/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 65 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 190 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(0(0(x1)))))) -> 0(0(3(4(0(x1))))) 1(5(5(3(1(4(x1)))))) -> 2(1(4(1(0(x1))))) 2(0(2(2(2(0(x1)))))) -> 2(1(0(5(0(x1))))) 2(5(2(2(3(0(x1)))))) -> 2(5(5(1(0(x1))))) 1(2(0(1(5(3(1(x1))))))) -> 0(2(4(3(1(5(x1)))))) 2(3(2(2(0(2(3(x1))))))) -> 2(5(4(1(0(0(x1)))))) 2(4(2(5(1(3(1(x1))))))) -> 2(1(1(3(4(3(x1)))))) 0(0(3(2(4(5(2(2(x1)))))))) -> 5(1(2(0(2(5(2(2(x1)))))))) 1(2(2(4(0(1(2(4(x1)))))))) -> 4(2(0(4(3(3(4(x1))))))) 0(0(2(0(3(5(4(2(0(x1))))))))) -> 5(5(1(5(5(0(4(0(x1)))))))) 4(1(3(4(1(2(3(4(2(x1))))))))) -> 1(1(0(4(3(5(2(2(x1)))))))) 0(2(2(0(3(5(2(4(1(2(x1)))))))))) -> 0(4(5(3(3(0(5(5(3(x1))))))))) 2(4(3(5(5(2(4(2(5(1(x1)))))))))) -> 4(1(4(1(4(4(0(0(1(x1))))))))) 1(3(2(5(1(1(1(1(0(1(3(x1))))))))))) -> 0(3(5(5(5(0(0(1(2(4(2(0(x1)))))))))))) 1(5(5(5(0(5(1(5(2(0(3(x1))))))))))) -> 0(0(4(4(5(4(3(4(3(3(x1)))))))))) 2(2(0(1(1(1(2(3(3(2(0(x1))))))))))) -> 3(0(1(3(1(5(1(5(1(0(x1)))))))))) 2(0(4(4(4(2(3(0(5(2(4(2(x1)))))))))))) -> 2(5(5(5(3(4(1(3(4(4(2(x1))))))))))) 2(2(2(1(1(0(5(3(1(4(4(3(x1)))))))))))) -> 5(4(1(2(0(3(3(1(3(5(5(3(x1)))))))))))) 2(2(4(2(1(1(2(0(0(5(2(1(x1)))))))))))) -> 4(2(1(0(1(0(4(2(3(3(x1)))))))))) 4(0(3(0(5(2(5(4(3(1(5(0(x1)))))))))))) -> 1(3(1(1(2(1(5(2(0(4(3(0(x1)))))))))))) 4(5(3(4(2(0(4(3(3(5(3(4(x1)))))))))))) -> 2(1(4(5(3(3(1(0(3(2(2(4(x1)))))))))))) 1(4(1(3(2(1(5(2(2(1(3(4(5(x1))))))))))))) -> 0(3(1(5(3(0(1(2(3(3(1(0(x1)))))))))))) 2(2(1(4(1(1(1(0(1(3(5(3(4(3(x1)))))))))))))) -> 2(5(3(4(1(5(3(0(0(5(2(2(4(2(3(x1))))))))))))))) 4(3(1(4(0(1(0(4(2(2(3(4(0(0(x1)))))))))))))) -> 3(4(0(0(0(1(0(1(1(0(1(3(0(x1))))))))))))) 0(1(2(0(5(3(4(5(2(4(3(4(1(3(5(x1))))))))))))))) -> 0(2(1(1(3(3(3(3(0(5(2(3(2(0(0(x1))))))))))))))) 1(5(5(4(3(3(5(1(2(0(0(2(4(3(0(x1))))))))))))))) -> 1(1(1(0(3(4(5(1(3(1(1(0(x1)))))))))))) 4(0(2(5(3(5(4(3(5(4(5(4(5(1(3(x1))))))))))))))) -> 4(0(3(1(4(3(2(4(5(1(1(5(1(0(x1)))))))))))))) 4(4(3(4(1(5(1(2(1(0(0(3(5(2(3(x1))))))))))))))) -> 1(3(2(1(2(3(2(4(5(5(5(0(3(1(3(x1))))))))))))))) 0(2(0(4(2(4(4(4(3(3(4(2(2(2(4(3(x1)))))))))))))))) -> 0(4(2(1(5(4(3(3(1(3(3(0(1(0(3(x1))))))))))))))) 2(5(0(0(1(3(4(1(0(5(3(2(2(3(0(3(x1)))))))))))))))) -> 3(5(3(3(0(3(0(2(0(1(4(5(2(0(0(3(x1)))))))))))))))) 2(4(5(5(3(2(0(0(1(4(2(1(3(2(2(0(5(x1))))))))))))))))) -> 0(5(2(0(5(2(4(1(3(2(3(1(2(3(0(0(x1)))))))))))))))) 0(5(5(3(4(0(1(4(1(4(4(2(3(2(5(4(1(3(x1)))))))))))))))))) -> 0(3(0(0(5(0(3(0(1(1(0(3(3(3(4(5(5(x1))))))))))))))))) 2(0(0(4(3(5(3(4(1(4(3(0(3(0(1(4(5(4(x1)))))))))))))))))) -> 5(0(1(1(3(3(0(1(2(0(5(4(2(5(2(0(4(5(x1)))))))))))))))))) 2(2(3(5(0(3(3(0(0(2(4(1(2(3(4(2(2(4(x1)))))))))))))))))) -> 4(1(5(0(2(5(4(0(2(1(3(3(0(0(4(5(4(x1))))))))))))))))) 4(0(4(1(5(4(5(5(2(4(5(4(4(0(5(3(5(0(x1)))))))))))))))))) -> 3(5(5(4(4(2(2(0(3(0(4(5(0(1(5(4(4(0(x1)))))))))))))))))) 4(2(1(4(0(0(2(1(1(4(3(4(1(5(4(0(1(4(x1)))))))))))))))))) -> 2(5(4(2(5(2(1(4(0(3(1(3(1(4(0(0(1(4(x1)))))))))))))))))) 4(5(1(4(5(3(3(5(1(2(4(3(4(3(5(1(3(3(1(x1))))))))))))))))))) -> 0(1(2(0(0(1(5(1(5(1(4(0(0(4(3(1(1(1(x1)))))))))))))))))) 4(1(5(2(2(4(2(3(3(1(1(4(2(0(5(1(0(0(3(5(x1)))))))))))))))))))) -> 4(1(0(4(5(3(2(4(4(5(4(5(2(4(1(2(2(1(3(x1))))))))))))))))))) 5(4(0(5(5(2(3(5(1(4(1(2(1(3(4(4(1(2(4(3(x1)))))))))))))))))))) -> 5(2(5(4(3(3(4(2(5(3(5(3(4(1(0(2(4(4(3(x1))))))))))))))))))) 3(2(1(5(5(4(5(3(4(2(2(4(5(5(4(4(0(4(2(5(5(x1))))))))))))))))))))) -> 3(5(4(3(1(3(4(1(1(4(3(0(0(0(4(3(3(3(2(5(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(0(1(2(0(0(x1)))))) -> 0(0(3(4(0(x1))))) 1(5(5(3(1(4(x1)))))) -> 2(1(4(1(0(x1))))) 2(0(2(2(2(0(x1)))))) -> 2(1(0(5(0(x1))))) 2(5(2(2(3(0(x1)))))) -> 2(5(5(1(0(x1))))) 1(2(0(1(5(3(1(x1))))))) -> 0(2(4(3(1(5(x1)))))) 2(3(2(2(0(2(3(x1))))))) -> 2(5(4(1(0(0(x1)))))) 2(4(2(5(1(3(1(x1))))))) -> 2(1(1(3(4(3(x1)))))) 0(0(3(2(4(5(2(2(x1)))))))) -> 5(1(2(0(2(5(2(2(x1)))))))) 1(2(2(4(0(1(2(4(x1)))))))) -> 4(2(0(4(3(3(4(x1))))))) 0(0(2(0(3(5(4(2(0(x1))))))))) -> 5(5(1(5(5(0(4(0(x1)))))))) 4(1(3(4(1(2(3(4(2(x1))))))))) -> 1(1(0(4(3(5(2(2(x1)))))))) 0(2(2(0(3(5(2(4(1(2(x1)))))))))) -> 0(4(5(3(3(0(5(5(3(x1))))))))) 2(4(3(5(5(2(4(2(5(1(x1)))))))))) -> 4(1(4(1(4(4(0(0(1(x1))))))))) 1(3(2(5(1(1(1(1(0(1(3(x1))))))))))) -> 0(3(5(5(5(0(0(1(2(4(2(0(x1)))))))))))) 1(5(5(5(0(5(1(5(2(0(3(x1))))))))))) -> 0(0(4(4(5(4(3(4(3(3(x1)))))))))) 2(2(0(1(1(1(2(3(3(2(0(x1))))))))))) -> 3(0(1(3(1(5(1(5(1(0(x1)))))))))) 2(0(4(4(4(2(3(0(5(2(4(2(x1)))))))))))) -> 2(5(5(5(3(4(1(3(4(4(2(x1))))))))))) 2(2(2(1(1(0(5(3(1(4(4(3(x1)))))))))))) -> 5(4(1(2(0(3(3(1(3(5(5(3(x1)))))))))))) 2(2(4(2(1(1(2(0(0(5(2(1(x1)))))))))))) -> 4(2(1(0(1(0(4(2(3(3(x1)))))))))) 4(0(3(0(5(2(5(4(3(1(5(0(x1)))))))))))) -> 1(3(1(1(2(1(5(2(0(4(3(0(x1)))))))))))) 4(5(3(4(2(0(4(3(3(5(3(4(x1)))))))))))) -> 2(1(4(5(3(3(1(0(3(2(2(4(x1)))))))))))) 1(4(1(3(2(1(5(2(2(1(3(4(5(x1))))))))))))) -> 0(3(1(5(3(0(1(2(3(3(1(0(x1)))))))))))) 2(2(1(4(1(1(1(0(1(3(5(3(4(3(x1)))))))))))))) -> 2(5(3(4(1(5(3(0(0(5(2(2(4(2(3(x1))))))))))))))) 4(3(1(4(0(1(0(4(2(2(3(4(0(0(x1)))))))))))))) -> 3(4(0(0(0(1(0(1(1(0(1(3(0(x1))))))))))))) 0(1(2(0(5(3(4(5(2(4(3(4(1(3(5(x1))))))))))))))) -> 0(2(1(1(3(3(3(3(0(5(2(3(2(0(0(x1))))))))))))))) 1(5(5(4(3(3(5(1(2(0(0(2(4(3(0(x1))))))))))))))) -> 1(1(1(0(3(4(5(1(3(1(1(0(x1)))))))))))) 4(0(2(5(3(5(4(3(5(4(5(4(5(1(3(x1))))))))))))))) -> 4(0(3(1(4(3(2(4(5(1(1(5(1(0(x1)))))))))))))) 4(4(3(4(1(5(1(2(1(0(0(3(5(2(3(x1))))))))))))))) -> 1(3(2(1(2(3(2(4(5(5(5(0(3(1(3(x1))))))))))))))) 0(2(0(4(2(4(4(4(3(3(4(2(2(2(4(3(x1)))))))))))))))) -> 0(4(2(1(5(4(3(3(1(3(3(0(1(0(3(x1))))))))))))))) 2(5(0(0(1(3(4(1(0(5(3(2(2(3(0(3(x1)))))))))))))))) -> 3(5(3(3(0(3(0(2(0(1(4(5(2(0(0(3(x1)))))))))))))))) 2(4(5(5(3(2(0(0(1(4(2(1(3(2(2(0(5(x1))))))))))))))))) -> 0(5(2(0(5(2(4(1(3(2(3(1(2(3(0(0(x1)))))))))))))))) 0(5(5(3(4(0(1(4(1(4(4(2(3(2(5(4(1(3(x1)))))))))))))))))) -> 0(3(0(0(5(0(3(0(1(1(0(3(3(3(4(5(5(x1))))))))))))))))) 2(0(0(4(3(5(3(4(1(4(3(0(3(0(1(4(5(4(x1)))))))))))))))))) -> 5(0(1(1(3(3(0(1(2(0(5(4(2(5(2(0(4(5(x1)))))))))))))))))) 2(2(3(5(0(3(3(0(0(2(4(1(2(3(4(2(2(4(x1)))))))))))))))))) -> 4(1(5(0(2(5(4(0(2(1(3(3(0(0(4(5(4(x1))))))))))))))))) 4(0(4(1(5(4(5(5(2(4(5(4(4(0(5(3(5(0(x1)))))))))))))))))) -> 3(5(5(4(4(2(2(0(3(0(4(5(0(1(5(4(4(0(x1)))))))))))))))))) 4(2(1(4(0(0(2(1(1(4(3(4(1(5(4(0(1(4(x1)))))))))))))))))) -> 2(5(4(2(5(2(1(4(0(3(1(3(1(4(0(0(1(4(x1)))))))))))))))))) 4(5(1(4(5(3(3(5(1(2(4(3(4(3(5(1(3(3(1(x1))))))))))))))))))) -> 0(1(2(0(0(1(5(1(5(1(4(0(0(4(3(1(1(1(x1)))))))))))))))))) 4(1(5(2(2(4(2(3(3(1(1(4(2(0(5(1(0(0(3(5(x1)))))))))))))))))))) -> 4(1(0(4(5(3(2(4(4(5(4(5(2(4(1(2(2(1(3(x1))))))))))))))))))) 5(4(0(5(5(2(3(5(1(4(1(2(1(3(4(4(1(2(4(3(x1)))))))))))))))))))) -> 5(2(5(4(3(3(4(2(5(3(5(3(4(1(0(2(4(4(3(x1))))))))))))))))))) 3(2(1(5(5(4(5(3(4(2(2(4(5(5(4(4(0(4(2(5(5(x1))))))))))))))))))))) -> 3(5(4(3(1(3(4(1(1(4(3(0(0(0(4(3(3(3(2(5(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(0(1(2(0(0(x1)))))) -> 0(0(3(4(0(x1))))) 1(5(5(3(1(4(x1)))))) -> 2(1(4(1(0(x1))))) 2(0(2(2(2(0(x1)))))) -> 2(1(0(5(0(x1))))) 2(5(2(2(3(0(x1)))))) -> 2(5(5(1(0(x1))))) 1(2(0(1(5(3(1(x1))))))) -> 0(2(4(3(1(5(x1)))))) 2(3(2(2(0(2(3(x1))))))) -> 2(5(4(1(0(0(x1)))))) 2(4(2(5(1(3(1(x1))))))) -> 2(1(1(3(4(3(x1)))))) 0(0(3(2(4(5(2(2(x1)))))))) -> 5(1(2(0(2(5(2(2(x1)))))))) 1(2(2(4(0(1(2(4(x1)))))))) -> 4(2(0(4(3(3(4(x1))))))) 0(0(2(0(3(5(4(2(0(x1))))))))) -> 5(5(1(5(5(0(4(0(x1)))))))) 4(1(3(4(1(2(3(4(2(x1))))))))) -> 1(1(0(4(3(5(2(2(x1)))))))) 0(2(2(0(3(5(2(4(1(2(x1)))))))))) -> 0(4(5(3(3(0(5(5(3(x1))))))))) 2(4(3(5(5(2(4(2(5(1(x1)))))))))) -> 4(1(4(1(4(4(0(0(1(x1))))))))) 1(3(2(5(1(1(1(1(0(1(3(x1))))))))))) -> 0(3(5(5(5(0(0(1(2(4(2(0(x1)))))))))))) 1(5(5(5(0(5(1(5(2(0(3(x1))))))))))) -> 0(0(4(4(5(4(3(4(3(3(x1)))))))))) 2(2(0(1(1(1(2(3(3(2(0(x1))))))))))) -> 3(0(1(3(1(5(1(5(1(0(x1)))))))))) 2(0(4(4(4(2(3(0(5(2(4(2(x1)))))))))))) -> 2(5(5(5(3(4(1(3(4(4(2(x1))))))))))) 2(2(2(1(1(0(5(3(1(4(4(3(x1)))))))))))) -> 5(4(1(2(0(3(3(1(3(5(5(3(x1)))))))))))) 2(2(4(2(1(1(2(0(0(5(2(1(x1)))))))))))) -> 4(2(1(0(1(0(4(2(3(3(x1)))))))))) 4(0(3(0(5(2(5(4(3(1(5(0(x1)))))))))))) -> 1(3(1(1(2(1(5(2(0(4(3(0(x1)))))))))))) 4(5(3(4(2(0(4(3(3(5(3(4(x1)))))))))))) -> 2(1(4(5(3(3(1(0(3(2(2(4(x1)))))))))))) 1(4(1(3(2(1(5(2(2(1(3(4(5(x1))))))))))))) -> 0(3(1(5(3(0(1(2(3(3(1(0(x1)))))))))))) 2(2(1(4(1(1(1(0(1(3(5(3(4(3(x1)))))))))))))) -> 2(5(3(4(1(5(3(0(0(5(2(2(4(2(3(x1))))))))))))))) 4(3(1(4(0(1(0(4(2(2(3(4(0(0(x1)))))))))))))) -> 3(4(0(0(0(1(0(1(1(0(1(3(0(x1))))))))))))) 0(1(2(0(5(3(4(5(2(4(3(4(1(3(5(x1))))))))))))))) -> 0(2(1(1(3(3(3(3(0(5(2(3(2(0(0(x1))))))))))))))) 1(5(5(4(3(3(5(1(2(0(0(2(4(3(0(x1))))))))))))))) -> 1(1(1(0(3(4(5(1(3(1(1(0(x1)))))))))))) 4(0(2(5(3(5(4(3(5(4(5(4(5(1(3(x1))))))))))))))) -> 4(0(3(1(4(3(2(4(5(1(1(5(1(0(x1)))))))))))))) 4(4(3(4(1(5(1(2(1(0(0(3(5(2(3(x1))))))))))))))) -> 1(3(2(1(2(3(2(4(5(5(5(0(3(1(3(x1))))))))))))))) 0(2(0(4(2(4(4(4(3(3(4(2(2(2(4(3(x1)))))))))))))))) -> 0(4(2(1(5(4(3(3(1(3(3(0(1(0(3(x1))))))))))))))) 2(5(0(0(1(3(4(1(0(5(3(2(2(3(0(3(x1)))))))))))))))) -> 3(5(3(3(0(3(0(2(0(1(4(5(2(0(0(3(x1)))))))))))))))) 2(4(5(5(3(2(0(0(1(4(2(1(3(2(2(0(5(x1))))))))))))))))) -> 0(5(2(0(5(2(4(1(3(2(3(1(2(3(0(0(x1)))))))))))))))) 0(5(5(3(4(0(1(4(1(4(4(2(3(2(5(4(1(3(x1)))))))))))))))))) -> 0(3(0(0(5(0(3(0(1(1(0(3(3(3(4(5(5(x1))))))))))))))))) 2(0(0(4(3(5(3(4(1(4(3(0(3(0(1(4(5(4(x1)))))))))))))))))) -> 5(0(1(1(3(3(0(1(2(0(5(4(2(5(2(0(4(5(x1)))))))))))))))))) 2(2(3(5(0(3(3(0(0(2(4(1(2(3(4(2(2(4(x1)))))))))))))))))) -> 4(1(5(0(2(5(4(0(2(1(3(3(0(0(4(5(4(x1))))))))))))))))) 4(0(4(1(5(4(5(5(2(4(5(4(4(0(5(3(5(0(x1)))))))))))))))))) -> 3(5(5(4(4(2(2(0(3(0(4(5(0(1(5(4(4(0(x1)))))))))))))))))) 4(2(1(4(0(0(2(1(1(4(3(4(1(5(4(0(1(4(x1)))))))))))))))))) -> 2(5(4(2(5(2(1(4(0(3(1(3(1(4(0(0(1(4(x1)))))))))))))))))) 4(5(1(4(5(3(3(5(1(2(4(3(4(3(5(1(3(3(1(x1))))))))))))))))))) -> 0(1(2(0(0(1(5(1(5(1(4(0(0(4(3(1(1(1(x1)))))))))))))))))) 4(1(5(2(2(4(2(3(3(1(1(4(2(0(5(1(0(0(3(5(x1)))))))))))))))))))) -> 4(1(0(4(5(3(2(4(4(5(4(5(2(4(1(2(2(1(3(x1))))))))))))))))))) 5(4(0(5(5(2(3(5(1(4(1(2(1(3(4(4(1(2(4(3(x1)))))))))))))))))))) -> 5(2(5(4(3(3(4(2(5(3(5(3(4(1(0(2(4(4(3(x1))))))))))))))))))) 3(2(1(5(5(4(5(3(4(2(2(4(5(5(4(4(0(4(2(5(5(x1))))))))))))))))))))) -> 3(5(4(3(1(3(4(1(1(4(3(0(0(0(4(3(3(3(2(5(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(0(1(2(0(0(x1)))))) -> 0(0(3(4(0(x1))))) 1(5(5(3(1(4(x1)))))) -> 2(1(4(1(0(x1))))) 2(0(2(2(2(0(x1)))))) -> 2(1(0(5(0(x1))))) 2(5(2(2(3(0(x1)))))) -> 2(5(5(1(0(x1))))) 1(2(0(1(5(3(1(x1))))))) -> 0(2(4(3(1(5(x1)))))) 2(3(2(2(0(2(3(x1))))))) -> 2(5(4(1(0(0(x1)))))) 2(4(2(5(1(3(1(x1))))))) -> 2(1(1(3(4(3(x1)))))) 0(0(3(2(4(5(2(2(x1)))))))) -> 5(1(2(0(2(5(2(2(x1)))))))) 1(2(2(4(0(1(2(4(x1)))))))) -> 4(2(0(4(3(3(4(x1))))))) 0(0(2(0(3(5(4(2(0(x1))))))))) -> 5(5(1(5(5(0(4(0(x1)))))))) 4(1(3(4(1(2(3(4(2(x1))))))))) -> 1(1(0(4(3(5(2(2(x1)))))))) 0(2(2(0(3(5(2(4(1(2(x1)))))))))) -> 0(4(5(3(3(0(5(5(3(x1))))))))) 2(4(3(5(5(2(4(2(5(1(x1)))))))))) -> 4(1(4(1(4(4(0(0(1(x1))))))))) 1(3(2(5(1(1(1(1(0(1(3(x1))))))))))) -> 0(3(5(5(5(0(0(1(2(4(2(0(x1)))))))))))) 1(5(5(5(0(5(1(5(2(0(3(x1))))))))))) -> 0(0(4(4(5(4(3(4(3(3(x1)))))))))) 2(2(0(1(1(1(2(3(3(2(0(x1))))))))))) -> 3(0(1(3(1(5(1(5(1(0(x1)))))))))) 2(0(4(4(4(2(3(0(5(2(4(2(x1)))))))))))) -> 2(5(5(5(3(4(1(3(4(4(2(x1))))))))))) 2(2(2(1(1(0(5(3(1(4(4(3(x1)))))))))))) -> 5(4(1(2(0(3(3(1(3(5(5(3(x1)))))))))))) 2(2(4(2(1(1(2(0(0(5(2(1(x1)))))))))))) -> 4(2(1(0(1(0(4(2(3(3(x1)))))))))) 4(0(3(0(5(2(5(4(3(1(5(0(x1)))))))))))) -> 1(3(1(1(2(1(5(2(0(4(3(0(x1)))))))))))) 4(5(3(4(2(0(4(3(3(5(3(4(x1)))))))))))) -> 2(1(4(5(3(3(1(0(3(2(2(4(x1)))))))))))) 1(4(1(3(2(1(5(2(2(1(3(4(5(x1))))))))))))) -> 0(3(1(5(3(0(1(2(3(3(1(0(x1)))))))))))) 2(2(1(4(1(1(1(0(1(3(5(3(4(3(x1)))))))))))))) -> 2(5(3(4(1(5(3(0(0(5(2(2(4(2(3(x1))))))))))))))) 4(3(1(4(0(1(0(4(2(2(3(4(0(0(x1)))))))))))))) -> 3(4(0(0(0(1(0(1(1(0(1(3(0(x1))))))))))))) 0(1(2(0(5(3(4(5(2(4(3(4(1(3(5(x1))))))))))))))) -> 0(2(1(1(3(3(3(3(0(5(2(3(2(0(0(x1))))))))))))))) 1(5(5(4(3(3(5(1(2(0(0(2(4(3(0(x1))))))))))))))) -> 1(1(1(0(3(4(5(1(3(1(1(0(x1)))))))))))) 4(0(2(5(3(5(4(3(5(4(5(4(5(1(3(x1))))))))))))))) -> 4(0(3(1(4(3(2(4(5(1(1(5(1(0(x1)))))))))))))) 4(4(3(4(1(5(1(2(1(0(0(3(5(2(3(x1))))))))))))))) -> 1(3(2(1(2(3(2(4(5(5(5(0(3(1(3(x1))))))))))))))) 0(2(0(4(2(4(4(4(3(3(4(2(2(2(4(3(x1)))))))))))))))) -> 0(4(2(1(5(4(3(3(1(3(3(0(1(0(3(x1))))))))))))))) 2(5(0(0(1(3(4(1(0(5(3(2(2(3(0(3(x1)))))))))))))))) -> 3(5(3(3(0(3(0(2(0(1(4(5(2(0(0(3(x1)))))))))))))))) 2(4(5(5(3(2(0(0(1(4(2(1(3(2(2(0(5(x1))))))))))))))))) -> 0(5(2(0(5(2(4(1(3(2(3(1(2(3(0(0(x1)))))))))))))))) 0(5(5(3(4(0(1(4(1(4(4(2(3(2(5(4(1(3(x1)))))))))))))))))) -> 0(3(0(0(5(0(3(0(1(1(0(3(3(3(4(5(5(x1))))))))))))))))) 2(0(0(4(3(5(3(4(1(4(3(0(3(0(1(4(5(4(x1)))))))))))))))))) -> 5(0(1(1(3(3(0(1(2(0(5(4(2(5(2(0(4(5(x1)))))))))))))))))) 2(2(3(5(0(3(3(0(0(2(4(1(2(3(4(2(2(4(x1)))))))))))))))))) -> 4(1(5(0(2(5(4(0(2(1(3(3(0(0(4(5(4(x1))))))))))))))))) 4(0(4(1(5(4(5(5(2(4(5(4(4(0(5(3(5(0(x1)))))))))))))))))) -> 3(5(5(4(4(2(2(0(3(0(4(5(0(1(5(4(4(0(x1)))))))))))))))))) 4(2(1(4(0(0(2(1(1(4(3(4(1(5(4(0(1(4(x1)))))))))))))))))) -> 2(5(4(2(5(2(1(4(0(3(1(3(1(4(0(0(1(4(x1)))))))))))))))))) 4(5(1(4(5(3(3(5(1(2(4(3(4(3(5(1(3(3(1(x1))))))))))))))))))) -> 0(1(2(0(0(1(5(1(5(1(4(0(0(4(3(1(1(1(x1)))))))))))))))))) 4(1(5(2(2(4(2(3(3(1(1(4(2(0(5(1(0(0(3(5(x1)))))))))))))))))))) -> 4(1(0(4(5(3(2(4(4(5(4(5(2(4(1(2(2(1(3(x1))))))))))))))))))) 5(4(0(5(5(2(3(5(1(4(1(2(1(3(4(4(1(2(4(3(x1)))))))))))))))))))) -> 5(2(5(4(3(3(4(2(5(3(5(3(4(1(0(2(4(4(3(x1))))))))))))))))))) 3(2(1(5(5(4(5(3(4(2(2(4(5(5(4(4(0(4(2(5(5(x1))))))))))))))))))))) -> 3(5(4(3(1(3(4(1(1(4(3(0(0(0(4(3(3(3(2(5(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. "[99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 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] {(99,100,[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]), (99,101,[0_1|1, 1_1|1, 2_1|1, 4_1|1, 5_1|1, 3_1|1]), (99,102,[0_1|2]), (99,106,[5_1|2]), (99,113,[5_1|2]), (99,120,[0_1|2]), (99,128,[0_1|2]), (99,142,[0_1|2]), (99,156,[0_1|2]), (99,172,[2_1|2]), (99,176,[0_1|2]), (99,185,[1_1|2]), (99,196,[0_1|2]), (99,201,[4_1|2]), (99,207,[0_1|2]), (99,218,[0_1|2]), (99,229,[2_1|2]), (99,233,[2_1|2]), (99,243,[5_1|2]), (99,260,[2_1|2]), (99,264,[3_1|2]), (99,279,[2_1|2]), (99,284,[2_1|2]), (99,289,[4_1|2]), (99,297,[0_1|2]), (99,312,[3_1|2]), (99,321,[5_1|2]), (99,332,[4_1|2]), (99,341,[2_1|2]), (99,355,[4_1|2]), (99,371,[1_1|2]), (99,378,[4_1|2]), (99,396,[1_1|2]), (99,407,[4_1|2]), (99,420,[3_1|2]), (99,437,[2_1|2]), (99,448,[0_1|2]), (99,465,[3_1|2]), (99,477,[1_1|2]), (99,491,[2_1|2]), (99,508,[5_1|2]), (99,526,[3_1|2]), (100,100,[cons_0_1|0, cons_1_1|0, cons_2_1|0, cons_4_1|0, cons_5_1|0, cons_3_1|0]), (101,100,[encArg_1|1]), (101,101,[0_1|1, 1_1|1, 2_1|1, 4_1|1, 5_1|1, 3_1|1]), (101,102,[0_1|2]), (101,106,[5_1|2]), (101,113,[5_1|2]), (101,120,[0_1|2]), (101,128,[0_1|2]), (101,142,[0_1|2]), (101,156,[0_1|2]), (101,172,[2_1|2]), (101,176,[0_1|2]), (101,185,[1_1|2]), (101,196,[0_1|2]), (101,201,[4_1|2]), (101,207,[0_1|2]), (101,218,[0_1|2]), (101,229,[2_1|2]), (101,233,[2_1|2]), (101,243,[5_1|2]), (101,260,[2_1|2]), (101,264,[3_1|2]), (101,279,[2_1|2]), (101,284,[2_1|2]), (101,289,[4_1|2]), (101,297,[0_1|2]), (101,312,[3_1|2]), (101,321,[5_1|2]), (101,332,[4_1|2]), (101,341,[2_1|2]), (101,355,[4_1|2]), (101,371,[1_1|2]), (101,378,[4_1|2]), (101,396,[1_1|2]), (101,407,[4_1|2]), (101,420,[3_1|2]), (101,437,[2_1|2]), (101,448,[0_1|2]), (101,465,[3_1|2]), (101,477,[1_1|2]), (101,491,[2_1|2]), (101,508,[5_1|2]), (101,526,[3_1|2]), (102,103,[0_1|2]), (103,104,[3_1|2]), (104,105,[4_1|2]), (104,396,[1_1|2]), (104,407,[4_1|2]), (104,420,[3_1|2]), (105,101,[0_1|2]), (105,102,[0_1|2]), (105,120,[0_1|2]), (105,128,[0_1|2]), (105,142,[0_1|2]), (105,156,[0_1|2]), (105,176,[0_1|2]), (105,196,[0_1|2]), (105,207,[0_1|2]), (105,218,[0_1|2]), (105,297,[0_1|2]), (105,448,[0_1|2]), (105,103,[0_1|2]), (105,177,[0_1|2]), (105,452,[0_1|2]), (105,106,[5_1|2]), (105,113,[5_1|2]), (105,545,[0_1|3]), (106,107,[1_1|2]), (107,108,[2_1|2]), (108,109,[0_1|2]), (109,110,[2_1|2]), (109,260,[2_1|2]), (109,549,[2_1|3]), (110,111,[5_1|2]), (111,112,[2_1|2]), (111,312,[3_1|2]), (111,321,[5_1|2]), (111,332,[4_1|2]), (111,341,[2_1|2]), (111,355,[4_1|2]), (112,101,[2_1|2]), (112,172,[2_1|2]), (112,229,[2_1|2]), (112,233,[2_1|2]), (112,260,[2_1|2]), (112,279,[2_1|2]), (112,284,[2_1|2]), (112,341,[2_1|2]), 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(184,101,[3_1|2]), (184,264,[3_1|2]), (184,312,[3_1|2]), (184,420,[3_1|2]), (184,465,[3_1|2]), (184,526,[3_1|2]), (184,157,[3_1|2]), (184,208,[3_1|2]), (184,219,[3_1|2]), (185,186,[1_1|2]), (186,187,[1_1|2]), (187,188,[0_1|2]), (188,189,[3_1|2]), (189,190,[4_1|2]), (190,191,[5_1|2]), (191,192,[1_1|2]), (192,193,[3_1|2]), (193,194,[1_1|2]), (194,195,[1_1|2]), (195,101,[0_1|2]), (195,102,[0_1|2]), (195,120,[0_1|2]), (195,128,[0_1|2]), (195,142,[0_1|2]), (195,156,[0_1|2]), (195,176,[0_1|2]), (195,196,[0_1|2]), (195,207,[0_1|2]), (195,218,[0_1|2]), (195,297,[0_1|2]), (195,448,[0_1|2]), (195,313,[0_1|2]), (195,106,[5_1|2]), (195,113,[5_1|2]), (195,545,[0_1|3]), (196,197,[2_1|2]), (197,198,[4_1|2]), (198,199,[3_1|2]), (199,200,[1_1|2]), (199,172,[2_1|2]), (199,176,[0_1|2]), (199,185,[1_1|2]), (200,101,[5_1|2]), (200,185,[5_1|2]), (200,371,[5_1|2]), (200,396,[5_1|2]), (200,477,[5_1|2]), (200,508,[5_1|2]), (201,202,[2_1|2]), (202,203,[0_1|2]), (203,204,[4_1|2]), (204,205,[3_1|2]), (205,206,[3_1|2]), (206,101,[4_1|2]), (206,201,[4_1|2]), (206,289,[4_1|2]), (206,332,[4_1|2]), (206,355,[4_1|2]), (206,378,[4_1|2]), (206,407,[4_1|2]), (206,371,[1_1|2]), (206,396,[1_1|2]), (206,420,[3_1|2]), (206,437,[2_1|2]), (206,448,[0_1|2]), (206,465,[3_1|2]), (206,477,[1_1|2]), (206,491,[2_1|2]), (207,208,[3_1|2]), (208,209,[5_1|2]), (209,210,[5_1|2]), (210,211,[5_1|2]), (211,212,[0_1|2]), (212,213,[0_1|2]), (213,214,[1_1|2]), (214,215,[2_1|2]), (215,216,[4_1|2]), (216,217,[2_1|2]), (216,229,[2_1|2]), (216,233,[2_1|2]), (216,243,[5_1|2]), (217,101,[0_1|2]), (217,264,[0_1|2]), (217,312,[0_1|2]), (217,420,[0_1|2]), (217,465,[0_1|2]), (217,526,[0_1|2]), (217,397,[0_1|2]), (217,478,[0_1|2]), (217,102,[0_1|2]), (217,106,[5_1|2]), (217,113,[5_1|2]), (217,120,[0_1|2]), (217,128,[0_1|2]), (217,142,[0_1|2]), (217,156,[0_1|2]), (217,545,[0_1|3]), (218,219,[3_1|2]), (219,220,[1_1|2]), (220,221,[5_1|2]), (221,222,[3_1|2]), (222,223,[0_1|2]), (223,224,[1_1|2]), (224,225,[2_1|2]), (225,226,[3_1|2]), (226,227,[3_1|2]), (227,228,[1_1|2]), (228,101,[0_1|2]), (228,106,[0_1|2, 5_1|2]), (228,113,[0_1|2, 5_1|2]), (228,243,[0_1|2]), (228,321,[0_1|2]), (228,508,[0_1|2]), (228,102,[0_1|2]), (228,120,[0_1|2]), (228,128,[0_1|2]), (228,142,[0_1|2]), (228,156,[0_1|2]), (228,545,[0_1|3]), (229,230,[1_1|2]), (230,231,[0_1|2]), (231,232,[5_1|2]), (232,101,[0_1|2]), (232,102,[0_1|2]), (232,120,[0_1|2]), (232,128,[0_1|2]), (232,142,[0_1|2]), (232,156,[0_1|2]), (232,176,[0_1|2]), (232,196,[0_1|2]), (232,207,[0_1|2]), (232,218,[0_1|2]), (232,297,[0_1|2]), (232,448,[0_1|2]), (232,106,[5_1|2]), (232,113,[5_1|2]), (232,545,[0_1|3]), (233,234,[5_1|2]), (234,235,[5_1|2]), (235,236,[5_1|2]), (236,237,[3_1|2]), (237,238,[4_1|2]), (238,239,[1_1|2]), (239,240,[3_1|2]), (240,241,[4_1|2]), (241,242,[4_1|2]), (241,491,[2_1|2]), (242,101,[2_1|2]), (242,172,[2_1|2]), (242,229,[2_1|2]), (242,233,[2_1|2]), (242,260,[2_1|2]), (242,279,[2_1|2]), (242,284,[2_1|2]), (242,341,[2_1|2]), (242,437,[2_1|2]), (242,491,[2_1|2]), (242,202,[2_1|2]), (242,333,[2_1|2]), (242,243,[5_1|2]), (242,264,[3_1|2]), (242,289,[4_1|2]), (242,297,[0_1|2]), (242,312,[3_1|2]), (242,321,[5_1|2]), (242,332,[4_1|2]), (242,355,[4_1|2]), (243,244,[0_1|2]), (244,245,[1_1|2]), (245,246,[1_1|2]), (246,247,[3_1|2]), (247,248,[3_1|2]), (248,249,[0_1|2]), (249,250,[1_1|2]), (250,251,[2_1|2]), (251,252,[0_1|2]), (252,253,[5_1|2]), (253,254,[4_1|2]), (254,255,[2_1|2]), (255,256,[5_1|2]), (256,257,[2_1|2]), (257,258,[0_1|2]), (257,545,[0_1|3]), (258,259,[4_1|2]), (258,437,[2_1|2]), (258,448,[0_1|2]), (259,101,[5_1|2]), (259,201,[5_1|2]), (259,289,[5_1|2]), (259,332,[5_1|2]), (259,355,[5_1|2]), (259,378,[5_1|2]), (259,407,[5_1|2]), (259,322,[5_1|2]), (259,508,[5_1|2]), (260,261,[5_1|2]), (261,262,[5_1|2]), (262,263,[1_1|2]), (263,101,[0_1|2]), (263,102,[0_1|2]), (263,120,[0_1|2]), (263,128,[0_1|2]), (263,142,[0_1|2]), (263,156,[0_1|2]), (263,176,[0_1|2]), (263,196,[0_1|2]), (263,207,[0_1|2]), (263,218,[0_1|2]), (263,297,[0_1|2]), (263,448,[0_1|2]), (263,313,[0_1|2]), (263,106,[5_1|2]), (263,113,[5_1|2]), (263,545,[0_1|3]), (264,265,[5_1|2]), (265,266,[3_1|2]), (266,267,[3_1|2]), (267,268,[0_1|2]), (268,269,[3_1|2]), (269,270,[0_1|2]), (270,271,[2_1|2]), (271,272,[0_1|2]), (272,273,[1_1|2]), (273,274,[4_1|2]), (274,275,[5_1|2]), (275,276,[2_1|2]), (276,277,[0_1|2]), (276,106,[5_1|2]), (277,278,[0_1|2]), (278,101,[3_1|2]), (278,264,[3_1|2]), (278,312,[3_1|2]), (278,420,[3_1|2]), (278,465,[3_1|2]), (278,526,[3_1|2]), (278,157,[3_1|2]), (278,208,[3_1|2]), (278,219,[3_1|2]), (279,280,[5_1|2]), (280,281,[4_1|2]), (281,282,[1_1|2]), (282,283,[0_1|2]), (282,102,[0_1|2]), (282,106,[5_1|2]), (282,113,[5_1|2]), (283,101,[0_1|2]), (283,264,[0_1|2]), (283,312,[0_1|2]), (283,420,[0_1|2]), (283,465,[0_1|2]), (283,526,[0_1|2]), (283,102,[0_1|2]), (283,106,[5_1|2]), (283,113,[5_1|2]), (283,120,[0_1|2]), (283,128,[0_1|2]), (283,142,[0_1|2]), (283,156,[0_1|2]), (283,545,[0_1|3]), 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(311,113,[0_1|2, 5_1|2]), (311,243,[0_1|2]), (311,321,[0_1|2]), (311,508,[0_1|2]), (311,298,[0_1|2]), (311,102,[0_1|2]), (311,120,[0_1|2]), (311,128,[0_1|2]), (311,142,[0_1|2]), (311,156,[0_1|2]), (311,545,[0_1|3]), (312,313,[0_1|2]), (313,314,[1_1|2]), (314,315,[3_1|2]), (315,316,[1_1|2]), (316,317,[5_1|2]), (317,318,[1_1|2]), (318,319,[5_1|2]), (319,320,[1_1|2]), (320,101,[0_1|2]), (320,102,[0_1|2]), (320,120,[0_1|2]), (320,128,[0_1|2]), (320,142,[0_1|2]), (320,156,[0_1|2]), (320,176,[0_1|2]), (320,196,[0_1|2]), (320,207,[0_1|2]), (320,218,[0_1|2]), (320,297,[0_1|2]), (320,448,[0_1|2]), (320,106,[5_1|2]), (320,113,[5_1|2]), (320,545,[0_1|3]), (321,322,[4_1|2]), (322,323,[1_1|2]), (323,324,[2_1|2]), (324,325,[0_1|2]), (325,326,[3_1|2]), (326,327,[3_1|2]), (327,328,[1_1|2]), (328,329,[3_1|2]), (329,330,[5_1|2]), (330,331,[5_1|2]), (331,101,[3_1|2]), (331,264,[3_1|2]), (331,312,[3_1|2]), (331,420,[3_1|2]), (331,465,[3_1|2]), (331,526,[3_1|2]), (332,333,[2_1|2]), (333,334,[1_1|2]), 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(384,385,[4_1|2]), (385,386,[4_1|2]), (386,387,[5_1|2]), (387,388,[4_1|2]), (388,389,[5_1|2]), (389,390,[2_1|2]), (390,391,[4_1|2]), (391,392,[1_1|2]), (392,393,[2_1|2]), (393,394,[2_1|2]), (394,395,[1_1|2]), (394,207,[0_1|2]), (395,101,[3_1|2]), (395,106,[3_1|2]), (395,113,[3_1|2]), (395,243,[3_1|2]), (395,321,[3_1|2]), (395,508,[3_1|2]), (395,265,[3_1|2]), (395,421,[3_1|2]), (395,527,[3_1|2]), (395,209,[3_1|2]), (395,526,[3_1|2]), (396,397,[3_1|2]), (397,398,[1_1|2]), (398,399,[1_1|2]), (399,400,[2_1|2]), (400,401,[1_1|2]), (401,402,[5_1|2]), (402,403,[2_1|2]), (403,404,[0_1|2]), (404,405,[4_1|2]), (405,406,[3_1|2]), (406,101,[0_1|2]), (406,102,[0_1|2]), (406,120,[0_1|2]), (406,128,[0_1|2]), (406,142,[0_1|2]), (406,156,[0_1|2]), (406,176,[0_1|2]), (406,196,[0_1|2]), (406,207,[0_1|2]), (406,218,[0_1|2]), (406,297,[0_1|2]), (406,448,[0_1|2]), (406,244,[0_1|2]), (406,106,[5_1|2]), (406,113,[5_1|2]), (406,545,[0_1|3]), (407,408,[0_1|2]), (408,409,[3_1|2]), (409,410,[1_1|2]), (410,411,[4_1|2]), (411,412,[3_1|2]), (412,413,[2_1|2]), (413,414,[4_1|2]), (414,415,[5_1|2]), (415,416,[1_1|2]), (416,417,[1_1|2]), (417,418,[5_1|2]), (418,419,[1_1|2]), (419,101,[0_1|2]), (419,264,[0_1|2]), (419,312,[0_1|2]), (419,420,[0_1|2]), (419,465,[0_1|2]), (419,526,[0_1|2]), (419,397,[0_1|2]), (419,478,[0_1|2]), (419,102,[0_1|2]), (419,106,[5_1|2]), (419,113,[5_1|2]), (419,120,[0_1|2]), (419,128,[0_1|2]), (419,142,[0_1|2]), (419,156,[0_1|2]), (419,545,[0_1|3]), (420,421,[5_1|2]), (421,422,[5_1|2]), (422,423,[4_1|2]), (423,424,[4_1|2]), (424,425,[2_1|2]), (425,426,[2_1|2]), (426,427,[0_1|2]), (427,428,[3_1|2]), (428,429,[0_1|2]), (429,430,[4_1|2]), (430,431,[5_1|2]), (431,432,[0_1|2]), (432,433,[1_1|2]), (433,434,[5_1|2]), (434,435,[4_1|2]), (435,436,[4_1|2]), (435,396,[1_1|2]), (435,407,[4_1|2]), (435,420,[3_1|2]), (436,101,[0_1|2]), (436,102,[0_1|2]), (436,120,[0_1|2]), (436,128,[0_1|2]), (436,142,[0_1|2]), (436,156,[0_1|2]), (436,176,[0_1|2]), (436,196,[0_1|2]), (436,207,[0_1|2]), (436,218,[0_1|2]), (436,297,[0_1|2]), (436,448,[0_1|2]), (436,244,[0_1|2]), (436,106,[5_1|2]), (436,113,[5_1|2]), (436,545,[0_1|3]), (437,438,[1_1|2]), (438,439,[4_1|2]), (439,440,[5_1|2]), (440,441,[3_1|2]), (441,442,[3_1|2]), (442,443,[1_1|2]), (443,444,[0_1|2]), (444,445,[3_1|2]), (445,446,[2_1|2]), (445,332,[4_1|2]), (446,447,[2_1|2]), (446,284,[2_1|2]), (446,289,[4_1|2]), (446,297,[0_1|2]), (447,101,[4_1|2]), (447,201,[4_1|2]), (447,289,[4_1|2]), (447,332,[4_1|2]), (447,355,[4_1|2]), (447,378,[4_1|2]), (447,407,[4_1|2]), (447,466,[4_1|2]), (447,371,[1_1|2]), (447,396,[1_1|2]), (447,420,[3_1|2]), (447,437,[2_1|2]), (447,448,[0_1|2]), (447,465,[3_1|2]), (447,477,[1_1|2]), (447,491,[2_1|2]), (448,449,[1_1|2]), (449,450,[2_1|2]), (450,451,[0_1|2]), (451,452,[0_1|2]), (452,453,[1_1|2]), (453,454,[5_1|2]), (454,455,[1_1|2]), (455,456,[5_1|2]), (456,457,[1_1|2]), (457,458,[4_1|2]), (458,459,[0_1|2]), (459,460,[0_1|2]), (460,461,[4_1|2]), (461,462,[3_1|2]), (462,463,[1_1|2]), (463,464,[1_1|2]), (464,101,[1_1|2]), (464,185,[1_1|2]), (464,371,[1_1|2]), (464,396,[1_1|2]), (464,477,[1_1|2]), (464,172,[2_1|2]), (464,176,[0_1|2]), (464,196,[0_1|2]), (464,201,[4_1|2]), (464,207,[0_1|2]), (464,218,[0_1|2]), (465,466,[4_1|2]), (466,467,[0_1|2]), (467,468,[0_1|2]), (468,469,[0_1|2]), (469,470,[1_1|2]), (470,471,[0_1|2]), (471,472,[1_1|2]), (472,473,[1_1|2]), (473,474,[0_1|2]), (474,475,[1_1|2]), (475,476,[3_1|2]), (476,101,[0_1|2]), (476,102,[0_1|2]), (476,120,[0_1|2]), (476,128,[0_1|2]), (476,142,[0_1|2]), (476,156,[0_1|2]), (476,176,[0_1|2]), (476,196,[0_1|2]), (476,207,[0_1|2]), (476,218,[0_1|2]), (476,297,[0_1|2]), (476,448,[0_1|2]), (476,103,[0_1|2]), (476,177,[0_1|2]), (476,468,[0_1|2]), (476,106,[5_1|2]), (476,113,[5_1|2]), (476,545,[0_1|3]), (477,478,[3_1|2]), (478,479,[2_1|2]), (479,480,[1_1|2]), (480,481,[2_1|2]), (481,482,[3_1|2]), (482,483,[2_1|2]), (483,484,[4_1|2]), (484,485,[5_1|2]), (485,486,[5_1|2]), (486,487,[5_1|2]), (487,488,[0_1|2]), (488,489,[3_1|2]), (489,490,[1_1|2]), (489,207,[0_1|2]), (490,101,[3_1|2]), (490,264,[3_1|2]), (490,312,[3_1|2]), (490,420,[3_1|2]), (490,465,[3_1|2]), (490,526,[3_1|2]), (491,492,[5_1|2]), (492,493,[4_1|2]), (493,494,[2_1|2]), (494,495,[5_1|2]), (495,496,[2_1|2]), (496,497,[1_1|2]), (497,498,[4_1|2]), (498,499,[0_1|2]), (499,500,[3_1|2]), (500,501,[1_1|2]), (501,502,[3_1|2]), (502,503,[1_1|2]), (503,504,[4_1|2]), (504,505,[0_1|2]), (505,506,[0_1|2]), (506,507,[1_1|2]), (506,218,[0_1|2]), (507,101,[4_1|2]), (507,201,[4_1|2]), (507,289,[4_1|2]), (507,332,[4_1|2]), (507,355,[4_1|2]), (507,378,[4_1|2]), (507,407,[4_1|2]), (507,371,[1_1|2]), (507,396,[1_1|2]), (507,420,[3_1|2]), (507,437,[2_1|2]), (507,448,[0_1|2]), (507,465,[3_1|2]), (507,477,[1_1|2]), (507,491,[2_1|2]), (508,509,[2_1|2]), (509,510,[5_1|2]), (510,511,[4_1|2]), (511,512,[3_1|2]), (512,513,[3_1|2]), (513,514,[4_1|2]), (514,515,[2_1|2]), (515,516,[5_1|2]), (516,517,[3_1|2]), (517,518,[5_1|2]), (518,519,[3_1|2]), (519,520,[4_1|2]), (520,521,[1_1|2]), (521,522,[0_1|2]), (522,523,[2_1|2]), (523,524,[4_1|2]), (523,477,[1_1|2]), (524,525,[4_1|2]), (524,465,[3_1|2]), (525,101,[3_1|2]), (525,264,[3_1|2]), (525,312,[3_1|2]), (525,420,[3_1|2]), (525,465,[3_1|2]), (525,526,[3_1|2]), (526,527,[5_1|2]), (527,528,[4_1|2]), (528,529,[3_1|2]), (529,530,[1_1|2]), (530,531,[3_1|2]), (531,532,[4_1|2]), (532,533,[1_1|2]), (533,534,[1_1|2]), (534,535,[4_1|2]), (535,536,[3_1|2]), (536,537,[0_1|2]), (537,538,[0_1|2]), (538,539,[0_1|2]), (539,540,[4_1|2]), (540,541,[3_1|2]), (541,542,[3_1|2]), (542,543,[3_1|2]), (543,544,[2_1|2]), (543,260,[2_1|2]), (543,264,[3_1|2]), (544,101,[5_1|2]), (544,106,[5_1|2]), (544,113,[5_1|2]), (544,243,[5_1|2]), (544,321,[5_1|2]), (544,508,[5_1|2]), (544,114,[5_1|2]), (544,235,[5_1|2]), (544,262,[5_1|2]), (545,546,[0_1|3]), (546,547,[3_1|3]), (547,548,[4_1|3]), (548,452,[0_1|3]), (549,550,[5_1|3]), (550,551,[5_1|3]), (551,552,[1_1|3]), (552,313,[0_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)