/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 106 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 130 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(0(1(1(x1)))) -> 0(2(1(x1))) 0(0(3(3(0(0(x1)))))) -> 0(0(4(0(4(0(x1)))))) 1(5(5(2(1(0(x1)))))) -> 1(5(4(3(1(0(x1)))))) 4(0(3(4(2(2(x1)))))) -> 4(5(2(2(3(x1))))) 2(2(4(1(3(4(1(x1))))))) -> 5(2(4(5(3(x1))))) 0(3(1(5(2(3(1(5(x1)))))))) -> 0(3(3(5(3(5(1(5(x1)))))))) 3(1(5(1(5(0(4(2(x1)))))))) -> 3(1(4(5(0(5(2(x1))))))) 3(0(0(2(2(0(4(4(0(x1))))))))) -> 2(5(5(0(2(0(2(0(x1)))))))) 3(0(1(3(1(5(1(4(2(x1))))))))) -> 1(1(2(4(2(4(1(0(2(x1))))))))) 3(0(4(4(0(2(4(4(4(x1))))))))) -> 2(5(5(0(3(3(4(x1))))))) 0(2(5(2(4(3(4(0(4(3(x1)))))))))) -> 0(3(5(3(1(3(4(0(3(x1))))))))) 1(4(5(3(1(1(1(0(3(2(x1)))))))))) -> 1(3(2(5(3(5(2(1(x1)))))))) 2(4(0(4(5(3(3(3(2(0(x1)))))))))) -> 0(3(1(5(4(5(5(0(x1)))))))) 1(3(2(1(5(1(1(0(5(2(2(x1))))))))))) -> 1(0(2(5(4(2(2(0(5(3(x1)))))))))) 3(2(4(0(1(0(0(2(0(1(3(x1))))))))))) -> 2(4(0(3(5(5(1(3(3(x1))))))))) 4(4(1(0(1(3(3(1(4(1(2(x1))))))))))) -> 3(1(2(4(4(4(2(1(2(2(x1)))))))))) 4(0(4(2(2(0(4(2(1(4(1(4(x1)))))))))))) -> 4(5(0(5(4(5(5(4(x1)))))))) 4(3(5(4(3(4(0(0(4(2(5(0(x1)))))))))))) -> 4(0(2(0(3(3(3(5(3(1(2(4(x1)))))))))))) 2(5(5(1(5(1(2(0(2(1(3(3(4(x1))))))))))))) -> 3(1(1(1(2(5(2(1(4(0(0(4(4(x1))))))))))))) 3(4(1(1(3(1(1(1(5(4(3(4(1(x1))))))))))))) -> 3(4(0(0(3(5(3(5(0(4(4(4(x1)))))))))))) 1(1(2(0(2(4(1(1(3(3(3(5(1(3(x1)))))))))))))) -> 5(1(3(4(5(1(1(0(3(4(0(2(0(x1))))))))))))) 1(4(0(0(5(2(2(5(2(2(3(0(2(5(x1)))))))))))))) -> 1(5(4(2(3(0(1(3(0(3(2(2(0(5(x1)))))))))))))) 2(2(0(2(0(0(5(3(2(3(2(0(3(2(x1)))))))))))))) -> 4(5(1(5(3(3(3(4(4(2(0(4(x1)))))))))))) 4(2(3(5(4(2(5(5(1(1(4(4(0(4(1(0(x1)))))))))))))))) -> 4(1(2(5(4(0(5(3(2(5(0(4(2(4(0(x1))))))))))))))) 5(0(3(4(0(0(0(4(3(4(2(4(3(3(2(0(4(x1))))))))))))))))) -> 5(2(3(3(1(2(0(4(3(0(1(5(5(2(3(4(x1)))))))))))))))) 5(5(4(4(0(5(5(2(4(0(5(1(2(3(2(4(0(x1))))))))))))))))) -> 0(3(2(0(4(3(1(2(4(5(3(3(0(1(1(5(1(3(x1)))))))))))))))))) 0(1(4(3(5(3(0(4(1(1(2(3(3(1(4(0(5(2(3(x1))))))))))))))))))) -> 0(3(0(0(5(4(5(0(4(0(2(2(1(4(0(0(0(4(x1)))))))))))))))))) 4(2(1(0(0(4(4(4(3(0(5(1(3(1(2(3(5(1(0(2(x1)))))))))))))))))))) -> 4(4(1(4(5(0(4(2(4(5(2(3(4(2(2(5(5(1(x1)))))))))))))))))) 4(4(4(1(4(5(2(2(0(1(4(5(2(2(1(4(5(0(0(4(x1)))))))))))))))))))) -> 2(1(2(1(4(0(4(5(3(2(5(0(3(2(0(2(2(5(1(4(x1)))))))))))))))))))) 5(3(2(0(4(1(4(1(4(2(5(2(3(4(4(4(3(2(5(2(4(x1))))))))))))))))))))) -> 5(0(4(3(0(0(2(1(5(4(4(2(5(3(4(3(0(5(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_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(0(1(1(x1)))) -> 0(2(1(x1))) 0(0(3(3(0(0(x1)))))) -> 0(0(4(0(4(0(x1)))))) 1(5(5(2(1(0(x1)))))) -> 1(5(4(3(1(0(x1)))))) 4(0(3(4(2(2(x1)))))) -> 4(5(2(2(3(x1))))) 2(2(4(1(3(4(1(x1))))))) -> 5(2(4(5(3(x1))))) 0(3(1(5(2(3(1(5(x1)))))))) -> 0(3(3(5(3(5(1(5(x1)))))))) 3(1(5(1(5(0(4(2(x1)))))))) -> 3(1(4(5(0(5(2(x1))))))) 3(0(0(2(2(0(4(4(0(x1))))))))) -> 2(5(5(0(2(0(2(0(x1)))))))) 3(0(1(3(1(5(1(4(2(x1))))))))) -> 1(1(2(4(2(4(1(0(2(x1))))))))) 3(0(4(4(0(2(4(4(4(x1))))))))) -> 2(5(5(0(3(3(4(x1))))))) 0(2(5(2(4(3(4(0(4(3(x1)))))))))) -> 0(3(5(3(1(3(4(0(3(x1))))))))) 1(4(5(3(1(1(1(0(3(2(x1)))))))))) -> 1(3(2(5(3(5(2(1(x1)))))))) 2(4(0(4(5(3(3(3(2(0(x1)))))))))) -> 0(3(1(5(4(5(5(0(x1)))))))) 1(3(2(1(5(1(1(0(5(2(2(x1))))))))))) -> 1(0(2(5(4(2(2(0(5(3(x1)))))))))) 3(2(4(0(1(0(0(2(0(1(3(x1))))))))))) -> 2(4(0(3(5(5(1(3(3(x1))))))))) 4(4(1(0(1(3(3(1(4(1(2(x1))))))))))) -> 3(1(2(4(4(4(2(1(2(2(x1)))))))))) 4(0(4(2(2(0(4(2(1(4(1(4(x1)))))))))))) -> 4(5(0(5(4(5(5(4(x1)))))))) 4(3(5(4(3(4(0(0(4(2(5(0(x1)))))))))))) -> 4(0(2(0(3(3(3(5(3(1(2(4(x1)))))))))))) 2(5(5(1(5(1(2(0(2(1(3(3(4(x1))))))))))))) -> 3(1(1(1(2(5(2(1(4(0(0(4(4(x1))))))))))))) 3(4(1(1(3(1(1(1(5(4(3(4(1(x1))))))))))))) -> 3(4(0(0(3(5(3(5(0(4(4(4(x1)))))))))))) 1(1(2(0(2(4(1(1(3(3(3(5(1(3(x1)))))))))))))) -> 5(1(3(4(5(1(1(0(3(4(0(2(0(x1))))))))))))) 1(4(0(0(5(2(2(5(2(2(3(0(2(5(x1)))))))))))))) -> 1(5(4(2(3(0(1(3(0(3(2(2(0(5(x1)))))))))))))) 2(2(0(2(0(0(5(3(2(3(2(0(3(2(x1)))))))))))))) -> 4(5(1(5(3(3(3(4(4(2(0(4(x1)))))))))))) 4(2(3(5(4(2(5(5(1(1(4(4(0(4(1(0(x1)))))))))))))))) -> 4(1(2(5(4(0(5(3(2(5(0(4(2(4(0(x1))))))))))))))) 5(0(3(4(0(0(0(4(3(4(2(4(3(3(2(0(4(x1))))))))))))))))) -> 5(2(3(3(1(2(0(4(3(0(1(5(5(2(3(4(x1)))))))))))))))) 5(5(4(4(0(5(5(2(4(0(5(1(2(3(2(4(0(x1))))))))))))))))) -> 0(3(2(0(4(3(1(2(4(5(3(3(0(1(1(5(1(3(x1)))))))))))))))))) 0(1(4(3(5(3(0(4(1(1(2(3(3(1(4(0(5(2(3(x1))))))))))))))))))) -> 0(3(0(0(5(4(5(0(4(0(2(2(1(4(0(0(0(4(x1)))))))))))))))))) 4(2(1(0(0(4(4(4(3(0(5(1(3(1(2(3(5(1(0(2(x1)))))))))))))))))))) -> 4(4(1(4(5(0(4(2(4(5(2(3(4(2(2(5(5(1(x1)))))))))))))))))) 4(4(4(1(4(5(2(2(0(1(4(5(2(2(1(4(5(0(0(4(x1)))))))))))))))))))) -> 2(1(2(1(4(0(4(5(3(2(5(0(3(2(0(2(2(5(1(4(x1)))))))))))))))))))) 5(3(2(0(4(1(4(1(4(2(5(2(3(4(4(4(3(2(5(2(4(x1))))))))))))))))))))) -> 5(0(4(3(0(0(2(1(5(4(4(2(5(3(4(3(0(5(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_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(0(1(1(x1)))) -> 0(2(1(x1))) 0(0(3(3(0(0(x1)))))) -> 0(0(4(0(4(0(x1)))))) 1(5(5(2(1(0(x1)))))) -> 1(5(4(3(1(0(x1)))))) 4(0(3(4(2(2(x1)))))) -> 4(5(2(2(3(x1))))) 2(2(4(1(3(4(1(x1))))))) -> 5(2(4(5(3(x1))))) 0(3(1(5(2(3(1(5(x1)))))))) -> 0(3(3(5(3(5(1(5(x1)))))))) 3(1(5(1(5(0(4(2(x1)))))))) -> 3(1(4(5(0(5(2(x1))))))) 3(0(0(2(2(0(4(4(0(x1))))))))) -> 2(5(5(0(2(0(2(0(x1)))))))) 3(0(1(3(1(5(1(4(2(x1))))))))) -> 1(1(2(4(2(4(1(0(2(x1))))))))) 3(0(4(4(0(2(4(4(4(x1))))))))) -> 2(5(5(0(3(3(4(x1))))))) 0(2(5(2(4(3(4(0(4(3(x1)))))))))) -> 0(3(5(3(1(3(4(0(3(x1))))))))) 1(4(5(3(1(1(1(0(3(2(x1)))))))))) -> 1(3(2(5(3(5(2(1(x1)))))))) 2(4(0(4(5(3(3(3(2(0(x1)))))))))) -> 0(3(1(5(4(5(5(0(x1)))))))) 1(3(2(1(5(1(1(0(5(2(2(x1))))))))))) -> 1(0(2(5(4(2(2(0(5(3(x1)))))))))) 3(2(4(0(1(0(0(2(0(1(3(x1))))))))))) -> 2(4(0(3(5(5(1(3(3(x1))))))))) 4(4(1(0(1(3(3(1(4(1(2(x1))))))))))) -> 3(1(2(4(4(4(2(1(2(2(x1)))))))))) 4(0(4(2(2(0(4(2(1(4(1(4(x1)))))))))))) -> 4(5(0(5(4(5(5(4(x1)))))))) 4(3(5(4(3(4(0(0(4(2(5(0(x1)))))))))))) -> 4(0(2(0(3(3(3(5(3(1(2(4(x1)))))))))))) 2(5(5(1(5(1(2(0(2(1(3(3(4(x1))))))))))))) -> 3(1(1(1(2(5(2(1(4(0(0(4(4(x1))))))))))))) 3(4(1(1(3(1(1(1(5(4(3(4(1(x1))))))))))))) -> 3(4(0(0(3(5(3(5(0(4(4(4(x1)))))))))))) 1(1(2(0(2(4(1(1(3(3(3(5(1(3(x1)))))))))))))) -> 5(1(3(4(5(1(1(0(3(4(0(2(0(x1))))))))))))) 1(4(0(0(5(2(2(5(2(2(3(0(2(5(x1)))))))))))))) -> 1(5(4(2(3(0(1(3(0(3(2(2(0(5(x1)))))))))))))) 2(2(0(2(0(0(5(3(2(3(2(0(3(2(x1)))))))))))))) -> 4(5(1(5(3(3(3(4(4(2(0(4(x1)))))))))))) 4(2(3(5(4(2(5(5(1(1(4(4(0(4(1(0(x1)))))))))))))))) -> 4(1(2(5(4(0(5(3(2(5(0(4(2(4(0(x1))))))))))))))) 5(0(3(4(0(0(0(4(3(4(2(4(3(3(2(0(4(x1))))))))))))))))) -> 5(2(3(3(1(2(0(4(3(0(1(5(5(2(3(4(x1)))))))))))))))) 5(5(4(4(0(5(5(2(4(0(5(1(2(3(2(4(0(x1))))))))))))))))) -> 0(3(2(0(4(3(1(2(4(5(3(3(0(1(1(5(1(3(x1)))))))))))))))))) 0(1(4(3(5(3(0(4(1(1(2(3(3(1(4(0(5(2(3(x1))))))))))))))))))) -> 0(3(0(0(5(4(5(0(4(0(2(2(1(4(0(0(0(4(x1)))))))))))))))))) 4(2(1(0(0(4(4(4(3(0(5(1(3(1(2(3(5(1(0(2(x1)))))))))))))))))))) -> 4(4(1(4(5(0(4(2(4(5(2(3(4(2(2(5(5(1(x1)))))))))))))))))) 4(4(4(1(4(5(2(2(0(1(4(5(2(2(1(4(5(0(0(4(x1)))))))))))))))))))) -> 2(1(2(1(4(0(4(5(3(2(5(0(3(2(0(2(2(5(1(4(x1)))))))))))))))))))) 5(3(2(0(4(1(4(1(4(2(5(2(3(4(4(4(3(2(5(2(4(x1))))))))))))))))))))) -> 5(0(4(3(0(0(2(1(5(4(4(2(5(3(4(3(0(5(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_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(0(1(1(x1)))) -> 0(2(1(x1))) 0(0(3(3(0(0(x1)))))) -> 0(0(4(0(4(0(x1)))))) 1(5(5(2(1(0(x1)))))) -> 1(5(4(3(1(0(x1)))))) 4(0(3(4(2(2(x1)))))) -> 4(5(2(2(3(x1))))) 2(2(4(1(3(4(1(x1))))))) -> 5(2(4(5(3(x1))))) 0(3(1(5(2(3(1(5(x1)))))))) -> 0(3(3(5(3(5(1(5(x1)))))))) 3(1(5(1(5(0(4(2(x1)))))))) -> 3(1(4(5(0(5(2(x1))))))) 3(0(0(2(2(0(4(4(0(x1))))))))) -> 2(5(5(0(2(0(2(0(x1)))))))) 3(0(1(3(1(5(1(4(2(x1))))))))) -> 1(1(2(4(2(4(1(0(2(x1))))))))) 3(0(4(4(0(2(4(4(4(x1))))))))) -> 2(5(5(0(3(3(4(x1))))))) 0(2(5(2(4(3(4(0(4(3(x1)))))))))) -> 0(3(5(3(1(3(4(0(3(x1))))))))) 1(4(5(3(1(1(1(0(3(2(x1)))))))))) -> 1(3(2(5(3(5(2(1(x1)))))))) 2(4(0(4(5(3(3(3(2(0(x1)))))))))) -> 0(3(1(5(4(5(5(0(x1)))))))) 1(3(2(1(5(1(1(0(5(2(2(x1))))))))))) -> 1(0(2(5(4(2(2(0(5(3(x1)))))))))) 3(2(4(0(1(0(0(2(0(1(3(x1))))))))))) -> 2(4(0(3(5(5(1(3(3(x1))))))))) 4(4(1(0(1(3(3(1(4(1(2(x1))))))))))) -> 3(1(2(4(4(4(2(1(2(2(x1)))))))))) 4(0(4(2(2(0(4(2(1(4(1(4(x1)))))))))))) -> 4(5(0(5(4(5(5(4(x1)))))))) 4(3(5(4(3(4(0(0(4(2(5(0(x1)))))))))))) -> 4(0(2(0(3(3(3(5(3(1(2(4(x1)))))))))))) 2(5(5(1(5(1(2(0(2(1(3(3(4(x1))))))))))))) -> 3(1(1(1(2(5(2(1(4(0(0(4(4(x1))))))))))))) 3(4(1(1(3(1(1(1(5(4(3(4(1(x1))))))))))))) -> 3(4(0(0(3(5(3(5(0(4(4(4(x1)))))))))))) 1(1(2(0(2(4(1(1(3(3(3(5(1(3(x1)))))))))))))) -> 5(1(3(4(5(1(1(0(3(4(0(2(0(x1))))))))))))) 1(4(0(0(5(2(2(5(2(2(3(0(2(5(x1)))))))))))))) -> 1(5(4(2(3(0(1(3(0(3(2(2(0(5(x1)))))))))))))) 2(2(0(2(0(0(5(3(2(3(2(0(3(2(x1)))))))))))))) -> 4(5(1(5(3(3(3(4(4(2(0(4(x1)))))))))))) 4(2(3(5(4(2(5(5(1(1(4(4(0(4(1(0(x1)))))))))))))))) -> 4(1(2(5(4(0(5(3(2(5(0(4(2(4(0(x1))))))))))))))) 5(0(3(4(0(0(0(4(3(4(2(4(3(3(2(0(4(x1))))))))))))))))) -> 5(2(3(3(1(2(0(4(3(0(1(5(5(2(3(4(x1)))))))))))))))) 5(5(4(4(0(5(5(2(4(0(5(1(2(3(2(4(0(x1))))))))))))))))) -> 0(3(2(0(4(3(1(2(4(5(3(3(0(1(1(5(1(3(x1)))))))))))))))))) 0(1(4(3(5(3(0(4(1(1(2(3(3(1(4(0(5(2(3(x1))))))))))))))))))) -> 0(3(0(0(5(4(5(0(4(0(2(2(1(4(0(0(0(4(x1)))))))))))))))))) 4(2(1(0(0(4(4(4(3(0(5(1(3(1(2(3(5(1(0(2(x1)))))))))))))))))))) -> 4(4(1(4(5(0(4(2(4(5(2(3(4(2(2(5(5(1(x1)))))))))))))))))) 4(4(4(1(4(5(2(2(0(1(4(5(2(2(1(4(5(0(0(4(x1)))))))))))))))))))) -> 2(1(2(1(4(0(4(5(3(2(5(0(3(2(0(2(2(5(1(4(x1)))))))))))))))))))) 5(3(2(0(4(1(4(1(4(2(5(2(3(4(4(4(3(2(5(2(4(x1))))))))))))))))))))) -> 5(0(4(3(0(0(2(1(5(4(4(2(5(3(4(3(0(5(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_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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 2. The certificate found is represented by the following graph. "[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] {(151,152,[0_1|0, 1_1|0, 4_1|0, 2_1|0, 3_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]), (151,153,[0_1|1, 1_1|1, 4_1|1, 2_1|1, 3_1|1, 5_1|1]), (151,154,[0_1|2]), (151,156,[0_1|2]), (151,161,[0_1|2]), (151,168,[0_1|2]), (151,176,[0_1|2]), (151,193,[1_1|2]), (151,198,[1_1|2]), (151,205,[1_1|2]), (151,218,[1_1|2]), (151,227,[5_1|2]), (151,239,[4_1|2]), (151,243,[4_1|2]), (151,250,[3_1|2]), (151,259,[2_1|2]), (151,278,[4_1|2]), (151,289,[4_1|2]), (151,303,[4_1|2]), (151,320,[5_1|2]), (151,324,[4_1|2]), (151,335,[0_1|2]), (151,342,[3_1|2]), (151,354,[3_1|2]), (151,360,[2_1|2]), (151,367,[1_1|2]), (151,375,[2_1|2]), (151,381,[2_1|2]), (151,389,[3_1|2]), (151,400,[5_1|2]), (151,415,[0_1|2]), (151,432,[5_1|2]), (152,152,[cons_0_1|0, cons_1_1|0, cons_4_1|0, cons_2_1|0, cons_3_1|0, cons_5_1|0]), (153,152,[encArg_1|1]), (153,153,[0_1|1, 1_1|1, 4_1|1, 2_1|1, 3_1|1, 5_1|1]), (153,154,[0_1|2]), (153,156,[0_1|2]), (153,161,[0_1|2]), (153,168,[0_1|2]), (153,176,[0_1|2]), (153,193,[1_1|2]), (153,198,[1_1|2]), (153,205,[1_1|2]), (153,218,[1_1|2]), (153,227,[5_1|2]), (153,239,[4_1|2]), (153,243,[4_1|2]), (153,250,[3_1|2]), (153,259,[2_1|2]), (153,278,[4_1|2]), (153,289,[4_1|2]), (153,303,[4_1|2]), (153,320,[5_1|2]), (153,324,[4_1|2]), (153,335,[0_1|2]), (153,342,[3_1|2]), (153,354,[3_1|2]), (153,360,[2_1|2]), (153,367,[1_1|2]), (153,375,[2_1|2]), (153,381,[2_1|2]), (153,389,[3_1|2]), (153,400,[5_1|2]), (153,415,[0_1|2]), (153,432,[5_1|2]), (154,155,[2_1|2]), (155,153,[1_1|2]), (155,193,[1_1|2]), (155,198,[1_1|2]), (155,205,[1_1|2]), (155,218,[1_1|2]), (155,367,[1_1|2]), (155,368,[1_1|2]), (155,227,[5_1|2]), (156,157,[0_1|2]), (157,158,[4_1|2]), (158,159,[0_1|2]), (159,160,[4_1|2]), (159,239,[4_1|2]), (159,243,[4_1|2]), (160,153,[0_1|2]), (160,154,[0_1|2]), (160,156,[0_1|2]), (160,161,[0_1|2]), (160,168,[0_1|2]), (160,176,[0_1|2]), (160,335,[0_1|2]), (160,415,[0_1|2]), (160,157,[0_1|2]), (161,162,[3_1|2]), (162,163,[3_1|2]), (163,164,[5_1|2]), (164,165,[3_1|2]), (165,166,[5_1|2]), (166,167,[1_1|2]), (166,193,[1_1|2]), (167,153,[5_1|2]), (167,227,[5_1|2]), (167,320,[5_1|2]), (167,400,[5_1|2]), (167,432,[5_1|2]), (167,194,[5_1|2]), (167,206,[5_1|2]), (167,415,[0_1|2]), (168,169,[3_1|2]), (169,170,[5_1|2]), (170,171,[3_1|2]), (171,172,[1_1|2]), (172,173,[3_1|2]), (173,174,[4_1|2]), (173,239,[4_1|2]), (174,175,[0_1|2]), (174,161,[0_1|2]), (175,153,[3_1|2]), (175,250,[3_1|2]), (175,342,[3_1|2]), (175,354,[3_1|2]), (175,389,[3_1|2]), (175,360,[2_1|2]), (175,367,[1_1|2]), (175,375,[2_1|2]), (175,381,[2_1|2]), (176,177,[3_1|2]), (177,178,[0_1|2]), (178,179,[0_1|2]), (179,180,[5_1|2]), (180,181,[4_1|2]), (181,182,[5_1|2]), (182,183,[0_1|2]), (183,184,[4_1|2]), (184,185,[0_1|2]), (185,186,[2_1|2]), (186,187,[2_1|2]), (187,188,[1_1|2]), (188,189,[4_1|2]), (189,190,[0_1|2]), (190,191,[0_1|2]), (191,192,[0_1|2]), (192,153,[4_1|2]), (192,250,[4_1|2, 3_1|2]), (192,342,[4_1|2]), (192,354,[4_1|2]), (192,389,[4_1|2]), (192,402,[4_1|2]), (192,239,[4_1|2]), (192,243,[4_1|2]), (192,259,[2_1|2]), (192,278,[4_1|2]), (192,289,[4_1|2]), (192,303,[4_1|2]), (193,194,[5_1|2]), (194,195,[4_1|2]), (195,196,[3_1|2]), (196,197,[1_1|2]), (197,153,[0_1|2]), (197,154,[0_1|2]), (197,156,[0_1|2]), (197,161,[0_1|2]), (197,168,[0_1|2]), (197,176,[0_1|2]), (197,335,[0_1|2]), (197,415,[0_1|2]), (197,219,[0_1|2]), (198,199,[3_1|2]), (199,200,[2_1|2]), (200,201,[5_1|2]), (201,202,[3_1|2]), (202,203,[5_1|2]), (203,204,[2_1|2]), (204,153,[1_1|2]), (204,259,[1_1|2]), (204,360,[1_1|2]), (204,375,[1_1|2]), (204,381,[1_1|2]), (204,417,[1_1|2]), (204,193,[1_1|2]), (204,198,[1_1|2]), (204,205,[1_1|2]), (204,218,[1_1|2]), (204,227,[5_1|2]), (205,206,[5_1|2]), (206,207,[4_1|2]), (207,208,[2_1|2]), (208,209,[3_1|2]), (209,210,[0_1|2]), (210,211,[1_1|2]), (211,212,[3_1|2]), (212,213,[0_1|2]), (213,214,[3_1|2]), (214,215,[2_1|2]), (215,216,[2_1|2]), (216,217,[0_1|2]), (217,153,[5_1|2]), (217,227,[5_1|2]), (217,320,[5_1|2]), (217,400,[5_1|2]), (217,432,[5_1|2]), (217,361,[5_1|2]), (217,376,[5_1|2]), (217,415,[0_1|2]), (218,219,[0_1|2]), (219,220,[2_1|2]), (220,221,[5_1|2]), (221,222,[4_1|2]), (222,223,[2_1|2]), (223,224,[2_1|2]), (224,225,[0_1|2]), (225,226,[5_1|2]), (225,432,[5_1|2]), (226,153,[3_1|2]), (226,259,[3_1|2]), (226,360,[3_1|2, 2_1|2]), (226,375,[3_1|2, 2_1|2]), (226,381,[3_1|2, 2_1|2]), (226,354,[3_1|2]), (226,367,[1_1|2]), (226,389,[3_1|2]), (227,228,[1_1|2]), (228,229,[3_1|2]), (229,230,[4_1|2]), (230,231,[5_1|2]), (231,232,[1_1|2]), (232,233,[1_1|2]), (233,234,[0_1|2]), (234,235,[3_1|2]), (235,236,[4_1|2]), (236,237,[0_1|2]), (237,238,[2_1|2]), (238,153,[0_1|2]), (238,250,[0_1|2]), (238,342,[0_1|2]), (238,354,[0_1|2]), (238,389,[0_1|2]), (238,199,[0_1|2]), (238,229,[0_1|2]), (238,154,[0_1|2]), (238,156,[0_1|2]), (238,161,[0_1|2]), (238,168,[0_1|2]), (238,176,[0_1|2]), (239,240,[5_1|2]), (240,241,[2_1|2]), (241,242,[2_1|2]), (242,153,[3_1|2]), (242,259,[3_1|2]), (242,360,[3_1|2, 2_1|2]), (242,375,[3_1|2, 2_1|2]), (242,381,[3_1|2, 2_1|2]), (242,354,[3_1|2]), (242,367,[1_1|2]), (242,389,[3_1|2]), (243,244,[5_1|2]), (244,245,[0_1|2]), (245,246,[5_1|2]), (246,247,[4_1|2]), (247,248,[5_1|2]), (247,415,[0_1|2]), (248,249,[5_1|2]), (249,153,[4_1|2]), (249,239,[4_1|2]), (249,243,[4_1|2]), (249,278,[4_1|2]), (249,289,[4_1|2]), (249,303,[4_1|2]), (249,324,[4_1|2]), (249,250,[3_1|2]), (249,259,[2_1|2]), (250,251,[1_1|2]), (251,252,[2_1|2]), (252,253,[4_1|2]), (253,254,[4_1|2]), (254,255,[4_1|2]), (255,256,[2_1|2]), (256,257,[1_1|2]), (257,258,[2_1|2]), (257,320,[5_1|2]), (257,324,[4_1|2]), (258,153,[2_1|2]), (258,259,[2_1|2]), (258,360,[2_1|2]), (258,375,[2_1|2]), (258,381,[2_1|2]), (258,291,[2_1|2]), (258,320,[5_1|2]), (258,324,[4_1|2]), (258,335,[0_1|2]), (258,342,[3_1|2]), (259,260,[1_1|2]), (260,261,[2_1|2]), (261,262,[1_1|2]), (262,263,[4_1|2]), (263,264,[0_1|2]), (264,265,[4_1|2]), (265,266,[5_1|2]), (266,267,[3_1|2]), (267,268,[2_1|2]), (268,269,[5_1|2]), (269,270,[0_1|2]), (270,271,[3_1|2]), (271,272,[2_1|2]), (272,273,[0_1|2]), (273,274,[2_1|2]), (274,275,[2_1|2]), (275,276,[5_1|2]), (276,277,[1_1|2]), (276,198,[1_1|2]), (276,205,[1_1|2]), (277,153,[4_1|2]), (277,239,[4_1|2]), (277,243,[4_1|2]), (277,278,[4_1|2]), (277,289,[4_1|2]), (277,303,[4_1|2]), (277,324,[4_1|2]), (277,158,[4_1|2]), (277,250,[3_1|2]), (277,259,[2_1|2]), (278,279,[0_1|2]), (279,280,[2_1|2]), (280,281,[0_1|2]), (281,282,[3_1|2]), (282,283,[3_1|2]), (283,284,[3_1|2]), (284,285,[5_1|2]), (285,286,[3_1|2]), (286,287,[1_1|2]), (287,288,[2_1|2]), (287,335,[0_1|2]), (288,153,[4_1|2]), (288,154,[4_1|2]), (288,156,[4_1|2]), (288,161,[4_1|2]), (288,168,[4_1|2]), (288,176,[4_1|2]), (288,335,[4_1|2]), (288,415,[4_1|2]), (288,433,[4_1|2]), (288,239,[4_1|2]), (288,243,[4_1|2]), (288,250,[3_1|2]), (288,259,[2_1|2]), (288,278,[4_1|2]), (288,289,[4_1|2]), (288,303,[4_1|2]), (289,290,[1_1|2]), (290,291,[2_1|2]), (291,292,[5_1|2]), (292,293,[4_1|2]), (293,294,[0_1|2]), (294,295,[5_1|2]), (295,296,[3_1|2]), (296,297,[2_1|2]), (297,298,[5_1|2]), (298,299,[0_1|2]), (299,300,[4_1|2]), (300,301,[2_1|2]), (300,335,[0_1|2]), (301,302,[4_1|2]), (301,239,[4_1|2]), (301,243,[4_1|2]), (302,153,[0_1|2]), (302,154,[0_1|2]), (302,156,[0_1|2]), (302,161,[0_1|2]), (302,168,[0_1|2]), (302,176,[0_1|2]), (302,335,[0_1|2]), (302,415,[0_1|2]), (302,219,[0_1|2]), (303,304,[4_1|2]), (304,305,[1_1|2]), (305,306,[4_1|2]), (306,307,[5_1|2]), (307,308,[0_1|2]), (308,309,[4_1|2]), (309,310,[2_1|2]), (310,311,[4_1|2]), (311,312,[5_1|2]), (312,313,[2_1|2]), (313,314,[3_1|2]), (314,315,[4_1|2]), (315,316,[2_1|2]), (316,317,[2_1|2]), (316,342,[3_1|2]), (317,318,[5_1|2]), (318,319,[5_1|2]), (319,153,[1_1|2]), (319,259,[1_1|2]), (319,360,[1_1|2]), (319,375,[1_1|2]), (319,381,[1_1|2]), (319,155,[1_1|2]), (319,220,[1_1|2]), (319,193,[1_1|2]), (319,198,[1_1|2]), (319,205,[1_1|2]), (319,218,[1_1|2]), (319,227,[5_1|2]), (320,321,[2_1|2]), (321,322,[4_1|2]), (322,323,[5_1|2]), (322,432,[5_1|2]), (323,153,[3_1|2]), (323,193,[3_1|2]), (323,198,[3_1|2]), (323,205,[3_1|2]), (323,218,[3_1|2]), (323,367,[3_1|2, 1_1|2]), (323,290,[3_1|2]), (323,354,[3_1|2]), (323,360,[2_1|2]), (323,375,[2_1|2]), (323,381,[2_1|2]), (323,389,[3_1|2]), (324,325,[5_1|2]), (325,326,[1_1|2]), (326,327,[5_1|2]), (327,328,[3_1|2]), (328,329,[3_1|2]), (329,330,[3_1|2]), (330,331,[4_1|2]), (331,332,[4_1|2]), (332,333,[2_1|2]), (333,334,[0_1|2]), (334,153,[4_1|2]), (334,259,[4_1|2, 2_1|2]), (334,360,[4_1|2]), (334,375,[4_1|2]), (334,381,[4_1|2]), (334,417,[4_1|2]), (334,239,[4_1|2]), (334,243,[4_1|2]), (334,250,[3_1|2]), (334,278,[4_1|2]), (334,289,[4_1|2]), (334,303,[4_1|2]), (335,336,[3_1|2]), (336,337,[1_1|2]), (337,338,[5_1|2]), (338,339,[4_1|2]), (339,340,[5_1|2]), (340,341,[5_1|2]), (340,400,[5_1|2]), (341,153,[0_1|2]), (341,154,[0_1|2]), (341,156,[0_1|2]), (341,161,[0_1|2]), (341,168,[0_1|2]), (341,176,[0_1|2]), (341,335,[0_1|2]), (341,415,[0_1|2]), (342,343,[1_1|2]), (343,344,[1_1|2]), (344,345,[1_1|2]), (345,346,[2_1|2]), (346,347,[5_1|2]), (347,348,[2_1|2]), (348,349,[1_1|2]), (349,350,[4_1|2]), (350,351,[0_1|2]), (351,352,[0_1|2]), (352,353,[4_1|2]), (352,250,[3_1|2]), (352,259,[2_1|2]), (353,153,[4_1|2]), (353,239,[4_1|2]), (353,243,[4_1|2]), (353,278,[4_1|2]), (353,289,[4_1|2]), (353,303,[4_1|2]), (353,324,[4_1|2]), (353,390,[4_1|2]), (353,250,[3_1|2]), (353,259,[2_1|2]), (354,355,[1_1|2]), (355,356,[4_1|2]), (356,357,[5_1|2]), (357,358,[0_1|2]), (358,359,[5_1|2]), (359,153,[2_1|2]), (359,259,[2_1|2]), (359,360,[2_1|2]), (359,375,[2_1|2]), (359,381,[2_1|2]), (359,320,[5_1|2]), (359,324,[4_1|2]), (359,335,[0_1|2]), (359,342,[3_1|2]), (360,361,[5_1|2]), (361,362,[5_1|2]), (362,363,[0_1|2]), (363,364,[2_1|2]), (364,365,[0_1|2]), (365,366,[2_1|2]), (366,153,[0_1|2]), (366,154,[0_1|2]), (366,156,[0_1|2]), (366,161,[0_1|2]), (366,168,[0_1|2]), (366,176,[0_1|2]), (366,335,[0_1|2]), (366,415,[0_1|2]), (366,279,[0_1|2]), (367,368,[1_1|2]), (368,369,[2_1|2]), (369,370,[4_1|2]), (370,371,[2_1|2]), (371,372,[4_1|2]), (372,373,[1_1|2]), (373,374,[0_1|2]), (373,168,[0_1|2]), (374,153,[2_1|2]), (374,259,[2_1|2]), (374,360,[2_1|2]), (374,375,[2_1|2]), (374,381,[2_1|2]), (374,320,[5_1|2]), (374,324,[4_1|2]), (374,335,[0_1|2]), (374,342,[3_1|2]), (375,376,[5_1|2]), (376,377,[5_1|2]), (377,378,[0_1|2]), (378,379,[3_1|2]), (379,380,[3_1|2]), (379,389,[3_1|2]), (380,153,[4_1|2]), (380,239,[4_1|2]), (380,243,[4_1|2]), (380,278,[4_1|2]), (380,289,[4_1|2]), (380,303,[4_1|2]), (380,324,[4_1|2]), (380,304,[4_1|2]), (380,250,[3_1|2]), (380,259,[2_1|2]), (381,382,[4_1|2]), (382,383,[0_1|2]), (383,384,[3_1|2]), (384,385,[5_1|2]), (385,386,[5_1|2]), (386,387,[1_1|2]), (387,388,[3_1|2]), (388,153,[3_1|2]), (388,250,[3_1|2]), (388,342,[3_1|2]), (388,354,[3_1|2]), (388,389,[3_1|2]), (388,199,[3_1|2]), (388,360,[2_1|2]), (388,367,[1_1|2]), (388,375,[2_1|2]), (388,381,[2_1|2]), (389,390,[4_1|2]), (390,391,[0_1|2]), (391,392,[0_1|2]), (392,393,[3_1|2]), (393,394,[5_1|2]), (394,395,[3_1|2]), (395,396,[5_1|2]), (396,397,[0_1|2]), (397,398,[4_1|2]), (397,259,[2_1|2]), (398,399,[4_1|2]), (398,250,[3_1|2]), (398,259,[2_1|2]), (399,153,[4_1|2]), (399,193,[4_1|2]), (399,198,[4_1|2]), (399,205,[4_1|2]), (399,218,[4_1|2]), (399,367,[4_1|2]), (399,290,[4_1|2]), (399,239,[4_1|2]), (399,243,[4_1|2]), (399,250,[3_1|2]), (399,259,[2_1|2]), (399,278,[4_1|2]), (399,289,[4_1|2]), (399,303,[4_1|2]), (400,401,[2_1|2]), (401,402,[3_1|2]), (402,403,[3_1|2]), (403,404,[1_1|2]), (404,405,[2_1|2]), (405,406,[0_1|2]), (406,407,[4_1|2]), (407,408,[3_1|2]), (408,409,[0_1|2]), (409,410,[1_1|2]), (410,411,[5_1|2]), (411,412,[5_1|2]), (412,413,[2_1|2]), (413,414,[3_1|2]), (413,389,[3_1|2]), (414,153,[4_1|2]), (414,239,[4_1|2]), (414,243,[4_1|2]), (414,278,[4_1|2]), (414,289,[4_1|2]), (414,303,[4_1|2]), (414,324,[4_1|2]), (414,250,[3_1|2]), (414,259,[2_1|2]), (415,416,[3_1|2]), (416,417,[2_1|2]), (417,418,[0_1|2]), (418,419,[4_1|2]), (419,420,[3_1|2]), (420,421,[1_1|2]), (421,422,[2_1|2]), (422,423,[4_1|2]), (423,424,[5_1|2]), (424,425,[3_1|2]), (425,426,[3_1|2]), (426,427,[0_1|2]), (427,428,[1_1|2]), (428,429,[1_1|2]), (429,430,[5_1|2]), (430,431,[1_1|2]), (430,218,[1_1|2]), (431,153,[3_1|2]), (431,154,[3_1|2]), (431,156,[3_1|2]), (431,161,[3_1|2]), (431,168,[3_1|2]), (431,176,[3_1|2]), (431,335,[3_1|2]), (431,415,[3_1|2]), (431,279,[3_1|2]), (431,383,[3_1|2]), (431,354,[3_1|2]), (431,360,[2_1|2]), (431,367,[1_1|2]), (431,375,[2_1|2]), (431,381,[2_1|2]), (431,389,[3_1|2]), (432,433,[0_1|2]), (433,434,[4_1|2]), (434,435,[3_1|2]), (435,436,[0_1|2]), (436,437,[0_1|2]), (437,438,[2_1|2]), (438,439,[1_1|2]), (439,440,[5_1|2]), (440,441,[4_1|2]), (441,442,[4_1|2]), (442,443,[2_1|2]), (443,444,[5_1|2]), (444,445,[3_1|2]), (445,446,[4_1|2]), (446,447,[3_1|2]), (447,448,[0_1|2]), (448,449,[5_1|2]), (448,415,[0_1|2]), (449,153,[5_1|2]), (449,239,[5_1|2]), (449,243,[5_1|2]), (449,278,[5_1|2]), (449,289,[5_1|2]), (449,303,[5_1|2]), (449,324,[5_1|2]), (449,382,[5_1|2]), (449,322,[5_1|2]), (449,400,[5_1|2]), (449,415,[0_1|2]), (449,432,[5_1|2])}" ---------------------------------------- (8) BOUNDS(1, n^1)