/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 87 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 297 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(0(x1)))) -> 3(4(0(x1))) 0(5(1(5(x1)))) -> 2(3(1(x1))) 2(3(3(5(1(x1))))) -> 3(5(5(3(x1)))) 4(5(1(2(0(x1))))) -> 4(5(5(3(x1)))) 0(5(3(1(1(1(x1)))))) -> 0(1(0(1(5(1(x1)))))) 0(0(1(2(4(1(1(x1))))))) -> 0(0(3(5(5(1(x1)))))) 0(2(4(3(1(1(5(x1))))))) -> 0(2(0(0(1(3(1(x1))))))) 0(3(5(0(4(0(0(x1))))))) -> 1(3(4(0(3(4(x1)))))) 1(5(4(5(5(4(5(x1))))))) -> 4(2(2(5(1(0(x1)))))) 4(4(3(5(1(0(5(x1))))))) -> 2(5(1(1(1(4(x1)))))) 3(2(5(2(2(4(0(5(1(1(x1)))))))))) -> 3(1(3(5(5(5(0(2(5(x1))))))))) 1(2(2(1(4(3(2(2(1(3(0(x1))))))))))) -> 4(2(3(3(3(5(3(1(0(1(5(x1))))))))))) 4(5(1(3(0(0(0(5(3(1(5(x1))))))))))) -> 2(4(0(5(2(3(0(0(5(4(x1)))))))))) 2(0(1(2(5(2(4(3(5(2(0(5(x1)))))))))))) -> 2(4(4(4(2(1(0(4(3(3(2(5(x1)))))))))))) 5(5(3(0(2(2(4(2(5(0(1(5(x1)))))))))))) -> 3(2(3(1(5(0(4(4(2(3(5(5(x1)))))))))))) 0(1(5(1(0(2(5(5(1(4(1(0(1(x1))))))))))))) -> 0(0(5(1(0(5(3(1(0(1(5(3(x1)))))))))))) 4(5(1(5(1(5(3(4(3(3(0(4(1(x1))))))))))))) -> 4(5(2(3(2(5(3(2(1(0(2(1(x1)))))))))))) 5(1(3(5(0(2(5(5(1(0(3(2(2(x1))))))))))))) -> 1(2(3(4(4(3(3(5(0(1(1(5(2(x1))))))))))))) 0(2(4(1(5(3(3(3(1(1(1(1(0(2(x1)))))))))))))) -> 0(2(2(2(4(5(2(0(2(0(0(3(2(x1))))))))))))) 0(4(4(5(2(0(3(0(2(4(2(5(1(1(0(x1))))))))))))))) -> 2(1(0(0(3(3(2(1(1(3(0(5(0(5(0(x1))))))))))))))) 0(2(5(3(4(2(0(5(0(0(0(4(3(4(2(3(x1)))))))))))))))) -> 0(0(1(0(5(2(0(1(4(1(4(2(2(1(1(3(x1)))))))))))))))) 1(3(3(4(0(2(5(1(2(2(2(3(1(0(3(4(x1)))))))))))))))) -> 0(5(2(4(3(1(3(2(5(2(5(5(2(2(4(x1))))))))))))))) 5(0(5(1(0(0(1(4(3(5(1(4(4(2(1(0(x1)))))))))))))))) -> 2(0(4(3(2(1(0(4(4(2(4(3(3(5(0(5(x1)))))))))))))))) 5(0(5(3(0(0(3(1(5(1(4(0(4(3(4(5(x1)))))))))))))))) -> 2(0(5(1(5(4(1(2(3(4(3(5(2(4(5(x1))))))))))))))) 5(2(4(0(4(4(3(2(3(5(4(5(4(3(4(5(x1)))))))))))))))) -> 4(3(5(5(2(2(0(1(1(1(2(5(3(1(5(x1))))))))))))))) 1(4(0(0(5(4(1(4(2(2(3(2(0(0(5(1(1(x1))))))))))))))))) -> 1(2(1(0(5(3(3(0(1(5(1(0(4(5(0(3(1(x1))))))))))))))))) 2(1(2(0(1(1(2(5(3(3(1(5(5(0(4(3(0(x1))))))))))))))))) -> 2(1(0(2(1(1(3(2(1(1(2(3(1(5(3(4(x1)))))))))))))))) 4(5(5(0(5(5(2(5(1(5(3(5(0(4(4(5(3(x1))))))))))))))))) -> 4(5(0(1(3(5(0(0(0(3(2(3(5(4(2(3(3(x1))))))))))))))))) 5(5(5(2(1(5(3(0(2(5(4(2(5(5(0(0(5(x1))))))))))))))))) -> 1(3(4(4(4(4(5(1(0(3(2(5(0(1(2(0(3(1(x1)))))))))))))))))) 1(4(1(5(2(4(0(2(3(0(0(1(5(5(1(1(0(3(x1)))))))))))))))))) -> 0(3(3(2(1(5(5(0(5(2(0(2(2(3(0(0(3(x1))))))))))))))))) 2(2(1(0(1(2(0(2(4(2(3(2(0(3(0(0(0(2(x1)))))))))))))))))) -> 0(0(3(4(2(5(3(0(1(4(5(2(0(5(5(1(2(x1))))))))))))))))) 2(3(0(3(0(3(3(3(4(2(4(4(5(4(4(5(0(0(x1)))))))))))))))))) -> 3(3(1(4(3(1(5(2(5(5(1(4(5(2(0(4(x1)))))))))))))))) 4(1(4(3(4(0(0(1(1(0(4(1(0(4(0(5(1(1(x1)))))))))))))))))) -> 2(0(0(0(5(0(3(2(4(4(4(2(1(4(4(4(1(x1))))))))))))))))) 0(5(0(2(1(4(0(1(1(0(0(2(4(2(5(2(2(2(0(x1))))))))))))))))))) -> 0(4(1(2(2(0(3(0(3(3(4(5(0(4(2(2(1(5(4(x1))))))))))))))))))) 5(0(4(0(4(5(2(5(5(0(4(0(2(5(4(1(4(3(4(5(x1)))))))))))))))))))) -> 5(0(4(0(5(4(5(3(2(4(1(5(5(1(3(3(2(3(1(1(x1)))))))))))))))))))) 0(3(3(4(4(0(3(1(5(5(0(1(4(2(4(3(0(2(1(1(5(x1))))))))))))))))))))) -> 0(3(2(0(5(3(3(5(0(1(0(4(0(1(2(0(1(1(4(2(5(x1))))))))))))))))))))) 4(1(1(0(0(3(1(5(1(1(5(4(2(0(3(4(4(5(1(3(3(x1))))))))))))))))))))) -> 3(0(1(0(0(4(1(2(0(5(5(3(4(4(5(3(5(2(5(0(3(x1))))))))))))))))))))) 5(0(1(0(0(2(2(0(3(1(1(2(3(2(4(1(0(0(5(1(3(x1))))))))))))))))))))) -> 5(4(0(5(5(5(3(1(5(1(0(5(5(1(4(4(3(2(4(3(x1)))))))))))))))))))) 5(0(5(4(4(1(4(4(1(1(5(1(0(0(1(5(4(0(1(3(0(x1))))))))))))))))))))) -> 1(5(3(4(5(2(5(4(2(1(4(0(3(5(0(2(3(1(x1)))))))))))))))))) 5(1(4(0(4(3(5(3(0(3(4(2(0(2(1(5(2(0(1(1(0(x1))))))))))))))))))))) -> 5(4(5(3(1(4(1(3(0(2(3(4(2(4(5(2(4(3(0(4(4(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_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(1(2(0(x1)))) -> 3(4(0(x1))) 0(5(1(5(x1)))) -> 2(3(1(x1))) 2(3(3(5(1(x1))))) -> 3(5(5(3(x1)))) 4(5(1(2(0(x1))))) -> 4(5(5(3(x1)))) 0(5(3(1(1(1(x1)))))) -> 0(1(0(1(5(1(x1)))))) 0(0(1(2(4(1(1(x1))))))) -> 0(0(3(5(5(1(x1)))))) 0(2(4(3(1(1(5(x1))))))) -> 0(2(0(0(1(3(1(x1))))))) 0(3(5(0(4(0(0(x1))))))) -> 1(3(4(0(3(4(x1)))))) 1(5(4(5(5(4(5(x1))))))) -> 4(2(2(5(1(0(x1)))))) 4(4(3(5(1(0(5(x1))))))) -> 2(5(1(1(1(4(x1)))))) 3(2(5(2(2(4(0(5(1(1(x1)))))))))) -> 3(1(3(5(5(5(0(2(5(x1))))))))) 1(2(2(1(4(3(2(2(1(3(0(x1))))))))))) -> 4(2(3(3(3(5(3(1(0(1(5(x1))))))))))) 4(5(1(3(0(0(0(5(3(1(5(x1))))))))))) -> 2(4(0(5(2(3(0(0(5(4(x1)))))))))) 2(0(1(2(5(2(4(3(5(2(0(5(x1)))))))))))) -> 2(4(4(4(2(1(0(4(3(3(2(5(x1)))))))))))) 5(5(3(0(2(2(4(2(5(0(1(5(x1)))))))))))) -> 3(2(3(1(5(0(4(4(2(3(5(5(x1)))))))))))) 0(1(5(1(0(2(5(5(1(4(1(0(1(x1))))))))))))) -> 0(0(5(1(0(5(3(1(0(1(5(3(x1)))))))))))) 4(5(1(5(1(5(3(4(3(3(0(4(1(x1))))))))))))) -> 4(5(2(3(2(5(3(2(1(0(2(1(x1)))))))))))) 5(1(3(5(0(2(5(5(1(0(3(2(2(x1))))))))))))) -> 1(2(3(4(4(3(3(5(0(1(1(5(2(x1))))))))))))) 0(2(4(1(5(3(3(3(1(1(1(1(0(2(x1)))))))))))))) -> 0(2(2(2(4(5(2(0(2(0(0(3(2(x1))))))))))))) 0(4(4(5(2(0(3(0(2(4(2(5(1(1(0(x1))))))))))))))) -> 2(1(0(0(3(3(2(1(1(3(0(5(0(5(0(x1))))))))))))))) 0(2(5(3(4(2(0(5(0(0(0(4(3(4(2(3(x1)))))))))))))))) -> 0(0(1(0(5(2(0(1(4(1(4(2(2(1(1(3(x1)))))))))))))))) 1(3(3(4(0(2(5(1(2(2(2(3(1(0(3(4(x1)))))))))))))))) -> 0(5(2(4(3(1(3(2(5(2(5(5(2(2(4(x1))))))))))))))) 5(0(5(1(0(0(1(4(3(5(1(4(4(2(1(0(x1)))))))))))))))) -> 2(0(4(3(2(1(0(4(4(2(4(3(3(5(0(5(x1)))))))))))))))) 5(0(5(3(0(0(3(1(5(1(4(0(4(3(4(5(x1)))))))))))))))) -> 2(0(5(1(5(4(1(2(3(4(3(5(2(4(5(x1))))))))))))))) 5(2(4(0(4(4(3(2(3(5(4(5(4(3(4(5(x1)))))))))))))))) -> 4(3(5(5(2(2(0(1(1(1(2(5(3(1(5(x1))))))))))))))) 1(4(0(0(5(4(1(4(2(2(3(2(0(0(5(1(1(x1))))))))))))))))) -> 1(2(1(0(5(3(3(0(1(5(1(0(4(5(0(3(1(x1))))))))))))))))) 2(1(2(0(1(1(2(5(3(3(1(5(5(0(4(3(0(x1))))))))))))))))) -> 2(1(0(2(1(1(3(2(1(1(2(3(1(5(3(4(x1)))))))))))))))) 4(5(5(0(5(5(2(5(1(5(3(5(0(4(4(5(3(x1))))))))))))))))) -> 4(5(0(1(3(5(0(0(0(3(2(3(5(4(2(3(3(x1))))))))))))))))) 5(5(5(2(1(5(3(0(2(5(4(2(5(5(0(0(5(x1))))))))))))))))) -> 1(3(4(4(4(4(5(1(0(3(2(5(0(1(2(0(3(1(x1)))))))))))))))))) 1(4(1(5(2(4(0(2(3(0(0(1(5(5(1(1(0(3(x1)))))))))))))))))) -> 0(3(3(2(1(5(5(0(5(2(0(2(2(3(0(0(3(x1))))))))))))))))) 2(2(1(0(1(2(0(2(4(2(3(2(0(3(0(0(0(2(x1)))))))))))))))))) -> 0(0(3(4(2(5(3(0(1(4(5(2(0(5(5(1(2(x1))))))))))))))))) 2(3(0(3(0(3(3(3(4(2(4(4(5(4(4(5(0(0(x1)))))))))))))))))) -> 3(3(1(4(3(1(5(2(5(5(1(4(5(2(0(4(x1)))))))))))))))) 4(1(4(3(4(0(0(1(1(0(4(1(0(4(0(5(1(1(x1)))))))))))))))))) -> 2(0(0(0(5(0(3(2(4(4(4(2(1(4(4(4(1(x1))))))))))))))))) 0(5(0(2(1(4(0(1(1(0(0(2(4(2(5(2(2(2(0(x1))))))))))))))))))) -> 0(4(1(2(2(0(3(0(3(3(4(5(0(4(2(2(1(5(4(x1))))))))))))))))))) 5(0(4(0(4(5(2(5(5(0(4(0(2(5(4(1(4(3(4(5(x1)))))))))))))))))))) -> 5(0(4(0(5(4(5(3(2(4(1(5(5(1(3(3(2(3(1(1(x1)))))))))))))))))))) 0(3(3(4(4(0(3(1(5(5(0(1(4(2(4(3(0(2(1(1(5(x1))))))))))))))))))))) -> 0(3(2(0(5(3(3(5(0(1(0(4(0(1(2(0(1(1(4(2(5(x1))))))))))))))))))))) 4(1(1(0(0(3(1(5(1(1(5(4(2(0(3(4(4(5(1(3(3(x1))))))))))))))))))))) -> 3(0(1(0(0(4(1(2(0(5(5(3(4(4(5(3(5(2(5(0(3(x1))))))))))))))))))))) 5(0(1(0(0(2(2(0(3(1(1(2(3(2(4(1(0(0(5(1(3(x1))))))))))))))))))))) -> 5(4(0(5(5(5(3(1(5(1(0(5(5(1(4(4(3(2(4(3(x1)))))))))))))))))))) 5(0(5(4(4(1(4(4(1(1(5(1(0(0(1(5(4(0(1(3(0(x1))))))))))))))))))))) -> 1(5(3(4(5(2(5(4(2(1(4(0(3(5(0(2(3(1(x1)))))))))))))))))) 5(1(4(0(4(3(5(3(0(3(4(2(0(2(1(5(2(0(1(1(0(x1))))))))))))))))))))) -> 5(4(5(3(1(4(1(3(0(2(3(4(2(4(5(2(4(3(0(4(4(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_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(1(2(0(x1)))) -> 3(4(0(x1))) 0(5(1(5(x1)))) -> 2(3(1(x1))) 2(3(3(5(1(x1))))) -> 3(5(5(3(x1)))) 4(5(1(2(0(x1))))) -> 4(5(5(3(x1)))) 0(5(3(1(1(1(x1)))))) -> 0(1(0(1(5(1(x1)))))) 0(0(1(2(4(1(1(x1))))))) -> 0(0(3(5(5(1(x1)))))) 0(2(4(3(1(1(5(x1))))))) -> 0(2(0(0(1(3(1(x1))))))) 0(3(5(0(4(0(0(x1))))))) -> 1(3(4(0(3(4(x1)))))) 1(5(4(5(5(4(5(x1))))))) -> 4(2(2(5(1(0(x1)))))) 4(4(3(5(1(0(5(x1))))))) -> 2(5(1(1(1(4(x1)))))) 3(2(5(2(2(4(0(5(1(1(x1)))))))))) -> 3(1(3(5(5(5(0(2(5(x1))))))))) 1(2(2(1(4(3(2(2(1(3(0(x1))))))))))) -> 4(2(3(3(3(5(3(1(0(1(5(x1))))))))))) 4(5(1(3(0(0(0(5(3(1(5(x1))))))))))) -> 2(4(0(5(2(3(0(0(5(4(x1)))))))))) 2(0(1(2(5(2(4(3(5(2(0(5(x1)))))))))))) -> 2(4(4(4(2(1(0(4(3(3(2(5(x1)))))))))))) 5(5(3(0(2(2(4(2(5(0(1(5(x1)))))))))))) -> 3(2(3(1(5(0(4(4(2(3(5(5(x1)))))))))))) 0(1(5(1(0(2(5(5(1(4(1(0(1(x1))))))))))))) -> 0(0(5(1(0(5(3(1(0(1(5(3(x1)))))))))))) 4(5(1(5(1(5(3(4(3(3(0(4(1(x1))))))))))))) -> 4(5(2(3(2(5(3(2(1(0(2(1(x1)))))))))))) 5(1(3(5(0(2(5(5(1(0(3(2(2(x1))))))))))))) -> 1(2(3(4(4(3(3(5(0(1(1(5(2(x1))))))))))))) 0(2(4(1(5(3(3(3(1(1(1(1(0(2(x1)))))))))))))) -> 0(2(2(2(4(5(2(0(2(0(0(3(2(x1))))))))))))) 0(4(4(5(2(0(3(0(2(4(2(5(1(1(0(x1))))))))))))))) -> 2(1(0(0(3(3(2(1(1(3(0(5(0(5(0(x1))))))))))))))) 0(2(5(3(4(2(0(5(0(0(0(4(3(4(2(3(x1)))))))))))))))) -> 0(0(1(0(5(2(0(1(4(1(4(2(2(1(1(3(x1)))))))))))))))) 1(3(3(4(0(2(5(1(2(2(2(3(1(0(3(4(x1)))))))))))))))) -> 0(5(2(4(3(1(3(2(5(2(5(5(2(2(4(x1))))))))))))))) 5(0(5(1(0(0(1(4(3(5(1(4(4(2(1(0(x1)))))))))))))))) -> 2(0(4(3(2(1(0(4(4(2(4(3(3(5(0(5(x1)))))))))))))))) 5(0(5(3(0(0(3(1(5(1(4(0(4(3(4(5(x1)))))))))))))))) -> 2(0(5(1(5(4(1(2(3(4(3(5(2(4(5(x1))))))))))))))) 5(2(4(0(4(4(3(2(3(5(4(5(4(3(4(5(x1)))))))))))))))) -> 4(3(5(5(2(2(0(1(1(1(2(5(3(1(5(x1))))))))))))))) 1(4(0(0(5(4(1(4(2(2(3(2(0(0(5(1(1(x1))))))))))))))))) -> 1(2(1(0(5(3(3(0(1(5(1(0(4(5(0(3(1(x1))))))))))))))))) 2(1(2(0(1(1(2(5(3(3(1(5(5(0(4(3(0(x1))))))))))))))))) -> 2(1(0(2(1(1(3(2(1(1(2(3(1(5(3(4(x1)))))))))))))))) 4(5(5(0(5(5(2(5(1(5(3(5(0(4(4(5(3(x1))))))))))))))))) -> 4(5(0(1(3(5(0(0(0(3(2(3(5(4(2(3(3(x1))))))))))))))))) 5(5(5(2(1(5(3(0(2(5(4(2(5(5(0(0(5(x1))))))))))))))))) -> 1(3(4(4(4(4(5(1(0(3(2(5(0(1(2(0(3(1(x1)))))))))))))))))) 1(4(1(5(2(4(0(2(3(0(0(1(5(5(1(1(0(3(x1)))))))))))))))))) -> 0(3(3(2(1(5(5(0(5(2(0(2(2(3(0(0(3(x1))))))))))))))))) 2(2(1(0(1(2(0(2(4(2(3(2(0(3(0(0(0(2(x1)))))))))))))))))) -> 0(0(3(4(2(5(3(0(1(4(5(2(0(5(5(1(2(x1))))))))))))))))) 2(3(0(3(0(3(3(3(4(2(4(4(5(4(4(5(0(0(x1)))))))))))))))))) -> 3(3(1(4(3(1(5(2(5(5(1(4(5(2(0(4(x1)))))))))))))))) 4(1(4(3(4(0(0(1(1(0(4(1(0(4(0(5(1(1(x1)))))))))))))))))) -> 2(0(0(0(5(0(3(2(4(4(4(2(1(4(4(4(1(x1))))))))))))))))) 0(5(0(2(1(4(0(1(1(0(0(2(4(2(5(2(2(2(0(x1))))))))))))))))))) -> 0(4(1(2(2(0(3(0(3(3(4(5(0(4(2(2(1(5(4(x1))))))))))))))))))) 5(0(4(0(4(5(2(5(5(0(4(0(2(5(4(1(4(3(4(5(x1)))))))))))))))))))) -> 5(0(4(0(5(4(5(3(2(4(1(5(5(1(3(3(2(3(1(1(x1)))))))))))))))))))) 0(3(3(4(4(0(3(1(5(5(0(1(4(2(4(3(0(2(1(1(5(x1))))))))))))))))))))) -> 0(3(2(0(5(3(3(5(0(1(0(4(0(1(2(0(1(1(4(2(5(x1))))))))))))))))))))) 4(1(1(0(0(3(1(5(1(1(5(4(2(0(3(4(4(5(1(3(3(x1))))))))))))))))))))) -> 3(0(1(0(0(4(1(2(0(5(5(3(4(4(5(3(5(2(5(0(3(x1))))))))))))))))))))) 5(0(1(0(0(2(2(0(3(1(1(2(3(2(4(1(0(0(5(1(3(x1))))))))))))))))))))) -> 5(4(0(5(5(5(3(1(5(1(0(5(5(1(4(4(3(2(4(3(x1)))))))))))))))))))) 5(0(5(4(4(1(4(4(1(1(5(1(0(0(1(5(4(0(1(3(0(x1))))))))))))))))))))) -> 1(5(3(4(5(2(5(4(2(1(4(0(3(5(0(2(3(1(x1)))))))))))))))))) 5(1(4(0(4(3(5(3(0(3(4(2(0(2(1(5(2(0(1(1(0(x1))))))))))))))))))))) -> 5(4(5(3(1(4(1(3(0(2(3(4(2(4(5(2(4(3(0(4(4(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_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(1(2(0(x1)))) -> 3(4(0(x1))) 0(5(1(5(x1)))) -> 2(3(1(x1))) 2(3(3(5(1(x1))))) -> 3(5(5(3(x1)))) 4(5(1(2(0(x1))))) -> 4(5(5(3(x1)))) 0(5(3(1(1(1(x1)))))) -> 0(1(0(1(5(1(x1)))))) 0(0(1(2(4(1(1(x1))))))) -> 0(0(3(5(5(1(x1)))))) 0(2(4(3(1(1(5(x1))))))) -> 0(2(0(0(1(3(1(x1))))))) 0(3(5(0(4(0(0(x1))))))) -> 1(3(4(0(3(4(x1)))))) 1(5(4(5(5(4(5(x1))))))) -> 4(2(2(5(1(0(x1)))))) 4(4(3(5(1(0(5(x1))))))) -> 2(5(1(1(1(4(x1)))))) 3(2(5(2(2(4(0(5(1(1(x1)))))))))) -> 3(1(3(5(5(5(0(2(5(x1))))))))) 1(2(2(1(4(3(2(2(1(3(0(x1))))))))))) -> 4(2(3(3(3(5(3(1(0(1(5(x1))))))))))) 4(5(1(3(0(0(0(5(3(1(5(x1))))))))))) -> 2(4(0(5(2(3(0(0(5(4(x1)))))))))) 2(0(1(2(5(2(4(3(5(2(0(5(x1)))))))))))) -> 2(4(4(4(2(1(0(4(3(3(2(5(x1)))))))))))) 5(5(3(0(2(2(4(2(5(0(1(5(x1)))))))))))) -> 3(2(3(1(5(0(4(4(2(3(5(5(x1)))))))))))) 0(1(5(1(0(2(5(5(1(4(1(0(1(x1))))))))))))) -> 0(0(5(1(0(5(3(1(0(1(5(3(x1)))))))))))) 4(5(1(5(1(5(3(4(3(3(0(4(1(x1))))))))))))) -> 4(5(2(3(2(5(3(2(1(0(2(1(x1)))))))))))) 5(1(3(5(0(2(5(5(1(0(3(2(2(x1))))))))))))) -> 1(2(3(4(4(3(3(5(0(1(1(5(2(x1))))))))))))) 0(2(4(1(5(3(3(3(1(1(1(1(0(2(x1)))))))))))))) -> 0(2(2(2(4(5(2(0(2(0(0(3(2(x1))))))))))))) 0(4(4(5(2(0(3(0(2(4(2(5(1(1(0(x1))))))))))))))) -> 2(1(0(0(3(3(2(1(1(3(0(5(0(5(0(x1))))))))))))))) 0(2(5(3(4(2(0(5(0(0(0(4(3(4(2(3(x1)))))))))))))))) -> 0(0(1(0(5(2(0(1(4(1(4(2(2(1(1(3(x1)))))))))))))))) 1(3(3(4(0(2(5(1(2(2(2(3(1(0(3(4(x1)))))))))))))))) -> 0(5(2(4(3(1(3(2(5(2(5(5(2(2(4(x1))))))))))))))) 5(0(5(1(0(0(1(4(3(5(1(4(4(2(1(0(x1)))))))))))))))) -> 2(0(4(3(2(1(0(4(4(2(4(3(3(5(0(5(x1)))))))))))))))) 5(0(5(3(0(0(3(1(5(1(4(0(4(3(4(5(x1)))))))))))))))) -> 2(0(5(1(5(4(1(2(3(4(3(5(2(4(5(x1))))))))))))))) 5(2(4(0(4(4(3(2(3(5(4(5(4(3(4(5(x1)))))))))))))))) -> 4(3(5(5(2(2(0(1(1(1(2(5(3(1(5(x1))))))))))))))) 1(4(0(0(5(4(1(4(2(2(3(2(0(0(5(1(1(x1))))))))))))))))) -> 1(2(1(0(5(3(3(0(1(5(1(0(4(5(0(3(1(x1))))))))))))))))) 2(1(2(0(1(1(2(5(3(3(1(5(5(0(4(3(0(x1))))))))))))))))) -> 2(1(0(2(1(1(3(2(1(1(2(3(1(5(3(4(x1)))))))))))))))) 4(5(5(0(5(5(2(5(1(5(3(5(0(4(4(5(3(x1))))))))))))))))) -> 4(5(0(1(3(5(0(0(0(3(2(3(5(4(2(3(3(x1))))))))))))))))) 5(5(5(2(1(5(3(0(2(5(4(2(5(5(0(0(5(x1))))))))))))))))) -> 1(3(4(4(4(4(5(1(0(3(2(5(0(1(2(0(3(1(x1)))))))))))))))))) 1(4(1(5(2(4(0(2(3(0(0(1(5(5(1(1(0(3(x1)))))))))))))))))) -> 0(3(3(2(1(5(5(0(5(2(0(2(2(3(0(0(3(x1))))))))))))))))) 2(2(1(0(1(2(0(2(4(2(3(2(0(3(0(0(0(2(x1)))))))))))))))))) -> 0(0(3(4(2(5(3(0(1(4(5(2(0(5(5(1(2(x1))))))))))))))))) 2(3(0(3(0(3(3(3(4(2(4(4(5(4(4(5(0(0(x1)))))))))))))))))) -> 3(3(1(4(3(1(5(2(5(5(1(4(5(2(0(4(x1)))))))))))))))) 4(1(4(3(4(0(0(1(1(0(4(1(0(4(0(5(1(1(x1)))))))))))))))))) -> 2(0(0(0(5(0(3(2(4(4(4(2(1(4(4(4(1(x1))))))))))))))))) 0(5(0(2(1(4(0(1(1(0(0(2(4(2(5(2(2(2(0(x1))))))))))))))))))) -> 0(4(1(2(2(0(3(0(3(3(4(5(0(4(2(2(1(5(4(x1))))))))))))))))))) 5(0(4(0(4(5(2(5(5(0(4(0(2(5(4(1(4(3(4(5(x1)))))))))))))))))))) -> 5(0(4(0(5(4(5(3(2(4(1(5(5(1(3(3(2(3(1(1(x1)))))))))))))))))))) 0(3(3(4(4(0(3(1(5(5(0(1(4(2(4(3(0(2(1(1(5(x1))))))))))))))))))))) -> 0(3(2(0(5(3(3(5(0(1(0(4(0(1(2(0(1(1(4(2(5(x1))))))))))))))))))))) 4(1(1(0(0(3(1(5(1(1(5(4(2(0(3(4(4(5(1(3(3(x1))))))))))))))))))))) -> 3(0(1(0(0(4(1(2(0(5(5(3(4(4(5(3(5(2(5(0(3(x1))))))))))))))))))))) 5(0(1(0(0(2(2(0(3(1(1(2(3(2(4(1(0(0(5(1(3(x1))))))))))))))))))))) -> 5(4(0(5(5(5(3(1(5(1(0(5(5(1(4(4(3(2(4(3(x1)))))))))))))))))))) 5(0(5(4(4(1(4(4(1(1(5(1(0(0(1(5(4(0(1(3(0(x1))))))))))))))))))))) -> 1(5(3(4(5(2(5(4(2(1(4(0(3(5(0(2(3(1(x1)))))))))))))))))) 5(1(4(0(4(3(5(3(0(3(4(2(0(2(1(5(2(0(1(1(0(x1))))))))))))))))))))) -> 5(4(5(3(1(4(1(3(0(2(3(4(2(4(5(2(4(3(0(4(4(x1))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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. "[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, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645] {(138,139,[0_1|0, 2_1|0, 4_1|0, 1_1|0, 3_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]), (138,140,[0_1|1, 2_1|1, 4_1|1, 1_1|1, 3_1|1, 5_1|1]), (138,141,[3_1|2]), (138,143,[0_1|2]), (138,154,[2_1|2]), (138,156,[0_1|2]), (138,161,[0_1|2]), (138,179,[0_1|2]), (138,184,[0_1|2]), (138,190,[0_1|2]), (138,202,[0_1|2]), (138,217,[1_1|2]), (138,222,[0_1|2]), (138,242,[2_1|2]), (138,256,[3_1|2]), (138,259,[3_1|2]), (138,274,[2_1|2]), (138,285,[2_1|2]), (138,300,[0_1|2]), (138,316,[4_1|2]), (138,319,[2_1|2]), (138,328,[4_1|2]), (138,339,[4_1|2]), (138,355,[2_1|2]), (138,360,[2_1|2]), (138,376,[3_1|2]), (138,396,[4_1|2]), (138,401,[4_1|2]), (138,411,[0_1|2]), (138,425,[1_1|2]), (138,441,[0_1|2]), (138,457,[3_1|2]), (138,465,[3_1|2]), (138,476,[1_1|2]), (138,493,[1_1|2]), (138,505,[5_1|2]), (138,525,[2_1|2]), (138,540,[2_1|2]), (138,554,[1_1|2]), (138,571,[5_1|2]), (138,590,[5_1|2]), (138,609,[4_1|2]), (139,139,[cons_0_1|0, cons_2_1|0, cons_4_1|0, cons_1_1|0, cons_3_1|0, cons_5_1|0]), (140,139,[encArg_1|1]), (140,140,[0_1|1, 2_1|1, 4_1|1, 1_1|1, 3_1|1, 5_1|1]), (140,141,[3_1|2]), (140,143,[0_1|2]), (140,154,[2_1|2]), (140,156,[0_1|2]), (140,161,[0_1|2]), (140,179,[0_1|2]), (140,184,[0_1|2]), (140,190,[0_1|2]), (140,202,[0_1|2]), (140,217,[1_1|2]), (140,222,[0_1|2]), (140,242,[2_1|2]), (140,256,[3_1|2]), (140,259,[3_1|2]), (140,274,[2_1|2]), (140,285,[2_1|2]), (140,300,[0_1|2]), (140,316,[4_1|2]), (140,319,[2_1|2]), (140,328,[4_1|2]), 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(402,403,[3_1|2]), (403,404,[3_1|2]), (404,405,[3_1|2]), (405,406,[5_1|2]), (406,407,[3_1|2]), (407,408,[1_1|2]), (408,409,[0_1|2]), (408,143,[0_1|2]), (408,644,[3_1|3]), (409,410,[1_1|2]), (409,396,[4_1|2]), (410,140,[5_1|2]), (410,143,[5_1|2]), (410,156,[5_1|2]), (410,161,[5_1|2]), (410,179,[5_1|2]), (410,184,[5_1|2]), (410,190,[5_1|2]), (410,202,[5_1|2]), (410,222,[5_1|2]), (410,300,[5_1|2]), (410,411,[5_1|2]), (410,441,[5_1|2]), (410,377,[5_1|2]), (410,465,[3_1|2]), (410,476,[1_1|2]), (410,493,[1_1|2]), (410,505,[5_1|2]), (410,525,[2_1|2]), (410,540,[2_1|2]), (410,554,[1_1|2]), (410,571,[5_1|2]), (410,590,[5_1|2]), (410,609,[4_1|2]), (411,412,[5_1|2]), (412,413,[2_1|2]), (413,414,[4_1|2]), (414,415,[3_1|2]), (415,416,[1_1|2]), (416,417,[3_1|2]), (417,418,[2_1|2]), (418,419,[5_1|2]), (419,420,[2_1|2]), (420,421,[5_1|2]), (421,422,[5_1|2]), (422,423,[2_1|2]), (423,424,[2_1|2]), (424,140,[4_1|2]), (424,316,[4_1|2]), (424,328,[4_1|2]), (424,339,[4_1|2]), (424,396,[4_1|2]), (424,401,[4_1|2]), (424,609,[4_1|2]), (424,142,[4_1|2]), (424,319,[2_1|2]), (424,355,[2_1|2]), (424,360,[2_1|2]), (424,376,[3_1|2]), (425,426,[2_1|2]), (426,427,[1_1|2]), (427,428,[0_1|2]), (428,429,[5_1|2]), (429,430,[3_1|2]), (430,431,[3_1|2]), (431,432,[0_1|2]), (432,433,[1_1|2]), (433,434,[5_1|2]), (434,435,[1_1|2]), (435,436,[0_1|2]), (436,437,[4_1|2]), (437,438,[5_1|2]), (438,439,[0_1|2]), (439,440,[3_1|2]), (440,140,[1_1|2]), (440,217,[1_1|2]), (440,425,[1_1|2]), (440,476,[1_1|2]), (440,493,[1_1|2]), (440,554,[1_1|2]), (440,396,[4_1|2]), (440,401,[4_1|2]), (440,411,[0_1|2]), (440,441,[0_1|2]), (441,442,[3_1|2]), (442,443,[3_1|2]), (443,444,[2_1|2]), (444,445,[1_1|2]), (445,446,[5_1|2]), (446,447,[5_1|2]), (447,448,[0_1|2]), (448,449,[5_1|2]), (449,450,[2_1|2]), (450,451,[0_1|2]), (451,452,[2_1|2]), (452,453,[2_1|2]), (453,454,[3_1|2]), (454,455,[0_1|2]), (455,456,[0_1|2]), (455,217,[1_1|2]), (455,222,[0_1|2]), (456,140,[3_1|2]), (456,141,[3_1|2]), (456,256,[3_1|2]), (456,259,[3_1|2]), (456,376,[3_1|2]), (456,457,[3_1|2]), (456,465,[3_1|2]), (456,223,[3_1|2]), (456,442,[3_1|2]), (457,458,[1_1|2]), (458,459,[3_1|2]), (459,460,[5_1|2]), (460,461,[5_1|2]), (461,462,[5_1|2]), (462,463,[0_1|2]), (462,202,[0_1|2]), (463,464,[2_1|2]), (464,140,[5_1|2]), (464,217,[5_1|2]), (464,425,[5_1|2]), (464,476,[5_1|2, 1_1|2]), (464,493,[5_1|2, 1_1|2]), (464,554,[5_1|2, 1_1|2]), (464,465,[3_1|2]), (464,505,[5_1|2]), (464,525,[2_1|2]), (464,540,[2_1|2]), (464,571,[5_1|2]), (464,590,[5_1|2]), (464,609,[4_1|2]), (465,466,[2_1|2]), (466,467,[3_1|2]), (467,468,[1_1|2]), (468,469,[5_1|2]), (469,470,[0_1|2]), (470,471,[4_1|2]), (471,472,[4_1|2]), (472,473,[2_1|2]), (473,474,[3_1|2]), (474,475,[5_1|2]), (474,465,[3_1|2]), (474,476,[1_1|2]), (475,140,[5_1|2]), (475,505,[5_1|2]), (475,571,[5_1|2]), (475,590,[5_1|2]), (475,555,[5_1|2]), (475,465,[3_1|2]), (475,476,[1_1|2]), (475,493,[1_1|2]), (475,525,[2_1|2]), (475,540,[2_1|2]), (475,554,[1_1|2]), (475,609,[4_1|2]), (476,477,[3_1|2]), (477,478,[4_1|2]), (478,479,[4_1|2]), (479,480,[4_1|2]), (480,481,[4_1|2]), (481,482,[5_1|2]), (482,483,[1_1|2]), (483,484,[0_1|2]), (484,485,[3_1|2]), (485,486,[2_1|2]), (486,487,[5_1|2]), (487,488,[0_1|2]), (487,638,[3_1|3]), (488,489,[1_1|2]), (489,490,[2_1|2]), (490,491,[0_1|2]), (491,492,[3_1|2]), (492,140,[1_1|2]), (492,505,[1_1|2]), (492,571,[1_1|2]), (492,590,[1_1|2]), (492,412,[1_1|2]), (492,145,[1_1|2]), (492,396,[4_1|2]), (492,401,[4_1|2]), (492,411,[0_1|2]), (492,425,[1_1|2]), (492,441,[0_1|2]), (493,494,[2_1|2]), (494,495,[3_1|2]), (495,496,[4_1|2]), (496,497,[4_1|2]), (497,498,[3_1|2]), (498,499,[3_1|2]), (499,500,[5_1|2]), (500,501,[0_1|2]), (501,502,[1_1|2]), (502,503,[1_1|2]), (503,504,[5_1|2]), (503,609,[4_1|2]), (504,140,[2_1|2]), (504,154,[2_1|2]), (504,242,[2_1|2]), (504,274,[2_1|2]), (504,285,[2_1|2]), (504,319,[2_1|2]), (504,355,[2_1|2]), (504,360,[2_1|2]), (504,525,[2_1|2]), (504,540,[2_1|2]), (504,256,[3_1|2]), (504,259,[3_1|2]), (504,300,[0_1|2]), (504,642,[2_1|2]), (505,506,[4_1|2]), (506,507,[5_1|2]), (507,508,[3_1|2]), (508,509,[1_1|2]), (509,510,[4_1|2]), (510,511,[1_1|2]), (511,512,[3_1|2]), (512,513,[0_1|2]), (513,514,[2_1|2]), (514,515,[3_1|2]), (515,516,[4_1|2]), (516,517,[2_1|2]), (517,518,[4_1|2]), (518,519,[5_1|2]), (519,520,[2_1|2]), (520,521,[4_1|2]), (521,522,[3_1|2]), (522,523,[0_1|2]), (522,242,[2_1|2]), (523,524,[4_1|2]), (523,355,[2_1|2]), (524,140,[4_1|2]), (524,143,[4_1|2]), (524,156,[4_1|2]), (524,161,[4_1|2]), (524,179,[4_1|2]), (524,184,[4_1|2]), (524,190,[4_1|2]), (524,202,[4_1|2]), (524,222,[4_1|2]), (524,300,[4_1|2]), (524,411,[4_1|2]), (524,441,[4_1|2]), (524,316,[4_1|2]), (524,319,[2_1|2]), (524,328,[4_1|2]), (524,339,[4_1|2]), (524,355,[2_1|2]), (524,360,[2_1|2]), (524,376,[3_1|2]), (525,526,[0_1|2]), (526,527,[4_1|2]), (527,528,[3_1|2]), (528,529,[2_1|2]), (529,530,[1_1|2]), (530,531,[0_1|2]), (531,532,[4_1|2]), (532,533,[4_1|2]), (533,534,[2_1|2]), (534,535,[4_1|2]), (535,536,[3_1|2]), (536,537,[3_1|2]), (537,538,[5_1|2]), (537,525,[2_1|2]), (537,540,[2_1|2]), (537,554,[1_1|2]), (538,539,[0_1|2]), (538,154,[2_1|2]), (538,156,[0_1|2]), (538,161,[0_1|2]), (538,640,[2_1|3]), (539,140,[5_1|2]), (539,143,[5_1|2]), (539,156,[5_1|2]), (539,161,[5_1|2]), (539,179,[5_1|2]), (539,184,[5_1|2]), (539,190,[5_1|2]), (539,202,[5_1|2]), (539,222,[5_1|2]), (539,300,[5_1|2]), (539,411,[5_1|2]), (539,441,[5_1|2]), (539,244,[5_1|2]), (539,287,[5_1|2]), (539,465,[3_1|2]), (539,476,[1_1|2]), (539,493,[1_1|2]), (539,505,[5_1|2]), (539,525,[2_1|2]), (539,540,[2_1|2]), (539,554,[1_1|2]), (539,571,[5_1|2]), (539,590,[5_1|2]), (539,609,[4_1|2]), (540,541,[0_1|2]), (540,642,[2_1|3]), (541,542,[5_1|2]), (542,543,[1_1|2]), (543,544,[5_1|2]), (544,545,[4_1|2]), (545,546,[1_1|2]), (546,547,[2_1|2]), (547,548,[3_1|2]), (548,549,[4_1|2]), (549,550,[3_1|2]), (550,551,[5_1|2]), (551,552,[2_1|2]), (552,553,[4_1|2]), (552,316,[4_1|2]), (552,319,[2_1|2]), (552,328,[4_1|2]), (552,339,[4_1|2]), (553,140,[5_1|2]), (553,505,[5_1|2]), (553,571,[5_1|2]), (553,590,[5_1|2]), (553,317,[5_1|2]), (553,329,[5_1|2]), (553,340,[5_1|2]), (553,465,[3_1|2]), (553,476,[1_1|2]), (553,493,[1_1|2]), (553,525,[2_1|2]), (553,540,[2_1|2]), (553,554,[1_1|2]), (553,609,[4_1|2]), (554,555,[5_1|2]), (555,556,[3_1|2]), (556,557,[4_1|2]), (557,558,[5_1|2]), (558,559,[2_1|2]), (559,560,[5_1|2]), (560,561,[4_1|2]), (561,562,[2_1|2]), (562,563,[1_1|2]), (563,564,[4_1|2]), (564,565,[0_1|2]), (565,566,[3_1|2]), (566,567,[5_1|2]), (567,568,[0_1|2]), (568,569,[2_1|2]), (569,570,[3_1|2]), (570,140,[1_1|2]), (570,143,[1_1|2]), (570,156,[1_1|2]), (570,161,[1_1|2]), (570,179,[1_1|2]), (570,184,[1_1|2]), (570,190,[1_1|2]), (570,202,[1_1|2]), (570,222,[1_1|2]), (570,300,[1_1|2]), (570,411,[1_1|2, 0_1|2]), (570,441,[1_1|2, 0_1|2]), (570,377,[1_1|2]), (570,396,[4_1|2]), (570,401,[4_1|2]), (570,425,[1_1|2]), (571,572,[0_1|2]), (572,573,[4_1|2]), (573,574,[0_1|2]), (574,575,[5_1|2]), (575,576,[4_1|2]), (576,577,[5_1|2]), (577,578,[3_1|2]), (578,579,[2_1|2]), (579,580,[4_1|2]), (580,581,[1_1|2]), (581,582,[5_1|2]), (582,583,[5_1|2]), (583,584,[1_1|2]), (584,585,[3_1|2]), (585,586,[3_1|2]), (586,587,[2_1|2]), (587,588,[3_1|2]), (588,589,[1_1|2]), (589,140,[1_1|2]), (589,505,[1_1|2]), (589,571,[1_1|2]), (589,590,[1_1|2]), (589,317,[1_1|2]), (589,329,[1_1|2]), (589,340,[1_1|2]), (589,396,[4_1|2]), (589,401,[4_1|2]), (589,411,[0_1|2]), (589,425,[1_1|2]), (589,441,[0_1|2]), (590,591,[4_1|2]), (591,592,[0_1|2]), (592,593,[5_1|2]), (593,594,[5_1|2]), (594,595,[5_1|2]), (595,596,[3_1|2]), (596,597,[1_1|2]), (597,598,[5_1|2]), (598,599,[1_1|2]), (599,600,[0_1|2]), (600,601,[5_1|2]), (601,602,[5_1|2]), (602,603,[1_1|2]), (603,604,[4_1|2]), (604,605,[4_1|2]), (605,606,[3_1|2]), (606,607,[2_1|2]), (607,608,[4_1|2]), (608,140,[3_1|2]), (608,141,[3_1|2]), (608,256,[3_1|2]), (608,259,[3_1|2]), (608,376,[3_1|2]), (608,457,[3_1|2]), (608,465,[3_1|2]), (608,218,[3_1|2]), (608,477,[3_1|2]), (609,610,[3_1|2]), (610,611,[5_1|2]), (611,612,[5_1|2]), (612,613,[2_1|2]), (613,614,[2_1|2]), (614,615,[0_1|2]), (615,616,[1_1|2]), (616,617,[1_1|2]), (617,618,[1_1|2]), (618,619,[2_1|2]), (619,620,[5_1|2]), (620,621,[3_1|2]), (621,622,[1_1|2]), (621,396,[4_1|2]), (622,140,[5_1|2]), (622,505,[5_1|2]), (622,571,[5_1|2]), (622,590,[5_1|2]), (622,317,[5_1|2]), (622,329,[5_1|2]), (622,340,[5_1|2]), (622,465,[3_1|2]), (622,476,[1_1|2]), (622,493,[1_1|2]), (622,525,[2_1|2]), (622,540,[2_1|2]), (622,554,[1_1|2]), (622,609,[4_1|2]), (636,637,[4_1|3]), (637,237,[0_1|3]), (638,639,[4_1|3]), (639,491,[0_1|3]), (640,641,[3_1|3]), (641,555,[1_1|3]), (642,643,[3_1|3]), (643,544,[1_1|3]), (644,645,[4_1|3]), (645,526,[0_1|3]), (645,541,[0_1|3]), (645,642,[2_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)