/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 68 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 249 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(3(x1)))) -> 3(4(5(x1))) 1(2(0(5(5(x1))))) -> 1(5(4(0(x1)))) 2(0(3(4(2(x1))))) -> 3(1(2(4(x1)))) 5(5(5(5(0(x1))))) -> 5(4(4(3(x1)))) 0(1(2(4(3(5(x1)))))) -> 2(4(5(3(0(x1))))) 0(3(0(4(2(0(x1)))))) -> 2(3(4(1(2(x1))))) 4(5(0(4(0(0(0(x1))))))) -> 4(3(4(2(5(0(x1)))))) 0(1(0(2(1(4(4(2(x1)))))))) -> 0(2(0(3(3(4(5(4(x1)))))))) 2(0(0(1(5(0(5(2(x1)))))))) -> 2(0(5(2(1(1(x1)))))) 3(4(1(4(3(0(3(2(x1)))))))) -> 5(3(5(4(3(1(1(x1))))))) 5(3(0(1(5(5(0(5(x1)))))))) -> 5(0(4(2(1(3(4(x1))))))) 5(5(5(3(1(3(4(4(x1)))))))) -> 1(5(2(4(4(5(4(x1))))))) 0(1(5(4(2(5(3(3(4(x1))))))))) -> 2(0(5(4(3(0(1(0(4(x1))))))))) 0(3(3(1(2(2(0(4(5(x1))))))))) -> 2(3(4(4(4(0(3(1(x1)))))))) 4(3(4(0(5(3(0(0(5(4(x1)))))))))) -> 3(1(1(2(1(2(0(4(2(x1))))))))) 4(2(5(4(5(2(1(1(0(2(1(x1))))))))))) -> 4(2(3(4(1(0(5(4(5(2(1(x1))))))))))) 5(5(4(2(5(3(1(0(5(3(1(x1))))))))))) -> 2(2(2(2(2(0(3(5(1(2(1(x1))))))))))) 5(5(5(0(3(5(2(4(1(2(4(x1))))))))))) -> 1(0(3(3(5(0(3(1(4(4(x1)))))))))) 0(3(3(2(0(1(1(2(1(3(0(5(x1)))))))))))) -> 2(3(0(2(5(4(1(0(1(2(4(3(x1)))))))))))) 3(3(2(5(2(5(4(5(0(5(4(2(1(x1))))))))))))) -> 2(1(2(3(3(4(4(2(0(3(4(1(x1)))))))))))) 4(3(4(2(2(5(4(5(0(0(0(2(5(x1))))))))))))) -> 4(4(5(1(4(5(0(1(0(5(3(x1))))))))))) 3(4(0(4(1(2(3(5(2(1(4(4(0(3(x1)))))))))))))) -> 3(2(2(5(0(4(5(5(0(5(5(4(1(2(x1)))))))))))))) 4(0(5(4(4(4(5(0(2(5(2(3(4(5(x1)))))))))))))) -> 4(1(0(4(3(4(2(3(1(3(2(3(3(x1))))))))))))) 5(3(5(4(2(4(4(5(0(5(4(1(2(2(x1)))))))))))))) -> 5(0(2(5(5(1(5(3(4(1(1(0(2(x1))))))))))))) 2(2(4(3(4(4(2(1(5(2(1(4(0(2(0(x1))))))))))))))) -> 3(5(3(3(1(2(1(3(0(4(5(3(4(0(x1)))))))))))))) 0(2(0(2(5(2(2(1(4(5(0(3(1(5(0(2(x1)))))))))))))))) -> 0(4(3(5(5(5(1(3(0(4(5(0(2(2(4(x1))))))))))))))) 5(0(0(2(0(2(2(0(1(1(3(4(4(3(3(5(x1)))))))))))))))) -> 5(4(0(3(4(4(1(0(0(3(5(1(4(5(5(5(x1)))))))))))))))) 5(0(2(3(2(4(4(3(4(1(0(0(0(4(4(3(x1)))))))))))))))) -> 5(2(4(4(4(0(1(1(4(2(5(5(1(3(x1)))))))))))))) 0(2(0(2(0(1(1(3(5(2(0(4(4(1(5(5(5(x1))))))))))))))))) -> 4(1(3(4(1(1(3(1(0(4(2(2(5(3(3(x1))))))))))))))) 0(4(3(0(2(1(3(3(3(0(5(1(2(3(2(5(4(0(x1)))))))))))))))))) -> 1(5(5(5(2(2(1(2(0(4(0(1(4(1(5(4(4(x1))))))))))))))))) 2(2(3(2(3(2(2(4(1(2(4(5(1(4(4(0(4(0(x1)))))))))))))))))) -> 5(2(2(0(4(4(5(4(2(3(2(3(1(0(5(3(3(4(x1)))))))))))))))))) 2(4(1(1(1(2(5(4(4(2(0(0(1(4(5(5(5(0(x1)))))))))))))))))) -> 3(3(2(4(5(2(5(4(5(4(5(3(3(3(0(5(0(2(3(x1))))))))))))))))))) 3(2(0(2(1(0(3(1(3(4(3(5(2(1(0(0(3(0(x1)))))))))))))))))) -> 5(2(4(0(1(5(2(3(3(5(4(4(5(2(3(3(3(0(x1)))))))))))))))))) 2(5(1(2(0(4(1(2(4(3(2(0(4(3(1(3(5(2(5(x1))))))))))))))))))) -> 2(4(5(1(2(3(0(4(1(3(2(3(4(2(0(3(3(3(x1)))))))))))))))))) 4(4(4(1(1(1(2(1(1(0(4(3(2(3(1(3(0(3(5(x1))))))))))))))))))) -> 4(1(0(2(3(3(0(1(1(4(5(3(1(1(5(3(2(2(3(5(x1)))))))))))))))))))) 3(5(3(3(0(0(4(4(4(4(0(1(1(5(2(5(0(5(0(2(x1)))))))))))))))))))) -> 2(0(5(2(4(3(3(4(5(4(3(1(4(0(0(2(5(1(1(x1))))))))))))))))))) 4(1(5(3(2(5(5(5(2(5(5(3(5(5(5(3(5(0(2(0(x1)))))))))))))))))))) -> 4(1(4(0(5(2(1(3(4(3(1(1(0(4(3(3(2(0(x1)))))))))))))))))) 0(0(4(0(0(0(0(1(0(4(4(5(3(2(2(4(0(5(3(0(5(x1))))))))))))))))))))) -> 0(2(2(2(1(2(4(4(5(0(5(1(0(0(5(5(2(5(3(2(x1)))))))))))))))))))) 2(2(0(3(4(0(5(2(5(2(2(5(2(5(5(1(5(2(4(1(4(x1))))))))))))))))))))) -> 0(0(5(2(4(1(4(3(4(3(2(4(4(3(4(4(1(1(4(x1))))))))))))))))))) 2(5(5(5(0(2(3(2(4(0(0(1(5(2(3(2(3(0(1(0(5(x1))))))))))))))))))))) -> 2(0(3(4(5(3(3(2(2(1(5(2(2(2(4(2(5(4(0(1(x1)))))))))))))))))))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(3(x1)))) -> 3(4(5(x1))) 1(2(0(5(5(x1))))) -> 1(5(4(0(x1)))) 2(0(3(4(2(x1))))) -> 3(1(2(4(x1)))) 5(5(5(5(0(x1))))) -> 5(4(4(3(x1)))) 0(1(2(4(3(5(x1)))))) -> 2(4(5(3(0(x1))))) 0(3(0(4(2(0(x1)))))) -> 2(3(4(1(2(x1))))) 4(5(0(4(0(0(0(x1))))))) -> 4(3(4(2(5(0(x1)))))) 0(1(0(2(1(4(4(2(x1)))))))) -> 0(2(0(3(3(4(5(4(x1)))))))) 2(0(0(1(5(0(5(2(x1)))))))) -> 2(0(5(2(1(1(x1)))))) 3(4(1(4(3(0(3(2(x1)))))))) -> 5(3(5(4(3(1(1(x1))))))) 5(3(0(1(5(5(0(5(x1)))))))) -> 5(0(4(2(1(3(4(x1))))))) 5(5(5(3(1(3(4(4(x1)))))))) -> 1(5(2(4(4(5(4(x1))))))) 0(1(5(4(2(5(3(3(4(x1))))))))) -> 2(0(5(4(3(0(1(0(4(x1))))))))) 0(3(3(1(2(2(0(4(5(x1))))))))) -> 2(3(4(4(4(0(3(1(x1)))))))) 4(3(4(0(5(3(0(0(5(4(x1)))))))))) -> 3(1(1(2(1(2(0(4(2(x1))))))))) 4(2(5(4(5(2(1(1(0(2(1(x1))))))))))) -> 4(2(3(4(1(0(5(4(5(2(1(x1))))))))))) 5(5(4(2(5(3(1(0(5(3(1(x1))))))))))) -> 2(2(2(2(2(0(3(5(1(2(1(x1))))))))))) 5(5(5(0(3(5(2(4(1(2(4(x1))))))))))) -> 1(0(3(3(5(0(3(1(4(4(x1)))))))))) 0(3(3(2(0(1(1(2(1(3(0(5(x1)))))))))))) -> 2(3(0(2(5(4(1(0(1(2(4(3(x1)))))))))))) 3(3(2(5(2(5(4(5(0(5(4(2(1(x1))))))))))))) -> 2(1(2(3(3(4(4(2(0(3(4(1(x1)))))))))))) 4(3(4(2(2(5(4(5(0(0(0(2(5(x1))))))))))))) -> 4(4(5(1(4(5(0(1(0(5(3(x1))))))))))) 3(4(0(4(1(2(3(5(2(1(4(4(0(3(x1)))))))))))))) -> 3(2(2(5(0(4(5(5(0(5(5(4(1(2(x1)))))))))))))) 4(0(5(4(4(4(5(0(2(5(2(3(4(5(x1)))))))))))))) -> 4(1(0(4(3(4(2(3(1(3(2(3(3(x1))))))))))))) 5(3(5(4(2(4(4(5(0(5(4(1(2(2(x1)))))))))))))) -> 5(0(2(5(5(1(5(3(4(1(1(0(2(x1))))))))))))) 2(2(4(3(4(4(2(1(5(2(1(4(0(2(0(x1))))))))))))))) -> 3(5(3(3(1(2(1(3(0(4(5(3(4(0(x1)))))))))))))) 0(2(0(2(5(2(2(1(4(5(0(3(1(5(0(2(x1)))))))))))))))) -> 0(4(3(5(5(5(1(3(0(4(5(0(2(2(4(x1))))))))))))))) 5(0(0(2(0(2(2(0(1(1(3(4(4(3(3(5(x1)))))))))))))))) -> 5(4(0(3(4(4(1(0(0(3(5(1(4(5(5(5(x1)))))))))))))))) 5(0(2(3(2(4(4(3(4(1(0(0(0(4(4(3(x1)))))))))))))))) -> 5(2(4(4(4(0(1(1(4(2(5(5(1(3(x1)))))))))))))) 0(2(0(2(0(1(1(3(5(2(0(4(4(1(5(5(5(x1))))))))))))))))) -> 4(1(3(4(1(1(3(1(0(4(2(2(5(3(3(x1))))))))))))))) 0(4(3(0(2(1(3(3(3(0(5(1(2(3(2(5(4(0(x1)))))))))))))))))) -> 1(5(5(5(2(2(1(2(0(4(0(1(4(1(5(4(4(x1))))))))))))))))) 2(2(3(2(3(2(2(4(1(2(4(5(1(4(4(0(4(0(x1)))))))))))))))))) -> 5(2(2(0(4(4(5(4(2(3(2(3(1(0(5(3(3(4(x1)))))))))))))))))) 2(4(1(1(1(2(5(4(4(2(0(0(1(4(5(5(5(0(x1)))))))))))))))))) -> 3(3(2(4(5(2(5(4(5(4(5(3(3(3(0(5(0(2(3(x1))))))))))))))))))) 3(2(0(2(1(0(3(1(3(4(3(5(2(1(0(0(3(0(x1)))))))))))))))))) -> 5(2(4(0(1(5(2(3(3(5(4(4(5(2(3(3(3(0(x1)))))))))))))))))) 2(5(1(2(0(4(1(2(4(3(2(0(4(3(1(3(5(2(5(x1))))))))))))))))))) -> 2(4(5(1(2(3(0(4(1(3(2(3(4(2(0(3(3(3(x1)))))))))))))))))) 4(4(4(1(1(1(2(1(1(0(4(3(2(3(1(3(0(3(5(x1))))))))))))))))))) -> 4(1(0(2(3(3(0(1(1(4(5(3(1(1(5(3(2(2(3(5(x1)))))))))))))))))))) 3(5(3(3(0(0(4(4(4(4(0(1(1(5(2(5(0(5(0(2(x1)))))))))))))))))))) -> 2(0(5(2(4(3(3(4(5(4(3(1(4(0(0(2(5(1(1(x1))))))))))))))))))) 4(1(5(3(2(5(5(5(2(5(5(3(5(5(5(3(5(0(2(0(x1)))))))))))))))))))) -> 4(1(4(0(5(2(1(3(4(3(1(1(0(4(3(3(2(0(x1)))))))))))))))))) 0(0(4(0(0(0(0(1(0(4(4(5(3(2(2(4(0(5(3(0(5(x1))))))))))))))))))))) -> 0(2(2(2(1(2(4(4(5(0(5(1(0(0(5(5(2(5(3(2(x1)))))))))))))))))))) 2(2(0(3(4(0(5(2(5(2(2(5(2(5(5(1(5(2(4(1(4(x1))))))))))))))))))))) -> 0(0(5(2(4(1(4(3(4(3(2(4(4(3(4(4(1(1(4(x1))))))))))))))))))) 2(5(5(5(0(2(3(2(4(0(0(1(5(2(3(2(3(0(1(0(5(x1))))))))))))))))))))) -> 2(0(3(4(5(3(3(2(2(1(5(2(2(2(4(2(5(4(0(1(x1)))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(3(x1)))) -> 3(4(5(x1))) 1(2(0(5(5(x1))))) -> 1(5(4(0(x1)))) 2(0(3(4(2(x1))))) -> 3(1(2(4(x1)))) 5(5(5(5(0(x1))))) -> 5(4(4(3(x1)))) 0(1(2(4(3(5(x1)))))) -> 2(4(5(3(0(x1))))) 0(3(0(4(2(0(x1)))))) -> 2(3(4(1(2(x1))))) 4(5(0(4(0(0(0(x1))))))) -> 4(3(4(2(5(0(x1)))))) 0(1(0(2(1(4(4(2(x1)))))))) -> 0(2(0(3(3(4(5(4(x1)))))))) 2(0(0(1(5(0(5(2(x1)))))))) -> 2(0(5(2(1(1(x1)))))) 3(4(1(4(3(0(3(2(x1)))))))) -> 5(3(5(4(3(1(1(x1))))))) 5(3(0(1(5(5(0(5(x1)))))))) -> 5(0(4(2(1(3(4(x1))))))) 5(5(5(3(1(3(4(4(x1)))))))) -> 1(5(2(4(4(5(4(x1))))))) 0(1(5(4(2(5(3(3(4(x1))))))))) -> 2(0(5(4(3(0(1(0(4(x1))))))))) 0(3(3(1(2(2(0(4(5(x1))))))))) -> 2(3(4(4(4(0(3(1(x1)))))))) 4(3(4(0(5(3(0(0(5(4(x1)))))))))) -> 3(1(1(2(1(2(0(4(2(x1))))))))) 4(2(5(4(5(2(1(1(0(2(1(x1))))))))))) -> 4(2(3(4(1(0(5(4(5(2(1(x1))))))))))) 5(5(4(2(5(3(1(0(5(3(1(x1))))))))))) -> 2(2(2(2(2(0(3(5(1(2(1(x1))))))))))) 5(5(5(0(3(5(2(4(1(2(4(x1))))))))))) -> 1(0(3(3(5(0(3(1(4(4(x1)))))))))) 0(3(3(2(0(1(1(2(1(3(0(5(x1)))))))))))) -> 2(3(0(2(5(4(1(0(1(2(4(3(x1)))))))))))) 3(3(2(5(2(5(4(5(0(5(4(2(1(x1))))))))))))) -> 2(1(2(3(3(4(4(2(0(3(4(1(x1)))))))))))) 4(3(4(2(2(5(4(5(0(0(0(2(5(x1))))))))))))) -> 4(4(5(1(4(5(0(1(0(5(3(x1))))))))))) 3(4(0(4(1(2(3(5(2(1(4(4(0(3(x1)))))))))))))) -> 3(2(2(5(0(4(5(5(0(5(5(4(1(2(x1)))))))))))))) 4(0(5(4(4(4(5(0(2(5(2(3(4(5(x1)))))))))))))) -> 4(1(0(4(3(4(2(3(1(3(2(3(3(x1))))))))))))) 5(3(5(4(2(4(4(5(0(5(4(1(2(2(x1)))))))))))))) -> 5(0(2(5(5(1(5(3(4(1(1(0(2(x1))))))))))))) 2(2(4(3(4(4(2(1(5(2(1(4(0(2(0(x1))))))))))))))) -> 3(5(3(3(1(2(1(3(0(4(5(3(4(0(x1)))))))))))))) 0(2(0(2(5(2(2(1(4(5(0(3(1(5(0(2(x1)))))))))))))))) -> 0(4(3(5(5(5(1(3(0(4(5(0(2(2(4(x1))))))))))))))) 5(0(0(2(0(2(2(0(1(1(3(4(4(3(3(5(x1)))))))))))))))) -> 5(4(0(3(4(4(1(0(0(3(5(1(4(5(5(5(x1)))))))))))))))) 5(0(2(3(2(4(4(3(4(1(0(0(0(4(4(3(x1)))))))))))))))) -> 5(2(4(4(4(0(1(1(4(2(5(5(1(3(x1)))))))))))))) 0(2(0(2(0(1(1(3(5(2(0(4(4(1(5(5(5(x1))))))))))))))))) -> 4(1(3(4(1(1(3(1(0(4(2(2(5(3(3(x1))))))))))))))) 0(4(3(0(2(1(3(3(3(0(5(1(2(3(2(5(4(0(x1)))))))))))))))))) -> 1(5(5(5(2(2(1(2(0(4(0(1(4(1(5(4(4(x1))))))))))))))))) 2(2(3(2(3(2(2(4(1(2(4(5(1(4(4(0(4(0(x1)))))))))))))))))) -> 5(2(2(0(4(4(5(4(2(3(2(3(1(0(5(3(3(4(x1)))))))))))))))))) 2(4(1(1(1(2(5(4(4(2(0(0(1(4(5(5(5(0(x1)))))))))))))))))) -> 3(3(2(4(5(2(5(4(5(4(5(3(3(3(0(5(0(2(3(x1))))))))))))))))))) 3(2(0(2(1(0(3(1(3(4(3(5(2(1(0(0(3(0(x1)))))))))))))))))) -> 5(2(4(0(1(5(2(3(3(5(4(4(5(2(3(3(3(0(x1)))))))))))))))))) 2(5(1(2(0(4(1(2(4(3(2(0(4(3(1(3(5(2(5(x1))))))))))))))))))) -> 2(4(5(1(2(3(0(4(1(3(2(3(4(2(0(3(3(3(x1)))))))))))))))))) 4(4(4(1(1(1(2(1(1(0(4(3(2(3(1(3(0(3(5(x1))))))))))))))))))) -> 4(1(0(2(3(3(0(1(1(4(5(3(1(1(5(3(2(2(3(5(x1)))))))))))))))))))) 3(5(3(3(0(0(4(4(4(4(0(1(1(5(2(5(0(5(0(2(x1)))))))))))))))))))) -> 2(0(5(2(4(3(3(4(5(4(3(1(4(0(0(2(5(1(1(x1))))))))))))))))))) 4(1(5(3(2(5(5(5(2(5(5(3(5(5(5(3(5(0(2(0(x1)))))))))))))))))))) -> 4(1(4(0(5(2(1(3(4(3(1(1(0(4(3(3(2(0(x1)))))))))))))))))) 0(0(4(0(0(0(0(1(0(4(4(5(3(2(2(4(0(5(3(0(5(x1))))))))))))))))))))) -> 0(2(2(2(1(2(4(4(5(0(5(1(0(0(5(5(2(5(3(2(x1)))))))))))))))))))) 2(2(0(3(4(0(5(2(5(2(2(5(2(5(5(1(5(2(4(1(4(x1))))))))))))))))))))) -> 0(0(5(2(4(1(4(3(4(3(2(4(4(3(4(4(1(1(4(x1))))))))))))))))))) 2(5(5(5(0(2(3(2(4(0(0(1(5(2(3(2(3(0(1(0(5(x1))))))))))))))))))))) -> 2(0(3(4(5(3(3(2(2(1(5(2(2(2(4(2(5(4(0(1(x1)))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(3(x1)))) -> 3(4(5(x1))) 1(2(0(5(5(x1))))) -> 1(5(4(0(x1)))) 2(0(3(4(2(x1))))) -> 3(1(2(4(x1)))) 5(5(5(5(0(x1))))) -> 5(4(4(3(x1)))) 0(1(2(4(3(5(x1)))))) -> 2(4(5(3(0(x1))))) 0(3(0(4(2(0(x1)))))) -> 2(3(4(1(2(x1))))) 4(5(0(4(0(0(0(x1))))))) -> 4(3(4(2(5(0(x1)))))) 0(1(0(2(1(4(4(2(x1)))))))) -> 0(2(0(3(3(4(5(4(x1)))))))) 2(0(0(1(5(0(5(2(x1)))))))) -> 2(0(5(2(1(1(x1)))))) 3(4(1(4(3(0(3(2(x1)))))))) -> 5(3(5(4(3(1(1(x1))))))) 5(3(0(1(5(5(0(5(x1)))))))) -> 5(0(4(2(1(3(4(x1))))))) 5(5(5(3(1(3(4(4(x1)))))))) -> 1(5(2(4(4(5(4(x1))))))) 0(1(5(4(2(5(3(3(4(x1))))))))) -> 2(0(5(4(3(0(1(0(4(x1))))))))) 0(3(3(1(2(2(0(4(5(x1))))))))) -> 2(3(4(4(4(0(3(1(x1)))))))) 4(3(4(0(5(3(0(0(5(4(x1)))))))))) -> 3(1(1(2(1(2(0(4(2(x1))))))))) 4(2(5(4(5(2(1(1(0(2(1(x1))))))))))) -> 4(2(3(4(1(0(5(4(5(2(1(x1))))))))))) 5(5(4(2(5(3(1(0(5(3(1(x1))))))))))) -> 2(2(2(2(2(0(3(5(1(2(1(x1))))))))))) 5(5(5(0(3(5(2(4(1(2(4(x1))))))))))) -> 1(0(3(3(5(0(3(1(4(4(x1)))))))))) 0(3(3(2(0(1(1(2(1(3(0(5(x1)))))))))))) -> 2(3(0(2(5(4(1(0(1(2(4(3(x1)))))))))))) 3(3(2(5(2(5(4(5(0(5(4(2(1(x1))))))))))))) -> 2(1(2(3(3(4(4(2(0(3(4(1(x1)))))))))))) 4(3(4(2(2(5(4(5(0(0(0(2(5(x1))))))))))))) -> 4(4(5(1(4(5(0(1(0(5(3(x1))))))))))) 3(4(0(4(1(2(3(5(2(1(4(4(0(3(x1)))))))))))))) -> 3(2(2(5(0(4(5(5(0(5(5(4(1(2(x1)))))))))))))) 4(0(5(4(4(4(5(0(2(5(2(3(4(5(x1)))))))))))))) -> 4(1(0(4(3(4(2(3(1(3(2(3(3(x1))))))))))))) 5(3(5(4(2(4(4(5(0(5(4(1(2(2(x1)))))))))))))) -> 5(0(2(5(5(1(5(3(4(1(1(0(2(x1))))))))))))) 2(2(4(3(4(4(2(1(5(2(1(4(0(2(0(x1))))))))))))))) -> 3(5(3(3(1(2(1(3(0(4(5(3(4(0(x1)))))))))))))) 0(2(0(2(5(2(2(1(4(5(0(3(1(5(0(2(x1)))))))))))))))) -> 0(4(3(5(5(5(1(3(0(4(5(0(2(2(4(x1))))))))))))))) 5(0(0(2(0(2(2(0(1(1(3(4(4(3(3(5(x1)))))))))))))))) -> 5(4(0(3(4(4(1(0(0(3(5(1(4(5(5(5(x1)))))))))))))))) 5(0(2(3(2(4(4(3(4(1(0(0(0(4(4(3(x1)))))))))))))))) -> 5(2(4(4(4(0(1(1(4(2(5(5(1(3(x1)))))))))))))) 0(2(0(2(0(1(1(3(5(2(0(4(4(1(5(5(5(x1))))))))))))))))) -> 4(1(3(4(1(1(3(1(0(4(2(2(5(3(3(x1))))))))))))))) 0(4(3(0(2(1(3(3(3(0(5(1(2(3(2(5(4(0(x1)))))))))))))))))) -> 1(5(5(5(2(2(1(2(0(4(0(1(4(1(5(4(4(x1))))))))))))))))) 2(2(3(2(3(2(2(4(1(2(4(5(1(4(4(0(4(0(x1)))))))))))))))))) -> 5(2(2(0(4(4(5(4(2(3(2(3(1(0(5(3(3(4(x1)))))))))))))))))) 2(4(1(1(1(2(5(4(4(2(0(0(1(4(5(5(5(0(x1)))))))))))))))))) -> 3(3(2(4(5(2(5(4(5(4(5(3(3(3(0(5(0(2(3(x1))))))))))))))))))) 3(2(0(2(1(0(3(1(3(4(3(5(2(1(0(0(3(0(x1)))))))))))))))))) -> 5(2(4(0(1(5(2(3(3(5(4(4(5(2(3(3(3(0(x1)))))))))))))))))) 2(5(1(2(0(4(1(2(4(3(2(0(4(3(1(3(5(2(5(x1))))))))))))))))))) -> 2(4(5(1(2(3(0(4(1(3(2(3(4(2(0(3(3(3(x1)))))))))))))))))) 4(4(4(1(1(1(2(1(1(0(4(3(2(3(1(3(0(3(5(x1))))))))))))))))))) -> 4(1(0(2(3(3(0(1(1(4(5(3(1(1(5(3(2(2(3(5(x1)))))))))))))))))))) 3(5(3(3(0(0(4(4(4(4(0(1(1(5(2(5(0(5(0(2(x1)))))))))))))))))))) -> 2(0(5(2(4(3(3(4(5(4(3(1(4(0(0(2(5(1(1(x1))))))))))))))))))) 4(1(5(3(2(5(5(5(2(5(5(3(5(5(5(3(5(0(2(0(x1)))))))))))))))))))) -> 4(1(4(0(5(2(1(3(4(3(1(1(0(4(3(3(2(0(x1)))))))))))))))))) 0(0(4(0(0(0(0(1(0(4(4(5(3(2(2(4(0(5(3(0(5(x1))))))))))))))))))))) -> 0(2(2(2(1(2(4(4(5(0(5(1(0(0(5(5(2(5(3(2(x1)))))))))))))))))))) 2(2(0(3(4(0(5(2(5(2(2(5(2(5(5(1(5(2(4(1(4(x1))))))))))))))))))))) -> 0(0(5(2(4(1(4(3(4(3(2(4(4(3(4(4(1(1(4(x1))))))))))))))))))) 2(5(5(5(0(2(3(2(4(0(0(1(5(2(3(2(3(0(1(0(5(x1))))))))))))))))))))) -> 2(0(3(4(5(3(3(2(2(1(5(2(2(2(4(2(5(4(0(1(x1)))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (7) CpxTrsMatchBoundsProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. The certificate found is represented by the following graph. "[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] {(151,152,[0_1|0, 1_1|0, 2_1|0, 5_1|0, 4_1|0, 3_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (151,153,[0_1|1, 1_1|1, 2_1|1, 5_1|1, 4_1|1, 3_1|1]), (151,154,[3_1|2]), (151,156,[2_1|2]), (151,160,[0_1|2]), (151,167,[2_1|2]), (151,175,[2_1|2]), (151,179,[2_1|2]), (151,186,[2_1|2]), (151,197,[0_1|2]), (151,211,[4_1|2]), (151,225,[1_1|2]), (151,241,[0_1|2]), (151,260,[1_1|2]), (151,263,[3_1|2]), (151,266,[2_1|2]), (151,271,[3_1|2]), (151,284,[5_1|2]), (151,301,[0_1|2]), (151,319,[3_1|2]), (151,337,[2_1|2]), (151,354,[2_1|2]), (151,373,[5_1|2]), (151,376,[1_1|2]), (151,382,[1_1|2]), (151,391,[2_1|2]), (151,401,[5_1|2]), (151,407,[5_1|2]), (151,419,[5_1|2]), (151,434,[5_1|2]), (151,447,[4_1|2]), (151,452,[3_1|2]), (151,460,[4_1|2]), (151,470,[4_1|2]), (151,480,[4_1|2]), (151,492,[4_1|2]), (151,511,[4_1|2]), (151,528,[5_1|2]), (151,534,[3_1|2]), (151,547,[2_1|2]), (151,558,[5_1|2]), (151,575,[2_1|2]), (152,152,[cons_0_1|0, cons_1_1|0, cons_2_1|0, cons_5_1|0, cons_4_1|0, cons_3_1|0]), (153,152,[encArg_1|1]), (153,153,[0_1|1, 1_1|1, 2_1|1, 5_1|1, 4_1|1, 3_1|1]), (153,154,[3_1|2]), (153,156,[2_1|2]), (153,160,[0_1|2]), (153,167,[2_1|2]), (153,175,[2_1|2]), (153,179,[2_1|2]), (153,186,[2_1|2]), (153,197,[0_1|2]), (153,211,[4_1|2]), (153,225,[1_1|2]), (153,241,[0_1|2]), (153,260,[1_1|2]), (153,263,[3_1|2]), (153,266,[2_1|2]), (153,271,[3_1|2]), (153,284,[5_1|2]), (153,301,[0_1|2]), (153,319,[3_1|2]), (153,337,[2_1|2]), (153,354,[2_1|2]), (153,373,[5_1|2]), (153,376,[1_1|2]), (153,382,[1_1|2]), (153,391,[2_1|2]), (153,401,[5_1|2]), (153,407,[5_1|2]), (153,419,[5_1|2]), (153,434,[5_1|2]), (153,447,[4_1|2]), (153,452,[3_1|2]), (153,460,[4_1|2]), (153,470,[4_1|2]), (153,480,[4_1|2]), (153,492,[4_1|2]), (153,511,[4_1|2]), (153,528,[5_1|2]), (153,534,[3_1|2]), (153,547,[2_1|2]), (153,558,[5_1|2]), (153,575,[2_1|2]), (154,155,[4_1|2]), (154,447,[4_1|2]), (155,153,[5_1|2]), (155,154,[5_1|2]), (155,263,[5_1|2]), (155,271,[5_1|2]), (155,319,[5_1|2]), (155,452,[5_1|2]), (155,534,[5_1|2]), (155,176,[5_1|2]), (155,180,[5_1|2]), (155,187,[5_1|2]), (155,373,[5_1|2]), (155,376,[1_1|2]), (155,382,[1_1|2]), (155,391,[2_1|2]), (155,401,[5_1|2]), (155,407,[5_1|2]), (155,419,[5_1|2]), (155,434,[5_1|2]), (156,157,[4_1|2]), (157,158,[5_1|2]), (157,401,[5_1|2]), (158,159,[3_1|2]), (159,153,[0_1|2]), (159,284,[0_1|2]), (159,373,[0_1|2]), (159,401,[0_1|2]), (159,407,[0_1|2]), (159,419,[0_1|2]), (159,434,[0_1|2]), (159,528,[0_1|2]), (159,558,[0_1|2]), (159,272,[0_1|2]), (159,154,[3_1|2]), (159,156,[2_1|2]), (159,160,[0_1|2]), (159,167,[2_1|2]), (159,175,[2_1|2]), 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(262,175,[2_1|2]), (262,179,[2_1|2]), (262,186,[2_1|2]), (262,197,[0_1|2]), (262,211,[4_1|2]), (262,225,[1_1|2]), (262,241,[0_1|2]), (263,264,[1_1|2]), (264,265,[2_1|2]), (264,319,[3_1|2]), (265,153,[4_1|2]), (265,156,[4_1|2]), (265,167,[4_1|2]), (265,175,[4_1|2]), (265,179,[4_1|2]), (265,186,[4_1|2]), (265,266,[4_1|2]), (265,337,[4_1|2]), (265,354,[4_1|2]), (265,391,[4_1|2]), (265,547,[4_1|2]), (265,575,[4_1|2]), (265,471,[4_1|2]), (265,447,[4_1|2]), (265,452,[3_1|2]), (265,460,[4_1|2]), (265,470,[4_1|2]), (265,480,[4_1|2]), (265,492,[4_1|2]), (265,511,[4_1|2]), (266,267,[0_1|2]), (267,268,[5_1|2]), (268,269,[2_1|2]), (269,270,[1_1|2]), (270,153,[1_1|2]), (270,156,[1_1|2]), (270,167,[1_1|2]), (270,175,[1_1|2]), (270,179,[1_1|2]), (270,186,[1_1|2]), (270,266,[1_1|2]), (270,337,[1_1|2]), (270,354,[1_1|2]), (270,391,[1_1|2]), (270,547,[1_1|2]), (270,575,[1_1|2]), (270,285,[1_1|2]), (270,435,[1_1|2]), (270,559,[1_1|2]), (270,260,[1_1|2]), (271,272,[5_1|2]), (272,273,[3_1|2]), 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(427,428,[3_1|2]), (428,429,[5_1|2]), (429,430,[1_1|2]), (430,431,[4_1|2]), (431,432,[5_1|2]), (431,373,[5_1|2]), (431,376,[1_1|2]), (431,382,[1_1|2]), (431,599,[5_1|3]), (432,433,[5_1|2]), (432,373,[5_1|2]), (432,376,[1_1|2]), (432,382,[1_1|2]), (432,391,[2_1|2]), (433,153,[5_1|2]), (433,284,[5_1|2]), (433,373,[5_1|2]), (433,401,[5_1|2]), (433,407,[5_1|2]), (433,419,[5_1|2]), (433,434,[5_1|2]), (433,528,[5_1|2]), (433,558,[5_1|2]), (433,272,[5_1|2]), (433,376,[1_1|2]), (433,382,[1_1|2]), (433,391,[2_1|2]), (434,435,[2_1|2]), (435,436,[4_1|2]), (436,437,[4_1|2]), (437,438,[4_1|2]), (438,439,[0_1|2]), (439,440,[1_1|2]), (440,441,[1_1|2]), (441,442,[4_1|2]), (442,443,[2_1|2]), (443,444,[5_1|2]), (444,445,[5_1|2]), (445,446,[1_1|2]), (446,153,[3_1|2]), (446,154,[3_1|2]), (446,263,[3_1|2]), (446,271,[3_1|2]), (446,319,[3_1|2]), (446,452,[3_1|2]), (446,534,[3_1|2]), (446,448,[3_1|2]), (446,528,[5_1|2]), (446,547,[2_1|2]), (446,558,[5_1|2]), (446,575,[2_1|2]), (447,448,[3_1|2]), (448,449,[4_1|2]), (449,450,[2_1|2]), (450,451,[5_1|2]), (450,419,[5_1|2]), (450,434,[5_1|2]), (451,153,[0_1|2]), (451,160,[0_1|2]), (451,197,[0_1|2]), (451,241,[0_1|2]), (451,301,[0_1|2]), (451,302,[0_1|2]), (451,154,[3_1|2]), (451,156,[2_1|2]), (451,167,[2_1|2]), (451,175,[2_1|2]), (451,179,[2_1|2]), (451,186,[2_1|2]), (451,211,[4_1|2]), (451,225,[1_1|2]), (452,453,[1_1|2]), (453,454,[1_1|2]), (454,455,[2_1|2]), (455,456,[1_1|2]), (456,457,[2_1|2]), (457,458,[0_1|2]), (458,459,[4_1|2]), (458,470,[4_1|2]), (459,153,[2_1|2]), (459,211,[2_1|2]), (459,447,[2_1|2]), (459,460,[2_1|2]), (459,470,[2_1|2]), (459,480,[2_1|2]), (459,492,[2_1|2]), (459,511,[2_1|2]), (459,374,[2_1|2]), (459,420,[2_1|2]), (459,263,[3_1|2]), (459,266,[2_1|2]), (459,271,[3_1|2]), (459,284,[5_1|2]), (459,301,[0_1|2]), (459,319,[3_1|2]), (459,337,[2_1|2]), (459,354,[2_1|2]), (460,461,[4_1|2]), (461,462,[5_1|2]), (462,463,[1_1|2]), (463,464,[4_1|2]), (464,465,[5_1|2]), (465,466,[0_1|2]), (466,467,[1_1|2]), (467,468,[0_1|2]), (468,469,[5_1|2]), (468,401,[5_1|2]), (468,407,[5_1|2]), (469,153,[3_1|2]), (469,284,[3_1|2]), (469,373,[3_1|2]), (469,401,[3_1|2]), (469,407,[3_1|2]), (469,419,[3_1|2]), (469,434,[3_1|2]), (469,528,[3_1|2, 5_1|2]), (469,558,[3_1|2, 5_1|2]), (469,534,[3_1|2]), (469,547,[2_1|2]), (469,575,[2_1|2]), (470,471,[2_1|2]), (471,472,[3_1|2]), (472,473,[4_1|2]), (473,474,[1_1|2]), (474,475,[0_1|2]), (475,476,[5_1|2]), (476,477,[4_1|2]), (477,478,[5_1|2]), (478,479,[2_1|2]), (479,153,[1_1|2]), (479,225,[1_1|2]), (479,260,[1_1|2]), (479,376,[1_1|2]), (479,382,[1_1|2]), (479,548,[1_1|2]), (480,481,[1_1|2]), (481,482,[0_1|2]), (482,483,[4_1|2]), (483,484,[3_1|2]), (484,485,[4_1|2]), (485,486,[2_1|2]), (486,487,[3_1|2]), (487,488,[1_1|2]), (488,489,[3_1|2]), (489,490,[2_1|2]), (490,491,[3_1|2]), (490,547,[2_1|2]), (491,153,[3_1|2]), (491,284,[3_1|2]), (491,373,[3_1|2]), (491,401,[3_1|2]), (491,407,[3_1|2]), (491,419,[3_1|2]), (491,434,[3_1|2]), (491,528,[3_1|2, 5_1|2]), (491,558,[3_1|2, 5_1|2]), (491,534,[3_1|2]), (491,547,[2_1|2]), (491,575,[2_1|2]), (491,154,[3_1|2]), (491,263,[3_1|2]), (491,271,[3_1|2]), (491,319,[3_1|2]), (491,452,[3_1|2]), (491,176,[3_1|2]), (491,180,[3_1|2]), (491,187,[3_1|2]), (492,493,[1_1|2]), (493,494,[0_1|2]), (494,495,[2_1|2]), (495,496,[3_1|2]), (496,497,[3_1|2]), (497,498,[0_1|2]), (498,499,[1_1|2]), (499,500,[1_1|2]), (500,501,[4_1|2]), (501,502,[5_1|2]), (502,503,[3_1|2]), (503,504,[1_1|2]), (504,505,[1_1|2]), (505,506,[5_1|2]), (506,507,[3_1|2]), (507,508,[2_1|2]), (508,509,[2_1|2]), (509,510,[3_1|2]), (509,575,[2_1|2]), (510,153,[5_1|2]), (510,284,[5_1|2]), (510,373,[5_1|2]), (510,401,[5_1|2]), (510,407,[5_1|2]), (510,419,[5_1|2]), (510,434,[5_1|2]), (510,528,[5_1|2]), (510,558,[5_1|2]), (510,272,[5_1|2]), (510,376,[1_1|2]), (510,382,[1_1|2]), (510,391,[2_1|2]), (511,512,[1_1|2]), (512,513,[4_1|2]), (513,514,[0_1|2]), (514,515,[5_1|2]), (515,516,[2_1|2]), (516,517,[1_1|2]), (517,518,[3_1|2]), (518,519,[4_1|2]), (519,520,[3_1|2]), (520,521,[1_1|2]), (521,522,[1_1|2]), (522,523,[0_1|2]), (523,524,[4_1|2]), (524,525,[3_1|2]), (525,526,[3_1|2]), (525,558,[5_1|2]), (526,527,[2_1|2]), (526,263,[3_1|2]), (526,266,[2_1|2]), (526,616,[3_1|3]), (527,153,[0_1|2]), (527,160,[0_1|2]), (527,197,[0_1|2]), (527,241,[0_1|2]), (527,301,[0_1|2]), (527,168,[0_1|2]), (527,267,[0_1|2]), (527,355,[0_1|2]), (527,576,[0_1|2]), (527,162,[0_1|2]), (527,154,[3_1|2]), (527,156,[2_1|2]), (527,167,[2_1|2]), (527,175,[2_1|2]), (527,179,[2_1|2]), (527,186,[2_1|2]), (527,211,[4_1|2]), (527,225,[1_1|2]), (528,529,[3_1|2]), (529,530,[5_1|2]), (530,531,[4_1|2]), (531,532,[3_1|2]), (532,533,[1_1|2]), (533,153,[1_1|2]), (533,156,[1_1|2]), (533,167,[1_1|2]), (533,175,[1_1|2]), (533,179,[1_1|2]), (533,186,[1_1|2]), (533,266,[1_1|2]), (533,337,[1_1|2]), (533,354,[1_1|2]), (533,391,[1_1|2]), (533,547,[1_1|2]), (533,575,[1_1|2]), (533,535,[1_1|2]), (533,260,[1_1|2]), (534,535,[2_1|2]), (535,536,[2_1|2]), (536,537,[5_1|2]), (537,538,[0_1|2]), (538,539,[4_1|2]), (539,540,[5_1|2]), (540,541,[5_1|2]), (541,542,[0_1|2]), (542,543,[5_1|2]), (543,544,[5_1|2]), (544,545,[4_1|2]), (545,546,[1_1|2]), (545,260,[1_1|2]), (546,153,[2_1|2]), (546,154,[2_1|2]), (546,263,[2_1|2, 3_1|2]), (546,271,[2_1|2, 3_1|2]), (546,319,[2_1|2, 3_1|2]), (546,452,[2_1|2]), (546,534,[2_1|2]), (546,266,[2_1|2]), (546,284,[5_1|2]), (546,301,[0_1|2]), (546,337,[2_1|2]), (546,354,[2_1|2]), (547,548,[1_1|2]), (548,549,[2_1|2]), (549,550,[3_1|2]), (550,551,[3_1|2]), (551,552,[4_1|2]), (552,553,[4_1|2]), (553,554,[2_1|2]), (554,555,[0_1|2]), (555,556,[3_1|2]), (555,528,[5_1|2]), (556,557,[4_1|2]), (556,511,[4_1|2]), (557,153,[1_1|2]), (557,225,[1_1|2]), (557,260,[1_1|2]), (557,376,[1_1|2]), (557,382,[1_1|2]), (557,548,[1_1|2]), (558,559,[2_1|2]), (559,560,[4_1|2]), (560,561,[0_1|2]), (561,562,[1_1|2]), (562,563,[5_1|2]), (563,564,[2_1|2]), (564,565,[3_1|2]), (565,566,[3_1|2]), (566,567,[5_1|2]), (567,568,[4_1|2]), (568,569,[4_1|2]), (569,570,[5_1|2]), (570,571,[2_1|2]), (571,572,[3_1|2]), (572,573,[3_1|2]), (573,574,[3_1|2]), (574,153,[0_1|2]), (574,160,[0_1|2]), (574,197,[0_1|2]), (574,241,[0_1|2]), (574,301,[0_1|2]), (574,154,[3_1|2]), (574,156,[2_1|2]), (574,167,[2_1|2]), (574,175,[2_1|2]), (574,179,[2_1|2]), (574,186,[2_1|2]), (574,211,[4_1|2]), (574,225,[1_1|2]), (575,576,[0_1|2]), (576,577,[5_1|2]), (577,578,[2_1|2]), (578,579,[4_1|2]), (579,580,[3_1|2]), (580,581,[3_1|2]), (581,582,[4_1|2]), (582,583,[5_1|2]), (583,584,[4_1|2]), (584,585,[3_1|2]), (585,586,[1_1|2]), (586,587,[4_1|2]), (587,588,[0_1|2]), (588,589,[0_1|2]), (589,590,[2_1|2]), (590,591,[5_1|2]), (591,592,[1_1|2]), (592,153,[1_1|2]), (592,156,[1_1|2]), (592,167,[1_1|2]), (592,175,[1_1|2]), (592,179,[1_1|2]), (592,186,[1_1|2]), (592,266,[1_1|2]), (592,337,[1_1|2]), (592,354,[1_1|2]), (592,391,[1_1|2]), (592,547,[1_1|2]), (592,575,[1_1|2]), (592,161,[1_1|2]), (592,242,[1_1|2]), (592,409,[1_1|2]), (592,260,[1_1|2]), (593,594,[4_1|3]), (594,595,[5_1|3]), (595,596,[3_1|3]), (596,284,[0_1|3]), (596,373,[0_1|3]), (596,401,[0_1|3]), (596,407,[0_1|3]), (596,419,[0_1|3]), (596,434,[0_1|3]), (596,528,[0_1|3]), (596,558,[0_1|3]), (597,598,[4_1|3]), (598,176,[5_1|3]), (598,180,[5_1|3]), (598,187,[5_1|3]), (599,600,[4_1|3]), (600,601,[4_1|3]), (601,402,[3_1|3]), (601,408,[3_1|3]), (602,603,[1_1|2]), (603,604,[0_1|2]), (604,605,[4_1|2]), (605,606,[3_1|2]), (606,607,[4_1|2]), (607,608,[2_1|2]), (608,609,[3_1|2]), (609,610,[1_1|2]), (610,611,[3_1|2]), (611,612,[2_1|2]), (612,613,[3_1|2]), (613,534,[3_1|2]), (613,176,[3_1|2]), (613,180,[3_1|2]), (613,187,[3_1|2]), (613,373,[3_1|2]), (613,401,[3_1|2]), (613,407,[3_1|2]), (613,419,[3_1|2]), (613,434,[3_1|2]), (614,615,[4_1|3]), (615,452,[5_1|3]), (616,617,[1_1|3]), (617,618,[2_1|3]), (618,391,[4_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)