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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 54 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 294 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(0(x1)))) -> 0(2(0(x1))) 1(0(3(0(x1)))) -> 2(0(0(x1))) 3(1(4(0(x1)))) -> 3(2(3(x1))) 4(0(3(3(x1)))) -> 1(0(2(x1))) 4(1(3(0(x1)))) -> 4(4(5(x1))) 4(2(3(4(x1)))) -> 4(4(3(4(x1)))) 4(3(4(0(x1)))) -> 2(4(0(x1))) 0(4(5(2(4(x1))))) -> 5(1(2(0(x1)))) 3(0(2(5(3(x1))))) -> 0(4(2(0(x1)))) 3(3(5(3(0(x1))))) -> 1(4(4(1(x1)))) 4(4(4(4(5(0(x1)))))) -> 4(5(5(2(4(4(x1)))))) 2(4(2(0(2(1(5(x1))))))) -> 2(0(1(3(3(3(5(x1))))))) 4(0(3(2(0(2(4(x1))))))) -> 5(2(3(0(2(1(x1)))))) 3(2(0(5(0(2(1(4(x1)))))))) -> 2(2(1(4(5(1(5(x1))))))) 0(3(4(1(4(0(4(1(5(x1))))))))) -> 0(5(2(2(1(3(3(5(x1)))))))) 1(2(5(2(4(0(5(3(3(x1))))))))) -> 2(1(3(3(5(1(0(5(x1)))))))) 3(4(0(4(0(5(4(0(5(x1))))))))) -> 3(0(3(4(0(2(0(0(x1)))))))) 3(3(4(5(2(1(1(4(1(4(x1)))))))))) -> 0(0(3(1(0(0(2(1(1(4(x1)))))))))) 0(2(4(5(4(3(2(3(4(5(5(x1))))))))))) -> 3(0(0(3(0(4(5(2(5(0(2(x1))))))))))) 1(4(2(2(0(2(3(2(2(4(4(x1))))))))))) -> 2(3(1(0(3(0(2(1(0(1(5(0(x1)))))))))))) 1(5(2(0(3(4(2(3(1(4(0(x1))))))))))) -> 4(5(3(1(1(3(4(4(1(3(5(x1))))))))))) 0(0(4(5(3(1(5(0(1(3(3(2(x1)))))))))))) -> 2(2(2(2(4(1(2(5(4(2(x1)))))))))) 3(1(0(1(4(5(3(5(1(1(2(4(x1)))))))))))) -> 3(1(2(3(5(0(4(2(2(4(4(x1))))))))))) 3(2(1(1(2(4(1(2(3(2(1(2(x1)))))))))))) -> 2(3(3(4(0(5(0(0(2(2(1(4(x1)))))))))))) 1(2(2(4(3(2(5(1(3(5(3(5(0(x1))))))))))))) -> 3(3(3(1(0(0(5(4(4(4(4(5(x1)))))))))))) 3(3(5(3(4(0(3(1(0(3(4(4(0(x1))))))))))))) -> 0(1(1(1(5(2(5(4(3(2(4(5(x1)))))))))))) 5(5(4(2(5(3(1(4(2(4(2(5(1(1(x1)))))))))))))) -> 5(3(0(5(3(5(1(5(1(4(4(1(1(x1))))))))))))) 1(0(1(3(0(2(1(3(2(3(5(3(0(5(5(x1))))))))))))))) -> 2(1(5(4(4(0(1(1(3(3(1(1(4(5(x1)))))))))))))) 4(2(4(0(1(3(1(2(1(1(4(1(3(2(0(x1))))))))))))))) -> 4(5(2(3(2(3(1(4(5(0(2(0(5(2(x1)))))))))))))) 3(3(0(1(5(1(1(0(1(2(0(2(4(0(2(5(1(x1))))))))))))))))) -> 1(0(0(0(2(4(0(3(5(0(2(4(5(0(4(5(1(x1))))))))))))))))) 0(1(2(3(0(0(0(1(0(2(0(5(5(5(2(2(0(4(x1)))))))))))))))))) -> 3(1(5(0(2(0(5(4(5(0(1(0(3(2(5(1(4(0(x1)))))))))))))))))) 4(2(1(2(3(5(3(3(1(2(2(1(3(0(0(5(5(5(x1)))))))))))))))))) -> 4(4(1(3(4(0(1(4(3(5(4(4(1(0(0(5(1(2(x1)))))))))))))))))) 5(4(5(5(1(2(0(2(3(0(5(0(3(4(2(0(4(3(x1)))))))))))))))))) -> 5(1(5(5(4(0(0(3(1(3(2(4(4(1(1(4(0(1(x1)))))))))))))))))) 1(5(2(3(1(2(0(2(3(2(2(3(0(1(5(1(1(5(5(x1))))))))))))))))))) -> 1(4(5(0(1(5(3(4(4(2(1(2(1(4(3(3(3(2(3(x1))))))))))))))))))) 2(5(3(3(2(5(5(3(4(5(2(3(0(1(4(3(1(3(4(x1))))))))))))))))))) -> 2(2(3(0(4(5(5(5(1(4(3(1(3(4(1(1(2(x1))))))))))))))))) 2(3(3(4(5(3(3(1(5(5(0(4(1(4(0(2(2(3(1(4(x1)))))))))))))))))))) -> 2(0(1(5(3(2(0(2(5(1(2(4(5(3(4(4(4(0(4(5(x1)))))))))))))))))))) 3(2(3(4(1(2(3(2(3(4(2(1(0(4(1(0(4(2(0(4(x1)))))))))))))))))))) -> 1(3(4(0(0(4(3(4(3(1(3(0(0(4(5(3(1(4(3(4(4(x1))))))))))))))))))))) 4(2(0(0(3(5(0(0(4(1(4(2(1(4(3(2(3(5(5(3(x1)))))))))))))))))))) -> 0(0(0(3(0(4(4(3(0(4(1(3(0(1(0(0(4(4(5(3(x1)))))))))))))))))))) 1(0(3(1(1(1(1(0(1(2(0(5(4(0(3(0(5(3(4(2(0(x1))))))))))))))))))))) -> 0(5(4(2(0(0(3(0(0(1(1(2(3(1(5(1(2(4(2(0(x1)))))))))))))))))))) 5(0(5(0(2(2(4(0(0(5(2(1(2(5(1(1(1(0(1(2(4(x1))))))))))))))))))))) -> 5(4(3(4(5(4(2(5(4(1(4(4(1(3(0(2(2(1(2(0(x1)))))))))))))))))))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(0(x1)))) -> 0(2(0(x1))) 1(0(3(0(x1)))) -> 2(0(0(x1))) 3(1(4(0(x1)))) -> 3(2(3(x1))) 4(0(3(3(x1)))) -> 1(0(2(x1))) 4(1(3(0(x1)))) -> 4(4(5(x1))) 4(2(3(4(x1)))) -> 4(4(3(4(x1)))) 4(3(4(0(x1)))) -> 2(4(0(x1))) 0(4(5(2(4(x1))))) -> 5(1(2(0(x1)))) 3(0(2(5(3(x1))))) -> 0(4(2(0(x1)))) 3(3(5(3(0(x1))))) -> 1(4(4(1(x1)))) 4(4(4(4(5(0(x1)))))) -> 4(5(5(2(4(4(x1)))))) 2(4(2(0(2(1(5(x1))))))) -> 2(0(1(3(3(3(5(x1))))))) 4(0(3(2(0(2(4(x1))))))) -> 5(2(3(0(2(1(x1)))))) 3(2(0(5(0(2(1(4(x1)))))))) -> 2(2(1(4(5(1(5(x1))))))) 0(3(4(1(4(0(4(1(5(x1))))))))) -> 0(5(2(2(1(3(3(5(x1)))))))) 1(2(5(2(4(0(5(3(3(x1))))))))) -> 2(1(3(3(5(1(0(5(x1)))))))) 3(4(0(4(0(5(4(0(5(x1))))))))) -> 3(0(3(4(0(2(0(0(x1)))))))) 3(3(4(5(2(1(1(4(1(4(x1)))))))))) -> 0(0(3(1(0(0(2(1(1(4(x1)))))))))) 0(2(4(5(4(3(2(3(4(5(5(x1))))))))))) -> 3(0(0(3(0(4(5(2(5(0(2(x1))))))))))) 1(4(2(2(0(2(3(2(2(4(4(x1))))))))))) -> 2(3(1(0(3(0(2(1(0(1(5(0(x1)))))))))))) 1(5(2(0(3(4(2(3(1(4(0(x1))))))))))) -> 4(5(3(1(1(3(4(4(1(3(5(x1))))))))))) 0(0(4(5(3(1(5(0(1(3(3(2(x1)))))))))))) -> 2(2(2(2(4(1(2(5(4(2(x1)))))))))) 3(1(0(1(4(5(3(5(1(1(2(4(x1)))))))))))) -> 3(1(2(3(5(0(4(2(2(4(4(x1))))))))))) 3(2(1(1(2(4(1(2(3(2(1(2(x1)))))))))))) -> 2(3(3(4(0(5(0(0(2(2(1(4(x1)))))))))))) 1(2(2(4(3(2(5(1(3(5(3(5(0(x1))))))))))))) -> 3(3(3(1(0(0(5(4(4(4(4(5(x1)))))))))))) 3(3(5(3(4(0(3(1(0(3(4(4(0(x1))))))))))))) -> 0(1(1(1(5(2(5(4(3(2(4(5(x1)))))))))))) 5(5(4(2(5(3(1(4(2(4(2(5(1(1(x1)))))))))))))) -> 5(3(0(5(3(5(1(5(1(4(4(1(1(x1))))))))))))) 1(0(1(3(0(2(1(3(2(3(5(3(0(5(5(x1))))))))))))))) -> 2(1(5(4(4(0(1(1(3(3(1(1(4(5(x1)))))))))))))) 4(2(4(0(1(3(1(2(1(1(4(1(3(2(0(x1))))))))))))))) -> 4(5(2(3(2(3(1(4(5(0(2(0(5(2(x1)))))))))))))) 3(3(0(1(5(1(1(0(1(2(0(2(4(0(2(5(1(x1))))))))))))))))) -> 1(0(0(0(2(4(0(3(5(0(2(4(5(0(4(5(1(x1))))))))))))))))) 0(1(2(3(0(0(0(1(0(2(0(5(5(5(2(2(0(4(x1)))))))))))))))))) -> 3(1(5(0(2(0(5(4(5(0(1(0(3(2(5(1(4(0(x1)))))))))))))))))) 4(2(1(2(3(5(3(3(1(2(2(1(3(0(0(5(5(5(x1)))))))))))))))))) -> 4(4(1(3(4(0(1(4(3(5(4(4(1(0(0(5(1(2(x1)))))))))))))))))) 5(4(5(5(1(2(0(2(3(0(5(0(3(4(2(0(4(3(x1)))))))))))))))))) -> 5(1(5(5(4(0(0(3(1(3(2(4(4(1(1(4(0(1(x1)))))))))))))))))) 1(5(2(3(1(2(0(2(3(2(2(3(0(1(5(1(1(5(5(x1))))))))))))))))))) -> 1(4(5(0(1(5(3(4(4(2(1(2(1(4(3(3(3(2(3(x1))))))))))))))))))) 2(5(3(3(2(5(5(3(4(5(2(3(0(1(4(3(1(3(4(x1))))))))))))))))))) -> 2(2(3(0(4(5(5(5(1(4(3(1(3(4(1(1(2(x1))))))))))))))))) 2(3(3(4(5(3(3(1(5(5(0(4(1(4(0(2(2(3(1(4(x1)))))))))))))))))))) -> 2(0(1(5(3(2(0(2(5(1(2(4(5(3(4(4(4(0(4(5(x1)))))))))))))))))))) 3(2(3(4(1(2(3(2(3(4(2(1(0(4(1(0(4(2(0(4(x1)))))))))))))))))))) -> 1(3(4(0(0(4(3(4(3(1(3(0(0(4(5(3(1(4(3(4(4(x1))))))))))))))))))))) 4(2(0(0(3(5(0(0(4(1(4(2(1(4(3(2(3(5(5(3(x1)))))))))))))))))))) -> 0(0(0(3(0(4(4(3(0(4(1(3(0(1(0(0(4(4(5(3(x1)))))))))))))))))))) 1(0(3(1(1(1(1(0(1(2(0(5(4(0(3(0(5(3(4(2(0(x1))))))))))))))))))))) -> 0(5(4(2(0(0(3(0(0(1(1(2(3(1(5(1(2(4(2(0(x1)))))))))))))))))))) 5(0(5(0(2(2(4(0(0(5(2(1(2(5(1(1(1(0(1(2(4(x1))))))))))))))))))))) -> 5(4(3(4(5(4(2(5(4(1(4(4(1(3(0(2(2(1(2(0(x1)))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(0(x1)))) -> 0(2(0(x1))) 1(0(3(0(x1)))) -> 2(0(0(x1))) 3(1(4(0(x1)))) -> 3(2(3(x1))) 4(0(3(3(x1)))) -> 1(0(2(x1))) 4(1(3(0(x1)))) -> 4(4(5(x1))) 4(2(3(4(x1)))) -> 4(4(3(4(x1)))) 4(3(4(0(x1)))) -> 2(4(0(x1))) 0(4(5(2(4(x1))))) -> 5(1(2(0(x1)))) 3(0(2(5(3(x1))))) -> 0(4(2(0(x1)))) 3(3(5(3(0(x1))))) -> 1(4(4(1(x1)))) 4(4(4(4(5(0(x1)))))) -> 4(5(5(2(4(4(x1)))))) 2(4(2(0(2(1(5(x1))))))) -> 2(0(1(3(3(3(5(x1))))))) 4(0(3(2(0(2(4(x1))))))) -> 5(2(3(0(2(1(x1)))))) 3(2(0(5(0(2(1(4(x1)))))))) -> 2(2(1(4(5(1(5(x1))))))) 0(3(4(1(4(0(4(1(5(x1))))))))) -> 0(5(2(2(1(3(3(5(x1)))))))) 1(2(5(2(4(0(5(3(3(x1))))))))) -> 2(1(3(3(5(1(0(5(x1)))))))) 3(4(0(4(0(5(4(0(5(x1))))))))) -> 3(0(3(4(0(2(0(0(x1)))))))) 3(3(4(5(2(1(1(4(1(4(x1)))))))))) -> 0(0(3(1(0(0(2(1(1(4(x1)))))))))) 0(2(4(5(4(3(2(3(4(5(5(x1))))))))))) -> 3(0(0(3(0(4(5(2(5(0(2(x1))))))))))) 1(4(2(2(0(2(3(2(2(4(4(x1))))))))))) -> 2(3(1(0(3(0(2(1(0(1(5(0(x1)))))))))))) 1(5(2(0(3(4(2(3(1(4(0(x1))))))))))) -> 4(5(3(1(1(3(4(4(1(3(5(x1))))))))))) 0(0(4(5(3(1(5(0(1(3(3(2(x1)))))))))))) -> 2(2(2(2(4(1(2(5(4(2(x1)))))))))) 3(1(0(1(4(5(3(5(1(1(2(4(x1)))))))))))) -> 3(1(2(3(5(0(4(2(2(4(4(x1))))))))))) 3(2(1(1(2(4(1(2(3(2(1(2(x1)))))))))))) -> 2(3(3(4(0(5(0(0(2(2(1(4(x1)))))))))))) 1(2(2(4(3(2(5(1(3(5(3(5(0(x1))))))))))))) -> 3(3(3(1(0(0(5(4(4(4(4(5(x1)))))))))))) 3(3(5(3(4(0(3(1(0(3(4(4(0(x1))))))))))))) -> 0(1(1(1(5(2(5(4(3(2(4(5(x1)))))))))))) 5(5(4(2(5(3(1(4(2(4(2(5(1(1(x1)))))))))))))) -> 5(3(0(5(3(5(1(5(1(4(4(1(1(x1))))))))))))) 1(0(1(3(0(2(1(3(2(3(5(3(0(5(5(x1))))))))))))))) -> 2(1(5(4(4(0(1(1(3(3(1(1(4(5(x1)))))))))))))) 4(2(4(0(1(3(1(2(1(1(4(1(3(2(0(x1))))))))))))))) -> 4(5(2(3(2(3(1(4(5(0(2(0(5(2(x1)))))))))))))) 3(3(0(1(5(1(1(0(1(2(0(2(4(0(2(5(1(x1))))))))))))))))) -> 1(0(0(0(2(4(0(3(5(0(2(4(5(0(4(5(1(x1))))))))))))))))) 0(1(2(3(0(0(0(1(0(2(0(5(5(5(2(2(0(4(x1)))))))))))))))))) -> 3(1(5(0(2(0(5(4(5(0(1(0(3(2(5(1(4(0(x1)))))))))))))))))) 4(2(1(2(3(5(3(3(1(2(2(1(3(0(0(5(5(5(x1)))))))))))))))))) -> 4(4(1(3(4(0(1(4(3(5(4(4(1(0(0(5(1(2(x1)))))))))))))))))) 5(4(5(5(1(2(0(2(3(0(5(0(3(4(2(0(4(3(x1)))))))))))))))))) -> 5(1(5(5(4(0(0(3(1(3(2(4(4(1(1(4(0(1(x1)))))))))))))))))) 1(5(2(3(1(2(0(2(3(2(2(3(0(1(5(1(1(5(5(x1))))))))))))))))))) -> 1(4(5(0(1(5(3(4(4(2(1(2(1(4(3(3(3(2(3(x1))))))))))))))))))) 2(5(3(3(2(5(5(3(4(5(2(3(0(1(4(3(1(3(4(x1))))))))))))))))))) -> 2(2(3(0(4(5(5(5(1(4(3(1(3(4(1(1(2(x1))))))))))))))))) 2(3(3(4(5(3(3(1(5(5(0(4(1(4(0(2(2(3(1(4(x1)))))))))))))))))))) -> 2(0(1(5(3(2(0(2(5(1(2(4(5(3(4(4(4(0(4(5(x1)))))))))))))))))))) 3(2(3(4(1(2(3(2(3(4(2(1(0(4(1(0(4(2(0(4(x1)))))))))))))))))))) -> 1(3(4(0(0(4(3(4(3(1(3(0(0(4(5(3(1(4(3(4(4(x1))))))))))))))))))))) 4(2(0(0(3(5(0(0(4(1(4(2(1(4(3(2(3(5(5(3(x1)))))))))))))))))))) -> 0(0(0(3(0(4(4(3(0(4(1(3(0(1(0(0(4(4(5(3(x1)))))))))))))))))))) 1(0(3(1(1(1(1(0(1(2(0(5(4(0(3(0(5(3(4(2(0(x1))))))))))))))))))))) -> 0(5(4(2(0(0(3(0(0(1(1(2(3(1(5(1(2(4(2(0(x1)))))))))))))))))))) 5(0(5(0(2(2(4(0(0(5(2(1(2(5(1(1(1(0(1(2(4(x1))))))))))))))))))))) -> 5(4(3(4(5(4(2(5(4(1(4(4(1(3(0(2(2(1(2(0(x1)))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(0(x1)))) -> 0(2(0(x1))) 1(0(3(0(x1)))) -> 2(0(0(x1))) 3(1(4(0(x1)))) -> 3(2(3(x1))) 4(0(3(3(x1)))) -> 1(0(2(x1))) 4(1(3(0(x1)))) -> 4(4(5(x1))) 4(2(3(4(x1)))) -> 4(4(3(4(x1)))) 4(3(4(0(x1)))) -> 2(4(0(x1))) 0(4(5(2(4(x1))))) -> 5(1(2(0(x1)))) 3(0(2(5(3(x1))))) -> 0(4(2(0(x1)))) 3(3(5(3(0(x1))))) -> 1(4(4(1(x1)))) 4(4(4(4(5(0(x1)))))) -> 4(5(5(2(4(4(x1)))))) 2(4(2(0(2(1(5(x1))))))) -> 2(0(1(3(3(3(5(x1))))))) 4(0(3(2(0(2(4(x1))))))) -> 5(2(3(0(2(1(x1)))))) 3(2(0(5(0(2(1(4(x1)))))))) -> 2(2(1(4(5(1(5(x1))))))) 0(3(4(1(4(0(4(1(5(x1))))))))) -> 0(5(2(2(1(3(3(5(x1)))))))) 1(2(5(2(4(0(5(3(3(x1))))))))) -> 2(1(3(3(5(1(0(5(x1)))))))) 3(4(0(4(0(5(4(0(5(x1))))))))) -> 3(0(3(4(0(2(0(0(x1)))))))) 3(3(4(5(2(1(1(4(1(4(x1)))))))))) -> 0(0(3(1(0(0(2(1(1(4(x1)))))))))) 0(2(4(5(4(3(2(3(4(5(5(x1))))))))))) -> 3(0(0(3(0(4(5(2(5(0(2(x1))))))))))) 1(4(2(2(0(2(3(2(2(4(4(x1))))))))))) -> 2(3(1(0(3(0(2(1(0(1(5(0(x1)))))))))))) 1(5(2(0(3(4(2(3(1(4(0(x1))))))))))) -> 4(5(3(1(1(3(4(4(1(3(5(x1))))))))))) 0(0(4(5(3(1(5(0(1(3(3(2(x1)))))))))))) -> 2(2(2(2(4(1(2(5(4(2(x1)))))))))) 3(1(0(1(4(5(3(5(1(1(2(4(x1)))))))))))) -> 3(1(2(3(5(0(4(2(2(4(4(x1))))))))))) 3(2(1(1(2(4(1(2(3(2(1(2(x1)))))))))))) -> 2(3(3(4(0(5(0(0(2(2(1(4(x1)))))))))))) 1(2(2(4(3(2(5(1(3(5(3(5(0(x1))))))))))))) -> 3(3(3(1(0(0(5(4(4(4(4(5(x1)))))))))))) 3(3(5(3(4(0(3(1(0(3(4(4(0(x1))))))))))))) -> 0(1(1(1(5(2(5(4(3(2(4(5(x1)))))))))))) 5(5(4(2(5(3(1(4(2(4(2(5(1(1(x1)))))))))))))) -> 5(3(0(5(3(5(1(5(1(4(4(1(1(x1))))))))))))) 1(0(1(3(0(2(1(3(2(3(5(3(0(5(5(x1))))))))))))))) -> 2(1(5(4(4(0(1(1(3(3(1(1(4(5(x1)))))))))))))) 4(2(4(0(1(3(1(2(1(1(4(1(3(2(0(x1))))))))))))))) -> 4(5(2(3(2(3(1(4(5(0(2(0(5(2(x1)))))))))))))) 3(3(0(1(5(1(1(0(1(2(0(2(4(0(2(5(1(x1))))))))))))))))) -> 1(0(0(0(2(4(0(3(5(0(2(4(5(0(4(5(1(x1))))))))))))))))) 0(1(2(3(0(0(0(1(0(2(0(5(5(5(2(2(0(4(x1)))))))))))))))))) -> 3(1(5(0(2(0(5(4(5(0(1(0(3(2(5(1(4(0(x1)))))))))))))))))) 4(2(1(2(3(5(3(3(1(2(2(1(3(0(0(5(5(5(x1)))))))))))))))))) -> 4(4(1(3(4(0(1(4(3(5(4(4(1(0(0(5(1(2(x1)))))))))))))))))) 5(4(5(5(1(2(0(2(3(0(5(0(3(4(2(0(4(3(x1)))))))))))))))))) -> 5(1(5(5(4(0(0(3(1(3(2(4(4(1(1(4(0(1(x1)))))))))))))))))) 1(5(2(3(1(2(0(2(3(2(2(3(0(1(5(1(1(5(5(x1))))))))))))))))))) -> 1(4(5(0(1(5(3(4(4(2(1(2(1(4(3(3(3(2(3(x1))))))))))))))))))) 2(5(3(3(2(5(5(3(4(5(2(3(0(1(4(3(1(3(4(x1))))))))))))))))))) -> 2(2(3(0(4(5(5(5(1(4(3(1(3(4(1(1(2(x1))))))))))))))))) 2(3(3(4(5(3(3(1(5(5(0(4(1(4(0(2(2(3(1(4(x1)))))))))))))))))))) -> 2(0(1(5(3(2(0(2(5(1(2(4(5(3(4(4(4(0(4(5(x1)))))))))))))))))))) 3(2(3(4(1(2(3(2(3(4(2(1(0(4(1(0(4(2(0(4(x1)))))))))))))))))))) -> 1(3(4(0(0(4(3(4(3(1(3(0(0(4(5(3(1(4(3(4(4(x1))))))))))))))))))))) 4(2(0(0(3(5(0(0(4(1(4(2(1(4(3(2(3(5(5(3(x1)))))))))))))))))))) -> 0(0(0(3(0(4(4(3(0(4(1(3(0(1(0(0(4(4(5(3(x1)))))))))))))))))))) 1(0(3(1(1(1(1(0(1(2(0(5(4(0(3(0(5(3(4(2(0(x1))))))))))))))))))))) -> 0(5(4(2(0(0(3(0(0(1(1(2(3(1(5(1(2(4(2(0(x1)))))))))))))))))))) 5(0(5(0(2(2(4(0(0(5(2(1(2(5(1(1(1(0(1(2(4(x1))))))))))))))))))))) -> 5(4(3(4(5(4(2(5(4(1(4(4(1(3(0(2(2(1(2(0(x1)))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (7) CpxTrsMatchBoundsProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. The certificate found is represented by the following graph. "[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] {(151,152,[0_1|0, 1_1|0, 3_1|0, 4_1|0, 2_1|0, 5_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (151,153,[0_1|1, 1_1|1, 3_1|1, 4_1|1, 2_1|1, 5_1|1]), (151,154,[0_1|2]), (151,156,[3_1|2]), (151,173,[5_1|2]), (151,176,[0_1|2]), (151,183,[3_1|2]), (151,193,[2_1|2]), (151,202,[2_1|2]), (151,204,[0_1|2]), (151,223,[2_1|2]), (151,236,[2_1|2]), (151,243,[3_1|2]), (151,254,[2_1|2]), (151,265,[4_1|2]), (151,275,[1_1|2]), (151,293,[3_1|2]), (151,295,[3_1|2]), (151,305,[0_1|2]), (151,308,[1_1|2]), (151,311,[0_1|2]), (151,322,[0_1|2]), (151,331,[1_1|2]), (151,347,[2_1|2]), (151,353,[2_1|2]), (151,364,[1_1|2]), (151,384,[3_1|2]), (151,391,[1_1|2]), (151,393,[5_1|2]), (151,398,[4_1|2]), (151,400,[4_1|2]), (151,403,[4_1|2]), (151,416,[4_1|2]), (151,433,[0_1|2]), (151,452,[2_1|2]), (151,454,[4_1|2]), (151,459,[2_1|2]), (151,465,[2_1|2]), (151,481,[2_1|2]), (151,500,[5_1|2]), (151,512,[5_1|2]), (151,529,[5_1|2]), (152,152,[cons_0_1|0, cons_1_1|0, cons_3_1|0, cons_4_1|0, cons_2_1|0, cons_5_1|0]), (153,152,[encArg_1|1]), (153,153,[0_1|1, 1_1|1, 3_1|1, 4_1|1, 2_1|1, 5_1|1]), (153,154,[0_1|2]), (153,156,[3_1|2]), (153,173,[5_1|2]), (153,176,[0_1|2]), (153,183,[3_1|2]), (153,193,[2_1|2]), (153,202,[2_1|2]), (153,204,[0_1|2]), (153,223,[2_1|2]), (153,236,[2_1|2]), (153,243,[3_1|2]), (153,254,[2_1|2]), (153,265,[4_1|2]), (153,275,[1_1|2]), (153,293,[3_1|2]), (153,295,[3_1|2]), (153,305,[0_1|2]), (153,308,[1_1|2]), (153,311,[0_1|2]), (153,322,[0_1|2]), (153,331,[1_1|2]), (153,347,[2_1|2]), (153,353,[2_1|2]), (153,364,[1_1|2]), (153,384,[3_1|2]), (153,391,[1_1|2]), (153,393,[5_1|2]), (153,398,[4_1|2]), (153,400,[4_1|2]), (153,403,[4_1|2]), (153,416,[4_1|2]), (153,433,[0_1|2]), (153,452,[2_1|2]), (153,454,[4_1|2]), (153,459,[2_1|2]), (153,465,[2_1|2]), (153,481,[2_1|2]), (153,500,[5_1|2]), (153,512,[5_1|2]), (153,529,[5_1|2]), (154,155,[2_1|2]), (155,153,[0_1|2]), (155,154,[0_1|2]), (155,176,[0_1|2]), (155,204,[0_1|2]), (155,305,[0_1|2]), (155,311,[0_1|2]), (155,322,[0_1|2]), (155,433,[0_1|2]), (155,323,[0_1|2]), (155,434,[0_1|2]), (155,333,[0_1|2]), (155,156,[3_1|2]), (155,173,[5_1|2]), (155,183,[3_1|2]), (155,193,[2_1|2]), (155,548,[0_1|3]), (156,157,[1_1|2]), (157,158,[5_1|2]), (158,159,[0_1|2]), (159,160,[2_1|2]), (160,161,[0_1|2]), (161,162,[5_1|2]), (162,163,[4_1|2]), (163,164,[5_1|2]), (164,165,[0_1|2]), (165,166,[1_1|2]), (166,167,[0_1|2]), (167,168,[3_1|2]), (168,169,[2_1|2]), (169,170,[5_1|2]), (170,171,[1_1|2]), (171,172,[4_1|2]), (171,391,[1_1|2]), (171,393,[5_1|2]), (171,550,[1_1|3]), (172,153,[0_1|2]), (172,265,[0_1|2]), (172,398,[0_1|2]), (172,400,[0_1|2]), (172,403,[0_1|2]), (172,416,[0_1|2]), (172,454,[0_1|2]), (172,306,[0_1|2]), (172,154,[0_1|2]), (172,156,[3_1|2]), (172,173,[5_1|2]), (172,176,[0_1|2]), (172,183,[3_1|2]), (172,193,[2_1|2]), (172,548,[0_1|3]), (172,576,[5_1|3]), (173,174,[1_1|2]), (174,175,[2_1|2]), (175,153,[0_1|2]), (175,265,[0_1|2]), (175,398,[0_1|2]), (175,400,[0_1|2]), (175,403,[0_1|2]), (175,416,[0_1|2]), (175,454,[0_1|2]), (175,453,[0_1|2]), (175,154,[0_1|2]), (175,156,[3_1|2]), (175,173,[5_1|2]), (175,176,[0_1|2]), (175,183,[3_1|2]), (175,193,[2_1|2]), (175,548,[0_1|3]), (175,576,[5_1|3]), (176,177,[5_1|2]), (177,178,[2_1|2]), (178,179,[2_1|2]), (179,180,[1_1|2]), (180,181,[3_1|2]), (180,308,[1_1|2]), (180,311,[0_1|2]), (180,552,[1_1|3]), (181,182,[3_1|2]), (182,153,[5_1|2]), (182,173,[5_1|2]), (182,393,[5_1|2]), (182,500,[5_1|2]), (182,512,[5_1|2]), (182,529,[5_1|2]), (183,184,[0_1|2]), (184,185,[0_1|2]), (185,186,[3_1|2]), (186,187,[0_1|2]), (187,188,[4_1|2]), (188,189,[5_1|2]), (189,190,[2_1|2]), (190,191,[5_1|2]), (191,192,[0_1|2]), (191,183,[3_1|2]), (192,153,[2_1|2]), (192,173,[2_1|2]), (192,393,[2_1|2]), (192,500,[2_1|2]), (192,512,[2_1|2]), (192,529,[2_1|2]), (192,456,[2_1|2]), (192,459,[2_1|2]), (192,465,[2_1|2]), (192,481,[2_1|2]), (193,194,[2_1|2]), (194,195,[2_1|2]), (195,196,[2_1|2]), (196,197,[4_1|2]), (197,198,[1_1|2]), (198,199,[2_1|2]), (199,200,[5_1|2]), (200,201,[4_1|2]), (200,400,[4_1|2]), (200,403,[4_1|2]), (200,416,[4_1|2]), (200,433,[0_1|2]), (200,583,[4_1|3]), (201,153,[2_1|2]), (201,193,[2_1|2]), (201,202,[2_1|2]), (201,223,[2_1|2]), (201,236,[2_1|2]), (201,254,[2_1|2]), (201,347,[2_1|2]), (201,353,[2_1|2]), (201,452,[2_1|2]), (201,459,[2_1|2]), (201,465,[2_1|2]), (201,481,[2_1|2]), (201,294,[2_1|2]), (202,203,[0_1|2]), (202,193,[2_1|2]), (203,153,[0_1|2]), (203,154,[0_1|2]), (203,176,[0_1|2]), (203,204,[0_1|2]), (203,305,[0_1|2]), (203,311,[0_1|2]), (203,322,[0_1|2]), (203,433,[0_1|2]), (203,184,[0_1|2]), (203,385,[0_1|2]), (203,156,[3_1|2]), (203,173,[5_1|2]), (203,183,[3_1|2]), (203,193,[2_1|2]), (203,548,[0_1|3]), (204,205,[5_1|2]), (205,206,[4_1|2]), (206,207,[2_1|2]), (207,208,[0_1|2]), (208,209,[0_1|2]), (209,210,[3_1|2]), (210,211,[0_1|2]), (211,212,[0_1|2]), (212,213,[1_1|2]), (213,214,[1_1|2]), (214,215,[2_1|2]), (215,216,[3_1|2]), (216,217,[1_1|2]), (217,218,[5_1|2]), (218,219,[1_1|2]), (219,220,[2_1|2]), (219,459,[2_1|2]), (219,555,[2_1|3]), (220,221,[4_1|2]), (220,433,[0_1|2]), (221,222,[2_1|2]), (222,153,[0_1|2]), (222,154,[0_1|2]), (222,176,[0_1|2]), (222,204,[0_1|2]), (222,305,[0_1|2]), (222,311,[0_1|2]), (222,322,[0_1|2]), (222,433,[0_1|2]), (222,203,[0_1|2]), (222,460,[0_1|2]), (222,482,[0_1|2]), (222,156,[3_1|2]), (222,173,[5_1|2]), (222,183,[3_1|2]), (222,193,[2_1|2]), (222,548,[0_1|3]), (223,224,[1_1|2]), (224,225,[5_1|2]), (225,226,[4_1|2]), (226,227,[4_1|2]), (227,228,[0_1|2]), (228,229,[1_1|2]), (229,230,[1_1|2]), (230,231,[3_1|2]), (231,232,[3_1|2]), (232,233,[1_1|2]), (233,234,[1_1|2]), (234,235,[4_1|2]), (235,153,[5_1|2]), (235,173,[5_1|2]), (235,393,[5_1|2]), (235,500,[5_1|2]), (235,512,[5_1|2]), (235,529,[5_1|2]), (236,237,[1_1|2]), (237,238,[3_1|2]), (238,239,[3_1|2]), (239,240,[5_1|2]), (240,241,[1_1|2]), (241,242,[0_1|2]), (242,153,[5_1|2]), (242,156,[5_1|2]), (242,183,[5_1|2]), (242,243,[5_1|2]), (242,293,[5_1|2]), (242,295,[5_1|2]), (242,384,[5_1|2]), (242,244,[5_1|2]), (242,500,[5_1|2]), (242,512,[5_1|2]), (242,529,[5_1|2]), (243,244,[3_1|2]), (244,245,[3_1|2]), (245,246,[1_1|2]), (246,247,[0_1|2]), (247,248,[0_1|2]), (248,249,[5_1|2]), (249,250,[4_1|2]), (249,454,[4_1|2]), (249,561,[4_1|3]), (250,251,[4_1|2]), (251,252,[4_1|2]), (252,253,[4_1|2]), (253,153,[5_1|2]), (253,154,[5_1|2]), (253,176,[5_1|2]), (253,204,[5_1|2]), (253,305,[5_1|2]), (253,311,[5_1|2]), (253,322,[5_1|2]), (253,433,[5_1|2]), (253,500,[5_1|2]), (253,512,[5_1|2]), (253,529,[5_1|2]), (254,255,[3_1|2]), (255,256,[1_1|2]), (255,566,[2_1|3]), (256,257,[0_1|2]), (257,258,[3_1|2]), (258,259,[0_1|2]), (259,260,[2_1|2]), (260,261,[1_1|2]), (261,262,[0_1|2]), (262,263,[1_1|2]), (263,264,[5_1|2]), (263,529,[5_1|2]), (264,153,[0_1|2]), (264,265,[0_1|2]), (264,398,[0_1|2]), (264,400,[0_1|2]), (264,403,[0_1|2]), (264,416,[0_1|2]), (264,454,[0_1|2]), (264,399,[0_1|2]), (264,401,[0_1|2]), (264,417,[0_1|2]), (264,154,[0_1|2]), (264,156,[3_1|2]), (264,173,[5_1|2]), (264,176,[0_1|2]), (264,183,[3_1|2]), (264,193,[2_1|2]), (264,548,[0_1|3]), (264,576,[5_1|3]), (265,266,[5_1|2]), (266,267,[3_1|2]), (267,268,[1_1|2]), (268,269,[1_1|2]), (269,270,[3_1|2]), (270,271,[4_1|2]), (271,272,[4_1|2]), (272,273,[1_1|2]), (273,274,[3_1|2]), (274,153,[5_1|2]), (274,154,[5_1|2]), (274,176,[5_1|2]), (274,204,[5_1|2]), (274,305,[5_1|2]), (274,311,[5_1|2]), (274,322,[5_1|2]), (274,433,[5_1|2]), (274,500,[5_1|2]), (274,512,[5_1|2]), (274,529,[5_1|2]), (275,276,[4_1|2]), (276,277,[5_1|2]), (277,278,[0_1|2]), (278,279,[1_1|2]), (279,280,[5_1|2]), (280,281,[3_1|2]), (281,282,[4_1|2]), (282,283,[4_1|2]), (283,284,[2_1|2]), (284,285,[1_1|2]), (285,286,[2_1|2]), (286,287,[1_1|2]), (287,288,[4_1|2]), (288,289,[3_1|2]), (289,290,[3_1|2]), (290,291,[3_1|2]), (290,364,[1_1|2]), (291,292,[2_1|2]), (291,481,[2_1|2]), (292,153,[3_1|2]), (292,173,[3_1|2]), (292,393,[3_1|2]), (292,500,[3_1|2]), (292,512,[3_1|2]), (292,529,[3_1|2]), (292,293,[3_1|2]), (292,295,[3_1|2]), (292,305,[0_1|2]), (292,308,[1_1|2]), (292,311,[0_1|2]), (292,322,[0_1|2]), (292,331,[1_1|2]), (292,347,[2_1|2]), (292,353,[2_1|2]), (292,364,[1_1|2]), (292,384,[3_1|2]), (292,590,[3_1|3]), (293,294,[2_1|2]), (293,481,[2_1|2]), (294,153,[3_1|2]), (294,154,[3_1|2]), (294,176,[3_1|2]), (294,204,[3_1|2]), (294,305,[3_1|2, 0_1|2]), (294,311,[3_1|2, 0_1|2]), (294,322,[3_1|2, 0_1|2]), (294,433,[3_1|2]), (294,293,[3_1|2]), (294,295,[3_1|2]), (294,308,[1_1|2]), (294,331,[1_1|2]), (294,347,[2_1|2]), (294,353,[2_1|2]), (294,364,[1_1|2]), (294,384,[3_1|2]), (294,590,[3_1|3]), (295,296,[1_1|2]), (296,297,[2_1|2]), (297,298,[3_1|2]), (298,299,[5_1|2]), (299,300,[0_1|2]), (300,301,[4_1|2]), (301,302,[2_1|2]), (302,303,[2_1|2]), (303,304,[4_1|2]), (303,454,[4_1|2]), (303,561,[4_1|3]), (303,568,[4_1|3]), (303,403,[4_1|2]), (304,153,[4_1|2]), (304,265,[4_1|2]), (304,398,[4_1|2]), (304,400,[4_1|2]), (304,403,[4_1|2]), (304,416,[4_1|2]), (304,454,[4_1|2]), (304,453,[4_1|2]), (304,391,[1_1|2]), (304,393,[5_1|2]), (304,433,[0_1|2]), (304,452,[2_1|2]), (304,568,[4_1|3]), (304,550,[1_1|3]), (305,306,[4_1|2]), (305,433,[0_1|2]), (306,307,[2_1|2]), (307,153,[0_1|2]), (307,156,[0_1|2, 3_1|2]), (307,183,[0_1|2, 3_1|2]), (307,243,[0_1|2]), (307,293,[0_1|2]), (307,295,[0_1|2]), (307,384,[0_1|2]), (307,501,[0_1|2]), (307,154,[0_1|2]), (307,173,[5_1|2]), (307,176,[0_1|2]), (307,193,[2_1|2]), (307,548,[0_1|3]), (308,309,[4_1|2]), (309,310,[4_1|2]), (309,398,[4_1|2]), (309,568,[4_1|3]), (309,433,[0_1|2]), (310,153,[1_1|2]), (310,154,[1_1|2]), (310,176,[1_1|2]), (310,204,[1_1|2, 0_1|2]), (310,305,[1_1|2]), (310,311,[1_1|2]), (310,322,[1_1|2]), (310,433,[1_1|2]), (310,184,[1_1|2]), (310,385,[1_1|2]), (310,502,[1_1|2]), (310,202,[2_1|2]), (310,223,[2_1|2]), (310,236,[2_1|2]), (310,243,[3_1|2]), (310,254,[2_1|2]), (310,265,[4_1|2]), (310,275,[1_1|2]), (310,586,[2_1|3]), (311,312,[1_1|2]), (312,313,[1_1|2]), (313,314,[1_1|2]), (314,315,[5_1|2]), (315,316,[2_1|2]), (316,317,[5_1|2]), (317,318,[4_1|2]), (318,319,[3_1|2]), (319,320,[2_1|2]), (320,321,[4_1|2]), (321,153,[5_1|2]), (321,154,[5_1|2]), (321,176,[5_1|2]), (321,204,[5_1|2]), (321,305,[5_1|2]), (321,311,[5_1|2]), (321,322,[5_1|2]), (321,433,[5_1|2]), (321,500,[5_1|2]), (321,512,[5_1|2]), (321,529,[5_1|2]), (322,323,[0_1|2]), (323,324,[3_1|2]), (324,325,[1_1|2]), (325,326,[0_1|2]), (326,327,[0_1|2]), (327,328,[2_1|2]), (328,329,[1_1|2]), (329,330,[1_1|2]), (329,254,[2_1|2]), (330,153,[4_1|2]), (330,265,[4_1|2]), (330,398,[4_1|2]), (330,400,[4_1|2]), (330,403,[4_1|2]), (330,416,[4_1|2]), (330,454,[4_1|2]), (330,276,[4_1|2]), (330,309,[4_1|2]), (330,391,[1_1|2]), (330,393,[5_1|2]), (330,433,[0_1|2]), (330,452,[2_1|2]), (330,568,[4_1|3]), (331,332,[0_1|2]), (332,333,[0_1|2]), (333,334,[0_1|2]), (334,335,[2_1|2]), (335,336,[4_1|2]), (336,337,[0_1|2]), (337,338,[3_1|2]), (338,339,[5_1|2]), (339,340,[0_1|2]), (340,341,[2_1|2]), (341,342,[4_1|2]), (342,343,[5_1|2]), (343,344,[0_1|2]), (344,345,[4_1|2]), (345,346,[5_1|2]), (346,153,[1_1|2]), (346,275,[1_1|2]), (346,308,[1_1|2]), (346,331,[1_1|2]), (346,364,[1_1|2]), (346,391,[1_1|2]), (346,174,[1_1|2]), (346,513,[1_1|2]), (346,202,[2_1|2]), (346,204,[0_1|2]), (346,223,[2_1|2]), (346,236,[2_1|2]), (346,243,[3_1|2]), (346,254,[2_1|2]), (346,265,[4_1|2]), (347,348,[2_1|2]), (348,349,[1_1|2]), (349,350,[4_1|2]), (350,351,[5_1|2]), (351,352,[1_1|2]), (351,265,[4_1|2]), (351,275,[1_1|2]), (352,153,[5_1|2]), (352,265,[5_1|2]), (352,398,[5_1|2]), (352,400,[5_1|2]), (352,403,[5_1|2]), (352,416,[5_1|2]), (352,454,[5_1|2]), (352,276,[5_1|2]), (352,309,[5_1|2]), (352,500,[5_1|2]), (352,512,[5_1|2]), (352,529,[5_1|2]), (353,354,[3_1|2]), (354,355,[3_1|2]), (355,356,[4_1|2]), (356,357,[0_1|2]), (357,358,[5_1|2]), (358,359,[0_1|2]), (359,360,[0_1|2]), (360,361,[2_1|2]), (361,362,[2_1|2]), (362,363,[1_1|2]), (362,254,[2_1|2]), (363,153,[4_1|2]), (363,193,[4_1|2]), (363,202,[4_1|2]), (363,223,[4_1|2]), (363,236,[4_1|2]), (363,254,[4_1|2]), (363,347,[4_1|2]), (363,353,[4_1|2]), (363,452,[4_1|2, 2_1|2]), (363,459,[4_1|2]), (363,465,[4_1|2]), (363,481,[4_1|2]), (363,391,[1_1|2]), (363,393,[5_1|2]), (363,398,[4_1|2]), (363,400,[4_1|2]), (363,403,[4_1|2]), (363,416,[4_1|2]), (363,433,[0_1|2]), (363,454,[4_1|2]), (363,568,[4_1|3]), (364,365,[3_1|2]), (365,366,[4_1|2]), (366,367,[0_1|2]), (367,368,[0_1|2]), (368,369,[4_1|2]), (369,370,[3_1|2]), (370,371,[4_1|2]), (371,372,[3_1|2]), (372,373,[1_1|2]), (373,374,[3_1|2]), (374,375,[0_1|2]), (375,376,[0_1|2]), (376,377,[4_1|2]), (377,378,[5_1|2]), (378,379,[3_1|2]), (379,380,[1_1|2]), (380,381,[4_1|2]), (380,570,[2_1|3]), (381,382,[3_1|2]), (382,383,[4_1|2]), (382,454,[4_1|2]), (382,561,[4_1|3]), (382,568,[4_1|3]), (382,403,[4_1|2]), (383,153,[4_1|2]), (383,265,[4_1|2]), (383,398,[4_1|2]), (383,400,[4_1|2]), (383,403,[4_1|2]), (383,416,[4_1|2]), (383,454,[4_1|2]), (383,306,[4_1|2]), (383,391,[1_1|2]), (383,393,[5_1|2]), (383,433,[0_1|2]), (383,452,[2_1|2]), (383,568,[4_1|3]), (384,385,[0_1|2]), (385,386,[3_1|2]), (386,387,[4_1|2]), (387,388,[0_1|2]), (388,389,[2_1|2]), (389,390,[0_1|2]), (389,193,[2_1|2]), (390,153,[0_1|2]), (390,173,[0_1|2, 5_1|2]), (390,393,[0_1|2]), (390,500,[0_1|2]), (390,512,[0_1|2]), (390,529,[0_1|2]), (390,177,[0_1|2]), (390,205,[0_1|2]), (390,154,[0_1|2]), (390,156,[3_1|2]), (390,176,[0_1|2]), (390,183,[3_1|2]), (390,193,[2_1|2]), (390,548,[0_1|3]), (391,392,[0_1|2]), (391,183,[3_1|2]), (392,153,[2_1|2]), (392,156,[2_1|2]), (392,183,[2_1|2]), (392,243,[2_1|2]), (392,293,[2_1|2]), (392,295,[2_1|2]), (392,384,[2_1|2]), (392,244,[2_1|2]), (392,459,[2_1|2]), (392,465,[2_1|2]), (392,481,[2_1|2]), (393,394,[2_1|2]), (394,395,[3_1|2]), (395,396,[0_1|2]), (396,397,[2_1|2]), (397,153,[1_1|2]), (397,265,[1_1|2, 4_1|2]), (397,398,[1_1|2]), (397,400,[1_1|2]), (397,403,[1_1|2]), (397,416,[1_1|2]), (397,454,[1_1|2]), (397,453,[1_1|2]), (397,202,[2_1|2]), (397,204,[0_1|2]), (397,223,[2_1|2]), (397,236,[2_1|2]), (397,243,[3_1|2]), (397,254,[2_1|2]), (397,275,[1_1|2]), (397,588,[2_1|3]), (398,399,[4_1|2]), (399,153,[5_1|2]), (399,154,[5_1|2]), (399,176,[5_1|2]), (399,204,[5_1|2]), (399,305,[5_1|2]), (399,311,[5_1|2]), (399,322,[5_1|2]), (399,433,[5_1|2]), (399,184,[5_1|2]), (399,385,[5_1|2]), (399,500,[5_1|2]), (399,512,[5_1|2]), (399,529,[5_1|2]), (400,401,[4_1|2]), (400,452,[2_1|2]), (400,570,[2_1|3]), (401,402,[3_1|2]), (401,384,[3_1|2]), (402,153,[4_1|2]), (402,265,[4_1|2]), (402,398,[4_1|2]), (402,400,[4_1|2]), (402,403,[4_1|2]), (402,416,[4_1|2]), (402,454,[4_1|2]), (402,391,[1_1|2]), (402,393,[5_1|2]), (402,433,[0_1|2]), (402,452,[2_1|2]), (402,568,[4_1|3]), (403,404,[5_1|2]), (404,405,[2_1|2]), (405,406,[3_1|2]), (406,407,[2_1|2]), (407,408,[3_1|2]), (408,409,[1_1|2]), (409,410,[4_1|2]), (410,411,[5_1|2]), (411,412,[0_1|2]), (412,413,[2_1|2]), (413,414,[0_1|2]), (414,415,[5_1|2]), (415,153,[2_1|2]), (415,154,[2_1|2]), (415,176,[2_1|2]), (415,204,[2_1|2]), (415,305,[2_1|2]), (415,311,[2_1|2]), (415,322,[2_1|2]), (415,433,[2_1|2]), (415,203,[2_1|2]), (415,460,[2_1|2]), (415,482,[2_1|2]), (415,459,[2_1|2]), (415,465,[2_1|2]), (415,481,[2_1|2]), (415,555,[2_1|3]), (416,417,[4_1|2]), (417,418,[1_1|2]), (418,419,[3_1|2]), (419,420,[4_1|2]), (420,421,[0_1|2]), (421,422,[1_1|2]), (422,423,[4_1|2]), (423,424,[3_1|2]), (424,425,[5_1|2]), (425,426,[4_1|2]), (426,427,[4_1|2]), (427,428,[1_1|2]), (428,429,[0_1|2]), (429,430,[0_1|2]), (430,431,[5_1|2]), (431,432,[1_1|2]), (431,236,[2_1|2]), (431,243,[3_1|2]), (432,153,[2_1|2]), (432,173,[2_1|2]), (432,393,[2_1|2]), (432,500,[2_1|2]), (432,512,[2_1|2]), (432,529,[2_1|2]), (432,459,[2_1|2]), (432,465,[2_1|2]), (432,481,[2_1|2]), (433,434,[0_1|2]), (434,435,[0_1|2]), (435,436,[3_1|2]), (436,437,[0_1|2]), (437,438,[4_1|2]), (438,439,[4_1|2]), (439,440,[3_1|2]), (440,441,[0_1|2]), (441,442,[4_1|2]), (441,572,[4_1|3]), (442,443,[1_1|2]), (443,444,[3_1|2]), (444,445,[0_1|2]), (444,574,[0_1|3]), (445,446,[1_1|2]), (446,447,[0_1|2]), (447,448,[0_1|2]), (448,449,[4_1|2]), (449,450,[4_1|2]), (450,451,[5_1|2]), (451,153,[3_1|2]), (451,156,[3_1|2]), (451,183,[3_1|2]), (451,243,[3_1|2]), (451,293,[3_1|2]), (451,295,[3_1|2]), (451,384,[3_1|2]), (451,501,[3_1|2]), (451,305,[0_1|2]), (451,308,[1_1|2]), (451,311,[0_1|2]), (451,322,[0_1|2]), (451,331,[1_1|2]), (451,347,[2_1|2]), (451,353,[2_1|2]), (451,364,[1_1|2]), (451,590,[3_1|3]), (452,453,[4_1|2]), (452,391,[1_1|2]), (452,393,[5_1|2]), (452,550,[1_1|3]), (453,153,[0_1|2]), (453,154,[0_1|2]), (453,176,[0_1|2]), (453,204,[0_1|2]), (453,305,[0_1|2]), (453,311,[0_1|2]), (453,322,[0_1|2]), (453,433,[0_1|2]), (453,156,[3_1|2]), (453,173,[5_1|2]), (453,183,[3_1|2]), (453,193,[2_1|2]), (453,548,[0_1|3]), (454,455,[5_1|2]), (455,456,[5_1|2]), (456,457,[2_1|2]), (457,458,[4_1|2]), (457,454,[4_1|2]), (457,561,[4_1|3]), (457,568,[4_1|3]), (457,403,[4_1|2]), (458,153,[4_1|2]), (458,154,[4_1|2]), (458,176,[4_1|2]), (458,204,[4_1|2]), (458,305,[4_1|2]), (458,311,[4_1|2]), (458,322,[4_1|2]), (458,433,[4_1|2, 0_1|2]), (458,391,[1_1|2]), (458,393,[5_1|2]), (458,398,[4_1|2]), (458,400,[4_1|2]), (458,403,[4_1|2]), (458,416,[4_1|2]), (458,452,[2_1|2]), (458,454,[4_1|2]), (458,323,[4_1|2]), (458,434,[4_1|2]), (458,185,[4_1|2]), (458,568,[4_1|3]), (459,460,[0_1|2]), (460,461,[1_1|2]), (461,462,[3_1|2]), (461,590,[3_1|3]), (462,463,[3_1|2]), (462,308,[1_1|2]), (462,311,[0_1|2]), (462,552,[1_1|3]), (463,464,[3_1|2]), (464,153,[5_1|2]), (464,173,[5_1|2]), (464,393,[5_1|2]), (464,500,[5_1|2]), (464,512,[5_1|2]), (464,529,[5_1|2]), (464,225,[5_1|2]), (465,466,[2_1|2]), (466,467,[3_1|2]), (467,468,[0_1|2]), (468,469,[4_1|2]), (469,470,[5_1|2]), (470,471,[5_1|2]), (471,472,[5_1|2]), (472,473,[1_1|2]), (473,474,[4_1|2]), (474,475,[3_1|2]), (475,476,[1_1|2]), (476,477,[3_1|2]), (477,478,[4_1|2]), (478,479,[1_1|2]), (479,480,[1_1|2]), (479,236,[2_1|2]), (479,243,[3_1|2]), (480,153,[2_1|2]), (480,265,[2_1|2]), (480,398,[2_1|2]), (480,400,[2_1|2]), (480,403,[2_1|2]), (480,416,[2_1|2]), (480,454,[2_1|2]), (480,366,[2_1|2]), (480,459,[2_1|2]), (480,465,[2_1|2]), (480,481,[2_1|2]), (481,482,[0_1|2]), (482,483,[1_1|2]), (483,484,[5_1|2]), (484,485,[3_1|2]), (485,486,[2_1|2]), (486,487,[0_1|2]), (487,488,[2_1|2]), (488,489,[5_1|2]), (489,490,[1_1|2]), (490,491,[2_1|2]), (491,492,[4_1|2]), (492,493,[5_1|2]), (493,494,[3_1|2]), (494,495,[4_1|2]), (495,496,[4_1|2]), (496,497,[4_1|2]), (497,498,[0_1|2]), (497,173,[5_1|2]), (497,576,[5_1|3]), (498,499,[4_1|2]), (499,153,[5_1|2]), (499,265,[5_1|2]), (499,398,[5_1|2]), (499,400,[5_1|2]), (499,403,[5_1|2]), (499,416,[5_1|2]), (499,454,[5_1|2]), (499,276,[5_1|2]), (499,309,[5_1|2]), (499,500,[5_1|2]), (499,512,[5_1|2]), (499,529,[5_1|2]), (500,501,[3_1|2]), (501,502,[0_1|2]), (502,503,[5_1|2]), (503,504,[3_1|2]), (504,505,[5_1|2]), (505,506,[1_1|2]), (506,507,[5_1|2]), (507,508,[1_1|2]), (508,509,[4_1|2]), (509,510,[4_1|2]), (510,511,[1_1|2]), (511,153,[1_1|2]), (511,275,[1_1|2]), (511,308,[1_1|2]), (511,331,[1_1|2]), (511,364,[1_1|2]), (511,391,[1_1|2]), (511,202,[2_1|2]), (511,204,[0_1|2]), (511,223,[2_1|2]), (511,236,[2_1|2]), (511,243,[3_1|2]), (511,254,[2_1|2]), (511,265,[4_1|2]), (512,513,[1_1|2]), (513,514,[5_1|2]), (514,515,[5_1|2]), (515,516,[4_1|2]), (516,517,[0_1|2]), (517,518,[0_1|2]), (518,519,[3_1|2]), (519,520,[1_1|2]), (520,521,[3_1|2]), (521,522,[2_1|2]), (522,523,[4_1|2]), (523,524,[4_1|2]), (524,525,[1_1|2]), (525,526,[1_1|2]), (526,527,[4_1|2]), (526,550,[1_1|3]), (527,528,[0_1|2]), (527,154,[0_1|2]), (527,156,[3_1|2]), (527,579,[0_1|3]), (528,153,[1_1|2]), (528,156,[1_1|2]), (528,183,[1_1|2]), (528,243,[1_1|2, 3_1|2]), (528,293,[1_1|2]), (528,295,[1_1|2]), (528,384,[1_1|2]), (528,202,[2_1|2]), (528,204,[0_1|2]), (528,223,[2_1|2]), (528,236,[2_1|2]), (528,254,[2_1|2]), (528,265,[4_1|2]), (528,275,[1_1|2]), (529,530,[4_1|2]), (530,531,[3_1|2]), (531,532,[4_1|2]), (532,533,[5_1|2]), (533,534,[4_1|2]), (534,535,[2_1|2]), (535,536,[5_1|2]), (536,537,[4_1|2]), (537,538,[1_1|2]), (538,539,[4_1|2]), (539,540,[4_1|2]), (539,581,[4_1|3]), (540,541,[1_1|2]), (541,542,[3_1|2]), (542,543,[0_1|2]), (543,544,[2_1|2]), (544,545,[2_1|2]), (545,546,[1_1|2]), (546,547,[2_1|2]), (547,153,[0_1|2]), (547,265,[0_1|2]), (547,398,[0_1|2]), (547,400,[0_1|2]), (547,403,[0_1|2]), (547,416,[0_1|2]), (547,454,[0_1|2]), (547,453,[0_1|2]), (547,154,[0_1|2]), (547,156,[3_1|2]), (547,173,[5_1|2]), (547,176,[0_1|2]), (547,183,[3_1|2]), (547,193,[2_1|2]), (547,548,[0_1|3]), (547,576,[5_1|3]), (548,549,[2_1|3]), (549,333,[0_1|3]), (550,551,[0_1|3]), (551,244,[2_1|3]), (552,553,[4_1|3]), (553,554,[4_1|3]), (554,184,[1_1|3]), (554,385,[1_1|3]), (554,502,[1_1|3]), (554,586,[2_1|3]), (555,556,[0_1|3]), (556,557,[1_1|3]), (557,558,[3_1|3]), (558,559,[3_1|3]), (559,560,[3_1|3]), (560,225,[5_1|3]), (561,562,[5_1|3]), (562,563,[5_1|3]), (563,564,[2_1|3]), (564,565,[4_1|3]), (565,154,[4_1|3]), (565,176,[4_1|3]), (565,204,[4_1|3]), (565,305,[4_1|3]), (565,311,[4_1|3]), (565,322,[4_1|3]), (565,433,[4_1|3, 0_1|2]), (565,323,[4_1|3]), (565,434,[4_1|3]), (565,185,[4_1|3]), (566,567,[0_1|3]), (567,259,[0_1|3]), (568,569,[4_1|3]), (569,184,[5_1|3]), (569,385,[5_1|3]), (570,571,[4_1|3]), (571,154,[0_1|3]), (571,176,[0_1|3]), (571,204,[0_1|3]), (571,305,[0_1|3]), (571,311,[0_1|3]), (571,322,[0_1|3]), (571,433,[0_1|3]), (572,573,[4_1|3]), (573,445,[5_1|3]), (573,574,[5_1|3]), (574,575,[2_1|3]), (575,448,[0_1|3]), (576,577,[1_1|3]), (577,578,[2_1|3]), (578,453,[0_1|3]), (578,571,[0_1|3]), (578,193,[2_1|2]), (579,580,[2_1|3]), (580,323,[0_1|3]), (580,434,[0_1|3]), (580,433,[0_1|3]), (580,185,[0_1|3]), (581,582,[4_1|3]), (582,543,[5_1|3]), (583,584,[4_1|3]), (584,585,[3_1|3]), (585,265,[4_1|3]), (585,398,[4_1|3]), (585,400,[4_1|3]), (585,403,[4_1|3, 4_1|2]), (585,416,[4_1|3]), (585,454,[4_1|3]), (585,306,[4_1|3]), (585,433,[0_1|2]), (586,587,[0_1|3]), (587,187,[0_1|3]), (588,589,[0_1|3]), (589,184,[0_1|3]), (589,385,[0_1|3]), (590,591,[2_1|3]), (591,433,[3_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)