/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 75 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 157 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(1(2(2(x1))))) -> 0(0(3(1(x1)))) 3(2(4(4(1(3(x1)))))) -> 3(5(1(3(1(x1))))) 4(3(2(0(4(1(x1)))))) -> 5(4(2(5(1(x1))))) 2(4(4(4(5(0(4(x1))))))) -> 2(3(2(5(2(3(2(0(x1)))))))) 5(3(5(0(2(3(2(x1))))))) -> 5(4(2(3(4(1(2(x1))))))) 5(4(0(2(5(3(4(0(x1)))))))) -> 3(5(0(1(5(4(0(x1))))))) 5(3(0(0(0(4(1(5(5(x1))))))))) -> 5(4(5(5(1(5(2(5(x1)))))))) 1(1(3(3(3(1(5(0(2(4(x1)))))))))) -> 1(1(2(5(5(3(2(5(0(x1))))))))) 0(2(0(0(3(3(5(4(1(4(0(x1))))))))))) -> 0(2(3(4(1(0(3(5(3(5(x1)))))))))) 1(1(0(1(3(3(0(1(3(2(5(x1))))))))))) -> 1(0(0(4(4(4(4(1(4(5(x1)))))))))) 3(3(3(3(1(0(1(4(3(1(2(x1))))))))))) -> 3(5(2(0(4(5(1(0(2(0(2(x1))))))))))) 3(4(2(3(2(1(5(4(2(4(2(x1))))))))))) -> 5(0(2(5(0(4(1(3(4(x1))))))))) 2(0(0(3(1(2(1(0(4(2(4(0(x1)))))))))))) -> 2(1(1(0(3(0(2(0(4(1(1(x1))))))))))) 4(1(5(1(4(5(0(3(1(5(2(4(x1)))))))))))) -> 5(0(0(2(2(2(5(3(2(4(1(4(4(x1))))))))))))) 4(4(5(5(5(1(3(2(5(4(4(3(x1)))))))))))) -> 5(4(2(5(4(4(5(2(3(1(2(3(x1)))))))))))) 3(2(4(2(5(1(3(4(5(1(4(5(2(x1))))))))))))) -> 5(1(0(4(0(1(1(3(2(0(1(5(2(x1))))))))))))) 4(5(3(1(5(4(4(5(2(5(2(5(0(4(x1)))))))))))))) -> 5(4(4(4(2(5(4(1(4(4(5(4(0(0(4(x1))))))))))))))) 0(4(4(4(0(5(2(1(5(0(3(1(0(1(4(x1))))))))))))))) -> 0(3(5(5(2(0(3(5(3(3(1(2(5(4(x1)))))))))))))) 4(2(0(2(5(3(1(0(2(1(0(0(4(3(0(x1))))))))))))))) -> 0(2(0(0(3(2(1(5(2(4(1(2(1(4(1(x1))))))))))))))) 5(1(4(5(3(3(0(5(2(1(0(2(5(1(4(x1))))))))))))))) -> 5(4(1(3(3(4(2(1(1(4(1(2(0(3(2(4(x1)))))))))))))))) 4(0(5(3(4(4(5(2(2(2(1(0(0(3(4(4(x1)))))))))))))))) -> 5(2(2(5(0(3(2(2(3(0(2(0(3(2(3(2(4(x1))))))))))))))))) 3(0(0(5(3(2(3(5(3(5(0(3(3(2(1(3(3(x1))))))))))))))))) -> 1(1(5(3(4(2(4(2(5(1(4(2(2(5(1(5(3(1(x1)))))))))))))))))) 0(0(4(3(4(5(2(1(1(1(5(1(2(5(3(3(1(5(x1)))))))))))))))))) -> 0(0(0(4(3(0(4(0(2(5(4(3(1(4(3(3(1(5(x1)))))))))))))))))) 4(5(5(3(4(4(2(2(0(3(1(1(1(0(4(2(0(4(x1)))))))))))))))))) -> 5(2(3(0(2(4(2(3(2(3(2(5(2(5(1(0(3(4(x1)))))))))))))))))) 0(0(0(4(4(2(3(4(5(0(3(1(2(5(5(1(3(4(4(x1))))))))))))))))))) -> 0(0(2(2(1(0(5(5(1(2(5(2(3(4(5(5(5(1(0(x1))))))))))))))))))) 4(2(0(1(5(1(4(4(4(3(2(5(1(5(1(3(2(0(0(x1))))))))))))))))))) -> 5(2(5(4(5(5(5(3(5(3(2(3(4(0(5(x1))))))))))))))) 5(2(2(5(0(0(0(3(1(3(3(3(4(3(1(4(2(4(1(x1))))))))))))))))))) -> 5(2(3(4(4(4(3(4(5(5(0(5(5(5(2(5(x1)))))))))))))))) 0(2(4(1(1(2(4(2(0(1(4(4(5(5(0(4(0(3(1(5(5(x1))))))))))))))))))))) -> 5(5(0(4(1(2(3(5(1(2(1(4(1(0(5(3(5(3(5(x1))))))))))))))))))) 1(3(2(2(2(0(4(5(2(5(3(5(5(3(4(4(2(3(0(0(0(x1))))))))))))))))))))) -> 1(3(3(3(2(5(4(2(4(0(5(4(4(5(4(3(2(0(0(4(x1)))))))))))))))))))) 5(2(1(4(1(2(3(4(1(3(5(0(4(3(3(5(5(3(5(2(5(x1))))))))))))))))))))) -> 5(2(1(2(5(5(0(5(1(2(1(5(5(4(3(2(2(5(0(3(5(x1))))))))))))))))))))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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 (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(1(2(2(x1))))) -> 0(0(3(1(x1)))) 3(2(4(4(1(3(x1)))))) -> 3(5(1(3(1(x1))))) 4(3(2(0(4(1(x1)))))) -> 5(4(2(5(1(x1))))) 2(4(4(4(5(0(4(x1))))))) -> 2(3(2(5(2(3(2(0(x1)))))))) 5(3(5(0(2(3(2(x1))))))) -> 5(4(2(3(4(1(2(x1))))))) 5(4(0(2(5(3(4(0(x1)))))))) -> 3(5(0(1(5(4(0(x1))))))) 5(3(0(0(0(4(1(5(5(x1))))))))) -> 5(4(5(5(1(5(2(5(x1)))))))) 1(1(3(3(3(1(5(0(2(4(x1)))))))))) -> 1(1(2(5(5(3(2(5(0(x1))))))))) 0(2(0(0(3(3(5(4(1(4(0(x1))))))))))) -> 0(2(3(4(1(0(3(5(3(5(x1)))))))))) 1(1(0(1(3(3(0(1(3(2(5(x1))))))))))) -> 1(0(0(4(4(4(4(1(4(5(x1)))))))))) 3(3(3(3(1(0(1(4(3(1(2(x1))))))))))) -> 3(5(2(0(4(5(1(0(2(0(2(x1))))))))))) 3(4(2(3(2(1(5(4(2(4(2(x1))))))))))) -> 5(0(2(5(0(4(1(3(4(x1))))))))) 2(0(0(3(1(2(1(0(4(2(4(0(x1)))))))))))) -> 2(1(1(0(3(0(2(0(4(1(1(x1))))))))))) 4(1(5(1(4(5(0(3(1(5(2(4(x1)))))))))))) -> 5(0(0(2(2(2(5(3(2(4(1(4(4(x1))))))))))))) 4(4(5(5(5(1(3(2(5(4(4(3(x1)))))))))))) -> 5(4(2(5(4(4(5(2(3(1(2(3(x1)))))))))))) 3(2(4(2(5(1(3(4(5(1(4(5(2(x1))))))))))))) -> 5(1(0(4(0(1(1(3(2(0(1(5(2(x1))))))))))))) 4(5(3(1(5(4(4(5(2(5(2(5(0(4(x1)))))))))))))) -> 5(4(4(4(2(5(4(1(4(4(5(4(0(0(4(x1))))))))))))))) 0(4(4(4(0(5(2(1(5(0(3(1(0(1(4(x1))))))))))))))) -> 0(3(5(5(2(0(3(5(3(3(1(2(5(4(x1)))))))))))))) 4(2(0(2(5(3(1(0(2(1(0(0(4(3(0(x1))))))))))))))) -> 0(2(0(0(3(2(1(5(2(4(1(2(1(4(1(x1))))))))))))))) 5(1(4(5(3(3(0(5(2(1(0(2(5(1(4(x1))))))))))))))) -> 5(4(1(3(3(4(2(1(1(4(1(2(0(3(2(4(x1)))))))))))))))) 4(0(5(3(4(4(5(2(2(2(1(0(0(3(4(4(x1)))))))))))))))) -> 5(2(2(5(0(3(2(2(3(0(2(0(3(2(3(2(4(x1))))))))))))))))) 3(0(0(5(3(2(3(5(3(5(0(3(3(2(1(3(3(x1))))))))))))))))) -> 1(1(5(3(4(2(4(2(5(1(4(2(2(5(1(5(3(1(x1)))))))))))))))))) 0(0(4(3(4(5(2(1(1(1(5(1(2(5(3(3(1(5(x1)))))))))))))))))) -> 0(0(0(4(3(0(4(0(2(5(4(3(1(4(3(3(1(5(x1)))))))))))))))))) 4(5(5(3(4(4(2(2(0(3(1(1(1(0(4(2(0(4(x1)))))))))))))))))) -> 5(2(3(0(2(4(2(3(2(3(2(5(2(5(1(0(3(4(x1)))))))))))))))))) 0(0(0(4(4(2(3(4(5(0(3(1(2(5(5(1(3(4(4(x1))))))))))))))))))) -> 0(0(2(2(1(0(5(5(1(2(5(2(3(4(5(5(5(1(0(x1))))))))))))))))))) 4(2(0(1(5(1(4(4(4(3(2(5(1(5(1(3(2(0(0(x1))))))))))))))))))) -> 5(2(5(4(5(5(5(3(5(3(2(3(4(0(5(x1))))))))))))))) 5(2(2(5(0(0(0(3(1(3(3(3(4(3(1(4(2(4(1(x1))))))))))))))))))) -> 5(2(3(4(4(4(3(4(5(5(0(5(5(5(2(5(x1)))))))))))))))) 0(2(4(1(1(2(4(2(0(1(4(4(5(5(0(4(0(3(1(5(5(x1))))))))))))))))))))) -> 5(5(0(4(1(2(3(5(1(2(1(4(1(0(5(3(5(3(5(x1))))))))))))))))))) 1(3(2(2(2(0(4(5(2(5(3(5(5(3(4(4(2(3(0(0(0(x1))))))))))))))))))))) -> 1(3(3(3(2(5(4(2(4(0(5(4(4(5(4(3(2(0(0(4(x1)))))))))))))))))))) 5(2(1(4(1(2(3(4(1(3(5(0(4(3(3(5(5(3(5(2(5(x1))))))))))))))))))))) -> 5(2(1(2(5(5(0(5(1(2(1(5(5(4(3(2(2(5(0(3(5(x1))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(1(2(2(x1))))) -> 0(0(3(1(x1)))) 3(2(4(4(1(3(x1)))))) -> 3(5(1(3(1(x1))))) 4(3(2(0(4(1(x1)))))) -> 5(4(2(5(1(x1))))) 2(4(4(4(5(0(4(x1))))))) -> 2(3(2(5(2(3(2(0(x1)))))))) 5(3(5(0(2(3(2(x1))))))) -> 5(4(2(3(4(1(2(x1))))))) 5(4(0(2(5(3(4(0(x1)))))))) -> 3(5(0(1(5(4(0(x1))))))) 5(3(0(0(0(4(1(5(5(x1))))))))) -> 5(4(5(5(1(5(2(5(x1)))))))) 1(1(3(3(3(1(5(0(2(4(x1)))))))))) -> 1(1(2(5(5(3(2(5(0(x1))))))))) 0(2(0(0(3(3(5(4(1(4(0(x1))))))))))) -> 0(2(3(4(1(0(3(5(3(5(x1)))))))))) 1(1(0(1(3(3(0(1(3(2(5(x1))))))))))) -> 1(0(0(4(4(4(4(1(4(5(x1)))))))))) 3(3(3(3(1(0(1(4(3(1(2(x1))))))))))) -> 3(5(2(0(4(5(1(0(2(0(2(x1))))))))))) 3(4(2(3(2(1(5(4(2(4(2(x1))))))))))) -> 5(0(2(5(0(4(1(3(4(x1))))))))) 2(0(0(3(1(2(1(0(4(2(4(0(x1)))))))))))) -> 2(1(1(0(3(0(2(0(4(1(1(x1))))))))))) 4(1(5(1(4(5(0(3(1(5(2(4(x1)))))))))))) -> 5(0(0(2(2(2(5(3(2(4(1(4(4(x1))))))))))))) 4(4(5(5(5(1(3(2(5(4(4(3(x1)))))))))))) -> 5(4(2(5(4(4(5(2(3(1(2(3(x1)))))))))))) 3(2(4(2(5(1(3(4(5(1(4(5(2(x1))))))))))))) -> 5(1(0(4(0(1(1(3(2(0(1(5(2(x1))))))))))))) 4(5(3(1(5(4(4(5(2(5(2(5(0(4(x1)))))))))))))) -> 5(4(4(4(2(5(4(1(4(4(5(4(0(0(4(x1))))))))))))))) 0(4(4(4(0(5(2(1(5(0(3(1(0(1(4(x1))))))))))))))) -> 0(3(5(5(2(0(3(5(3(3(1(2(5(4(x1)))))))))))))) 4(2(0(2(5(3(1(0(2(1(0(0(4(3(0(x1))))))))))))))) -> 0(2(0(0(3(2(1(5(2(4(1(2(1(4(1(x1))))))))))))))) 5(1(4(5(3(3(0(5(2(1(0(2(5(1(4(x1))))))))))))))) -> 5(4(1(3(3(4(2(1(1(4(1(2(0(3(2(4(x1)))))))))))))))) 4(0(5(3(4(4(5(2(2(2(1(0(0(3(4(4(x1)))))))))))))))) -> 5(2(2(5(0(3(2(2(3(0(2(0(3(2(3(2(4(x1))))))))))))))))) 3(0(0(5(3(2(3(5(3(5(0(3(3(2(1(3(3(x1))))))))))))))))) -> 1(1(5(3(4(2(4(2(5(1(4(2(2(5(1(5(3(1(x1)))))))))))))))))) 0(0(4(3(4(5(2(1(1(1(5(1(2(5(3(3(1(5(x1)))))))))))))))))) -> 0(0(0(4(3(0(4(0(2(5(4(3(1(4(3(3(1(5(x1)))))))))))))))))) 4(5(5(3(4(4(2(2(0(3(1(1(1(0(4(2(0(4(x1)))))))))))))))))) -> 5(2(3(0(2(4(2(3(2(3(2(5(2(5(1(0(3(4(x1)))))))))))))))))) 0(0(0(4(4(2(3(4(5(0(3(1(2(5(5(1(3(4(4(x1))))))))))))))))))) -> 0(0(2(2(1(0(5(5(1(2(5(2(3(4(5(5(5(1(0(x1))))))))))))))))))) 4(2(0(1(5(1(4(4(4(3(2(5(1(5(1(3(2(0(0(x1))))))))))))))))))) -> 5(2(5(4(5(5(5(3(5(3(2(3(4(0(5(x1))))))))))))))) 5(2(2(5(0(0(0(3(1(3(3(3(4(3(1(4(2(4(1(x1))))))))))))))))))) -> 5(2(3(4(4(4(3(4(5(5(0(5(5(5(2(5(x1)))))))))))))))) 0(2(4(1(1(2(4(2(0(1(4(4(5(5(0(4(0(3(1(5(5(x1))))))))))))))))))))) -> 5(5(0(4(1(2(3(5(1(2(1(4(1(0(5(3(5(3(5(x1))))))))))))))))))) 1(3(2(2(2(0(4(5(2(5(3(5(5(3(4(4(2(3(0(0(0(x1))))))))))))))))))))) -> 1(3(3(3(2(5(4(2(4(0(5(4(4(5(4(3(2(0(0(4(x1)))))))))))))))))))) 5(2(1(4(1(2(3(4(1(3(5(0(4(3(3(5(5(3(5(2(5(x1))))))))))))))))))))) -> 5(2(1(2(5(5(0(5(1(2(1(5(5(4(3(2(2(5(0(3(5(x1))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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: FULL ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(1(2(2(x1))))) -> 0(0(3(1(x1)))) 3(2(4(4(1(3(x1)))))) -> 3(5(1(3(1(x1))))) 4(3(2(0(4(1(x1)))))) -> 5(4(2(5(1(x1))))) 2(4(4(4(5(0(4(x1))))))) -> 2(3(2(5(2(3(2(0(x1)))))))) 5(3(5(0(2(3(2(x1))))))) -> 5(4(2(3(4(1(2(x1))))))) 5(4(0(2(5(3(4(0(x1)))))))) -> 3(5(0(1(5(4(0(x1))))))) 5(3(0(0(0(4(1(5(5(x1))))))))) -> 5(4(5(5(1(5(2(5(x1)))))))) 1(1(3(3(3(1(5(0(2(4(x1)))))))))) -> 1(1(2(5(5(3(2(5(0(x1))))))))) 0(2(0(0(3(3(5(4(1(4(0(x1))))))))))) -> 0(2(3(4(1(0(3(5(3(5(x1)))))))))) 1(1(0(1(3(3(0(1(3(2(5(x1))))))))))) -> 1(0(0(4(4(4(4(1(4(5(x1)))))))))) 3(3(3(3(1(0(1(4(3(1(2(x1))))))))))) -> 3(5(2(0(4(5(1(0(2(0(2(x1))))))))))) 3(4(2(3(2(1(5(4(2(4(2(x1))))))))))) -> 5(0(2(5(0(4(1(3(4(x1))))))))) 2(0(0(3(1(2(1(0(4(2(4(0(x1)))))))))))) -> 2(1(1(0(3(0(2(0(4(1(1(x1))))))))))) 4(1(5(1(4(5(0(3(1(5(2(4(x1)))))))))))) -> 5(0(0(2(2(2(5(3(2(4(1(4(4(x1))))))))))))) 4(4(5(5(5(1(3(2(5(4(4(3(x1)))))))))))) -> 5(4(2(5(4(4(5(2(3(1(2(3(x1)))))))))))) 3(2(4(2(5(1(3(4(5(1(4(5(2(x1))))))))))))) -> 5(1(0(4(0(1(1(3(2(0(1(5(2(x1))))))))))))) 4(5(3(1(5(4(4(5(2(5(2(5(0(4(x1)))))))))))))) -> 5(4(4(4(2(5(4(1(4(4(5(4(0(0(4(x1))))))))))))))) 0(4(4(4(0(5(2(1(5(0(3(1(0(1(4(x1))))))))))))))) -> 0(3(5(5(2(0(3(5(3(3(1(2(5(4(x1)))))))))))))) 4(2(0(2(5(3(1(0(2(1(0(0(4(3(0(x1))))))))))))))) -> 0(2(0(0(3(2(1(5(2(4(1(2(1(4(1(x1))))))))))))))) 5(1(4(5(3(3(0(5(2(1(0(2(5(1(4(x1))))))))))))))) -> 5(4(1(3(3(4(2(1(1(4(1(2(0(3(2(4(x1)))))))))))))))) 4(0(5(3(4(4(5(2(2(2(1(0(0(3(4(4(x1)))))))))))))))) -> 5(2(2(5(0(3(2(2(3(0(2(0(3(2(3(2(4(x1))))))))))))))))) 3(0(0(5(3(2(3(5(3(5(0(3(3(2(1(3(3(x1))))))))))))))))) -> 1(1(5(3(4(2(4(2(5(1(4(2(2(5(1(5(3(1(x1)))))))))))))))))) 0(0(4(3(4(5(2(1(1(1(5(1(2(5(3(3(1(5(x1)))))))))))))))))) -> 0(0(0(4(3(0(4(0(2(5(4(3(1(4(3(3(1(5(x1)))))))))))))))))) 4(5(5(3(4(4(2(2(0(3(1(1(1(0(4(2(0(4(x1)))))))))))))))))) -> 5(2(3(0(2(4(2(3(2(3(2(5(2(5(1(0(3(4(x1)))))))))))))))))) 0(0(0(4(4(2(3(4(5(0(3(1(2(5(5(1(3(4(4(x1))))))))))))))))))) -> 0(0(2(2(1(0(5(5(1(2(5(2(3(4(5(5(5(1(0(x1))))))))))))))))))) 4(2(0(1(5(1(4(4(4(3(2(5(1(5(1(3(2(0(0(x1))))))))))))))))))) -> 5(2(5(4(5(5(5(3(5(3(2(3(4(0(5(x1))))))))))))))) 5(2(2(5(0(0(0(3(1(3(3(3(4(3(1(4(2(4(1(x1))))))))))))))))))) -> 5(2(3(4(4(4(3(4(5(5(0(5(5(5(2(5(x1)))))))))))))))) 0(2(4(1(1(2(4(2(0(1(4(4(5(5(0(4(0(3(1(5(5(x1))))))))))))))))))))) -> 5(5(0(4(1(2(3(5(1(2(1(4(1(0(5(3(5(3(5(x1))))))))))))))))))) 1(3(2(2(2(0(4(5(2(5(3(5(5(3(4(4(2(3(0(0(0(x1))))))))))))))))))))) -> 1(3(3(3(2(5(4(2(4(0(5(4(4(5(4(3(2(0(0(4(x1)))))))))))))))))))) 5(2(1(4(1(2(3(4(1(3(5(0(4(3(3(5(5(3(5(2(5(x1))))))))))))))))))))) -> 5(2(1(2(5(5(0(5(1(2(1(5(5(4(3(2(2(5(0(3(5(x1))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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: FULL ---------------------------------------- (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. 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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] {(148,149,[0_1|0, 3_1|0, 4_1|0, 2_1|0, 5_1|0, 1_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]), (148,150,[0_1|1, 3_1|1, 4_1|1, 2_1|1, 5_1|1, 1_1|1]), 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(458,459,[5_1|2]), (459,460,[5_1|2]), (460,461,[4_1|2]), (461,462,[3_1|2]), (462,463,[2_1|2]), (463,464,[2_1|2]), (464,465,[5_1|2]), (465,466,[0_1|2]), (466,467,[3_1|2]), (467,150,[5_1|2]), (467,163,[5_1|2]), (467,233,[5_1|2]), (467,255,[5_1|2]), (467,280,[5_1|2]), (467,284,[5_1|2]), (467,296,[5_1|2]), (467,307,[5_1|2]), (467,321,[5_1|2]), (467,352,[5_1|2]), (467,366,[5_1|2]), (467,399,[5_1|2]), (467,405,[5_1|2]), (467,418,[5_1|2]), (467,433,[5_1|2]), (467,448,[5_1|2]), (467,354,[5_1|2]), (467,412,[3_1|2]), (468,469,[1_1|2]), (469,470,[2_1|2]), (470,471,[5_1|2]), (471,472,[5_1|2]), (472,473,[3_1|2]), (473,474,[2_1|2]), (474,475,[5_1|2]), (475,150,[0_1|2]), (475,151,[0_1|2]), (475,154,[0_1|2]), (475,163,[5_1|2]), (475,181,[0_1|2]), (475,194,[0_1|2]), (475,211,[0_1|2]), (476,477,[0_1|2]), (477,478,[0_1|2]), (478,479,[4_1|2]), (479,480,[4_1|2]), (480,481,[4_1|2]), (481,482,[4_1|2]), (482,483,[1_1|2]), (483,484,[4_1|2]), (483,307,[5_1|2]), (483,321,[5_1|2]), (484,150,[5_1|2]), (484,163,[5_1|2]), (484,233,[5_1|2]), (484,255,[5_1|2]), (484,280,[5_1|2]), (484,284,[5_1|2]), (484,296,[5_1|2]), (484,307,[5_1|2]), (484,321,[5_1|2]), (484,352,[5_1|2]), (484,366,[5_1|2]), (484,399,[5_1|2]), (484,405,[5_1|2]), (484,418,[5_1|2]), (484,433,[5_1|2]), (484,448,[5_1|2]), (484,412,[3_1|2]), (485,486,[3_1|2]), (486,487,[3_1|2]), (487,488,[3_1|2]), (488,489,[2_1|2]), (489,490,[5_1|2]), (490,491,[4_1|2]), (491,492,[2_1|2]), (492,493,[4_1|2]), (493,494,[0_1|2]), (494,495,[5_1|2]), (495,496,[4_1|2]), (496,497,[4_1|2]), (497,498,[5_1|2]), (498,499,[4_1|2]), (499,500,[3_1|2]), (500,501,[2_1|2]), (501,502,[0_1|2]), (501,194,[0_1|2]), (502,503,[0_1|2]), (502,181,[0_1|2]), (503,150,[4_1|2]), (503,151,[4_1|2]), (503,154,[4_1|2]), (503,181,[4_1|2]), (503,194,[4_1|2]), (503,211,[4_1|2]), (503,338,[4_1|2, 0_1|2]), (503,152,[4_1|2]), (503,195,[4_1|2]), (503,212,[4_1|2]), (503,196,[4_1|2]), (503,280,[5_1|2]), (503,284,[5_1|2]), (503,296,[5_1|2]), (503,307,[5_1|2]), (503,321,[5_1|2]), (503,352,[5_1|2]), (503,366,[5_1|2])}" ---------------------------------------- (8) BOUNDS(1, n^1)