/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 104 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 115 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)))) -> 3(2(1(x1))) 2(4(1(5(2(x1))))) -> 2(2(2(4(4(x1))))) 3(0(0(1(0(x1))))) -> 1(1(3(0(x1)))) 0(1(3(5(4(2(2(x1))))))) -> 3(5(1(3(1(2(x1)))))) 0(2(4(1(2(0(5(3(x1)))))))) -> 5(3(2(0(1(1(2(x1))))))) 2(1(2(3(0(3(5(0(x1)))))))) -> 2(1(2(0(4(5(3(0(x1)))))))) 3(4(0(3(2(1(2(2(x1)))))))) -> 1(2(5(0(2(0(2(x1))))))) 0(4(0(3(3(2(1(1(3(x1))))))))) -> 3(4(2(3(1(3(1(1(x1)))))))) 3(2(2(2(5(5(3(5(0(x1))))))))) -> 1(2(1(0(1(4(0(5(0(x1))))))))) 0(1(1(3(0(4(4(4(4(2(x1)))))))))) -> 3(0(5(4(1(1(3(5(x1)))))))) 4(0(2(0(2(0(2(0(5(4(x1)))))))))) -> 4(0(1(4(1(3(2(2(3(x1))))))))) 0(1(5(0(4(3(5(2(1(5(2(x1))))))))))) -> 5(4(2(0(1(2(4(4(5(1(2(2(x1)))))))))))) 1(1(2(4(0(2(2(1(5(5(0(x1))))))))))) -> 1(1(1(0(1(3(1(2(1(0(x1)))))))))) 5(1(3(5(1(1(2(1(2(0(2(2(x1)))))))))))) -> 3(5(1(0(3(4(3(5(2(0(4(3(x1)))))))))))) 5(2(4(2(4(0(5(1(1(0(4(3(x1)))))))))))) -> 1(2(0(5(5(0(3(2(2(1(3(x1))))))))))) 1(4(2(4(5(3(0(0(2(3(4(5(3(x1))))))))))))) -> 1(3(2(2(0(0(5(1(2(0(4(0(3(x1))))))))))))) 2(3(3(4(0(4(1(0(0(2(3(0(1(x1))))))))))))) -> 2(4(0(3(5(0(3(1(4(4(2(0(1(x1))))))))))))) 5(4(1(4(1(0(5(2(1(5(0(4(4(x1))))))))))))) -> 3(0(0(0(2(5(5(1(0(1(2(2(0(4(x1)))))))))))))) 0(3(0(1(1(0(4(5(3(5(1(0(3(2(x1)))))))))))))) -> 5(5(1(3(3(3(3(1(5(5(1(3(x1)))))))))))) 2(0(3(1(5(5(0(1(5(5(1(5(2(0(4(x1))))))))))))))) -> 2(1(3(4(1(4(3(4(1(2(4(1(1(4(4(x1))))))))))))))) 0(3(3(0(4(4(0(0(2(1(5(0(5(5(1(2(x1)))))))))))))))) -> 1(4(2(2(4(4(0(0(0(4(0(3(1(5(5(1(x1)))))))))))))))) 4(2(1(4(0(4(4(2(2(1(2(4(3(5(1(0(x1)))))))))))))))) -> 4(1(3(1(3(3(2(5(0(4(5(5(4(0(x1)))))))))))))) 2(2(1(4(4(4(5(4(0(2(2(5(3(2(3(3(2(x1))))))))))))))))) -> 2(2(4(4(2(4(0(2(3(1(1(1(1(4(1(1(x1)))))))))))))))) 2(1(2(0(1(5(1(0(3(2(0(1(1(1(4(4(0(2(x1)))))))))))))))))) -> 2(5(4(0(3(5(2(4(2(3(0(2(2(0(1(1(4(1(x1)))))))))))))))))) 4(2(0(5(2(5(5(5(5(5(5(3(3(3(0(0(2(5(x1)))))))))))))))))) -> 4(0(1(4(5(0(1(5(1(2(2(5(2(2(5(4(1(5(x1)))))))))))))))))) 0(3(1(0(0(3(5(1(2(1(2(2(0(3(3(0(5(4(2(x1))))))))))))))))))) -> 5(2(1(0(4(4(0(1(0(1(2(2(5(1(2(5(4(5(x1)))))))))))))))))) 0(1(3(4(4(5(3(0(2(0(3(5(2(1(0(1(5(2(0(1(x1)))))))))))))))))))) -> 1(5(3(2(4(4(4(1(2(3(0(3(2(4(1(0(0(0(2(1(x1)))))))))))))))))))) 0(5(1(5(2(1(1(5(3(2(3(1(3(4(1(2(3(5(4(3(x1)))))))))))))))))))) -> 2(1(4(0(1(0(2(0(3(3(4(0(3(5(4(3(2(5(4(1(3(x1))))))))))))))))))))) 2(2(1(5(0(4(3(4(5(3(3(3(3(1(5(3(1(4(0(1(x1)))))))))))))))))))) -> 2(5(0(5(4(2(1(2(5(5(4(4(1(1(4(5(3(1(3(1(x1)))))))))))))))))))) 3(0(1(3(5(1(3(4(2(5(4(0(5(0(1(5(5(5(1(0(2(x1))))))))))))))))))))) -> 3(0(1(5(5(0(3(2(4(4(0(2(4(5(3(3(2(5(1(1(1(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_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(2(2(x1)))) -> 3(2(1(x1))) 2(4(1(5(2(x1))))) -> 2(2(2(4(4(x1))))) 3(0(0(1(0(x1))))) -> 1(1(3(0(x1)))) 0(1(3(5(4(2(2(x1))))))) -> 3(5(1(3(1(2(x1)))))) 0(2(4(1(2(0(5(3(x1)))))))) -> 5(3(2(0(1(1(2(x1))))))) 2(1(2(3(0(3(5(0(x1)))))))) -> 2(1(2(0(4(5(3(0(x1)))))))) 3(4(0(3(2(1(2(2(x1)))))))) -> 1(2(5(0(2(0(2(x1))))))) 0(4(0(3(3(2(1(1(3(x1))))))))) -> 3(4(2(3(1(3(1(1(x1)))))))) 3(2(2(2(5(5(3(5(0(x1))))))))) -> 1(2(1(0(1(4(0(5(0(x1))))))))) 0(1(1(3(0(4(4(4(4(2(x1)))))))))) -> 3(0(5(4(1(1(3(5(x1)))))))) 4(0(2(0(2(0(2(0(5(4(x1)))))))))) -> 4(0(1(4(1(3(2(2(3(x1))))))))) 0(1(5(0(4(3(5(2(1(5(2(x1))))))))))) -> 5(4(2(0(1(2(4(4(5(1(2(2(x1)))))))))))) 1(1(2(4(0(2(2(1(5(5(0(x1))))))))))) -> 1(1(1(0(1(3(1(2(1(0(x1)))))))))) 5(1(3(5(1(1(2(1(2(0(2(2(x1)))))))))))) -> 3(5(1(0(3(4(3(5(2(0(4(3(x1)))))))))))) 5(2(4(2(4(0(5(1(1(0(4(3(x1)))))))))))) -> 1(2(0(5(5(0(3(2(2(1(3(x1))))))))))) 1(4(2(4(5(3(0(0(2(3(4(5(3(x1))))))))))))) -> 1(3(2(2(0(0(5(1(2(0(4(0(3(x1))))))))))))) 2(3(3(4(0(4(1(0(0(2(3(0(1(x1))))))))))))) -> 2(4(0(3(5(0(3(1(4(4(2(0(1(x1))))))))))))) 5(4(1(4(1(0(5(2(1(5(0(4(4(x1))))))))))))) -> 3(0(0(0(2(5(5(1(0(1(2(2(0(4(x1)))))))))))))) 0(3(0(1(1(0(4(5(3(5(1(0(3(2(x1)))))))))))))) -> 5(5(1(3(3(3(3(1(5(5(1(3(x1)))))))))))) 2(0(3(1(5(5(0(1(5(5(1(5(2(0(4(x1))))))))))))))) -> 2(1(3(4(1(4(3(4(1(2(4(1(1(4(4(x1))))))))))))))) 0(3(3(0(4(4(0(0(2(1(5(0(5(5(1(2(x1)))))))))))))))) -> 1(4(2(2(4(4(0(0(0(4(0(3(1(5(5(1(x1)))))))))))))))) 4(2(1(4(0(4(4(2(2(1(2(4(3(5(1(0(x1)))))))))))))))) -> 4(1(3(1(3(3(2(5(0(4(5(5(4(0(x1)))))))))))))) 2(2(1(4(4(4(5(4(0(2(2(5(3(2(3(3(2(x1))))))))))))))))) -> 2(2(4(4(2(4(0(2(3(1(1(1(1(4(1(1(x1)))))))))))))))) 2(1(2(0(1(5(1(0(3(2(0(1(1(1(4(4(0(2(x1)))))))))))))))))) -> 2(5(4(0(3(5(2(4(2(3(0(2(2(0(1(1(4(1(x1)))))))))))))))))) 4(2(0(5(2(5(5(5(5(5(5(3(3(3(0(0(2(5(x1)))))))))))))))))) -> 4(0(1(4(5(0(1(5(1(2(2(5(2(2(5(4(1(5(x1)))))))))))))))))) 0(3(1(0(0(3(5(1(2(1(2(2(0(3(3(0(5(4(2(x1))))))))))))))))))) -> 5(2(1(0(4(4(0(1(0(1(2(2(5(1(2(5(4(5(x1)))))))))))))))))) 0(1(3(4(4(5(3(0(2(0(3(5(2(1(0(1(5(2(0(1(x1)))))))))))))))))))) -> 1(5(3(2(4(4(4(1(2(3(0(3(2(4(1(0(0(0(2(1(x1)))))))))))))))))))) 0(5(1(5(2(1(1(5(3(2(3(1(3(4(1(2(3(5(4(3(x1)))))))))))))))))))) -> 2(1(4(0(1(0(2(0(3(3(4(0(3(5(4(3(2(5(4(1(3(x1))))))))))))))))))))) 2(2(1(5(0(4(3(4(5(3(3(3(3(1(5(3(1(4(0(1(x1)))))))))))))))))))) -> 2(5(0(5(4(2(1(2(5(5(4(4(1(1(4(5(3(1(3(1(x1)))))))))))))))))))) 3(0(1(3(5(1(3(4(2(5(4(0(5(0(1(5(5(5(1(0(2(x1))))))))))))))))))))) -> 3(0(1(5(5(0(3(2(4(4(0(2(4(5(3(3(2(5(1(1(1(x1))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(2(2(x1)))) -> 3(2(1(x1))) 2(4(1(5(2(x1))))) -> 2(2(2(4(4(x1))))) 3(0(0(1(0(x1))))) -> 1(1(3(0(x1)))) 0(1(3(5(4(2(2(x1))))))) -> 3(5(1(3(1(2(x1)))))) 0(2(4(1(2(0(5(3(x1)))))))) -> 5(3(2(0(1(1(2(x1))))))) 2(1(2(3(0(3(5(0(x1)))))))) -> 2(1(2(0(4(5(3(0(x1)))))))) 3(4(0(3(2(1(2(2(x1)))))))) -> 1(2(5(0(2(0(2(x1))))))) 0(4(0(3(3(2(1(1(3(x1))))))))) -> 3(4(2(3(1(3(1(1(x1)))))))) 3(2(2(2(5(5(3(5(0(x1))))))))) -> 1(2(1(0(1(4(0(5(0(x1))))))))) 0(1(1(3(0(4(4(4(4(2(x1)))))))))) -> 3(0(5(4(1(1(3(5(x1)))))))) 4(0(2(0(2(0(2(0(5(4(x1)))))))))) -> 4(0(1(4(1(3(2(2(3(x1))))))))) 0(1(5(0(4(3(5(2(1(5(2(x1))))))))))) -> 5(4(2(0(1(2(4(4(5(1(2(2(x1)))))))))))) 1(1(2(4(0(2(2(1(5(5(0(x1))))))))))) -> 1(1(1(0(1(3(1(2(1(0(x1)))))))))) 5(1(3(5(1(1(2(1(2(0(2(2(x1)))))))))))) -> 3(5(1(0(3(4(3(5(2(0(4(3(x1)))))))))))) 5(2(4(2(4(0(5(1(1(0(4(3(x1)))))))))))) -> 1(2(0(5(5(0(3(2(2(1(3(x1))))))))))) 1(4(2(4(5(3(0(0(2(3(4(5(3(x1))))))))))))) -> 1(3(2(2(0(0(5(1(2(0(4(0(3(x1))))))))))))) 2(3(3(4(0(4(1(0(0(2(3(0(1(x1))))))))))))) -> 2(4(0(3(5(0(3(1(4(4(2(0(1(x1))))))))))))) 5(4(1(4(1(0(5(2(1(5(0(4(4(x1))))))))))))) -> 3(0(0(0(2(5(5(1(0(1(2(2(0(4(x1)))))))))))))) 0(3(0(1(1(0(4(5(3(5(1(0(3(2(x1)))))))))))))) -> 5(5(1(3(3(3(3(1(5(5(1(3(x1)))))))))))) 2(0(3(1(5(5(0(1(5(5(1(5(2(0(4(x1))))))))))))))) -> 2(1(3(4(1(4(3(4(1(2(4(1(1(4(4(x1))))))))))))))) 0(3(3(0(4(4(0(0(2(1(5(0(5(5(1(2(x1)))))))))))))))) -> 1(4(2(2(4(4(0(0(0(4(0(3(1(5(5(1(x1)))))))))))))))) 4(2(1(4(0(4(4(2(2(1(2(4(3(5(1(0(x1)))))))))))))))) -> 4(1(3(1(3(3(2(5(0(4(5(5(4(0(x1)))))))))))))) 2(2(1(4(4(4(5(4(0(2(2(5(3(2(3(3(2(x1))))))))))))))))) -> 2(2(4(4(2(4(0(2(3(1(1(1(1(4(1(1(x1)))))))))))))))) 2(1(2(0(1(5(1(0(3(2(0(1(1(1(4(4(0(2(x1)))))))))))))))))) -> 2(5(4(0(3(5(2(4(2(3(0(2(2(0(1(1(4(1(x1)))))))))))))))))) 4(2(0(5(2(5(5(5(5(5(5(3(3(3(0(0(2(5(x1)))))))))))))))))) -> 4(0(1(4(5(0(1(5(1(2(2(5(2(2(5(4(1(5(x1)))))))))))))))))) 0(3(1(0(0(3(5(1(2(1(2(2(0(3(3(0(5(4(2(x1))))))))))))))))))) -> 5(2(1(0(4(4(0(1(0(1(2(2(5(1(2(5(4(5(x1)))))))))))))))))) 0(1(3(4(4(5(3(0(2(0(3(5(2(1(0(1(5(2(0(1(x1)))))))))))))))))))) -> 1(5(3(2(4(4(4(1(2(3(0(3(2(4(1(0(0(0(2(1(x1)))))))))))))))))))) 0(5(1(5(2(1(1(5(3(2(3(1(3(4(1(2(3(5(4(3(x1)))))))))))))))))))) -> 2(1(4(0(1(0(2(0(3(3(4(0(3(5(4(3(2(5(4(1(3(x1))))))))))))))))))))) 2(2(1(5(0(4(3(4(5(3(3(3(3(1(5(3(1(4(0(1(x1)))))))))))))))))))) -> 2(5(0(5(4(2(1(2(5(5(4(4(1(1(4(5(3(1(3(1(x1)))))))))))))))))))) 3(0(1(3(5(1(3(4(2(5(4(0(5(0(1(5(5(5(1(0(2(x1))))))))))))))))))))) -> 3(0(1(5(5(0(3(2(4(4(0(2(4(5(3(3(2(5(1(1(1(x1))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(2(2(x1)))) -> 3(2(1(x1))) 2(4(1(5(2(x1))))) -> 2(2(2(4(4(x1))))) 3(0(0(1(0(x1))))) -> 1(1(3(0(x1)))) 0(1(3(5(4(2(2(x1))))))) -> 3(5(1(3(1(2(x1)))))) 0(2(4(1(2(0(5(3(x1)))))))) -> 5(3(2(0(1(1(2(x1))))))) 2(1(2(3(0(3(5(0(x1)))))))) -> 2(1(2(0(4(5(3(0(x1)))))))) 3(4(0(3(2(1(2(2(x1)))))))) -> 1(2(5(0(2(0(2(x1))))))) 0(4(0(3(3(2(1(1(3(x1))))))))) -> 3(4(2(3(1(3(1(1(x1)))))))) 3(2(2(2(5(5(3(5(0(x1))))))))) -> 1(2(1(0(1(4(0(5(0(x1))))))))) 0(1(1(3(0(4(4(4(4(2(x1)))))))))) -> 3(0(5(4(1(1(3(5(x1)))))))) 4(0(2(0(2(0(2(0(5(4(x1)))))))))) -> 4(0(1(4(1(3(2(2(3(x1))))))))) 0(1(5(0(4(3(5(2(1(5(2(x1))))))))))) -> 5(4(2(0(1(2(4(4(5(1(2(2(x1)))))))))))) 1(1(2(4(0(2(2(1(5(5(0(x1))))))))))) -> 1(1(1(0(1(3(1(2(1(0(x1)))))))))) 5(1(3(5(1(1(2(1(2(0(2(2(x1)))))))))))) -> 3(5(1(0(3(4(3(5(2(0(4(3(x1)))))))))))) 5(2(4(2(4(0(5(1(1(0(4(3(x1)))))))))))) -> 1(2(0(5(5(0(3(2(2(1(3(x1))))))))))) 1(4(2(4(5(3(0(0(2(3(4(5(3(x1))))))))))))) -> 1(3(2(2(0(0(5(1(2(0(4(0(3(x1))))))))))))) 2(3(3(4(0(4(1(0(0(2(3(0(1(x1))))))))))))) -> 2(4(0(3(5(0(3(1(4(4(2(0(1(x1))))))))))))) 5(4(1(4(1(0(5(2(1(5(0(4(4(x1))))))))))))) -> 3(0(0(0(2(5(5(1(0(1(2(2(0(4(x1)))))))))))))) 0(3(0(1(1(0(4(5(3(5(1(0(3(2(x1)))))))))))))) -> 5(5(1(3(3(3(3(1(5(5(1(3(x1)))))))))))) 2(0(3(1(5(5(0(1(5(5(1(5(2(0(4(x1))))))))))))))) -> 2(1(3(4(1(4(3(4(1(2(4(1(1(4(4(x1))))))))))))))) 0(3(3(0(4(4(0(0(2(1(5(0(5(5(1(2(x1)))))))))))))))) -> 1(4(2(2(4(4(0(0(0(4(0(3(1(5(5(1(x1)))))))))))))))) 4(2(1(4(0(4(4(2(2(1(2(4(3(5(1(0(x1)))))))))))))))) -> 4(1(3(1(3(3(2(5(0(4(5(5(4(0(x1)))))))))))))) 2(2(1(4(4(4(5(4(0(2(2(5(3(2(3(3(2(x1))))))))))))))))) -> 2(2(4(4(2(4(0(2(3(1(1(1(1(4(1(1(x1)))))))))))))))) 2(1(2(0(1(5(1(0(3(2(0(1(1(1(4(4(0(2(x1)))))))))))))))))) -> 2(5(4(0(3(5(2(4(2(3(0(2(2(0(1(1(4(1(x1)))))))))))))))))) 4(2(0(5(2(5(5(5(5(5(5(3(3(3(0(0(2(5(x1)))))))))))))))))) -> 4(0(1(4(5(0(1(5(1(2(2(5(2(2(5(4(1(5(x1)))))))))))))))))) 0(3(1(0(0(3(5(1(2(1(2(2(0(3(3(0(5(4(2(x1))))))))))))))))))) -> 5(2(1(0(4(4(0(1(0(1(2(2(5(1(2(5(4(5(x1)))))))))))))))))) 0(1(3(4(4(5(3(0(2(0(3(5(2(1(0(1(5(2(0(1(x1)))))))))))))))))))) -> 1(5(3(2(4(4(4(1(2(3(0(3(2(4(1(0(0(0(2(1(x1)))))))))))))))))))) 0(5(1(5(2(1(1(5(3(2(3(1(3(4(1(2(3(5(4(3(x1)))))))))))))))))))) -> 2(1(4(0(1(0(2(0(3(3(4(0(3(5(4(3(2(5(4(1(3(x1))))))))))))))))))))) 2(2(1(5(0(4(3(4(5(3(3(3(3(1(5(3(1(4(0(1(x1)))))))))))))))))))) -> 2(5(0(5(4(2(1(2(5(5(4(4(1(1(4(5(3(1(3(1(x1)))))))))))))))))))) 3(0(1(3(5(1(3(4(2(5(4(0(5(0(1(5(5(5(1(0(2(x1))))))))))))))))))))) -> 3(0(1(5(5(0(3(2(4(4(0(2(4(5(3(3(2(5(1(1(1(x1))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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. "[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] {(96,97,[0_1|0, 2_1|0, 3_1|0, 4_1|0, 1_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]), (96,98,[0_1|1, 2_1|1, 3_1|1, 4_1|1, 1_1|1, 5_1|1]), (96,99,[3_1|2]), (96,101,[3_1|2]), (96,106,[1_1|2]), (96,125,[3_1|2]), (96,132,[5_1|2]), (96,143,[5_1|2]), (96,149,[3_1|2]), (96,156,[5_1|2]), (96,167,[1_1|2]), (96,182,[5_1|2]), (96,199,[2_1|2]), (96,219,[2_1|2]), (96,223,[2_1|2]), (96,230,[2_1|2]), (96,247,[2_1|2]), (96,259,[2_1|2]), (96,273,[2_1|2]), (96,288,[2_1|2]), (96,307,[1_1|2]), (96,310,[3_1|2]), (96,330,[1_1|2]), (96,336,[1_1|2]), (96,344,[4_1|2]), (96,352,[4_1|2]), (96,365,[4_1|2]), (96,382,[1_1|2]), (96,391,[1_1|2]), (96,403,[3_1|2]), (96,414,[1_1|2]), (96,424,[3_1|2]), (97,97,[cons_0_1|0, cons_2_1|0, cons_3_1|0, cons_4_1|0, cons_1_1|0, cons_5_1|0]), (98,97,[encArg_1|1]), (98,98,[0_1|1, 2_1|1, 3_1|1, 4_1|1, 1_1|1, 5_1|1]), (98,99,[3_1|2]), (98,101,[3_1|2]), (98,106,[1_1|2]), (98,125,[3_1|2]), (98,132,[5_1|2]), (98,143,[5_1|2]), (98,149,[3_1|2]), (98,156,[5_1|2]), (98,167,[1_1|2]), (98,182,[5_1|2]), (98,199,[2_1|2]), (98,219,[2_1|2]), (98,223,[2_1|2]), (98,230,[2_1|2]), (98,247,[2_1|2]), (98,259,[2_1|2]), (98,273,[2_1|2]), (98,288,[2_1|2]), 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(350,351,[2_1|2]), (350,247,[2_1|2]), (351,98,[3_1|2]), (351,344,[3_1|2]), (351,352,[3_1|2]), (351,365,[3_1|2]), (351,133,[3_1|2]), (351,307,[1_1|2]), (351,310,[3_1|2]), (351,330,[1_1|2]), (351,336,[1_1|2]), (352,353,[1_1|2]), (353,354,[3_1|2]), (354,355,[1_1|2]), (355,356,[3_1|2]), (356,357,[3_1|2]), (357,358,[2_1|2]), (358,359,[5_1|2]), (359,360,[0_1|2]), (360,361,[4_1|2]), (361,362,[5_1|2]), (362,363,[5_1|2]), (363,364,[4_1|2]), (363,344,[4_1|2]), (364,98,[0_1|2]), (364,406,[0_1|2]), (364,99,[3_1|2]), (364,101,[3_1|2]), (364,106,[1_1|2]), (364,125,[3_1|2]), (364,132,[5_1|2]), (364,143,[5_1|2]), (364,149,[3_1|2]), (364,156,[5_1|2]), (364,167,[1_1|2]), (364,182,[5_1|2]), (364,199,[2_1|2]), (365,366,[0_1|2]), (366,367,[1_1|2]), (367,368,[4_1|2]), (368,369,[5_1|2]), (369,370,[0_1|2]), (370,371,[1_1|2]), (371,372,[5_1|2]), (372,373,[1_1|2]), (373,374,[2_1|2]), (374,375,[2_1|2]), (375,376,[5_1|2]), (376,377,[2_1|2]), (377,378,[2_1|2]), (378,379,[5_1|2]), (379,380,[4_1|2]), (380,381,[1_1|2]), (381,98,[5_1|2]), (381,132,[5_1|2]), (381,143,[5_1|2]), (381,156,[5_1|2]), (381,182,[5_1|2]), (381,231,[5_1|2]), (381,289,[5_1|2]), (381,403,[3_1|2]), (381,414,[1_1|2]), (381,424,[3_1|2]), (382,383,[1_1|2]), (383,384,[1_1|2]), (384,385,[0_1|2]), (385,386,[1_1|2]), (386,387,[3_1|2]), (387,388,[1_1|2]), (388,389,[2_1|2]), (389,390,[1_1|2]), (390,98,[0_1|2]), (390,99,[3_1|2]), (390,101,[3_1|2]), (390,106,[1_1|2]), (390,125,[3_1|2]), (390,132,[5_1|2]), (390,143,[5_1|2]), (390,149,[3_1|2]), (390,156,[5_1|2]), (390,167,[1_1|2]), (390,182,[5_1|2]), (390,199,[2_1|2]), (391,392,[3_1|2]), (392,393,[2_1|2]), (393,394,[2_1|2]), (394,395,[0_1|2]), (395,396,[0_1|2]), (396,397,[5_1|2]), (397,398,[1_1|2]), (398,399,[2_1|2]), (399,400,[0_1|2]), (399,149,[3_1|2]), (399,441,[3_1|3]), (400,401,[4_1|2]), (401,402,[0_1|2]), (401,156,[5_1|2]), (401,167,[1_1|2]), (401,182,[5_1|2]), (401,125,[3_1|2]), (402,98,[3_1|2]), (402,99,[3_1|2]), (402,101,[3_1|2]), (402,125,[3_1|2]), (402,149,[3_1|2]), (402,310,[3_1|2]), (402,403,[3_1|2]), (402,424,[3_1|2]), (402,144,[3_1|2]), (402,307,[1_1|2]), (402,330,[1_1|2]), (402,336,[1_1|2]), (403,404,[5_1|2]), (404,405,[1_1|2]), (405,406,[0_1|2]), (406,407,[3_1|2]), (407,408,[4_1|2]), (408,409,[3_1|2]), (409,410,[5_1|2]), (410,411,[2_1|2]), (411,412,[0_1|2]), (412,413,[4_1|2]), (413,98,[3_1|2]), (413,199,[3_1|2]), (413,219,[3_1|2]), (413,223,[3_1|2]), (413,230,[3_1|2]), (413,247,[3_1|2]), (413,259,[3_1|2]), (413,273,[3_1|2]), (413,288,[3_1|2]), (413,220,[3_1|2]), (413,274,[3_1|2]), (413,307,[1_1|2]), (413,310,[3_1|2]), (413,330,[1_1|2]), (413,336,[1_1|2]), (414,415,[2_1|2]), (415,416,[0_1|2]), (416,417,[5_1|2]), (417,418,[5_1|2]), (418,419,[0_1|2]), (419,420,[3_1|2]), (420,421,[2_1|2]), (421,422,[2_1|2]), (422,423,[1_1|2]), (423,98,[3_1|2]), (423,99,[3_1|2]), (423,101,[3_1|2]), (423,125,[3_1|2]), (423,149,[3_1|2]), (423,310,[3_1|2]), (423,403,[3_1|2]), (423,424,[3_1|2]), (423,307,[1_1|2]), (423,330,[1_1|2]), (423,336,[1_1|2]), (424,425,[0_1|2]), (425,426,[0_1|2]), (426,427,[0_1|2]), (427,428,[2_1|2]), (428,429,[5_1|2]), (429,430,[5_1|2]), (430,431,[1_1|2]), (431,432,[0_1|2]), (431,448,[3_1|3]), (432,433,[1_1|2]), (433,434,[2_1|2]), (434,435,[2_1|2]), (435,436,[0_1|2]), (435,149,[3_1|2]), (436,98,[4_1|2]), (436,344,[4_1|2]), (436,352,[4_1|2]), (436,365,[4_1|2]), (437,438,[2_1|3]), (438,193,[1_1|3]), (439,440,[2_1|3]), (440,220,[1_1|3]), (440,274,[1_1|3]), (441,442,[4_1|3]), (442,443,[2_1|3]), (443,444,[3_1|3]), (444,445,[1_1|3]), (445,446,[3_1|3]), (446,447,[1_1|3]), (447,392,[1_1|3]), (447,261,[1_1|3]), (448,449,[2_1|3]), (449,435,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)