WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 164 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 119 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(0(2(x1)))) -> 3(4(4(x1))) 2(0(0(3(x1)))) -> 3(4(1(x1))) 5(3(5(0(1(x1))))) -> 5(2(3(0(x1)))) 0(0(1(2(2(3(x1)))))) -> 4(0(2(2(3(x1))))) 0(5(3(1(4(3(x1)))))) -> 1(4(0(5(2(x1))))) 2(0(4(3(5(3(3(1(x1)))))))) -> 2(1(2(2(2(0(3(1(x1)))))))) 2(4(0(2(3(0(0(2(x1)))))))) -> 2(4(0(3(4(4(2(x1))))))) 2(1(4(0(4(1(5(0(2(x1))))))))) -> 3(3(2(2(3(0(3(3(4(x1))))))))) 5(0(4(0(0(1(3(5(0(x1))))))))) -> 5(0(0(0(3(5(5(3(2(x1))))))))) 5(3(5(4(4(2(2(2(1(x1))))))))) -> 5(0(3(0(0(4(5(2(1(x1))))))))) 2(0(4(2(3(3(3(5(4(2(x1)))))))))) -> 3(4(4(2(0(2(3(3(5(2(x1)))))))))) 4(4(3(2(0(1(1(4(0(2(x1)))))))))) -> 2(3(4(0(0(1(2(1(3(4(x1)))))))))) 1(5(5(2(4(2(4(0(3(3(0(x1))))))))))) -> 1(3(5(4(5(5(5(3(2(4(2(x1))))))))))) 2(5(5(0(1(1(5(1(4(2(3(3(x1)))))))))))) -> 4(2(3(0(3(0(0(2(3(2(3(x1))))))))))) 3(0(2(4(5(2(1(2(0(2(5(1(x1)))))))))))) -> 3(1(3(0(5(0(2(2(4(0(4(x1))))))))))) 3(3(3(4(3(0(0(4(4(5(0(5(x1)))))))))))) -> 3(1(5(5(0(3(1(0(5(2(5(x1))))))))))) 0(5(3(5(1(0(5(1(2(4(4(5(0(x1))))))))))))) -> 0(3(1(0(4(5(5(2(5(5(2(4(0(x1))))))))))))) 2(5(2(4(1(5(3(3(1(0(2(5(3(x1))))))))))))) -> 2(3(1(3(3(5(1(2(0(3(2(3(0(x1))))))))))))) 2(5(5(3(5(3(1(3(1(2(5(0(0(x1))))))))))))) -> 2(5(5(5(0(4(5(5(1(1(3(2(2(x1))))))))))))) 3(5(3(3(3(2(3(0(2(4(2(1(3(x1))))))))))))) -> 5(1(3(1(4(0(0(1(5(0(4(5(x1)))))))))))) 2(0(3(0(2(3(1(0(0(3(0(3(5(3(x1)))))))))))))) -> 3(4(0(2(1(4(4(4(0(5(5(5(2(x1))))))))))))) 3(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 5(2(0(1(4(4(3(3(3(5(3(4(1(2(x1)))))))))))))) 3(5(5(0(2(2(0(0(3(5(1(3(3(5(3(5(x1)))))))))))))))) -> 3(1(4(2(0(3(4(0(4(1(5(4(2(5(x1)))))))))))))) 5(5(3(5(0(5(3(5(2(3(1(3(3(4(0(2(x1)))))))))))))))) -> 5(2(4(2(4(4(0(5(5(1(3(4(0(4(0(x1))))))))))))))) 2(2(1(3(4(0(1(1(4(2(2(2(0(4(4(2(4(4(x1)))))))))))))))))) -> 4(3(4(4(5(5(0(1(0(1(3(2(5(5(1(1(4(4(x1)))))))))))))))))) 0(3(0(2(2(2(5(5(2(4(4(3(5(1(0(0(0(3(3(x1))))))))))))))))))) -> 3(3(1(3(4(5(5(2(0(4(2(3(1(1(5(1(2(3(x1)))))))))))))))))) 3(3(4(3(3(4(3(0(2(5(3(1(4(5(2(5(2(4(3(5(x1)))))))))))))))))))) -> 5(2(5(0(5(0(1(1(1(3(2(4(4(0(3(2(4(1(5(x1))))))))))))))))))) 2(1(5(5(3(0(1(3(3(3(1(2(0(5(2(0(3(5(2(2(2(x1))))))))))))))))))))) -> 3(0(3(3(4(0(1(4(5(1(3(3(3(4(1(2(1(3(2(1(x1)))))))))))))))))))) 5(1(3(4(0(3(0(2(5(3(0(2(2(0(1(2(3(3(4(1(1(x1))))))))))))))))))))) -> 5(0(1(1(4(2(0(1(1(2(1(4(0(4(3(1(2(0(0(2(x1)))))))))))))))))))) 5(4(0(0(3(2(5(3(0(3(0(4(5(0(4(4(5(1(1(1(3(x1))))))))))))))))))))) -> 5(2(5(1(0(3(5(3(2(1(0(0(5(5(4(5(4(4(2(2(2(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_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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 (full) 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(x1)))) -> 3(4(4(x1))) 2(0(0(3(x1)))) -> 3(4(1(x1))) 5(3(5(0(1(x1))))) -> 5(2(3(0(x1)))) 0(0(1(2(2(3(x1)))))) -> 4(0(2(2(3(x1))))) 0(5(3(1(4(3(x1)))))) -> 1(4(0(5(2(x1))))) 2(0(4(3(5(3(3(1(x1)))))))) -> 2(1(2(2(2(0(3(1(x1)))))))) 2(4(0(2(3(0(0(2(x1)))))))) -> 2(4(0(3(4(4(2(x1))))))) 2(1(4(0(4(1(5(0(2(x1))))))))) -> 3(3(2(2(3(0(3(3(4(x1))))))))) 5(0(4(0(0(1(3(5(0(x1))))))))) -> 5(0(0(0(3(5(5(3(2(x1))))))))) 5(3(5(4(4(2(2(2(1(x1))))))))) -> 5(0(3(0(0(4(5(2(1(x1))))))))) 2(0(4(2(3(3(3(5(4(2(x1)))))))))) -> 3(4(4(2(0(2(3(3(5(2(x1)))))))))) 4(4(3(2(0(1(1(4(0(2(x1)))))))))) -> 2(3(4(0(0(1(2(1(3(4(x1)))))))))) 1(5(5(2(4(2(4(0(3(3(0(x1))))))))))) -> 1(3(5(4(5(5(5(3(2(4(2(x1))))))))))) 2(5(5(0(1(1(5(1(4(2(3(3(x1)))))))))))) -> 4(2(3(0(3(0(0(2(3(2(3(x1))))))))))) 3(0(2(4(5(2(1(2(0(2(5(1(x1)))))))))))) -> 3(1(3(0(5(0(2(2(4(0(4(x1))))))))))) 3(3(3(4(3(0(0(4(4(5(0(5(x1)))))))))))) -> 3(1(5(5(0(3(1(0(5(2(5(x1))))))))))) 0(5(3(5(1(0(5(1(2(4(4(5(0(x1))))))))))))) -> 0(3(1(0(4(5(5(2(5(5(2(4(0(x1))))))))))))) 2(5(2(4(1(5(3(3(1(0(2(5(3(x1))))))))))))) -> 2(3(1(3(3(5(1(2(0(3(2(3(0(x1))))))))))))) 2(5(5(3(5(3(1(3(1(2(5(0(0(x1))))))))))))) -> 2(5(5(5(0(4(5(5(1(1(3(2(2(x1))))))))))))) 3(5(3(3(3(2(3(0(2(4(2(1(3(x1))))))))))))) -> 5(1(3(1(4(0(0(1(5(0(4(5(x1)))))))))))) 2(0(3(0(2(3(1(0(0(3(0(3(5(3(x1)))))))))))))) -> 3(4(0(2(1(4(4(4(0(5(5(5(2(x1))))))))))))) 3(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 5(2(0(1(4(4(3(3(3(5(3(4(1(2(x1)))))))))))))) 3(5(5(0(2(2(0(0(3(5(1(3(3(5(3(5(x1)))))))))))))))) -> 3(1(4(2(0(3(4(0(4(1(5(4(2(5(x1)))))))))))))) 5(5(3(5(0(5(3(5(2(3(1(3(3(4(0(2(x1)))))))))))))))) -> 5(2(4(2(4(4(0(5(5(1(3(4(0(4(0(x1))))))))))))))) 2(2(1(3(4(0(1(1(4(2(2(2(0(4(4(2(4(4(x1)))))))))))))))))) -> 4(3(4(4(5(5(0(1(0(1(3(2(5(5(1(1(4(4(x1)))))))))))))))))) 0(3(0(2(2(2(5(5(2(4(4(3(5(1(0(0(0(3(3(x1))))))))))))))))))) -> 3(3(1(3(4(5(5(2(0(4(2(3(1(1(5(1(2(3(x1)))))))))))))))))) 3(3(4(3(3(4(3(0(2(5(3(1(4(5(2(5(2(4(3(5(x1)))))))))))))))))))) -> 5(2(5(0(5(0(1(1(1(3(2(4(4(0(3(2(4(1(5(x1))))))))))))))))))) 2(1(5(5(3(0(1(3(3(3(1(2(0(5(2(0(3(5(2(2(2(x1))))))))))))))))))))) -> 3(0(3(3(4(0(1(4(5(1(3(3(3(4(1(2(1(3(2(1(x1)))))))))))))))))))) 5(1(3(4(0(3(0(2(5(3(0(2(2(0(1(2(3(3(4(1(1(x1))))))))))))))))))))) -> 5(0(1(1(4(2(0(1(1(2(1(4(0(4(3(1(2(0(0(2(x1)))))))))))))))))))) 5(4(0(0(3(2(5(3(0(3(0(4(5(0(4(4(5(1(1(1(3(x1))))))))))))))))))))) -> 5(2(5(1(0(3(5(3(2(1(0(0(5(5(4(5(4(4(2(2(2(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_5(x_1)) -> 5(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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: 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(0(2(x1)))) -> 3(4(4(x1))) 2(0(0(3(x1)))) -> 3(4(1(x1))) 5(3(5(0(1(x1))))) -> 5(2(3(0(x1)))) 0(0(1(2(2(3(x1)))))) -> 4(0(2(2(3(x1))))) 0(5(3(1(4(3(x1)))))) -> 1(4(0(5(2(x1))))) 2(0(4(3(5(3(3(1(x1)))))))) -> 2(1(2(2(2(0(3(1(x1)))))))) 2(4(0(2(3(0(0(2(x1)))))))) -> 2(4(0(3(4(4(2(x1))))))) 2(1(4(0(4(1(5(0(2(x1))))))))) -> 3(3(2(2(3(0(3(3(4(x1))))))))) 5(0(4(0(0(1(3(5(0(x1))))))))) -> 5(0(0(0(3(5(5(3(2(x1))))))))) 5(3(5(4(4(2(2(2(1(x1))))))))) -> 5(0(3(0(0(4(5(2(1(x1))))))))) 2(0(4(2(3(3(3(5(4(2(x1)))))))))) -> 3(4(4(2(0(2(3(3(5(2(x1)))))))))) 4(4(3(2(0(1(1(4(0(2(x1)))))))))) -> 2(3(4(0(0(1(2(1(3(4(x1)))))))))) 1(5(5(2(4(2(4(0(3(3(0(x1))))))))))) -> 1(3(5(4(5(5(5(3(2(4(2(x1))))))))))) 2(5(5(0(1(1(5(1(4(2(3(3(x1)))))))))))) -> 4(2(3(0(3(0(0(2(3(2(3(x1))))))))))) 3(0(2(4(5(2(1(2(0(2(5(1(x1)))))))))))) -> 3(1(3(0(5(0(2(2(4(0(4(x1))))))))))) 3(3(3(4(3(0(0(4(4(5(0(5(x1)))))))))))) -> 3(1(5(5(0(3(1(0(5(2(5(x1))))))))))) 0(5(3(5(1(0(5(1(2(4(4(5(0(x1))))))))))))) -> 0(3(1(0(4(5(5(2(5(5(2(4(0(x1))))))))))))) 2(5(2(4(1(5(3(3(1(0(2(5(3(x1))))))))))))) -> 2(3(1(3(3(5(1(2(0(3(2(3(0(x1))))))))))))) 2(5(5(3(5(3(1(3(1(2(5(0(0(x1))))))))))))) -> 2(5(5(5(0(4(5(5(1(1(3(2(2(x1))))))))))))) 3(5(3(3(3(2(3(0(2(4(2(1(3(x1))))))))))))) -> 5(1(3(1(4(0(0(1(5(0(4(5(x1)))))))))))) 2(0(3(0(2(3(1(0(0(3(0(3(5(3(x1)))))))))))))) -> 3(4(0(2(1(4(4(4(0(5(5(5(2(x1))))))))))))) 3(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 5(2(0(1(4(4(3(3(3(5(3(4(1(2(x1)))))))))))))) 3(5(5(0(2(2(0(0(3(5(1(3(3(5(3(5(x1)))))))))))))))) -> 3(1(4(2(0(3(4(0(4(1(5(4(2(5(x1)))))))))))))) 5(5(3(5(0(5(3(5(2(3(1(3(3(4(0(2(x1)))))))))))))))) -> 5(2(4(2(4(4(0(5(5(1(3(4(0(4(0(x1))))))))))))))) 2(2(1(3(4(0(1(1(4(2(2(2(0(4(4(2(4(4(x1)))))))))))))))))) -> 4(3(4(4(5(5(0(1(0(1(3(2(5(5(1(1(4(4(x1)))))))))))))))))) 0(3(0(2(2(2(5(5(2(4(4(3(5(1(0(0(0(3(3(x1))))))))))))))))))) -> 3(3(1(3(4(5(5(2(0(4(2(3(1(1(5(1(2(3(x1)))))))))))))))))) 3(3(4(3(3(4(3(0(2(5(3(1(4(5(2(5(2(4(3(5(x1)))))))))))))))))))) -> 5(2(5(0(5(0(1(1(1(3(2(4(4(0(3(2(4(1(5(x1))))))))))))))))))) 2(1(5(5(3(0(1(3(3(3(1(2(0(5(2(0(3(5(2(2(2(x1))))))))))))))))))))) -> 3(0(3(3(4(0(1(4(5(1(3(3(3(4(1(2(1(3(2(1(x1)))))))))))))))))))) 5(1(3(4(0(3(0(2(5(3(0(2(2(0(1(2(3(3(4(1(1(x1))))))))))))))))))))) -> 5(0(1(1(4(2(0(1(1(2(1(4(0(4(3(1(2(0(0(2(x1)))))))))))))))))))) 5(4(0(0(3(2(5(3(0(3(0(4(5(0(4(4(5(1(1(1(3(x1))))))))))))))))))))) -> 5(2(5(1(0(3(5(3(2(1(0(0(5(5(4(5(4(4(2(2(2(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_5(x_1)) -> 5(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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: 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(0(2(x1)))) -> 3(4(4(x1))) 2(0(0(3(x1)))) -> 3(4(1(x1))) 5(3(5(0(1(x1))))) -> 5(2(3(0(x1)))) 0(0(1(2(2(3(x1)))))) -> 4(0(2(2(3(x1))))) 0(5(3(1(4(3(x1)))))) -> 1(4(0(5(2(x1))))) 2(0(4(3(5(3(3(1(x1)))))))) -> 2(1(2(2(2(0(3(1(x1)))))))) 2(4(0(2(3(0(0(2(x1)))))))) -> 2(4(0(3(4(4(2(x1))))))) 2(1(4(0(4(1(5(0(2(x1))))))))) -> 3(3(2(2(3(0(3(3(4(x1))))))))) 5(0(4(0(0(1(3(5(0(x1))))))))) -> 5(0(0(0(3(5(5(3(2(x1))))))))) 5(3(5(4(4(2(2(2(1(x1))))))))) -> 5(0(3(0(0(4(5(2(1(x1))))))))) 2(0(4(2(3(3(3(5(4(2(x1)))))))))) -> 3(4(4(2(0(2(3(3(5(2(x1)))))))))) 4(4(3(2(0(1(1(4(0(2(x1)))))))))) -> 2(3(4(0(0(1(2(1(3(4(x1)))))))))) 1(5(5(2(4(2(4(0(3(3(0(x1))))))))))) -> 1(3(5(4(5(5(5(3(2(4(2(x1))))))))))) 2(5(5(0(1(1(5(1(4(2(3(3(x1)))))))))))) -> 4(2(3(0(3(0(0(2(3(2(3(x1))))))))))) 3(0(2(4(5(2(1(2(0(2(5(1(x1)))))))))))) -> 3(1(3(0(5(0(2(2(4(0(4(x1))))))))))) 3(3(3(4(3(0(0(4(4(5(0(5(x1)))))))))))) -> 3(1(5(5(0(3(1(0(5(2(5(x1))))))))))) 0(5(3(5(1(0(5(1(2(4(4(5(0(x1))))))))))))) -> 0(3(1(0(4(5(5(2(5(5(2(4(0(x1))))))))))))) 2(5(2(4(1(5(3(3(1(0(2(5(3(x1))))))))))))) -> 2(3(1(3(3(5(1(2(0(3(2(3(0(x1))))))))))))) 2(5(5(3(5(3(1(3(1(2(5(0(0(x1))))))))))))) -> 2(5(5(5(0(4(5(5(1(1(3(2(2(x1))))))))))))) 3(5(3(3(3(2(3(0(2(4(2(1(3(x1))))))))))))) -> 5(1(3(1(4(0(0(1(5(0(4(5(x1)))))))))))) 2(0(3(0(2(3(1(0(0(3(0(3(5(3(x1)))))))))))))) -> 3(4(0(2(1(4(4(4(0(5(5(5(2(x1))))))))))))) 3(5(3(3(1(2(4(0(4(3(5(4(2(1(x1)))))))))))))) -> 5(2(0(1(4(4(3(3(3(5(3(4(1(2(x1)))))))))))))) 3(5(5(0(2(2(0(0(3(5(1(3(3(5(3(5(x1)))))))))))))))) -> 3(1(4(2(0(3(4(0(4(1(5(4(2(5(x1)))))))))))))) 5(5(3(5(0(5(3(5(2(3(1(3(3(4(0(2(x1)))))))))))))))) -> 5(2(4(2(4(4(0(5(5(1(3(4(0(4(0(x1))))))))))))))) 2(2(1(3(4(0(1(1(4(2(2(2(0(4(4(2(4(4(x1)))))))))))))))))) -> 4(3(4(4(5(5(0(1(0(1(3(2(5(5(1(1(4(4(x1)))))))))))))))))) 0(3(0(2(2(2(5(5(2(4(4(3(5(1(0(0(0(3(3(x1))))))))))))))))))) -> 3(3(1(3(4(5(5(2(0(4(2(3(1(1(5(1(2(3(x1)))))))))))))))))) 3(3(4(3(3(4(3(0(2(5(3(1(4(5(2(5(2(4(3(5(x1)))))))))))))))))))) -> 5(2(5(0(5(0(1(1(1(3(2(4(4(0(3(2(4(1(5(x1))))))))))))))))))) 2(1(5(5(3(0(1(3(3(3(1(2(0(5(2(0(3(5(2(2(2(x1))))))))))))))))))))) -> 3(0(3(3(4(0(1(4(5(1(3(3(3(4(1(2(1(3(2(1(x1)))))))))))))))))))) 5(1(3(4(0(3(0(2(5(3(0(2(2(0(1(2(3(3(4(1(1(x1))))))))))))))))))))) -> 5(0(1(1(4(2(0(1(1(2(1(4(0(4(3(1(2(0(0(2(x1)))))))))))))))))))) 5(4(0(0(3(2(5(3(0(3(0(4(5(0(4(4(5(1(1(1(3(x1))))))))))))))))))))) -> 5(2(5(1(0(3(5(3(2(1(0(0(5(5(4(5(4(4(2(2(2(x1))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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: 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 3. 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, 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] {(151,152,[0_1|0, 2_1|0, 5_1|0, 4_1|0, 1_1|0, 3_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, 2_1|1, 5_1|1, 4_1|1, 1_1|1, 3_1|1]), (151,154,[3_1|2]), (151,156,[4_1|2]), (151,160,[1_1|2]), (151,164,[0_1|2]), (151,176,[3_1|2]), (151,193,[3_1|2]), (151,195,[2_1|2]), (151,202,[3_1|2]), (151,211,[3_1|2]), (151,223,[2_1|2]), (151,229,[3_1|2]), (151,237,[3_1|2]), (151,256,[4_1|2]), (151,266,[2_1|2]), (151,278,[2_1|2]), (151,290,[4_1|2]), (151,307,[5_1|2]), (151,310,[5_1|2]), (151,318,[5_1|2]), (151,326,[5_1|2]), (151,340,[5_1|2]), (151,359,[5_1|2]), (151,379,[2_1|2]), (151,388,[1_1|2]), (151,398,[3_1|2]), (151,408,[3_1|2]), (151,418,[5_1|2]), (151,436,[5_1|2]), (151,447,[5_1|2]), (151,460,[3_1|2]), (152,152,[cons_0_1|0, cons_2_1|0, cons_5_1|0, cons_4_1|0, cons_1_1|0, cons_3_1|0]), (153,152,[encArg_1|1]), (153,153,[0_1|1, 2_1|1, 5_1|1, 4_1|1, 1_1|1, 3_1|1]), (153,154,[3_1|2]), (153,156,[4_1|2]), (153,160,[1_1|2]), (153,164,[0_1|2]), (153,176,[3_1|2]), (153,193,[3_1|2]), (153,195,[2_1|2]), (153,202,[3_1|2]), (153,211,[3_1|2]), (153,223,[2_1|2]), (153,229,[3_1|2]), (153,237,[3_1|2]), (153,256,[4_1|2]), (153,266,[2_1|2]), (153,278,[2_1|2]), (153,290,[4_1|2]), (153,307,[5_1|2]), (153,310,[5_1|2]), (153,318,[5_1|2]), (153,326,[5_1|2]), (153,340,[5_1|2]), (153,359,[5_1|2]), 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(393,394,[5_1|2]), (394,395,[3_1|2]), (395,396,[2_1|2]), (396,397,[4_1|2]), (397,153,[2_1|2]), (397,164,[2_1|2]), (397,238,[2_1|2]), (397,193,[3_1|2]), (397,195,[2_1|2]), (397,202,[3_1|2]), (397,211,[3_1|2]), (397,223,[2_1|2]), (397,229,[3_1|2]), (397,237,[3_1|2]), (397,256,[4_1|2]), (397,266,[2_1|2]), (397,278,[2_1|2]), (397,290,[4_1|2]), (398,399,[1_1|2]), (399,400,[3_1|2]), (400,401,[0_1|2]), (401,402,[5_1|2]), (402,403,[0_1|2]), (403,404,[2_1|2]), (404,405,[2_1|2]), (405,406,[4_1|2]), (406,407,[0_1|2]), (407,153,[4_1|2]), (407,160,[4_1|2]), (407,388,[4_1|2]), (407,437,[4_1|2]), (407,379,[2_1|2]), (408,409,[1_1|2]), (409,410,[5_1|2]), (410,411,[5_1|2]), (411,412,[0_1|2]), (412,413,[3_1|2]), (413,414,[1_1|2]), (414,415,[0_1|2]), (415,416,[5_1|2]), (416,417,[2_1|2]), (416,256,[4_1|2]), (416,266,[2_1|2]), (416,278,[2_1|2]), (417,153,[5_1|2]), (417,307,[5_1|2]), (417,310,[5_1|2]), (417,318,[5_1|2]), (417,326,[5_1|2]), (417,340,[5_1|2]), (417,359,[5_1|2]), (417,418,[5_1|2]), (417,436,[5_1|2]), (417,447,[5_1|2]), (418,419,[2_1|2]), (419,420,[5_1|2]), (420,421,[0_1|2]), (421,422,[5_1|2]), (422,423,[0_1|2]), (423,424,[1_1|2]), (424,425,[1_1|2]), (425,426,[1_1|2]), (426,427,[3_1|2]), (427,428,[2_1|2]), (428,429,[4_1|2]), (429,430,[4_1|2]), (430,431,[0_1|2]), (431,432,[3_1|2]), (432,433,[2_1|2]), (433,434,[4_1|2]), (434,435,[1_1|2]), (434,388,[1_1|2]), (435,153,[5_1|2]), (435,307,[5_1|2]), (435,310,[5_1|2]), (435,318,[5_1|2]), (435,326,[5_1|2]), (435,340,[5_1|2]), (435,359,[5_1|2]), (435,418,[5_1|2]), (435,436,[5_1|2]), (435,447,[5_1|2]), (436,437,[1_1|2]), (437,438,[3_1|2]), (438,439,[1_1|2]), (439,440,[4_1|2]), (440,441,[0_1|2]), (441,442,[0_1|2]), (442,443,[1_1|2]), (443,444,[5_1|2]), (444,445,[0_1|2]), (445,446,[4_1|2]), (446,153,[5_1|2]), (446,154,[5_1|2]), (446,176,[5_1|2]), (446,193,[5_1|2]), (446,202,[5_1|2]), (446,211,[5_1|2]), (446,229,[5_1|2]), (446,237,[5_1|2]), (446,398,[5_1|2]), (446,408,[5_1|2]), (446,460,[5_1|2]), (446,389,[5_1|2]), (446,307,[5_1|2]), (446,310,[5_1|2]), (446,318,[5_1|2]), (446,326,[5_1|2]), (446,340,[5_1|2]), (446,359,[5_1|2]), (447,448,[2_1|2]), (448,449,[0_1|2]), (449,450,[1_1|2]), (450,451,[4_1|2]), (451,452,[4_1|2]), (452,453,[3_1|2]), (453,454,[3_1|2]), (454,455,[3_1|2]), (455,456,[5_1|2]), (456,457,[3_1|2]), (457,458,[4_1|2]), (458,459,[1_1|2]), (459,153,[2_1|2]), (459,160,[2_1|2]), (459,388,[2_1|2]), (459,196,[2_1|2]), (459,193,[3_1|2]), (459,195,[2_1|2]), (459,202,[3_1|2]), (459,211,[3_1|2]), (459,223,[2_1|2]), (459,229,[3_1|2]), (459,237,[3_1|2]), (459,256,[4_1|2]), (459,266,[2_1|2]), (459,278,[2_1|2]), (459,290,[4_1|2]), (460,461,[1_1|2]), (461,462,[4_1|2]), (462,463,[2_1|2]), (463,464,[0_1|2]), (464,465,[3_1|2]), (465,466,[4_1|2]), (466,467,[0_1|2]), (467,468,[4_1|2]), (468,469,[1_1|2]), (469,470,[5_1|2]), (470,471,[4_1|2]), (471,472,[2_1|2]), (471,256,[4_1|2]), (471,266,[2_1|2]), (471,278,[2_1|2]), (472,153,[5_1|2]), (472,307,[5_1|2]), (472,310,[5_1|2]), (472,318,[5_1|2]), (472,326,[5_1|2]), (472,340,[5_1|2]), (472,359,[5_1|2]), (472,418,[5_1|2]), (472,436,[5_1|2]), (472,447,[5_1|2]), (473,474,[4_1|3]), (474,322,[1_1|3]), (475,476,[4_1|3]), (476,193,[1_1|3]), (476,202,[1_1|3]), (476,211,[1_1|3]), (476,229,[1_1|3]), (476,237,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)