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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 51 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 98 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: 1(3(4(2(x1)))) -> 0(0(3(0(1(0(1(2(0(3(x1)))))))))) 0(4(4(2(0(x1))))) -> 5(2(3(3(2(0(1(1(2(0(x1)))))))))) 1(5(1(5(1(x1))))) -> 1(2(3(3(0(3(3(2(0(1(x1)))))))))) 3(1(3(5(0(x1))))) -> 1(5(2(2(0(1(2(3(2(0(x1)))))))))) 3(3(2(4(5(x1))))) -> 3(0(3(0(2(0(2(2(0(5(x1)))))))))) 0(0(2(4(1(3(x1)))))) -> 0(3(1(0(0(3(2(0(1(1(x1)))))))))) 0(2(3(4(4(2(x1)))))) -> 0(0(0(3(0(5(5(5(5(0(x1)))))))))) 0(4(4(5(2(3(x1)))))) -> 0(3(1(2(0(0(1(0(5(1(x1)))))))))) 0(5(3(4(5(1(x1)))))) -> 5(0(0(0(2(2(0(5(4(1(x1)))))))))) 1(0(0(5(1(3(x1)))))) -> 2(2(0(1(3(3(2(0(4(1(x1)))))))))) 1(0(2(2(5(0(x1)))))) -> 3(0(0(1(0(3(3(0(0(0(x1)))))))))) 1(1(0(2(4(2(x1)))))) -> 2(3(3(1(0(2(0(2(5(3(x1)))))))))) 1(5(0(5(2(0(x1)))))) -> 1(0(4(0(1(2(0(2(2(0(x1)))))))))) 2(2(3(2(4(0(x1)))))) -> 1(2(0(0(2(0(5(1(4(0(x1)))))))))) 2(2(4(4(2(0(x1)))))) -> 1(2(3(2(5(4(1(3(0(0(x1)))))))))) 2(2(5(0(0(4(x1)))))) -> 3(2(0(0(2(2(0(0(0(4(x1)))))))))) 2(2(5(1(1(2(x1)))))) -> 2(3(0(0(2(2(0(2(2(2(x1)))))))))) 3(2(4(4(1(0(x1)))))) -> 5(1(5(4(1(0(2(2(2(0(x1)))))))))) 4(2(2(3(5(0(x1)))))) -> 4(4(1(4(3(2(0(0(2(0(x1)))))))))) 5(1(3(4(0(2(x1)))))) -> 1(5(4(1(4(5(5(0(1(2(x1)))))))))) 5(2(2(4(2(0(x1)))))) -> 5(0(2(0(1(5(4(3(2(0(x1)))))))))) 0(2(2(4(3(1(4(x1))))))) -> 2(5(4(2(5(3(5(2(5(4(x1)))))))))) 0(2(4(3(0(4(0(x1))))))) -> 5(4(0(0(2(2(5(2(4(0(x1)))))))))) 0(4(1(0(0(3(4(x1))))))) -> 1(0(2(0(0(1(1(3(5(4(x1)))))))))) 0(4(2(4(0(2(2(x1))))))) -> 0(1(1(0(0(0(1(4(1(2(x1)))))))))) 0(4(4(0(2(4(0(x1))))))) -> 0(3(5(2(0(5(4(1(1(0(x1)))))))))) 2(0(2(4(4(1(0(x1))))))) -> 2(2(0(2(5(5(5(2(0(0(x1)))))))))) 2(2(0(4(4(0(5(x1))))))) -> 1(2(2(1(1(5(5(3(0(5(x1)))))))))) 2(2(4(5(5(1(4(x1))))))) -> 1(0(1(0(1(4(5(4(4(1(x1)))))))))) 2(3(3(2(4(5(3(x1))))))) -> 0(3(1(0(2(0(0(5(0(4(x1)))))))))) 2(4(1(0(4(0(2(x1))))))) -> 2(2(0(0(1(3(0(4(1(2(x1)))))))))) 2(5(1(1(4(0(2(x1))))))) -> 2(0(0(2(5(4(1(1(3(2(x1)))))))))) 2(5(2(4(1(4(3(x1))))))) -> 1(2(0(1(0(5(5(0(1(5(x1)))))))))) 2(5(2(4(2(0(1(x1))))))) -> 2(2(2(0(2(0(0(4(0(1(x1)))))))))) 3(3(0(4(4(0(5(x1))))))) -> 3(5(4(1(4(1(4(0(0(5(x1)))))))))) 3(3(3(3(4(5(5(x1))))))) -> 0(1(3(0(0(5(5(0(3(5(x1)))))))))) 3(3(4(1(5(5(1(x1))))))) -> 5(5(3(2(2(2(0(3(5(1(x1)))))))))) 4(0(2(4(2(4(1(x1))))))) -> 3(0(3(3(2(2(0(0(2(4(x1)))))))))) 5(1(1(1(4(3(1(x1))))))) -> 3(0(2(2(5(4(4(0(3(1(x1)))))))))) 5(1(4(4(4(0(0(x1))))))) -> 2(2(0(3(0(1(0(1(4(0(x1)))))))))) 5(3(4(0(4(5(1(x1))))))) -> 1(2(2(5(4(1(4(2(2(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_1(x_1)) -> 1(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_0(x_1) -> 0(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: 1(3(4(2(x1)))) -> 0(0(3(0(1(0(1(2(0(3(x1)))))))))) 0(4(4(2(0(x1))))) -> 5(2(3(3(2(0(1(1(2(0(x1)))))))))) 1(5(1(5(1(x1))))) -> 1(2(3(3(0(3(3(2(0(1(x1)))))))))) 3(1(3(5(0(x1))))) -> 1(5(2(2(0(1(2(3(2(0(x1)))))))))) 3(3(2(4(5(x1))))) -> 3(0(3(0(2(0(2(2(0(5(x1)))))))))) 0(0(2(4(1(3(x1)))))) -> 0(3(1(0(0(3(2(0(1(1(x1)))))))))) 0(2(3(4(4(2(x1)))))) -> 0(0(0(3(0(5(5(5(5(0(x1)))))))))) 0(4(4(5(2(3(x1)))))) -> 0(3(1(2(0(0(1(0(5(1(x1)))))))))) 0(5(3(4(5(1(x1)))))) -> 5(0(0(0(2(2(0(5(4(1(x1)))))))))) 1(0(0(5(1(3(x1)))))) -> 2(2(0(1(3(3(2(0(4(1(x1)))))))))) 1(0(2(2(5(0(x1)))))) -> 3(0(0(1(0(3(3(0(0(0(x1)))))))))) 1(1(0(2(4(2(x1)))))) -> 2(3(3(1(0(2(0(2(5(3(x1)))))))))) 1(5(0(5(2(0(x1)))))) -> 1(0(4(0(1(2(0(2(2(0(x1)))))))))) 2(2(3(2(4(0(x1)))))) -> 1(2(0(0(2(0(5(1(4(0(x1)))))))))) 2(2(4(4(2(0(x1)))))) -> 1(2(3(2(5(4(1(3(0(0(x1)))))))))) 2(2(5(0(0(4(x1)))))) -> 3(2(0(0(2(2(0(0(0(4(x1)))))))))) 2(2(5(1(1(2(x1)))))) -> 2(3(0(0(2(2(0(2(2(2(x1)))))))))) 3(2(4(4(1(0(x1)))))) -> 5(1(5(4(1(0(2(2(2(0(x1)))))))))) 4(2(2(3(5(0(x1)))))) -> 4(4(1(4(3(2(0(0(2(0(x1)))))))))) 5(1(3(4(0(2(x1)))))) -> 1(5(4(1(4(5(5(0(1(2(x1)))))))))) 5(2(2(4(2(0(x1)))))) -> 5(0(2(0(1(5(4(3(2(0(x1)))))))))) 0(2(2(4(3(1(4(x1))))))) -> 2(5(4(2(5(3(5(2(5(4(x1)))))))))) 0(2(4(3(0(4(0(x1))))))) -> 5(4(0(0(2(2(5(2(4(0(x1)))))))))) 0(4(1(0(0(3(4(x1))))))) -> 1(0(2(0(0(1(1(3(5(4(x1)))))))))) 0(4(2(4(0(2(2(x1))))))) -> 0(1(1(0(0(0(1(4(1(2(x1)))))))))) 0(4(4(0(2(4(0(x1))))))) -> 0(3(5(2(0(5(4(1(1(0(x1)))))))))) 2(0(2(4(4(1(0(x1))))))) -> 2(2(0(2(5(5(5(2(0(0(x1)))))))))) 2(2(0(4(4(0(5(x1))))))) -> 1(2(2(1(1(5(5(3(0(5(x1)))))))))) 2(2(4(5(5(1(4(x1))))))) -> 1(0(1(0(1(4(5(4(4(1(x1)))))))))) 2(3(3(2(4(5(3(x1))))))) -> 0(3(1(0(2(0(0(5(0(4(x1)))))))))) 2(4(1(0(4(0(2(x1))))))) -> 2(2(0(0(1(3(0(4(1(2(x1)))))))))) 2(5(1(1(4(0(2(x1))))))) -> 2(0(0(2(5(4(1(1(3(2(x1)))))))))) 2(5(2(4(1(4(3(x1))))))) -> 1(2(0(1(0(5(5(0(1(5(x1)))))))))) 2(5(2(4(2(0(1(x1))))))) -> 2(2(2(0(2(0(0(4(0(1(x1)))))))))) 3(3(0(4(4(0(5(x1))))))) -> 3(5(4(1(4(1(4(0(0(5(x1)))))))))) 3(3(3(3(4(5(5(x1))))))) -> 0(1(3(0(0(5(5(0(3(5(x1)))))))))) 3(3(4(1(5(5(1(x1))))))) -> 5(5(3(2(2(2(0(3(5(1(x1)))))))))) 4(0(2(4(2(4(1(x1))))))) -> 3(0(3(3(2(2(0(0(2(4(x1)))))))))) 5(1(1(1(4(3(1(x1))))))) -> 3(0(2(2(5(4(4(0(3(1(x1)))))))))) 5(1(4(4(4(0(0(x1))))))) -> 2(2(0(3(0(1(0(1(4(0(x1)))))))))) 5(3(4(0(4(5(1(x1))))))) -> 1(2(2(5(4(1(4(2(2(5(x1)))))))))) The (relative) TRS S consists of the following rules: encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_0(x_1) -> 0(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: 1(3(4(2(x1)))) -> 0(0(3(0(1(0(1(2(0(3(x1)))))))))) 0(4(4(2(0(x1))))) -> 5(2(3(3(2(0(1(1(2(0(x1)))))))))) 1(5(1(5(1(x1))))) -> 1(2(3(3(0(3(3(2(0(1(x1)))))))))) 3(1(3(5(0(x1))))) -> 1(5(2(2(0(1(2(3(2(0(x1)))))))))) 3(3(2(4(5(x1))))) -> 3(0(3(0(2(0(2(2(0(5(x1)))))))))) 0(0(2(4(1(3(x1)))))) -> 0(3(1(0(0(3(2(0(1(1(x1)))))))))) 0(2(3(4(4(2(x1)))))) -> 0(0(0(3(0(5(5(5(5(0(x1)))))))))) 0(4(4(5(2(3(x1)))))) -> 0(3(1(2(0(0(1(0(5(1(x1)))))))))) 0(5(3(4(5(1(x1)))))) -> 5(0(0(0(2(2(0(5(4(1(x1)))))))))) 1(0(0(5(1(3(x1)))))) -> 2(2(0(1(3(3(2(0(4(1(x1)))))))))) 1(0(2(2(5(0(x1)))))) -> 3(0(0(1(0(3(3(0(0(0(x1)))))))))) 1(1(0(2(4(2(x1)))))) -> 2(3(3(1(0(2(0(2(5(3(x1)))))))))) 1(5(0(5(2(0(x1)))))) -> 1(0(4(0(1(2(0(2(2(0(x1)))))))))) 2(2(3(2(4(0(x1)))))) -> 1(2(0(0(2(0(5(1(4(0(x1)))))))))) 2(2(4(4(2(0(x1)))))) -> 1(2(3(2(5(4(1(3(0(0(x1)))))))))) 2(2(5(0(0(4(x1)))))) -> 3(2(0(0(2(2(0(0(0(4(x1)))))))))) 2(2(5(1(1(2(x1)))))) -> 2(3(0(0(2(2(0(2(2(2(x1)))))))))) 3(2(4(4(1(0(x1)))))) -> 5(1(5(4(1(0(2(2(2(0(x1)))))))))) 4(2(2(3(5(0(x1)))))) -> 4(4(1(4(3(2(0(0(2(0(x1)))))))))) 5(1(3(4(0(2(x1)))))) -> 1(5(4(1(4(5(5(0(1(2(x1)))))))))) 5(2(2(4(2(0(x1)))))) -> 5(0(2(0(1(5(4(3(2(0(x1)))))))))) 0(2(2(4(3(1(4(x1))))))) -> 2(5(4(2(5(3(5(2(5(4(x1)))))))))) 0(2(4(3(0(4(0(x1))))))) -> 5(4(0(0(2(2(5(2(4(0(x1)))))))))) 0(4(1(0(0(3(4(x1))))))) -> 1(0(2(0(0(1(1(3(5(4(x1)))))))))) 0(4(2(4(0(2(2(x1))))))) -> 0(1(1(0(0(0(1(4(1(2(x1)))))))))) 0(4(4(0(2(4(0(x1))))))) -> 0(3(5(2(0(5(4(1(1(0(x1)))))))))) 2(0(2(4(4(1(0(x1))))))) -> 2(2(0(2(5(5(5(2(0(0(x1)))))))))) 2(2(0(4(4(0(5(x1))))))) -> 1(2(2(1(1(5(5(3(0(5(x1)))))))))) 2(2(4(5(5(1(4(x1))))))) -> 1(0(1(0(1(4(5(4(4(1(x1)))))))))) 2(3(3(2(4(5(3(x1))))))) -> 0(3(1(0(2(0(0(5(0(4(x1)))))))))) 2(4(1(0(4(0(2(x1))))))) -> 2(2(0(0(1(3(0(4(1(2(x1)))))))))) 2(5(1(1(4(0(2(x1))))))) -> 2(0(0(2(5(4(1(1(3(2(x1)))))))))) 2(5(2(4(1(4(3(x1))))))) -> 1(2(0(1(0(5(5(0(1(5(x1)))))))))) 2(5(2(4(2(0(1(x1))))))) -> 2(2(2(0(2(0(0(4(0(1(x1)))))))))) 3(3(0(4(4(0(5(x1))))))) -> 3(5(4(1(4(1(4(0(0(5(x1)))))))))) 3(3(3(3(4(5(5(x1))))))) -> 0(1(3(0(0(5(5(0(3(5(x1)))))))))) 3(3(4(1(5(5(1(x1))))))) -> 5(5(3(2(2(2(0(3(5(1(x1)))))))))) 4(0(2(4(2(4(1(x1))))))) -> 3(0(3(3(2(2(0(0(2(4(x1)))))))))) 5(1(1(1(4(3(1(x1))))))) -> 3(0(2(2(5(4(4(0(3(1(x1)))))))))) 5(1(4(4(4(0(0(x1))))))) -> 2(2(0(3(0(1(0(1(4(0(x1)))))))))) 5(3(4(0(4(5(1(x1))))))) -> 1(2(2(5(4(1(4(2(2(5(x1)))))))))) The (relative) TRS S consists of the following rules: encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_0(x_1) -> 0(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: 1(3(4(2(x1)))) -> 0(0(3(0(1(0(1(2(0(3(x1)))))))))) 0(4(4(2(0(x1))))) -> 5(2(3(3(2(0(1(1(2(0(x1)))))))))) 1(5(1(5(1(x1))))) -> 1(2(3(3(0(3(3(2(0(1(x1)))))))))) 3(1(3(5(0(x1))))) -> 1(5(2(2(0(1(2(3(2(0(x1)))))))))) 3(3(2(4(5(x1))))) -> 3(0(3(0(2(0(2(2(0(5(x1)))))))))) 0(0(2(4(1(3(x1)))))) -> 0(3(1(0(0(3(2(0(1(1(x1)))))))))) 0(2(3(4(4(2(x1)))))) -> 0(0(0(3(0(5(5(5(5(0(x1)))))))))) 0(4(4(5(2(3(x1)))))) -> 0(3(1(2(0(0(1(0(5(1(x1)))))))))) 0(5(3(4(5(1(x1)))))) -> 5(0(0(0(2(2(0(5(4(1(x1)))))))))) 1(0(0(5(1(3(x1)))))) -> 2(2(0(1(3(3(2(0(4(1(x1)))))))))) 1(0(2(2(5(0(x1)))))) -> 3(0(0(1(0(3(3(0(0(0(x1)))))))))) 1(1(0(2(4(2(x1)))))) -> 2(3(3(1(0(2(0(2(5(3(x1)))))))))) 1(5(0(5(2(0(x1)))))) -> 1(0(4(0(1(2(0(2(2(0(x1)))))))))) 2(2(3(2(4(0(x1)))))) -> 1(2(0(0(2(0(5(1(4(0(x1)))))))))) 2(2(4(4(2(0(x1)))))) -> 1(2(3(2(5(4(1(3(0(0(x1)))))))))) 2(2(5(0(0(4(x1)))))) -> 3(2(0(0(2(2(0(0(0(4(x1)))))))))) 2(2(5(1(1(2(x1)))))) -> 2(3(0(0(2(2(0(2(2(2(x1)))))))))) 3(2(4(4(1(0(x1)))))) -> 5(1(5(4(1(0(2(2(2(0(x1)))))))))) 4(2(2(3(5(0(x1)))))) -> 4(4(1(4(3(2(0(0(2(0(x1)))))))))) 5(1(3(4(0(2(x1)))))) -> 1(5(4(1(4(5(5(0(1(2(x1)))))))))) 5(2(2(4(2(0(x1)))))) -> 5(0(2(0(1(5(4(3(2(0(x1)))))))))) 0(2(2(4(3(1(4(x1))))))) -> 2(5(4(2(5(3(5(2(5(4(x1)))))))))) 0(2(4(3(0(4(0(x1))))))) -> 5(4(0(0(2(2(5(2(4(0(x1)))))))))) 0(4(1(0(0(3(4(x1))))))) -> 1(0(2(0(0(1(1(3(5(4(x1)))))))))) 0(4(2(4(0(2(2(x1))))))) -> 0(1(1(0(0(0(1(4(1(2(x1)))))))))) 0(4(4(0(2(4(0(x1))))))) -> 0(3(5(2(0(5(4(1(1(0(x1)))))))))) 2(0(2(4(4(1(0(x1))))))) -> 2(2(0(2(5(5(5(2(0(0(x1)))))))))) 2(2(0(4(4(0(5(x1))))))) -> 1(2(2(1(1(5(5(3(0(5(x1)))))))))) 2(2(4(5(5(1(4(x1))))))) -> 1(0(1(0(1(4(5(4(4(1(x1)))))))))) 2(3(3(2(4(5(3(x1))))))) -> 0(3(1(0(2(0(0(5(0(4(x1)))))))))) 2(4(1(0(4(0(2(x1))))))) -> 2(2(0(0(1(3(0(4(1(2(x1)))))))))) 2(5(1(1(4(0(2(x1))))))) -> 2(0(0(2(5(4(1(1(3(2(x1)))))))))) 2(5(2(4(1(4(3(x1))))))) -> 1(2(0(1(0(5(5(0(1(5(x1)))))))))) 2(5(2(4(2(0(1(x1))))))) -> 2(2(2(0(2(0(0(4(0(1(x1)))))))))) 3(3(0(4(4(0(5(x1))))))) -> 3(5(4(1(4(1(4(0(0(5(x1)))))))))) 3(3(3(3(4(5(5(x1))))))) -> 0(1(3(0(0(5(5(0(3(5(x1)))))))))) 3(3(4(1(5(5(1(x1))))))) -> 5(5(3(2(2(2(0(3(5(1(x1)))))))))) 4(0(2(4(2(4(1(x1))))))) -> 3(0(3(3(2(2(0(0(2(4(x1)))))))))) 5(1(1(1(4(3(1(x1))))))) -> 3(0(2(2(5(4(4(0(3(1(x1)))))))))) 5(1(4(4(4(0(0(x1))))))) -> 2(2(0(3(0(1(0(1(4(0(x1)))))))))) 5(3(4(0(4(5(1(x1))))))) -> 1(2(2(5(4(1(4(2(2(5(x1)))))))))) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_0(x_1) -> 0(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. "[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, 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] {(151,152,[1_1|0, 0_1|0, 3_1|0, 2_1|0, 4_1|0, 5_1|0, encArg_1|0, encode_1_1|0, encode_3_1|0, encode_4_1|0, encode_2_1|0, encode_0_1|0, encode_5_1|0]), (151,153,[1_1|1, 0_1|1, 3_1|1, 2_1|1, 4_1|1, 5_1|1]), (151,154,[0_1|2]), (151,163,[1_1|2]), (151,172,[1_1|2]), (151,181,[2_1|2]), (151,190,[3_1|2]), (151,199,[2_1|2]), (151,208,[5_1|2]), (151,217,[0_1|2]), (151,226,[0_1|2]), (151,235,[1_1|2]), (151,244,[0_1|2]), (151,253,[0_1|2]), (151,262,[0_1|2]), (151,271,[2_1|2]), (151,280,[5_1|2]), (151,289,[5_1|2]), (151,298,[1_1|2]), (151,307,[3_1|2]), (151,316,[3_1|2]), (151,325,[0_1|2]), (151,334,[5_1|2]), (151,343,[5_1|2]), (151,352,[1_1|2]), (151,361,[1_1|2]), (151,370,[1_1|2]), (151,379,[3_1|2]), (151,388,[2_1|2]), (151,397,[1_1|2]), (151,406,[2_1|2]), (151,415,[0_1|2]), (151,424,[2_1|2]), (151,433,[2_1|2]), (151,442,[1_1|2]), (151,451,[2_1|2]), (151,460,[4_1|2]), (151,469,[3_1|2]), (151,478,[1_1|2]), (151,487,[3_1|2]), (151,496,[2_1|2]), (151,505,[5_1|2]), (151,514,[1_1|2]), (152,152,[cons_1_1|0, cons_0_1|0, cons_3_1|0, cons_2_1|0, cons_4_1|0, cons_5_1|0]), (153,152,[encArg_1|1]), (153,153,[1_1|1, 0_1|1, 3_1|1, 2_1|1, 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(386,226,[0_1|2]), (386,235,[1_1|2]), (386,244,[0_1|2]), (387,153,[4_1|2]), (387,460,[4_1|2]), (387,469,[3_1|2]), (388,389,[3_1|2]), (389,390,[0_1|2]), (390,391,[0_1|2]), (391,392,[2_1|2]), (392,393,[2_1|2]), (393,394,[0_1|2]), (394,395,[2_1|2]), (395,396,[2_1|2]), (395,352,[1_1|2]), (395,361,[1_1|2]), (395,370,[1_1|2]), (395,379,[3_1|2]), (395,388,[2_1|2]), (395,397,[1_1|2]), (396,153,[2_1|2]), (396,181,[2_1|2]), (396,199,[2_1|2]), (396,271,[2_1|2]), (396,388,[2_1|2]), (396,406,[2_1|2]), (396,424,[2_1|2]), (396,433,[2_1|2]), (396,451,[2_1|2]), (396,496,[2_1|2]), (396,164,[2_1|2]), (396,353,[2_1|2]), (396,362,[2_1|2]), (396,398,[2_1|2]), (396,443,[2_1|2]), (396,515,[2_1|2]), (396,352,[1_1|2]), (396,361,[1_1|2]), (396,370,[1_1|2]), (396,379,[3_1|2]), (396,397,[1_1|2]), (396,415,[0_1|2]), (396,442,[1_1|2]), (397,398,[2_1|2]), (398,399,[2_1|2]), (399,400,[1_1|2]), (400,401,[1_1|2]), (401,402,[5_1|2]), (402,403,[5_1|2]), (403,404,[3_1|2]), (404,405,[0_1|2]), (404,289,[5_1|2]), (405,153,[5_1|2]), (405,208,[5_1|2]), (405,280,[5_1|2]), (405,289,[5_1|2]), (405,334,[5_1|2]), (405,343,[5_1|2]), (405,505,[5_1|2]), (405,478,[1_1|2]), (405,487,[3_1|2]), (405,496,[2_1|2]), (405,514,[1_1|2]), (406,407,[2_1|2]), (407,408,[0_1|2]), (408,409,[2_1|2]), (409,410,[5_1|2]), (410,411,[5_1|2]), (411,412,[5_1|2]), (412,413,[2_1|2]), (413,414,[0_1|2]), (413,253,[0_1|2]), (414,153,[0_1|2]), (414,154,[0_1|2]), (414,217,[0_1|2]), (414,226,[0_1|2]), (414,244,[0_1|2]), (414,253,[0_1|2]), (414,262,[0_1|2]), (414,325,[0_1|2]), (414,415,[0_1|2]), (414,173,[0_1|2]), (414,236,[0_1|2]), (414,371,[0_1|2]), (414,208,[5_1|2]), (414,235,[1_1|2]), (414,271,[2_1|2]), (414,280,[5_1|2]), (414,289,[5_1|2]), (415,416,[3_1|2]), (416,417,[1_1|2]), (417,418,[0_1|2]), (418,419,[2_1|2]), (419,420,[0_1|2]), (420,421,[0_1|2]), (421,422,[5_1|2]), (422,423,[0_1|2]), (422,208,[5_1|2]), (422,217,[0_1|2]), (422,226,[0_1|2]), (422,235,[1_1|2]), (422,244,[0_1|2]), (423,153,[4_1|2]), (423,190,[4_1|2]), (423,307,[4_1|2]), (423,316,[4_1|2]), (423,379,[4_1|2]), (423,469,[4_1|2, 3_1|2]), (423,487,[4_1|2]), (423,460,[4_1|2]), (424,425,[2_1|2]), (425,426,[0_1|2]), (426,427,[0_1|2]), (427,428,[1_1|2]), (428,429,[3_1|2]), (429,430,[0_1|2]), (430,431,[4_1|2]), (431,432,[1_1|2]), (432,153,[2_1|2]), (432,181,[2_1|2]), (432,199,[2_1|2]), (432,271,[2_1|2]), (432,388,[2_1|2]), (432,406,[2_1|2]), (432,424,[2_1|2]), (432,433,[2_1|2]), (432,451,[2_1|2]), (432,496,[2_1|2]), (432,352,[1_1|2]), (432,361,[1_1|2]), (432,370,[1_1|2]), (432,379,[3_1|2]), (432,397,[1_1|2]), (432,415,[0_1|2]), (432,442,[1_1|2]), (433,434,[0_1|2]), (434,435,[0_1|2]), (435,436,[2_1|2]), (436,437,[5_1|2]), (437,438,[4_1|2]), (438,439,[1_1|2]), (439,440,[1_1|2]), (440,441,[3_1|2]), (440,343,[5_1|2]), (441,153,[2_1|2]), (441,181,[2_1|2]), (441,199,[2_1|2]), (441,271,[2_1|2]), (441,388,[2_1|2]), (441,406,[2_1|2]), (441,424,[2_1|2]), (441,433,[2_1|2]), (441,451,[2_1|2]), (441,496,[2_1|2]), (441,352,[1_1|2]), (441,361,[1_1|2]), (441,370,[1_1|2]), (441,379,[3_1|2]), (441,397,[1_1|2]), (441,415,[0_1|2]), (441,442,[1_1|2]), (442,443,[2_1|2]), (443,444,[0_1|2]), (444,445,[1_1|2]), (445,446,[0_1|2]), (446,447,[5_1|2]), (447,448,[5_1|2]), (448,449,[0_1|2]), (449,450,[1_1|2]), (449,163,[1_1|2]), (449,172,[1_1|2]), (450,153,[5_1|2]), (450,190,[5_1|2]), (450,307,[5_1|2]), (450,316,[5_1|2]), (450,379,[5_1|2]), (450,469,[5_1|2]), (450,487,[5_1|2, 3_1|2]), (450,478,[1_1|2]), (450,496,[2_1|2]), (450,505,[5_1|2]), (450,514,[1_1|2]), (451,452,[2_1|2]), (452,453,[2_1|2]), (453,454,[0_1|2]), (454,455,[2_1|2]), (455,456,[0_1|2]), (456,457,[0_1|2]), (457,458,[4_1|2]), (458,459,[0_1|2]), (459,153,[1_1|2]), (459,163,[1_1|2]), (459,172,[1_1|2]), (459,235,[1_1|2]), (459,298,[1_1|2]), (459,352,[1_1|2]), (459,361,[1_1|2]), (459,370,[1_1|2]), (459,397,[1_1|2]), (459,442,[1_1|2]), (459,478,[1_1|2]), (459,514,[1_1|2]), (459,245,[1_1|2]), (459,326,[1_1|2]), (459,154,[0_1|2]), (459,181,[2_1|2]), (459,190,[3_1|2]), (459,199,[2_1|2]), (460,461,[4_1|2]), (461,462,[1_1|2]), (462,463,[4_1|2]), (463,464,[3_1|2]), (464,465,[2_1|2]), (465,466,[0_1|2]), (466,467,[0_1|2]), (467,468,[2_1|2]), (467,406,[2_1|2]), (468,153,[0_1|2]), (468,154,[0_1|2]), (468,217,[0_1|2]), (468,226,[0_1|2]), (468,244,[0_1|2]), (468,253,[0_1|2]), (468,262,[0_1|2]), (468,325,[0_1|2]), (468,415,[0_1|2]), (468,290,[0_1|2]), (468,506,[0_1|2]), (468,208,[5_1|2]), (468,235,[1_1|2]), (468,271,[2_1|2]), (468,280,[5_1|2]), (468,289,[5_1|2]), (469,470,[0_1|2]), (470,471,[3_1|2]), (471,472,[3_1|2]), (472,473,[2_1|2]), (473,474,[2_1|2]), (474,475,[0_1|2]), (474,253,[0_1|2]), (475,476,[0_1|2]), (475,280,[5_1|2]), (476,477,[2_1|2]), (476,424,[2_1|2]), (477,153,[4_1|2]), (477,163,[4_1|2]), (477,172,[4_1|2]), (477,235,[4_1|2]), (477,298,[4_1|2]), (477,352,[4_1|2]), (477,361,[4_1|2]), (477,370,[4_1|2]), (477,397,[4_1|2]), (477,442,[4_1|2]), (477,478,[4_1|2]), (477,514,[4_1|2]), (477,460,[4_1|2]), (477,469,[3_1|2]), (478,479,[5_1|2]), (479,480,[4_1|2]), (480,481,[1_1|2]), (481,482,[4_1|2]), (482,483,[5_1|2]), (483,484,[5_1|2]), (484,485,[0_1|2]), (485,486,[1_1|2]), (486,153,[2_1|2]), (486,181,[2_1|2]), (486,199,[2_1|2]), (486,271,[2_1|2]), (486,388,[2_1|2]), (486,406,[2_1|2]), (486,424,[2_1|2]), (486,433,[2_1|2]), (486,451,[2_1|2]), (486,496,[2_1|2]), (486,352,[1_1|2]), (486,361,[1_1|2]), (486,370,[1_1|2]), (486,379,[3_1|2]), (486,397,[1_1|2]), (486,415,[0_1|2]), (486,442,[1_1|2]), (487,488,[0_1|2]), (488,489,[2_1|2]), (489,490,[2_1|2]), (490,491,[5_1|2]), (491,492,[4_1|2]), (492,493,[4_1|2]), (493,494,[0_1|2]), (494,495,[3_1|2]), (494,298,[1_1|2]), (495,153,[1_1|2]), (495,163,[1_1|2]), (495,172,[1_1|2]), (495,235,[1_1|2]), (495,298,[1_1|2]), (495,352,[1_1|2]), (495,361,[1_1|2]), (495,370,[1_1|2]), (495,397,[1_1|2]), (495,442,[1_1|2]), (495,478,[1_1|2]), (495,514,[1_1|2]), (495,154,[0_1|2]), (495,181,[2_1|2]), (495,190,[3_1|2]), (495,199,[2_1|2]), (496,497,[2_1|2]), (497,498,[0_1|2]), (498,499,[3_1|2]), (499,500,[0_1|2]), (500,501,[1_1|2]), (501,502,[0_1|2]), (502,503,[1_1|2]), (503,504,[4_1|2]), (503,469,[3_1|2]), (504,153,[0_1|2]), (504,154,[0_1|2]), (504,217,[0_1|2]), (504,226,[0_1|2]), (504,244,[0_1|2]), (504,253,[0_1|2]), (504,262,[0_1|2]), (504,325,[0_1|2]), (504,415,[0_1|2]), (504,155,[0_1|2]), (504,263,[0_1|2]), (504,208,[5_1|2]), (504,235,[1_1|2]), (504,271,[2_1|2]), (504,280,[5_1|2]), (504,289,[5_1|2]), (505,506,[0_1|2]), (506,507,[2_1|2]), (507,508,[0_1|2]), (508,509,[1_1|2]), (509,510,[5_1|2]), (510,511,[4_1|2]), (511,512,[3_1|2]), (512,513,[2_1|2]), (512,406,[2_1|2]), (513,153,[0_1|2]), (513,154,[0_1|2]), (513,217,[0_1|2]), (513,226,[0_1|2]), (513,244,[0_1|2]), (513,253,[0_1|2]), (513,262,[0_1|2]), (513,325,[0_1|2]), (513,415,[0_1|2]), (513,434,[0_1|2]), (513,208,[5_1|2]), (513,235,[1_1|2]), (513,271,[2_1|2]), (513,280,[5_1|2]), (513,289,[5_1|2]), (514,515,[2_1|2]), (515,516,[2_1|2]), (516,517,[5_1|2]), (517,518,[4_1|2]), (518,519,[1_1|2]), (519,520,[4_1|2]), (520,521,[2_1|2]), (520,379,[3_1|2]), (520,388,[2_1|2]), (521,522,[2_1|2]), (521,433,[2_1|2]), (521,442,[1_1|2]), (521,451,[2_1|2]), (522,153,[5_1|2]), (522,163,[5_1|2]), (522,172,[5_1|2]), (522,235,[5_1|2]), (522,298,[5_1|2]), (522,352,[5_1|2]), (522,361,[5_1|2]), (522,370,[5_1|2]), (522,397,[5_1|2]), (522,442,[5_1|2]), (522,478,[5_1|2, 1_1|2]), (522,514,[5_1|2, 1_1|2]), (522,344,[5_1|2]), (522,487,[3_1|2]), (522,496,[2_1|2]), (522,505,[5_1|2])}" ---------------------------------------- (8) BOUNDS(1, n^1)