/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 44 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 226 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(x1)))) -> 2(1(2(x1))) 0(3(4(2(2(1(x1)))))) -> 2(2(5(5(3(x1))))) 2(2(2(5(0(2(1(x1))))))) -> 4(2(4(5(4(4(5(x1))))))) 2(2(5(1(1(3(4(x1))))))) -> 2(5(0(3(3(4(x1)))))) 3(2(2(4(0(3(4(x1))))))) -> 3(2(1(0(4(0(x1)))))) 4(5(1(4(2(4(1(x1))))))) -> 0(0(4(4(0(1(x1)))))) 0(3(4(3(0(0(0(3(x1)))))))) -> 2(2(1(1(4(2(3(x1))))))) 0(4(4(3(4(1(0(4(x1)))))))) -> 2(5(2(0(3(1(x1)))))) 4(4(1(5(1(3(1(1(3(x1))))))))) -> 3(2(2(1(3(0(0(x1))))))) 1(4(5(3(3(1(1(1(4(3(x1)))))))))) -> 3(0(4(0(5(0(0(3(x1)))))))) 1(0(3(2(4(5(3(3(2(3(5(x1))))))))))) -> 4(0(3(0(1(2(3(2(3(5(x1)))))))))) 1(0(3(5(5(2(0(0(4(2(5(x1))))))))))) -> 3(0(2(0(1(1(1(3(3(3(5(3(x1)))))))))))) 3(1(5(1(2(4(5(1(4(5(2(x1))))))))))) -> 3(2(2(2(5(0(0(3(2(x1))))))))) 3(3(4(4(0(4(0(1(2(0(4(x1))))))))))) -> 3(0(5(1(5(0(3(1(5(3(1(x1))))))))))) 1(4(5(0(1(4(1(0(3(3(1(3(x1)))))))))))) -> 0(2(2(4(5(4(3(5(0(0(x1)))))))))) 1(5(0(5(4(3(1(3(4(4(1(4(x1)))))))))))) -> 4(5(0(3(4(5(0(5(3(2(x1)))))))))) 2(0(5(2(2(4(4(1(5(2(2(4(x1)))))))))))) -> 2(3(5(3(1(0(1(0(3(4(2(4(1(x1))))))))))))) 0(3(3(0(5(1(3(0(4(3(3(2(3(x1))))))))))))) -> 0(5(0(1(2(3(0(2(0(2(3(x1))))))))))) 3(3(5(4(5(5(4(2(3(1(1(0(1(x1))))))))))))) -> 4(1(3(3(3(4(5(2(4(3(4(1(5(x1))))))))))))) 3(5(3(0(0(1(4(5(4(2(5(1(0(x1))))))))))))) -> 3(0(2(0(0(1(2(5(3(0(0(x1))))))))))) 3(5(3(0(2(5(0(1(5(2(1(1(3(x1))))))))))))) -> 3(3(3(3(5(1(3(5(0(4(0(1(5(5(x1)))))))))))))) 0(4(0(4(1(3(4(0(2(4(0(5(0(3(x1)))))))))))))) -> 2(3(3(3(1(0(0(2(1(5(5(5(3(x1))))))))))))) 1(1(0(4(1(3(0(3(2(4(2(3(2(2(x1)))))))))))))) -> 3(0(1(4(1(5(0(5(2(0(4(4(5(1(x1)))))))))))))) 5(0(1(4(5(5(2(2(2(0(3(4(4(3(4(x1))))))))))))))) -> 5(4(1(4(1(1(3(1(2(2(2(1(3(1(2(x1))))))))))))))) 0(4(4(3(4(2(3(5(0(4(2(4(3(1(1(0(x1)))))))))))))))) -> 2(5(2(1(0(5(4(0(4(3(3(2(1(3(x1)))))))))))))) 1(3(3(0(1(2(4(1(1(4(5(5(2(3(0(0(x1)))))))))))))))) -> 0(3(5(0(5(0(0(4(4(4(2(1(4(0(2(2(x1)))))))))))))))) 3(1(2(1(1(1(4(4(1(0(2(5(2(1(3(3(x1)))))))))))))))) -> 1(3(4(2(0(3(0(5(3(1(0(1(4(4(5(3(x1)))))))))))))))) 3(3(2(5(2(3(0(5(3(1(0(2(0(1(0(4(x1)))))))))))))))) -> 0(2(0(3(5(1(2(1(5(2(4(2(3(0(4(5(x1)))))))))))))))) 3(3(3(5(5(4(0(2(1(0(1(0(4(3(4(3(x1)))))))))))))))) -> 3(2(4(4(3(5(4(0(4(4(0(4(1(4(3(3(x1)))))))))))))))) 0(5(0(2(3(3(5(1(4(5(2(5(2(0(3(4(1(2(x1)))))))))))))))))) -> 0(3(0(2(1(4(5(3(0(5(1(1(3(5(2(0(4(2(x1)))))))))))))))))) 1(5(5(2(3(3(1(3(4(0(4(5(1(0(2(5(2(0(x1)))))))))))))))))) -> 2(0(3(5(3(1(0(4(5(1(1(2(1(3(4(4(1(2(5(x1))))))))))))))))))) 3(0(3(5(1(3(4(0(1(2(3(4(5(4(4(1(1(0(x1)))))))))))))))))) -> 0(2(0(1(1(5(0(0(4(2(3(4(5(3(3(0(x1)))))))))))))))) 5(1(1(0(0(2(4(2(1(5(0(5(4(1(3(5(4(0(x1)))))))))))))))))) -> 5(0(3(1(4(5(5(2(5(1(5(1(4(3(5(5(4(x1))))))))))))))))) 1(0(1(0(4(4(1(1(2(1(2(1(4(0(4(2(1(2(5(x1))))))))))))))))))) -> 0(2(4(4(5(4(1(1(1(3(5(4(0(4(5(2(1(3(3(3(x1)))))))))))))))))))) 1(5(5(4(1(5(2(3(0(3(3(2(4(5(3(4(1(1(4(x1))))))))))))))))))) -> 4(4(0(4(4(0(0(5(5(0(5(4(0(3(3(0(1(1(4(x1))))))))))))))))))) 2(2(3(5(1(5(4(0(0(1(4(0(1(3(5(0(3(5(1(x1))))))))))))))))))) -> 2(1(5(0(2(1(4(4(3(1(3(5(0(4(3(1(2(x1))))))))))))))))) 3(5(4(3(1(5(0(1(4(5(0(5(2(1(5(2(3(2(2(x1))))))))))))))))))) -> 3(4(2(4(1(4(3(4(0(1(2(2(0(0(2(2(5(2(x1)))))))))))))))))) 4(2(2(4(0(5(5(0(5(3(2(5(3(1(3(2(3(4(4(x1))))))))))))))))))) -> 2(4(5(1(4(2(1(3(2(0(1(5(4(4(4(5(2(4(x1)))))))))))))))))) 1(4(1(1(5(0(1(4(4(1(2(0(5(1(0(0(4(5(1(0(1(x1))))))))))))))))))))) -> 0(4(3(5(3(4(2(4(2(4(1(0(2(4(4(1(3(4(4(4(1(x1))))))))))))))))))))) 4(0(3(0(3(4(2(2(1(3(5(4(4(5(3(1(2(0(1(4(1(x1))))))))))))))))))))) -> 2(1(0(2(5(0(0(2(0(3(3(0(5(0(2(1(3(1(x1)))))))))))))))))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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 (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(x1)))) -> 2(1(2(x1))) 0(3(4(2(2(1(x1)))))) -> 2(2(5(5(3(x1))))) 2(2(2(5(0(2(1(x1))))))) -> 4(2(4(5(4(4(5(x1))))))) 2(2(5(1(1(3(4(x1))))))) -> 2(5(0(3(3(4(x1)))))) 3(2(2(4(0(3(4(x1))))))) -> 3(2(1(0(4(0(x1)))))) 4(5(1(4(2(4(1(x1))))))) -> 0(0(4(4(0(1(x1)))))) 0(3(4(3(0(0(0(3(x1)))))))) -> 2(2(1(1(4(2(3(x1))))))) 0(4(4(3(4(1(0(4(x1)))))))) -> 2(5(2(0(3(1(x1)))))) 4(4(1(5(1(3(1(1(3(x1))))))))) -> 3(2(2(1(3(0(0(x1))))))) 1(4(5(3(3(1(1(1(4(3(x1)))))))))) -> 3(0(4(0(5(0(0(3(x1)))))))) 1(0(3(2(4(5(3(3(2(3(5(x1))))))))))) -> 4(0(3(0(1(2(3(2(3(5(x1)))))))))) 1(0(3(5(5(2(0(0(4(2(5(x1))))))))))) -> 3(0(2(0(1(1(1(3(3(3(5(3(x1)))))))))))) 3(1(5(1(2(4(5(1(4(5(2(x1))))))))))) -> 3(2(2(2(5(0(0(3(2(x1))))))))) 3(3(4(4(0(4(0(1(2(0(4(x1))))))))))) -> 3(0(5(1(5(0(3(1(5(3(1(x1))))))))))) 1(4(5(0(1(4(1(0(3(3(1(3(x1)))))))))))) -> 0(2(2(4(5(4(3(5(0(0(x1)))))))))) 1(5(0(5(4(3(1(3(4(4(1(4(x1)))))))))))) -> 4(5(0(3(4(5(0(5(3(2(x1)))))))))) 2(0(5(2(2(4(4(1(5(2(2(4(x1)))))))))))) -> 2(3(5(3(1(0(1(0(3(4(2(4(1(x1))))))))))))) 0(3(3(0(5(1(3(0(4(3(3(2(3(x1))))))))))))) -> 0(5(0(1(2(3(0(2(0(2(3(x1))))))))))) 3(3(5(4(5(5(4(2(3(1(1(0(1(x1))))))))))))) -> 4(1(3(3(3(4(5(2(4(3(4(1(5(x1))))))))))))) 3(5(3(0(0(1(4(5(4(2(5(1(0(x1))))))))))))) -> 3(0(2(0(0(1(2(5(3(0(0(x1))))))))))) 3(5(3(0(2(5(0(1(5(2(1(1(3(x1))))))))))))) -> 3(3(3(3(5(1(3(5(0(4(0(1(5(5(x1)))))))))))))) 0(4(0(4(1(3(4(0(2(4(0(5(0(3(x1)))))))))))))) -> 2(3(3(3(1(0(0(2(1(5(5(5(3(x1))))))))))))) 1(1(0(4(1(3(0(3(2(4(2(3(2(2(x1)))))))))))))) -> 3(0(1(4(1(5(0(5(2(0(4(4(5(1(x1)))))))))))))) 5(0(1(4(5(5(2(2(2(0(3(4(4(3(4(x1))))))))))))))) -> 5(4(1(4(1(1(3(1(2(2(2(1(3(1(2(x1))))))))))))))) 0(4(4(3(4(2(3(5(0(4(2(4(3(1(1(0(x1)))))))))))))))) -> 2(5(2(1(0(5(4(0(4(3(3(2(1(3(x1)))))))))))))) 1(3(3(0(1(2(4(1(1(4(5(5(2(3(0(0(x1)))))))))))))))) -> 0(3(5(0(5(0(0(4(4(4(2(1(4(0(2(2(x1)))))))))))))))) 3(1(2(1(1(1(4(4(1(0(2(5(2(1(3(3(x1)))))))))))))))) -> 1(3(4(2(0(3(0(5(3(1(0(1(4(4(5(3(x1)))))))))))))))) 3(3(2(5(2(3(0(5(3(1(0(2(0(1(0(4(x1)))))))))))))))) -> 0(2(0(3(5(1(2(1(5(2(4(2(3(0(4(5(x1)))))))))))))))) 3(3(3(5(5(4(0(2(1(0(1(0(4(3(4(3(x1)))))))))))))))) -> 3(2(4(4(3(5(4(0(4(4(0(4(1(4(3(3(x1)))))))))))))))) 0(5(0(2(3(3(5(1(4(5(2(5(2(0(3(4(1(2(x1)))))))))))))))))) -> 0(3(0(2(1(4(5(3(0(5(1(1(3(5(2(0(4(2(x1)))))))))))))))))) 1(5(5(2(3(3(1(3(4(0(4(5(1(0(2(5(2(0(x1)))))))))))))))))) -> 2(0(3(5(3(1(0(4(5(1(1(2(1(3(4(4(1(2(5(x1))))))))))))))))))) 3(0(3(5(1(3(4(0(1(2(3(4(5(4(4(1(1(0(x1)))))))))))))))))) -> 0(2(0(1(1(5(0(0(4(2(3(4(5(3(3(0(x1)))))))))))))))) 5(1(1(0(0(2(4(2(1(5(0(5(4(1(3(5(4(0(x1)))))))))))))))))) -> 5(0(3(1(4(5(5(2(5(1(5(1(4(3(5(5(4(x1))))))))))))))))) 1(0(1(0(4(4(1(1(2(1(2(1(4(0(4(2(1(2(5(x1))))))))))))))))))) -> 0(2(4(4(5(4(1(1(1(3(5(4(0(4(5(2(1(3(3(3(x1)))))))))))))))))))) 1(5(5(4(1(5(2(3(0(3(3(2(4(5(3(4(1(1(4(x1))))))))))))))))))) -> 4(4(0(4(4(0(0(5(5(0(5(4(0(3(3(0(1(1(4(x1))))))))))))))))))) 2(2(3(5(1(5(4(0(0(1(4(0(1(3(5(0(3(5(1(x1))))))))))))))))))) -> 2(1(5(0(2(1(4(4(3(1(3(5(0(4(3(1(2(x1))))))))))))))))) 3(5(4(3(1(5(0(1(4(5(0(5(2(1(5(2(3(2(2(x1))))))))))))))))))) -> 3(4(2(4(1(4(3(4(0(1(2(2(0(0(2(2(5(2(x1)))))))))))))))))) 4(2(2(4(0(5(5(0(5(3(2(5(3(1(3(2(3(4(4(x1))))))))))))))))))) -> 2(4(5(1(4(2(1(3(2(0(1(5(4(4(4(5(2(4(x1)))))))))))))))))) 1(4(1(1(5(0(1(4(4(1(2(0(5(1(0(0(4(5(1(0(1(x1))))))))))))))))))))) -> 0(4(3(5(3(4(2(4(2(4(1(0(2(4(4(1(3(4(4(4(1(x1))))))))))))))))))))) 4(0(3(0(3(4(2(2(1(3(5(4(4(5(3(1(2(0(1(4(1(x1))))))))))))))))))))) -> 2(1(0(2(5(0(0(2(0(3(3(0(5(0(2(1(3(1(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_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(x1)))) -> 2(1(2(x1))) 0(3(4(2(2(1(x1)))))) -> 2(2(5(5(3(x1))))) 2(2(2(5(0(2(1(x1))))))) -> 4(2(4(5(4(4(5(x1))))))) 2(2(5(1(1(3(4(x1))))))) -> 2(5(0(3(3(4(x1)))))) 3(2(2(4(0(3(4(x1))))))) -> 3(2(1(0(4(0(x1)))))) 4(5(1(4(2(4(1(x1))))))) -> 0(0(4(4(0(1(x1)))))) 0(3(4(3(0(0(0(3(x1)))))))) -> 2(2(1(1(4(2(3(x1))))))) 0(4(4(3(4(1(0(4(x1)))))))) -> 2(5(2(0(3(1(x1)))))) 4(4(1(5(1(3(1(1(3(x1))))))))) -> 3(2(2(1(3(0(0(x1))))))) 1(4(5(3(3(1(1(1(4(3(x1)))))))))) -> 3(0(4(0(5(0(0(3(x1)))))))) 1(0(3(2(4(5(3(3(2(3(5(x1))))))))))) -> 4(0(3(0(1(2(3(2(3(5(x1)))))))))) 1(0(3(5(5(2(0(0(4(2(5(x1))))))))))) -> 3(0(2(0(1(1(1(3(3(3(5(3(x1)))))))))))) 3(1(5(1(2(4(5(1(4(5(2(x1))))))))))) -> 3(2(2(2(5(0(0(3(2(x1))))))))) 3(3(4(4(0(4(0(1(2(0(4(x1))))))))))) -> 3(0(5(1(5(0(3(1(5(3(1(x1))))))))))) 1(4(5(0(1(4(1(0(3(3(1(3(x1)))))))))))) -> 0(2(2(4(5(4(3(5(0(0(x1)))))))))) 1(5(0(5(4(3(1(3(4(4(1(4(x1)))))))))))) -> 4(5(0(3(4(5(0(5(3(2(x1)))))))))) 2(0(5(2(2(4(4(1(5(2(2(4(x1)))))))))))) -> 2(3(5(3(1(0(1(0(3(4(2(4(1(x1))))))))))))) 0(3(3(0(5(1(3(0(4(3(3(2(3(x1))))))))))))) -> 0(5(0(1(2(3(0(2(0(2(3(x1))))))))))) 3(3(5(4(5(5(4(2(3(1(1(0(1(x1))))))))))))) -> 4(1(3(3(3(4(5(2(4(3(4(1(5(x1))))))))))))) 3(5(3(0(0(1(4(5(4(2(5(1(0(x1))))))))))))) -> 3(0(2(0(0(1(2(5(3(0(0(x1))))))))))) 3(5(3(0(2(5(0(1(5(2(1(1(3(x1))))))))))))) -> 3(3(3(3(5(1(3(5(0(4(0(1(5(5(x1)))))))))))))) 0(4(0(4(1(3(4(0(2(4(0(5(0(3(x1)))))))))))))) -> 2(3(3(3(1(0(0(2(1(5(5(5(3(x1))))))))))))) 1(1(0(4(1(3(0(3(2(4(2(3(2(2(x1)))))))))))))) -> 3(0(1(4(1(5(0(5(2(0(4(4(5(1(x1)))))))))))))) 5(0(1(4(5(5(2(2(2(0(3(4(4(3(4(x1))))))))))))))) -> 5(4(1(4(1(1(3(1(2(2(2(1(3(1(2(x1))))))))))))))) 0(4(4(3(4(2(3(5(0(4(2(4(3(1(1(0(x1)))))))))))))))) -> 2(5(2(1(0(5(4(0(4(3(3(2(1(3(x1)))))))))))))) 1(3(3(0(1(2(4(1(1(4(5(5(2(3(0(0(x1)))))))))))))))) -> 0(3(5(0(5(0(0(4(4(4(2(1(4(0(2(2(x1)))))))))))))))) 3(1(2(1(1(1(4(4(1(0(2(5(2(1(3(3(x1)))))))))))))))) -> 1(3(4(2(0(3(0(5(3(1(0(1(4(4(5(3(x1)))))))))))))))) 3(3(2(5(2(3(0(5(3(1(0(2(0(1(0(4(x1)))))))))))))))) -> 0(2(0(3(5(1(2(1(5(2(4(2(3(0(4(5(x1)))))))))))))))) 3(3(3(5(5(4(0(2(1(0(1(0(4(3(4(3(x1)))))))))))))))) -> 3(2(4(4(3(5(4(0(4(4(0(4(1(4(3(3(x1)))))))))))))))) 0(5(0(2(3(3(5(1(4(5(2(5(2(0(3(4(1(2(x1)))))))))))))))))) -> 0(3(0(2(1(4(5(3(0(5(1(1(3(5(2(0(4(2(x1)))))))))))))))))) 1(5(5(2(3(3(1(3(4(0(4(5(1(0(2(5(2(0(x1)))))))))))))))))) -> 2(0(3(5(3(1(0(4(5(1(1(2(1(3(4(4(1(2(5(x1))))))))))))))))))) 3(0(3(5(1(3(4(0(1(2(3(4(5(4(4(1(1(0(x1)))))))))))))))))) -> 0(2(0(1(1(5(0(0(4(2(3(4(5(3(3(0(x1)))))))))))))))) 5(1(1(0(0(2(4(2(1(5(0(5(4(1(3(5(4(0(x1)))))))))))))))))) -> 5(0(3(1(4(5(5(2(5(1(5(1(4(3(5(5(4(x1))))))))))))))))) 1(0(1(0(4(4(1(1(2(1(2(1(4(0(4(2(1(2(5(x1))))))))))))))))))) -> 0(2(4(4(5(4(1(1(1(3(5(4(0(4(5(2(1(3(3(3(x1)))))))))))))))))))) 1(5(5(4(1(5(2(3(0(3(3(2(4(5(3(4(1(1(4(x1))))))))))))))))))) -> 4(4(0(4(4(0(0(5(5(0(5(4(0(3(3(0(1(1(4(x1))))))))))))))))))) 2(2(3(5(1(5(4(0(0(1(4(0(1(3(5(0(3(5(1(x1))))))))))))))))))) -> 2(1(5(0(2(1(4(4(3(1(3(5(0(4(3(1(2(x1))))))))))))))))) 3(5(4(3(1(5(0(1(4(5(0(5(2(1(5(2(3(2(2(x1))))))))))))))))))) -> 3(4(2(4(1(4(3(4(0(1(2(2(0(0(2(2(5(2(x1)))))))))))))))))) 4(2(2(4(0(5(5(0(5(3(2(5(3(1(3(2(3(4(4(x1))))))))))))))))))) -> 2(4(5(1(4(2(1(3(2(0(1(5(4(4(4(5(2(4(x1)))))))))))))))))) 1(4(1(1(5(0(1(4(4(1(2(0(5(1(0(0(4(5(1(0(1(x1))))))))))))))))))))) -> 0(4(3(5(3(4(2(4(2(4(1(0(2(4(4(1(3(4(4(4(1(x1))))))))))))))))))))) 4(0(3(0(3(4(2(2(1(3(5(4(4(5(3(1(2(0(1(4(1(x1))))))))))))))))))))) -> 2(1(0(2(5(0(0(2(0(3(3(0(5(0(2(1(3(1(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_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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: INNERMOST ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(x1)))) -> 2(1(2(x1))) 0(3(4(2(2(1(x1)))))) -> 2(2(5(5(3(x1))))) 2(2(2(5(0(2(1(x1))))))) -> 4(2(4(5(4(4(5(x1))))))) 2(2(5(1(1(3(4(x1))))))) -> 2(5(0(3(3(4(x1)))))) 3(2(2(4(0(3(4(x1))))))) -> 3(2(1(0(4(0(x1)))))) 4(5(1(4(2(4(1(x1))))))) -> 0(0(4(4(0(1(x1)))))) 0(3(4(3(0(0(0(3(x1)))))))) -> 2(2(1(1(4(2(3(x1))))))) 0(4(4(3(4(1(0(4(x1)))))))) -> 2(5(2(0(3(1(x1)))))) 4(4(1(5(1(3(1(1(3(x1))))))))) -> 3(2(2(1(3(0(0(x1))))))) 1(4(5(3(3(1(1(1(4(3(x1)))))))))) -> 3(0(4(0(5(0(0(3(x1)))))))) 1(0(3(2(4(5(3(3(2(3(5(x1))))))))))) -> 4(0(3(0(1(2(3(2(3(5(x1)))))))))) 1(0(3(5(5(2(0(0(4(2(5(x1))))))))))) -> 3(0(2(0(1(1(1(3(3(3(5(3(x1)))))))))))) 3(1(5(1(2(4(5(1(4(5(2(x1))))))))))) -> 3(2(2(2(5(0(0(3(2(x1))))))))) 3(3(4(4(0(4(0(1(2(0(4(x1))))))))))) -> 3(0(5(1(5(0(3(1(5(3(1(x1))))))))))) 1(4(5(0(1(4(1(0(3(3(1(3(x1)))))))))))) -> 0(2(2(4(5(4(3(5(0(0(x1)))))))))) 1(5(0(5(4(3(1(3(4(4(1(4(x1)))))))))))) -> 4(5(0(3(4(5(0(5(3(2(x1)))))))))) 2(0(5(2(2(4(4(1(5(2(2(4(x1)))))))))))) -> 2(3(5(3(1(0(1(0(3(4(2(4(1(x1))))))))))))) 0(3(3(0(5(1(3(0(4(3(3(2(3(x1))))))))))))) -> 0(5(0(1(2(3(0(2(0(2(3(x1))))))))))) 3(3(5(4(5(5(4(2(3(1(1(0(1(x1))))))))))))) -> 4(1(3(3(3(4(5(2(4(3(4(1(5(x1))))))))))))) 3(5(3(0(0(1(4(5(4(2(5(1(0(x1))))))))))))) -> 3(0(2(0(0(1(2(5(3(0(0(x1))))))))))) 3(5(3(0(2(5(0(1(5(2(1(1(3(x1))))))))))))) -> 3(3(3(3(5(1(3(5(0(4(0(1(5(5(x1)))))))))))))) 0(4(0(4(1(3(4(0(2(4(0(5(0(3(x1)))))))))))))) -> 2(3(3(3(1(0(0(2(1(5(5(5(3(x1))))))))))))) 1(1(0(4(1(3(0(3(2(4(2(3(2(2(x1)))))))))))))) -> 3(0(1(4(1(5(0(5(2(0(4(4(5(1(x1)))))))))))))) 5(0(1(4(5(5(2(2(2(0(3(4(4(3(4(x1))))))))))))))) -> 5(4(1(4(1(1(3(1(2(2(2(1(3(1(2(x1))))))))))))))) 0(4(4(3(4(2(3(5(0(4(2(4(3(1(1(0(x1)))))))))))))))) -> 2(5(2(1(0(5(4(0(4(3(3(2(1(3(x1)))))))))))))) 1(3(3(0(1(2(4(1(1(4(5(5(2(3(0(0(x1)))))))))))))))) -> 0(3(5(0(5(0(0(4(4(4(2(1(4(0(2(2(x1)))))))))))))))) 3(1(2(1(1(1(4(4(1(0(2(5(2(1(3(3(x1)))))))))))))))) -> 1(3(4(2(0(3(0(5(3(1(0(1(4(4(5(3(x1)))))))))))))))) 3(3(2(5(2(3(0(5(3(1(0(2(0(1(0(4(x1)))))))))))))))) -> 0(2(0(3(5(1(2(1(5(2(4(2(3(0(4(5(x1)))))))))))))))) 3(3(3(5(5(4(0(2(1(0(1(0(4(3(4(3(x1)))))))))))))))) -> 3(2(4(4(3(5(4(0(4(4(0(4(1(4(3(3(x1)))))))))))))))) 0(5(0(2(3(3(5(1(4(5(2(5(2(0(3(4(1(2(x1)))))))))))))))))) -> 0(3(0(2(1(4(5(3(0(5(1(1(3(5(2(0(4(2(x1)))))))))))))))))) 1(5(5(2(3(3(1(3(4(0(4(5(1(0(2(5(2(0(x1)))))))))))))))))) -> 2(0(3(5(3(1(0(4(5(1(1(2(1(3(4(4(1(2(5(x1))))))))))))))))))) 3(0(3(5(1(3(4(0(1(2(3(4(5(4(4(1(1(0(x1)))))))))))))))))) -> 0(2(0(1(1(5(0(0(4(2(3(4(5(3(3(0(x1)))))))))))))))) 5(1(1(0(0(2(4(2(1(5(0(5(4(1(3(5(4(0(x1)))))))))))))))))) -> 5(0(3(1(4(5(5(2(5(1(5(1(4(3(5(5(4(x1))))))))))))))))) 1(0(1(0(4(4(1(1(2(1(2(1(4(0(4(2(1(2(5(x1))))))))))))))))))) -> 0(2(4(4(5(4(1(1(1(3(5(4(0(4(5(2(1(3(3(3(x1)))))))))))))))))))) 1(5(5(4(1(5(2(3(0(3(3(2(4(5(3(4(1(1(4(x1))))))))))))))))))) -> 4(4(0(4(4(0(0(5(5(0(5(4(0(3(3(0(1(1(4(x1))))))))))))))))))) 2(2(3(5(1(5(4(0(0(1(4(0(1(3(5(0(3(5(1(x1))))))))))))))))))) -> 2(1(5(0(2(1(4(4(3(1(3(5(0(4(3(1(2(x1))))))))))))))))) 3(5(4(3(1(5(0(1(4(5(0(5(2(1(5(2(3(2(2(x1))))))))))))))))))) -> 3(4(2(4(1(4(3(4(0(1(2(2(0(0(2(2(5(2(x1)))))))))))))))))) 4(2(2(4(0(5(5(0(5(3(2(5(3(1(3(2(3(4(4(x1))))))))))))))))))) -> 2(4(5(1(4(2(1(3(2(0(1(5(4(4(4(5(2(4(x1)))))))))))))))))) 1(4(1(1(5(0(1(4(4(1(2(0(5(1(0(0(4(5(1(0(1(x1))))))))))))))))))))) -> 0(4(3(5(3(4(2(4(2(4(1(0(2(4(4(1(3(4(4(4(1(x1))))))))))))))))))))) 4(0(3(0(3(4(2(2(1(3(5(4(4(5(3(1(2(0(1(4(1(x1))))))))))))))))))))) -> 2(1(0(2(5(0(0(2(0(3(3(0(5(0(2(1(3(1(x1)))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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: INNERMOST ---------------------------------------- (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. "[122, 123, 124, 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, 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] {(122,123,[0_1|0, 2_1|0, 3_1|0, 4_1|0, 1_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]), (122,124,[0_1|1, 2_1|1, 3_1|1, 4_1|1, 1_1|1, 5_1|1]), (122,138,[2_1|2]), (122,140,[2_1|2]), (122,144,[2_1|2]), (122,150,[0_1|2]), (122,160,[2_1|2]), (122,165,[2_1|2]), (122,178,[2_1|2]), (122,190,[0_1|2]), (122,207,[4_1|2]), (122,213,[2_1|2]), (122,218,[2_1|2]), (122,234,[2_1|2]), (122,246,[3_1|2]), (122,251,[3_1|2]), (122,259,[1_1|2]), (122,274,[3_1|2]), (122,297,[4_1|2]), (122,309,[0_1|2]), (122,324,[3_1|2]), (122,339,[3_1|2]), (122,349,[3_1|2]), (122,362,[3_1|2]), (122,379,[0_1|2]), (122,394,[0_1|2]), (122,399,[3_1|2]), (122,405,[2_1|2]), (122,422,[2_1|2]), (122,439,[3_1|2]), (122,446,[0_1|2]), (122,455,[0_1|2]), (122,475,[4_1|2]), (122,484,[3_1|2]), (122,495,[0_1|2]), (122,514,[4_1|2]), (122,523,[2_1|2]), (122,541,[4_1|2]), (122,559,[3_1|2]), (122,572,[0_1|2]), (122,587,[5_1|2]), (122,601,[5_1|2]), (123,123,[cons_0_1|0, cons_2_1|0, cons_3_1|0, cons_4_1|0, cons_1_1|0, cons_5_1|0]), (124,123,[encArg_1|1]), (124,124,[0_1|1, 2_1|1, 3_1|1, 4_1|1, 1_1|1, 5_1|1]), (124,138,[2_1|2]), (124,140,[2_1|2]), (124,144,[2_1|2]), (124,150,[0_1|2]), (124,160,[2_1|2]), (124,165,[2_1|2]), (124,178,[2_1|2]), (124,190,[0_1|2]), (124,207,[4_1|2]), (124,213,[2_1|2]), (124,218,[2_1|2]), (124,234,[2_1|2]), (124,246,[3_1|2]), (124,251,[3_1|2]), (124,259,[1_1|2]), (124,274,[3_1|2]), (124,297,[4_1|2]), (124,309,[0_1|2]), (124,324,[3_1|2]), (124,339,[3_1|2]), (124,349,[3_1|2]), (124,362,[3_1|2]), (124,379,[0_1|2]), (124,394,[0_1|2]), (124,399,[3_1|2]), (124,405,[2_1|2]), 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(404,439,[0_1|2]), (404,484,[0_1|2]), (404,559,[0_1|2]), (404,260,[0_1|2]), (404,138,[2_1|2]), (404,140,[2_1|2]), (404,144,[2_1|2]), (404,150,[0_1|2]), (404,160,[2_1|2]), (404,165,[2_1|2]), (404,178,[2_1|2]), (404,190,[0_1|2]), (405,406,[4_1|2]), (406,407,[5_1|2]), (407,408,[1_1|2]), (408,409,[4_1|2]), (409,410,[2_1|2]), (410,411,[1_1|2]), (411,412,[3_1|2]), (412,413,[2_1|2]), (413,414,[0_1|2]), (414,415,[1_1|2]), (415,416,[5_1|2]), (416,417,[4_1|2]), (417,418,[4_1|2]), (418,419,[4_1|2]), (419,420,[5_1|2]), (420,421,[2_1|2]), (421,124,[4_1|2]), (421,207,[4_1|2]), (421,297,[4_1|2]), (421,475,[4_1|2]), (421,514,[4_1|2]), (421,541,[4_1|2]), (421,542,[4_1|2]), (421,394,[0_1|2]), (421,399,[3_1|2]), (421,405,[2_1|2]), (421,422,[2_1|2]), (422,423,[1_1|2]), (423,424,[0_1|2]), (424,425,[2_1|2]), (425,426,[5_1|2]), (426,427,[0_1|2]), (427,428,[0_1|2]), (428,429,[2_1|2]), (429,430,[0_1|2]), (430,431,[3_1|2]), (431,432,[3_1|2]), (432,433,[0_1|2]), (433,434,[5_1|2]), (434,435,[0_1|2]), (435,436,[2_1|2]), (436,437,[1_1|2]), (437,438,[3_1|2]), (437,251,[3_1|2]), (437,259,[1_1|2]), (438,124,[1_1|2]), (438,259,[1_1|2]), (438,298,[1_1|2]), (438,439,[3_1|2]), (438,446,[0_1|2]), (438,455,[0_1|2]), (438,475,[4_1|2]), (438,484,[3_1|2]), (438,495,[0_1|2]), (438,514,[4_1|2]), (438,523,[2_1|2]), (438,541,[4_1|2]), (438,559,[3_1|2]), (438,572,[0_1|2]), (439,440,[0_1|2]), (440,441,[4_1|2]), (441,442,[0_1|2]), (442,443,[5_1|2]), (443,444,[0_1|2]), (444,445,[0_1|2]), (444,140,[2_1|2]), (444,144,[2_1|2]), (444,150,[0_1|2]), (445,124,[3_1|2]), (445,246,[3_1|2]), (445,251,[3_1|2]), (445,274,[3_1|2]), (445,324,[3_1|2]), (445,339,[3_1|2]), (445,349,[3_1|2]), (445,362,[3_1|2]), (445,399,[3_1|2]), (445,439,[3_1|2]), (445,484,[3_1|2]), (445,559,[3_1|2]), (445,259,[1_1|2]), (445,297,[4_1|2]), (445,309,[0_1|2]), (445,379,[0_1|2]), (446,447,[2_1|2]), (447,448,[2_1|2]), (448,449,[4_1|2]), (449,450,[5_1|2]), (450,451,[4_1|2]), (451,452,[3_1|2]), (452,453,[5_1|2]), (453,454,[0_1|2]), (453,138,[2_1|2]), (454,124,[0_1|2]), (454,246,[0_1|2]), (454,251,[0_1|2]), (454,274,[0_1|2]), (454,324,[0_1|2]), (454,339,[0_1|2]), (454,349,[0_1|2]), (454,362,[0_1|2]), (454,399,[0_1|2]), (454,439,[0_1|2]), (454,484,[0_1|2]), (454,559,[0_1|2]), (454,260,[0_1|2]), (454,138,[2_1|2]), (454,140,[2_1|2]), (454,144,[2_1|2]), (454,150,[0_1|2]), (454,160,[2_1|2]), (454,165,[2_1|2]), (454,178,[2_1|2]), (454,190,[0_1|2]), (455,456,[4_1|2]), (456,457,[3_1|2]), (457,458,[5_1|2]), (458,459,[3_1|2]), (459,460,[4_1|2]), (460,461,[2_1|2]), (461,462,[4_1|2]), (462,463,[2_1|2]), (463,464,[4_1|2]), (464,465,[1_1|2]), (465,466,[0_1|2]), (466,467,[2_1|2]), (467,468,[4_1|2]), (468,469,[4_1|2]), (469,470,[1_1|2]), (470,471,[3_1|2]), (471,472,[4_1|2]), (472,473,[4_1|2]), (472,399,[3_1|2]), (473,474,[4_1|2]), (474,124,[1_1|2]), (474,259,[1_1|2]), (474,439,[3_1|2]), (474,446,[0_1|2]), (474,455,[0_1|2]), (474,475,[4_1|2]), (474,484,[3_1|2]), (474,495,[0_1|2]), (474,514,[4_1|2]), (474,523,[2_1|2]), (474,541,[4_1|2]), (474,559,[3_1|2]), (474,572,[0_1|2]), (475,476,[0_1|2]), (476,477,[3_1|2]), (477,478,[0_1|2]), (478,479,[1_1|2]), (479,480,[2_1|2]), (480,481,[3_1|2]), (481,482,[2_1|2]), (482,483,[3_1|2]), (482,339,[3_1|2]), (482,349,[3_1|2]), (482,362,[3_1|2]), (483,124,[5_1|2]), (483,587,[5_1|2]), (483,601,[5_1|2]), (483,236,[5_1|2]), (484,485,[0_1|2]), (485,486,[2_1|2]), (486,487,[0_1|2]), (487,488,[1_1|2]), (488,489,[1_1|2]), (489,490,[1_1|2]), (490,491,[3_1|2]), (491,492,[3_1|2]), (492,493,[3_1|2]), (492,339,[3_1|2]), (492,349,[3_1|2]), (493,494,[5_1|2]), (494,124,[3_1|2]), (494,587,[3_1|2]), (494,601,[3_1|2]), (494,161,[3_1|2]), (494,166,[3_1|2]), (494,214,[3_1|2]), (494,246,[3_1|2]), (494,251,[3_1|2]), (494,259,[1_1|2]), (494,274,[3_1|2]), (494,297,[4_1|2]), (494,309,[0_1|2]), (494,324,[3_1|2]), (494,339,[3_1|2]), (494,349,[3_1|2]), (494,362,[3_1|2]), (494,379,[0_1|2]), (495,496,[2_1|2]), (496,497,[4_1|2]), (497,498,[4_1|2]), (498,499,[5_1|2]), (499,500,[4_1|2]), (500,501,[1_1|2]), (501,502,[1_1|2]), (502,503,[1_1|2]), (503,504,[3_1|2]), (504,505,[5_1|2]), (505,506,[4_1|2]), (506,507,[0_1|2]), (507,508,[4_1|2]), (508,509,[5_1|2]), (509,510,[2_1|2]), (510,511,[1_1|2]), (511,512,[3_1|2]), (511,324,[3_1|2]), (512,513,[3_1|2]), (512,274,[3_1|2]), (512,297,[4_1|2]), (512,309,[0_1|2]), (512,324,[3_1|2]), (513,124,[3_1|2]), (513,587,[3_1|2]), (513,601,[3_1|2]), (513,161,[3_1|2]), (513,166,[3_1|2]), (513,214,[3_1|2]), (513,246,[3_1|2]), (513,251,[3_1|2]), (513,259,[1_1|2]), (513,274,[3_1|2]), (513,297,[4_1|2]), (513,309,[0_1|2]), (513,324,[3_1|2]), (513,339,[3_1|2]), (513,349,[3_1|2]), (513,362,[3_1|2]), (513,379,[0_1|2]), (514,515,[5_1|2]), (515,516,[0_1|2]), (516,517,[3_1|2]), (517,518,[4_1|2]), (518,519,[5_1|2]), (519,520,[0_1|2]), (520,521,[5_1|2]), (521,522,[3_1|2]), (521,246,[3_1|2]), (522,124,[2_1|2]), (522,207,[2_1|2, 4_1|2]), (522,297,[2_1|2]), (522,475,[2_1|2]), (522,514,[2_1|2]), (522,541,[2_1|2]), (522,213,[2_1|2]), (522,218,[2_1|2]), (522,234,[2_1|2]), (523,524,[0_1|2]), (524,525,[3_1|2]), (525,526,[5_1|2]), (526,527,[3_1|2]), (527,528,[1_1|2]), (528,529,[0_1|2]), (529,530,[4_1|2]), (530,531,[5_1|2]), (531,532,[1_1|2]), (532,533,[1_1|2]), (533,534,[2_1|2]), (534,535,[1_1|2]), (535,536,[3_1|2]), (536,537,[4_1|2]), (537,538,[4_1|2]), (538,539,[1_1|2]), (539,540,[2_1|2]), (540,124,[5_1|2]), (540,150,[5_1|2]), (540,190,[5_1|2]), (540,309,[5_1|2]), (540,379,[5_1|2]), (540,394,[5_1|2]), (540,446,[5_1|2]), (540,455,[5_1|2]), (540,495,[5_1|2]), (540,572,[5_1|2]), (540,524,[5_1|2]), (540,163,[5_1|2]), (540,587,[5_1|2]), (540,601,[5_1|2]), (541,542,[4_1|2]), (542,543,[0_1|2]), (543,544,[4_1|2]), (544,545,[4_1|2]), (545,546,[0_1|2]), (546,547,[0_1|2]), (547,548,[5_1|2]), (548,549,[5_1|2]), (549,550,[0_1|2]), (550,551,[5_1|2]), (551,552,[4_1|2]), (552,553,[0_1|2]), (553,554,[3_1|2]), (554,555,[3_1|2]), (555,556,[0_1|2]), (556,557,[1_1|2]), (557,558,[1_1|2]), (557,439,[3_1|2]), (557,446,[0_1|2]), (557,455,[0_1|2]), (558,124,[4_1|2]), (558,207,[4_1|2]), (558,297,[4_1|2]), (558,475,[4_1|2]), (558,514,[4_1|2]), (558,541,[4_1|2]), (558,394,[0_1|2]), (558,399,[3_1|2]), (558,405,[2_1|2]), (558,422,[2_1|2]), (559,560,[0_1|2]), (560,561,[1_1|2]), (561,562,[4_1|2]), (562,563,[1_1|2]), (563,564,[5_1|2]), (564,565,[0_1|2]), (565,566,[5_1|2]), (566,567,[2_1|2]), (567,568,[0_1|2]), (568,569,[4_1|2]), (569,570,[4_1|2]), (569,394,[0_1|2]), (570,571,[5_1|2]), (570,601,[5_1|2]), (571,124,[1_1|2]), (571,138,[1_1|2]), (571,140,[1_1|2]), (571,144,[1_1|2]), (571,160,[1_1|2]), (571,165,[1_1|2]), (571,178,[1_1|2]), (571,213,[1_1|2]), (571,218,[1_1|2]), (571,234,[1_1|2]), (571,405,[1_1|2]), (571,422,[1_1|2]), (571,523,[1_1|2, 2_1|2]), (571,141,[1_1|2]), (571,145,[1_1|2]), (571,253,[1_1|2]), (571,401,[1_1|2]), (571,439,[3_1|2]), (571,446,[0_1|2]), (571,455,[0_1|2]), (571,475,[4_1|2]), (571,484,[3_1|2]), (571,495,[0_1|2]), (571,514,[4_1|2]), (571,541,[4_1|2]), (571,559,[3_1|2]), (571,572,[0_1|2]), (572,573,[3_1|2]), (573,574,[5_1|2]), (574,575,[0_1|2]), (575,576,[5_1|2]), (576,577,[0_1|2]), (577,578,[0_1|2]), (578,579,[4_1|2]), (579,580,[4_1|2]), (580,581,[4_1|2]), (581,582,[2_1|2]), (582,583,[1_1|2]), (583,584,[4_1|2]), (584,585,[0_1|2]), (585,586,[2_1|2]), (585,207,[4_1|2]), (585,213,[2_1|2]), (585,218,[2_1|2]), (586,124,[2_1|2]), (586,150,[2_1|2]), (586,190,[2_1|2]), (586,309,[2_1|2]), (586,379,[2_1|2]), (586,394,[2_1|2]), (586,446,[2_1|2]), (586,455,[2_1|2]), (586,495,[2_1|2]), (586,572,[2_1|2]), (586,395,[2_1|2]), (586,207,[4_1|2]), (586,213,[2_1|2]), (586,218,[2_1|2]), (586,234,[2_1|2]), (587,588,[4_1|2]), (588,589,[1_1|2]), (589,590,[4_1|2]), (590,591,[1_1|2]), (591,592,[1_1|2]), (592,593,[3_1|2]), (593,594,[1_1|2]), (594,595,[2_1|2]), (595,596,[2_1|2]), (596,597,[2_1|2]), (597,598,[1_1|2]), (598,599,[3_1|2]), (598,259,[1_1|2]), (599,600,[1_1|2]), (600,124,[2_1|2]), (600,207,[2_1|2, 4_1|2]), (600,297,[2_1|2]), (600,475,[2_1|2]), (600,514,[2_1|2]), (600,541,[2_1|2]), (600,363,[2_1|2]), (600,213,[2_1|2]), (600,218,[2_1|2]), (600,234,[2_1|2]), (601,602,[0_1|2]), (602,603,[3_1|2]), (603,604,[1_1|2]), (604,605,[4_1|2]), (605,606,[5_1|2]), (606,607,[5_1|2]), (607,608,[2_1|2]), (608,609,[5_1|2]), (609,610,[1_1|2]), (610,611,[5_1|2]), (611,612,[1_1|2]), (612,613,[4_1|2]), (613,614,[3_1|2]), (614,615,[5_1|2]), (615,616,[5_1|2]), (616,124,[4_1|2]), (616,150,[4_1|2]), (616,190,[4_1|2]), (616,309,[4_1|2]), (616,379,[4_1|2]), (616,394,[4_1|2, 0_1|2]), (616,446,[4_1|2]), (616,455,[4_1|2]), (616,495,[4_1|2]), (616,572,[4_1|2]), (616,476,[4_1|2]), (616,399,[3_1|2]), (616,405,[2_1|2]), (616,422,[2_1|2]), (617,618,[1_1|3]), (618,345,[2_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)