/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 45 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 112 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(2(2(x1)))) -> 0(1(1(x1))) 1(3(0(2(4(3(2(x1))))))) -> 0(2(4(5(3(4(x1)))))) 4(5(3(0(4(0(3(x1))))))) -> 3(5(1(2(2(5(0(x1))))))) 5(2(0(3(3(2(5(2(x1)))))))) -> 3(4(1(3(4(2(2(1(x1)))))))) 1(5(1(1(4(5(4(2(0(x1))))))))) -> 5(1(5(0(2(2(1(0(x1)))))))) 2(5(4(4(0(0(2(1(2(x1))))))))) -> 2(2(0(4(4(3(0(2(x1)))))))) 1(5(1(5(1(0(4(0(3(1(x1)))))))))) -> 1(3(0(0(0(1(4(2(4(1(1(x1))))))))))) 4(3(2(1(2(0(1(0(3(3(x1)))))))))) -> 0(1(5(5(0(2(0(3(3(x1))))))))) 1(4(2(0(2(3(1(3(4(0(4(x1))))))))))) -> 0(4(2(5(2(0(3(2(5(4(1(x1))))))))))) 3(2(4(5(3(3(4(1(5(4(0(3(x1)))))))))))) -> 3(0(4(1(5(1(3(3(3(4(3(x1))))))))))) 4(0(3(3(3(1(4(2(2(1(0(2(x1)))))))))))) -> 4(0(4(2(2(2(2(4(4(2(1(0(1(x1))))))))))))) 1(0(2(3(3(2(5(2(1(3(3(1(4(x1))))))))))))) -> 0(3(3(4(0(0(0(2(3(3(3(0(x1)))))))))))) 1(2(5(3(5(2(4(1(0(2(4(3(2(x1))))))))))))) -> 5(3(1(4(3(2(2(0(0(5(3(4(x1)))))))))))) 2(2(0(3(2(2(3(1(1(1(1(0(4(x1))))))))))))) -> 2(2(3(0(2(4(5(0(3(3(2(1(1(x1))))))))))))) 3(0(1(0(0(5(3(5(2(0(1(0(2(x1))))))))))))) -> 2(3(2(5(5(2(1(2(2(0(4(4(5(2(x1)))))))))))))) 4(2(4(3(3(0(1(0(3(3(2(1(0(x1))))))))))))) -> 4(5(4(0(3(1(4(2(5(1(5(2(0(x1))))))))))))) 3(1(4(3(5(5(1(2(5(1(3(2(2(0(4(x1))))))))))))))) -> 3(5(5(5(2(3(4(1(3(4(2(0(0(2(2(x1))))))))))))))) 2(3(5(4(0(1(3(4(4(4(2(5(4(4(1(2(x1)))))))))))))))) -> 4(2(0(0(0(0(5(2(5(1(3(3(2(1(x1)))))))))))))) 1(2(3(0(5(4(4(0(1(2(0(5(0(3(0(4(4(x1))))))))))))))))) -> 1(4(0(1(0(2(4(4(5(3(0(2(1(0(1(2(x1)))))))))))))))) 1(3(2(4(1(1(5(5(1(2(0(2(0(2(2(4(1(x1))))))))))))))))) -> 1(0(2(4(3(5(2(1(1(1(0(1(5(4(0(1(x1)))))))))))))))) 1(3(5(2(3(5(1(2(0(5(0(4(2(4(3(3(0(x1))))))))))))))))) -> 5(5(2(0(0(0(5(5(2(1(4(4(3(0(1(0(x1)))))))))))))))) 1(4(1(3(0(5(4(1(2(3(0(3(5(4(4(1(4(2(x1)))))))))))))))))) -> 1(3(1(3(2(2(0(0(5(1(4(1(5(5(1(5(1(x1))))))))))))))))) 3(1(0(2(1(3(5(4(3(5(5(2(4(5(3(0(0(2(x1)))))))))))))))))) -> 2(2(2(0(2(3(1(4(5(3(5(4(4(4(0(4(0(5(x1)))))))))))))))))) 3(4(1(2(3(1(3(5(0(4(0(1(1(5(5(2(2(3(x1)))))))))))))))))) -> 0(3(5(2(3(2(0(0(0(0(4(0(0(5(3(2(3(x1))))))))))))))))) 5(2(4(3(2(3(1(5(5(1(3(0(5(1(5(1(4(4(x1)))))))))))))))))) -> 5(5(5(4(4(4(2(5(0(0(3(4(2(1(5(4(5(2(x1)))))))))))))))))) 3(4(3(1(0(0(5(5(2(0(2(3(0(1(4(0(1(2(2(x1))))))))))))))))))) -> 0(5(2(2(1(0(3(1(4(5(3(2(2(1(5(4(4(2(1(x1))))))))))))))))))) 4(2(3(0(0(3(5(1(0(4(0(0(3(5(2(2(5(2(2(x1))))))))))))))))))) -> 5(5(4(5(3(2(2(0(2(2(5(2(0(5(4(4(4(0(1(x1))))))))))))))))))) 4(2(5(1(0(4(4(2(2(5(5(3(4(3(2(3(4(1(4(x1))))))))))))))))))) -> 4(0(4(2(3(3(2(2(1(4(4(0(3(0(0(5(1(1(x1)))))))))))))))))) 2(4(4(0(4(2(1(1(0(4(3(2(2(0(3(4(4(5(2(4(4(x1))))))))))))))))))))) -> 2(4(1(4(3(0(3(5(4(5(4(2(1(3(0(5(2(4(0(3(2(x1))))))))))))))))))))) 5(2(0(5(3(4(0(2(3(5(0(2(3(2(1(5(0(1(5(0(3(x1))))))))))))))))))))) -> 5(5(3(2(1(4(1(3(5(0(1(5(0(5(1(4(2(3(0(0(3(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_5(x_1)) -> 5(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(2(2(x1)))) -> 0(1(1(x1))) 1(3(0(2(4(3(2(x1))))))) -> 0(2(4(5(3(4(x1)))))) 4(5(3(0(4(0(3(x1))))))) -> 3(5(1(2(2(5(0(x1))))))) 5(2(0(3(3(2(5(2(x1)))))))) -> 3(4(1(3(4(2(2(1(x1)))))))) 1(5(1(1(4(5(4(2(0(x1))))))))) -> 5(1(5(0(2(2(1(0(x1)))))))) 2(5(4(4(0(0(2(1(2(x1))))))))) -> 2(2(0(4(4(3(0(2(x1)))))))) 1(5(1(5(1(0(4(0(3(1(x1)))))))))) -> 1(3(0(0(0(1(4(2(4(1(1(x1))))))))))) 4(3(2(1(2(0(1(0(3(3(x1)))))))))) -> 0(1(5(5(0(2(0(3(3(x1))))))))) 1(4(2(0(2(3(1(3(4(0(4(x1))))))))))) -> 0(4(2(5(2(0(3(2(5(4(1(x1))))))))))) 3(2(4(5(3(3(4(1(5(4(0(3(x1)))))))))))) -> 3(0(4(1(5(1(3(3(3(4(3(x1))))))))))) 4(0(3(3(3(1(4(2(2(1(0(2(x1)))))))))))) -> 4(0(4(2(2(2(2(4(4(2(1(0(1(x1))))))))))))) 1(0(2(3(3(2(5(2(1(3(3(1(4(x1))))))))))))) -> 0(3(3(4(0(0(0(2(3(3(3(0(x1)))))))))))) 1(2(5(3(5(2(4(1(0(2(4(3(2(x1))))))))))))) -> 5(3(1(4(3(2(2(0(0(5(3(4(x1)))))))))))) 2(2(0(3(2(2(3(1(1(1(1(0(4(x1))))))))))))) -> 2(2(3(0(2(4(5(0(3(3(2(1(1(x1))))))))))))) 3(0(1(0(0(5(3(5(2(0(1(0(2(x1))))))))))))) -> 2(3(2(5(5(2(1(2(2(0(4(4(5(2(x1)))))))))))))) 4(2(4(3(3(0(1(0(3(3(2(1(0(x1))))))))))))) -> 4(5(4(0(3(1(4(2(5(1(5(2(0(x1))))))))))))) 3(1(4(3(5(5(1(2(5(1(3(2(2(0(4(x1))))))))))))))) -> 3(5(5(5(2(3(4(1(3(4(2(0(0(2(2(x1))))))))))))))) 2(3(5(4(0(1(3(4(4(4(2(5(4(4(1(2(x1)))))))))))))))) -> 4(2(0(0(0(0(5(2(5(1(3(3(2(1(x1)))))))))))))) 1(2(3(0(5(4(4(0(1(2(0(5(0(3(0(4(4(x1))))))))))))))))) -> 1(4(0(1(0(2(4(4(5(3(0(2(1(0(1(2(x1)))))))))))))))) 1(3(2(4(1(1(5(5(1(2(0(2(0(2(2(4(1(x1))))))))))))))))) -> 1(0(2(4(3(5(2(1(1(1(0(1(5(4(0(1(x1)))))))))))))))) 1(3(5(2(3(5(1(2(0(5(0(4(2(4(3(3(0(x1))))))))))))))))) -> 5(5(2(0(0(0(5(5(2(1(4(4(3(0(1(0(x1)))))))))))))))) 1(4(1(3(0(5(4(1(2(3(0(3(5(4(4(1(4(2(x1)))))))))))))))))) -> 1(3(1(3(2(2(0(0(5(1(4(1(5(5(1(5(1(x1))))))))))))))))) 3(1(0(2(1(3(5(4(3(5(5(2(4(5(3(0(0(2(x1)))))))))))))))))) -> 2(2(2(0(2(3(1(4(5(3(5(4(4(4(0(4(0(5(x1)))))))))))))))))) 3(4(1(2(3(1(3(5(0(4(0(1(1(5(5(2(2(3(x1)))))))))))))))))) -> 0(3(5(2(3(2(0(0(0(0(4(0(0(5(3(2(3(x1))))))))))))))))) 5(2(4(3(2(3(1(5(5(1(3(0(5(1(5(1(4(4(x1)))))))))))))))))) -> 5(5(5(4(4(4(2(5(0(0(3(4(2(1(5(4(5(2(x1)))))))))))))))))) 3(4(3(1(0(0(5(5(2(0(2(3(0(1(4(0(1(2(2(x1))))))))))))))))))) -> 0(5(2(2(1(0(3(1(4(5(3(2(2(1(5(4(4(2(1(x1))))))))))))))))))) 4(2(3(0(0(3(5(1(0(4(0(0(3(5(2(2(5(2(2(x1))))))))))))))))))) -> 5(5(4(5(3(2(2(0(2(2(5(2(0(5(4(4(4(0(1(x1))))))))))))))))))) 4(2(5(1(0(4(4(2(2(5(5(3(4(3(2(3(4(1(4(x1))))))))))))))))))) -> 4(0(4(2(3(3(2(2(1(4(4(0(3(0(0(5(1(1(x1)))))))))))))))))) 2(4(4(0(4(2(1(1(0(4(3(2(2(0(3(4(4(5(2(4(4(x1))))))))))))))))))))) -> 2(4(1(4(3(0(3(5(4(5(4(2(1(3(0(5(2(4(0(3(2(x1))))))))))))))))))))) 5(2(0(5(3(4(0(2(3(5(0(2(3(2(1(5(0(1(5(0(3(x1))))))))))))))))))))) -> 5(5(3(2(1(4(1(3(5(0(1(5(0(5(1(4(2(3(0(0(3(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_5(x_1)) -> 5(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(2(2(x1)))) -> 0(1(1(x1))) 1(3(0(2(4(3(2(x1))))))) -> 0(2(4(5(3(4(x1)))))) 4(5(3(0(4(0(3(x1))))))) -> 3(5(1(2(2(5(0(x1))))))) 5(2(0(3(3(2(5(2(x1)))))))) -> 3(4(1(3(4(2(2(1(x1)))))))) 1(5(1(1(4(5(4(2(0(x1))))))))) -> 5(1(5(0(2(2(1(0(x1)))))))) 2(5(4(4(0(0(2(1(2(x1))))))))) -> 2(2(0(4(4(3(0(2(x1)))))))) 1(5(1(5(1(0(4(0(3(1(x1)))))))))) -> 1(3(0(0(0(1(4(2(4(1(1(x1))))))))))) 4(3(2(1(2(0(1(0(3(3(x1)))))))))) -> 0(1(5(5(0(2(0(3(3(x1))))))))) 1(4(2(0(2(3(1(3(4(0(4(x1))))))))))) -> 0(4(2(5(2(0(3(2(5(4(1(x1))))))))))) 3(2(4(5(3(3(4(1(5(4(0(3(x1)))))))))))) -> 3(0(4(1(5(1(3(3(3(4(3(x1))))))))))) 4(0(3(3(3(1(4(2(2(1(0(2(x1)))))))))))) -> 4(0(4(2(2(2(2(4(4(2(1(0(1(x1))))))))))))) 1(0(2(3(3(2(5(2(1(3(3(1(4(x1))))))))))))) -> 0(3(3(4(0(0(0(2(3(3(3(0(x1)))))))))))) 1(2(5(3(5(2(4(1(0(2(4(3(2(x1))))))))))))) -> 5(3(1(4(3(2(2(0(0(5(3(4(x1)))))))))))) 2(2(0(3(2(2(3(1(1(1(1(0(4(x1))))))))))))) -> 2(2(3(0(2(4(5(0(3(3(2(1(1(x1))))))))))))) 3(0(1(0(0(5(3(5(2(0(1(0(2(x1))))))))))))) -> 2(3(2(5(5(2(1(2(2(0(4(4(5(2(x1)))))))))))))) 4(2(4(3(3(0(1(0(3(3(2(1(0(x1))))))))))))) -> 4(5(4(0(3(1(4(2(5(1(5(2(0(x1))))))))))))) 3(1(4(3(5(5(1(2(5(1(3(2(2(0(4(x1))))))))))))))) -> 3(5(5(5(2(3(4(1(3(4(2(0(0(2(2(x1))))))))))))))) 2(3(5(4(0(1(3(4(4(4(2(5(4(4(1(2(x1)))))))))))))))) -> 4(2(0(0(0(0(5(2(5(1(3(3(2(1(x1)))))))))))))) 1(2(3(0(5(4(4(0(1(2(0(5(0(3(0(4(4(x1))))))))))))))))) -> 1(4(0(1(0(2(4(4(5(3(0(2(1(0(1(2(x1)))))))))))))))) 1(3(2(4(1(1(5(5(1(2(0(2(0(2(2(4(1(x1))))))))))))))))) -> 1(0(2(4(3(5(2(1(1(1(0(1(5(4(0(1(x1)))))))))))))))) 1(3(5(2(3(5(1(2(0(5(0(4(2(4(3(3(0(x1))))))))))))))))) -> 5(5(2(0(0(0(5(5(2(1(4(4(3(0(1(0(x1)))))))))))))))) 1(4(1(3(0(5(4(1(2(3(0(3(5(4(4(1(4(2(x1)))))))))))))))))) -> 1(3(1(3(2(2(0(0(5(1(4(1(5(5(1(5(1(x1))))))))))))))))) 3(1(0(2(1(3(5(4(3(5(5(2(4(5(3(0(0(2(x1)))))))))))))))))) -> 2(2(2(0(2(3(1(4(5(3(5(4(4(4(0(4(0(5(x1)))))))))))))))))) 3(4(1(2(3(1(3(5(0(4(0(1(1(5(5(2(2(3(x1)))))))))))))))))) -> 0(3(5(2(3(2(0(0(0(0(4(0(0(5(3(2(3(x1))))))))))))))))) 5(2(4(3(2(3(1(5(5(1(3(0(5(1(5(1(4(4(x1)))))))))))))))))) -> 5(5(5(4(4(4(2(5(0(0(3(4(2(1(5(4(5(2(x1)))))))))))))))))) 3(4(3(1(0(0(5(5(2(0(2(3(0(1(4(0(1(2(2(x1))))))))))))))))))) -> 0(5(2(2(1(0(3(1(4(5(3(2(2(1(5(4(4(2(1(x1))))))))))))))))))) 4(2(3(0(0(3(5(1(0(4(0(0(3(5(2(2(5(2(2(x1))))))))))))))))))) -> 5(5(4(5(3(2(2(0(2(2(5(2(0(5(4(4(4(0(1(x1))))))))))))))))))) 4(2(5(1(0(4(4(2(2(5(5(3(4(3(2(3(4(1(4(x1))))))))))))))))))) -> 4(0(4(2(3(3(2(2(1(4(4(0(3(0(0(5(1(1(x1)))))))))))))))))) 2(4(4(0(4(2(1(1(0(4(3(2(2(0(3(4(4(5(2(4(4(x1))))))))))))))))))))) -> 2(4(1(4(3(0(3(5(4(5(4(2(1(3(0(5(2(4(0(3(2(x1))))))))))))))))))))) 5(2(0(5(3(4(0(2(3(5(0(2(3(2(1(5(0(1(5(0(3(x1))))))))))))))))))))) -> 5(5(3(2(1(4(1(3(5(0(1(5(0(5(1(4(2(3(0(0(3(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_5(x_1)) -> 5(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(2(2(x1)))) -> 0(1(1(x1))) 1(3(0(2(4(3(2(x1))))))) -> 0(2(4(5(3(4(x1)))))) 4(5(3(0(4(0(3(x1))))))) -> 3(5(1(2(2(5(0(x1))))))) 5(2(0(3(3(2(5(2(x1)))))))) -> 3(4(1(3(4(2(2(1(x1)))))))) 1(5(1(1(4(5(4(2(0(x1))))))))) -> 5(1(5(0(2(2(1(0(x1)))))))) 2(5(4(4(0(0(2(1(2(x1))))))))) -> 2(2(0(4(4(3(0(2(x1)))))))) 1(5(1(5(1(0(4(0(3(1(x1)))))))))) -> 1(3(0(0(0(1(4(2(4(1(1(x1))))))))))) 4(3(2(1(2(0(1(0(3(3(x1)))))))))) -> 0(1(5(5(0(2(0(3(3(x1))))))))) 1(4(2(0(2(3(1(3(4(0(4(x1))))))))))) -> 0(4(2(5(2(0(3(2(5(4(1(x1))))))))))) 3(2(4(5(3(3(4(1(5(4(0(3(x1)))))))))))) -> 3(0(4(1(5(1(3(3(3(4(3(x1))))))))))) 4(0(3(3(3(1(4(2(2(1(0(2(x1)))))))))))) -> 4(0(4(2(2(2(2(4(4(2(1(0(1(x1))))))))))))) 1(0(2(3(3(2(5(2(1(3(3(1(4(x1))))))))))))) -> 0(3(3(4(0(0(0(2(3(3(3(0(x1)))))))))))) 1(2(5(3(5(2(4(1(0(2(4(3(2(x1))))))))))))) -> 5(3(1(4(3(2(2(0(0(5(3(4(x1)))))))))))) 2(2(0(3(2(2(3(1(1(1(1(0(4(x1))))))))))))) -> 2(2(3(0(2(4(5(0(3(3(2(1(1(x1))))))))))))) 3(0(1(0(0(5(3(5(2(0(1(0(2(x1))))))))))))) -> 2(3(2(5(5(2(1(2(2(0(4(4(5(2(x1)))))))))))))) 4(2(4(3(3(0(1(0(3(3(2(1(0(x1))))))))))))) -> 4(5(4(0(3(1(4(2(5(1(5(2(0(x1))))))))))))) 3(1(4(3(5(5(1(2(5(1(3(2(2(0(4(x1))))))))))))))) -> 3(5(5(5(2(3(4(1(3(4(2(0(0(2(2(x1))))))))))))))) 2(3(5(4(0(1(3(4(4(4(2(5(4(4(1(2(x1)))))))))))))))) -> 4(2(0(0(0(0(5(2(5(1(3(3(2(1(x1)))))))))))))) 1(2(3(0(5(4(4(0(1(2(0(5(0(3(0(4(4(x1))))))))))))))))) -> 1(4(0(1(0(2(4(4(5(3(0(2(1(0(1(2(x1)))))))))))))))) 1(3(2(4(1(1(5(5(1(2(0(2(0(2(2(4(1(x1))))))))))))))))) -> 1(0(2(4(3(5(2(1(1(1(0(1(5(4(0(1(x1)))))))))))))))) 1(3(5(2(3(5(1(2(0(5(0(4(2(4(3(3(0(x1))))))))))))))))) -> 5(5(2(0(0(0(5(5(2(1(4(4(3(0(1(0(x1)))))))))))))))) 1(4(1(3(0(5(4(1(2(3(0(3(5(4(4(1(4(2(x1)))))))))))))))))) -> 1(3(1(3(2(2(0(0(5(1(4(1(5(5(1(5(1(x1))))))))))))))))) 3(1(0(2(1(3(5(4(3(5(5(2(4(5(3(0(0(2(x1)))))))))))))))))) -> 2(2(2(0(2(3(1(4(5(3(5(4(4(4(0(4(0(5(x1)))))))))))))))))) 3(4(1(2(3(1(3(5(0(4(0(1(1(5(5(2(2(3(x1)))))))))))))))))) -> 0(3(5(2(3(2(0(0(0(0(4(0(0(5(3(2(3(x1))))))))))))))))) 5(2(4(3(2(3(1(5(5(1(3(0(5(1(5(1(4(4(x1)))))))))))))))))) -> 5(5(5(4(4(4(2(5(0(0(3(4(2(1(5(4(5(2(x1)))))))))))))))))) 3(4(3(1(0(0(5(5(2(0(2(3(0(1(4(0(1(2(2(x1))))))))))))))))))) -> 0(5(2(2(1(0(3(1(4(5(3(2(2(1(5(4(4(2(1(x1))))))))))))))))))) 4(2(3(0(0(3(5(1(0(4(0(0(3(5(2(2(5(2(2(x1))))))))))))))))))) -> 5(5(4(5(3(2(2(0(2(2(5(2(0(5(4(4(4(0(1(x1))))))))))))))))))) 4(2(5(1(0(4(4(2(2(5(5(3(4(3(2(3(4(1(4(x1))))))))))))))))))) -> 4(0(4(2(3(3(2(2(1(4(4(0(3(0(0(5(1(1(x1)))))))))))))))))) 2(4(4(0(4(2(1(1(0(4(3(2(2(0(3(4(4(5(2(4(4(x1))))))))))))))))))))) -> 2(4(1(4(3(0(3(5(4(5(4(2(1(3(0(5(2(4(0(3(2(x1))))))))))))))))))))) 5(2(0(5(3(4(0(2(3(5(0(2(3(2(1(5(0(1(5(0(3(x1))))))))))))))))))))) -> 5(5(3(2(1(4(1(3(5(0(1(5(0(5(1(4(2(3(0(0(3(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_5(x_1)) -> 5(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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. 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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] {(150,151,[0_1|0, 1_1|0, 4_1|0, 5_1|0, 2_1|0, 3_1|0, encArg_1|0, encode_0_1|0, 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(418,175,[5_1|2]), (418,190,[5_1|2]), (418,197,[1_1|2]), (418,207,[0_1|2]), (418,217,[1_1|2]), (418,233,[0_1|2]), (418,244,[5_1|2]), (418,255,[1_1|2]), (419,420,[4_1|2]), (420,421,[1_1|2]), (421,422,[4_1|2]), (422,423,[3_1|2]), (423,424,[0_1|2]), (424,425,[3_1|2]), (425,426,[5_1|2]), (426,427,[4_1|2]), (427,428,[5_1|2]), (428,429,[4_1|2]), (429,430,[2_1|2]), (430,431,[1_1|2]), (431,432,[3_1|2]), (432,433,[0_1|2]), (433,434,[5_1|2]), (434,435,[2_1|2]), (435,436,[4_1|2]), (436,437,[0_1|2]), (437,438,[3_1|2]), (437,439,[3_1|2]), (438,152,[2_1|2]), (438,284,[2_1|2]), (438,296,[2_1|2]), (438,326,[2_1|2]), (438,406,[2_1|2, 4_1|2]), (438,387,[2_1|2]), (438,394,[2_1|2]), (438,419,[2_1|2]), (439,440,[0_1|2]), (440,441,[4_1|2]), (441,442,[1_1|2]), (442,443,[5_1|2]), (443,444,[1_1|2]), (444,445,[3_1|2]), (445,446,[3_1|2]), (446,447,[3_1|2]), (446,509,[0_1|2]), (447,448,[4_1|2]), (447,276,[0_1|2]), (448,152,[3_1|2]), (448,270,[3_1|2]), (448,343,[3_1|2]), (448,439,[3_1|2]), (448,462,[3_1|2]), (448,234,[3_1|2]), (448,494,[3_1|2]), (448,449,[2_1|2]), (448,476,[2_1|2]), (448,493,[0_1|2]), (448,509,[0_1|2]), (449,450,[3_1|2]), (450,451,[2_1|2]), (451,452,[5_1|2]), (452,453,[5_1|2]), (453,454,[2_1|2]), (454,455,[1_1|2]), (455,456,[2_1|2]), (456,457,[2_1|2]), (457,458,[0_1|2]), (458,459,[4_1|2]), (459,460,[4_1|2]), (460,461,[5_1|2]), (460,343,[3_1|2]), (460,350,[5_1|2]), (460,370,[5_1|2]), (461,152,[2_1|2]), (461,387,[2_1|2]), (461,394,[2_1|2]), (461,419,[2_1|2]), (461,449,[2_1|2]), (461,476,[2_1|2]), (461,156,[2_1|2]), (461,162,[2_1|2]), (461,406,[4_1|2]), (462,463,[5_1|2]), (463,464,[5_1|2]), (464,465,[5_1|2]), (465,466,[2_1|2]), (466,467,[3_1|2]), (467,468,[4_1|2]), (468,469,[1_1|2]), (469,470,[3_1|2]), (470,471,[4_1|2]), (471,472,[2_1|2]), (472,473,[0_1|2]), (473,474,[0_1|2]), (474,475,[2_1|2]), (474,394,[2_1|2]), (475,152,[2_1|2]), (475,284,[2_1|2]), (475,296,[2_1|2]), (475,326,[2_1|2]), (475,406,[2_1|2, 4_1|2]), (475,208,[2_1|2]), (475,390,[2_1|2]), (475,387,[2_1|2]), (475,394,[2_1|2]), (475,419,[2_1|2]), (476,477,[2_1|2]), (477,478,[2_1|2]), (478,479,[0_1|2]), (479,480,[2_1|2]), (480,481,[3_1|2]), (481,482,[1_1|2]), (482,483,[4_1|2]), (483,484,[5_1|2]), (484,485,[3_1|2]), (485,486,[5_1|2]), (486,487,[4_1|2]), (487,488,[4_1|2]), (488,489,[4_1|2]), (489,490,[0_1|2]), (490,491,[4_1|2]), (491,492,[0_1|2]), (492,152,[5_1|2]), (492,387,[5_1|2]), (492,394,[5_1|2]), (492,419,[5_1|2]), (492,449,[5_1|2]), (492,476,[5_1|2]), (492,156,[5_1|2]), (492,343,[3_1|2]), (492,350,[5_1|2]), (492,370,[5_1|2]), (493,494,[3_1|2]), (494,495,[5_1|2]), (495,496,[2_1|2]), (496,497,[3_1|2]), (497,498,[2_1|2]), (498,499,[0_1|2]), (499,500,[0_1|2]), (500,501,[0_1|2]), (501,502,[0_1|2]), (502,503,[4_1|2]), (503,504,[0_1|2]), (504,505,[0_1|2]), (505,506,[5_1|2]), (506,507,[3_1|2]), (507,508,[2_1|2]), (507,406,[4_1|2]), (508,152,[3_1|2]), (508,270,[3_1|2]), (508,343,[3_1|2]), (508,439,[3_1|2]), (508,462,[3_1|2]), (508,450,[3_1|2]), (508,396,[3_1|2]), (508,449,[2_1|2]), (508,476,[2_1|2]), (508,493,[0_1|2]), (508,509,[0_1|2]), (509,510,[5_1|2]), (510,511,[2_1|2]), (511,512,[2_1|2]), (512,513,[1_1|2]), (513,514,[0_1|2]), (514,515,[3_1|2]), (515,516,[1_1|2]), (516,517,[4_1|2]), (517,518,[5_1|2]), (518,519,[3_1|2]), (519,520,[2_1|2]), (520,521,[2_1|2]), (521,522,[1_1|2]), (522,523,[5_1|2]), (523,524,[4_1|2]), (524,525,[4_1|2]), (525,526,[2_1|2]), (526,152,[1_1|2]), (526,387,[1_1|2]), (526,394,[1_1|2]), (526,419,[1_1|2]), (526,449,[1_1|2]), (526,476,[1_1|2]), (526,388,[1_1|2]), (526,395,[1_1|2]), (526,477,[1_1|2]), (526,155,[0_1|2]), (526,160,[1_1|2]), (526,175,[5_1|2]), (526,190,[5_1|2]), (526,197,[1_1|2]), (526,207,[0_1|2]), (526,217,[1_1|2]), (526,233,[0_1|2]), (526,244,[5_1|2]), (526,255,[1_1|2]), (527,528,[1_1|3]), (528,388,[1_1|3]), (528,395,[1_1|3]), (528,477,[1_1|3]), (528,478,[1_1|3]), (529,530,[1_1|3]), (530,387,[1_1|3]), (530,394,[1_1|3]), (530,419,[1_1|3]), (530,449,[1_1|3]), (530,476,[1_1|3]), (530,407,[1_1|3]), (530,388,[1_1|3]), (530,395,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)