/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 81 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 609 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(2(2(3(x1)))))) -> 0(2(2(1(0(3(x1)))))) 0(4(4(1(0(4(x1)))))) -> 0(4(4(4(0(1(x1)))))) 0(4(0(0(4(2(3(5(1(x1))))))))) -> 5(0(3(2(4(0(0(1(4(x1))))))))) 1(2(3(1(0(1(4(2(0(x1))))))))) -> 4(0(3(2(1(1(2(1(0(x1))))))))) 1(3(4(0(4(1(1(2(3(5(4(4(x1)))))))))))) -> 2(4(4(0(1(3(5(1(4(3(4(1(x1)))))))))))) 4(1(1(3(3(0(1(5(0(4(4(2(2(3(3(5(4(3(x1)))))))))))))))))) -> 4(0(4(2(4(3(1(3(4(3(5(1(2(0(3(5(1(3(x1)))))))))))))))))) 1(0(4(3(1(2(1(2(0(4(3(3(2(1(5(2(3(2(1(x1))))))))))))))))))) -> 1(4(2(1(1(4(1(0(3(0(5(3(1(3(2(2(3(2(2(x1))))))))))))))))))) 1(1(1(3(0(4(5(0(3(0(1(1(3(0(4(5(3(3(0(x1))))))))))))))))))) -> 4(5(0(3(3(4(1(0(0(1(1(1(3(1(0(3(5(3(0(x1))))))))))))))))))) 1(3(2(3(0(5(0(4(1(1(2(4(4(3(3(5(4(0(5(x1))))))))))))))))))) -> 4(2(1(2(5(3(4(1(1(3(0(0(3(3(4(0(5(4(5(x1))))))))))))))))))) 3(0(2(2(0(1(1(5(0(1(1(1(0(2(0(4(5(0(1(x1))))))))))))))))))) -> 5(1(2(1(4(0(0(3(0(1(0(0(1(0(1(2(5(1(2(x1))))))))))))))))))) 0(2(1(5(4(1(5(4(0(1(2(0(2(1(2(1(1(1(3(5(2(5(x1)))))))))))))))))))))) -> 2(1(1(3(5(4(2(5(0(5(2(1(1(1(2(1(4(0(2(0(5(1(x1)))))))))))))))))))))) 2(2(5(3(3(3(0(4(1(3(5(4(5(1(3(4(1(0(3(5(4(0(x1)))))))))))))))))))))) -> 0(1(5(3(4(1(3(5(3(3(1(3(4(5(3(4(4(0(2(2(5(0(x1)))))))))))))))))))))) 2(5(5(1(4(3(3(2(1(1(1(5(0(4(4(3(5(1(4(1(4(5(2(x1))))))))))))))))))))))) -> 3(4(5(1(4(4(5(2(1(5(5(5(0(1(2(1(1(1(3(4(3(4(2(x1))))))))))))))))))))))) 3(4(0(2(2(3(2(4(2(3(5(3(5(0(1(3(5(5(2(4(4(2(3(3(x1)))))))))))))))))))))))) -> 5(5(3(2(2(2(0(5(4(3(3(3(2(0(2(4(2(1(5(3(4(3(4(3(x1)))))))))))))))))))))))) 5(5(2(0(2(1(5(5(2(1(4(4(5(2(4(4(1(1(1(3(2(5(5(5(x1)))))))))))))))))))))))) -> 5(4(5(0(5(4(2(1(2(4(1(1(2(1(2(4(5(3(1(5(2(5(5(5(x1)))))))))))))))))))))))) 1(5(2(4(1(3(3(5(3(0(4(2(5(1(5(2(0(1(0(3(0(5(5(1(4(x1))))))))))))))))))))))))) -> 1(5(2(3(1(5(4(5(5(2(3(4(2(3(5(4(1(1(3(0(0(1(0(5(0(x1))))))))))))))))))))))))) 3(1(5(1(0(4(4(1(1(2(2(0(2(3(3(2(2(3(3(5(4(1(2(5(1(x1))))))))))))))))))))))))) -> 1(3(0(3(5(5(2(1(2(3(2(5(2(3(1(0(2(1(3(1(4(1(2(4(4(x1))))))))))))))))))))))))) 0(0(1(4(0(0(4(2(1(5(5(3(0(3(4(0(1(4(3(1(5(5(2(0(0(2(3(x1))))))))))))))))))))))))))) -> 0(0(5(4(1(2(4(2(1(5(4(2(0(5(0(0(0(3(4(1(3(5(3(0(1(0(3(x1))))))))))))))))))))))))))) 1(1(5(4(4(5(0(4(5(1(1(0(3(2(1(3(0(2(1(5(3(2(0(4(5(0(2(x1))))))))))))))))))))))))))) -> 2(3(4(0(1(5(0(5(1(1(2(0(3(4(1(3(0(4(1(5(2(5(0(4(2(5(1(x1))))))))))))))))))))))))))) 1(5(2(4(3(0(1(4(3(5(0(5(0(1(3(2(0(1(4(3(3(2(1(0(1(5(5(x1))))))))))))))))))))))))))) -> 1(5(1(4(1(0(0(3(5(5(0(0(3(0(1(1(4(5(3(2(3(1(2(4(2(5(3(x1))))))))))))))))))))))))))) 0(1(2(5(3(3(1(0(4(1(4(2(0(1(0(4(4(1(0(5(3(2(1(2(5(2(5(1(x1)))))))))))))))))))))))))))) -> 0(1(1(5(3(5(4(0(2(3(0(0(0(4(5(1(4(1(2(1(5(2(1(4(3(2(2(1(x1)))))))))))))))))))))))))))) 0(4(1(4(2(2(4(0(0(3(5(3(0(0(5(0(4(5(5(5(3(2(1(1(0(2(3(1(x1)))))))))))))))))))))))))))) -> 0(1(2(4(1(1(3(0(5(2(3(0(3(0(5(0(4(5(2(4(5(4(1(5(0(2(0(3(x1)))))))))))))))))))))))))))) 2(0(3(1(0(4(3(1(5(2(2(4(1(1(3(0(2(4(2(5(2(2(2(4(1(5(5(1(2(x1))))))))))))))))))))))))))))) -> 2(0(0(2(2(1(5(2(3(1(3(3(1(4(5(2(1(4(2(5(2(2(2(0(5(4(4(1(1(x1))))))))))))))))))))))))))))) 0(5(0(2(3(0(4(0(0(4(3(3(5(0(4(5(4(1(4(0(2(5(5(5(3(1(5(2(2(3(3(x1))))))))))))))))))))))))))))))) -> 2(3(5(3(5(0(4(0(0(0(3(3(4(0(4(1(4(5(3(4(2(5(5(5(5(2(0(0(2(1(3(x1))))))))))))))))))))))))))))))) 1(2(3(5(3(5(0(3(3(3(1(3(1(0(3(3(5(2(0(3(4(4(0(0(4(0(4(0(0(2(2(x1))))))))))))))))))))))))))))))) -> 1(3(3(5(0(5(5(3(4(1(2(3(3(0(0(4(2(1(0(0(0(3(2(3(4(0(3(0(4(3(2(x1))))))))))))))))))))))))))))))) 3(2(4(2(2(3(1(4(1(2(0(1(0(5(2(1(3(0(1(1(2(0(4(0(1(0(3(4(2(1(4(x1))))))))))))))))))))))))))))))) -> 0(2(1(2(1(4(1(3(1(2(4(5(0(0(2(1(1(4(1(3(4(0(1(0(2(3(3(2(0(2(4(x1))))))))))))))))))))))))))))))) 4(0(4(0(4(2(1(5(1(2(3(1(0(0(3(3(4(3(5(4(2(1(5(5(3(4(0(1(3(5(2(x1))))))))))))))))))))))))))))))) -> 4(0(4(3(1(2(3(4(2(5(3(2(0(5(1(3(4(1(0(3(5(1(2(4(1(3(0(4(0(5(5(x1))))))))))))))))))))))))))))))) 2(2(4(3(5(5(4(1(3(0(4(5(5(2(2(3(3(5(2(1(0(3(1(1(0(3(3(3(0(0(1(0(3(x1))))))))))))))))))))))))))))))))) -> 2(4(1(5(1(5(0(4(0(0(0(2(3(2(3(3(2(5(1(5(1(3(3(2(5(3(3(4(3(1(0(0(3(x1))))))))))))))))))))))))))))))))) 2(4(4(0(2(1(3(5(0(0(1(4(4(2(1(1(2(0(0(5(2(2(3(2(5(5(1(0(1(1(3(4(4(5(x1)))))))))))))))))))))))))))))))))) -> 2(4(3(0(5(0(1(1(1(0(2(1(1(2(2(2(4(0(0(4(5(2(4(3(5(5(0(4(1(1(3(4(2(5(x1)))))))))))))))))))))))))))))))))) 5(4(3(5(2(3(5(1(2(2(3(1(3(2(3(2(4(1(0(1(4(5(4(1(4(4(0(1(0(2(5(2(2(0(x1)))))))))))))))))))))))))))))))))) -> 5(4(1(5(2(2(5(3(4(0(5(0(4(2(3(0(0(3(4(5(2(1(4(2(3(4(1(1(2(1(1(2(2(3(x1)))))))))))))))))))))))))))))))))) 0(3(0(4(5(5(5(1(3(0(4(4(3(4(5(2(5(0(0(1(5(0(5(5(0(4(5(1(1(0(4(3(4(5(2(x1))))))))))))))))))))))))))))))))))) -> 0(3(0(0(1(5(5(1(3(4(4(1(4(0(4(5(5(4(2(2(5(5(5(5(0(0(0(1(3(4(5(3(4(5(0(x1))))))))))))))))))))))))))))))))))) 4(2(1(2(2(1(5(1(5(3(0(5(3(5(0(4(4(3(1(2(1(2(0(2(4(4(3(1(1(4(4(5(5(1(2(x1))))))))))))))))))))))))))))))))))) -> 4(1(5(2(2(0(5(3(0(2(2(2(1(5(3(4(1(2(1(5(3(1(0(3(4(4(4(1(1(4(4(5(5(2(1(x1))))))))))))))))))))))))))))))))))) 5(4(4(1(1(3(5(2(2(2(5(3(3(3(0(4(5(3(2(3(0(5(5(1(2(2(0(1(1(3(1(5(0(0(2(x1))))))))))))))))))))))))))))))))))) -> 3(4(5(1(0(2(3(2(3(2(0(3(5(3(1(4(5(2(2(2(0(1(5(5(2(1(1(4(5(3(5(0(0(1(3(x1))))))))))))))))))))))))))))))))))) 0(0(3(0(0(0(3(4(1(4(0(5(2(1(5(2(4(1(1(1(5(2(2(5(3(4(0(0(4(3(1(3(5(4(1(1(x1)))))))))))))))))))))))))))))))))))) -> 0(0(1(4(0(5(0(1(4(4(0(0(2(1(5(3(1(0(1(0(5(2(2(5(3(4(3(1(4(3(3(4(5(1(2(1(x1)))))))))))))))))))))))))))))))))))) 2(1(1(4(3(2(2(4(1(5(3(3(3(3(2(4(4(3(0(1(4(3(2(0(0(2(1(5(2(2(3(0(1(5(1(2(x1)))))))))))))))))))))))))))))))))))) -> 0(3(1(2(3(4(0(2(2(3(1(3(1(3(5(4(4(3(2(1(4(3(4(2(0(1(1(5(2(2(3(0(5(2(1(2(x1)))))))))))))))))))))))))))))))))))) 4(5(4(4(4(0(4(4(5(5(2(0(2(5(0(3(1(4(3(4(3(0(1(4(4(1(0(4(5(4(3(3(1(1(0(5(x1)))))))))))))))))))))))))))))))))))) -> 4(4(4(5(3(1(1(2(5(5(3(4(4(5(1(3(3(4(4(0(0(0(5(0(1(1(0(4(5(2(0(3(4(4(4(4(x1)))))))))))))))))))))))))))))))))))) 0(0(5(5(1(0(1(4(5(2(0(5(2(5(2(1(0(5(1(1(4(5(0(2(1(0(3(4(1(2(5(0(1(4(4(5(3(5(x1)))))))))))))))))))))))))))))))))))))) -> 0(3(4(5(1(0(0(5(1(0(0(5(4(5(0(1(2(5(5(4(4(1(0(2(1(3(2(2(1(0(5(1(5(1(4(5(2(5(x1)))))))))))))))))))))))))))))))))))))) 0(1(3(0(3(1(0(3(0(4(3(0(3(2(1(3(5(0(5(3(0(1(0(1(1(4(3(0(5(1(4(3(3(3(0(0(0(5(3(4(x1)))))))))))))))))))))))))))))))))))))))) -> 0(3(1(0(5(4(0(3(0(4(5(0(5(1(3(3(0(0(3(0(3(1(3(2(1(1(5(4(3(1(1(0(3(3(0(0(3(4(3(0(x1)))))))))))))))))))))))))))))))))))))))) 4(3(3(0(0(0(3(2(4(3(0(0(4(4(2(4(4(2(1(2(5(5(0(0(4(2(5(5(1(0(4(4(5(0(2(3(3(2(4(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) -> 4(2(2(4(0(0(3(2(5(3(4(5(4(0(0(4(0(2(1(0(5(5(2(4(3(3(5(4(1(0(4(4(0(0(4(3(3(2(2(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) 0(1(0(4(0(1(1(1(1(1(0(3(4(3(3(1(4(0(2(0(1(1(0(4(4(3(3(5(0(1(1(0(3(0(4(0(0(4(0(3(1(3(5(3(5(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(3(1(0(1(3(1(0(1(5(3(4(0(3(1(4(0(2(3(1(4(0(5(4(0(3(0(1(1(1(0(0(0(4(0(0(4(1(5(1(1(4(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) 0(2(2(3(1(3(4(0(5(3(3(2(0(2(1(5(0(2(0(3(2(1(4(5(0(4(4(0(2(3(0(1(2(1(2(1(1(5(3(2(3(0(3(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(5(0(3(4(2(5(0(3(2(1(2(1(3(0(1(0(3(4(0(4(4(0(2(2(0(2(3(3(3(2(1(3(1(1(5(2(1(3(5(0(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) 2(2(0(4(5(5(3(5(1(2(3(5(2(5(5(3(3(2(1(1(1(3(1(3(5(3(4(1(5(2(1(1(4(1(1(2(2(3(2(4(2(2(5(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(5(1(3(2(1(3(1(3(2(5(5(3(5(5(1(2(1(3(5(3(1(2(4(0(3(5(4(2(4(1(1(2(2(3(3(2(2(4(5(5(3(x1))))))))))))))))))))))))))))))))))))))))))))) 2(5(0(5(0(1(5(1(3(4(4(3(1(3(3(3(0(5(3(3(0(4(3(3(3(2(4(4(2(2(5(2(4(3(3(5(1(2(1(0(4(1(5(2(3(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(0(5(0(2(5(1(3(3(2(3(1(4(3(2(0(5(3(3(4(4(3(2(3(2(4(1(0(4(5(2(4(3(0(5(1(1(2(3(4(1(5(3(3(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))) 4(5(4(2(3(3(2(4(1(0(3(4(4(3(1(4(0(0(1(4(4(4(5(2(0(4(2(2(2(2(0(4(3(4(3(0(3(2(5(3(3(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(3(2(5(4(2(3(1(4(4(4(4(3(2(4(4(0(1(4(4(2(0(0(3(4(3(2(0(2(0(1(3(4(3(0(3(5(2(3(2(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) 0(3(1(4(5(1(2(2(4(5(1(3(5(3(2(3(0(4(5(2(1(4(4(5(3(1(0(1(1(2(5(3(4(5(5(0(2(3(0(4(1(0(3(3(0(2(4(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(1(4(5(1(5(2(2(5(2(3(4(4(4(3(0(5(4(2(2(3(4(0(5(1(0(0(1(2(1(3(5(5(2(0(5(3(1(4(1(0(3(3(4(1(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(4(4(2(5(4(5(2(1(4(4(2(0(2(3(5(0(3(3(5(0(3(5(0(4(0(0(5(5(2(5(0(4(0(3(2(2(1(5(3(2(4(3(1(5(4(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(2(1(2(0(4(5(5(5(4(4(5(0(0(3(4(0(2(3(4(3(3(1(2(4(5(4(5(2(5(2(0(5(0(3(0(0(1(5(3(2(1(2(1(5(4(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 2(3(1(5(1(2(3(3(3(5(2(1(5(5(3(4(0(5(2(2(2(3(2(3(3(3(3(1(3(2(2(0(2(1(4(1(4(4(3(2(4(4(0(4(2(4(3(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 1(3(2(3(3(2(3(4(2(4(2(0(1(5(3(4(0(5(2(2(1(3(2(1(5(3(3(3(3(2(2(0(2(2(4(4(3(1(5(3(0(4(5(4(2(3(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) 4(5(5(4(4(4(3(3(2(0(1(4(5(3(1(1(5(4(3(0(2(4(2(5(4(2(0(3(4(1(4(2(5(1(5(4(0(4(0(0(2(2(2(0(3(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(5(4(4(5(3(1(2(1(3(4(5(3(3(1(2(4(3(1(4(2(5(4(4(4(0(4(0(0(4(2(0(1(5(2(2(2(0(0(5(2(2(0(3(5(4(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(3(5(2(5(4(0(1(4(5(5(2(1(2(5(4(1(3(1(3(5(3(4(2(5(0(1(3(5(3(3(0(2(2(2(2(5(1(4(5(3(1(4(0(2(1(5(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(3(5(2(5(4(0(5(5(5(4(2(1(3(3(0(1(1(2(3(5(1(4(2(1(5(1(4(0(2(3(0(3(2(2(3(5(1(1(5(3(1(1(4(2(4(5(1(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) 4(0(3(4(1(4(0(4(5(3(0(2(3(4(2(0(5(2(4(1(5(3(0(4(2(5(3(5(1(0(1(1(0(3(5(3(3(4(5(0(4(4(3(3(2(1(1(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(0(4(5(1(0(4(5(3(0(2(3(4(2(0(5(2(4(1(0(3(0(1(1(5(0(3(1(1(4(3(5(2(5(2(5(4(4(3(5(4(3(3(3(4(0(3(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(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)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(2(2(3(x1)))))) -> 0(2(2(1(0(3(x1)))))) 0(4(4(1(0(4(x1)))))) -> 0(4(4(4(0(1(x1)))))) 0(4(0(0(4(2(3(5(1(x1))))))))) -> 5(0(3(2(4(0(0(1(4(x1))))))))) 1(2(3(1(0(1(4(2(0(x1))))))))) -> 4(0(3(2(1(1(2(1(0(x1))))))))) 1(3(4(0(4(1(1(2(3(5(4(4(x1)))))))))))) -> 2(4(4(0(1(3(5(1(4(3(4(1(x1)))))))))))) 4(1(1(3(3(0(1(5(0(4(4(2(2(3(3(5(4(3(x1)))))))))))))))))) -> 4(0(4(2(4(3(1(3(4(3(5(1(2(0(3(5(1(3(x1)))))))))))))))))) 1(0(4(3(1(2(1(2(0(4(3(3(2(1(5(2(3(2(1(x1))))))))))))))))))) -> 1(4(2(1(1(4(1(0(3(0(5(3(1(3(2(2(3(2(2(x1))))))))))))))))))) 1(1(1(3(0(4(5(0(3(0(1(1(3(0(4(5(3(3(0(x1))))))))))))))))))) -> 4(5(0(3(3(4(1(0(0(1(1(1(3(1(0(3(5(3(0(x1))))))))))))))))))) 1(3(2(3(0(5(0(4(1(1(2(4(4(3(3(5(4(0(5(x1))))))))))))))))))) -> 4(2(1(2(5(3(4(1(1(3(0(0(3(3(4(0(5(4(5(x1))))))))))))))))))) 3(0(2(2(0(1(1(5(0(1(1(1(0(2(0(4(5(0(1(x1))))))))))))))))))) -> 5(1(2(1(4(0(0(3(0(1(0(0(1(0(1(2(5(1(2(x1))))))))))))))))))) 0(2(1(5(4(1(5(4(0(1(2(0(2(1(2(1(1(1(3(5(2(5(x1)))))))))))))))))))))) -> 2(1(1(3(5(4(2(5(0(5(2(1(1(1(2(1(4(0(2(0(5(1(x1)))))))))))))))))))))) 2(2(5(3(3(3(0(4(1(3(5(4(5(1(3(4(1(0(3(5(4(0(x1)))))))))))))))))))))) -> 0(1(5(3(4(1(3(5(3(3(1(3(4(5(3(4(4(0(2(2(5(0(x1)))))))))))))))))))))) 2(5(5(1(4(3(3(2(1(1(1(5(0(4(4(3(5(1(4(1(4(5(2(x1))))))))))))))))))))))) -> 3(4(5(1(4(4(5(2(1(5(5(5(0(1(2(1(1(1(3(4(3(4(2(x1))))))))))))))))))))))) 3(4(0(2(2(3(2(4(2(3(5(3(5(0(1(3(5(5(2(4(4(2(3(3(x1)))))))))))))))))))))))) -> 5(5(3(2(2(2(0(5(4(3(3(3(2(0(2(4(2(1(5(3(4(3(4(3(x1)))))))))))))))))))))))) 5(5(2(0(2(1(5(5(2(1(4(4(5(2(4(4(1(1(1(3(2(5(5(5(x1)))))))))))))))))))))))) -> 5(4(5(0(5(4(2(1(2(4(1(1(2(1(2(4(5(3(1(5(2(5(5(5(x1)))))))))))))))))))))))) 1(5(2(4(1(3(3(5(3(0(4(2(5(1(5(2(0(1(0(3(0(5(5(1(4(x1))))))))))))))))))))))))) -> 1(5(2(3(1(5(4(5(5(2(3(4(2(3(5(4(1(1(3(0(0(1(0(5(0(x1))))))))))))))))))))))))) 3(1(5(1(0(4(4(1(1(2(2(0(2(3(3(2(2(3(3(5(4(1(2(5(1(x1))))))))))))))))))))))))) -> 1(3(0(3(5(5(2(1(2(3(2(5(2(3(1(0(2(1(3(1(4(1(2(4(4(x1))))))))))))))))))))))))) 0(0(1(4(0(0(4(2(1(5(5(3(0(3(4(0(1(4(3(1(5(5(2(0(0(2(3(x1))))))))))))))))))))))))))) -> 0(0(5(4(1(2(4(2(1(5(4(2(0(5(0(0(0(3(4(1(3(5(3(0(1(0(3(x1))))))))))))))))))))))))))) 1(1(5(4(4(5(0(4(5(1(1(0(3(2(1(3(0(2(1(5(3(2(0(4(5(0(2(x1))))))))))))))))))))))))))) -> 2(3(4(0(1(5(0(5(1(1(2(0(3(4(1(3(0(4(1(5(2(5(0(4(2(5(1(x1))))))))))))))))))))))))))) 1(5(2(4(3(0(1(4(3(5(0(5(0(1(3(2(0(1(4(3(3(2(1(0(1(5(5(x1))))))))))))))))))))))))))) -> 1(5(1(4(1(0(0(3(5(5(0(0(3(0(1(1(4(5(3(2(3(1(2(4(2(5(3(x1))))))))))))))))))))))))))) 0(1(2(5(3(3(1(0(4(1(4(2(0(1(0(4(4(1(0(5(3(2(1(2(5(2(5(1(x1)))))))))))))))))))))))))))) -> 0(1(1(5(3(5(4(0(2(3(0(0(0(4(5(1(4(1(2(1(5(2(1(4(3(2(2(1(x1)))))))))))))))))))))))))))) 0(4(1(4(2(2(4(0(0(3(5(3(0(0(5(0(4(5(5(5(3(2(1(1(0(2(3(1(x1)))))))))))))))))))))))))))) -> 0(1(2(4(1(1(3(0(5(2(3(0(3(0(5(0(4(5(2(4(5(4(1(5(0(2(0(3(x1)))))))))))))))))))))))))))) 2(0(3(1(0(4(3(1(5(2(2(4(1(1(3(0(2(4(2(5(2(2(2(4(1(5(5(1(2(x1))))))))))))))))))))))))))))) -> 2(0(0(2(2(1(5(2(3(1(3(3(1(4(5(2(1(4(2(5(2(2(2(0(5(4(4(1(1(x1))))))))))))))))))))))))))))) 0(5(0(2(3(0(4(0(0(4(3(3(5(0(4(5(4(1(4(0(2(5(5(5(3(1(5(2(2(3(3(x1))))))))))))))))))))))))))))))) -> 2(3(5(3(5(0(4(0(0(0(3(3(4(0(4(1(4(5(3(4(2(5(5(5(5(2(0(0(2(1(3(x1))))))))))))))))))))))))))))))) 1(2(3(5(3(5(0(3(3(3(1(3(1(0(3(3(5(2(0(3(4(4(0(0(4(0(4(0(0(2(2(x1))))))))))))))))))))))))))))))) -> 1(3(3(5(0(5(5(3(4(1(2(3(3(0(0(4(2(1(0(0(0(3(2(3(4(0(3(0(4(3(2(x1))))))))))))))))))))))))))))))) 3(2(4(2(2(3(1(4(1(2(0(1(0(5(2(1(3(0(1(1(2(0(4(0(1(0(3(4(2(1(4(x1))))))))))))))))))))))))))))))) -> 0(2(1(2(1(4(1(3(1(2(4(5(0(0(2(1(1(4(1(3(4(0(1(0(2(3(3(2(0(2(4(x1))))))))))))))))))))))))))))))) 4(0(4(0(4(2(1(5(1(2(3(1(0(0(3(3(4(3(5(4(2(1(5(5(3(4(0(1(3(5(2(x1))))))))))))))))))))))))))))))) -> 4(0(4(3(1(2(3(4(2(5(3(2(0(5(1(3(4(1(0(3(5(1(2(4(1(3(0(4(0(5(5(x1))))))))))))))))))))))))))))))) 2(2(4(3(5(5(4(1(3(0(4(5(5(2(2(3(3(5(2(1(0(3(1(1(0(3(3(3(0(0(1(0(3(x1))))))))))))))))))))))))))))))))) -> 2(4(1(5(1(5(0(4(0(0(0(2(3(2(3(3(2(5(1(5(1(3(3(2(5(3(3(4(3(1(0(0(3(x1))))))))))))))))))))))))))))))))) 2(4(4(0(2(1(3(5(0(0(1(4(4(2(1(1(2(0(0(5(2(2(3(2(5(5(1(0(1(1(3(4(4(5(x1)))))))))))))))))))))))))))))))))) -> 2(4(3(0(5(0(1(1(1(0(2(1(1(2(2(2(4(0(0(4(5(2(4(3(5(5(0(4(1(1(3(4(2(5(x1)))))))))))))))))))))))))))))))))) 5(4(3(5(2(3(5(1(2(2(3(1(3(2(3(2(4(1(0(1(4(5(4(1(4(4(0(1(0(2(5(2(2(0(x1)))))))))))))))))))))))))))))))))) -> 5(4(1(5(2(2(5(3(4(0(5(0(4(2(3(0(0(3(4(5(2(1(4(2(3(4(1(1(2(1(1(2(2(3(x1)))))))))))))))))))))))))))))))))) 0(3(0(4(5(5(5(1(3(0(4(4(3(4(5(2(5(0(0(1(5(0(5(5(0(4(5(1(1(0(4(3(4(5(2(x1))))))))))))))))))))))))))))))))))) -> 0(3(0(0(1(5(5(1(3(4(4(1(4(0(4(5(5(4(2(2(5(5(5(5(0(0(0(1(3(4(5(3(4(5(0(x1))))))))))))))))))))))))))))))))))) 4(2(1(2(2(1(5(1(5(3(0(5(3(5(0(4(4(3(1(2(1(2(0(2(4(4(3(1(1(4(4(5(5(1(2(x1))))))))))))))))))))))))))))))))))) -> 4(1(5(2(2(0(5(3(0(2(2(2(1(5(3(4(1(2(1(5(3(1(0(3(4(4(4(1(1(4(4(5(5(2(1(x1))))))))))))))))))))))))))))))))))) 5(4(4(1(1(3(5(2(2(2(5(3(3(3(0(4(5(3(2(3(0(5(5(1(2(2(0(1(1(3(1(5(0(0(2(x1))))))))))))))))))))))))))))))))))) -> 3(4(5(1(0(2(3(2(3(2(0(3(5(3(1(4(5(2(2(2(0(1(5(5(2(1(1(4(5(3(5(0(0(1(3(x1))))))))))))))))))))))))))))))))))) 0(0(3(0(0(0(3(4(1(4(0(5(2(1(5(2(4(1(1(1(5(2(2(5(3(4(0(0(4(3(1(3(5(4(1(1(x1)))))))))))))))))))))))))))))))))))) -> 0(0(1(4(0(5(0(1(4(4(0(0(2(1(5(3(1(0(1(0(5(2(2(5(3(4(3(1(4(3(3(4(5(1(2(1(x1)))))))))))))))))))))))))))))))))))) 2(1(1(4(3(2(2(4(1(5(3(3(3(3(2(4(4(3(0(1(4(3(2(0(0(2(1(5(2(2(3(0(1(5(1(2(x1)))))))))))))))))))))))))))))))))))) -> 0(3(1(2(3(4(0(2(2(3(1(3(1(3(5(4(4(3(2(1(4(3(4(2(0(1(1(5(2(2(3(0(5(2(1(2(x1)))))))))))))))))))))))))))))))))))) 4(5(4(4(4(0(4(4(5(5(2(0(2(5(0(3(1(4(3(4(3(0(1(4(4(1(0(4(5(4(3(3(1(1(0(5(x1)))))))))))))))))))))))))))))))))))) -> 4(4(4(5(3(1(1(2(5(5(3(4(4(5(1(3(3(4(4(0(0(0(5(0(1(1(0(4(5(2(0(3(4(4(4(4(x1)))))))))))))))))))))))))))))))))))) 0(0(5(5(1(0(1(4(5(2(0(5(2(5(2(1(0(5(1(1(4(5(0(2(1(0(3(4(1(2(5(0(1(4(4(5(3(5(x1)))))))))))))))))))))))))))))))))))))) -> 0(3(4(5(1(0(0(5(1(0(0(5(4(5(0(1(2(5(5(4(4(1(0(2(1(3(2(2(1(0(5(1(5(1(4(5(2(5(x1)))))))))))))))))))))))))))))))))))))) 0(1(3(0(3(1(0(3(0(4(3(0(3(2(1(3(5(0(5(3(0(1(0(1(1(4(3(0(5(1(4(3(3(3(0(0(0(5(3(4(x1)))))))))))))))))))))))))))))))))))))))) -> 0(3(1(0(5(4(0(3(0(4(5(0(5(1(3(3(0(0(3(0(3(1(3(2(1(1(5(4(3(1(1(0(3(3(0(0(3(4(3(0(x1)))))))))))))))))))))))))))))))))))))))) 4(3(3(0(0(0(3(2(4(3(0(0(4(4(2(4(4(2(1(2(5(5(0(0(4(2(5(5(1(0(4(4(5(0(2(3(3(2(4(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) -> 4(2(2(4(0(0(3(2(5(3(4(5(4(0(0(4(0(2(1(0(5(5(2(4(3(3(5(4(1(0(4(4(0(0(4(3(3(2(2(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) 0(1(0(4(0(1(1(1(1(1(0(3(4(3(3(1(4(0(2(0(1(1(0(4(4(3(3(5(0(1(1(0(3(0(4(0(0(4(0(3(1(3(5(3(5(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(3(1(0(1(3(1(0(1(5(3(4(0(3(1(4(0(2(3(1(4(0(5(4(0(3(0(1(1(1(0(0(0(4(0(0(4(1(5(1(1(4(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) 0(2(2(3(1(3(4(0(5(3(3(2(0(2(1(5(0(2(0(3(2(1(4(5(0(4(4(0(2(3(0(1(2(1(2(1(1(5(3(2(3(0(3(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(5(0(3(4(2(5(0(3(2(1(2(1(3(0(1(0(3(4(0(4(4(0(2(2(0(2(3(3(3(2(1(3(1(1(5(2(1(3(5(0(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) 2(2(0(4(5(5(3(5(1(2(3(5(2(5(5(3(3(2(1(1(1(3(1(3(5(3(4(1(5(2(1(1(4(1(1(2(2(3(2(4(2(2(5(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(5(1(3(2(1(3(1(3(2(5(5(3(5(5(1(2(1(3(5(3(1(2(4(0(3(5(4(2(4(1(1(2(2(3(3(2(2(4(5(5(3(x1))))))))))))))))))))))))))))))))))))))))))))) 2(5(0(5(0(1(5(1(3(4(4(3(1(3(3(3(0(5(3(3(0(4(3(3(3(2(4(4(2(2(5(2(4(3(3(5(1(2(1(0(4(1(5(2(3(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(0(5(0(2(5(1(3(3(2(3(1(4(3(2(0(5(3(3(4(4(3(2(3(2(4(1(0(4(5(2(4(3(0(5(1(1(2(3(4(1(5(3(3(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))) 4(5(4(2(3(3(2(4(1(0(3(4(4(3(1(4(0(0(1(4(4(4(5(2(0(4(2(2(2(2(0(4(3(4(3(0(3(2(5(3(3(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(3(2(5(4(2(3(1(4(4(4(4(3(2(4(4(0(1(4(4(2(0(0(3(4(3(2(0(2(0(1(3(4(3(0(3(5(2(3(2(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) 0(3(1(4(5(1(2(2(4(5(1(3(5(3(2(3(0(4(5(2(1(4(4(5(3(1(0(1(1(2(5(3(4(5(5(0(2(3(0(4(1(0(3(3(0(2(4(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(1(4(5(1(5(2(2(5(2(3(4(4(4(3(0(5(4(2(2(3(4(0(5(1(0(0(1(2(1(3(5(5(2(0(5(3(1(4(1(0(3(3(4(1(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(4(4(2(5(4(5(2(1(4(4(2(0(2(3(5(0(3(3(5(0(3(5(0(4(0(0(5(5(2(5(0(4(0(3(2(2(1(5(3(2(4(3(1(5(4(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(2(1(2(0(4(5(5(5(4(4(5(0(0(3(4(0(2(3(4(3(3(1(2(4(5(4(5(2(5(2(0(5(0(3(0(0(1(5(3(2(1(2(1(5(4(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 2(3(1(5(1(2(3(3(3(5(2(1(5(5(3(4(0(5(2(2(2(3(2(3(3(3(3(1(3(2(2(0(2(1(4(1(4(4(3(2(4(4(0(4(2(4(3(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 1(3(2(3(3(2(3(4(2(4(2(0(1(5(3(4(0(5(2(2(1(3(2(1(5(3(3(3(3(2(2(0(2(2(4(4(3(1(5(3(0(4(5(4(2(3(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) 4(5(5(4(4(4(3(3(2(0(1(4(5(3(1(1(5(4(3(0(2(4(2(5(4(2(0(3(4(1(4(2(5(1(5(4(0(4(0(0(2(2(2(0(3(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(5(4(4(5(3(1(2(1(3(4(5(3(3(1(2(4(3(1(4(2(5(4(4(4(0(4(0(0(4(2(0(1(5(2(2(2(0(0(5(2(2(0(3(5(4(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(3(5(2(5(4(0(1(4(5(5(2(1(2(5(4(1(3(1(3(5(3(4(2(5(0(1(3(5(3(3(0(2(2(2(2(5(1(4(5(3(1(4(0(2(1(5(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(3(5(2(5(4(0(5(5(5(4(2(1(3(3(0(1(1(2(3(5(1(4(2(1(5(1(4(0(2(3(0(3(2(2(3(5(1(1(5(3(1(1(4(2(4(5(1(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) 4(0(3(4(1(4(0(4(5(3(0(2(3(4(2(0(5(2(4(1(5(3(0(4(2(5(3(5(1(0(1(1(0(3(5(3(3(4(5(0(4(4(3(3(2(1(1(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(0(4(5(1(0(4(5(3(0(2(3(4(2(0(5(2(4(1(0(3(0(1(1(5(0(3(1(1(4(3(5(2(5(2(5(4(4(3(5(4(3(3(3(4(0(3(5(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_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(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)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(2(2(3(x1)))))) -> 0(2(2(1(0(3(x1)))))) 0(4(4(1(0(4(x1)))))) -> 0(4(4(4(0(1(x1)))))) 0(4(0(0(4(2(3(5(1(x1))))))))) -> 5(0(3(2(4(0(0(1(4(x1))))))))) 1(2(3(1(0(1(4(2(0(x1))))))))) -> 4(0(3(2(1(1(2(1(0(x1))))))))) 1(3(4(0(4(1(1(2(3(5(4(4(x1)))))))))))) -> 2(4(4(0(1(3(5(1(4(3(4(1(x1)))))))))))) 4(1(1(3(3(0(1(5(0(4(4(2(2(3(3(5(4(3(x1)))))))))))))))))) -> 4(0(4(2(4(3(1(3(4(3(5(1(2(0(3(5(1(3(x1)))))))))))))))))) 1(0(4(3(1(2(1(2(0(4(3(3(2(1(5(2(3(2(1(x1))))))))))))))))))) -> 1(4(2(1(1(4(1(0(3(0(5(3(1(3(2(2(3(2(2(x1))))))))))))))))))) 1(1(1(3(0(4(5(0(3(0(1(1(3(0(4(5(3(3(0(x1))))))))))))))))))) -> 4(5(0(3(3(4(1(0(0(1(1(1(3(1(0(3(5(3(0(x1))))))))))))))))))) 1(3(2(3(0(5(0(4(1(1(2(4(4(3(3(5(4(0(5(x1))))))))))))))))))) -> 4(2(1(2(5(3(4(1(1(3(0(0(3(3(4(0(5(4(5(x1))))))))))))))))))) 3(0(2(2(0(1(1(5(0(1(1(1(0(2(0(4(5(0(1(x1))))))))))))))))))) -> 5(1(2(1(4(0(0(3(0(1(0(0(1(0(1(2(5(1(2(x1))))))))))))))))))) 0(2(1(5(4(1(5(4(0(1(2(0(2(1(2(1(1(1(3(5(2(5(x1)))))))))))))))))))))) -> 2(1(1(3(5(4(2(5(0(5(2(1(1(1(2(1(4(0(2(0(5(1(x1)))))))))))))))))))))) 2(2(5(3(3(3(0(4(1(3(5(4(5(1(3(4(1(0(3(5(4(0(x1)))))))))))))))))))))) -> 0(1(5(3(4(1(3(5(3(3(1(3(4(5(3(4(4(0(2(2(5(0(x1)))))))))))))))))))))) 2(5(5(1(4(3(3(2(1(1(1(5(0(4(4(3(5(1(4(1(4(5(2(x1))))))))))))))))))))))) -> 3(4(5(1(4(4(5(2(1(5(5(5(0(1(2(1(1(1(3(4(3(4(2(x1))))))))))))))))))))))) 3(4(0(2(2(3(2(4(2(3(5(3(5(0(1(3(5(5(2(4(4(2(3(3(x1)))))))))))))))))))))))) -> 5(5(3(2(2(2(0(5(4(3(3(3(2(0(2(4(2(1(5(3(4(3(4(3(x1)))))))))))))))))))))))) 5(5(2(0(2(1(5(5(2(1(4(4(5(2(4(4(1(1(1(3(2(5(5(5(x1)))))))))))))))))))))))) -> 5(4(5(0(5(4(2(1(2(4(1(1(2(1(2(4(5(3(1(5(2(5(5(5(x1)))))))))))))))))))))))) 1(5(2(4(1(3(3(5(3(0(4(2(5(1(5(2(0(1(0(3(0(5(5(1(4(x1))))))))))))))))))))))))) -> 1(5(2(3(1(5(4(5(5(2(3(4(2(3(5(4(1(1(3(0(0(1(0(5(0(x1))))))))))))))))))))))))) 3(1(5(1(0(4(4(1(1(2(2(0(2(3(3(2(2(3(3(5(4(1(2(5(1(x1))))))))))))))))))))))))) -> 1(3(0(3(5(5(2(1(2(3(2(5(2(3(1(0(2(1(3(1(4(1(2(4(4(x1))))))))))))))))))))))))) 0(0(1(4(0(0(4(2(1(5(5(3(0(3(4(0(1(4(3(1(5(5(2(0(0(2(3(x1))))))))))))))))))))))))))) -> 0(0(5(4(1(2(4(2(1(5(4(2(0(5(0(0(0(3(4(1(3(5(3(0(1(0(3(x1))))))))))))))))))))))))))) 1(1(5(4(4(5(0(4(5(1(1(0(3(2(1(3(0(2(1(5(3(2(0(4(5(0(2(x1))))))))))))))))))))))))))) -> 2(3(4(0(1(5(0(5(1(1(2(0(3(4(1(3(0(4(1(5(2(5(0(4(2(5(1(x1))))))))))))))))))))))))))) 1(5(2(4(3(0(1(4(3(5(0(5(0(1(3(2(0(1(4(3(3(2(1(0(1(5(5(x1))))))))))))))))))))))))))) -> 1(5(1(4(1(0(0(3(5(5(0(0(3(0(1(1(4(5(3(2(3(1(2(4(2(5(3(x1))))))))))))))))))))))))))) 0(1(2(5(3(3(1(0(4(1(4(2(0(1(0(4(4(1(0(5(3(2(1(2(5(2(5(1(x1)))))))))))))))))))))))))))) -> 0(1(1(5(3(5(4(0(2(3(0(0(0(4(5(1(4(1(2(1(5(2(1(4(3(2(2(1(x1)))))))))))))))))))))))))))) 0(4(1(4(2(2(4(0(0(3(5(3(0(0(5(0(4(5(5(5(3(2(1(1(0(2(3(1(x1)))))))))))))))))))))))))))) -> 0(1(2(4(1(1(3(0(5(2(3(0(3(0(5(0(4(5(2(4(5(4(1(5(0(2(0(3(x1)))))))))))))))))))))))))))) 2(0(3(1(0(4(3(1(5(2(2(4(1(1(3(0(2(4(2(5(2(2(2(4(1(5(5(1(2(x1))))))))))))))))))))))))))))) -> 2(0(0(2(2(1(5(2(3(1(3(3(1(4(5(2(1(4(2(5(2(2(2(0(5(4(4(1(1(x1))))))))))))))))))))))))))))) 0(5(0(2(3(0(4(0(0(4(3(3(5(0(4(5(4(1(4(0(2(5(5(5(3(1(5(2(2(3(3(x1))))))))))))))))))))))))))))))) -> 2(3(5(3(5(0(4(0(0(0(3(3(4(0(4(1(4(5(3(4(2(5(5(5(5(2(0(0(2(1(3(x1))))))))))))))))))))))))))))))) 1(2(3(5(3(5(0(3(3(3(1(3(1(0(3(3(5(2(0(3(4(4(0(0(4(0(4(0(0(2(2(x1))))))))))))))))))))))))))))))) -> 1(3(3(5(0(5(5(3(4(1(2(3(3(0(0(4(2(1(0(0(0(3(2(3(4(0(3(0(4(3(2(x1))))))))))))))))))))))))))))))) 3(2(4(2(2(3(1(4(1(2(0(1(0(5(2(1(3(0(1(1(2(0(4(0(1(0(3(4(2(1(4(x1))))))))))))))))))))))))))))))) -> 0(2(1(2(1(4(1(3(1(2(4(5(0(0(2(1(1(4(1(3(4(0(1(0(2(3(3(2(0(2(4(x1))))))))))))))))))))))))))))))) 4(0(4(0(4(2(1(5(1(2(3(1(0(0(3(3(4(3(5(4(2(1(5(5(3(4(0(1(3(5(2(x1))))))))))))))))))))))))))))))) -> 4(0(4(3(1(2(3(4(2(5(3(2(0(5(1(3(4(1(0(3(5(1(2(4(1(3(0(4(0(5(5(x1))))))))))))))))))))))))))))))) 2(2(4(3(5(5(4(1(3(0(4(5(5(2(2(3(3(5(2(1(0(3(1(1(0(3(3(3(0(0(1(0(3(x1))))))))))))))))))))))))))))))))) -> 2(4(1(5(1(5(0(4(0(0(0(2(3(2(3(3(2(5(1(5(1(3(3(2(5(3(3(4(3(1(0(0(3(x1))))))))))))))))))))))))))))))))) 2(4(4(0(2(1(3(5(0(0(1(4(4(2(1(1(2(0(0(5(2(2(3(2(5(5(1(0(1(1(3(4(4(5(x1)))))))))))))))))))))))))))))))))) -> 2(4(3(0(5(0(1(1(1(0(2(1(1(2(2(2(4(0(0(4(5(2(4(3(5(5(0(4(1(1(3(4(2(5(x1)))))))))))))))))))))))))))))))))) 5(4(3(5(2(3(5(1(2(2(3(1(3(2(3(2(4(1(0(1(4(5(4(1(4(4(0(1(0(2(5(2(2(0(x1)))))))))))))))))))))))))))))))))) -> 5(4(1(5(2(2(5(3(4(0(5(0(4(2(3(0(0(3(4(5(2(1(4(2(3(4(1(1(2(1(1(2(2(3(x1)))))))))))))))))))))))))))))))))) 0(3(0(4(5(5(5(1(3(0(4(4(3(4(5(2(5(0(0(1(5(0(5(5(0(4(5(1(1(0(4(3(4(5(2(x1))))))))))))))))))))))))))))))))))) -> 0(3(0(0(1(5(5(1(3(4(4(1(4(0(4(5(5(4(2(2(5(5(5(5(0(0(0(1(3(4(5(3(4(5(0(x1))))))))))))))))))))))))))))))))))) 4(2(1(2(2(1(5(1(5(3(0(5(3(5(0(4(4(3(1(2(1(2(0(2(4(4(3(1(1(4(4(5(5(1(2(x1))))))))))))))))))))))))))))))))))) -> 4(1(5(2(2(0(5(3(0(2(2(2(1(5(3(4(1(2(1(5(3(1(0(3(4(4(4(1(1(4(4(5(5(2(1(x1))))))))))))))))))))))))))))))))))) 5(4(4(1(1(3(5(2(2(2(5(3(3(3(0(4(5(3(2(3(0(5(5(1(2(2(0(1(1(3(1(5(0(0(2(x1))))))))))))))))))))))))))))))))))) -> 3(4(5(1(0(2(3(2(3(2(0(3(5(3(1(4(5(2(2(2(0(1(5(5(2(1(1(4(5(3(5(0(0(1(3(x1))))))))))))))))))))))))))))))))))) 0(0(3(0(0(0(3(4(1(4(0(5(2(1(5(2(4(1(1(1(5(2(2(5(3(4(0(0(4(3(1(3(5(4(1(1(x1)))))))))))))))))))))))))))))))))))) -> 0(0(1(4(0(5(0(1(4(4(0(0(2(1(5(3(1(0(1(0(5(2(2(5(3(4(3(1(4(3(3(4(5(1(2(1(x1)))))))))))))))))))))))))))))))))))) 2(1(1(4(3(2(2(4(1(5(3(3(3(3(2(4(4(3(0(1(4(3(2(0(0(2(1(5(2(2(3(0(1(5(1(2(x1)))))))))))))))))))))))))))))))))))) -> 0(3(1(2(3(4(0(2(2(3(1(3(1(3(5(4(4(3(2(1(4(3(4(2(0(1(1(5(2(2(3(0(5(2(1(2(x1)))))))))))))))))))))))))))))))))))) 4(5(4(4(4(0(4(4(5(5(2(0(2(5(0(3(1(4(3(4(3(0(1(4(4(1(0(4(5(4(3(3(1(1(0(5(x1)))))))))))))))))))))))))))))))))))) -> 4(4(4(5(3(1(1(2(5(5(3(4(4(5(1(3(3(4(4(0(0(0(5(0(1(1(0(4(5(2(0(3(4(4(4(4(x1)))))))))))))))))))))))))))))))))))) 0(0(5(5(1(0(1(4(5(2(0(5(2(5(2(1(0(5(1(1(4(5(0(2(1(0(3(4(1(2(5(0(1(4(4(5(3(5(x1)))))))))))))))))))))))))))))))))))))) -> 0(3(4(5(1(0(0(5(1(0(0(5(4(5(0(1(2(5(5(4(4(1(0(2(1(3(2(2(1(0(5(1(5(1(4(5(2(5(x1)))))))))))))))))))))))))))))))))))))) 0(1(3(0(3(1(0(3(0(4(3(0(3(2(1(3(5(0(5(3(0(1(0(1(1(4(3(0(5(1(4(3(3(3(0(0(0(5(3(4(x1)))))))))))))))))))))))))))))))))))))))) -> 0(3(1(0(5(4(0(3(0(4(5(0(5(1(3(3(0(0(3(0(3(1(3(2(1(1(5(4(3(1(1(0(3(3(0(0(3(4(3(0(x1)))))))))))))))))))))))))))))))))))))))) 4(3(3(0(0(0(3(2(4(3(0(0(4(4(2(4(4(2(1(2(5(5(0(0(4(2(5(5(1(0(4(4(5(0(2(3(3(2(4(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) -> 4(2(2(4(0(0(3(2(5(3(4(5(4(0(0(4(0(2(1(0(5(5(2(4(3(3(5(4(1(0(4(4(0(0(4(3(3(2(2(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) 0(1(0(4(0(1(1(1(1(1(0(3(4(3(3(1(4(0(2(0(1(1(0(4(4(3(3(5(0(1(1(0(3(0(4(0(0(4(0(3(1(3(5(3(5(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(3(1(0(1(3(1(0(1(5(3(4(0(3(1(4(0(2(3(1(4(0(5(4(0(3(0(1(1(1(0(0(0(4(0(0(4(1(5(1(1(4(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) 0(2(2(3(1(3(4(0(5(3(3(2(0(2(1(5(0(2(0(3(2(1(4(5(0(4(4(0(2(3(0(1(2(1(2(1(1(5(3(2(3(0(3(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(5(0(3(4(2(5(0(3(2(1(2(1(3(0(1(0(3(4(0(4(4(0(2(2(0(2(3(3(3(2(1(3(1(1(5(2(1(3(5(0(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) 2(2(0(4(5(5(3(5(1(2(3(5(2(5(5(3(3(2(1(1(1(3(1(3(5(3(4(1(5(2(1(1(4(1(1(2(2(3(2(4(2(2(5(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(5(1(3(2(1(3(1(3(2(5(5(3(5(5(1(2(1(3(5(3(1(2(4(0(3(5(4(2(4(1(1(2(2(3(3(2(2(4(5(5(3(x1))))))))))))))))))))))))))))))))))))))))))))) 2(5(0(5(0(1(5(1(3(4(4(3(1(3(3(3(0(5(3(3(0(4(3(3(3(2(4(4(2(2(5(2(4(3(3(5(1(2(1(0(4(1(5(2(3(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(0(5(0(2(5(1(3(3(2(3(1(4(3(2(0(5(3(3(4(4(3(2(3(2(4(1(0(4(5(2(4(3(0(5(1(1(2(3(4(1(5(3(3(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))) 4(5(4(2(3(3(2(4(1(0(3(4(4(3(1(4(0(0(1(4(4(4(5(2(0(4(2(2(2(2(0(4(3(4(3(0(3(2(5(3(3(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(3(2(5(4(2(3(1(4(4(4(4(3(2(4(4(0(1(4(4(2(0(0(3(4(3(2(0(2(0(1(3(4(3(0(3(5(2(3(2(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) 0(3(1(4(5(1(2(2(4(5(1(3(5(3(2(3(0(4(5(2(1(4(4(5(3(1(0(1(1(2(5(3(4(5(5(0(2(3(0(4(1(0(3(3(0(2(4(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(1(4(5(1(5(2(2(5(2(3(4(4(4(3(0(5(4(2(2(3(4(0(5(1(0(0(1(2(1(3(5(5(2(0(5(3(1(4(1(0(3(3(4(1(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(4(4(2(5(4(5(2(1(4(4(2(0(2(3(5(0(3(3(5(0(3(5(0(4(0(0(5(5(2(5(0(4(0(3(2(2(1(5(3(2(4(3(1(5(4(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(2(1(2(0(4(5(5(5(4(4(5(0(0(3(4(0(2(3(4(3(3(1(2(4(5(4(5(2(5(2(0(5(0(3(0(0(1(5(3(2(1(2(1(5(4(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 2(3(1(5(1(2(3(3(3(5(2(1(5(5(3(4(0(5(2(2(2(3(2(3(3(3(3(1(3(2(2(0(2(1(4(1(4(4(3(2(4(4(0(4(2(4(3(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 1(3(2(3(3(2(3(4(2(4(2(0(1(5(3(4(0(5(2(2(1(3(2(1(5(3(3(3(3(2(2(0(2(2(4(4(3(1(5(3(0(4(5(4(2(3(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) 4(5(5(4(4(4(3(3(2(0(1(4(5(3(1(1(5(4(3(0(2(4(2(5(4(2(0(3(4(1(4(2(5(1(5(4(0(4(0(0(2(2(2(0(3(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(5(4(4(5(3(1(2(1(3(4(5(3(3(1(2(4(3(1(4(2(5(4(4(4(0(4(0(0(4(2(0(1(5(2(2(2(0(0(5(2(2(0(3(5(4(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(3(5(2(5(4(0(1(4(5(5(2(1(2(5(4(1(3(1(3(5(3(4(2(5(0(1(3(5(3(3(0(2(2(2(2(5(1(4(5(3(1(4(0(2(1(5(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(3(5(2(5(4(0(5(5(5(4(2(1(3(3(0(1(1(2(3(5(1(4(2(1(5(1(4(0(2(3(0(3(2(2(3(5(1(1(5(3(1(1(4(2(4(5(1(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) 4(0(3(4(1(4(0(4(5(3(0(2(3(4(2(0(5(2(4(1(5(3(0(4(2(5(3(5(1(0(1(1(0(3(5(3(3(4(5(0(4(4(3(3(2(1(1(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(0(4(5(1(0(4(5(3(0(2(3(4(2(0(5(2(4(1(0(3(0(1(1(5(0(3(1(1(4(3(5(2(5(2(5(4(4(3(5(4(3(3(3(4(0(3(5(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_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(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)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(2(2(3(x1)))))) -> 0(2(2(1(0(3(x1)))))) 0(4(4(1(0(4(x1)))))) -> 0(4(4(4(0(1(x1)))))) 0(4(0(0(4(2(3(5(1(x1))))))))) -> 5(0(3(2(4(0(0(1(4(x1))))))))) 1(2(3(1(0(1(4(2(0(x1))))))))) -> 4(0(3(2(1(1(2(1(0(x1))))))))) 1(3(4(0(4(1(1(2(3(5(4(4(x1)))))))))))) -> 2(4(4(0(1(3(5(1(4(3(4(1(x1)))))))))))) 4(1(1(3(3(0(1(5(0(4(4(2(2(3(3(5(4(3(x1)))))))))))))))))) -> 4(0(4(2(4(3(1(3(4(3(5(1(2(0(3(5(1(3(x1)))))))))))))))))) 1(0(4(3(1(2(1(2(0(4(3(3(2(1(5(2(3(2(1(x1))))))))))))))))))) -> 1(4(2(1(1(4(1(0(3(0(5(3(1(3(2(2(3(2(2(x1))))))))))))))))))) 1(1(1(3(0(4(5(0(3(0(1(1(3(0(4(5(3(3(0(x1))))))))))))))))))) -> 4(5(0(3(3(4(1(0(0(1(1(1(3(1(0(3(5(3(0(x1))))))))))))))))))) 1(3(2(3(0(5(0(4(1(1(2(4(4(3(3(5(4(0(5(x1))))))))))))))))))) -> 4(2(1(2(5(3(4(1(1(3(0(0(3(3(4(0(5(4(5(x1))))))))))))))))))) 3(0(2(2(0(1(1(5(0(1(1(1(0(2(0(4(5(0(1(x1))))))))))))))))))) -> 5(1(2(1(4(0(0(3(0(1(0(0(1(0(1(2(5(1(2(x1))))))))))))))))))) 0(2(1(5(4(1(5(4(0(1(2(0(2(1(2(1(1(1(3(5(2(5(x1)))))))))))))))))))))) -> 2(1(1(3(5(4(2(5(0(5(2(1(1(1(2(1(4(0(2(0(5(1(x1)))))))))))))))))))))) 2(2(5(3(3(3(0(4(1(3(5(4(5(1(3(4(1(0(3(5(4(0(x1)))))))))))))))))))))) -> 0(1(5(3(4(1(3(5(3(3(1(3(4(5(3(4(4(0(2(2(5(0(x1)))))))))))))))))))))) 2(5(5(1(4(3(3(2(1(1(1(5(0(4(4(3(5(1(4(1(4(5(2(x1))))))))))))))))))))))) -> 3(4(5(1(4(4(5(2(1(5(5(5(0(1(2(1(1(1(3(4(3(4(2(x1))))))))))))))))))))))) 3(4(0(2(2(3(2(4(2(3(5(3(5(0(1(3(5(5(2(4(4(2(3(3(x1)))))))))))))))))))))))) -> 5(5(3(2(2(2(0(5(4(3(3(3(2(0(2(4(2(1(5(3(4(3(4(3(x1)))))))))))))))))))))))) 5(5(2(0(2(1(5(5(2(1(4(4(5(2(4(4(1(1(1(3(2(5(5(5(x1)))))))))))))))))))))))) -> 5(4(5(0(5(4(2(1(2(4(1(1(2(1(2(4(5(3(1(5(2(5(5(5(x1)))))))))))))))))))))))) 1(5(2(4(1(3(3(5(3(0(4(2(5(1(5(2(0(1(0(3(0(5(5(1(4(x1))))))))))))))))))))))))) -> 1(5(2(3(1(5(4(5(5(2(3(4(2(3(5(4(1(1(3(0(0(1(0(5(0(x1))))))))))))))))))))))))) 3(1(5(1(0(4(4(1(1(2(2(0(2(3(3(2(2(3(3(5(4(1(2(5(1(x1))))))))))))))))))))))))) -> 1(3(0(3(5(5(2(1(2(3(2(5(2(3(1(0(2(1(3(1(4(1(2(4(4(x1))))))))))))))))))))))))) 0(0(1(4(0(0(4(2(1(5(5(3(0(3(4(0(1(4(3(1(5(5(2(0(0(2(3(x1))))))))))))))))))))))))))) -> 0(0(5(4(1(2(4(2(1(5(4(2(0(5(0(0(0(3(4(1(3(5(3(0(1(0(3(x1))))))))))))))))))))))))))) 1(1(5(4(4(5(0(4(5(1(1(0(3(2(1(3(0(2(1(5(3(2(0(4(5(0(2(x1))))))))))))))))))))))))))) -> 2(3(4(0(1(5(0(5(1(1(2(0(3(4(1(3(0(4(1(5(2(5(0(4(2(5(1(x1))))))))))))))))))))))))))) 1(5(2(4(3(0(1(4(3(5(0(5(0(1(3(2(0(1(4(3(3(2(1(0(1(5(5(x1))))))))))))))))))))))))))) -> 1(5(1(4(1(0(0(3(5(5(0(0(3(0(1(1(4(5(3(2(3(1(2(4(2(5(3(x1))))))))))))))))))))))))))) 0(1(2(5(3(3(1(0(4(1(4(2(0(1(0(4(4(1(0(5(3(2(1(2(5(2(5(1(x1)))))))))))))))))))))))))))) -> 0(1(1(5(3(5(4(0(2(3(0(0(0(4(5(1(4(1(2(1(5(2(1(4(3(2(2(1(x1)))))))))))))))))))))))))))) 0(4(1(4(2(2(4(0(0(3(5(3(0(0(5(0(4(5(5(5(3(2(1(1(0(2(3(1(x1)))))))))))))))))))))))))))) -> 0(1(2(4(1(1(3(0(5(2(3(0(3(0(5(0(4(5(2(4(5(4(1(5(0(2(0(3(x1)))))))))))))))))))))))))))) 2(0(3(1(0(4(3(1(5(2(2(4(1(1(3(0(2(4(2(5(2(2(2(4(1(5(5(1(2(x1))))))))))))))))))))))))))))) -> 2(0(0(2(2(1(5(2(3(1(3(3(1(4(5(2(1(4(2(5(2(2(2(0(5(4(4(1(1(x1))))))))))))))))))))))))))))) 0(5(0(2(3(0(4(0(0(4(3(3(5(0(4(5(4(1(4(0(2(5(5(5(3(1(5(2(2(3(3(x1))))))))))))))))))))))))))))))) -> 2(3(5(3(5(0(4(0(0(0(3(3(4(0(4(1(4(5(3(4(2(5(5(5(5(2(0(0(2(1(3(x1))))))))))))))))))))))))))))))) 1(2(3(5(3(5(0(3(3(3(1(3(1(0(3(3(5(2(0(3(4(4(0(0(4(0(4(0(0(2(2(x1))))))))))))))))))))))))))))))) -> 1(3(3(5(0(5(5(3(4(1(2(3(3(0(0(4(2(1(0(0(0(3(2(3(4(0(3(0(4(3(2(x1))))))))))))))))))))))))))))))) 3(2(4(2(2(3(1(4(1(2(0(1(0(5(2(1(3(0(1(1(2(0(4(0(1(0(3(4(2(1(4(x1))))))))))))))))))))))))))))))) -> 0(2(1(2(1(4(1(3(1(2(4(5(0(0(2(1(1(4(1(3(4(0(1(0(2(3(3(2(0(2(4(x1))))))))))))))))))))))))))))))) 4(0(4(0(4(2(1(5(1(2(3(1(0(0(3(3(4(3(5(4(2(1(5(5(3(4(0(1(3(5(2(x1))))))))))))))))))))))))))))))) -> 4(0(4(3(1(2(3(4(2(5(3(2(0(5(1(3(4(1(0(3(5(1(2(4(1(3(0(4(0(5(5(x1))))))))))))))))))))))))))))))) 2(2(4(3(5(5(4(1(3(0(4(5(5(2(2(3(3(5(2(1(0(3(1(1(0(3(3(3(0(0(1(0(3(x1))))))))))))))))))))))))))))))))) -> 2(4(1(5(1(5(0(4(0(0(0(2(3(2(3(3(2(5(1(5(1(3(3(2(5(3(3(4(3(1(0(0(3(x1))))))))))))))))))))))))))))))))) 2(4(4(0(2(1(3(5(0(0(1(4(4(2(1(1(2(0(0(5(2(2(3(2(5(5(1(0(1(1(3(4(4(5(x1)))))))))))))))))))))))))))))))))) -> 2(4(3(0(5(0(1(1(1(0(2(1(1(2(2(2(4(0(0(4(5(2(4(3(5(5(0(4(1(1(3(4(2(5(x1)))))))))))))))))))))))))))))))))) 5(4(3(5(2(3(5(1(2(2(3(1(3(2(3(2(4(1(0(1(4(5(4(1(4(4(0(1(0(2(5(2(2(0(x1)))))))))))))))))))))))))))))))))) -> 5(4(1(5(2(2(5(3(4(0(5(0(4(2(3(0(0(3(4(5(2(1(4(2(3(4(1(1(2(1(1(2(2(3(x1)))))))))))))))))))))))))))))))))) 0(3(0(4(5(5(5(1(3(0(4(4(3(4(5(2(5(0(0(1(5(0(5(5(0(4(5(1(1(0(4(3(4(5(2(x1))))))))))))))))))))))))))))))))))) -> 0(3(0(0(1(5(5(1(3(4(4(1(4(0(4(5(5(4(2(2(5(5(5(5(0(0(0(1(3(4(5(3(4(5(0(x1))))))))))))))))))))))))))))))))))) 4(2(1(2(2(1(5(1(5(3(0(5(3(5(0(4(4(3(1(2(1(2(0(2(4(4(3(1(1(4(4(5(5(1(2(x1))))))))))))))))))))))))))))))))))) -> 4(1(5(2(2(0(5(3(0(2(2(2(1(5(3(4(1(2(1(5(3(1(0(3(4(4(4(1(1(4(4(5(5(2(1(x1))))))))))))))))))))))))))))))))))) 5(4(4(1(1(3(5(2(2(2(5(3(3(3(0(4(5(3(2(3(0(5(5(1(2(2(0(1(1(3(1(5(0(0(2(x1))))))))))))))))))))))))))))))))))) -> 3(4(5(1(0(2(3(2(3(2(0(3(5(3(1(4(5(2(2(2(0(1(5(5(2(1(1(4(5(3(5(0(0(1(3(x1))))))))))))))))))))))))))))))))))) 0(0(3(0(0(0(3(4(1(4(0(5(2(1(5(2(4(1(1(1(5(2(2(5(3(4(0(0(4(3(1(3(5(4(1(1(x1)))))))))))))))))))))))))))))))))))) -> 0(0(1(4(0(5(0(1(4(4(0(0(2(1(5(3(1(0(1(0(5(2(2(5(3(4(3(1(4(3(3(4(5(1(2(1(x1)))))))))))))))))))))))))))))))))))) 2(1(1(4(3(2(2(4(1(5(3(3(3(3(2(4(4(3(0(1(4(3(2(0(0(2(1(5(2(2(3(0(1(5(1(2(x1)))))))))))))))))))))))))))))))))))) -> 0(3(1(2(3(4(0(2(2(3(1(3(1(3(5(4(4(3(2(1(4(3(4(2(0(1(1(5(2(2(3(0(5(2(1(2(x1)))))))))))))))))))))))))))))))))))) 4(5(4(4(4(0(4(4(5(5(2(0(2(5(0(3(1(4(3(4(3(0(1(4(4(1(0(4(5(4(3(3(1(1(0(5(x1)))))))))))))))))))))))))))))))))))) -> 4(4(4(5(3(1(1(2(5(5(3(4(4(5(1(3(3(4(4(0(0(0(5(0(1(1(0(4(5(2(0(3(4(4(4(4(x1)))))))))))))))))))))))))))))))))))) 0(0(5(5(1(0(1(4(5(2(0(5(2(5(2(1(0(5(1(1(4(5(0(2(1(0(3(4(1(2(5(0(1(4(4(5(3(5(x1)))))))))))))))))))))))))))))))))))))) -> 0(3(4(5(1(0(0(5(1(0(0(5(4(5(0(1(2(5(5(4(4(1(0(2(1(3(2(2(1(0(5(1(5(1(4(5(2(5(x1)))))))))))))))))))))))))))))))))))))) 0(1(3(0(3(1(0(3(0(4(3(0(3(2(1(3(5(0(5(3(0(1(0(1(1(4(3(0(5(1(4(3(3(3(0(0(0(5(3(4(x1)))))))))))))))))))))))))))))))))))))))) -> 0(3(1(0(5(4(0(3(0(4(5(0(5(1(3(3(0(0(3(0(3(1(3(2(1(1(5(4(3(1(1(0(3(3(0(0(3(4(3(0(x1)))))))))))))))))))))))))))))))))))))))) 4(3(3(0(0(0(3(2(4(3(0(0(4(4(2(4(4(2(1(2(5(5(0(0(4(2(5(5(1(0(4(4(5(0(2(3(3(2(4(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) -> 4(2(2(4(0(0(3(2(5(3(4(5(4(0(0(4(0(2(1(0(5(5(2(4(3(3(5(4(1(0(4(4(0(0(4(3(3(2(2(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) 0(1(0(4(0(1(1(1(1(1(0(3(4(3(3(1(4(0(2(0(1(1(0(4(4(3(3(5(0(1(1(0(3(0(4(0(0(4(0(3(1(3(5(3(5(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(3(1(0(1(3(1(0(1(5(3(4(0(3(1(4(0(2(3(1(4(0(5(4(0(3(0(1(1(1(0(0(0(4(0(0(4(1(5(1(1(4(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) 0(2(2(3(1(3(4(0(5(3(3(2(0(2(1(5(0(2(0(3(2(1(4(5(0(4(4(0(2(3(0(1(2(1(2(1(1(5(3(2(3(0(3(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(5(0(3(4(2(5(0(3(2(1(2(1(3(0(1(0(3(4(0(4(4(0(2(2(0(2(3(3(3(2(1(3(1(1(5(2(1(3(5(0(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) 2(2(0(4(5(5(3(5(1(2(3(5(2(5(5(3(3(2(1(1(1(3(1(3(5(3(4(1(5(2(1(1(4(1(1(2(2(3(2(4(2(2(5(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(5(1(3(2(1(3(1(3(2(5(5(3(5(5(1(2(1(3(5(3(1(2(4(0(3(5(4(2(4(1(1(2(2(3(3(2(2(4(5(5(3(x1))))))))))))))))))))))))))))))))))))))))))))) 2(5(0(5(0(1(5(1(3(4(4(3(1(3(3(3(0(5(3(3(0(4(3(3(3(2(4(4(2(2(5(2(4(3(3(5(1(2(1(0(4(1(5(2(3(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(0(5(0(2(5(1(3(3(2(3(1(4(3(2(0(5(3(3(4(4(3(2(3(2(4(1(0(4(5(2(4(3(0(5(1(1(2(3(4(1(5(3(3(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))) 4(5(4(2(3(3(2(4(1(0(3(4(4(3(1(4(0(0(1(4(4(4(5(2(0(4(2(2(2(2(0(4(3(4(3(0(3(2(5(3(3(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(3(2(5(4(2(3(1(4(4(4(4(3(2(4(4(0(1(4(4(2(0(0(3(4(3(2(0(2(0(1(3(4(3(0(3(5(2(3(2(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) 0(3(1(4(5(1(2(2(4(5(1(3(5(3(2(3(0(4(5(2(1(4(4(5(3(1(0(1(1(2(5(3(4(5(5(0(2(3(0(4(1(0(3(3(0(2(4(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(1(4(5(1(5(2(2(5(2(3(4(4(4(3(0(5(4(2(2(3(4(0(5(1(0(0(1(2(1(3(5(5(2(0(5(3(1(4(1(0(3(3(4(1(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(4(4(2(5(4(5(2(1(4(4(2(0(2(3(5(0(3(3(5(0(3(5(0(4(0(0(5(5(2(5(0(4(0(3(2(2(1(5(3(2(4(3(1(5(4(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(2(1(2(0(4(5(5(5(4(4(5(0(0(3(4(0(2(3(4(3(3(1(2(4(5(4(5(2(5(2(0(5(0(3(0(0(1(5(3(2(1(2(1(5(4(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 2(3(1(5(1(2(3(3(3(5(2(1(5(5(3(4(0(5(2(2(2(3(2(3(3(3(3(1(3(2(2(0(2(1(4(1(4(4(3(2(4(4(0(4(2(4(3(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 1(3(2(3(3(2(3(4(2(4(2(0(1(5(3(4(0(5(2(2(1(3(2(1(5(3(3(3(3(2(2(0(2(2(4(4(3(1(5(3(0(4(5(4(2(3(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) 4(5(5(4(4(4(3(3(2(0(1(4(5(3(1(1(5(4(3(0(2(4(2(5(4(2(0(3(4(1(4(2(5(1(5(4(0(4(0(0(2(2(2(0(3(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(5(4(4(5(3(1(2(1(3(4(5(3(3(1(2(4(3(1(4(2(5(4(4(4(0(4(0(0(4(2(0(1(5(2(2(2(0(0(5(2(2(0(3(5(4(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(3(5(2(5(4(0(1(4(5(5(2(1(2(5(4(1(3(1(3(5(3(4(2(5(0(1(3(5(3(3(0(2(2(2(2(5(1(4(5(3(1(4(0(2(1(5(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(3(5(2(5(4(0(5(5(5(4(2(1(3(3(0(1(1(2(3(5(1(4(2(1(5(1(4(0(2(3(0(3(2(2(3(5(1(1(5(3(1(1(4(2(4(5(1(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) 4(0(3(4(1(4(0(4(5(3(0(2(3(4(2(0(5(2(4(1(5(3(0(4(2(5(3(5(1(0(1(1(0(3(5(3(3(4(5(0(4(4(3(3(2(1(1(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(0(4(5(1(0(4(5(3(0(2(3(4(2(0(5(2(4(1(0(3(0(1(1(5(0(3(1(1(4(3(5(2(5(2(5(4(4(3(5(4(3(3(3(4(0(3(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(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)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (7) CpxTrsMatchBoundsProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. The certificate found is represented by the following graph. "[85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 1110, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 1237, 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1404, 1405, 1406, 1407, 1408, 1409, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 1580, 1581, 1582, 1583, 1584, 1585, 1586] {(85,86,[0_1|0, 1_1|0, 4_1|0, 3_1|0, 2_1|0, 5_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (85,87,[0_1|1, 1_1|1, 4_1|1, 3_1|1, 2_1|1, 5_1|1]), (85,88,[0_1|2]), (85,93,[0_1|2]), (85,137,[0_1|2]), (85,164,[0_1|2]), (85,203,[0_1|2]), (85,208,[5_1|2]), (85,216,[0_1|2]), (85,243,[2_1|2]), (85,264,[0_1|2]), (85,308,[0_1|2]), (85,334,[0_1|2]), (85,369,[0_1|2]), (85,406,[2_1|2]), (85,436,[0_1|2]), (85,470,[0_1|2]), (85,517,[4_1|2]), (85,525,[1_1|2]), (85,555,[2_1|2]), (85,566,[4_1|2]), (85,584,[2_1|2]), (85,632,[1_1|2]), (85,650,[4_1|2]), (85,668,[2_1|2]), (85,694,[1_1|2]), (85,718,[1_1|2]), (85,744,[4_1|2]), (85,791,[4_1|2]), (85,808,[4_1|2]), (85,838,[4_1|2]), (85,886,[4_1|2]), (85,920,[4_1|2]), (85,955,[4_1|2]), (85,1001,[4_1|2]), (85,1048,[4_1|2]), (85,1089,[5_1|2]), (85,1107,[5_1|2]), (85,1130,[1_1|2]), (85,1154,[0_1|2]), (85,1184,[0_1|2]), (85,1205,[2_1|2]), (85,1237,[2_1|2]), (85,1281,[3_1|2]), (85,1303,[2_1|2]), (85,1349,[2_1|2]), (85,1377,[2_1|2]), (85,1410,[0_1|2]), (85,1445,[1_1|2]), (85,1492,[5_1|2]), (85,1515,[5_1|2]), (85,1548,[3_1|2]), (86,86,[cons_0_1|0, cons_1_1|0, cons_4_1|0, cons_3_1|0, cons_2_1|0, cons_5_1|0]), (87,86,[encArg_1|1]), (87,87,[0_1|1, 1_1|1, 4_1|1, 3_1|1, 2_1|1, 5_1|1]), (87,88,[0_1|2]), (87,93,[0_1|2]), (87,137,[0_1|2]), (87,164,[0_1|2]), (87,203,[0_1|2]), (87,208,[5_1|2]), (87,216,[0_1|2]), (87,243,[2_1|2]), (87,264,[0_1|2]), (87,308,[0_1|2]), (87,334,[0_1|2]), (87,369,[0_1|2]), (87,406,[2_1|2]), (87,436,[0_1|2]), (87,470,[0_1|2]), (87,517,[4_1|2]), (87,525,[1_1|2]), (87,555,[2_1|2]), (87,566,[4_1|2]), (87,584,[2_1|2]), (87,632,[1_1|2]), (87,650,[4_1|2]), (87,668,[2_1|2]), (87,694,[1_1|2]), (87,718,[1_1|2]), (87,744,[4_1|2]), (87,791,[4_1|2]), (87,808,[4_1|2]), (87,838,[4_1|2]), (87,886,[4_1|2]), (87,920,[4_1|2]), (87,955,[4_1|2]), (87,1001,[4_1|2]), (87,1048,[4_1|2]), (87,1089,[5_1|2]), (87,1107,[5_1|2]), (87,1130,[1_1|2]), (87,1154,[0_1|2]), (87,1184,[0_1|2]), (87,1205,[2_1|2]), (87,1237,[2_1|2]), (87,1281,[3_1|2]), (87,1303,[2_1|2]), (87,1349,[2_1|2]), (87,1377,[2_1|2]), (87,1410,[0_1|2]), (87,1445,[1_1|2]), (87,1492,[5_1|2]), (87,1515,[5_1|2]), (87,1548,[3_1|2]), (88,89,[2_1|2]), (89,90,[2_1|2]), (90,91,[1_1|2]), (91,92,[0_1|2]), (91,436,[0_1|2]), (91,470,[0_1|2]), (92,87,[3_1|2]), (92,1281,[3_1|2]), (92,1548,[3_1|2]), (92,407,[3_1|2]), (92,585,[3_1|2]), (92,669,[3_1|2]), (92,1089,[5_1|2]), (92,1107,[5_1|2]), (92,1130,[1_1|2]), (92,1154,[0_1|2]), (93,94,[3_1|2]), (94,95,[3_1|2]), (95,96,[1_1|2]), (96,97,[0_1|2]), (97,98,[1_1|2]), (98,99,[3_1|2]), (99,100,[1_1|2]), (100,101,[0_1|2]), (101,102,[1_1|2]), (102,103,[5_1|2]), (103,104,[3_1|2]), (104,105,[4_1|2]), (105,106,[0_1|2]), (106,107,[3_1|2]), (107,108,[1_1|2]), (108,109,[4_1|2]), (109,110,[0_1|2]), (110,111,[2_1|2]), (111,112,[3_1|2]), (112,113,[1_1|2]), (113,114,[4_1|2]), (114,115,[0_1|2]), (115,116,[5_1|2]), (116,117,[4_1|2]), (117,118,[0_1|2]), (118,119,[3_1|2]), (119,120,[0_1|2]), (120,121,[1_1|2]), (121,122,[1_1|2]), (122,123,[1_1|2]), (123,124,[0_1|2]), (124,125,[0_1|2]), (125,126,[0_1|2]), (126,127,[4_1|2]), (127,128,[0_1|2]), (128,129,[0_1|2]), (129,130,[4_1|2]), (130,131,[1_1|2]), (131,132,[5_1|2]), (132,133,[1_1|2]), (133,134,[1_1|2]), (134,135,[4_1|2]), (134,1048,[4_1|2]), (135,136,[3_1|2]), (136,87,[3_1|2]), (136,208,[3_1|2]), (136,1089,[3_1|2, 5_1|2]), (136,1107,[3_1|2, 5_1|2]), (136,1492,[3_1|2]), (136,1515,[3_1|2]), (136,1130,[1_1|2]), (136,1154,[0_1|2]), (137,138,[1_1|2]), (138,139,[1_1|2]), (139,140,[5_1|2]), (140,141,[3_1|2]), (141,142,[5_1|2]), (142,143,[4_1|2]), (143,144,[0_1|2]), (144,145,[2_1|2]), (145,146,[3_1|2]), (146,147,[0_1|2]), (147,148,[0_1|2]), (148,149,[0_1|2]), (149,150,[4_1|2]), (150,151,[5_1|2]), (151,152,[1_1|2]), (152,153,[4_1|2]), (153,154,[1_1|2]), (154,155,[2_1|2]), (155,156,[1_1|2]), (156,157,[5_1|2]), (157,158,[2_1|2]), 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(1339,1340,[1_1|2]), (1340,1341,[2_1|2]), (1341,1342,[3_1|2]), (1342,1343,[4_1|2]), (1343,1344,[1_1|2]), (1344,1345,[5_1|2]), (1345,1346,[3_1|2]), (1346,1347,[3_1|2]), (1347,1348,[5_1|2]), (1348,87,[3_1|2]), (1348,243,[3_1|2]), (1348,406,[3_1|2]), (1348,555,[3_1|2]), (1348,584,[3_1|2]), (1348,668,[3_1|2]), (1348,1205,[3_1|2]), (1348,1237,[3_1|2]), (1348,1303,[3_1|2]), (1348,1349,[3_1|2]), (1348,1377,[3_1|2]), (1348,1238,[3_1|2]), (1348,1304,[3_1|2]), (1348,1089,[5_1|2]), (1348,1107,[5_1|2]), (1348,1130,[1_1|2]), (1348,1154,[0_1|2]), (1349,1350,[0_1|2]), (1350,1351,[0_1|2]), (1351,1352,[2_1|2]), (1352,1353,[2_1|2]), (1353,1354,[1_1|2]), (1354,1355,[5_1|2]), (1355,1356,[2_1|2]), (1356,1357,[3_1|2]), (1357,1358,[1_1|2]), (1358,1359,[3_1|2]), (1359,1360,[3_1|2]), (1360,1361,[1_1|2]), (1361,1362,[4_1|2]), (1362,1363,[5_1|2]), (1363,1364,[2_1|2]), (1364,1365,[1_1|2]), (1365,1366,[4_1|2]), (1366,1367,[2_1|2]), (1367,1368,[5_1|2]), (1368,1369,[2_1|2]), (1369,1370,[2_1|2]), (1370,1371,[2_1|2]), (1371,1372,[0_1|2]), (1372,1373,[5_1|2]), (1372,1548,[3_1|2]), (1373,1374,[4_1|2]), (1374,1375,[4_1|2]), (1374,791,[4_1|2]), (1375,1376,[1_1|2]), (1375,650,[4_1|2]), (1375,668,[2_1|2]), (1376,87,[1_1|2]), (1376,243,[1_1|2]), (1376,406,[1_1|2]), (1376,555,[1_1|2, 2_1|2]), (1376,584,[1_1|2, 2_1|2]), (1376,668,[1_1|2, 2_1|2]), (1376,1205,[1_1|2]), (1376,1237,[1_1|2]), (1376,1303,[1_1|2]), (1376,1349,[1_1|2]), (1376,1377,[1_1|2]), (1376,1091,[1_1|2]), (1376,517,[4_1|2]), (1376,525,[1_1|2]), (1376,566,[4_1|2]), (1376,632,[1_1|2]), (1376,650,[4_1|2]), (1376,694,[1_1|2]), (1376,718,[1_1|2]), (1376,744,[4_1|2]), (1377,1378,[4_1|2]), (1378,1379,[3_1|2]), (1379,1380,[0_1|2]), (1380,1381,[5_1|2]), (1381,1382,[0_1|2]), (1382,1383,[1_1|2]), (1383,1384,[1_1|2]), (1384,1385,[1_1|2]), (1385,1386,[0_1|2]), (1386,1387,[2_1|2]), (1387,1388,[1_1|2]), (1388,1389,[1_1|2]), (1389,1390,[2_1|2]), (1390,1391,[2_1|2]), (1391,1392,[2_1|2]), (1392,1393,[4_1|2]), (1393,1394,[0_1|2]), (1394,1395,[0_1|2]), (1395,1396,[4_1|2]), (1396,1397,[5_1|2]), (1397,1398,[2_1|2]), (1398,1399,[4_1|2]), (1399,1400,[3_1|2]), (1400,1401,[5_1|2]), (1401,1402,[5_1|2]), (1402,1403,[0_1|2]), (1403,1404,[4_1|2]), (1404,1405,[1_1|2]), (1405,1406,[1_1|2]), (1406,1407,[3_1|2]), (1407,1408,[4_1|2]), (1408,1409,[2_1|2]), (1408,1281,[3_1|2]), (1408,1303,[2_1|2]), (1409,87,[5_1|2]), (1409,208,[5_1|2]), (1409,1089,[5_1|2]), (1409,1107,[5_1|2]), (1409,1492,[5_1|2]), (1409,1515,[5_1|2]), (1409,651,[5_1|2]), (1409,956,[5_1|2]), (1409,1548,[3_1|2]), (1410,1411,[3_1|2]), (1411,1412,[1_1|2]), (1412,1413,[2_1|2]), (1413,1414,[3_1|2]), (1414,1415,[4_1|2]), (1415,1416,[0_1|2]), (1416,1417,[2_1|2]), (1417,1418,[2_1|2]), (1418,1419,[3_1|2]), (1419,1420,[1_1|2]), (1420,1421,[3_1|2]), (1421,1422,[1_1|2]), (1422,1423,[3_1|2]), (1423,1424,[5_1|2]), (1424,1425,[4_1|2]), (1425,1426,[4_1|2]), (1426,1427,[3_1|2]), (1427,1428,[2_1|2]), (1428,1429,[1_1|2]), (1429,1430,[4_1|2]), (1430,1431,[3_1|2]), (1431,1432,[4_1|2]), (1432,1433,[2_1|2]), (1433,1434,[0_1|2]), (1434,1435,[1_1|2]), (1435,1436,[1_1|2]), (1436,1437,[5_1|2]), (1437,1438,[2_1|2]), (1438,1439,[2_1|2]), (1439,1440,[3_1|2]), (1440,1441,[0_1|2]), (1441,1442,[5_1|2]), (1442,1443,[2_1|2]), (1443,1444,[1_1|2]), (1443,517,[4_1|2]), (1443,525,[1_1|2]), (1444,87,[2_1|2]), (1444,243,[2_1|2]), (1444,406,[2_1|2]), (1444,555,[2_1|2]), (1444,584,[2_1|2]), (1444,668,[2_1|2]), (1444,1205,[2_1|2]), (1444,1237,[2_1|2]), (1444,1303,[2_1|2]), (1444,1349,[2_1|2]), (1444,1377,[2_1|2]), (1444,1091,[2_1|2]), (1444,1184,[0_1|2]), (1444,1281,[3_1|2]), (1444,1410,[0_1|2]), (1444,1445,[1_1|2]), (1445,1446,[3_1|2]), (1446,1447,[2_1|2]), (1447,1448,[3_1|2]), (1448,1449,[3_1|2]), (1449,1450,[2_1|2]), (1450,1451,[3_1|2]), (1451,1452,[4_1|2]), (1452,1453,[2_1|2]), (1453,1454,[4_1|2]), (1454,1455,[2_1|2]), (1455,1456,[0_1|2]), (1456,1457,[1_1|2]), (1457,1458,[5_1|2]), (1458,1459,[3_1|2]), (1459,1460,[4_1|2]), (1460,1461,[0_1|2]), (1461,1462,[5_1|2]), (1462,1463,[2_1|2]), (1463,1464,[2_1|2]), (1464,1465,[1_1|2]), (1465,1466,[3_1|2]), (1466,1467,[2_1|2]), (1467,1468,[1_1|2]), (1468,1469,[5_1|2]), (1469,1470,[3_1|2]), (1470,1471,[3_1|2]), (1471,1472,[3_1|2]), (1472,1473,[3_1|2]), (1473,1474,[2_1|2]), (1474,1475,[2_1|2]), (1475,1476,[0_1|2]), (1476,1477,[2_1|2]), (1477,1478,[2_1|2]), (1478,1479,[4_1|2]), (1479,1480,[4_1|2]), (1480,1481,[3_1|2]), (1481,1482,[1_1|2]), (1482,1483,[5_1|2]), (1483,1484,[3_1|2]), (1484,1485,[0_1|2]), (1485,1486,[4_1|2]), (1486,1487,[5_1|2]), (1487,1488,[4_1|2]), (1488,1489,[2_1|2]), (1489,1490,[3_1|2]), (1490,1491,[4_1|2]), (1490,791,[4_1|2]), (1491,87,[1_1|2]), (1491,88,[1_1|2]), (1491,93,[1_1|2]), (1491,137,[1_1|2]), (1491,164,[1_1|2]), (1491,203,[1_1|2]), (1491,216,[1_1|2]), (1491,264,[1_1|2]), (1491,308,[1_1|2]), (1491,334,[1_1|2]), (1491,369,[1_1|2]), (1491,436,[1_1|2]), (1491,470,[1_1|2]), (1491,1154,[1_1|2]), (1491,1184,[1_1|2]), (1491,1410,[1_1|2]), (1491,1380,[1_1|2]), (1491,517,[4_1|2]), (1491,525,[1_1|2]), (1491,555,[2_1|2]), (1491,566,[4_1|2]), (1491,584,[2_1|2]), (1491,632,[1_1|2]), (1491,650,[4_1|2]), (1491,668,[2_1|2]), (1491,694,[1_1|2]), (1491,718,[1_1|2]), (1491,744,[4_1|2]), (1492,1493,[4_1|2]), (1493,1494,[5_1|2]), (1494,1495,[0_1|2]), (1495,1496,[5_1|2]), (1496,1497,[4_1|2]), (1497,1498,[2_1|2]), (1498,1499,[1_1|2]), (1499,1500,[2_1|2]), (1500,1501,[4_1|2]), (1501,1502,[1_1|2]), (1502,1503,[1_1|2]), (1503,1504,[2_1|2]), (1504,1505,[1_1|2]), (1505,1506,[2_1|2]), (1506,1507,[4_1|2]), (1507,1508,[5_1|2]), (1508,1509,[3_1|2]), (1509,1510,[1_1|2]), (1510,1511,[5_1|2]), (1511,1512,[2_1|2]), (1512,1513,[5_1|2]), (1513,1514,[5_1|2]), (1513,1492,[5_1|2]), (1514,87,[5_1|2]), (1514,208,[5_1|2]), (1514,1089,[5_1|2]), (1514,1107,[5_1|2]), (1514,1492,[5_1|2]), (1514,1515,[5_1|2]), (1514,1108,[5_1|2]), (1514,1548,[3_1|2]), (1515,1516,[4_1|2]), (1516,1517,[1_1|2]), (1517,1518,[5_1|2]), (1518,1519,[2_1|2]), (1519,1520,[2_1|2]), (1520,1521,[5_1|2]), (1521,1522,[3_1|2]), (1522,1523,[4_1|2]), (1523,1524,[0_1|2]), (1524,1525,[5_1|2]), (1525,1526,[0_1|2]), (1526,1527,[4_1|2]), (1527,1528,[2_1|2]), (1528,1529,[3_1|2]), (1529,1530,[0_1|2]), (1530,1531,[0_1|2]), (1531,1532,[3_1|2]), (1532,1533,[4_1|2]), (1533,1534,[5_1|2]), (1534,1535,[2_1|2]), (1535,1536,[1_1|2]), (1536,1537,[4_1|2]), (1537,1538,[2_1|2]), (1538,1539,[3_1|2]), (1539,1540,[4_1|2]), (1540,1541,[1_1|2]), (1541,1542,[1_1|2]), (1542,1543,[2_1|2]), (1543,1544,[1_1|2]), (1544,1545,[1_1|2]), (1545,1546,[2_1|2]), (1546,1547,[2_1|2]), (1546,1445,[1_1|2]), (1547,87,[3_1|2]), (1547,88,[3_1|2]), (1547,93,[3_1|2]), (1547,137,[3_1|2]), (1547,164,[3_1|2]), (1547,203,[3_1|2]), (1547,216,[3_1|2]), (1547,264,[3_1|2]), (1547,308,[3_1|2]), (1547,334,[3_1|2]), (1547,369,[3_1|2]), (1547,436,[3_1|2]), (1547,470,[3_1|2]), (1547,1154,[3_1|2, 0_1|2]), (1547,1184,[3_1|2]), (1547,1410,[3_1|2]), (1547,1350,[3_1|2]), (1547,1305,[3_1|2]), (1547,1089,[5_1|2]), (1547,1107,[5_1|2]), (1547,1130,[1_1|2]), (1548,1549,[4_1|2]), (1549,1550,[5_1|2]), (1550,1551,[1_1|2]), (1551,1552,[0_1|2]), (1552,1553,[2_1|2]), (1553,1554,[3_1|2]), (1554,1555,[2_1|2]), (1555,1556,[3_1|2]), (1556,1557,[2_1|2]), (1557,1558,[0_1|2]), (1558,1559,[3_1|2]), (1559,1560,[5_1|2]), (1560,1561,[3_1|2]), (1561,1562,[1_1|2]), (1562,1563,[4_1|2]), (1563,1564,[5_1|2]), (1564,1565,[2_1|2]), (1565,1566,[2_1|2]), (1566,1567,[2_1|2]), (1567,1568,[0_1|2]), (1568,1569,[1_1|2]), (1569,1570,[5_1|2]), (1570,1571,[5_1|2]), (1571,1572,[2_1|2]), (1572,1573,[1_1|2]), (1573,1574,[1_1|2]), (1574,1575,[4_1|2]), (1575,1576,[5_1|2]), (1576,1577,[3_1|2]), (1577,1578,[5_1|2]), (1578,1579,[0_1|2]), (1579,1580,[0_1|2]), (1579,164,[0_1|2]), (1580,1581,[1_1|2]), (1580,555,[2_1|2]), (1580,566,[4_1|2]), (1580,584,[2_1|2]), (1581,87,[3_1|2]), (1581,243,[3_1|2]), (1581,406,[3_1|2]), (1581,555,[3_1|2]), (1581,584,[3_1|2]), (1581,668,[3_1|2]), (1581,1205,[3_1|2]), (1581,1237,[3_1|2]), (1581,1303,[3_1|2]), (1581,1349,[3_1|2]), (1581,1377,[3_1|2]), (1581,89,[3_1|2]), (1581,265,[3_1|2]), (1581,1155,[3_1|2]), (1581,1089,[5_1|2]), (1581,1107,[5_1|2]), (1581,1130,[1_1|2]), (1581,1154,[0_1|2]), (1582,1583,[4_1|3]), (1583,1584,[4_1|3]), (1584,1585,[4_1|3]), (1585,1586,[0_1|3]), (1586,841,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)