/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 43 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 239 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(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(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(2(x_1)) -> 2(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (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(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) The (relative) TRS S consists of the following rules: encArg(2(x_1)) -> 2(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: 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(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) The (relative) TRS S consists of the following rules: encArg(2(x_1)) -> 2(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: 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(x1))) -> 2(3(3(2(2(3(2(4(2(4(x1)))))))))) 0(0(0(4(0(x1))))) -> 3(4(4(4(1(2(2(0(3(4(x1)))))))))) 0(4(4(1(1(x1))))) -> 0(4(2(3(2(2(2(2(2(2(x1)))))))))) 0(5(4(1(2(x1))))) -> 3(2(1(3(3(4(2(3(2(1(x1)))))))))) 1(0(0(3(0(x1))))) -> 1(1(2(3(2(3(2(4(3(0(x1)))))))))) 0(0(0(0(4(5(x1)))))) -> 0(2(3(2(4(1(5(2(3(5(x1)))))))))) 0(0(0(2(0(4(x1)))))) -> 3(2(2(1(2(4(1(1(0(4(x1)))))))))) 0(0(4(5(3(0(x1)))))) -> 1(2(2(3(5(2(2(1(1(4(x1)))))))))) 0(1(5(3(1(1(x1)))))) -> 3(2(1(3(2(1(2(5(5(3(x1)))))))))) 0(2(0(0(1(1(x1)))))) -> 3(4(2(3(1(2(3(2(3(3(x1)))))))))) 0(5(0(0(0(2(x1)))))) -> 2(3(2(0(5(4(3(1(2(1(x1)))))))))) 1(4(0(3(0(4(x1)))))) -> 3(2(2(5(3(3(2(1(4(4(x1)))))))))) 3(0(0(1(3(5(x1)))))) -> 2(1(3(3(2(0(5(3(1(5(x1)))))))))) 3(1(4(0(1(2(x1)))))) -> 2(3(2(2(1(0(3(1(1(2(x1)))))))))) 4(0(0(1(3(1(x1)))))) -> 3(2(2(1(2(0(5(4(4(1(x1)))))))))) 4(5(0(2(4(1(x1)))))) -> 2(1(4(2(3(2(2(3(4(1(x1)))))))))) 5(4(3(0(1(5(x1)))))) -> 5(2(3(3(3(2(1(5(3(2(x1)))))))))) 0(0(1(2(3(0(5(x1))))))) -> 3(2(1(3(2(1(4(3(5(5(x1)))))))))) 0(0(5(1(5(1(3(x1))))))) -> 3(3(1(3(3(5(0(3(2(2(x1)))))))))) 0(0(5(2(5(2(1(x1))))))) -> 2(3(5(3(4(2(2(1(2(0(x1)))))))))) 0(0(5(4(2(0(2(x1))))))) -> 3(2(3(2(2(0(0(3(1(3(x1)))))))))) 0(1(0(5(5(2(0(x1))))))) -> 3(2(2(4(3(3(3(0(2(0(x1)))))))))) 0(2(0(3(0(0(2(x1))))))) -> 3(2(3(1(3(4(4(5(2(3(x1)))))))))) 0(2(2(5(0(4(3(x1))))))) -> 0(4(1(1(2(2(3(2(5(3(x1)))))))))) 0(2(4(0(1(5(4(x1))))))) -> 3(2(0(1(3(2(1(5(3(4(x1)))))))))) 0(3(0(0(0(0(0(x1))))))) -> 2(0(5(2(3(1(0(2(4(4(x1)))))))))) 0(4(0(0(0(4(3(x1))))))) -> 0(5(5(2(1(3(2(3(3(3(x1)))))))))) 0(4(5(5(5(0(4(x1))))))) -> 2(3(5(1(2(3(0(2(4(4(x1)))))))))) 0(5(1(1(5(0(0(x1))))))) -> 3(2(1(0(5(2(0(3(3(4(x1)))))))))) 0(5(2(2(4(1(0(x1))))))) -> 2(3(3(1(2(3(2(3(0(4(x1)))))))))) 0(5(3(1(4(3(1(x1))))))) -> 2(3(2(1(3(4(4(1(0(1(x1)))))))))) 1(0(3(1(0(0(0(x1))))))) -> 2(4(2(2(5(3(2(4(4(4(x1)))))))))) 1(1(2(4(4(0(2(x1))))))) -> 1(1(2(2(3(2(1(5(2(2(x1)))))))))) 1(2(4(4(0(5(1(x1))))))) -> 1(3(3(2(2(3(5(1(0(3(x1)))))))))) 1(3(0(0(3(3(5(x1))))))) -> 3(2(2(1(2(4(5(4(3(5(x1)))))))))) 1(4(1(3(0(4(3(x1))))))) -> 1(3(5(1(2(3(2(2(5(1(x1)))))))))) 1(4(4(0(0(0(0(x1))))))) -> 2(1(2(4(3(3(5(3(1(0(x1)))))))))) 1(5(0(0(5(3(3(x1))))))) -> 1(5(4(3(2(1(1(3(2(1(x1)))))))))) 4(0(0(0(4(0(2(x1))))))) -> 4(4(2(2(3(2(4(1(2(2(x1)))))))))) 4(0(0(0(4(1(4(x1))))))) -> 4(4(3(2(1(1(2(1(0(0(x1)))))))))) 4(0(0(4(0(0(2(x1))))))) -> 3(0(3(2(3(3(5(4(1(5(x1)))))))))) 4(0(0(4(5(2(4(x1))))))) -> 3(3(5(2(2(2(3(4(4(0(x1)))))))))) 4(0(3(0(2(5(1(x1))))))) -> 4(3(3(2(3(4(3(1(0(3(x1)))))))))) 4(0(4(0(1(1(2(x1))))))) -> 2(2(0(3(1(4(3(2(2(2(x1)))))))))) 4(0(4(1(4(0(0(x1))))))) -> 3(1(2(2(0(0(2(1(1(4(x1)))))))))) 4(1(0(5(4(1(4(x1))))))) -> 2(5(1(2(1(3(2(4(3(4(x1)))))))))) 4(1(2(5(4(0(0(x1))))))) -> 2(4(5(1(3(0(3(2(0(4(x1)))))))))) 4(1(4(0(3(1(0(x1))))))) -> 5(3(2(0(2(2(2(5(1(4(x1)))))))))) 4(3(0(5(5(0(2(x1))))))) -> 3(0(3(2(3(2(2(4(5(2(x1)))))))))) 4(3(5(5(4(1(0(x1))))))) -> 3(5(1(3(4(5(2(3(3(4(x1)))))))))) 5(0(0(0(1(4(0(x1))))))) -> 5(2(5(3(2(2(3(0(5(4(x1)))))))))) 5(0(2(1(5(1(5(x1))))))) -> 5(3(2(3(3(3(4(3(3(2(x1)))))))))) 5(0(2(5(4(4(0(x1))))))) -> 5(4(0(3(2(2(1(1(3(4(x1)))))))))) 5(0(5(0(1(5(2(x1))))))) -> 5(3(2(3(2(4(3(2(0(2(x1)))))))))) 5(0(5(5(5(4(5(x1))))))) -> 5(2(3(3(2(3(3(0(3(2(x1)))))))))) 5(3(0(1(4(3(1(x1))))))) -> 3(2(2(1(2(1(0(0(3(1(x1)))))))))) 5(3(5(0(1(0(1(x1))))))) -> 5(3(2(2(1(5(5(3(5(1(x1)))))))))) 5(4(0(4(1(0(3(x1))))))) -> 5(3(2(2(4(4(3(2(4(3(x1)))))))))) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) S is empty. Rewrite Strategy: 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. "[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, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649] {(89,90,[0_1|0, 1_1|0, 3_1|0, 4_1|0, 5_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (89,91,[2_1|1, 0_1|1, 1_1|1, 3_1|1, 4_1|1, 5_1|1]), (89,92,[2_1|2]), (89,101,[3_1|2]), (89,110,[3_1|2]), (89,119,[3_1|2]), (89,128,[0_1|2]), (89,137,[3_1|2]), (89,146,[1_1|2]), (89,155,[3_1|2]), (89,164,[3_1|2]), (89,173,[2_1|2]), (89,182,[3_1|2]), (89,191,[0_1|2]), (89,200,[0_1|2]), (89,209,[2_1|2]), (89,218,[3_1|2]), (89,227,[2_1|2]), (89,236,[3_1|2]), (89,245,[2_1|2]), (89,254,[2_1|2]), (89,263,[3_1|2]), (89,272,[3_1|2]), (89,281,[0_1|2]), (89,290,[3_1|2]), (89,299,[2_1|2]), (89,308,[1_1|2]), (89,317,[2_1|2]), (89,326,[3_1|2]), (89,335,[1_1|2]), (89,344,[2_1|2]), (89,353,[1_1|2]), (89,362,[1_1|2]), (89,371,[3_1|2]), (89,380,[1_1|2]), (89,389,[2_1|2]), (89,398,[2_1|2]), (89,407,[3_1|2]), (89,416,[4_1|2]), (89,425,[4_1|2]), (89,434,[3_1|2]), (89,443,[3_1|2]), (89,452,[4_1|2]), (89,461,[2_1|2]), (89,470,[3_1|2]), (89,479,[2_1|2]), (89,488,[2_1|2]), (89,497,[2_1|2]), (89,506,[5_1|2]), (89,515,[3_1|2]), (89,524,[3_1|2]), (89,533,[5_1|2]), (89,542,[5_1|2]), (89,551,[5_1|2]), (89,560,[5_1|2]), (89,569,[5_1|2]), (89,578,[5_1|2]), (89,587,[5_1|2]), (89,596,[3_1|2]), (89,605,[5_1|2]), (90,90,[2_1|0, cons_0_1|0, cons_1_1|0, cons_3_1|0, cons_4_1|0, cons_5_1|0]), (91,90,[encArg_1|1]), (91,91,[2_1|1, 0_1|1, 1_1|1, 3_1|1, 4_1|1, 5_1|1]), (91,92,[2_1|2]), (91,101,[3_1|2]), (91,110,[3_1|2]), (91,119,[3_1|2]), (91,128,[0_1|2]), (91,137,[3_1|2]), (91,146,[1_1|2]), (91,155,[3_1|2]), (91,164,[3_1|2]), (91,173,[2_1|2]), (91,182,[3_1|2]), (91,191,[0_1|2]), (91,200,[0_1|2]), (91,209,[2_1|2]), (91,218,[3_1|2]), (91,227,[2_1|2]), (91,236,[3_1|2]), (91,245,[2_1|2]), (91,254,[2_1|2]), (91,263,[3_1|2]), (91,272,[3_1|2]), (91,281,[0_1|2]), (91,290,[3_1|2]), (91,299,[2_1|2]), (91,308,[1_1|2]), (91,317,[2_1|2]), (91,326,[3_1|2]), (91,335,[1_1|2]), (91,344,[2_1|2]), (91,353,[1_1|2]), (91,362,[1_1|2]), (91,371,[3_1|2]), (91,380,[1_1|2]), (91,389,[2_1|2]), (91,398,[2_1|2]), (91,407,[3_1|2]), (91,416,[4_1|2]), (91,425,[4_1|2]), (91,434,[3_1|2]), (91,443,[3_1|2]), (91,452,[4_1|2]), (91,461,[2_1|2]), (91,470,[3_1|2]), (91,479,[2_1|2]), 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(469,173,[2_1|2]), (469,209,[2_1|2]), (469,227,[2_1|2]), (469,245,[2_1|2]), (469,254,[2_1|2]), (469,299,[2_1|2]), (469,317,[2_1|2]), (469,344,[2_1|2]), (469,389,[2_1|2]), (469,398,[2_1|2]), (469,461,[2_1|2]), (469,479,[2_1|2]), (469,488,[2_1|2]), (469,497,[2_1|2]), (469,147,[2_1|2]), (469,310,[2_1|2]), (469,355,[2_1|2]), (470,471,[1_1|2]), (471,472,[2_1|2]), (472,473,[2_1|2]), (473,474,[0_1|2]), (474,475,[0_1|2]), (475,476,[2_1|2]), (476,477,[1_1|2]), (477,478,[1_1|2]), (477,326,[3_1|2]), (477,335,[1_1|2]), (477,344,[2_1|2]), (478,91,[4_1|2]), (478,128,[4_1|2]), (478,191,[4_1|2]), (478,200,[4_1|2]), (478,281,[4_1|2]), (478,407,[3_1|2]), (478,416,[4_1|2]), (478,425,[4_1|2]), (478,434,[3_1|2]), (478,443,[3_1|2]), (478,452,[4_1|2]), (478,461,[2_1|2]), (478,470,[3_1|2]), (478,479,[2_1|2]), (478,488,[2_1|2]), (478,497,[2_1|2]), (478,506,[5_1|2]), (478,515,[3_1|2]), (478,524,[3_1|2]), (479,480,[1_1|2]), (480,481,[4_1|2]), (481,482,[2_1|2]), (482,483,[3_1|2]), (483,484,[2_1|2]), (484,485,[2_1|2]), (485,486,[3_1|2]), (486,487,[4_1|2]), (486,488,[2_1|2]), (486,497,[2_1|2]), (486,506,[5_1|2]), (487,91,[1_1|2]), (487,146,[1_1|2]), (487,308,[1_1|2]), (487,335,[1_1|2]), (487,353,[1_1|2]), (487,362,[1_1|2]), (487,380,[1_1|2]), (487,317,[2_1|2]), (487,326,[3_1|2]), (487,344,[2_1|2]), (487,371,[3_1|2]), (488,489,[5_1|2]), (489,490,[1_1|2]), (490,491,[2_1|2]), (491,492,[1_1|2]), (492,493,[3_1|2]), (493,494,[2_1|2]), (494,495,[4_1|2]), (495,496,[3_1|2]), (496,91,[4_1|2]), (496,416,[4_1|2]), (496,425,[4_1|2]), (496,452,[4_1|2]), (496,407,[3_1|2]), (496,434,[3_1|2]), (496,443,[3_1|2]), (496,461,[2_1|2]), (496,470,[3_1|2]), (496,479,[2_1|2]), (496,488,[2_1|2]), (496,497,[2_1|2]), (496,506,[5_1|2]), (496,515,[3_1|2]), (496,524,[3_1|2]), (497,498,[4_1|2]), (498,499,[5_1|2]), (499,500,[1_1|2]), (500,501,[3_1|2]), (501,502,[0_1|2]), (502,503,[3_1|2]), (503,504,[2_1|2]), (504,505,[0_1|2]), (504,191,[0_1|2]), (504,200,[0_1|2]), (504,209,[2_1|2]), (504,641,[0_1|3]), (505,91,[4_1|2]), (505,128,[4_1|2]), (505,191,[4_1|2]), (505,200,[4_1|2]), (505,281,[4_1|2]), (505,407,[3_1|2]), (505,416,[4_1|2]), (505,425,[4_1|2]), (505,434,[3_1|2]), (505,443,[3_1|2]), (505,452,[4_1|2]), (505,461,[2_1|2]), (505,470,[3_1|2]), (505,479,[2_1|2]), (505,488,[2_1|2]), (505,497,[2_1|2]), (505,506,[5_1|2]), (505,515,[3_1|2]), (505,524,[3_1|2]), (506,507,[3_1|2]), (507,508,[2_1|2]), (508,509,[0_1|2]), (509,510,[2_1|2]), (510,511,[2_1|2]), (511,512,[2_1|2]), (512,513,[5_1|2]), (513,514,[1_1|2]), (513,326,[3_1|2]), (513,335,[1_1|2]), (513,344,[2_1|2]), (514,91,[4_1|2]), (514,128,[4_1|2]), (514,191,[4_1|2]), (514,200,[4_1|2]), (514,281,[4_1|2]), (514,407,[3_1|2]), (514,416,[4_1|2]), (514,425,[4_1|2]), (514,434,[3_1|2]), (514,443,[3_1|2]), (514,452,[4_1|2]), (514,461,[2_1|2]), (514,470,[3_1|2]), (514,479,[2_1|2]), (514,488,[2_1|2]), (514,497,[2_1|2]), (514,506,[5_1|2]), (514,515,[3_1|2]), (514,524,[3_1|2]), (515,516,[0_1|2]), (516,517,[3_1|2]), (517,518,[2_1|2]), (518,519,[3_1|2]), (519,520,[2_1|2]), (520,521,[2_1|2]), (521,522,[4_1|2]), (522,523,[5_1|2]), (523,91,[2_1|2]), (523,92,[2_1|2]), (523,173,[2_1|2]), (523,209,[2_1|2]), (523,227,[2_1|2]), (523,245,[2_1|2]), (523,254,[2_1|2]), (523,299,[2_1|2]), (523,317,[2_1|2]), (523,344,[2_1|2]), (523,389,[2_1|2]), (523,398,[2_1|2]), (523,461,[2_1|2]), (523,479,[2_1|2]), (523,488,[2_1|2]), (523,497,[2_1|2]), (523,129,[2_1|2]), (524,525,[5_1|2]), (525,526,[1_1|2]), (526,527,[3_1|2]), (527,528,[4_1|2]), (528,529,[5_1|2]), (529,530,[2_1|2]), (530,531,[3_1|2]), (531,532,[3_1|2]), (532,91,[4_1|2]), (532,128,[4_1|2]), (532,191,[4_1|2]), (532,200,[4_1|2]), (532,281,[4_1|2]), (532,407,[3_1|2]), (532,416,[4_1|2]), (532,425,[4_1|2]), (532,434,[3_1|2]), (532,443,[3_1|2]), (532,452,[4_1|2]), (532,461,[2_1|2]), (532,470,[3_1|2]), (532,479,[2_1|2]), (532,488,[2_1|2]), (532,497,[2_1|2]), (532,506,[5_1|2]), (532,515,[3_1|2]), (532,524,[3_1|2]), (533,534,[2_1|2]), (534,535,[3_1|2]), (535,536,[3_1|2]), (536,537,[3_1|2]), (537,538,[2_1|2]), (538,539,[1_1|2]), (539,540,[5_1|2]), (540,541,[3_1|2]), (541,91,[2_1|2]), (541,506,[2_1|2]), (541,533,[2_1|2]), (541,542,[2_1|2]), (541,551,[2_1|2]), (541,560,[2_1|2]), (541,569,[2_1|2]), (541,578,[2_1|2]), (541,587,[2_1|2]), (541,605,[2_1|2]), (541,381,[2_1|2]), (542,543,[3_1|2]), (543,544,[2_1|2]), (544,545,[2_1|2]), (545,546,[4_1|2]), (546,547,[4_1|2]), (547,548,[3_1|2]), (548,549,[2_1|2]), (549,550,[4_1|2]), (549,515,[3_1|2]), (549,524,[3_1|2]), (550,91,[3_1|2]), (550,101,[3_1|2]), (550,110,[3_1|2]), (550,119,[3_1|2]), (550,137,[3_1|2]), (550,155,[3_1|2]), (550,164,[3_1|2]), (550,182,[3_1|2]), (550,218,[3_1|2]), (550,236,[3_1|2]), (550,263,[3_1|2]), (550,272,[3_1|2]), (550,290,[3_1|2]), (550,326,[3_1|2]), (550,371,[3_1|2]), (550,407,[3_1|2]), (550,434,[3_1|2]), (550,443,[3_1|2]), (550,470,[3_1|2]), (550,515,[3_1|2]), (550,524,[3_1|2]), (550,596,[3_1|2]), (550,389,[2_1|2]), (550,398,[2_1|2]), (551,552,[2_1|2]), (552,553,[5_1|2]), (553,554,[3_1|2]), (554,555,[2_1|2]), (555,556,[2_1|2]), (556,557,[3_1|2]), (557,558,[0_1|2]), (557,218,[3_1|2]), (557,632,[3_1|3]), (558,559,[5_1|2]), (558,533,[5_1|2]), (558,542,[5_1|2]), (559,91,[4_1|2]), (559,128,[4_1|2]), (559,191,[4_1|2]), (559,200,[4_1|2]), (559,281,[4_1|2]), (559,407,[3_1|2]), (559,416,[4_1|2]), (559,425,[4_1|2]), (559,434,[3_1|2]), (559,443,[3_1|2]), (559,452,[4_1|2]), (559,461,[2_1|2]), (559,470,[3_1|2]), (559,479,[2_1|2]), (559,488,[2_1|2]), (559,497,[2_1|2]), (559,506,[5_1|2]), (559,515,[3_1|2]), (559,524,[3_1|2]), (560,561,[3_1|2]), (561,562,[2_1|2]), (562,563,[3_1|2]), (563,564,[3_1|2]), (564,565,[3_1|2]), (565,566,[4_1|2]), (566,567,[3_1|2]), (567,568,[3_1|2]), (568,91,[2_1|2]), (568,506,[2_1|2]), (568,533,[2_1|2]), (568,542,[2_1|2]), (568,551,[2_1|2]), (568,560,[2_1|2]), (568,569,[2_1|2]), (568,578,[2_1|2]), (568,587,[2_1|2]), (568,605,[2_1|2]), (568,381,[2_1|2]), (569,570,[4_1|2]), (570,571,[0_1|2]), (571,572,[3_1|2]), (572,573,[2_1|2]), (573,574,[2_1|2]), (574,575,[1_1|2]), (575,576,[1_1|2]), (576,577,[3_1|2]), (577,91,[4_1|2]), (577,128,[4_1|2]), (577,191,[4_1|2]), (577,200,[4_1|2]), (577,281,[4_1|2]), (577,407,[3_1|2]), (577,416,[4_1|2]), (577,425,[4_1|2]), (577,434,[3_1|2]), (577,443,[3_1|2]), (577,452,[4_1|2]), (577,461,[2_1|2]), (577,470,[3_1|2]), (577,479,[2_1|2]), (577,488,[2_1|2]), (577,497,[2_1|2]), (577,506,[5_1|2]), (577,515,[3_1|2]), (577,524,[3_1|2]), (578,579,[3_1|2]), (579,580,[2_1|2]), (580,581,[3_1|2]), (581,582,[2_1|2]), (582,583,[4_1|2]), (583,584,[3_1|2]), (584,585,[2_1|2]), (585,586,[0_1|2]), (585,263,[3_1|2]), (585,272,[3_1|2]), (585,281,[0_1|2]), (585,290,[3_1|2]), (586,91,[2_1|2]), (586,92,[2_1|2]), (586,173,[2_1|2]), (586,209,[2_1|2]), (586,227,[2_1|2]), (586,245,[2_1|2]), (586,254,[2_1|2]), (586,299,[2_1|2]), (586,317,[2_1|2]), (586,344,[2_1|2]), (586,389,[2_1|2]), (586,398,[2_1|2]), (586,461,[2_1|2]), (586,479,[2_1|2]), (586,488,[2_1|2]), (586,497,[2_1|2]), (586,534,[2_1|2]), (586,552,[2_1|2]), (586,588,[2_1|2]), (587,588,[2_1|2]), (588,589,[3_1|2]), (589,590,[3_1|2]), (590,591,[2_1|2]), (591,592,[3_1|2]), (592,593,[3_1|2]), (593,594,[0_1|2]), (594,595,[3_1|2]), (595,91,[2_1|2]), (595,506,[2_1|2]), (595,533,[2_1|2]), (595,542,[2_1|2]), (595,551,[2_1|2]), (595,560,[2_1|2]), (595,569,[2_1|2]), (595,578,[2_1|2]), (595,587,[2_1|2]), (595,605,[2_1|2]), (596,597,[2_1|2]), (597,598,[2_1|2]), (598,599,[1_1|2]), (599,600,[2_1|2]), (600,601,[1_1|2]), (601,602,[0_1|2]), (602,603,[0_1|2]), (603,604,[3_1|2]), (603,398,[2_1|2]), (604,91,[1_1|2]), (604,146,[1_1|2]), (604,308,[1_1|2]), (604,335,[1_1|2]), (604,353,[1_1|2]), (604,362,[1_1|2]), (604,380,[1_1|2]), (604,471,[1_1|2]), (604,317,[2_1|2]), (604,326,[3_1|2]), (604,344,[2_1|2]), (604,371,[3_1|2]), (605,606,[3_1|2]), (606,607,[2_1|2]), (607,608,[2_1|2]), (608,609,[1_1|2]), (609,610,[5_1|2]), (610,611,[5_1|2]), (611,612,[3_1|2]), (612,613,[5_1|2]), (613,91,[1_1|2]), (613,146,[1_1|2]), (613,308,[1_1|2]), (613,335,[1_1|2]), (613,353,[1_1|2]), (613,362,[1_1|2]), (613,380,[1_1|2]), (613,317,[2_1|2]), (613,326,[3_1|2]), (613,344,[2_1|2]), (613,371,[3_1|2]), (614,615,[3_1|3]), (615,616,[3_1|3]), (616,617,[2_1|3]), (617,618,[2_1|3]), (618,619,[3_1|3]), (619,620,[2_1|3]), (620,621,[4_1|3]), (621,622,[2_1|3]), (622,128,[4_1|3]), (622,191,[4_1|3]), (622,200,[4_1|3]), (622,281,[4_1|3]), (623,624,[1_1|3]), (624,625,[2_1|3]), (625,626,[3_1|3]), (626,627,[2_1|3]), (627,628,[3_1|3]), (628,629,[2_1|3]), (629,630,[4_1|3]), (630,631,[3_1|3]), (631,435,[0_1|3]), (631,516,[0_1|3]), (632,633,[2_1|3]), (633,634,[1_1|3]), (634,635,[3_1|3]), (635,636,[3_1|3]), (636,637,[4_1|3]), (637,638,[2_1|3]), (638,639,[3_1|3]), (639,640,[2_1|3]), (640,147,[1_1|3]), (641,642,[4_1|3]), (642,643,[2_1|3]), (643,644,[3_1|3]), (644,645,[2_1|3]), (645,646,[2_1|3]), (646,647,[2_1|3]), (647,648,[2_1|3]), (648,649,[2_1|3]), (649,284,[2_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)