/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 58 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 143 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(1(2(1(x1)))) -> 0(3(4(1(x1)))) 1(3(5(5(x1)))) -> 3(1(2(x1))) 2(0(2(3(4(x1))))) -> 2(4(4(1(x1)))) 2(3(4(3(2(x1))))) -> 0(3(1(3(x1)))) 4(1(0(3(0(0(x1)))))) -> 4(0(5(3(2(0(x1)))))) 5(0(2(4(1(5(x1)))))) -> 5(4(4(2(4(x1))))) 0(5(3(5(0(2(3(x1))))))) -> 4(0(1(1(1(3(x1)))))) 4(3(1(4(2(4(0(x1))))))) -> 1(0(3(5(2(1(4(x1))))))) 2(0(3(3(5(5(0(3(x1)))))))) -> 2(0(0(3(0(1(3(x1))))))) 3(5(5(0(0(3(5(4(x1)))))))) -> 3(4(4(1(2(0(2(x1))))))) 4(3(1(3(4(4(1(5(x1)))))))) -> 4(5(2(3(2(4(5(5(x1)))))))) 4(1(1(4(5(0(0(1(3(x1))))))))) -> 4(2(3(3(3(2(3(1(3(x1))))))))) 5(2(1(5(3(1(3(1(5(x1))))))))) -> 5(5(0(2(1(5(4(5(5(x1))))))))) 0(1(1(3(1(4(4(5(0(0(x1)))))))))) -> 5(3(2(3(4(4(4(1(2(4(x1)))))))))) 1(1(5(3(1(2(4(4(0(4(x1)))))))))) -> 3(1(2(1(4(2(2(0(4(4(x1)))))))))) 5(5(1(3(2(2(2(2(5(3(x1)))))))))) -> 5(2(1(2(2(0(2(3(3(x1))))))))) 0(5(0(3(1(3(1(5(1(5(1(x1))))))))))) -> 0(2(5(3(2(0(0(4(1(2(0(x1))))))))))) 1(1(1(3(3(3(4(4(3(1(0(x1))))))))))) -> 3(2(5(1(3(1(5(0(0(4(2(x1))))))))))) 1(4(4(3(1(0(1(2(0(1(5(x1))))))))))) -> 4(3(3(5(0(5(3(4(5(5(3(5(x1)))))))))))) 2(5(4(0(3(1(5(5(1(5(5(x1))))))))))) -> 2(4(0(1(3(4(5(4(4(5(x1)))))))))) 4(1(3(4(1(0(4(0(4(0(3(x1))))))))))) -> 4(3(2(4(5(2(4(2(5(3(3(x1))))))))))) 5(0(1(4(5(3(0(5(1(1(0(x1))))))))))) -> 5(5(3(0(0(0(5(3(3(3(1(x1))))))))))) 2(4(1(3(3(1(2(4(0(1(2(0(2(x1))))))))))))) -> 4(0(3(2(5(1(0(1(1(1(0(0(2(x1))))))))))))) 3(4(1(4(5(2(1(5(0(1(4(2(2(x1))))))))))))) -> 5(3(5(5(1(1(1(4(2(0(2(0(0(x1))))))))))))) 4(0(2(2(2(1(2(4(3(1(0(4(3(x1))))))))))))) -> 3(3(2(0(1(2(0(3(2(0(4(0(3(x1))))))))))))) 0(2(1(1(5(0(4(0(5(2(3(3(4(4(0(x1))))))))))))))) -> 0(5(1(2(3(2(1(3(3(1(1(0(3(5(4(x1))))))))))))))) 3(1(0(5(2(0(2(0(3(1(4(2(3(0(5(x1))))))))))))))) -> 3(3(1(2(4(3(3(1(5(5(2(0(5(3(5(x1))))))))))))))) 2(0(5(3(0(4(1(2(5(5(3(2(4(2(5(2(x1)))))))))))))))) -> 5(3(4(4(3(3(3(3(1(4(5(1(1(5(0(x1))))))))))))))) 4(1(2(5(5(5(5(4(2(2(4(2(4(4(2(2(x1)))))))))))))))) -> 4(5(1(0(1(4(2(1(0(4(2(5(3(2(4(5(x1)))))))))))))))) 0(3(0(5(4(2(2(0(0(5(3(5(0(1(2(2(0(x1))))))))))))))))) -> 0(2(5(5(2(3(3(4(0(4(4(5(3(3(5(5(2(x1))))))))))))))))) 4(3(2(2(1(4(2(1(4(0(5(5(5(1(1(4(3(x1))))))))))))))))) -> 3(3(1(3(1(2(1(1(0(5(1(3(1(3(4(3(x1)))))))))))))))) 0(3(0(0(5(3(5(5(2(0(4(0(2(1(5(4(3(2(x1)))))))))))))))))) -> 2(5(0(2(1(0(0(5(5(2(4(0(5(2(0(3(3(x1))))))))))))))))) 5(1(2(1(5(1(4(0(3(1(2(1(5(1(4(2(3(3(x1)))))))))))))))))) -> 5(0(0(2(3(3(2(0(0(5(0(2(0(0(1(2(3(2(x1)))))))))))))))))) 3(0(5(2(2(2(4(3(4(3(4(1(0(1(3(0(4(2(0(x1))))))))))))))))))) -> 5(3(4(2(2(4(1(4(2(3(1(5(4(0(4(4(1(2(x1)))))))))))))))))) 5(2(1(5(2(3(4(1(1(1(2(3(3(1(3(3(4(1(3(x1))))))))))))))))))) -> 0(4(2(1(0(5(3(5(0(5(0(1(2(4(2(1(2(3(x1)))))))))))))))))) 0(1(0(1(4(5(2(2(5(0(0(1(4(4(2(4(0(4(0(0(x1)))))))))))))))))))) -> 1(2(4(0(3(3(4(2(4(4(1(0(4(0(3(2(2(1(1(4(x1)))))))))))))))))))) 2(1(4(3(4(0(1(1(0(3(4(0(2(1(2(0(4(4(1(0(x1)))))))))))))))))))) -> 4(1(4(4(5(4(2(2(2(5(5(3(4(4(0(2(5(5(0(1(x1)))))))))))))))))))) 5(3(1(0(2(0(0(5(0(2(1(0(5(5(1(5(3(2(0(1(x1)))))))))))))))))))) -> 5(3(3(4(2(3(5(3(4(1(0(0(0(2(3(0(2(4(5(0(x1)))))))))))))))))))) 0(1(4(1(4(5(2(0(1(4(5(5(2(0(3(5(3(4(4(1(4(x1))))))))))))))))))))) -> 5(3(0(1(1(2(4(5(1(0(0(5(5(3(4(3(1(3(2(0(4(x1))))))))))))))))))))) 1(5(0(4(1(1(3(5(4(3(4(4(3(1(5(4(0(1(3(3(3(x1))))))))))))))))))))) -> 3(5(1(0(5(1(0(3(1(3(2(2(1(0(4(4(2(1(3(0(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_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) 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 (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(1(x1)))) -> 0(3(4(1(x1)))) 1(3(5(5(x1)))) -> 3(1(2(x1))) 2(0(2(3(4(x1))))) -> 2(4(4(1(x1)))) 2(3(4(3(2(x1))))) -> 0(3(1(3(x1)))) 4(1(0(3(0(0(x1)))))) -> 4(0(5(3(2(0(x1)))))) 5(0(2(4(1(5(x1)))))) -> 5(4(4(2(4(x1))))) 0(5(3(5(0(2(3(x1))))))) -> 4(0(1(1(1(3(x1)))))) 4(3(1(4(2(4(0(x1))))))) -> 1(0(3(5(2(1(4(x1))))))) 2(0(3(3(5(5(0(3(x1)))))))) -> 2(0(0(3(0(1(3(x1))))))) 3(5(5(0(0(3(5(4(x1)))))))) -> 3(4(4(1(2(0(2(x1))))))) 4(3(1(3(4(4(1(5(x1)))))))) -> 4(5(2(3(2(4(5(5(x1)))))))) 4(1(1(4(5(0(0(1(3(x1))))))))) -> 4(2(3(3(3(2(3(1(3(x1))))))))) 5(2(1(5(3(1(3(1(5(x1))))))))) -> 5(5(0(2(1(5(4(5(5(x1))))))))) 0(1(1(3(1(4(4(5(0(0(x1)))))))))) -> 5(3(2(3(4(4(4(1(2(4(x1)))))))))) 1(1(5(3(1(2(4(4(0(4(x1)))))))))) -> 3(1(2(1(4(2(2(0(4(4(x1)))))))))) 5(5(1(3(2(2(2(2(5(3(x1)))))))))) -> 5(2(1(2(2(0(2(3(3(x1))))))))) 0(5(0(3(1(3(1(5(1(5(1(x1))))))))))) -> 0(2(5(3(2(0(0(4(1(2(0(x1))))))))))) 1(1(1(3(3(3(4(4(3(1(0(x1))))))))))) -> 3(2(5(1(3(1(5(0(0(4(2(x1))))))))))) 1(4(4(3(1(0(1(2(0(1(5(x1))))))))))) -> 4(3(3(5(0(5(3(4(5(5(3(5(x1)))))))))))) 2(5(4(0(3(1(5(5(1(5(5(x1))))))))))) -> 2(4(0(1(3(4(5(4(4(5(x1)))))))))) 4(1(3(4(1(0(4(0(4(0(3(x1))))))))))) -> 4(3(2(4(5(2(4(2(5(3(3(x1))))))))))) 5(0(1(4(5(3(0(5(1(1(0(x1))))))))))) -> 5(5(3(0(0(0(5(3(3(3(1(x1))))))))))) 2(4(1(3(3(1(2(4(0(1(2(0(2(x1))))))))))))) -> 4(0(3(2(5(1(0(1(1(1(0(0(2(x1))))))))))))) 3(4(1(4(5(2(1(5(0(1(4(2(2(x1))))))))))))) -> 5(3(5(5(1(1(1(4(2(0(2(0(0(x1))))))))))))) 4(0(2(2(2(1(2(4(3(1(0(4(3(x1))))))))))))) -> 3(3(2(0(1(2(0(3(2(0(4(0(3(x1))))))))))))) 0(2(1(1(5(0(4(0(5(2(3(3(4(4(0(x1))))))))))))))) -> 0(5(1(2(3(2(1(3(3(1(1(0(3(5(4(x1))))))))))))))) 3(1(0(5(2(0(2(0(3(1(4(2(3(0(5(x1))))))))))))))) -> 3(3(1(2(4(3(3(1(5(5(2(0(5(3(5(x1))))))))))))))) 2(0(5(3(0(4(1(2(5(5(3(2(4(2(5(2(x1)))))))))))))))) -> 5(3(4(4(3(3(3(3(1(4(5(1(1(5(0(x1))))))))))))))) 4(1(2(5(5(5(5(4(2(2(4(2(4(4(2(2(x1)))))))))))))))) -> 4(5(1(0(1(4(2(1(0(4(2(5(3(2(4(5(x1)))))))))))))))) 0(3(0(5(4(2(2(0(0(5(3(5(0(1(2(2(0(x1))))))))))))))))) -> 0(2(5(5(2(3(3(4(0(4(4(5(3(3(5(5(2(x1))))))))))))))))) 4(3(2(2(1(4(2(1(4(0(5(5(5(1(1(4(3(x1))))))))))))))))) -> 3(3(1(3(1(2(1(1(0(5(1(3(1(3(4(3(x1)))))))))))))))) 0(3(0(0(5(3(5(5(2(0(4(0(2(1(5(4(3(2(x1)))))))))))))))))) -> 2(5(0(2(1(0(0(5(5(2(4(0(5(2(0(3(3(x1))))))))))))))))) 5(1(2(1(5(1(4(0(3(1(2(1(5(1(4(2(3(3(x1)))))))))))))))))) -> 5(0(0(2(3(3(2(0(0(5(0(2(0(0(1(2(3(2(x1)))))))))))))))))) 3(0(5(2(2(2(4(3(4(3(4(1(0(1(3(0(4(2(0(x1))))))))))))))))))) -> 5(3(4(2(2(4(1(4(2(3(1(5(4(0(4(4(1(2(x1)))))))))))))))))) 5(2(1(5(2(3(4(1(1(1(2(3(3(1(3(3(4(1(3(x1))))))))))))))))))) -> 0(4(2(1(0(5(3(5(0(5(0(1(2(4(2(1(2(3(x1)))))))))))))))))) 0(1(0(1(4(5(2(2(5(0(0(1(4(4(2(4(0(4(0(0(x1)))))))))))))))))))) -> 1(2(4(0(3(3(4(2(4(4(1(0(4(0(3(2(2(1(1(4(x1)))))))))))))))))))) 2(1(4(3(4(0(1(1(0(3(4(0(2(1(2(0(4(4(1(0(x1)))))))))))))))))))) -> 4(1(4(4(5(4(2(2(2(5(5(3(4(4(0(2(5(5(0(1(x1)))))))))))))))))))) 5(3(1(0(2(0(0(5(0(2(1(0(5(5(1(5(3(2(0(1(x1)))))))))))))))))))) -> 5(3(3(4(2(3(5(3(4(1(0(0(0(2(3(0(2(4(5(0(x1)))))))))))))))))))) 0(1(4(1(4(5(2(0(1(4(5(5(2(0(3(5(3(4(4(1(4(x1))))))))))))))))))))) -> 5(3(0(1(1(2(4(5(1(0(0(5(5(3(4(3(1(3(2(0(4(x1))))))))))))))))))))) 1(5(0(4(1(1(3(5(4(3(4(4(3(1(5(4(0(1(3(3(3(x1))))))))))))))))))))) -> 3(5(1(0(5(1(0(3(1(3(2(2(1(0(4(4(2(1(3(0(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_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(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: 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(1(2(1(x1)))) -> 0(3(4(1(x1)))) 1(3(5(5(x1)))) -> 3(1(2(x1))) 2(0(2(3(4(x1))))) -> 2(4(4(1(x1)))) 2(3(4(3(2(x1))))) -> 0(3(1(3(x1)))) 4(1(0(3(0(0(x1)))))) -> 4(0(5(3(2(0(x1)))))) 5(0(2(4(1(5(x1)))))) -> 5(4(4(2(4(x1))))) 0(5(3(5(0(2(3(x1))))))) -> 4(0(1(1(1(3(x1)))))) 4(3(1(4(2(4(0(x1))))))) -> 1(0(3(5(2(1(4(x1))))))) 2(0(3(3(5(5(0(3(x1)))))))) -> 2(0(0(3(0(1(3(x1))))))) 3(5(5(0(0(3(5(4(x1)))))))) -> 3(4(4(1(2(0(2(x1))))))) 4(3(1(3(4(4(1(5(x1)))))))) -> 4(5(2(3(2(4(5(5(x1)))))))) 4(1(1(4(5(0(0(1(3(x1))))))))) -> 4(2(3(3(3(2(3(1(3(x1))))))))) 5(2(1(5(3(1(3(1(5(x1))))))))) -> 5(5(0(2(1(5(4(5(5(x1))))))))) 0(1(1(3(1(4(4(5(0(0(x1)))))))))) -> 5(3(2(3(4(4(4(1(2(4(x1)))))))))) 1(1(5(3(1(2(4(4(0(4(x1)))))))))) -> 3(1(2(1(4(2(2(0(4(4(x1)))))))))) 5(5(1(3(2(2(2(2(5(3(x1)))))))))) -> 5(2(1(2(2(0(2(3(3(x1))))))))) 0(5(0(3(1(3(1(5(1(5(1(x1))))))))))) -> 0(2(5(3(2(0(0(4(1(2(0(x1))))))))))) 1(1(1(3(3(3(4(4(3(1(0(x1))))))))))) -> 3(2(5(1(3(1(5(0(0(4(2(x1))))))))))) 1(4(4(3(1(0(1(2(0(1(5(x1))))))))))) -> 4(3(3(5(0(5(3(4(5(5(3(5(x1)))))))))))) 2(5(4(0(3(1(5(5(1(5(5(x1))))))))))) -> 2(4(0(1(3(4(5(4(4(5(x1)))))))))) 4(1(3(4(1(0(4(0(4(0(3(x1))))))))))) -> 4(3(2(4(5(2(4(2(5(3(3(x1))))))))))) 5(0(1(4(5(3(0(5(1(1(0(x1))))))))))) -> 5(5(3(0(0(0(5(3(3(3(1(x1))))))))))) 2(4(1(3(3(1(2(4(0(1(2(0(2(x1))))))))))))) -> 4(0(3(2(5(1(0(1(1(1(0(0(2(x1))))))))))))) 3(4(1(4(5(2(1(5(0(1(4(2(2(x1))))))))))))) -> 5(3(5(5(1(1(1(4(2(0(2(0(0(x1))))))))))))) 4(0(2(2(2(1(2(4(3(1(0(4(3(x1))))))))))))) -> 3(3(2(0(1(2(0(3(2(0(4(0(3(x1))))))))))))) 0(2(1(1(5(0(4(0(5(2(3(3(4(4(0(x1))))))))))))))) -> 0(5(1(2(3(2(1(3(3(1(1(0(3(5(4(x1))))))))))))))) 3(1(0(5(2(0(2(0(3(1(4(2(3(0(5(x1))))))))))))))) -> 3(3(1(2(4(3(3(1(5(5(2(0(5(3(5(x1))))))))))))))) 2(0(5(3(0(4(1(2(5(5(3(2(4(2(5(2(x1)))))))))))))))) -> 5(3(4(4(3(3(3(3(1(4(5(1(1(5(0(x1))))))))))))))) 4(1(2(5(5(5(5(4(2(2(4(2(4(4(2(2(x1)))))))))))))))) -> 4(5(1(0(1(4(2(1(0(4(2(5(3(2(4(5(x1)))))))))))))))) 0(3(0(5(4(2(2(0(0(5(3(5(0(1(2(2(0(x1))))))))))))))))) -> 0(2(5(5(2(3(3(4(0(4(4(5(3(3(5(5(2(x1))))))))))))))))) 4(3(2(2(1(4(2(1(4(0(5(5(5(1(1(4(3(x1))))))))))))))))) -> 3(3(1(3(1(2(1(1(0(5(1(3(1(3(4(3(x1)))))))))))))))) 0(3(0(0(5(3(5(5(2(0(4(0(2(1(5(4(3(2(x1)))))))))))))))))) -> 2(5(0(2(1(0(0(5(5(2(4(0(5(2(0(3(3(x1))))))))))))))))) 5(1(2(1(5(1(4(0(3(1(2(1(5(1(4(2(3(3(x1)))))))))))))))))) -> 5(0(0(2(3(3(2(0(0(5(0(2(0(0(1(2(3(2(x1)))))))))))))))))) 3(0(5(2(2(2(4(3(4(3(4(1(0(1(3(0(4(2(0(x1))))))))))))))))))) -> 5(3(4(2(2(4(1(4(2(3(1(5(4(0(4(4(1(2(x1)))))))))))))))))) 5(2(1(5(2(3(4(1(1(1(2(3(3(1(3(3(4(1(3(x1))))))))))))))))))) -> 0(4(2(1(0(5(3(5(0(5(0(1(2(4(2(1(2(3(x1)))))))))))))))))) 0(1(0(1(4(5(2(2(5(0(0(1(4(4(2(4(0(4(0(0(x1)))))))))))))))))))) -> 1(2(4(0(3(3(4(2(4(4(1(0(4(0(3(2(2(1(1(4(x1)))))))))))))))))))) 2(1(4(3(4(0(1(1(0(3(4(0(2(1(2(0(4(4(1(0(x1)))))))))))))))))))) -> 4(1(4(4(5(4(2(2(2(5(5(3(4(4(0(2(5(5(0(1(x1)))))))))))))))))))) 5(3(1(0(2(0(0(5(0(2(1(0(5(5(1(5(3(2(0(1(x1)))))))))))))))))))) -> 5(3(3(4(2(3(5(3(4(1(0(0(0(2(3(0(2(4(5(0(x1)))))))))))))))))))) 0(1(4(1(4(5(2(0(1(4(5(5(2(0(3(5(3(4(4(1(4(x1))))))))))))))))))))) -> 5(3(0(1(1(2(4(5(1(0(0(5(5(3(4(3(1(3(2(0(4(x1))))))))))))))))))))) 1(5(0(4(1(1(3(5(4(3(4(4(3(1(5(4(0(1(3(3(3(x1))))))))))))))))))))) -> 3(5(1(0(5(1(0(3(1(3(2(2(1(0(4(4(2(1(3(0(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_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(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: 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(1(2(1(x1)))) -> 0(3(4(1(x1)))) 1(3(5(5(x1)))) -> 3(1(2(x1))) 2(0(2(3(4(x1))))) -> 2(4(4(1(x1)))) 2(3(4(3(2(x1))))) -> 0(3(1(3(x1)))) 4(1(0(3(0(0(x1)))))) -> 4(0(5(3(2(0(x1)))))) 5(0(2(4(1(5(x1)))))) -> 5(4(4(2(4(x1))))) 0(5(3(5(0(2(3(x1))))))) -> 4(0(1(1(1(3(x1)))))) 4(3(1(4(2(4(0(x1))))))) -> 1(0(3(5(2(1(4(x1))))))) 2(0(3(3(5(5(0(3(x1)))))))) -> 2(0(0(3(0(1(3(x1))))))) 3(5(5(0(0(3(5(4(x1)))))))) -> 3(4(4(1(2(0(2(x1))))))) 4(3(1(3(4(4(1(5(x1)))))))) -> 4(5(2(3(2(4(5(5(x1)))))))) 4(1(1(4(5(0(0(1(3(x1))))))))) -> 4(2(3(3(3(2(3(1(3(x1))))))))) 5(2(1(5(3(1(3(1(5(x1))))))))) -> 5(5(0(2(1(5(4(5(5(x1))))))))) 0(1(1(3(1(4(4(5(0(0(x1)))))))))) -> 5(3(2(3(4(4(4(1(2(4(x1)))))))))) 1(1(5(3(1(2(4(4(0(4(x1)))))))))) -> 3(1(2(1(4(2(2(0(4(4(x1)))))))))) 5(5(1(3(2(2(2(2(5(3(x1)))))))))) -> 5(2(1(2(2(0(2(3(3(x1))))))))) 0(5(0(3(1(3(1(5(1(5(1(x1))))))))))) -> 0(2(5(3(2(0(0(4(1(2(0(x1))))))))))) 1(1(1(3(3(3(4(4(3(1(0(x1))))))))))) -> 3(2(5(1(3(1(5(0(0(4(2(x1))))))))))) 1(4(4(3(1(0(1(2(0(1(5(x1))))))))))) -> 4(3(3(5(0(5(3(4(5(5(3(5(x1)))))))))))) 2(5(4(0(3(1(5(5(1(5(5(x1))))))))))) -> 2(4(0(1(3(4(5(4(4(5(x1)))))))))) 4(1(3(4(1(0(4(0(4(0(3(x1))))))))))) -> 4(3(2(4(5(2(4(2(5(3(3(x1))))))))))) 5(0(1(4(5(3(0(5(1(1(0(x1))))))))))) -> 5(5(3(0(0(0(5(3(3(3(1(x1))))))))))) 2(4(1(3(3(1(2(4(0(1(2(0(2(x1))))))))))))) -> 4(0(3(2(5(1(0(1(1(1(0(0(2(x1))))))))))))) 3(4(1(4(5(2(1(5(0(1(4(2(2(x1))))))))))))) -> 5(3(5(5(1(1(1(4(2(0(2(0(0(x1))))))))))))) 4(0(2(2(2(1(2(4(3(1(0(4(3(x1))))))))))))) -> 3(3(2(0(1(2(0(3(2(0(4(0(3(x1))))))))))))) 0(2(1(1(5(0(4(0(5(2(3(3(4(4(0(x1))))))))))))))) -> 0(5(1(2(3(2(1(3(3(1(1(0(3(5(4(x1))))))))))))))) 3(1(0(5(2(0(2(0(3(1(4(2(3(0(5(x1))))))))))))))) -> 3(3(1(2(4(3(3(1(5(5(2(0(5(3(5(x1))))))))))))))) 2(0(5(3(0(4(1(2(5(5(3(2(4(2(5(2(x1)))))))))))))))) -> 5(3(4(4(3(3(3(3(1(4(5(1(1(5(0(x1))))))))))))))) 4(1(2(5(5(5(5(4(2(2(4(2(4(4(2(2(x1)))))))))))))))) -> 4(5(1(0(1(4(2(1(0(4(2(5(3(2(4(5(x1)))))))))))))))) 0(3(0(5(4(2(2(0(0(5(3(5(0(1(2(2(0(x1))))))))))))))))) -> 0(2(5(5(2(3(3(4(0(4(4(5(3(3(5(5(2(x1))))))))))))))))) 4(3(2(2(1(4(2(1(4(0(5(5(5(1(1(4(3(x1))))))))))))))))) -> 3(3(1(3(1(2(1(1(0(5(1(3(1(3(4(3(x1)))))))))))))))) 0(3(0(0(5(3(5(5(2(0(4(0(2(1(5(4(3(2(x1)))))))))))))))))) -> 2(5(0(2(1(0(0(5(5(2(4(0(5(2(0(3(3(x1))))))))))))))))) 5(1(2(1(5(1(4(0(3(1(2(1(5(1(4(2(3(3(x1)))))))))))))))))) -> 5(0(0(2(3(3(2(0(0(5(0(2(0(0(1(2(3(2(x1)))))))))))))))))) 3(0(5(2(2(2(4(3(4(3(4(1(0(1(3(0(4(2(0(x1))))))))))))))))))) -> 5(3(4(2(2(4(1(4(2(3(1(5(4(0(4(4(1(2(x1)))))))))))))))))) 5(2(1(5(2(3(4(1(1(1(2(3(3(1(3(3(4(1(3(x1))))))))))))))))))) -> 0(4(2(1(0(5(3(5(0(5(0(1(2(4(2(1(2(3(x1)))))))))))))))))) 0(1(0(1(4(5(2(2(5(0(0(1(4(4(2(4(0(4(0(0(x1)))))))))))))))))))) -> 1(2(4(0(3(3(4(2(4(4(1(0(4(0(3(2(2(1(1(4(x1)))))))))))))))))))) 2(1(4(3(4(0(1(1(0(3(4(0(2(1(2(0(4(4(1(0(x1)))))))))))))))))))) -> 4(1(4(4(5(4(2(2(2(5(5(3(4(4(0(2(5(5(0(1(x1)))))))))))))))))))) 5(3(1(0(2(0(0(5(0(2(1(0(5(5(1(5(3(2(0(1(x1)))))))))))))))))))) -> 5(3(3(4(2(3(5(3(4(1(0(0(0(2(3(0(2(4(5(0(x1)))))))))))))))))))) 0(1(4(1(4(5(2(0(1(4(5(5(2(0(3(5(3(4(4(1(4(x1))))))))))))))))))))) -> 5(3(0(1(1(2(4(5(1(0(0(5(5(3(4(3(1(3(2(0(4(x1))))))))))))))))))))) 1(5(0(4(1(1(3(5(4(3(4(4(3(1(5(4(0(1(3(3(3(x1))))))))))))))))))))) -> 3(5(1(0(5(1(0(3(1(3(2(2(1(0(4(4(2(1(3(0(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_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(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: 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. "[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] {(148,149,[0_1|0, 1_1|0, 2_1|0, 4_1|0, 5_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]), (148,150,[0_1|1, 1_1|1, 2_1|1, 4_1|1, 5_1|1, 3_1|1]), (148,151,[0_1|2]), (148,154,[5_1|2]), (148,163,[1_1|2]), (148,182,[5_1|2]), (148,202,[4_1|2]), (148,207,[0_1|2]), (148,217,[0_1|2]), (148,231,[0_1|2]), (148,247,[2_1|2]), (148,263,[3_1|2]), (148,265,[3_1|2]), (148,274,[3_1|2]), (148,284,[4_1|2]), (148,295,[3_1|2]), (148,314,[2_1|2]), (148,317,[2_1|2]), (148,323,[5_1|2]), (148,337,[0_1|2]), (148,340,[2_1|2]), (148,349,[4_1|2]), (148,361,[4_1|2]), (148,380,[4_1|2]), (148,385,[4_1|2]), (148,393,[4_1|2]), (148,403,[4_1|2]), (148,418,[1_1|2]), (148,424,[4_1|2]), (148,431,[3_1|2]), (148,446,[3_1|2]), (148,458,[5_1|2]), (148,462,[5_1|2]), (148,472,[5_1|2]), (148,480,[0_1|2]), (148,497,[5_1|2]), (148,505,[5_1|2]), (148,522,[5_1|2]), (148,541,[3_1|2]), (148,547,[5_1|2]), (148,559,[3_1|2]), (148,573,[5_1|2]), (149,149,[cons_0_1|0, cons_1_1|0, cons_2_1|0, cons_4_1|0, cons_5_1|0, cons_3_1|0]), (150,149,[encArg_1|1]), (150,150,[0_1|1, 1_1|1, 2_1|1, 4_1|1, 5_1|1, 3_1|1]), (150,151,[0_1|2]), (150,154,[5_1|2]), (150,163,[1_1|2]), (150,182,[5_1|2]), (150,202,[4_1|2]), (150,207,[0_1|2]), (150,217,[0_1|2]), (150,231,[0_1|2]), (150,247,[2_1|2]), (150,263,[3_1|2]), (150,265,[3_1|2]), (150,274,[3_1|2]), (150,284,[4_1|2]), (150,295,[3_1|2]), (150,314,[2_1|2]), (150,317,[2_1|2]), (150,323,[5_1|2]), (150,337,[0_1|2]), (150,340,[2_1|2]), (150,349,[4_1|2]), (150,361,[4_1|2]), (150,380,[4_1|2]), (150,385,[4_1|2]), (150,393,[4_1|2]), (150,403,[4_1|2]), (150,418,[1_1|2]), (150,424,[4_1|2]), (150,431,[3_1|2]), (150,446,[3_1|2]), (150,458,[5_1|2]), (150,462,[5_1|2]), (150,472,[5_1|2]), (150,480,[0_1|2]), (150,497,[5_1|2]), (150,505,[5_1|2]), (150,522,[5_1|2]), (150,541,[3_1|2]), (150,547,[5_1|2]), (150,559,[3_1|2]), (150,573,[5_1|2]), (151,152,[3_1|2]), (151,547,[5_1|2]), (152,153,[4_1|2]), (152,380,[4_1|2]), (152,385,[4_1|2]), (152,393,[4_1|2]), (152,403,[4_1|2]), (153,150,[1_1|2]), (153,163,[1_1|2]), (153,418,[1_1|2]), (153,263,[3_1|2]), (153,265,[3_1|2]), (153,274,[3_1|2]), (153,284,[4_1|2]), (153,295,[3_1|2]), (154,155,[3_1|2]), (155,156,[2_1|2]), (156,157,[3_1|2]), (157,158,[4_1|2]), (158,159,[4_1|2]), (159,160,[4_1|2]), (160,161,[1_1|2]), (161,162,[2_1|2]), (161,349,[4_1|2]), (162,150,[4_1|2]), (162,151,[4_1|2]), (162,207,[4_1|2]), (162,217,[4_1|2]), (162,231,[4_1|2]), (162,337,[4_1|2]), (162,480,[4_1|2]), (162,507,[4_1|2]), (162,380,[4_1|2]), (162,385,[4_1|2]), (162,393,[4_1|2]), (162,403,[4_1|2]), (162,418,[1_1|2]), (162,424,[4_1|2]), (162,431,[3_1|2]), (162,446,[3_1|2]), (162,598,[4_1|3]), 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(430,154,[5_1|2]), (430,182,[5_1|2]), (430,323,[5_1|2]), (430,458,[5_1|2]), (430,462,[5_1|2]), (430,472,[5_1|2]), (430,497,[5_1|2]), (430,505,[5_1|2]), (430,522,[5_1|2]), (430,547,[5_1|2]), (430,573,[5_1|2]), (430,480,[0_1|2]), (431,432,[3_1|2]), (432,433,[1_1|2]), (433,434,[3_1|2]), (434,435,[1_1|2]), (435,436,[2_1|2]), (436,437,[1_1|2]), (437,438,[1_1|2]), (438,439,[0_1|2]), (439,440,[5_1|2]), (440,441,[1_1|2]), (441,442,[3_1|2]), (442,443,[1_1|2]), (443,444,[3_1|2]), (444,445,[4_1|2]), (444,418,[1_1|2]), (444,424,[4_1|2]), (444,431,[3_1|2]), (445,150,[3_1|2]), (445,263,[3_1|2]), (445,265,[3_1|2]), (445,274,[3_1|2]), (445,295,[3_1|2]), (445,431,[3_1|2]), (445,446,[3_1|2]), (445,541,[3_1|2]), (445,559,[3_1|2]), (445,285,[3_1|2]), (445,394,[3_1|2]), (445,547,[5_1|2]), (445,573,[5_1|2]), (446,447,[3_1|2]), (447,448,[2_1|2]), (448,449,[0_1|2]), (449,450,[1_1|2]), (450,451,[2_1|2]), (451,452,[0_1|2]), (452,453,[3_1|2]), (453,454,[2_1|2]), (454,455,[0_1|2]), (455,456,[4_1|2]), (456,457,[0_1|2]), (456,231,[0_1|2]), (456,247,[2_1|2]), (457,150,[3_1|2]), (457,263,[3_1|2]), (457,265,[3_1|2]), (457,274,[3_1|2]), (457,295,[3_1|2]), (457,431,[3_1|2]), (457,446,[3_1|2]), (457,541,[3_1|2]), (457,559,[3_1|2]), (457,285,[3_1|2]), (457,394,[3_1|2]), (457,547,[5_1|2]), (457,573,[5_1|2]), (458,459,[4_1|2]), (459,460,[4_1|2]), (460,461,[2_1|2]), (460,349,[4_1|2]), (461,150,[4_1|2]), (461,154,[4_1|2]), (461,182,[4_1|2]), (461,323,[4_1|2]), (461,458,[4_1|2]), (461,462,[4_1|2]), (461,472,[4_1|2]), (461,497,[4_1|2]), (461,505,[4_1|2]), (461,522,[4_1|2]), (461,547,[4_1|2]), (461,573,[4_1|2]), (461,380,[4_1|2]), (461,385,[4_1|2]), (461,393,[4_1|2]), (461,403,[4_1|2]), (461,418,[1_1|2]), (461,424,[4_1|2]), (461,431,[3_1|2]), (461,446,[3_1|2]), (462,463,[5_1|2]), (463,464,[3_1|2]), (464,465,[0_1|2]), (465,466,[0_1|2]), (466,467,[0_1|2]), (467,468,[5_1|2]), (468,469,[3_1|2]), (469,470,[3_1|2]), (470,471,[3_1|2]), (470,559,[3_1|2]), (471,150,[1_1|2]), (471,151,[1_1|2]), (471,207,[1_1|2]), (471,217,[1_1|2]), (471,231,[1_1|2]), (471,337,[1_1|2]), (471,480,[1_1|2]), (471,419,[1_1|2]), (471,263,[3_1|2]), (471,265,[3_1|2]), (471,274,[3_1|2]), (471,284,[4_1|2]), (471,295,[3_1|2]), (472,473,[5_1|2]), (473,474,[0_1|2]), (474,475,[2_1|2]), (475,476,[1_1|2]), (476,477,[5_1|2]), (477,478,[4_1|2]), (478,479,[5_1|2]), (478,497,[5_1|2]), (479,150,[5_1|2]), (479,154,[5_1|2]), (479,182,[5_1|2]), (479,323,[5_1|2]), (479,458,[5_1|2]), (479,462,[5_1|2]), (479,472,[5_1|2]), (479,497,[5_1|2]), (479,505,[5_1|2]), (479,522,[5_1|2]), (479,547,[5_1|2]), (479,573,[5_1|2]), (479,480,[0_1|2]), (480,481,[4_1|2]), (481,482,[2_1|2]), (482,483,[1_1|2]), (483,484,[0_1|2]), (484,485,[5_1|2]), (485,486,[3_1|2]), (486,487,[5_1|2]), (487,488,[0_1|2]), (488,489,[5_1|2]), (489,490,[0_1|2]), (490,491,[1_1|2]), (491,492,[2_1|2]), (492,493,[4_1|2]), (493,494,[2_1|2]), (494,495,[1_1|2]), (495,496,[2_1|2]), (495,337,[0_1|2]), (495,592,[0_1|3]), (496,150,[3_1|2]), (496,263,[3_1|2]), (496,265,[3_1|2]), (496,274,[3_1|2]), (496,295,[3_1|2]), (496,431,[3_1|2]), (496,446,[3_1|2]), (496,541,[3_1|2]), (496,559,[3_1|2]), (496,547,[5_1|2]), (496,573,[5_1|2]), (497,498,[2_1|2]), (498,499,[1_1|2]), (499,500,[2_1|2]), (500,501,[2_1|2]), (501,502,[0_1|2]), (502,503,[2_1|2]), (503,504,[3_1|2]), (504,150,[3_1|2]), (504,263,[3_1|2]), (504,265,[3_1|2]), (504,274,[3_1|2]), (504,295,[3_1|2]), (504,431,[3_1|2]), (504,446,[3_1|2]), (504,541,[3_1|2]), (504,559,[3_1|2]), (504,155,[3_1|2]), (504,183,[3_1|2]), (504,324,[3_1|2]), (504,523,[3_1|2]), (504,548,[3_1|2]), (504,574,[3_1|2]), (504,547,[5_1|2]), (504,573,[5_1|2]), (505,506,[0_1|2]), (506,507,[0_1|2]), (507,508,[2_1|2]), (508,509,[3_1|2]), (509,510,[3_1|2]), (510,511,[2_1|2]), (511,512,[0_1|2]), (512,513,[0_1|2]), (513,514,[5_1|2]), (514,515,[0_1|2]), (515,516,[2_1|2]), (516,517,[0_1|2]), (517,518,[0_1|2]), (518,519,[1_1|2]), (519,520,[2_1|2]), (520,521,[3_1|2]), (521,150,[2_1|2]), (521,263,[2_1|2]), (521,265,[2_1|2]), (521,274,[2_1|2]), (521,295,[2_1|2]), (521,431,[2_1|2]), (521,446,[2_1|2]), (521,541,[2_1|2]), (521,559,[2_1|2]), (521,432,[2_1|2]), (521,447,[2_1|2]), (521,560,[2_1|2]), (521,388,[2_1|2]), (521,314,[2_1|2]), (521,317,[2_1|2]), (521,323,[5_1|2]), (521,337,[0_1|2]), (521,340,[2_1|2]), (521,349,[4_1|2]), (521,361,[4_1|2]), (522,523,[3_1|2]), (523,524,[3_1|2]), (524,525,[4_1|2]), (525,526,[2_1|2]), (526,527,[3_1|2]), (527,528,[5_1|2]), (528,529,[3_1|2]), (529,530,[4_1|2]), (530,531,[1_1|2]), (531,532,[0_1|2]), (532,533,[0_1|2]), (533,534,[0_1|2]), (534,535,[2_1|2]), (535,536,[3_1|2]), (536,537,[0_1|2]), (537,538,[2_1|2]), (538,539,[4_1|2]), (539,540,[5_1|2]), (539,458,[5_1|2]), (539,462,[5_1|2]), (540,150,[0_1|2]), (540,163,[0_1|2, 1_1|2]), (540,418,[0_1|2]), (540,151,[0_1|2]), (540,154,[5_1|2]), (540,182,[5_1|2]), (540,202,[4_1|2]), (540,207,[0_1|2]), (540,217,[0_1|2]), (540,231,[0_1|2]), (540,247,[2_1|2]), (541,542,[4_1|2]), (542,543,[4_1|2]), (543,544,[1_1|2]), (544,545,[2_1|2]), (544,314,[2_1|2]), (544,595,[2_1|3]), (545,546,[0_1|2]), (545,217,[0_1|2]), (546,150,[2_1|2]), (546,202,[2_1|2]), (546,284,[2_1|2]), (546,349,[2_1|2, 4_1|2]), (546,361,[2_1|2, 4_1|2]), (546,380,[2_1|2]), (546,385,[2_1|2]), (546,393,[2_1|2]), (546,403,[2_1|2]), (546,424,[2_1|2]), (546,459,[2_1|2]), (546,314,[2_1|2]), (546,317,[2_1|2]), (546,323,[5_1|2]), (546,337,[0_1|2]), (546,340,[2_1|2]), (547,548,[3_1|2]), (548,549,[5_1|2]), (549,550,[5_1|2]), (550,551,[1_1|2]), (551,552,[1_1|2]), (552,553,[1_1|2]), (553,554,[4_1|2]), (554,555,[2_1|2]), (555,556,[0_1|2]), (556,557,[2_1|2]), (557,558,[0_1|2]), (558,150,[0_1|2]), (558,247,[0_1|2, 2_1|2]), (558,314,[0_1|2]), (558,317,[0_1|2]), (558,340,[0_1|2]), (558,151,[0_1|2]), (558,154,[5_1|2]), (558,163,[1_1|2]), (558,182,[5_1|2]), (558,202,[4_1|2]), (558,207,[0_1|2]), (558,217,[0_1|2]), (558,231,[0_1|2]), (559,560,[3_1|2]), (560,561,[1_1|2]), (561,562,[2_1|2]), (562,563,[4_1|2]), (563,564,[3_1|2]), (564,565,[3_1|2]), (565,566,[1_1|2]), (566,567,[5_1|2]), (567,568,[5_1|2]), (568,569,[2_1|2]), (569,570,[0_1|2]), (569,202,[4_1|2]), (570,571,[5_1|2]), (571,572,[3_1|2]), (571,541,[3_1|2]), (572,150,[5_1|2]), (572,154,[5_1|2]), (572,182,[5_1|2]), (572,323,[5_1|2]), (572,458,[5_1|2]), (572,462,[5_1|2]), (572,472,[5_1|2]), (572,497,[5_1|2]), (572,505,[5_1|2]), (572,522,[5_1|2]), (572,547,[5_1|2]), (572,573,[5_1|2]), (572,218,[5_1|2]), (572,480,[0_1|2]), (573,574,[3_1|2]), (574,575,[4_1|2]), (575,576,[2_1|2]), (576,577,[2_1|2]), (577,578,[4_1|2]), (578,579,[1_1|2]), (579,580,[4_1|2]), (580,581,[2_1|2]), (581,582,[3_1|2]), (582,583,[1_1|2]), (583,584,[5_1|2]), (584,585,[4_1|2]), (585,586,[0_1|2]), (586,587,[4_1|2]), (587,588,[4_1|2]), (587,403,[4_1|2]), (588,589,[1_1|2]), (589,150,[2_1|2]), (589,151,[2_1|2]), (589,207,[2_1|2]), (589,217,[2_1|2]), (589,231,[2_1|2]), (589,337,[2_1|2, 0_1|2]), (589,480,[2_1|2]), (589,318,[2_1|2]), (589,314,[2_1|2]), (589,317,[2_1|2]), (589,323,[5_1|2]), (589,340,[2_1|2]), (589,349,[4_1|2]), (589,361,[4_1|2]), (589,605,[0_1|3]), (590,591,[1_1|3]), (591,463,[2_1|3]), (591,473,[2_1|3]), (592,593,[3_1|3]), (593,594,[1_1|3]), (594,395,[3_1|3]), (595,596,[4_1|3]), (596,597,[4_1|3]), (597,542,[1_1|3]), (598,599,[5_1|3]), (599,600,[2_1|3]), (600,601,[3_1|3]), (601,602,[2_1|3]), (602,603,[4_1|3]), (603,604,[5_1|3]), (604,154,[5_1|3]), (604,182,[5_1|3]), (604,323,[5_1|3]), (604,458,[5_1|3]), (604,462,[5_1|3]), (604,472,[5_1|3]), (604,497,[5_1|3]), (604,505,[5_1|3]), (604,522,[5_1|3]), (604,547,[5_1|3]), (604,573,[5_1|3]), (604,404,[5_1|3]), (604,425,[5_1|3]), (605,606,[3_1|3]), (606,607,[1_1|3]), (607,275,[3_1|3]), (607,395,[3_1|3]), (608,609,[3_1|3]), (609,610,[4_1|3]), (610,163,[1_1|3]), (610,418,[1_1|3]), (610,268,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)