/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 26 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 176 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(2(3(x1)))) -> 1(4(0(5(4(0(5(4(4(2(x1)))))))))) 1(0(2(4(5(x1))))) -> 1(0(5(4(4(1(3(5(5(5(x1)))))))))) 1(4(0(3(3(x1))))) -> 1(4(5(1(1(1(2(1(3(0(x1)))))))))) 1(4(0(3(5(x1))))) -> 5(1(3(1(1(5(1(1(0(5(x1)))))))))) 1(4(3(5(2(x1))))) -> 2(4(3(1(0(1(5(5(0(2(x1)))))))))) 1(4(5(0(3(x1))))) -> 5(1(5(5(1(1(5(0(4(2(x1)))))))))) 2(3(3(3(3(x1))))) -> 3(5(5(5(2(4(4(5(1(2(x1)))))))))) 2(3(3(4(1(x1))))) -> 2(5(0(3(1(5(1(0(5(5(x1)))))))))) 5(0(3(5(2(x1))))) -> 1(3(4(4(4(4(4(4(4(0(x1)))))))))) 5(3(0(3(3(x1))))) -> 5(4(4(3(5(1(1(1(1(5(x1)))))))))) 0(1(4(3(2(3(x1)))))) -> 2(5(1(2(1(1(5(5(3(2(x1)))))))))) 0(2(3(4(1(4(x1)))))) -> 2(1(1(5(4(2(1(4(4(5(x1)))))))))) 1(0(2(3(3(3(x1)))))) -> 1(4(0(4(3(1(5(1(2(5(x1)))))))))) 1(3(5(3(1(3(x1)))))) -> 1(0(5(1(1(2(4(5(5(1(x1)))))))))) 1(5(3(5(3(0(x1)))))) -> 0(1(5(1(1(1(0(5(0(0(x1)))))))))) 2(1(4(3(5(3(x1)))))) -> 3(1(0(1(3(4(2(0(4(2(x1)))))))))) 4(0(3(2(3(5(x1)))))) -> 4(2(5(1(1(1(3(1(1(1(x1)))))))))) 4(1(0(3(3(3(x1)))))) -> 4(5(5(5(2(2(4(4(2(3(x1)))))))))) 5(0(0(2(3(1(x1)))))) -> 1(1(5(5(5(2(0(2(4(1(x1)))))))))) 5(0(2(3(4(1(x1)))))) -> 5(1(3(2(5(1(4(1(5(5(x1)))))))))) 5(0(4(5(0(2(x1)))))) -> 1(5(5(2(3(3(4(4(0(2(x1)))))))))) 5(2(3(2(3(3(x1)))))) -> 1(1(3(2(2(2(1(1(3(2(x1)))))))))) 0(1(2(0(0(4(5(x1))))))) -> 0(1(1(1(1(4(2(0(5(5(x1)))))))))) 0(2(0(3(5(3(1(x1))))))) -> 3(1(0(1(2(5(0(1(1(4(x1)))))))))) 0(2(2(4(5(3(3(x1))))))) -> 2(4(3(1(2(2(5(5(4(3(x1)))))))))) 1(0(4(1(0(1(5(x1))))))) -> 5(5(5(1(5(1(1(5(1(5(x1)))))))))) 1(3(5(3(4(5(2(x1))))))) -> 1(0(1(4(3(4(4(1(5(2(x1)))))))))) 1(4(0(3(2(1(3(x1))))))) -> 2(0(3(1(4(5(2(2(4(4(x1)))))))))) 1(5(2(1(0(2(3(x1))))))) -> 1(4(1(3(5(0(1(0(5(5(x1)))))))))) 1(5(2(3(1(4(0(x1))))))) -> 1(4(4(4(5(2(4(0(5(5(x1)))))))))) 1(5(3(1(2(3(3(x1))))))) -> 3(0(3(1(0(1(3(4(2(0(x1)))))))))) 2(0(1(2(5(0(4(x1))))))) -> 2(4(4(1(1(0(1(3(4(4(x1)))))))))) 2(2(0(0(3(3(1(x1))))))) -> 4(4(2(3(4(1(5(5(4(1(x1)))))))))) 2(3(0(2(0(0(1(x1))))))) -> 2(3(2(2(4(4(1(0(5(5(x1)))))))))) 2(3(3(4(5(2(1(x1))))))) -> 4(4(2(3(1(4(2(1(5(5(x1)))))))))) 2(3(5(3(4(3(5(x1))))))) -> 2(2(3(2(1(5(5(4(4(0(x1)))))))))) 2(4(1(5(3(3(4(x1))))))) -> 2(3(5(1(5(5(5(2(0(4(x1)))))))))) 2(4(2(0(3(5(3(x1))))))) -> 4(2(5(1(5(1(1(3(1(3(x1)))))))))) 3(0(5(3(4(5(2(x1))))))) -> 3(1(0(1(2(2(4(4(5(5(x1)))))))))) 3(2(1(4(0(3(5(x1))))))) -> 3(1(4(0(5(3(3(0(1(5(x1)))))))))) 3(3(0(5(3(0(3(x1))))))) -> 3(0(1(4(2(5(5(5(3(2(x1)))))))))) 3(3(3(3(0(5(1(x1))))))) -> 3(2(0(1(3(4(2(1(1(1(x1)))))))))) 3(3(5(2(0(3(1(x1))))))) -> 3(3(4(2(4(4(2(2(1(1(x1)))))))))) 3(3(5(2(5(2(3(x1))))))) -> 3(4(2(2(1(5(1(3(1(2(x1)))))))))) 3(5(0(4(5(2(0(x1))))))) -> 3(1(3(1(1(3(3(1(0(5(x1)))))))))) 4(0(5(2(3(4(5(x1))))))) -> 4(4(3(3(1(5(5(2(1(5(x1)))))))))) 4(1(5(3(3(4(0(x1))))))) -> 3(1(1(1(0(4(2(4(2(2(x1)))))))))) 4(5(2(3(3(4(0(x1))))))) -> 0(5(1(1(2(4(3(1(1(3(x1)))))))))) 4(5(4(3(4(2(3(x1))))))) -> 4(4(0(5(4(4(4(5(1(3(x1)))))))))) 5(0(3(3(1(2(5(x1))))))) -> 5(5(5(4(0(0(1(1(1(0(x1)))))))))) 5(0(3(3(4(5(4(x1))))))) -> 5(1(3(3(3(5(4(4(4(4(x1)))))))))) 5(3(4(5(2(3(3(x1))))))) -> 5(4(3(1(1(5(0(1(3(1(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_1(x_1)) -> 1(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_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(2(3(x1)))) -> 1(4(0(5(4(0(5(4(4(2(x1)))))))))) 1(0(2(4(5(x1))))) -> 1(0(5(4(4(1(3(5(5(5(x1)))))))))) 1(4(0(3(3(x1))))) -> 1(4(5(1(1(1(2(1(3(0(x1)))))))))) 1(4(0(3(5(x1))))) -> 5(1(3(1(1(5(1(1(0(5(x1)))))))))) 1(4(3(5(2(x1))))) -> 2(4(3(1(0(1(5(5(0(2(x1)))))))))) 1(4(5(0(3(x1))))) -> 5(1(5(5(1(1(5(0(4(2(x1)))))))))) 2(3(3(3(3(x1))))) -> 3(5(5(5(2(4(4(5(1(2(x1)))))))))) 2(3(3(4(1(x1))))) -> 2(5(0(3(1(5(1(0(5(5(x1)))))))))) 5(0(3(5(2(x1))))) -> 1(3(4(4(4(4(4(4(4(0(x1)))))))))) 5(3(0(3(3(x1))))) -> 5(4(4(3(5(1(1(1(1(5(x1)))))))))) 0(1(4(3(2(3(x1)))))) -> 2(5(1(2(1(1(5(5(3(2(x1)))))))))) 0(2(3(4(1(4(x1)))))) -> 2(1(1(5(4(2(1(4(4(5(x1)))))))))) 1(0(2(3(3(3(x1)))))) -> 1(4(0(4(3(1(5(1(2(5(x1)))))))))) 1(3(5(3(1(3(x1)))))) -> 1(0(5(1(1(2(4(5(5(1(x1)))))))))) 1(5(3(5(3(0(x1)))))) -> 0(1(5(1(1(1(0(5(0(0(x1)))))))))) 2(1(4(3(5(3(x1)))))) -> 3(1(0(1(3(4(2(0(4(2(x1)))))))))) 4(0(3(2(3(5(x1)))))) -> 4(2(5(1(1(1(3(1(1(1(x1)))))))))) 4(1(0(3(3(3(x1)))))) -> 4(5(5(5(2(2(4(4(2(3(x1)))))))))) 5(0(0(2(3(1(x1)))))) -> 1(1(5(5(5(2(0(2(4(1(x1)))))))))) 5(0(2(3(4(1(x1)))))) -> 5(1(3(2(5(1(4(1(5(5(x1)))))))))) 5(0(4(5(0(2(x1)))))) -> 1(5(5(2(3(3(4(4(0(2(x1)))))))))) 5(2(3(2(3(3(x1)))))) -> 1(1(3(2(2(2(1(1(3(2(x1)))))))))) 0(1(2(0(0(4(5(x1))))))) -> 0(1(1(1(1(4(2(0(5(5(x1)))))))))) 0(2(0(3(5(3(1(x1))))))) -> 3(1(0(1(2(5(0(1(1(4(x1)))))))))) 0(2(2(4(5(3(3(x1))))))) -> 2(4(3(1(2(2(5(5(4(3(x1)))))))))) 1(0(4(1(0(1(5(x1))))))) -> 5(5(5(1(5(1(1(5(1(5(x1)))))))))) 1(3(5(3(4(5(2(x1))))))) -> 1(0(1(4(3(4(4(1(5(2(x1)))))))))) 1(4(0(3(2(1(3(x1))))))) -> 2(0(3(1(4(5(2(2(4(4(x1)))))))))) 1(5(2(1(0(2(3(x1))))))) -> 1(4(1(3(5(0(1(0(5(5(x1)))))))))) 1(5(2(3(1(4(0(x1))))))) -> 1(4(4(4(5(2(4(0(5(5(x1)))))))))) 1(5(3(1(2(3(3(x1))))))) -> 3(0(3(1(0(1(3(4(2(0(x1)))))))))) 2(0(1(2(5(0(4(x1))))))) -> 2(4(4(1(1(0(1(3(4(4(x1)))))))))) 2(2(0(0(3(3(1(x1))))))) -> 4(4(2(3(4(1(5(5(4(1(x1)))))))))) 2(3(0(2(0(0(1(x1))))))) -> 2(3(2(2(4(4(1(0(5(5(x1)))))))))) 2(3(3(4(5(2(1(x1))))))) -> 4(4(2(3(1(4(2(1(5(5(x1)))))))))) 2(3(5(3(4(3(5(x1))))))) -> 2(2(3(2(1(5(5(4(4(0(x1)))))))))) 2(4(1(5(3(3(4(x1))))))) -> 2(3(5(1(5(5(5(2(0(4(x1)))))))))) 2(4(2(0(3(5(3(x1))))))) -> 4(2(5(1(5(1(1(3(1(3(x1)))))))))) 3(0(5(3(4(5(2(x1))))))) -> 3(1(0(1(2(2(4(4(5(5(x1)))))))))) 3(2(1(4(0(3(5(x1))))))) -> 3(1(4(0(5(3(3(0(1(5(x1)))))))))) 3(3(0(5(3(0(3(x1))))))) -> 3(0(1(4(2(5(5(5(3(2(x1)))))))))) 3(3(3(3(0(5(1(x1))))))) -> 3(2(0(1(3(4(2(1(1(1(x1)))))))))) 3(3(5(2(0(3(1(x1))))))) -> 3(3(4(2(4(4(2(2(1(1(x1)))))))))) 3(3(5(2(5(2(3(x1))))))) -> 3(4(2(2(1(5(1(3(1(2(x1)))))))))) 3(5(0(4(5(2(0(x1))))))) -> 3(1(3(1(1(3(3(1(0(5(x1)))))))))) 4(0(5(2(3(4(5(x1))))))) -> 4(4(3(3(1(5(5(2(1(5(x1)))))))))) 4(1(5(3(3(4(0(x1))))))) -> 3(1(1(1(0(4(2(4(2(2(x1)))))))))) 4(5(2(3(3(4(0(x1))))))) -> 0(5(1(1(2(4(3(1(1(3(x1)))))))))) 4(5(4(3(4(2(3(x1))))))) -> 4(4(0(5(4(4(4(5(1(3(x1)))))))))) 5(0(3(3(1(2(5(x1))))))) -> 5(5(5(4(0(0(1(1(1(0(x1)))))))))) 5(0(3(3(4(5(4(x1))))))) -> 5(1(3(3(3(5(4(4(4(4(x1)))))))))) 5(3(4(5(2(3(3(x1))))))) -> 5(4(3(1(1(5(0(1(3(1(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_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_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(2(3(x1)))) -> 1(4(0(5(4(0(5(4(4(2(x1)))))))))) 1(0(2(4(5(x1))))) -> 1(0(5(4(4(1(3(5(5(5(x1)))))))))) 1(4(0(3(3(x1))))) -> 1(4(5(1(1(1(2(1(3(0(x1)))))))))) 1(4(0(3(5(x1))))) -> 5(1(3(1(1(5(1(1(0(5(x1)))))))))) 1(4(3(5(2(x1))))) -> 2(4(3(1(0(1(5(5(0(2(x1)))))))))) 1(4(5(0(3(x1))))) -> 5(1(5(5(1(1(5(0(4(2(x1)))))))))) 2(3(3(3(3(x1))))) -> 3(5(5(5(2(4(4(5(1(2(x1)))))))))) 2(3(3(4(1(x1))))) -> 2(5(0(3(1(5(1(0(5(5(x1)))))))))) 5(0(3(5(2(x1))))) -> 1(3(4(4(4(4(4(4(4(0(x1)))))))))) 5(3(0(3(3(x1))))) -> 5(4(4(3(5(1(1(1(1(5(x1)))))))))) 0(1(4(3(2(3(x1)))))) -> 2(5(1(2(1(1(5(5(3(2(x1)))))))))) 0(2(3(4(1(4(x1)))))) -> 2(1(1(5(4(2(1(4(4(5(x1)))))))))) 1(0(2(3(3(3(x1)))))) -> 1(4(0(4(3(1(5(1(2(5(x1)))))))))) 1(3(5(3(1(3(x1)))))) -> 1(0(5(1(1(2(4(5(5(1(x1)))))))))) 1(5(3(5(3(0(x1)))))) -> 0(1(5(1(1(1(0(5(0(0(x1)))))))))) 2(1(4(3(5(3(x1)))))) -> 3(1(0(1(3(4(2(0(4(2(x1)))))))))) 4(0(3(2(3(5(x1)))))) -> 4(2(5(1(1(1(3(1(1(1(x1)))))))))) 4(1(0(3(3(3(x1)))))) -> 4(5(5(5(2(2(4(4(2(3(x1)))))))))) 5(0(0(2(3(1(x1)))))) -> 1(1(5(5(5(2(0(2(4(1(x1)))))))))) 5(0(2(3(4(1(x1)))))) -> 5(1(3(2(5(1(4(1(5(5(x1)))))))))) 5(0(4(5(0(2(x1)))))) -> 1(5(5(2(3(3(4(4(0(2(x1)))))))))) 5(2(3(2(3(3(x1)))))) -> 1(1(3(2(2(2(1(1(3(2(x1)))))))))) 0(1(2(0(0(4(5(x1))))))) -> 0(1(1(1(1(4(2(0(5(5(x1)))))))))) 0(2(0(3(5(3(1(x1))))))) -> 3(1(0(1(2(5(0(1(1(4(x1)))))))))) 0(2(2(4(5(3(3(x1))))))) -> 2(4(3(1(2(2(5(5(4(3(x1)))))))))) 1(0(4(1(0(1(5(x1))))))) -> 5(5(5(1(5(1(1(5(1(5(x1)))))))))) 1(3(5(3(4(5(2(x1))))))) -> 1(0(1(4(3(4(4(1(5(2(x1)))))))))) 1(4(0(3(2(1(3(x1))))))) -> 2(0(3(1(4(5(2(2(4(4(x1)))))))))) 1(5(2(1(0(2(3(x1))))))) -> 1(4(1(3(5(0(1(0(5(5(x1)))))))))) 1(5(2(3(1(4(0(x1))))))) -> 1(4(4(4(5(2(4(0(5(5(x1)))))))))) 1(5(3(1(2(3(3(x1))))))) -> 3(0(3(1(0(1(3(4(2(0(x1)))))))))) 2(0(1(2(5(0(4(x1))))))) -> 2(4(4(1(1(0(1(3(4(4(x1)))))))))) 2(2(0(0(3(3(1(x1))))))) -> 4(4(2(3(4(1(5(5(4(1(x1)))))))))) 2(3(0(2(0(0(1(x1))))))) -> 2(3(2(2(4(4(1(0(5(5(x1)))))))))) 2(3(3(4(5(2(1(x1))))))) -> 4(4(2(3(1(4(2(1(5(5(x1)))))))))) 2(3(5(3(4(3(5(x1))))))) -> 2(2(3(2(1(5(5(4(4(0(x1)))))))))) 2(4(1(5(3(3(4(x1))))))) -> 2(3(5(1(5(5(5(2(0(4(x1)))))))))) 2(4(2(0(3(5(3(x1))))))) -> 4(2(5(1(5(1(1(3(1(3(x1)))))))))) 3(0(5(3(4(5(2(x1))))))) -> 3(1(0(1(2(2(4(4(5(5(x1)))))))))) 3(2(1(4(0(3(5(x1))))))) -> 3(1(4(0(5(3(3(0(1(5(x1)))))))))) 3(3(0(5(3(0(3(x1))))))) -> 3(0(1(4(2(5(5(5(3(2(x1)))))))))) 3(3(3(3(0(5(1(x1))))))) -> 3(2(0(1(3(4(2(1(1(1(x1)))))))))) 3(3(5(2(0(3(1(x1))))))) -> 3(3(4(2(4(4(2(2(1(1(x1)))))))))) 3(3(5(2(5(2(3(x1))))))) -> 3(4(2(2(1(5(1(3(1(2(x1)))))))))) 3(5(0(4(5(2(0(x1))))))) -> 3(1(3(1(1(3(3(1(0(5(x1)))))))))) 4(0(5(2(3(4(5(x1))))))) -> 4(4(3(3(1(5(5(2(1(5(x1)))))))))) 4(1(5(3(3(4(0(x1))))))) -> 3(1(1(1(0(4(2(4(2(2(x1)))))))))) 4(5(2(3(3(4(0(x1))))))) -> 0(5(1(1(2(4(3(1(1(3(x1)))))))))) 4(5(4(3(4(2(3(x1))))))) -> 4(4(0(5(4(4(4(5(1(3(x1)))))))))) 5(0(3(3(1(2(5(x1))))))) -> 5(5(5(4(0(0(1(1(1(0(x1)))))))))) 5(0(3(3(4(5(4(x1))))))) -> 5(1(3(3(3(5(4(4(4(4(x1)))))))))) 5(3(4(5(2(3(3(x1))))))) -> 5(4(3(1(1(5(0(1(3(1(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_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_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(2(3(x1)))) -> 1(4(0(5(4(0(5(4(4(2(x1)))))))))) 1(0(2(4(5(x1))))) -> 1(0(5(4(4(1(3(5(5(5(x1)))))))))) 1(4(0(3(3(x1))))) -> 1(4(5(1(1(1(2(1(3(0(x1)))))))))) 1(4(0(3(5(x1))))) -> 5(1(3(1(1(5(1(1(0(5(x1)))))))))) 1(4(3(5(2(x1))))) -> 2(4(3(1(0(1(5(5(0(2(x1)))))))))) 1(4(5(0(3(x1))))) -> 5(1(5(5(1(1(5(0(4(2(x1)))))))))) 2(3(3(3(3(x1))))) -> 3(5(5(5(2(4(4(5(1(2(x1)))))))))) 2(3(3(4(1(x1))))) -> 2(5(0(3(1(5(1(0(5(5(x1)))))))))) 5(0(3(5(2(x1))))) -> 1(3(4(4(4(4(4(4(4(0(x1)))))))))) 5(3(0(3(3(x1))))) -> 5(4(4(3(5(1(1(1(1(5(x1)))))))))) 0(1(4(3(2(3(x1)))))) -> 2(5(1(2(1(1(5(5(3(2(x1)))))))))) 0(2(3(4(1(4(x1)))))) -> 2(1(1(5(4(2(1(4(4(5(x1)))))))))) 1(0(2(3(3(3(x1)))))) -> 1(4(0(4(3(1(5(1(2(5(x1)))))))))) 1(3(5(3(1(3(x1)))))) -> 1(0(5(1(1(2(4(5(5(1(x1)))))))))) 1(5(3(5(3(0(x1)))))) -> 0(1(5(1(1(1(0(5(0(0(x1)))))))))) 2(1(4(3(5(3(x1)))))) -> 3(1(0(1(3(4(2(0(4(2(x1)))))))))) 4(0(3(2(3(5(x1)))))) -> 4(2(5(1(1(1(3(1(1(1(x1)))))))))) 4(1(0(3(3(3(x1)))))) -> 4(5(5(5(2(2(4(4(2(3(x1)))))))))) 5(0(0(2(3(1(x1)))))) -> 1(1(5(5(5(2(0(2(4(1(x1)))))))))) 5(0(2(3(4(1(x1)))))) -> 5(1(3(2(5(1(4(1(5(5(x1)))))))))) 5(0(4(5(0(2(x1)))))) -> 1(5(5(2(3(3(4(4(0(2(x1)))))))))) 5(2(3(2(3(3(x1)))))) -> 1(1(3(2(2(2(1(1(3(2(x1)))))))))) 0(1(2(0(0(4(5(x1))))))) -> 0(1(1(1(1(4(2(0(5(5(x1)))))))))) 0(2(0(3(5(3(1(x1))))))) -> 3(1(0(1(2(5(0(1(1(4(x1)))))))))) 0(2(2(4(5(3(3(x1))))))) -> 2(4(3(1(2(2(5(5(4(3(x1)))))))))) 1(0(4(1(0(1(5(x1))))))) -> 5(5(5(1(5(1(1(5(1(5(x1)))))))))) 1(3(5(3(4(5(2(x1))))))) -> 1(0(1(4(3(4(4(1(5(2(x1)))))))))) 1(4(0(3(2(1(3(x1))))))) -> 2(0(3(1(4(5(2(2(4(4(x1)))))))))) 1(5(2(1(0(2(3(x1))))))) -> 1(4(1(3(5(0(1(0(5(5(x1)))))))))) 1(5(2(3(1(4(0(x1))))))) -> 1(4(4(4(5(2(4(0(5(5(x1)))))))))) 1(5(3(1(2(3(3(x1))))))) -> 3(0(3(1(0(1(3(4(2(0(x1)))))))))) 2(0(1(2(5(0(4(x1))))))) -> 2(4(4(1(1(0(1(3(4(4(x1)))))))))) 2(2(0(0(3(3(1(x1))))))) -> 4(4(2(3(4(1(5(5(4(1(x1)))))))))) 2(3(0(2(0(0(1(x1))))))) -> 2(3(2(2(4(4(1(0(5(5(x1)))))))))) 2(3(3(4(5(2(1(x1))))))) -> 4(4(2(3(1(4(2(1(5(5(x1)))))))))) 2(3(5(3(4(3(5(x1))))))) -> 2(2(3(2(1(5(5(4(4(0(x1)))))))))) 2(4(1(5(3(3(4(x1))))))) -> 2(3(5(1(5(5(5(2(0(4(x1)))))))))) 2(4(2(0(3(5(3(x1))))))) -> 4(2(5(1(5(1(1(3(1(3(x1)))))))))) 3(0(5(3(4(5(2(x1))))))) -> 3(1(0(1(2(2(4(4(5(5(x1)))))))))) 3(2(1(4(0(3(5(x1))))))) -> 3(1(4(0(5(3(3(0(1(5(x1)))))))))) 3(3(0(5(3(0(3(x1))))))) -> 3(0(1(4(2(5(5(5(3(2(x1)))))))))) 3(3(3(3(0(5(1(x1))))))) -> 3(2(0(1(3(4(2(1(1(1(x1)))))))))) 3(3(5(2(0(3(1(x1))))))) -> 3(3(4(2(4(4(2(2(1(1(x1)))))))))) 3(3(5(2(5(2(3(x1))))))) -> 3(4(2(2(1(5(1(3(1(2(x1)))))))))) 3(5(0(4(5(2(0(x1))))))) -> 3(1(3(1(1(3(3(1(0(5(x1)))))))))) 4(0(5(2(3(4(5(x1))))))) -> 4(4(3(3(1(5(5(2(1(5(x1)))))))))) 4(1(5(3(3(4(0(x1))))))) -> 3(1(1(1(0(4(2(4(2(2(x1)))))))))) 4(5(2(3(3(4(0(x1))))))) -> 0(5(1(1(2(4(3(1(1(3(x1)))))))))) 4(5(4(3(4(2(3(x1))))))) -> 4(4(0(5(4(4(4(5(1(3(x1)))))))))) 5(0(3(3(1(2(5(x1))))))) -> 5(5(5(4(0(0(1(1(1(0(x1)))))))))) 5(0(3(3(4(5(4(x1))))))) -> 5(1(3(3(3(5(4(4(4(4(x1)))))))))) 5(3(4(5(2(3(3(x1))))))) -> 5(4(3(1(1(5(0(1(3(1(x1)))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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_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. "[70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 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, 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, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549] {(70,71,[0_1|0, 1_1|0, 2_1|0, 5_1|0, 4_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]), (70,72,[0_1|1, 1_1|1, 2_1|1, 5_1|1, 4_1|1, 3_1|1]), (70,73,[1_1|2]), (70,82,[0_1|2]), (70,91,[2_1|2]), (70,100,[2_1|2]), (70,109,[3_1|2]), (70,118,[2_1|2]), (70,127,[1_1|2]), (70,136,[1_1|2]), (70,145,[5_1|2]), (70,154,[1_1|2]), (70,163,[5_1|2]), (70,172,[2_1|2]), (70,181,[2_1|2]), (70,190,[5_1|2]), (70,199,[1_1|2]), (70,208,[1_1|2]), (70,217,[0_1|2]), (70,226,[3_1|2]), (70,235,[1_1|2]), (70,244,[1_1|2]), (70,253,[3_1|2]), (70,262,[2_1|2]), (70,271,[4_1|2]), (70,280,[2_1|2]), (70,289,[2_1|2]), (70,298,[3_1|2]), (70,307,[2_1|2]), (70,316,[4_1|2]), (70,325,[2_1|2]), (70,334,[4_1|2]), (70,343,[1_1|2]), (70,352,[5_1|2]), (70,361,[5_1|2]), (70,370,[1_1|2]), (70,379,[5_1|2]), (70,388,[1_1|2]), (70,397,[5_1|2]), (70,406,[5_1|2]), (70,415,[1_1|2]), (70,424,[4_1|2]), (70,433,[4_1|2]), (70,442,[4_1|2]), (70,451,[3_1|2]), (70,460,[0_1|2]), (70,469,[4_1|2]), (70,478,[3_1|2]), (70,487,[3_1|2]), (70,496,[3_1|2]), (70,505,[3_1|2]), (70,514,[3_1|2]), (70,523,[3_1|2]), (70,532,[3_1|2]), (71,71,[cons_0_1|0, cons_1_1|0, cons_2_1|0, cons_5_1|0, cons_4_1|0, cons_3_1|0]), (72,71,[encArg_1|1]), (72,72,[0_1|1, 1_1|1, 2_1|1, 5_1|1, 4_1|1, 3_1|1]), (72,73,[1_1|2]), (72,82,[0_1|2]), (72,91,[2_1|2]), (72,100,[2_1|2]), (72,109,[3_1|2]), (72,118,[2_1|2]), (72,127,[1_1|2]), (72,136,[1_1|2]), (72,145,[5_1|2]), (72,154,[1_1|2]), (72,163,[5_1|2]), (72,172,[2_1|2]), (72,181,[2_1|2]), (72,190,[5_1|2]), (72,199,[1_1|2]), (72,208,[1_1|2]), (72,217,[0_1|2]), (72,226,[3_1|2]), (72,235,[1_1|2]), (72,244,[1_1|2]), (72,253,[3_1|2]), (72,262,[2_1|2]), (72,271,[4_1|2]), (72,280,[2_1|2]), (72,289,[2_1|2]), (72,298,[3_1|2]), (72,307,[2_1|2]), (72,316,[4_1|2]), (72,325,[2_1|2]), (72,334,[4_1|2]), (72,343,[1_1|2]), (72,352,[5_1|2]), (72,361,[5_1|2]), (72,370,[1_1|2]), (72,379,[5_1|2]), (72,388,[1_1|2]), (72,397,[5_1|2]), (72,406,[5_1|2]), (72,415,[1_1|2]), (72,424,[4_1|2]), (72,433,[4_1|2]), (72,442,[4_1|2]), (72,451,[3_1|2]), (72,460,[0_1|2]), (72,469,[4_1|2]), (72,478,[3_1|2]), (72,487,[3_1|2]), (72,496,[3_1|2]), (72,505,[3_1|2]), (72,514,[3_1|2]), (72,523,[3_1|2]), (72,532,[3_1|2]), (73,74,[4_1|2]), (74,75,[0_1|2]), (75,76,[5_1|2]), (76,77,[4_1|2]), (77,78,[0_1|2]), (78,79,[5_1|2]), (79,80,[4_1|2]), (80,81,[4_1|2]), (81,72,[2_1|2]), (81,109,[2_1|2]), (81,226,[2_1|2]), (81,253,[2_1|2, 3_1|2]), (81,298,[2_1|2, 3_1|2]), (81,451,[2_1|2]), (81,478,[2_1|2]), (81,487,[2_1|2]), (81,496,[2_1|2]), (81,505,[2_1|2]), (81,514,[2_1|2]), (81,523,[2_1|2]), (81,532,[2_1|2]), (81,281,[2_1|2]), (81,326,[2_1|2]), (81,262,[2_1|2]), (81,271,[4_1|2]), (81,280,[2_1|2]), (81,289,[2_1|2]), (81,307,[2_1|2]), (81,316,[4_1|2]), (81,325,[2_1|2]), (81,334,[4_1|2]), (82,83,[1_1|2]), (83,84,[1_1|2]), (84,85,[1_1|2]), (85,86,[1_1|2]), (86,87,[4_1|2]), (87,88,[2_1|2]), (88,89,[0_1|2]), (89,90,[5_1|2]), (90,72,[5_1|2]), (90,145,[5_1|2]), (90,163,[5_1|2]), (90,190,[5_1|2]), (90,352,[5_1|2]), (90,361,[5_1|2]), (90,379,[5_1|2]), (90,397,[5_1|2]), (90,406,[5_1|2]), (90,443,[5_1|2]), (90,343,[1_1|2]), (90,370,[1_1|2]), (90,388,[1_1|2]), (90,415,[1_1|2]), (91,92,[5_1|2]), (92,93,[1_1|2]), (93,94,[2_1|2]), (94,95,[1_1|2]), (95,96,[1_1|2]), (96,97,[5_1|2]), (97,98,[5_1|2]), (98,99,[3_1|2]), (98,487,[3_1|2]), (99,72,[2_1|2]), (99,109,[2_1|2]), (99,226,[2_1|2]), (99,253,[2_1|2, 3_1|2]), (99,298,[2_1|2, 3_1|2]), (99,451,[2_1|2]), (99,478,[2_1|2]), (99,487,[2_1|2]), (99,496,[2_1|2]), (99,505,[2_1|2]), (99,514,[2_1|2]), (99,523,[2_1|2]), (99,532,[2_1|2]), (99,281,[2_1|2]), (99,326,[2_1|2]), (99,262,[2_1|2]), (99,271,[4_1|2]), (99,280,[2_1|2]), (99,289,[2_1|2]), (99,307,[2_1|2]), (99,316,[4_1|2]), (99,325,[2_1|2]), (99,334,[4_1|2]), (100,101,[1_1|2]), (101,102,[1_1|2]), (102,103,[5_1|2]), (103,104,[4_1|2]), (104,105,[2_1|2]), (105,106,[1_1|2]), (106,107,[4_1|2]), (107,108,[4_1|2]), (107,460,[0_1|2]), (107,469,[4_1|2]), (108,72,[5_1|2]), (108,271,[5_1|2]), (108,316,[5_1|2]), (108,334,[5_1|2]), (108,424,[5_1|2]), (108,433,[5_1|2]), (108,442,[5_1|2]), (108,469,[5_1|2]), (108,74,[5_1|2]), (108,137,[5_1|2]), (108,155,[5_1|2]), (108,236,[5_1|2]), (108,245,[5_1|2]), (108,343,[1_1|2]), (108,352,[5_1|2]), (108,361,[5_1|2]), (108,370,[1_1|2]), (108,379,[5_1|2]), (108,388,[1_1|2]), (108,397,[5_1|2]), (108,406,[5_1|2]), (108,415,[1_1|2]), (109,110,[1_1|2]), (110,111,[0_1|2]), (111,112,[1_1|2]), (112,113,[2_1|2]), (113,114,[5_1|2]), (114,115,[0_1|2]), (115,116,[1_1|2]), (116,117,[1_1|2]), (116,154,[1_1|2]), (116,163,[5_1|2]), (116,172,[2_1|2]), (116,181,[2_1|2]), (116,190,[5_1|2]), (117,72,[4_1|2]), (117,73,[4_1|2]), (117,127,[4_1|2]), (117,136,[4_1|2]), (117,154,[4_1|2]), (117,199,[4_1|2]), (117,208,[4_1|2]), (117,235,[4_1|2]), (117,244,[4_1|2]), (117,343,[4_1|2]), (117,370,[4_1|2]), (117,388,[4_1|2]), (117,415,[4_1|2]), (117,110,[4_1|2]), (117,299,[4_1|2]), (117,452,[4_1|2]), (117,479,[4_1|2]), (117,488,[4_1|2]), (117,533,[4_1|2]), (117,424,[4_1|2]), (117,433,[4_1|2]), (117,442,[4_1|2]), (117,451,[3_1|2]), (117,460,[0_1|2]), (117,469,[4_1|2]), (118,119,[4_1|2]), (119,120,[3_1|2]), (120,121,[1_1|2]), (121,122,[2_1|2]), (122,123,[2_1|2]), (123,124,[5_1|2]), (124,125,[5_1|2]), (125,126,[4_1|2]), (126,72,[3_1|2]), (126,109,[3_1|2]), (126,226,[3_1|2]), (126,253,[3_1|2]), (126,298,[3_1|2]), (126,451,[3_1|2]), (126,478,[3_1|2]), (126,487,[3_1|2]), (126,496,[3_1|2]), (126,505,[3_1|2]), (126,514,[3_1|2]), (126,523,[3_1|2]), (126,532,[3_1|2]), (126,515,[3_1|2]), (127,128,[0_1|2]), (128,129,[5_1|2]), (129,130,[4_1|2]), (130,131,[4_1|2]), (131,132,[1_1|2]), (132,133,[3_1|2]), (133,134,[5_1|2]), (134,135,[5_1|2]), (135,72,[5_1|2]), (135,145,[5_1|2]), (135,163,[5_1|2]), (135,190,[5_1|2]), (135,352,[5_1|2]), (135,361,[5_1|2]), (135,379,[5_1|2]), (135,397,[5_1|2]), (135,406,[5_1|2]), (135,443,[5_1|2]), (135,343,[1_1|2]), (135,370,[1_1|2]), (135,388,[1_1|2]), (135,415,[1_1|2]), (136,137,[4_1|2]), (137,138,[0_1|2]), (138,139,[4_1|2]), (139,140,[3_1|2]), (140,141,[1_1|2]), (141,142,[5_1|2]), (142,143,[1_1|2]), (143,144,[2_1|2]), (144,72,[5_1|2]), (144,109,[5_1|2]), (144,226,[5_1|2]), (144,253,[5_1|2]), (144,298,[5_1|2]), (144,451,[5_1|2]), (144,478,[5_1|2]), (144,487,[5_1|2]), (144,496,[5_1|2]), (144,505,[5_1|2]), (144,514,[5_1|2]), (144,523,[5_1|2]), (144,532,[5_1|2]), (144,515,[5_1|2]), (144,343,[1_1|2]), (144,352,[5_1|2]), (144,361,[5_1|2]), (144,370,[1_1|2]), (144,379,[5_1|2]), (144,388,[1_1|2]), (144,397,[5_1|2]), (144,406,[5_1|2]), (144,415,[1_1|2]), (145,146,[5_1|2]), (146,147,[5_1|2]), (147,148,[1_1|2]), (148,149,[5_1|2]), (149,150,[1_1|2]), (150,151,[1_1|2]), (151,152,[5_1|2]), (152,153,[1_1|2]), (152,217,[0_1|2]), (152,226,[3_1|2]), (152,235,[1_1|2]), (152,244,[1_1|2]), (153,72,[5_1|2]), (153,145,[5_1|2]), (153,163,[5_1|2]), (153,190,[5_1|2]), (153,352,[5_1|2]), (153,361,[5_1|2]), (153,379,[5_1|2]), (153,397,[5_1|2]), (153,406,[5_1|2]), (153,389,[5_1|2]), (153,219,[5_1|2]), (153,343,[1_1|2]), (153,370,[1_1|2]), (153,388,[1_1|2]), (153,415,[1_1|2]), (154,155,[4_1|2]), (155,156,[5_1|2]), (156,157,[1_1|2]), (157,158,[1_1|2]), (158,159,[1_1|2]), (159,160,[2_1|2]), (160,161,[1_1|2]), (161,162,[3_1|2]), (161,478,[3_1|2]), (162,72,[0_1|2]), (162,109,[0_1|2, 3_1|2]), (162,226,[0_1|2]), (162,253,[0_1|2]), (162,298,[0_1|2]), (162,451,[0_1|2]), (162,478,[0_1|2]), (162,487,[0_1|2]), (162,496,[0_1|2]), (162,505,[0_1|2]), (162,514,[0_1|2]), (162,523,[0_1|2]), (162,532,[0_1|2]), (162,515,[0_1|2]), (162,73,[1_1|2]), (162,82,[0_1|2]), (162,91,[2_1|2]), (162,100,[2_1|2]), (162,118,[2_1|2]), (163,164,[1_1|2]), (164,165,[3_1|2]), (165,166,[1_1|2]), (166,167,[1_1|2]), (167,168,[5_1|2]), (168,169,[1_1|2]), (169,170,[1_1|2]), (170,171,[0_1|2]), (171,72,[5_1|2]), (171,145,[5_1|2]), (171,163,[5_1|2]), (171,190,[5_1|2]), (171,352,[5_1|2]), (171,361,[5_1|2]), (171,379,[5_1|2]), (171,397,[5_1|2]), (171,406,[5_1|2]), (171,254,[5_1|2]), (171,343,[1_1|2]), (171,370,[1_1|2]), (171,388,[1_1|2]), (171,415,[1_1|2]), (172,173,[0_1|2]), (173,174,[3_1|2]), (174,175,[1_1|2]), (175,176,[4_1|2]), (176,177,[5_1|2]), (177,178,[2_1|2]), (178,179,[2_1|2]), (179,180,[4_1|2]), (180,72,[4_1|2]), (180,109,[4_1|2]), (180,226,[4_1|2]), (180,253,[4_1|2]), (180,298,[4_1|2]), (180,451,[4_1|2, 3_1|2]), (180,478,[4_1|2]), (180,487,[4_1|2]), (180,496,[4_1|2]), (180,505,[4_1|2]), (180,514,[4_1|2]), (180,523,[4_1|2]), (180,532,[4_1|2]), (180,344,[4_1|2]), (180,424,[4_1|2]), (180,433,[4_1|2]), (180,442,[4_1|2]), (180,460,[0_1|2]), (180,469,[4_1|2]), (181,182,[4_1|2]), (182,183,[3_1|2]), (183,184,[1_1|2]), 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(432,217,[0_1|2]), (432,226,[3_1|2]), (432,235,[1_1|2]), (432,244,[1_1|2]), (433,434,[4_1|2]), (434,435,[3_1|2]), (435,436,[3_1|2]), (436,437,[1_1|2]), (437,438,[5_1|2]), (438,439,[5_1|2]), (439,440,[2_1|2]), (440,441,[1_1|2]), (440,217,[0_1|2]), (440,226,[3_1|2]), (440,235,[1_1|2]), (440,244,[1_1|2]), (441,72,[5_1|2]), (441,145,[5_1|2]), (441,163,[5_1|2]), (441,190,[5_1|2]), (441,352,[5_1|2]), (441,361,[5_1|2]), (441,379,[5_1|2]), (441,397,[5_1|2]), (441,406,[5_1|2]), (441,443,[5_1|2]), (441,343,[1_1|2]), (441,370,[1_1|2]), (441,388,[1_1|2]), (441,415,[1_1|2]), (442,443,[5_1|2]), (443,444,[5_1|2]), (444,445,[5_1|2]), (445,446,[2_1|2]), (446,447,[2_1|2]), (447,448,[4_1|2]), (448,449,[4_1|2]), (449,450,[2_1|2]), (449,253,[3_1|2]), (449,262,[2_1|2]), (449,271,[4_1|2]), (449,280,[2_1|2]), (449,289,[2_1|2]), (450,72,[3_1|2]), (450,109,[3_1|2]), (450,226,[3_1|2]), (450,253,[3_1|2]), (450,298,[3_1|2]), (450,451,[3_1|2]), (450,478,[3_1|2]), (450,487,[3_1|2]), (450,496,[3_1|2]), (450,505,[3_1|2]), (450,514,[3_1|2]), (450,523,[3_1|2]), (450,532,[3_1|2]), (450,515,[3_1|2]), (451,452,[1_1|2]), (452,453,[1_1|2]), (453,454,[1_1|2]), (454,455,[0_1|2]), (455,456,[4_1|2]), (456,457,[2_1|2]), (457,458,[4_1|2]), (458,459,[2_1|2]), (458,316,[4_1|2]), (459,72,[2_1|2]), (459,82,[2_1|2]), (459,217,[2_1|2]), (459,460,[2_1|2]), (459,253,[3_1|2]), (459,262,[2_1|2]), (459,271,[4_1|2]), (459,280,[2_1|2]), (459,289,[2_1|2]), (459,298,[3_1|2]), (459,307,[2_1|2]), (459,316,[4_1|2]), (459,325,[2_1|2]), (459,334,[4_1|2]), (460,461,[5_1|2]), (461,462,[1_1|2]), (462,463,[1_1|2]), (463,464,[2_1|2]), (464,465,[4_1|2]), (465,466,[3_1|2]), (466,467,[1_1|2]), (467,468,[1_1|2]), (467,199,[1_1|2]), (467,208,[1_1|2]), (468,72,[3_1|2]), (468,82,[3_1|2]), (468,217,[3_1|2]), (468,460,[3_1|2]), (468,478,[3_1|2]), (468,487,[3_1|2]), (468,496,[3_1|2]), (468,505,[3_1|2]), (468,514,[3_1|2]), (468,523,[3_1|2]), (468,532,[3_1|2]), (469,470,[4_1|2]), (470,471,[0_1|2]), (471,472,[5_1|2]), (472,473,[4_1|2]), (473,474,[4_1|2]), (474,475,[4_1|2]), (475,476,[5_1|2]), (476,477,[1_1|2]), (476,199,[1_1|2]), (476,208,[1_1|2]), (477,72,[3_1|2]), (477,109,[3_1|2]), (477,226,[3_1|2]), (477,253,[3_1|2]), (477,298,[3_1|2]), (477,451,[3_1|2]), (477,478,[3_1|2]), (477,487,[3_1|2]), (477,496,[3_1|2]), (477,505,[3_1|2]), (477,514,[3_1|2]), (477,523,[3_1|2]), (477,532,[3_1|2]), (477,281,[3_1|2]), (477,326,[3_1|2]), (478,479,[1_1|2]), (479,480,[0_1|2]), (480,481,[1_1|2]), (481,482,[2_1|2]), (482,483,[2_1|2]), (483,484,[4_1|2]), (484,485,[4_1|2]), (485,486,[5_1|2]), (486,72,[5_1|2]), (486,91,[5_1|2]), (486,100,[5_1|2]), (486,118,[5_1|2]), (486,172,[5_1|2]), (486,181,[5_1|2]), (486,262,[5_1|2]), (486,280,[5_1|2]), (486,289,[5_1|2]), (486,307,[5_1|2]), (486,325,[5_1|2]), (486,343,[1_1|2]), (486,352,[5_1|2]), (486,361,[5_1|2]), (486,370,[1_1|2]), (486,379,[5_1|2]), (486,388,[1_1|2]), (486,397,[5_1|2]), (486,406,[5_1|2]), (486,415,[1_1|2]), (487,488,[1_1|2]), (488,489,[4_1|2]), (489,490,[0_1|2]), (490,491,[5_1|2]), (491,492,[3_1|2]), (492,493,[3_1|2]), (493,494,[0_1|2]), (494,495,[1_1|2]), (494,217,[0_1|2]), (494,226,[3_1|2]), (494,235,[1_1|2]), (494,244,[1_1|2]), (495,72,[5_1|2]), (495,145,[5_1|2]), (495,163,[5_1|2]), (495,190,[5_1|2]), (495,352,[5_1|2]), (495,361,[5_1|2]), (495,379,[5_1|2]), (495,397,[5_1|2]), (495,406,[5_1|2]), (495,254,[5_1|2]), (495,343,[1_1|2]), (495,370,[1_1|2]), (495,388,[1_1|2]), (495,415,[1_1|2]), (496,497,[0_1|2]), (497,498,[1_1|2]), (498,499,[4_1|2]), (499,500,[2_1|2]), (500,501,[5_1|2]), (501,502,[5_1|2]), (502,503,[5_1|2]), (503,504,[3_1|2]), (503,487,[3_1|2]), (504,72,[2_1|2]), (504,109,[2_1|2]), (504,226,[2_1|2]), (504,253,[2_1|2, 3_1|2]), (504,298,[2_1|2, 3_1|2]), (504,451,[2_1|2]), (504,478,[2_1|2]), (504,487,[2_1|2]), (504,496,[2_1|2]), (504,505,[2_1|2]), (504,514,[2_1|2]), (504,523,[2_1|2]), (504,532,[2_1|2]), (504,228,[2_1|2]), (504,262,[2_1|2]), (504,271,[4_1|2]), (504,280,[2_1|2]), (504,289,[2_1|2]), (504,307,[2_1|2]), (504,316,[4_1|2]), (504,325,[2_1|2]), (504,334,[4_1|2]), (505,506,[2_1|2]), (506,507,[0_1|2]), (507,508,[1_1|2]), (508,509,[3_1|2]), (509,510,[4_1|2]), (510,511,[2_1|2]), (511,512,[1_1|2]), (512,513,[1_1|2]), (513,72,[1_1|2]), (513,73,[1_1|2]), (513,127,[1_1|2]), (513,136,[1_1|2]), (513,154,[1_1|2]), (513,199,[1_1|2]), (513,208,[1_1|2]), (513,235,[1_1|2]), (513,244,[1_1|2]), (513,343,[1_1|2]), (513,370,[1_1|2]), (513,388,[1_1|2]), (513,415,[1_1|2]), (513,164,[1_1|2]), (513,191,[1_1|2]), (513,362,[1_1|2]), (513,380,[1_1|2]), (513,462,[1_1|2]), (513,145,[5_1|2]), (513,163,[5_1|2]), (513,172,[2_1|2]), (513,181,[2_1|2]), (513,190,[5_1|2]), (513,217,[0_1|2]), (513,226,[3_1|2]), (514,515,[3_1|2]), (515,516,[4_1|2]), (516,517,[2_1|2]), (517,518,[4_1|2]), (518,519,[4_1|2]), (519,520,[2_1|2]), (520,521,[2_1|2]), (521,522,[1_1|2]), (522,72,[1_1|2]), (522,73,[1_1|2]), (522,127,[1_1|2]), (522,136,[1_1|2]), (522,154,[1_1|2]), (522,199,[1_1|2]), (522,208,[1_1|2]), (522,235,[1_1|2]), (522,244,[1_1|2]), (522,343,[1_1|2]), (522,370,[1_1|2]), (522,388,[1_1|2]), (522,415,[1_1|2]), (522,110,[1_1|2]), (522,299,[1_1|2]), (522,452,[1_1|2]), (522,479,[1_1|2]), (522,488,[1_1|2]), (522,533,[1_1|2]), (522,175,[1_1|2]), (522,145,[5_1|2]), (522,163,[5_1|2]), (522,172,[2_1|2]), (522,181,[2_1|2]), (522,190,[5_1|2]), (522,217,[0_1|2]), (522,226,[3_1|2]), (523,524,[4_1|2]), (524,525,[2_1|2]), (525,526,[2_1|2]), (526,527,[1_1|2]), (527,528,[5_1|2]), (528,529,[1_1|2]), (529,530,[3_1|2]), (530,531,[1_1|2]), (531,72,[2_1|2]), (531,109,[2_1|2]), (531,226,[2_1|2]), (531,253,[2_1|2, 3_1|2]), (531,298,[2_1|2, 3_1|2]), (531,451,[2_1|2]), (531,478,[2_1|2]), (531,487,[2_1|2]), (531,496,[2_1|2]), (531,505,[2_1|2]), (531,514,[2_1|2]), (531,523,[2_1|2]), (531,532,[2_1|2]), (531,281,[2_1|2]), (531,326,[2_1|2]), (531,262,[2_1|2]), (531,271,[4_1|2]), (531,280,[2_1|2]), (531,289,[2_1|2]), (531,307,[2_1|2]), (531,316,[4_1|2]), (531,325,[2_1|2]), (531,334,[4_1|2]), (532,533,[1_1|2]), (533,534,[3_1|2]), (534,535,[1_1|2]), (535,536,[1_1|2]), (536,537,[3_1|2]), (537,538,[3_1|2]), (538,539,[1_1|2]), (539,540,[0_1|2]), (540,72,[5_1|2]), (540,82,[5_1|2]), (540,217,[5_1|2]), (540,460,[5_1|2]), (540,173,[5_1|2]), (540,343,[1_1|2]), (540,352,[5_1|2]), (540,361,[5_1|2]), (540,370,[1_1|2]), (540,379,[5_1|2]), (540,388,[1_1|2]), (540,397,[5_1|2]), (540,406,[5_1|2]), (540,415,[1_1|2]), (541,542,[4_1|3]), (542,543,[4_1|3]), (543,544,[4_1|3]), (544,545,[5_1|3]), (545,546,[2_1|3]), (546,547,[4_1|3]), (547,548,[0_1|3]), (548,549,[5_1|3]), (549,490,[5_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)