(1(1(z0)))))))))), 1'(0(1(0(2(2(2(1(1(z0))))))))), 0'(1(0(2(2(2(1(1(z0)))))))), 1'(0(2(2(2(1(1(z0))))))), 0'(2(2(2(1(1(z0)))))), 2'(2(2(1(1(z0))))), 2'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 2'(c_1(c_2(c_1(c_2(c_1(c_0(c_0(c_1(c_2(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_1(c_0(z0)))))))))))))))))))))))) -> c115(2'(0(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))))), 0'(1(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))))), 1'(1(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))))), 1'(0(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))))), 0'(0(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))))), 0'(2(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))))), 2'(0(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))))), 0'(1(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))))), 1'(2(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))))), 2'(1(1(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))))), 1'(1(2(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))))), 1'(2(0(0(1(0(2(1(2(1(1(1(0(z0))))))))))))), 2'(0(0(1(0(2(1(2(1(1(1(0(z0)))))))))))), 0'(0(1(0(2(1(2(1(1(1(0(z0))))))))))), 0'(1(0(2(1(2(1(1(1(0(z0)))))))))), 1'(0(2(1(2(1(1(1(0(z0))))))))), 0'(2(1(2(1(1(1(0(z0)))))))), 2'(1(2(1(1(1(0(z0))))))), 1'(2(1(1(1(0(z0)))))), 2'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_0(c_1(c_0(z0)))))) -> c116(1'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) ENCODE_0(z0) -> c6(0'(encArg(z0))) ENCODE_1(z0) -> c6(1'(encArg(z0))) ENCODE_2(z0) -> c6(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))) ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(1'(2(encArg(z0))), ENCARG(cons_2(z0))) ENCARG(cons_2(cons_0(z0))) -> c2(2'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_2(cons_1(z0))) -> c2(2'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_2(cons_2(z0))) -> c2(2'(2(encArg(z0))), ENCARG(cons_2(z0))) 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x0))))))))))))))))))))))))))) -> c7(1'(c_2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))), 1'(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))), 1'(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))), 0'(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))), 1'(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))), 0'(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))), 1'(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))), 2'(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))), 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0'(1(0(1(1(0(2(1(2(0(z0)))))))))), 1'(0(1(1(0(2(1(2(0(z0))))))))), 0'(1(1(0(2(1(2(0(z0)))))))), 1'(1(0(2(1(2(0(z0))))))), 1'(0(2(1(2(0(z0)))))), 0'(2(1(2(0(z0))))), 2'(1(2(0(z0)))), 1'(2(0(z0))), 2'(0(z0)), 0'(z0)) 0'(c_0(c_2(c_2(c_0(c_2(c_1(c_2(c_2(c_0(c_0(c_0(c_2(c_2(c_0(c_2(c_2(c_2(c_1(c_0(c_1(c_0(c_1(c_2(c_2(c_0(c_0(c_0(z0)))))))))))))))))))))))))))) -> c11(0'(2(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))))), 2'(2(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))))), 2'(1(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))))), 1'(1(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))))), 1'(2(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))))), 2'(2(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0)))))))))))))))))))))))), 2'(2(1(1(1(0(0(1(2(1(2(2(1(1(1(2(0(2(1(2(2(1(1(z0))))))))))))))))))))))), 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2'(c_0(c_1(c_1(c_2(c_1(c_0(c_2(c_0(c_0(c_1(z0))))))))))) -> c117(0'(1(0(0(2(1(0(1(1(1(1(0(z0)))))))))))), 1'(0(0(2(1(0(1(1(1(1(0(z0))))))))))), 0'(0(2(1(0(1(1(1(1(0(z0)))))))))), 0'(2(1(0(1(1(1(1(0(z0))))))))), 2'(1(0(1(1(1(1(0(z0)))))))), 1'(0(1(1(1(1(0(z0))))))), 0'(1(1(1(1(0(z0)))))), 1'(1(1(1(0(z0))))), 1'(1(1(0(z0)))), 1'(1(0(z0))), 1'(0(z0)), 0'(z0)) 2'(c_0(c_2(c_2(c_1(c_2(z0)))))) -> c118(1'(1(0(0(1(1(2(z0))))))), 1'(0(0(1(1(2(z0)))))), 0'(0(1(1(2(z0))))), 0'(1(1(2(z0)))), 1'(1(2(z0))), 1'(2(z0)), 2'(z0)) 0'(c_1(c_2(c_1(c_0(c_2(c_2(c_2(c_2(c_0(c_0(c_1(c_2(c_1(c_0(c_0(c_0(c_0(c_2(c_0(c_0(c_0(c_2(c_0(c_1(c_0(c_2(x0))))))))))))))))))))))))))) -> c7(1'(c_2(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))))), 2'(1(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))))), 1'(2(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0)))))))))))))))))))))))))), 2'(1(1(0(1(0(1(2(2(2(2(0(2(2(0(1(2(2(0(1(0(1(1(0(0(x0))))))))))))))))))))))))), 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0'(1(2(2(0(1(0(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0)))))))))))))))))))))))))))), 1'(2(2(0(1(0(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0))))))))))))))))))))))))))), 2'(2(0(1(0(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0)))))))))))))))))))))))))), 2'(0(1(0(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0))))))))))))))))))))))))), 0'(1(0(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0)))))))))))))))))))))))), 1'(0(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0))))))))))))))))))))))), 0'(1(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0)))))))))))))))))))))), 1'(1(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0))))))))))))))))))))), 1'(0(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0)))))))))))))))))))), 0'(0(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0))))))))))))))))))), 0'(c_0(c_0(c_2(c_0(c_1(c_2(c_0(c_0(c_1(c_0(c_2(c_0(c_1(c_1(c_2(c_0(c_2(z0))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, 0_1, 1_1, 2_1 Defined Pair Symbols: 0'_1, 1'_1, 2'_1, ENCODE_0_1, ENCODE_1_1, ENCODE_2_1, ENCARG_1 Compound Symbols: c8_19, c9_29, c10_28, c11_29, c12_7, c13_26, c14_28, c15_24, c16_25, c17_16, c18_21, c19_12, c20_23, c21_27, c22_11, c23_27, c24_29, c25_29, c26_30, c27_17, c28_28, c29_20, c30_23, c31_30, c32_9, c33_14, c34_16, c35_17, c36_18, c37_23, c38_30, c39_29, c40_23, c41_20, c42_22, c43_28, c44_16, c45_16, c46_26, c47_16, c48_17, c49_23, c50_13, c51_19, c53_21, c54_28, c55_21, c56_24, c57_16, c58_20, c59_14, c60_8, c61_26, c62_30, c63_11, c64_23, c65_13, c66_25, c67_8, c68_26, c69_21, c70_21, c71_30, c72_24, c73_9, c74_22, c75_26, c76_18, c77_28, c78_26, c79_25, c80_21, c82_28, c83_27, c84_29, c85_15, c86_21, c87_30, c88_22, c89_23, c90_26, c91_15, c92_23, c93_14, c94_22, c95_25, c96_18, c97_23, c98_24, c99_27, c100_21, c101_24, c102_20, c103_29, c104_13, c105_15, c106_21, c107_28, c108_24, c109_17, c110_8, c111_24, c112_20, c113_17, c114_19, c115_24, c116_8, c117_12, c118_7, c6_1, c_2, c1_2, c2_2, c7_28