/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 43 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 283 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(0(1(2(x1)))) -> 1(3(2(x1))) 0(1(0(1(x1)))) -> 4(3(2(x1))) 0(5(5(2(x1)))) -> 1(2(2(x1))) 0(4(5(2(5(x1))))) -> 1(3(2(5(x1)))) 4(0(2(4(2(x1))))) -> 1(3(3(x1))) 1(0(4(4(5(5(x1)))))) -> 4(3(2(0(1(x1))))) 4(5(1(4(5(1(x1)))))) -> 5(2(0(3(2(x1))))) 5(2(1(5(5(4(x1)))))) -> 4(3(4(2(0(x1))))) 0(5(0(3(0(4(0(4(x1)))))))) -> 1(3(4(5(2(4(4(x1))))))) 4(0(2(1(2(5(2(0(1(x1))))))))) -> 3(1(2(0(5(4(3(0(x1)))))))) 1(0(5(3(0(0(4(4(3(4(x1)))))))))) -> 2(1(3(1(2(2(2(1(1(x1))))))))) 3(1(0(4(0(3(0(5(5(5(x1)))))))))) -> 3(2(1(5(0(0(0(4(4(4(x1)))))))))) 4(3(5(0(1(4(1(5(1(4(x1)))))))))) -> 5(0(3(5(4(2(2(2(x1)))))))) 0(3(3(3(2(4(1(1(0(4(5(x1))))))))))) -> 0(3(1(5(2(2(0(1(5(4(0(2(x1)))))))))))) 2(2(0(1(0(4(5(2(5(1(2(x1))))))))))) -> 4(1(5(1(3(0(3(5(4(1(x1)))))))))) 4(1(5(3(1(5(3(2(5(5(0(x1))))))))))) -> 5(3(0(2(1(5(4(3(5(4(x1)))))))))) 5(0(2(1(4(5(0(3(4(2(0(0(x1)))))))))))) -> 0(4(0(4(0(5(1(4(0(3(3(x1))))))))))) 5(0(3(3(2(0(2(2(5(3(2(3(x1)))))))))))) -> 4(2(0(3(3(2(5(3(3(3(x1)))))))))) 3(0(4(5(2(5(4(5(5(1(5(4(0(x1))))))))))))) -> 3(2(3(0(0(2(4(1(2(4(3(x1))))))))))) 3(4(0(1(4(1(2(5(3(5(5(1(2(x1))))))))))))) -> 3(3(3(2(1(3(3(5(5(1(x1)))))))))) 0(5(2(4(3(4(5(1(5(1(2(2(5(2(x1)))))))))))))) -> 0(3(4(4(1(2(3(5(3(0(1(3(x1)))))))))))) 5(1(4(3(3(2(3(5(5(1(5(3(4(2(x1)))))))))))))) -> 5(3(5(1(4(4(4(3(3(5(5(5(0(3(x1)))))))))))))) 2(0(0(5(5(5(4(5(2(2(3(2(4(0(5(x1))))))))))))))) -> 2(5(2(3(5(2(4(2(4(4(1(5(1(x1))))))))))))) 2(0(3(4(3(3(0(1(3(5(2(5(2(4(5(x1))))))))))))))) -> 0(3(3(5(2(4(4(2(2(2(3(1(5(2(0(x1))))))))))))))) 2(2(3(0(5(2(1(0(3(2(0(3(2(2(2(x1))))))))))))))) -> 1(5(2(4(2(5(4(4(0(1(5(3(4(3(0(x1))))))))))))))) 3(0(3(2(5(5(1(3(2(4(3(1(1(1(1(5(x1)))))))))))))))) -> 3(3(0(4(0(1(0(2(2(1(5(3(4(0(1(x1))))))))))))))) 1(1(0(0(5(1(2(2(5(2(5(3(0(2(0(1(3(x1))))))))))))))))) -> 5(3(3(5(5(1(4(0(3(1(3(1(2(1(3(x1))))))))))))))) 1(2(2(5(3(4(4(3(4(0(5(3(5(3(5(0(1(x1))))))))))))))))) -> 1(3(2(4(5(3(5(2(1(1(4(4(3(5(0(1(5(x1))))))))))))))))) 0(1(1(3(0(2(2(2(5(4(5(0(3(0(1(2(2(3(x1)))))))))))))))))) -> 2(4(1(1(3(5(3(2(5(5(1(0(2(1(2(1(5(3(x1)))))))))))))))))) 1(5(1(2(0(2(2(3(1(0(0(0(5(1(0(2(2(1(x1)))))))))))))))))) -> 3(3(4(5(3(5(4(0(0(2(2(0(3(2(4(x1))))))))))))))) 5(2(1(3(0(0(0(0(3(2(2(4(1(0(2(1(1(0(x1)))))))))))))))))) -> 4(2(1(5(4(5(1(5(4(0(0(3(3(1(5(2(1(x1))))))))))))))))) 1(5(3(5(0(5(3(1(1(1(5(0(1(2(0(0(4(5(0(x1))))))))))))))))))) -> 4(3(3(5(4(4(2(0(4(0(2(2(5(5(4(3(0(x1))))))))))))))))) 1(5(4(4(3(0(1(2(5(4(3(5(0(2(5(1(1(2(5(x1))))))))))))))))))) -> 3(3(1(3(4(1(2(2(5(3(4(0(0(4(4(3(x1)))))))))))))))) 3(5(1(5(3(0(2(2(1(4(5(5(5(1(4(3(0(2(1(x1))))))))))))))))))) -> 1(2(3(5(4(5(1(0(5(1(3(4(4(0(0(4(0(4(0(x1))))))))))))))))))) 4(5(4(1(0(3(3(4(4(2(2(0(2(5(1(5(3(4(1(x1))))))))))))))))))) -> 1(4(1(1(2(4(1(4(0(2(4(2(1(4(2(0(2(0(2(2(x1)))))))))))))))))))) 5(2(5(3(1(2(1(2(3(4(5(4(1(1(2(2(1(3(4(2(x1)))))))))))))))))))) -> 3(2(3(0(1(4(3(3(0(2(2(5(2(3(5(3(1(4(2(x1))))))))))))))))))) 1(5(2(4(4(2(0(5(1(3(5(4(1(1(5(2(0(2(1(1(5(x1))))))))))))))))))))) -> 0(1(5(2(1(5(3(1(5(4(4(4(0(4(1(1(4(5(2(1(0(x1))))))))))))))))))))) 4(0(1(3(4(2(2(1(4(0(1(4(2(0(1(0(5(2(2(2(0(x1))))))))))))))))))))) -> 3(3(4(0(3(3(4(3(2(5(5(1(1(4(2(1(5(3(x1)))))))))))))))))) 4(5(0(0(3(5(2(3(2(3(1(3(5(4(0(3(3(0(0(0(1(x1))))))))))))))))))))) -> 3(1(1(2(1(4(5(2(2(3(4(1(3(3(5(2(0(4(4(5(3(x1))))))))))))))))))))) 5(4(1(5(4(0(3(1(3(3(4(5(4(4(3(1(3(4(0(1(4(x1))))))))))))))))))))) -> 3(3(1(3(2(2(0(1(1(0(2(3(3(5(3(2(2(5(5(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_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(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(0(1(2(x1)))) -> 1(3(2(x1))) 0(1(0(1(x1)))) -> 4(3(2(x1))) 0(5(5(2(x1)))) -> 1(2(2(x1))) 0(4(5(2(5(x1))))) -> 1(3(2(5(x1)))) 4(0(2(4(2(x1))))) -> 1(3(3(x1))) 1(0(4(4(5(5(x1)))))) -> 4(3(2(0(1(x1))))) 4(5(1(4(5(1(x1)))))) -> 5(2(0(3(2(x1))))) 5(2(1(5(5(4(x1)))))) -> 4(3(4(2(0(x1))))) 0(5(0(3(0(4(0(4(x1)))))))) -> 1(3(4(5(2(4(4(x1))))))) 4(0(2(1(2(5(2(0(1(x1))))))))) -> 3(1(2(0(5(4(3(0(x1)))))))) 1(0(5(3(0(0(4(4(3(4(x1)))))))))) -> 2(1(3(1(2(2(2(1(1(x1))))))))) 3(1(0(4(0(3(0(5(5(5(x1)))))))))) -> 3(2(1(5(0(0(0(4(4(4(x1)))))))))) 4(3(5(0(1(4(1(5(1(4(x1)))))))))) -> 5(0(3(5(4(2(2(2(x1)))))))) 0(3(3(3(2(4(1(1(0(4(5(x1))))))))))) -> 0(3(1(5(2(2(0(1(5(4(0(2(x1)))))))))))) 2(2(0(1(0(4(5(2(5(1(2(x1))))))))))) -> 4(1(5(1(3(0(3(5(4(1(x1)))))))))) 4(1(5(3(1(5(3(2(5(5(0(x1))))))))))) -> 5(3(0(2(1(5(4(3(5(4(x1)))))))))) 5(0(2(1(4(5(0(3(4(2(0(0(x1)))))))))))) -> 0(4(0(4(0(5(1(4(0(3(3(x1))))))))))) 5(0(3(3(2(0(2(2(5(3(2(3(x1)))))))))))) -> 4(2(0(3(3(2(5(3(3(3(x1)))))))))) 3(0(4(5(2(5(4(5(5(1(5(4(0(x1))))))))))))) -> 3(2(3(0(0(2(4(1(2(4(3(x1))))))))))) 3(4(0(1(4(1(2(5(3(5(5(1(2(x1))))))))))))) -> 3(3(3(2(1(3(3(5(5(1(x1)))))))))) 0(5(2(4(3(4(5(1(5(1(2(2(5(2(x1)))))))))))))) -> 0(3(4(4(1(2(3(5(3(0(1(3(x1)))))))))))) 5(1(4(3(3(2(3(5(5(1(5(3(4(2(x1)))))))))))))) -> 5(3(5(1(4(4(4(3(3(5(5(5(0(3(x1)))))))))))))) 2(0(0(5(5(5(4(5(2(2(3(2(4(0(5(x1))))))))))))))) -> 2(5(2(3(5(2(4(2(4(4(1(5(1(x1))))))))))))) 2(0(3(4(3(3(0(1(3(5(2(5(2(4(5(x1))))))))))))))) -> 0(3(3(5(2(4(4(2(2(2(3(1(5(2(0(x1))))))))))))))) 2(2(3(0(5(2(1(0(3(2(0(3(2(2(2(x1))))))))))))))) -> 1(5(2(4(2(5(4(4(0(1(5(3(4(3(0(x1))))))))))))))) 3(0(3(2(5(5(1(3(2(4(3(1(1(1(1(5(x1)))))))))))))))) -> 3(3(0(4(0(1(0(2(2(1(5(3(4(0(1(x1))))))))))))))) 1(1(0(0(5(1(2(2(5(2(5(3(0(2(0(1(3(x1))))))))))))))))) -> 5(3(3(5(5(1(4(0(3(1(3(1(2(1(3(x1))))))))))))))) 1(2(2(5(3(4(4(3(4(0(5(3(5(3(5(0(1(x1))))))))))))))))) -> 1(3(2(4(5(3(5(2(1(1(4(4(3(5(0(1(5(x1))))))))))))))))) 0(1(1(3(0(2(2(2(5(4(5(0(3(0(1(2(2(3(x1)))))))))))))))))) -> 2(4(1(1(3(5(3(2(5(5(1(0(2(1(2(1(5(3(x1)))))))))))))))))) 1(5(1(2(0(2(2(3(1(0(0(0(5(1(0(2(2(1(x1)))))))))))))))))) -> 3(3(4(5(3(5(4(0(0(2(2(0(3(2(4(x1))))))))))))))) 5(2(1(3(0(0(0(0(3(2(2(4(1(0(2(1(1(0(x1)))))))))))))))))) -> 4(2(1(5(4(5(1(5(4(0(0(3(3(1(5(2(1(x1))))))))))))))))) 1(5(3(5(0(5(3(1(1(1(5(0(1(2(0(0(4(5(0(x1))))))))))))))))))) -> 4(3(3(5(4(4(2(0(4(0(2(2(5(5(4(3(0(x1))))))))))))))))) 1(5(4(4(3(0(1(2(5(4(3(5(0(2(5(1(1(2(5(x1))))))))))))))))))) -> 3(3(1(3(4(1(2(2(5(3(4(0(0(4(4(3(x1)))))))))))))))) 3(5(1(5(3(0(2(2(1(4(5(5(5(1(4(3(0(2(1(x1))))))))))))))))))) -> 1(2(3(5(4(5(1(0(5(1(3(4(4(0(0(4(0(4(0(x1))))))))))))))))))) 4(5(4(1(0(3(3(4(4(2(2(0(2(5(1(5(3(4(1(x1))))))))))))))))))) -> 1(4(1(1(2(4(1(4(0(2(4(2(1(4(2(0(2(0(2(2(x1)))))))))))))))))))) 5(2(5(3(1(2(1(2(3(4(5(4(1(1(2(2(1(3(4(2(x1)))))))))))))))))))) -> 3(2(3(0(1(4(3(3(0(2(2(5(2(3(5(3(1(4(2(x1))))))))))))))))))) 1(5(2(4(4(2(0(5(1(3(5(4(1(1(5(2(0(2(1(1(5(x1))))))))))))))))))))) -> 0(1(5(2(1(5(3(1(5(4(4(4(0(4(1(1(4(5(2(1(0(x1))))))))))))))))))))) 4(0(1(3(4(2(2(1(4(0(1(4(2(0(1(0(5(2(2(2(0(x1))))))))))))))))))))) -> 3(3(4(0(3(3(4(3(2(5(5(1(1(4(2(1(5(3(x1)))))))))))))))))) 4(5(0(0(3(5(2(3(2(3(1(3(5(4(0(3(3(0(0(0(1(x1))))))))))))))))))))) -> 3(1(1(2(1(4(5(2(2(3(4(1(3(3(5(2(0(4(4(5(3(x1))))))))))))))))))))) 5(4(1(5(4(0(3(1(3(3(4(5(4(4(3(1(3(4(0(1(4(x1))))))))))))))))))))) -> 3(3(1(3(2(2(0(1(1(0(2(3(3(5(3(2(2(5(5(x1))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(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(0(1(2(x1)))) -> 1(3(2(x1))) 0(1(0(1(x1)))) -> 4(3(2(x1))) 0(5(5(2(x1)))) -> 1(2(2(x1))) 0(4(5(2(5(x1))))) -> 1(3(2(5(x1)))) 4(0(2(4(2(x1))))) -> 1(3(3(x1))) 1(0(4(4(5(5(x1)))))) -> 4(3(2(0(1(x1))))) 4(5(1(4(5(1(x1)))))) -> 5(2(0(3(2(x1))))) 5(2(1(5(5(4(x1)))))) -> 4(3(4(2(0(x1))))) 0(5(0(3(0(4(0(4(x1)))))))) -> 1(3(4(5(2(4(4(x1))))))) 4(0(2(1(2(5(2(0(1(x1))))))))) -> 3(1(2(0(5(4(3(0(x1)))))))) 1(0(5(3(0(0(4(4(3(4(x1)))))))))) -> 2(1(3(1(2(2(2(1(1(x1))))))))) 3(1(0(4(0(3(0(5(5(5(x1)))))))))) -> 3(2(1(5(0(0(0(4(4(4(x1)))))))))) 4(3(5(0(1(4(1(5(1(4(x1)))))))))) -> 5(0(3(5(4(2(2(2(x1)))))))) 0(3(3(3(2(4(1(1(0(4(5(x1))))))))))) -> 0(3(1(5(2(2(0(1(5(4(0(2(x1)))))))))))) 2(2(0(1(0(4(5(2(5(1(2(x1))))))))))) -> 4(1(5(1(3(0(3(5(4(1(x1)))))))))) 4(1(5(3(1(5(3(2(5(5(0(x1))))))))))) -> 5(3(0(2(1(5(4(3(5(4(x1)))))))))) 5(0(2(1(4(5(0(3(4(2(0(0(x1)))))))))))) -> 0(4(0(4(0(5(1(4(0(3(3(x1))))))))))) 5(0(3(3(2(0(2(2(5(3(2(3(x1)))))))))))) -> 4(2(0(3(3(2(5(3(3(3(x1)))))))))) 3(0(4(5(2(5(4(5(5(1(5(4(0(x1))))))))))))) -> 3(2(3(0(0(2(4(1(2(4(3(x1))))))))))) 3(4(0(1(4(1(2(5(3(5(5(1(2(x1))))))))))))) -> 3(3(3(2(1(3(3(5(5(1(x1)))))))))) 0(5(2(4(3(4(5(1(5(1(2(2(5(2(x1)))))))))))))) -> 0(3(4(4(1(2(3(5(3(0(1(3(x1)))))))))))) 5(1(4(3(3(2(3(5(5(1(5(3(4(2(x1)))))))))))))) -> 5(3(5(1(4(4(4(3(3(5(5(5(0(3(x1)))))))))))))) 2(0(0(5(5(5(4(5(2(2(3(2(4(0(5(x1))))))))))))))) -> 2(5(2(3(5(2(4(2(4(4(1(5(1(x1))))))))))))) 2(0(3(4(3(3(0(1(3(5(2(5(2(4(5(x1))))))))))))))) -> 0(3(3(5(2(4(4(2(2(2(3(1(5(2(0(x1))))))))))))))) 2(2(3(0(5(2(1(0(3(2(0(3(2(2(2(x1))))))))))))))) -> 1(5(2(4(2(5(4(4(0(1(5(3(4(3(0(x1))))))))))))))) 3(0(3(2(5(5(1(3(2(4(3(1(1(1(1(5(x1)))))))))))))))) -> 3(3(0(4(0(1(0(2(2(1(5(3(4(0(1(x1))))))))))))))) 1(1(0(0(5(1(2(2(5(2(5(3(0(2(0(1(3(x1))))))))))))))))) -> 5(3(3(5(5(1(4(0(3(1(3(1(2(1(3(x1))))))))))))))) 1(2(2(5(3(4(4(3(4(0(5(3(5(3(5(0(1(x1))))))))))))))))) -> 1(3(2(4(5(3(5(2(1(1(4(4(3(5(0(1(5(x1))))))))))))))))) 0(1(1(3(0(2(2(2(5(4(5(0(3(0(1(2(2(3(x1)))))))))))))))))) -> 2(4(1(1(3(5(3(2(5(5(1(0(2(1(2(1(5(3(x1)))))))))))))))))) 1(5(1(2(0(2(2(3(1(0(0(0(5(1(0(2(2(1(x1)))))))))))))))))) -> 3(3(4(5(3(5(4(0(0(2(2(0(3(2(4(x1))))))))))))))) 5(2(1(3(0(0(0(0(3(2(2(4(1(0(2(1(1(0(x1)))))))))))))))))) -> 4(2(1(5(4(5(1(5(4(0(0(3(3(1(5(2(1(x1))))))))))))))))) 1(5(3(5(0(5(3(1(1(1(5(0(1(2(0(0(4(5(0(x1))))))))))))))))))) -> 4(3(3(5(4(4(2(0(4(0(2(2(5(5(4(3(0(x1))))))))))))))))) 1(5(4(4(3(0(1(2(5(4(3(5(0(2(5(1(1(2(5(x1))))))))))))))))))) -> 3(3(1(3(4(1(2(2(5(3(4(0(0(4(4(3(x1)))))))))))))))) 3(5(1(5(3(0(2(2(1(4(5(5(5(1(4(3(0(2(1(x1))))))))))))))))))) -> 1(2(3(5(4(5(1(0(5(1(3(4(4(0(0(4(0(4(0(x1))))))))))))))))))) 4(5(4(1(0(3(3(4(4(2(2(0(2(5(1(5(3(4(1(x1))))))))))))))))))) -> 1(4(1(1(2(4(1(4(0(2(4(2(1(4(2(0(2(0(2(2(x1)))))))))))))))))))) 5(2(5(3(1(2(1(2(3(4(5(4(1(1(2(2(1(3(4(2(x1)))))))))))))))))))) -> 3(2(3(0(1(4(3(3(0(2(2(5(2(3(5(3(1(4(2(x1))))))))))))))))))) 1(5(2(4(4(2(0(5(1(3(5(4(1(1(5(2(0(2(1(1(5(x1))))))))))))))))))))) -> 0(1(5(2(1(5(3(1(5(4(4(4(0(4(1(1(4(5(2(1(0(x1))))))))))))))))))))) 4(0(1(3(4(2(2(1(4(0(1(4(2(0(1(0(5(2(2(2(0(x1))))))))))))))))))))) -> 3(3(4(0(3(3(4(3(2(5(5(1(1(4(2(1(5(3(x1)))))))))))))))))) 4(5(0(0(3(5(2(3(2(3(1(3(5(4(0(3(3(0(0(0(1(x1))))))))))))))))))))) -> 3(1(1(2(1(4(5(2(2(3(4(1(3(3(5(2(0(4(4(5(3(x1))))))))))))))))))))) 5(4(1(5(4(0(3(1(3(3(4(5(4(4(3(1(3(4(0(1(4(x1))))))))))))))))))))) -> 3(3(1(3(2(2(0(1(1(0(2(3(3(5(3(2(2(5(5(x1))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(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(0(1(2(x1)))) -> 1(3(2(x1))) 0(1(0(1(x1)))) -> 4(3(2(x1))) 0(5(5(2(x1)))) -> 1(2(2(x1))) 0(4(5(2(5(x1))))) -> 1(3(2(5(x1)))) 4(0(2(4(2(x1))))) -> 1(3(3(x1))) 1(0(4(4(5(5(x1)))))) -> 4(3(2(0(1(x1))))) 4(5(1(4(5(1(x1)))))) -> 5(2(0(3(2(x1))))) 5(2(1(5(5(4(x1)))))) -> 4(3(4(2(0(x1))))) 0(5(0(3(0(4(0(4(x1)))))))) -> 1(3(4(5(2(4(4(x1))))))) 4(0(2(1(2(5(2(0(1(x1))))))))) -> 3(1(2(0(5(4(3(0(x1)))))))) 1(0(5(3(0(0(4(4(3(4(x1)))))))))) -> 2(1(3(1(2(2(2(1(1(x1))))))))) 3(1(0(4(0(3(0(5(5(5(x1)))))))))) -> 3(2(1(5(0(0(0(4(4(4(x1)))))))))) 4(3(5(0(1(4(1(5(1(4(x1)))))))))) -> 5(0(3(5(4(2(2(2(x1)))))))) 0(3(3(3(2(4(1(1(0(4(5(x1))))))))))) -> 0(3(1(5(2(2(0(1(5(4(0(2(x1)))))))))))) 2(2(0(1(0(4(5(2(5(1(2(x1))))))))))) -> 4(1(5(1(3(0(3(5(4(1(x1)))))))))) 4(1(5(3(1(5(3(2(5(5(0(x1))))))))))) -> 5(3(0(2(1(5(4(3(5(4(x1)))))))))) 5(0(2(1(4(5(0(3(4(2(0(0(x1)))))))))))) -> 0(4(0(4(0(5(1(4(0(3(3(x1))))))))))) 5(0(3(3(2(0(2(2(5(3(2(3(x1)))))))))))) -> 4(2(0(3(3(2(5(3(3(3(x1)))))))))) 3(0(4(5(2(5(4(5(5(1(5(4(0(x1))))))))))))) -> 3(2(3(0(0(2(4(1(2(4(3(x1))))))))))) 3(4(0(1(4(1(2(5(3(5(5(1(2(x1))))))))))))) -> 3(3(3(2(1(3(3(5(5(1(x1)))))))))) 0(5(2(4(3(4(5(1(5(1(2(2(5(2(x1)))))))))))))) -> 0(3(4(4(1(2(3(5(3(0(1(3(x1)))))))))))) 5(1(4(3(3(2(3(5(5(1(5(3(4(2(x1)))))))))))))) -> 5(3(5(1(4(4(4(3(3(5(5(5(0(3(x1)))))))))))))) 2(0(0(5(5(5(4(5(2(2(3(2(4(0(5(x1))))))))))))))) -> 2(5(2(3(5(2(4(2(4(4(1(5(1(x1))))))))))))) 2(0(3(4(3(3(0(1(3(5(2(5(2(4(5(x1))))))))))))))) -> 0(3(3(5(2(4(4(2(2(2(3(1(5(2(0(x1))))))))))))))) 2(2(3(0(5(2(1(0(3(2(0(3(2(2(2(x1))))))))))))))) -> 1(5(2(4(2(5(4(4(0(1(5(3(4(3(0(x1))))))))))))))) 3(0(3(2(5(5(1(3(2(4(3(1(1(1(1(5(x1)))))))))))))))) -> 3(3(0(4(0(1(0(2(2(1(5(3(4(0(1(x1))))))))))))))) 1(1(0(0(5(1(2(2(5(2(5(3(0(2(0(1(3(x1))))))))))))))))) -> 5(3(3(5(5(1(4(0(3(1(3(1(2(1(3(x1))))))))))))))) 1(2(2(5(3(4(4(3(4(0(5(3(5(3(5(0(1(x1))))))))))))))))) -> 1(3(2(4(5(3(5(2(1(1(4(4(3(5(0(1(5(x1))))))))))))))))) 0(1(1(3(0(2(2(2(5(4(5(0(3(0(1(2(2(3(x1)))))))))))))))))) -> 2(4(1(1(3(5(3(2(5(5(1(0(2(1(2(1(5(3(x1)))))))))))))))))) 1(5(1(2(0(2(2(3(1(0(0(0(5(1(0(2(2(1(x1)))))))))))))))))) -> 3(3(4(5(3(5(4(0(0(2(2(0(3(2(4(x1))))))))))))))) 5(2(1(3(0(0(0(0(3(2(2(4(1(0(2(1(1(0(x1)))))))))))))))))) -> 4(2(1(5(4(5(1(5(4(0(0(3(3(1(5(2(1(x1))))))))))))))))) 1(5(3(5(0(5(3(1(1(1(5(0(1(2(0(0(4(5(0(x1))))))))))))))))))) -> 4(3(3(5(4(4(2(0(4(0(2(2(5(5(4(3(0(x1))))))))))))))))) 1(5(4(4(3(0(1(2(5(4(3(5(0(2(5(1(1(2(5(x1))))))))))))))))))) -> 3(3(1(3(4(1(2(2(5(3(4(0(0(4(4(3(x1)))))))))))))))) 3(5(1(5(3(0(2(2(1(4(5(5(5(1(4(3(0(2(1(x1))))))))))))))))))) -> 1(2(3(5(4(5(1(0(5(1(3(4(4(0(0(4(0(4(0(x1))))))))))))))))))) 4(5(4(1(0(3(3(4(4(2(2(0(2(5(1(5(3(4(1(x1))))))))))))))))))) -> 1(4(1(1(2(4(1(4(0(2(4(2(1(4(2(0(2(0(2(2(x1)))))))))))))))))))) 5(2(5(3(1(2(1(2(3(4(5(4(1(1(2(2(1(3(4(2(x1)))))))))))))))))))) -> 3(2(3(0(1(4(3(3(0(2(2(5(2(3(5(3(1(4(2(x1))))))))))))))))))) 1(5(2(4(4(2(0(5(1(3(5(4(1(1(5(2(0(2(1(1(5(x1))))))))))))))))))))) -> 0(1(5(2(1(5(3(1(5(4(4(4(0(4(1(1(4(5(2(1(0(x1))))))))))))))))))))) 4(0(1(3(4(2(2(1(4(0(1(4(2(0(1(0(5(2(2(2(0(x1))))))))))))))))))))) -> 3(3(4(0(3(3(4(3(2(5(5(1(1(4(2(1(5(3(x1)))))))))))))))))) 4(5(0(0(3(5(2(3(2(3(1(3(5(4(0(3(3(0(0(0(1(x1))))))))))))))))))))) -> 3(1(1(2(1(4(5(2(2(3(4(1(3(3(5(2(0(4(4(5(3(x1))))))))))))))))))))) 5(4(1(5(4(0(3(1(3(3(4(5(4(4(3(1(3(4(0(1(4(x1))))))))))))))))))))) -> 3(3(1(3(2(2(0(1(1(0(2(3(3(5(3(2(2(5(5(x1))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(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. "[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] {(148,149,[0_1|0, 4_1|0, 1_1|0, 5_1|0, 3_1|0, 2_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, 4_1|1, 1_1|1, 5_1|1, 3_1|1, 2_1|1]), (148,151,[1_1|2]), (148,153,[4_1|2]), (148,155,[2_1|2]), (148,172,[1_1|2]), (148,174,[1_1|2]), (148,180,[0_1|2]), (148,191,[1_1|2]), (148,194,[0_1|2]), (148,205,[1_1|2]), (148,207,[3_1|2]), (148,214,[3_1|2]), (148,231,[5_1|2]), (148,235,[1_1|2]), (148,254,[3_1|2]), (148,274,[5_1|2]), (148,281,[5_1|2]), (148,290,[4_1|2]), (148,294,[2_1|2]), (148,302,[5_1|2]), (148,316,[1_1|2]), (148,332,[3_1|2]), (148,346,[4_1|2]), (148,362,[3_1|2]), (148,377,[0_1|2]), (148,397,[4_1|2]), (148,401,[4_1|2]), (148,417,[3_1|2]), (148,435,[0_1|2]), (148,445,[4_1|2]), (148,454,[5_1|2]), (148,467,[3_1|2]), (148,485,[3_1|2]), (148,494,[3_1|2]), (148,504,[3_1|2]), (148,518,[3_1|2]), (148,527,[1_1|2]), (148,545,[4_1|2]), (148,554,[1_1|2]), (148,568,[2_1|2]), (148,580,[0_1|2]), (149,149,[cons_0_1|0, cons_4_1|0, cons_1_1|0, cons_5_1|0, cons_3_1|0, cons_2_1|0]), (150,149,[encArg_1|1]), (150,150,[0_1|1, 4_1|1, 1_1|1, 5_1|1, 3_1|1, 2_1|1]), (150,151,[1_1|2]), (150,153,[4_1|2]), (150,155,[2_1|2]), (150,172,[1_1|2]), (150,174,[1_1|2]), (150,180,[0_1|2]), (150,191,[1_1|2]), (150,194,[0_1|2]), (150,205,[1_1|2]), (150,207,[3_1|2]), (150,214,[3_1|2]), (150,231,[5_1|2]), (150,235,[1_1|2]), (150,254,[3_1|2]), (150,274,[5_1|2]), (150,281,[5_1|2]), (150,290,[4_1|2]), (150,294,[2_1|2]), (150,302,[5_1|2]), (150,316,[1_1|2]), (150,332,[3_1|2]), (150,346,[4_1|2]), (150,362,[3_1|2]), (150,377,[0_1|2]), (150,397,[4_1|2]), (150,401,[4_1|2]), (150,417,[3_1|2]), (150,435,[0_1|2]), (150,445,[4_1|2]), (150,454,[5_1|2]), (150,467,[3_1|2]), 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(414,415,[5_1|2]), (414,397,[4_1|2]), (414,401,[4_1|2]), (415,416,[2_1|2]), (416,150,[1_1|2]), (416,180,[1_1|2]), (416,194,[1_1|2]), (416,377,[1_1|2, 0_1|2]), (416,435,[1_1|2]), (416,580,[1_1|2]), (416,290,[4_1|2]), (416,294,[2_1|2]), (416,302,[5_1|2]), (416,316,[1_1|2]), (416,332,[3_1|2]), (416,346,[4_1|2]), (416,362,[3_1|2]), (417,418,[2_1|2]), (418,419,[3_1|2]), (419,420,[0_1|2]), (420,421,[1_1|2]), (421,422,[4_1|2]), (422,423,[3_1|2]), (423,424,[3_1|2]), (424,425,[0_1|2]), (425,426,[2_1|2]), (426,427,[2_1|2]), (427,428,[5_1|2]), (428,429,[2_1|2]), (429,430,[3_1|2]), (430,431,[5_1|2]), (431,432,[3_1|2]), (432,433,[1_1|2]), (433,434,[4_1|2]), (434,150,[2_1|2]), (434,155,[2_1|2]), (434,294,[2_1|2]), (434,568,[2_1|2]), (434,402,[2_1|2]), (434,446,[2_1|2]), (434,545,[4_1|2]), (434,554,[1_1|2]), (434,580,[0_1|2]), (435,436,[4_1|2]), (436,437,[0_1|2]), (437,438,[4_1|2]), (438,439,[0_1|2]), (439,440,[5_1|2]), (440,441,[1_1|2]), (441,442,[4_1|2]), (442,443,[0_1|2]), (442,194,[0_1|2]), (443,444,[3_1|2]), (444,150,[3_1|2]), (444,180,[3_1|2]), (444,194,[3_1|2]), (444,377,[3_1|2]), (444,435,[3_1|2]), (444,580,[3_1|2]), (444,485,[3_1|2]), (444,494,[3_1|2]), (444,504,[3_1|2]), (444,518,[3_1|2]), (444,527,[1_1|2]), (445,446,[2_1|2]), (446,447,[0_1|2]), (447,448,[3_1|2]), (448,449,[3_1|2]), (449,450,[2_1|2]), (450,451,[5_1|2]), (451,452,[3_1|2]), (452,453,[3_1|2]), (453,150,[3_1|2]), (453,207,[3_1|2]), (453,214,[3_1|2]), (453,254,[3_1|2]), (453,332,[3_1|2]), (453,362,[3_1|2]), (453,417,[3_1|2]), (453,467,[3_1|2]), (453,485,[3_1|2]), (453,494,[3_1|2]), (453,504,[3_1|2]), (453,518,[3_1|2]), (453,419,[3_1|2]), (453,496,[3_1|2]), (453,527,[1_1|2]), (454,455,[3_1|2]), (455,456,[5_1|2]), (456,457,[1_1|2]), (457,458,[4_1|2]), (458,459,[4_1|2]), (459,460,[4_1|2]), (460,461,[3_1|2]), (461,462,[3_1|2]), (462,463,[5_1|2]), (463,464,[5_1|2]), (464,465,[5_1|2]), (464,445,[4_1|2]), (465,466,[0_1|2]), (465,194,[0_1|2]), (466,150,[3_1|2]), (466,155,[3_1|2]), (466,294,[3_1|2]), (466,568,[3_1|2]), (466,402,[3_1|2]), (466,446,[3_1|2]), (466,485,[3_1|2]), (466,494,[3_1|2]), (466,504,[3_1|2]), (466,518,[3_1|2]), (466,527,[1_1|2]), (467,468,[3_1|2]), (468,469,[1_1|2]), (469,470,[3_1|2]), (470,471,[2_1|2]), (471,472,[2_1|2]), (472,473,[0_1|2]), (473,474,[1_1|2]), (474,475,[1_1|2]), (475,476,[0_1|2]), (476,477,[2_1|2]), (477,478,[3_1|2]), (478,479,[3_1|2]), (479,480,[5_1|2]), (480,481,[3_1|2]), (481,482,[2_1|2]), (482,483,[2_1|2]), (483,484,[5_1|2]), (484,150,[5_1|2]), (484,153,[5_1|2]), (484,290,[5_1|2]), (484,346,[5_1|2]), (484,397,[5_1|2, 4_1|2]), (484,401,[5_1|2, 4_1|2]), (484,445,[5_1|2, 4_1|2]), (484,545,[5_1|2]), (484,236,[5_1|2]), (484,417,[3_1|2]), (484,435,[0_1|2]), (484,454,[5_1|2]), (484,467,[3_1|2]), (485,486,[2_1|2]), (486,487,[1_1|2]), (487,488,[5_1|2]), (488,489,[0_1|2]), (489,490,[0_1|2]), (490,491,[0_1|2]), (491,492,[4_1|2]), (492,493,[4_1|2]), (493,150,[4_1|2]), (493,231,[4_1|2, 5_1|2]), (493,274,[4_1|2, 5_1|2]), (493,281,[4_1|2, 5_1|2]), (493,302,[4_1|2]), (493,454,[4_1|2]), (493,205,[1_1|2]), (493,207,[3_1|2]), (493,214,[3_1|2]), (493,235,[1_1|2]), (493,254,[3_1|2]), (494,495,[2_1|2]), (495,496,[3_1|2]), (496,497,[0_1|2]), (497,498,[0_1|2]), (498,499,[2_1|2]), (499,500,[4_1|2]), (500,501,[1_1|2]), (501,502,[2_1|2]), (502,503,[4_1|2]), (502,274,[5_1|2]), (503,150,[3_1|2]), (503,180,[3_1|2]), (503,194,[3_1|2]), (503,377,[3_1|2]), (503,435,[3_1|2]), (503,580,[3_1|2]), (503,485,[3_1|2]), (503,494,[3_1|2]), (503,504,[3_1|2]), (503,518,[3_1|2]), (503,527,[1_1|2]), (504,505,[3_1|2]), (505,506,[0_1|2]), (506,507,[4_1|2]), (507,508,[0_1|2]), (508,509,[1_1|2]), (509,510,[0_1|2]), (510,511,[2_1|2]), (511,512,[2_1|2]), (512,513,[1_1|2]), (513,514,[5_1|2]), (514,515,[3_1|2]), (514,518,[3_1|2]), (515,516,[4_1|2]), (515,214,[3_1|2]), (516,517,[0_1|2]), (516,153,[4_1|2]), (516,155,[2_1|2]), (516,598,[4_1|3]), (517,150,[1_1|2]), (517,231,[1_1|2]), (517,274,[1_1|2]), (517,281,[1_1|2]), (517,302,[1_1|2, 5_1|2]), (517,454,[1_1|2]), (517,555,[1_1|2]), (517,290,[4_1|2]), (517,294,[2_1|2]), (517,316,[1_1|2]), (517,332,[3_1|2]), (517,346,[4_1|2]), (517,362,[3_1|2]), (517,377,[0_1|2]), (518,519,[3_1|2]), (519,520,[3_1|2]), (520,521,[2_1|2]), (521,522,[1_1|2]), (522,523,[3_1|2]), (523,524,[3_1|2]), (524,525,[5_1|2]), (525,526,[5_1|2]), (525,454,[5_1|2]), (526,150,[1_1|2]), (526,155,[1_1|2]), (526,294,[1_1|2, 2_1|2]), (526,568,[1_1|2]), (526,173,[1_1|2]), (526,528,[1_1|2]), (526,290,[4_1|2]), (526,302,[5_1|2]), (526,316,[1_1|2]), (526,332,[3_1|2]), (526,346,[4_1|2]), (526,362,[3_1|2]), (526,377,[0_1|2]), (527,528,[2_1|2]), (528,529,[3_1|2]), (529,530,[5_1|2]), (530,531,[4_1|2]), (531,532,[5_1|2]), (532,533,[1_1|2]), (533,534,[0_1|2]), (534,535,[5_1|2]), (535,536,[1_1|2]), (536,537,[3_1|2]), (537,538,[4_1|2]), (538,539,[4_1|2]), (539,540,[0_1|2]), (540,541,[0_1|2]), (541,542,[4_1|2]), (542,543,[0_1|2]), (543,544,[4_1|2]), (543,205,[1_1|2]), (543,207,[3_1|2]), (543,214,[3_1|2]), (544,150,[0_1|2]), (544,151,[0_1|2, 1_1|2]), (544,172,[0_1|2, 1_1|2]), (544,174,[0_1|2, 1_1|2]), (544,191,[0_1|2, 1_1|2]), (544,205,[0_1|2]), (544,235,[0_1|2]), (544,316,[0_1|2, 1_1|2]), (544,527,[0_1|2]), (544,554,[0_1|2]), (544,295,[0_1|2]), (544,153,[4_1|2]), (544,155,[2_1|2]), (544,180,[0_1|2]), (544,194,[0_1|2]), (545,546,[1_1|2]), (546,547,[5_1|2]), (547,548,[1_1|2]), (548,549,[3_1|2]), (549,550,[0_1|2]), (550,551,[3_1|2]), (551,552,[5_1|2]), (551,467,[3_1|2]), (552,553,[4_1|2]), (552,281,[5_1|2]), (553,150,[1_1|2]), (553,155,[1_1|2]), (553,294,[1_1|2, 2_1|2]), (553,568,[1_1|2]), (553,173,[1_1|2]), (553,528,[1_1|2]), (553,290,[4_1|2]), (553,302,[5_1|2]), (553,316,[1_1|2]), (553,332,[3_1|2]), (553,346,[4_1|2]), (553,362,[3_1|2]), (553,377,[0_1|2]), (554,555,[5_1|2]), (555,556,[2_1|2]), (556,557,[4_1|2]), (557,558,[2_1|2]), (558,559,[5_1|2]), (559,560,[4_1|2]), (560,561,[4_1|2]), (561,562,[0_1|2]), (562,563,[1_1|2]), (563,564,[5_1|2]), (564,565,[3_1|2]), (565,566,[4_1|2]), (566,567,[3_1|2]), (566,494,[3_1|2]), (566,504,[3_1|2]), (567,150,[0_1|2]), (567,155,[0_1|2, 2_1|2]), (567,294,[0_1|2]), (567,568,[0_1|2]), (567,151,[1_1|2]), (567,153,[4_1|2]), (567,172,[1_1|2]), (567,174,[1_1|2]), (567,180,[0_1|2]), (567,191,[1_1|2]), (567,194,[0_1|2]), (567,316,[1_1|2]), (568,569,[5_1|2]), (569,570,[2_1|2]), (570,571,[3_1|2]), (571,572,[5_1|2]), (572,573,[2_1|2]), (573,574,[4_1|2]), (574,575,[2_1|2]), (575,576,[4_1|2]), (576,577,[4_1|2]), (577,578,[1_1|2]), (577,332,[3_1|2]), (578,579,[5_1|2]), (578,454,[5_1|2]), (579,150,[1_1|2]), (579,231,[1_1|2]), (579,274,[1_1|2]), (579,281,[1_1|2]), (579,302,[1_1|2, 5_1|2]), (579,454,[1_1|2]), (579,290,[4_1|2]), (579,294,[2_1|2]), (579,316,[1_1|2]), (579,332,[3_1|2]), (579,346,[4_1|2]), (579,362,[3_1|2]), (579,377,[0_1|2]), (580,581,[3_1|2]), (581,582,[3_1|2]), (582,583,[5_1|2]), (583,584,[2_1|2]), (584,585,[4_1|2]), (585,586,[4_1|2]), (586,587,[2_1|2]), (587,588,[2_1|2]), (588,589,[2_1|2]), (589,590,[3_1|2]), (590,591,[1_1|2]), (591,592,[5_1|2]), (592,593,[2_1|2]), (592,568,[2_1|2]), (592,580,[0_1|2]), (593,150,[0_1|2]), (593,231,[0_1|2]), (593,274,[0_1|2]), (593,281,[0_1|2]), (593,302,[0_1|2]), (593,454,[0_1|2]), (593,151,[1_1|2]), (593,153,[4_1|2]), (593,155,[2_1|2]), (593,172,[1_1|2]), (593,174,[1_1|2]), (593,180,[0_1|2]), (593,191,[1_1|2]), (593,194,[0_1|2]), (593,316,[1_1|2]), (594,595,[3_1|3]), (595,402,[3_1|3]), (595,446,[3_1|3]), (596,597,[3_1|3]), (597,246,[3_1|3]), (598,599,[3_1|3]), (599,378,[2_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)