/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 41 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 513 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(x1))) -> 0(2(1(1(x1)))) 0(3(2(x1))) -> 0(2(1(3(x1)))) 0(3(2(x1))) -> 0(2(1(1(3(x1))))) 0(1(2(4(x1)))) -> 0(2(4(1(1(x1))))) 0(3(2(4(x1)))) -> 0(1(4(3(2(x1))))) 0(3(4(2(x1)))) -> 0(4(2(1(3(x1))))) 0(3(4(4(x1)))) -> 0(1(4(4(3(1(x1)))))) 1(2(0(3(x1)))) -> 3(1(0(2(1(x1))))) 3(0(3(2(x1)))) -> 3(0(2(3(1(x1))))) 0(1(2(0(3(x1))))) -> 0(2(1(3(1(0(x1)))))) 0(1(2(2(2(x1))))) -> 0(2(1(2(1(2(x1)))))) 0(1(2(5(1(x1))))) -> 0(2(1(1(0(5(x1)))))) 0(3(2(4(4(x1))))) -> 4(0(4(2(1(3(x1)))))) 0(3(2(5(3(x1))))) -> 5(1(3(0(2(3(x1)))))) 2(2(0(3(5(x1))))) -> 2(5(0(2(1(3(x1)))))) 2(4(0(3(2(x1))))) -> 2(4(3(0(0(2(x1)))))) 3(0(3(4(2(x1))))) -> 1(3(4(0(2(3(x1)))))) 4(2(5(0(3(x1))))) -> 5(4(3(0(2(1(x1)))))) 4(5(0(3(2(x1))))) -> 4(5(0(2(3(1(x1)))))) 4(5(0(3(3(x1))))) -> 0(5(4(1(3(3(x1)))))) 5(0(3(1(2(x1))))) -> 0(5(2(1(1(3(x1)))))) 5(1(2(0(3(x1))))) -> 1(0(2(1(3(5(x1)))))) 5(2(0(1(2(x1))))) -> 0(2(1(5(0(2(x1)))))) 0(1(1(4(4(2(x1)))))) -> 4(1(1(1(0(4(2(x1))))))) 0(1(5(3(0(2(x1)))))) -> 0(2(0(5(1(1(3(x1))))))) 0(3(0(5(4(2(x1)))))) -> 4(1(0(2(3(0(5(x1))))))) 0(3(1(4(3(2(x1)))))) -> 1(0(2(1(4(3(3(x1))))))) 0(3(2(0(3(4(x1)))))) -> 1(0(2(3(3(0(4(x1))))))) 0(3(2(2(4(5(x1)))))) -> 0(2(5(4(1(2(3(x1))))))) 0(3(2(3(4(1(x1)))))) -> 4(1(1(3(0(2(1(3(x1)))))))) 0(3(2(4(1(4(x1)))))) -> 4(1(3(0(2(4(1(x1))))))) 0(3(2(5(5(1(x1)))))) -> 0(2(1(1(3(5(5(1(x1)))))))) 4(2(2(0(3(2(x1)))))) -> 2(2(0(2(4(1(1(3(x1)))))))) 5(4(0(3(1(2(x1)))))) -> 0(1(4(5(2(1(3(x1))))))) 5(4(0(3(2(4(x1)))))) -> 4(2(0(5(4(1(1(3(x1)))))))) 0(1(2(4(3(5(4(x1))))))) -> 0(2(4(5(4(1(1(3(x1)))))))) 0(1(2(5(3(5(4(x1))))))) -> 5(1(4(3(1(2(0(5(x1)))))))) 0(3(1(4(4(2(4(x1))))))) -> 4(1(2(1(0(4(3(4(x1)))))))) 0(3(2(0(0(3(2(x1))))))) -> 0(0(2(3(0(2(3(1(x1)))))))) 0(5(3(3(2(1(5(x1))))))) -> 0(2(1(3(1(3(5(5(x1)))))))) 2(3(0(3(0(1(2(x1))))))) -> 3(0(2(1(1(0(2(3(x1)))))))) 2(4(1(0(3(0(2(x1))))))) -> 2(0(2(1(3(1(0(4(x1)))))))) 2(5(0(0(4(4(2(x1))))))) -> 2(0(4(1(0(4(5(2(x1)))))))) 3(3(4(1(0(3(2(x1))))))) -> 3(3(4(1(1(3(0(2(x1)))))))) 4(2(1(0(3(5(5(x1))))))) -> 5(0(1(4(3(1(2(5(x1)))))))) 4(3(0(3(2(5(3(x1))))))) -> 0(2(1(3(1(3(4(5(3(x1))))))))) 4(3(4(5(2(1(2(x1))))))) -> 5(2(2(4(4(1(1(3(x1)))))))) 4(4(2(5(3(1(1(x1))))))) -> 5(4(3(4(1(2(1(1(x1)))))))) 5(3(5(0(1(2(4(x1))))))) -> 4(5(0(2(1(3(1(5(x1)))))))) 0(1(1(2(5(0(3(1(x1)))))))) -> 0(5(1(1(0(2(1(1(3(x1))))))))) 0(3(0(3(4(2(5(2(x1)))))))) -> 0(1(2(4(3(5(0(2(3(x1))))))))) 0(3(4(4(4(0(4(5(x1)))))))) -> 4(3(0(1(4(4(0(4(5(x1))))))))) 2(2(0(3(1(5(3(1(x1)))))))) -> 2(3(0(2(1(1(3(5(1(x1))))))))) 2(2(4(2(3(3(1(5(x1)))))))) -> 2(2(1(3(4(3(2(1(5(x1))))))))) 3(0(0(1(4(2(4(2(x1)))))))) -> 3(2(1(4(0(2(0(4(1(x1))))))))) 3(1(0(3(1(2(1(2(x1)))))))) -> 3(1(3(1(1(0(0(2(2(x1))))))))) 3(2(3(0(3(2(3(2(x1)))))))) -> 3(3(2(1(3(2(3(0(2(x1))))))))) 4(2(3(1(0(0(5(2(x1)))))))) -> 2(0(0(2(1(1(5(4(3(x1))))))))) 4(5(0(0(3(3(0(2(x1)))))))) -> 1(4(3(0(5(3(0(0(2(x1))))))))) 5(0(3(4(2(1(1(4(x1)))))))) -> 5(4(0(0(2(3(1(1(4(x1))))))))) 5(2(0(1(5(1(2(3(x1)))))))) -> 0(2(2(3(1(1(1(5(5(x1))))))))) 0(1(4(2(2(5(5(5(2(x1))))))))) -> 0(2(5(0(2(5(4(1(5(2(x1)))))))))) 0(2(1(4(2(2(0(3(1(x1))))))))) -> 0(2(3(4(1(2(0(0(2(1(x1)))))))))) 0(3(2(0(3(4(3(1(3(x1))))))))) -> 1(3(0(1(4(3(1(3(3(0(2(x1))))))))))) 0(3(5(1(2(2(0(1(3(x1))))))))) -> 0(4(2(0(2(1(1(3(5(3(x1)))))))))) 0(4(0(3(2(5(0(5(2(x1))))))))) -> 0(4(0(0(2(5(5(1(3(2(x1)))))))))) 1(4(2(4(0(0(0(3(4(x1))))))))) -> 4(0(2(1(4(3(0(0(4(1(x1)))))))))) 2(1(4(0(3(2(4(1(5(x1))))))))) -> 2(1(1(3(0(2(5(4(0(4(x1)))))))))) 3(0(0(1(2(0(3(2(5(x1))))))))) -> 0(2(2(0(5(1(0(1(3(3(x1)))))))))) 3(0(1(3(5(1(4(5(4(x1))))))))) -> 1(1(0(4(5(5(1(3(3(4(x1)))))))))) 4(2(1(5(3(0(1(2(2(x1))))))))) -> 2(5(0(2(1(4(3(2(1(1(x1)))))))))) 5(1(2(2(0(3(5(1(2(x1))))))))) -> 1(0(2(1(3(2(5(5(2(1(1(x1))))))))))) 0(1(3(4(2(5(0(3(5(1(x1)))))))))) -> 5(2(3(1(4(3(0(5(0(0(1(x1))))))))))) 0(3(4(2(3(2(2(3(2(4(x1)))))))))) -> 4(3(2(2(3(0(2(1(3(2(4(x1))))))))))) 0(3(5(4(1(4(3(5(3(4(x1)))))))))) -> 0(5(4(3(3(1(5(4(4(3(1(x1))))))))))) 0(4(3(3(4(0(3(2(5(4(x1)))))))))) -> 0(1(4(4(3(2(3(3(4(5(0(x1))))))))))) 1(0(3(2(5(2(5(4(1(2(x1)))))))))) -> 1(5(2(0(2(1(4(5(0(2(3(x1))))))))))) 1(4(5(1(4(2(5(1(3(1(x1)))))))))) -> 5(5(1(4(3(1(4(1(1(2(1(x1))))))))))) 1(5(2(0(3(4(2(2(5(5(x1)))))))))) -> 1(5(2(5(0(2(2(5(1(4(3(x1))))))))))) 2(0(1(2(5(0(3(2(1(1(x1)))))))))) -> 2(5(4(1(1(1(3(0(2(0(2(x1))))))))))) 2(4(0(1(5(3(0(0(3(3(x1)))))))))) -> 3(0(3(0(5(4(0(2(1(1(3(x1))))))))))) 2(4(2(0(1(0(3(4(4(3(x1)))))))))) -> 2(1(0(0(1(4(3(2(4(4(3(x1))))))))))) 4(2(0(3(1(1(5(0(3(1(x1)))))))))) -> 1(3(0(1(5(0(2(3(1(1(4(x1))))))))))) 4(4(2(5(0(5(5(0(0(3(x1)))))))))) -> 0(2(5(4(3(1(4(0(5(5(0(x1))))))))))) 4(5(0(4(0(0(5(2(0(3(x1)))))))))) -> 5(1(5(4(0(0(2(3(0(4(0(x1))))))))))) 5(5(0(1(0(0(3(2(2(4(x1)))))))))) -> 0(0(2(0(5(2(5(4(1(1(3(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_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)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(x1))) -> 0(2(1(1(x1)))) 0(3(2(x1))) -> 0(2(1(3(x1)))) 0(3(2(x1))) -> 0(2(1(1(3(x1))))) 0(1(2(4(x1)))) -> 0(2(4(1(1(x1))))) 0(3(2(4(x1)))) -> 0(1(4(3(2(x1))))) 0(3(4(2(x1)))) -> 0(4(2(1(3(x1))))) 0(3(4(4(x1)))) -> 0(1(4(4(3(1(x1)))))) 1(2(0(3(x1)))) -> 3(1(0(2(1(x1))))) 3(0(3(2(x1)))) -> 3(0(2(3(1(x1))))) 0(1(2(0(3(x1))))) -> 0(2(1(3(1(0(x1)))))) 0(1(2(2(2(x1))))) -> 0(2(1(2(1(2(x1)))))) 0(1(2(5(1(x1))))) -> 0(2(1(1(0(5(x1)))))) 0(3(2(4(4(x1))))) -> 4(0(4(2(1(3(x1)))))) 0(3(2(5(3(x1))))) -> 5(1(3(0(2(3(x1)))))) 2(2(0(3(5(x1))))) -> 2(5(0(2(1(3(x1)))))) 2(4(0(3(2(x1))))) -> 2(4(3(0(0(2(x1)))))) 3(0(3(4(2(x1))))) -> 1(3(4(0(2(3(x1)))))) 4(2(5(0(3(x1))))) -> 5(4(3(0(2(1(x1)))))) 4(5(0(3(2(x1))))) -> 4(5(0(2(3(1(x1)))))) 4(5(0(3(3(x1))))) -> 0(5(4(1(3(3(x1)))))) 5(0(3(1(2(x1))))) -> 0(5(2(1(1(3(x1)))))) 5(1(2(0(3(x1))))) -> 1(0(2(1(3(5(x1)))))) 5(2(0(1(2(x1))))) -> 0(2(1(5(0(2(x1)))))) 0(1(1(4(4(2(x1)))))) -> 4(1(1(1(0(4(2(x1))))))) 0(1(5(3(0(2(x1)))))) -> 0(2(0(5(1(1(3(x1))))))) 0(3(0(5(4(2(x1)))))) -> 4(1(0(2(3(0(5(x1))))))) 0(3(1(4(3(2(x1)))))) -> 1(0(2(1(4(3(3(x1))))))) 0(3(2(0(3(4(x1)))))) -> 1(0(2(3(3(0(4(x1))))))) 0(3(2(2(4(5(x1)))))) -> 0(2(5(4(1(2(3(x1))))))) 0(3(2(3(4(1(x1)))))) -> 4(1(1(3(0(2(1(3(x1)))))))) 0(3(2(4(1(4(x1)))))) -> 4(1(3(0(2(4(1(x1))))))) 0(3(2(5(5(1(x1)))))) -> 0(2(1(1(3(5(5(1(x1)))))))) 4(2(2(0(3(2(x1)))))) -> 2(2(0(2(4(1(1(3(x1)))))))) 5(4(0(3(1(2(x1)))))) -> 0(1(4(5(2(1(3(x1))))))) 5(4(0(3(2(4(x1)))))) -> 4(2(0(5(4(1(1(3(x1)))))))) 0(1(2(4(3(5(4(x1))))))) -> 0(2(4(5(4(1(1(3(x1)))))))) 0(1(2(5(3(5(4(x1))))))) -> 5(1(4(3(1(2(0(5(x1)))))))) 0(3(1(4(4(2(4(x1))))))) -> 4(1(2(1(0(4(3(4(x1)))))))) 0(3(2(0(0(3(2(x1))))))) -> 0(0(2(3(0(2(3(1(x1)))))))) 0(5(3(3(2(1(5(x1))))))) -> 0(2(1(3(1(3(5(5(x1)))))))) 2(3(0(3(0(1(2(x1))))))) -> 3(0(2(1(1(0(2(3(x1)))))))) 2(4(1(0(3(0(2(x1))))))) -> 2(0(2(1(3(1(0(4(x1)))))))) 2(5(0(0(4(4(2(x1))))))) -> 2(0(4(1(0(4(5(2(x1)))))))) 3(3(4(1(0(3(2(x1))))))) -> 3(3(4(1(1(3(0(2(x1)))))))) 4(2(1(0(3(5(5(x1))))))) -> 5(0(1(4(3(1(2(5(x1)))))))) 4(3(0(3(2(5(3(x1))))))) -> 0(2(1(3(1(3(4(5(3(x1))))))))) 4(3(4(5(2(1(2(x1))))))) -> 5(2(2(4(4(1(1(3(x1)))))))) 4(4(2(5(3(1(1(x1))))))) -> 5(4(3(4(1(2(1(1(x1)))))))) 5(3(5(0(1(2(4(x1))))))) -> 4(5(0(2(1(3(1(5(x1)))))))) 0(1(1(2(5(0(3(1(x1)))))))) -> 0(5(1(1(0(2(1(1(3(x1))))))))) 0(3(0(3(4(2(5(2(x1)))))))) -> 0(1(2(4(3(5(0(2(3(x1))))))))) 0(3(4(4(4(0(4(5(x1)))))))) -> 4(3(0(1(4(4(0(4(5(x1))))))))) 2(2(0(3(1(5(3(1(x1)))))))) -> 2(3(0(2(1(1(3(5(1(x1))))))))) 2(2(4(2(3(3(1(5(x1)))))))) -> 2(2(1(3(4(3(2(1(5(x1))))))))) 3(0(0(1(4(2(4(2(x1)))))))) -> 3(2(1(4(0(2(0(4(1(x1))))))))) 3(1(0(3(1(2(1(2(x1)))))))) -> 3(1(3(1(1(0(0(2(2(x1))))))))) 3(2(3(0(3(2(3(2(x1)))))))) -> 3(3(2(1(3(2(3(0(2(x1))))))))) 4(2(3(1(0(0(5(2(x1)))))))) -> 2(0(0(2(1(1(5(4(3(x1))))))))) 4(5(0(0(3(3(0(2(x1)))))))) -> 1(4(3(0(5(3(0(0(2(x1))))))))) 5(0(3(4(2(1(1(4(x1)))))))) -> 5(4(0(0(2(3(1(1(4(x1))))))))) 5(2(0(1(5(1(2(3(x1)))))))) -> 0(2(2(3(1(1(1(5(5(x1))))))))) 0(1(4(2(2(5(5(5(2(x1))))))))) -> 0(2(5(0(2(5(4(1(5(2(x1)))))))))) 0(2(1(4(2(2(0(3(1(x1))))))))) -> 0(2(3(4(1(2(0(0(2(1(x1)))))))))) 0(3(2(0(3(4(3(1(3(x1))))))))) -> 1(3(0(1(4(3(1(3(3(0(2(x1))))))))))) 0(3(5(1(2(2(0(1(3(x1))))))))) -> 0(4(2(0(2(1(1(3(5(3(x1)))))))))) 0(4(0(3(2(5(0(5(2(x1))))))))) -> 0(4(0(0(2(5(5(1(3(2(x1)))))))))) 1(4(2(4(0(0(0(3(4(x1))))))))) -> 4(0(2(1(4(3(0(0(4(1(x1)))))))))) 2(1(4(0(3(2(4(1(5(x1))))))))) -> 2(1(1(3(0(2(5(4(0(4(x1)))))))))) 3(0(0(1(2(0(3(2(5(x1))))))))) -> 0(2(2(0(5(1(0(1(3(3(x1)))))))))) 3(0(1(3(5(1(4(5(4(x1))))))))) -> 1(1(0(4(5(5(1(3(3(4(x1)))))))))) 4(2(1(5(3(0(1(2(2(x1))))))))) -> 2(5(0(2(1(4(3(2(1(1(x1)))))))))) 5(1(2(2(0(3(5(1(2(x1))))))))) -> 1(0(2(1(3(2(5(5(2(1(1(x1))))))))))) 0(1(3(4(2(5(0(3(5(1(x1)))))))))) -> 5(2(3(1(4(3(0(5(0(0(1(x1))))))))))) 0(3(4(2(3(2(2(3(2(4(x1)))))))))) -> 4(3(2(2(3(0(2(1(3(2(4(x1))))))))))) 0(3(5(4(1(4(3(5(3(4(x1)))))))))) -> 0(5(4(3(3(1(5(4(4(3(1(x1))))))))))) 0(4(3(3(4(0(3(2(5(4(x1)))))))))) -> 0(1(4(4(3(2(3(3(4(5(0(x1))))))))))) 1(0(3(2(5(2(5(4(1(2(x1)))))))))) -> 1(5(2(0(2(1(4(5(0(2(3(x1))))))))))) 1(4(5(1(4(2(5(1(3(1(x1)))))))))) -> 5(5(1(4(3(1(4(1(1(2(1(x1))))))))))) 1(5(2(0(3(4(2(2(5(5(x1)))))))))) -> 1(5(2(5(0(2(2(5(1(4(3(x1))))))))))) 2(0(1(2(5(0(3(2(1(1(x1)))))))))) -> 2(5(4(1(1(1(3(0(2(0(2(x1))))))))))) 2(4(0(1(5(3(0(0(3(3(x1)))))))))) -> 3(0(3(0(5(4(0(2(1(1(3(x1))))))))))) 2(4(2(0(1(0(3(4(4(3(x1)))))))))) -> 2(1(0(0(1(4(3(2(4(4(3(x1))))))))))) 4(2(0(3(1(1(5(0(3(1(x1)))))))))) -> 1(3(0(1(5(0(2(3(1(1(4(x1))))))))))) 4(4(2(5(0(5(5(0(0(3(x1)))))))))) -> 0(2(5(4(3(1(4(0(5(5(0(x1))))))))))) 4(5(0(4(0(0(5(2(0(3(x1)))))))))) -> 5(1(5(4(0(0(2(3(0(4(0(x1))))))))))) 5(5(0(1(0(0(3(2(2(4(x1)))))))))) -> 0(0(2(0(5(2(5(4(1(1(3(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_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)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(x1))) -> 0(2(1(1(x1)))) 0(3(2(x1))) -> 0(2(1(3(x1)))) 0(3(2(x1))) -> 0(2(1(1(3(x1))))) 0(1(2(4(x1)))) -> 0(2(4(1(1(x1))))) 0(3(2(4(x1)))) -> 0(1(4(3(2(x1))))) 0(3(4(2(x1)))) -> 0(4(2(1(3(x1))))) 0(3(4(4(x1)))) -> 0(1(4(4(3(1(x1)))))) 1(2(0(3(x1)))) -> 3(1(0(2(1(x1))))) 3(0(3(2(x1)))) -> 3(0(2(3(1(x1))))) 0(1(2(0(3(x1))))) -> 0(2(1(3(1(0(x1)))))) 0(1(2(2(2(x1))))) -> 0(2(1(2(1(2(x1)))))) 0(1(2(5(1(x1))))) -> 0(2(1(1(0(5(x1)))))) 0(3(2(4(4(x1))))) -> 4(0(4(2(1(3(x1)))))) 0(3(2(5(3(x1))))) -> 5(1(3(0(2(3(x1)))))) 2(2(0(3(5(x1))))) -> 2(5(0(2(1(3(x1)))))) 2(4(0(3(2(x1))))) -> 2(4(3(0(0(2(x1)))))) 3(0(3(4(2(x1))))) -> 1(3(4(0(2(3(x1)))))) 4(2(5(0(3(x1))))) -> 5(4(3(0(2(1(x1)))))) 4(5(0(3(2(x1))))) -> 4(5(0(2(3(1(x1)))))) 4(5(0(3(3(x1))))) -> 0(5(4(1(3(3(x1)))))) 5(0(3(1(2(x1))))) -> 0(5(2(1(1(3(x1)))))) 5(1(2(0(3(x1))))) -> 1(0(2(1(3(5(x1)))))) 5(2(0(1(2(x1))))) -> 0(2(1(5(0(2(x1)))))) 0(1(1(4(4(2(x1)))))) -> 4(1(1(1(0(4(2(x1))))))) 0(1(5(3(0(2(x1)))))) -> 0(2(0(5(1(1(3(x1))))))) 0(3(0(5(4(2(x1)))))) -> 4(1(0(2(3(0(5(x1))))))) 0(3(1(4(3(2(x1)))))) -> 1(0(2(1(4(3(3(x1))))))) 0(3(2(0(3(4(x1)))))) -> 1(0(2(3(3(0(4(x1))))))) 0(3(2(2(4(5(x1)))))) -> 0(2(5(4(1(2(3(x1))))))) 0(3(2(3(4(1(x1)))))) -> 4(1(1(3(0(2(1(3(x1)))))))) 0(3(2(4(1(4(x1)))))) -> 4(1(3(0(2(4(1(x1))))))) 0(3(2(5(5(1(x1)))))) -> 0(2(1(1(3(5(5(1(x1)))))))) 4(2(2(0(3(2(x1)))))) -> 2(2(0(2(4(1(1(3(x1)))))))) 5(4(0(3(1(2(x1)))))) -> 0(1(4(5(2(1(3(x1))))))) 5(4(0(3(2(4(x1)))))) -> 4(2(0(5(4(1(1(3(x1)))))))) 0(1(2(4(3(5(4(x1))))))) -> 0(2(4(5(4(1(1(3(x1)))))))) 0(1(2(5(3(5(4(x1))))))) -> 5(1(4(3(1(2(0(5(x1)))))))) 0(3(1(4(4(2(4(x1))))))) -> 4(1(2(1(0(4(3(4(x1)))))))) 0(3(2(0(0(3(2(x1))))))) -> 0(0(2(3(0(2(3(1(x1)))))))) 0(5(3(3(2(1(5(x1))))))) -> 0(2(1(3(1(3(5(5(x1)))))))) 2(3(0(3(0(1(2(x1))))))) -> 3(0(2(1(1(0(2(3(x1)))))))) 2(4(1(0(3(0(2(x1))))))) -> 2(0(2(1(3(1(0(4(x1)))))))) 2(5(0(0(4(4(2(x1))))))) -> 2(0(4(1(0(4(5(2(x1)))))))) 3(3(4(1(0(3(2(x1))))))) -> 3(3(4(1(1(3(0(2(x1)))))))) 4(2(1(0(3(5(5(x1))))))) -> 5(0(1(4(3(1(2(5(x1)))))))) 4(3(0(3(2(5(3(x1))))))) -> 0(2(1(3(1(3(4(5(3(x1))))))))) 4(3(4(5(2(1(2(x1))))))) -> 5(2(2(4(4(1(1(3(x1)))))))) 4(4(2(5(3(1(1(x1))))))) -> 5(4(3(4(1(2(1(1(x1)))))))) 5(3(5(0(1(2(4(x1))))))) -> 4(5(0(2(1(3(1(5(x1)))))))) 0(1(1(2(5(0(3(1(x1)))))))) -> 0(5(1(1(0(2(1(1(3(x1))))))))) 0(3(0(3(4(2(5(2(x1)))))))) -> 0(1(2(4(3(5(0(2(3(x1))))))))) 0(3(4(4(4(0(4(5(x1)))))))) -> 4(3(0(1(4(4(0(4(5(x1))))))))) 2(2(0(3(1(5(3(1(x1)))))))) -> 2(3(0(2(1(1(3(5(1(x1))))))))) 2(2(4(2(3(3(1(5(x1)))))))) -> 2(2(1(3(4(3(2(1(5(x1))))))))) 3(0(0(1(4(2(4(2(x1)))))))) -> 3(2(1(4(0(2(0(4(1(x1))))))))) 3(1(0(3(1(2(1(2(x1)))))))) -> 3(1(3(1(1(0(0(2(2(x1))))))))) 3(2(3(0(3(2(3(2(x1)))))))) -> 3(3(2(1(3(2(3(0(2(x1))))))))) 4(2(3(1(0(0(5(2(x1)))))))) -> 2(0(0(2(1(1(5(4(3(x1))))))))) 4(5(0(0(3(3(0(2(x1)))))))) -> 1(4(3(0(5(3(0(0(2(x1))))))))) 5(0(3(4(2(1(1(4(x1)))))))) -> 5(4(0(0(2(3(1(1(4(x1))))))))) 5(2(0(1(5(1(2(3(x1)))))))) -> 0(2(2(3(1(1(1(5(5(x1))))))))) 0(1(4(2(2(5(5(5(2(x1))))))))) -> 0(2(5(0(2(5(4(1(5(2(x1)))))))))) 0(2(1(4(2(2(0(3(1(x1))))))))) -> 0(2(3(4(1(2(0(0(2(1(x1)))))))))) 0(3(2(0(3(4(3(1(3(x1))))))))) -> 1(3(0(1(4(3(1(3(3(0(2(x1))))))))))) 0(3(5(1(2(2(0(1(3(x1))))))))) -> 0(4(2(0(2(1(1(3(5(3(x1)))))))))) 0(4(0(3(2(5(0(5(2(x1))))))))) -> 0(4(0(0(2(5(5(1(3(2(x1)))))))))) 1(4(2(4(0(0(0(3(4(x1))))))))) -> 4(0(2(1(4(3(0(0(4(1(x1)))))))))) 2(1(4(0(3(2(4(1(5(x1))))))))) -> 2(1(1(3(0(2(5(4(0(4(x1)))))))))) 3(0(0(1(2(0(3(2(5(x1))))))))) -> 0(2(2(0(5(1(0(1(3(3(x1)))))))))) 3(0(1(3(5(1(4(5(4(x1))))))))) -> 1(1(0(4(5(5(1(3(3(4(x1)))))))))) 4(2(1(5(3(0(1(2(2(x1))))))))) -> 2(5(0(2(1(4(3(2(1(1(x1)))))))))) 5(1(2(2(0(3(5(1(2(x1))))))))) -> 1(0(2(1(3(2(5(5(2(1(1(x1))))))))))) 0(1(3(4(2(5(0(3(5(1(x1)))))))))) -> 5(2(3(1(4(3(0(5(0(0(1(x1))))))))))) 0(3(4(2(3(2(2(3(2(4(x1)))))))))) -> 4(3(2(2(3(0(2(1(3(2(4(x1))))))))))) 0(3(5(4(1(4(3(5(3(4(x1)))))))))) -> 0(5(4(3(3(1(5(4(4(3(1(x1))))))))))) 0(4(3(3(4(0(3(2(5(4(x1)))))))))) -> 0(1(4(4(3(2(3(3(4(5(0(x1))))))))))) 1(0(3(2(5(2(5(4(1(2(x1)))))))))) -> 1(5(2(0(2(1(4(5(0(2(3(x1))))))))))) 1(4(5(1(4(2(5(1(3(1(x1)))))))))) -> 5(5(1(4(3(1(4(1(1(2(1(x1))))))))))) 1(5(2(0(3(4(2(2(5(5(x1)))))))))) -> 1(5(2(5(0(2(2(5(1(4(3(x1))))))))))) 2(0(1(2(5(0(3(2(1(1(x1)))))))))) -> 2(5(4(1(1(1(3(0(2(0(2(x1))))))))))) 2(4(0(1(5(3(0(0(3(3(x1)))))))))) -> 3(0(3(0(5(4(0(2(1(1(3(x1))))))))))) 2(4(2(0(1(0(3(4(4(3(x1)))))))))) -> 2(1(0(0(1(4(3(2(4(4(3(x1))))))))))) 4(2(0(3(1(1(5(0(3(1(x1)))))))))) -> 1(3(0(1(5(0(2(3(1(1(4(x1))))))))))) 4(4(2(5(0(5(5(0(0(3(x1)))))))))) -> 0(2(5(4(3(1(4(0(5(5(0(x1))))))))))) 4(5(0(4(0(0(5(2(0(3(x1)))))))))) -> 5(1(5(4(0(0(2(3(0(4(0(x1))))))))))) 5(5(0(1(0(0(3(2(2(4(x1)))))))))) -> 0(0(2(0(5(2(5(4(1(1(3(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_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)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(x1))) -> 0(2(1(1(x1)))) 0(3(2(x1))) -> 0(2(1(3(x1)))) 0(3(2(x1))) -> 0(2(1(1(3(x1))))) 0(1(2(4(x1)))) -> 0(2(4(1(1(x1))))) 0(3(2(4(x1)))) -> 0(1(4(3(2(x1))))) 0(3(4(2(x1)))) -> 0(4(2(1(3(x1))))) 0(3(4(4(x1)))) -> 0(1(4(4(3(1(x1)))))) 1(2(0(3(x1)))) -> 3(1(0(2(1(x1))))) 3(0(3(2(x1)))) -> 3(0(2(3(1(x1))))) 0(1(2(0(3(x1))))) -> 0(2(1(3(1(0(x1)))))) 0(1(2(2(2(x1))))) -> 0(2(1(2(1(2(x1)))))) 0(1(2(5(1(x1))))) -> 0(2(1(1(0(5(x1)))))) 0(3(2(4(4(x1))))) -> 4(0(4(2(1(3(x1)))))) 0(3(2(5(3(x1))))) -> 5(1(3(0(2(3(x1)))))) 2(2(0(3(5(x1))))) -> 2(5(0(2(1(3(x1)))))) 2(4(0(3(2(x1))))) -> 2(4(3(0(0(2(x1)))))) 3(0(3(4(2(x1))))) -> 1(3(4(0(2(3(x1)))))) 4(2(5(0(3(x1))))) -> 5(4(3(0(2(1(x1)))))) 4(5(0(3(2(x1))))) -> 4(5(0(2(3(1(x1)))))) 4(5(0(3(3(x1))))) -> 0(5(4(1(3(3(x1)))))) 5(0(3(1(2(x1))))) -> 0(5(2(1(1(3(x1)))))) 5(1(2(0(3(x1))))) -> 1(0(2(1(3(5(x1)))))) 5(2(0(1(2(x1))))) -> 0(2(1(5(0(2(x1)))))) 0(1(1(4(4(2(x1)))))) -> 4(1(1(1(0(4(2(x1))))))) 0(1(5(3(0(2(x1)))))) -> 0(2(0(5(1(1(3(x1))))))) 0(3(0(5(4(2(x1)))))) -> 4(1(0(2(3(0(5(x1))))))) 0(3(1(4(3(2(x1)))))) -> 1(0(2(1(4(3(3(x1))))))) 0(3(2(0(3(4(x1)))))) -> 1(0(2(3(3(0(4(x1))))))) 0(3(2(2(4(5(x1)))))) -> 0(2(5(4(1(2(3(x1))))))) 0(3(2(3(4(1(x1)))))) -> 4(1(1(3(0(2(1(3(x1)))))))) 0(3(2(4(1(4(x1)))))) -> 4(1(3(0(2(4(1(x1))))))) 0(3(2(5(5(1(x1)))))) -> 0(2(1(1(3(5(5(1(x1)))))))) 4(2(2(0(3(2(x1)))))) -> 2(2(0(2(4(1(1(3(x1)))))))) 5(4(0(3(1(2(x1)))))) -> 0(1(4(5(2(1(3(x1))))))) 5(4(0(3(2(4(x1)))))) -> 4(2(0(5(4(1(1(3(x1)))))))) 0(1(2(4(3(5(4(x1))))))) -> 0(2(4(5(4(1(1(3(x1)))))))) 0(1(2(5(3(5(4(x1))))))) -> 5(1(4(3(1(2(0(5(x1)))))))) 0(3(1(4(4(2(4(x1))))))) -> 4(1(2(1(0(4(3(4(x1)))))))) 0(3(2(0(0(3(2(x1))))))) -> 0(0(2(3(0(2(3(1(x1)))))))) 0(5(3(3(2(1(5(x1))))))) -> 0(2(1(3(1(3(5(5(x1)))))))) 2(3(0(3(0(1(2(x1))))))) -> 3(0(2(1(1(0(2(3(x1)))))))) 2(4(1(0(3(0(2(x1))))))) -> 2(0(2(1(3(1(0(4(x1)))))))) 2(5(0(0(4(4(2(x1))))))) -> 2(0(4(1(0(4(5(2(x1)))))))) 3(3(4(1(0(3(2(x1))))))) -> 3(3(4(1(1(3(0(2(x1)))))))) 4(2(1(0(3(5(5(x1))))))) -> 5(0(1(4(3(1(2(5(x1)))))))) 4(3(0(3(2(5(3(x1))))))) -> 0(2(1(3(1(3(4(5(3(x1))))))))) 4(3(4(5(2(1(2(x1))))))) -> 5(2(2(4(4(1(1(3(x1)))))))) 4(4(2(5(3(1(1(x1))))))) -> 5(4(3(4(1(2(1(1(x1)))))))) 5(3(5(0(1(2(4(x1))))))) -> 4(5(0(2(1(3(1(5(x1)))))))) 0(1(1(2(5(0(3(1(x1)))))))) -> 0(5(1(1(0(2(1(1(3(x1))))))))) 0(3(0(3(4(2(5(2(x1)))))))) -> 0(1(2(4(3(5(0(2(3(x1))))))))) 0(3(4(4(4(0(4(5(x1)))))))) -> 4(3(0(1(4(4(0(4(5(x1))))))))) 2(2(0(3(1(5(3(1(x1)))))))) -> 2(3(0(2(1(1(3(5(1(x1))))))))) 2(2(4(2(3(3(1(5(x1)))))))) -> 2(2(1(3(4(3(2(1(5(x1))))))))) 3(0(0(1(4(2(4(2(x1)))))))) -> 3(2(1(4(0(2(0(4(1(x1))))))))) 3(1(0(3(1(2(1(2(x1)))))))) -> 3(1(3(1(1(0(0(2(2(x1))))))))) 3(2(3(0(3(2(3(2(x1)))))))) -> 3(3(2(1(3(2(3(0(2(x1))))))))) 4(2(3(1(0(0(5(2(x1)))))))) -> 2(0(0(2(1(1(5(4(3(x1))))))))) 4(5(0(0(3(3(0(2(x1)))))))) -> 1(4(3(0(5(3(0(0(2(x1))))))))) 5(0(3(4(2(1(1(4(x1)))))))) -> 5(4(0(0(2(3(1(1(4(x1))))))))) 5(2(0(1(5(1(2(3(x1)))))))) -> 0(2(2(3(1(1(1(5(5(x1))))))))) 0(1(4(2(2(5(5(5(2(x1))))))))) -> 0(2(5(0(2(5(4(1(5(2(x1)))))))))) 0(2(1(4(2(2(0(3(1(x1))))))))) -> 0(2(3(4(1(2(0(0(2(1(x1)))))))))) 0(3(2(0(3(4(3(1(3(x1))))))))) -> 1(3(0(1(4(3(1(3(3(0(2(x1))))))))))) 0(3(5(1(2(2(0(1(3(x1))))))))) -> 0(4(2(0(2(1(1(3(5(3(x1)))))))))) 0(4(0(3(2(5(0(5(2(x1))))))))) -> 0(4(0(0(2(5(5(1(3(2(x1)))))))))) 1(4(2(4(0(0(0(3(4(x1))))))))) -> 4(0(2(1(4(3(0(0(4(1(x1)))))))))) 2(1(4(0(3(2(4(1(5(x1))))))))) -> 2(1(1(3(0(2(5(4(0(4(x1)))))))))) 3(0(0(1(2(0(3(2(5(x1))))))))) -> 0(2(2(0(5(1(0(1(3(3(x1)))))))))) 3(0(1(3(5(1(4(5(4(x1))))))))) -> 1(1(0(4(5(5(1(3(3(4(x1)))))))))) 4(2(1(5(3(0(1(2(2(x1))))))))) -> 2(5(0(2(1(4(3(2(1(1(x1)))))))))) 5(1(2(2(0(3(5(1(2(x1))))))))) -> 1(0(2(1(3(2(5(5(2(1(1(x1))))))))))) 0(1(3(4(2(5(0(3(5(1(x1)))))))))) -> 5(2(3(1(4(3(0(5(0(0(1(x1))))))))))) 0(3(4(2(3(2(2(3(2(4(x1)))))))))) -> 4(3(2(2(3(0(2(1(3(2(4(x1))))))))))) 0(3(5(4(1(4(3(5(3(4(x1)))))))))) -> 0(5(4(3(3(1(5(4(4(3(1(x1))))))))))) 0(4(3(3(4(0(3(2(5(4(x1)))))))))) -> 0(1(4(4(3(2(3(3(4(5(0(x1))))))))))) 1(0(3(2(5(2(5(4(1(2(x1)))))))))) -> 1(5(2(0(2(1(4(5(0(2(3(x1))))))))))) 1(4(5(1(4(2(5(1(3(1(x1)))))))))) -> 5(5(1(4(3(1(4(1(1(2(1(x1))))))))))) 1(5(2(0(3(4(2(2(5(5(x1)))))))))) -> 1(5(2(5(0(2(2(5(1(4(3(x1))))))))))) 2(0(1(2(5(0(3(2(1(1(x1)))))))))) -> 2(5(4(1(1(1(3(0(2(0(2(x1))))))))))) 2(4(0(1(5(3(0(0(3(3(x1)))))))))) -> 3(0(3(0(5(4(0(2(1(1(3(x1))))))))))) 2(4(2(0(1(0(3(4(4(3(x1)))))))))) -> 2(1(0(0(1(4(3(2(4(4(3(x1))))))))))) 4(2(0(3(1(1(5(0(3(1(x1)))))))))) -> 1(3(0(1(5(0(2(3(1(1(4(x1))))))))))) 4(4(2(5(0(5(5(0(0(3(x1)))))))))) -> 0(2(5(4(3(1(4(0(5(5(0(x1))))))))))) 4(5(0(4(0(0(5(2(0(3(x1)))))))))) -> 5(1(5(4(0(0(2(3(0(4(0(x1))))))))))) 5(5(0(1(0(0(3(2(2(4(x1)))))))))) -> 0(0(2(0(5(2(5(4(1(1(3(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_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)) 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. "[96, 97, 98, 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, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754] {(96,97,[0_1|0, 1_1|0, 3_1|0, 2_1|0, 4_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]), (96,98,[0_1|1, 1_1|1, 3_1|1, 2_1|1, 4_1|1, 5_1|1]), (96,99,[0_1|2]), (96,102,[0_1|2]), (96,106,[0_1|2]), (96,113,[0_1|2]), (96,118,[0_1|2]), (96,123,[0_1|2]), (96,128,[5_1|2]), (96,135,[4_1|2]), (96,141,[0_1|2]), (96,149,[0_1|2]), (96,155,[0_1|2]), (96,164,[5_1|2]), (96,174,[0_1|2]), (96,177,[0_1|2]), (96,181,[0_1|2]), (96,185,[4_1|2]), (96,190,[4_1|2]), (96,196,[5_1|2]), (96,201,[0_1|2]), (96,208,[1_1|2]), (96,214,[1_1|2]), (96,224,[0_1|2]), (96,231,[0_1|2]), (96,237,[4_1|2]), (96,244,[0_1|2]), (96,248,[4_1|2]), (96,258,[0_1|2]), (96,263,[4_1|2]), (96,271,[4_1|2]), (96,277,[0_1|2]), (96,285,[1_1|2]), (96,291,[4_1|2]), (96,298,[0_1|2]), (96,307,[0_1|2]), (96,317,[0_1|2]), (96,324,[0_1|2]), (96,333,[0_1|2]), (96,342,[0_1|2]), (96,352,[3_1|2]), (96,356,[4_1|2]), (96,365,[5_1|2]), (96,375,[1_1|2]), (96,385,[1_1|2]), (96,395,[3_1|2]), (96,399,[1_1|2]), (96,404,[3_1|2]), (96,412,[0_1|2]), (96,421,[1_1|2]), (96,430,[3_1|2]), (96,437,[3_1|2]), (96,445,[3_1|2]), (96,453,[2_1|2]), (96,458,[2_1|2]), (96,466,[2_1|2]), (96,474,[2_1|2]), (96,479,[3_1|2]), (96,489,[2_1|2]), (96,496,[2_1|2]), (96,506,[3_1|2]), (96,513,[2_1|2]), (96,520,[2_1|2]), (96,529,[2_1|2]), (96,539,[5_1|2]), (96,544,[2_1|2]), (96,551,[5_1|2]), (96,558,[2_1|2]), (96,567,[2_1|2]), (96,575,[1_1|2]), (96,585,[4_1|2]), (96,590,[0_1|2]), (96,595,[1_1|2]), (96,603,[5_1|2]), (96,613,[0_1|2]), (96,621,[5_1|2]), (96,628,[5_1|2]), (96,635,[0_1|2]), (96,645,[0_1|2]), (96,650,[5_1|2]), (96,658,[1_1|2]), (96,663,[1_1|2]), (96,673,[0_1|2]), (96,678,[0_1|2]), (96,686,[0_1|2]), (96,692,[4_1|2]), (96,699,[4_1|2]), (96,706,[0_1|2]), (96,716,[0_1|3]), (96,719,[0_1|3]), (97,97,[cons_0_1|0, cons_1_1|0, cons_3_1|0, cons_2_1|0, cons_4_1|0, cons_5_1|0]), (98,97,[encArg_1|1]), (98,98,[0_1|1, 1_1|1, 3_1|1, 2_1|1, 4_1|1, 5_1|1]), (98,99,[0_1|2]), (98,102,[0_1|2]), (98,106,[0_1|2]), (98,113,[0_1|2]), (98,118,[0_1|2]), (98,123,[0_1|2]), (98,128,[5_1|2]), (98,135,[4_1|2]), (98,141,[0_1|2]), (98,149,[0_1|2]), (98,155,[0_1|2]), (98,164,[5_1|2]), (98,174,[0_1|2]), (98,177,[0_1|2]), (98,181,[0_1|2]), (98,185,[4_1|2]), (98,190,[4_1|2]), (98,196,[5_1|2]), (98,201,[0_1|2]), (98,208,[1_1|2]), (98,214,[1_1|2]), (98,224,[0_1|2]), (98,231,[0_1|2]), (98,237,[4_1|2]), (98,244,[0_1|2]), (98,248,[4_1|2]), (98,258,[0_1|2]), (98,263,[4_1|2]), (98,271,[4_1|2]), (98,277,[0_1|2]), (98,285,[1_1|2]), (98,291,[4_1|2]), (98,298,[0_1|2]), (98,307,[0_1|2]), (98,317,[0_1|2]), (98,324,[0_1|2]), (98,333,[0_1|2]), (98,342,[0_1|2]), (98,352,[3_1|2]), (98,356,[4_1|2]), (98,365,[5_1|2]), (98,375,[1_1|2]), (98,385,[1_1|2]), (98,395,[3_1|2]), (98,399,[1_1|2]), (98,404,[3_1|2]), (98,412,[0_1|2]), (98,421,[1_1|2]), (98,430,[3_1|2]), (98,437,[3_1|2]), (98,445,[3_1|2]), (98,453,[2_1|2]), (98,458,[2_1|2]), (98,466,[2_1|2]), (98,474,[2_1|2]), (98,479,[3_1|2]), (98,489,[2_1|2]), (98,496,[2_1|2]), (98,506,[3_1|2]), (98,513,[2_1|2]), (98,520,[2_1|2]), (98,529,[2_1|2]), (98,539,[5_1|2]), (98,544,[2_1|2]), (98,551,[5_1|2]), (98,558,[2_1|2]), (98,567,[2_1|2]), (98,575,[1_1|2]), (98,585,[4_1|2]), (98,590,[0_1|2]), (98,595,[1_1|2]), (98,603,[5_1|2]), (98,613,[0_1|2]), (98,621,[5_1|2]), (98,628,[5_1|2]), (98,635,[0_1|2]), (98,645,[0_1|2]), (98,650,[5_1|2]), (98,658,[1_1|2]), (98,663,[1_1|2]), (98,673,[0_1|2]), (98,678,[0_1|2]), (98,686,[0_1|2]), (98,692,[4_1|2]), (98,699,[4_1|2]), (98,706,[0_1|2]), (98,716,[0_1|3]), (98,719,[0_1|3]), (99,100,[2_1|2]), (100,101,[1_1|2]), (101,98,[1_1|2]), (101,453,[1_1|2]), (101,458,[1_1|2]), (101,466,[1_1|2]), (101,474,[1_1|2]), (101,489,[1_1|2]), (101,496,[1_1|2]), (101,513,[1_1|2]), (101,520,[1_1|2]), (101,529,[1_1|2]), (101,544,[1_1|2]), (101,558,[1_1|2]), (101,567,[1_1|2]), (101,352,[3_1|2]), (101,356,[4_1|2]), (101,365,[5_1|2]), (101,375,[1_1|2]), (101,385,[1_1|2]), (102,103,[2_1|2]), (103,104,[4_1|2]), (104,105,[1_1|2]), (105,98,[1_1|2]), (105,135,[1_1|2]), (105,185,[1_1|2]), (105,190,[1_1|2]), (105,237,[1_1|2]), (105,248,[1_1|2]), (105,263,[1_1|2]), (105,271,[1_1|2]), (105,291,[1_1|2]), (105,356,[1_1|2, 4_1|2]), (105,585,[1_1|2]), (105,692,[1_1|2]), (105,699,[1_1|2]), (105,475,[1_1|2]), (105,352,[3_1|2]), (105,365,[5_1|2]), (105,375,[1_1|2]), (105,385,[1_1|2]), (106,107,[2_1|2]), (107,108,[4_1|2]), (108,109,[5_1|2]), (109,110,[4_1|2]), (110,111,[1_1|2]), (111,112,[1_1|2]), (112,98,[3_1|2]), (112,135,[3_1|2]), (112,185,[3_1|2]), (112,190,[3_1|2]), (112,237,[3_1|2]), (112,248,[3_1|2]), (112,263,[3_1|2]), (112,271,[3_1|2]), (112,291,[3_1|2]), (112,356,[3_1|2]), (112,585,[3_1|2]), (112,692,[3_1|2]), (112,699,[3_1|2]), (112,540,[3_1|2]), 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(604,605,[5_1|2]), (605,606,[4_1|2]), (606,607,[0_1|2]), (607,608,[0_1|2]), (608,609,[2_1|2]), (609,610,[3_1|2]), (610,611,[0_1|2]), (610,333,[0_1|2]), (611,612,[4_1|2]), (612,98,[0_1|2]), (612,352,[0_1|2]), (612,395,[0_1|2]), (612,404,[0_1|2]), (612,430,[0_1|2]), (612,437,[0_1|2]), (612,445,[0_1|2]), (612,479,[0_1|2]), (612,506,[0_1|2]), (612,99,[0_1|2]), (612,102,[0_1|2]), (612,106,[0_1|2]), (612,113,[0_1|2]), (612,118,[0_1|2]), (612,123,[0_1|2]), (612,128,[5_1|2]), (612,135,[4_1|2]), (612,141,[0_1|2]), (612,149,[0_1|2]), (612,155,[0_1|2]), (612,164,[5_1|2]), (612,174,[0_1|2]), (612,177,[0_1|2]), (612,181,[0_1|2]), (612,185,[4_1|2]), (612,190,[4_1|2]), (612,196,[5_1|2]), (612,201,[0_1|2]), (612,208,[1_1|2]), (612,214,[1_1|2]), (612,224,[0_1|2]), (612,231,[0_1|2]), (612,237,[4_1|2]), (612,244,[0_1|2]), (612,248,[4_1|2]), (612,258,[0_1|2]), (612,263,[4_1|2]), (612,271,[4_1|2]), (612,277,[0_1|2]), (612,285,[1_1|2]), (612,291,[4_1|2]), (612,298,[0_1|2]), (612,307,[0_1|2]), (612,317,[0_1|2]), (612,324,[0_1|2]), (612,333,[0_1|2]), (612,342,[0_1|2]), (612,723,[0_1|3]), (612,726,[0_1|3]), (612,716,[0_1|3]), (612,719,[0_1|3]), (613,614,[2_1|2]), (614,615,[1_1|2]), (615,616,[3_1|2]), (616,617,[1_1|2]), (617,618,[3_1|2]), (618,619,[4_1|2]), (619,620,[5_1|2]), (619,699,[4_1|2]), (620,98,[3_1|2]), (620,352,[3_1|2]), (620,395,[3_1|2]), (620,404,[3_1|2]), (620,430,[3_1|2]), (620,437,[3_1|2]), (620,445,[3_1|2]), (620,479,[3_1|2]), (620,506,[3_1|2]), (620,399,[1_1|2]), (620,412,[0_1|2]), (620,421,[1_1|2]), (621,622,[2_1|2]), (622,623,[2_1|2]), (623,624,[4_1|2]), (624,625,[4_1|2]), (625,626,[1_1|2]), (626,627,[1_1|2]), (627,98,[3_1|2]), (627,453,[3_1|2]), (627,458,[3_1|2]), (627,466,[3_1|2]), (627,474,[3_1|2]), (627,489,[3_1|2]), (627,496,[3_1|2]), (627,513,[3_1|2]), (627,520,[3_1|2]), (627,529,[3_1|2]), (627,544,[3_1|2]), (627,558,[3_1|2]), (627,567,[3_1|2]), (627,395,[3_1|2]), (627,399,[1_1|2]), (627,404,[3_1|2]), (627,412,[0_1|2]), (627,421,[1_1|2]), (627,430,[3_1|2]), (627,437,[3_1|2]), (627,445,[3_1|2]), (628,629,[4_1|2]), (629,630,[3_1|2]), (630,631,[4_1|2]), (631,632,[1_1|2]), (632,633,[2_1|2]), (633,634,[1_1|2]), (634,98,[1_1|2]), (634,208,[1_1|2]), (634,214,[1_1|2]), (634,285,[1_1|2]), (634,375,[1_1|2]), (634,385,[1_1|2]), (634,399,[1_1|2]), (634,421,[1_1|2]), (634,575,[1_1|2]), (634,595,[1_1|2]), (634,658,[1_1|2]), (634,663,[1_1|2]), (634,422,[1_1|2]), (634,352,[3_1|2]), (634,356,[4_1|2]), (634,365,[5_1|2]), (635,636,[2_1|2]), (636,637,[5_1|2]), (637,638,[4_1|2]), (638,639,[3_1|2]), (639,640,[1_1|2]), (640,641,[4_1|2]), (641,642,[0_1|2]), (642,643,[5_1|2]), (642,706,[0_1|2]), (643,644,[5_1|2]), (643,645,[0_1|2]), (643,650,[5_1|2]), (644,98,[0_1|2]), (644,352,[0_1|2]), (644,395,[0_1|2]), (644,404,[0_1|2]), (644,430,[0_1|2]), (644,437,[0_1|2]), (644,445,[0_1|2]), (644,479,[0_1|2]), (644,506,[0_1|2]), (644,99,[0_1|2]), (644,102,[0_1|2]), (644,106,[0_1|2]), (644,113,[0_1|2]), (644,118,[0_1|2]), (644,123,[0_1|2]), (644,128,[5_1|2]), (644,135,[4_1|2]), (644,141,[0_1|2]), (644,149,[0_1|2]), (644,155,[0_1|2]), (644,164,[5_1|2]), (644,174,[0_1|2]), (644,177,[0_1|2]), (644,181,[0_1|2]), (644,185,[4_1|2]), (644,190,[4_1|2]), (644,196,[5_1|2]), (644,201,[0_1|2]), (644,208,[1_1|2]), (644,214,[1_1|2]), (644,224,[0_1|2]), (644,231,[0_1|2]), (644,237,[4_1|2]), (644,244,[0_1|2]), (644,248,[4_1|2]), (644,258,[0_1|2]), (644,263,[4_1|2]), (644,271,[4_1|2]), (644,277,[0_1|2]), (644,285,[1_1|2]), (644,291,[4_1|2]), (644,298,[0_1|2]), (644,307,[0_1|2]), (644,317,[0_1|2]), (644,324,[0_1|2]), (644,333,[0_1|2]), (644,342,[0_1|2]), (644,723,[0_1|3]), (644,726,[0_1|3]), (644,716,[0_1|3]), (644,719,[0_1|3]), (645,646,[5_1|2]), (646,647,[2_1|2]), (647,648,[1_1|2]), (648,649,[1_1|2]), (649,98,[3_1|2]), (649,453,[3_1|2]), (649,458,[3_1|2]), (649,466,[3_1|2]), (649,474,[3_1|2]), (649,489,[3_1|2]), (649,496,[3_1|2]), (649,513,[3_1|2]), (649,520,[3_1|2]), (649,529,[3_1|2]), (649,544,[3_1|2]), (649,558,[3_1|2]), (649,567,[3_1|2]), (649,395,[3_1|2]), (649,399,[1_1|2]), (649,404,[3_1|2]), (649,412,[0_1|2]), (649,421,[1_1|2]), (649,430,[3_1|2]), (649,437,[3_1|2]), (649,445,[3_1|2]), (650,651,[4_1|2]), (651,652,[0_1|2]), (652,653,[0_1|2]), (653,654,[2_1|2]), (654,655,[3_1|2]), (655,656,[1_1|2]), (656,657,[1_1|2]), (656,356,[4_1|2]), (656,365,[5_1|2]), (657,98,[4_1|2]), (657,135,[4_1|2]), (657,185,[4_1|2]), (657,190,[4_1|2]), (657,237,[4_1|2]), (657,248,[4_1|2]), (657,263,[4_1|2]), (657,271,[4_1|2]), (657,291,[4_1|2]), (657,356,[4_1|2]), (657,585,[4_1|2]), (657,692,[4_1|2]), (657,699,[4_1|2]), (657,596,[4_1|2]), (657,539,[5_1|2]), (657,544,[2_1|2]), (657,551,[5_1|2]), (657,558,[2_1|2]), (657,567,[2_1|2]), (657,575,[1_1|2]), (657,590,[0_1|2]), (657,595,[1_1|2]), (657,603,[5_1|2]), (657,613,[0_1|2]), (657,621,[5_1|2]), (657,628,[5_1|2]), (657,635,[0_1|2]), (658,659,[0_1|2]), (659,660,[2_1|2]), (660,661,[1_1|2]), (661,662,[3_1|2]), (662,98,[5_1|2]), (662,352,[5_1|2]), (662,395,[5_1|2]), (662,404,[5_1|2]), (662,430,[5_1|2]), (662,437,[5_1|2]), (662,445,[5_1|2]), (662,479,[5_1|2]), (662,506,[5_1|2]), (662,645,[0_1|2]), (662,650,[5_1|2]), (662,658,[1_1|2]), (662,663,[1_1|2]), (662,673,[0_1|2]), (662,678,[0_1|2]), (662,686,[0_1|2]), (662,692,[4_1|2]), (662,699,[4_1|2]), (662,706,[0_1|2]), (663,664,[0_1|2]), (664,665,[2_1|2]), (665,666,[1_1|2]), (666,667,[3_1|2]), (667,668,[2_1|2]), (668,669,[5_1|2]), (669,670,[5_1|2]), (670,671,[2_1|2]), (671,672,[1_1|2]), (672,98,[1_1|2]), (672,453,[1_1|2]), (672,458,[1_1|2]), (672,466,[1_1|2]), (672,474,[1_1|2]), (672,489,[1_1|2]), (672,496,[1_1|2]), (672,513,[1_1|2]), (672,520,[1_1|2]), (672,529,[1_1|2]), (672,544,[1_1|2]), (672,558,[1_1|2]), (672,567,[1_1|2]), (672,352,[3_1|2]), (672,356,[4_1|2]), (672,365,[5_1|2]), (672,375,[1_1|2]), (672,385,[1_1|2]), (673,674,[2_1|2]), (674,675,[1_1|2]), (675,676,[5_1|2]), (676,677,[0_1|2]), (676,324,[0_1|2]), (677,98,[2_1|2]), (677,453,[2_1|2]), (677,458,[2_1|2]), (677,466,[2_1|2]), 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(691,513,[3_1|2]), (691,520,[3_1|2]), (691,529,[3_1|2]), (691,544,[3_1|2]), (691,558,[3_1|2]), (691,567,[3_1|2]), (691,395,[3_1|2]), (691,399,[1_1|2]), (691,404,[3_1|2]), (691,412,[0_1|2]), (691,421,[1_1|2]), (691,430,[3_1|2]), (691,437,[3_1|2]), (691,445,[3_1|2]), (692,693,[2_1|2]), (693,694,[0_1|2]), (694,695,[5_1|2]), (695,696,[4_1|2]), (696,697,[1_1|2]), (697,698,[1_1|2]), (698,98,[3_1|2]), (698,135,[3_1|2]), (698,185,[3_1|2]), (698,190,[3_1|2]), (698,237,[3_1|2]), (698,248,[3_1|2]), (698,263,[3_1|2]), (698,271,[3_1|2]), (698,291,[3_1|2]), (698,356,[3_1|2]), (698,585,[3_1|2]), (698,692,[3_1|2]), (698,699,[3_1|2]), (698,475,[3_1|2]), (698,395,[3_1|2]), (698,399,[1_1|2]), (698,404,[3_1|2]), (698,412,[0_1|2]), (698,421,[1_1|2]), (698,430,[3_1|2]), (698,437,[3_1|2]), (698,445,[3_1|2]), (699,700,[5_1|2]), (700,701,[0_1|2]), (701,702,[2_1|2]), (702,703,[1_1|2]), (703,704,[3_1|2]), (704,705,[1_1|2]), (704,385,[1_1|2]), (705,98,[5_1|2]), (705,135,[5_1|2]), (705,185,[5_1|2]), (705,190,[5_1|2]), (705,237,[5_1|2]), (705,248,[5_1|2]), (705,263,[5_1|2]), (705,271,[5_1|2]), (705,291,[5_1|2]), (705,356,[5_1|2]), (705,585,[5_1|2]), (705,692,[5_1|2, 4_1|2]), (705,699,[5_1|2, 4_1|2]), (705,475,[5_1|2]), (705,280,[5_1|2]), (705,645,[0_1|2]), (705,650,[5_1|2]), (705,658,[1_1|2]), (705,663,[1_1|2]), (705,673,[0_1|2]), (705,678,[0_1|2]), (705,686,[0_1|2]), (705,706,[0_1|2]), (706,707,[0_1|2]), (707,708,[2_1|2]), (708,709,[0_1|2]), (709,710,[5_1|2]), (710,711,[2_1|2]), (711,712,[5_1|2]), (712,713,[4_1|2]), (713,714,[1_1|2]), (714,715,[1_1|2]), (715,98,[3_1|2]), (715,135,[3_1|2]), (715,185,[3_1|2]), (715,190,[3_1|2]), (715,237,[3_1|2]), (715,248,[3_1|2]), (715,263,[3_1|2]), (715,271,[3_1|2]), (715,291,[3_1|2]), (715,356,[3_1|2]), (715,585,[3_1|2]), (715,692,[3_1|2]), (715,699,[3_1|2]), (715,475,[3_1|2]), (715,395,[3_1|2]), (715,399,[1_1|2]), (715,404,[3_1|2]), (715,412,[0_1|2]), (715,421,[1_1|2]), (715,430,[3_1|2]), (715,437,[3_1|2]), (715,445,[3_1|2]), (716,717,[2_1|3]), (717,718,[1_1|3]), (718,279,[1_1|3]), (719,720,[2_1|3]), (720,721,[4_1|3]), (721,722,[1_1|3]), (722,280,[1_1|3]), (723,724,[2_1|3]), (724,725,[1_1|3]), (725,405,[3_1|3]), (725,447,[3_1|3]), (725,250,[3_1|3]), (726,727,[2_1|3]), (727,728,[1_1|3]), (728,729,[1_1|3]), (729,405,[3_1|3]), (729,447,[3_1|3]), (729,250,[3_1|3]), (730,731,[2_1|3]), (731,732,[1_1|3]), (732,733,[5_1|3]), (733,734,[0_1|3]), (734,279,[2_1|3]), (735,736,[2_1|3]), (736,737,[1_1|3]), (737,453,[1_1|3]), (737,458,[1_1|3]), (737,466,[1_1|3]), (737,474,[1_1|3]), (737,489,[1_1|3]), (737,496,[1_1|3]), (737,513,[1_1|3]), (737,520,[1_1|3]), (737,529,[1_1|3]), (737,544,[1_1|3]), (737,558,[1_1|3]), (737,567,[1_1|3]), (738,739,[2_1|3]), (739,740,[4_1|3]), (740,741,[1_1|3]), (741,475,[1_1|3]), (742,743,[5_1|3]), (743,744,[0_1|3]), (744,745,[2_1|3]), (745,746,[3_1|3]), (746,405,[1_1|3]), (746,250,[1_1|3]), (747,748,[5_1|3]), (748,749,[4_1|3]), (749,750,[1_1|3]), (750,751,[3_1|3]), (751,431,[3_1|3]), (751,446,[3_1|3]), (752,753,[2_1|3]), (753,754,[1_1|3]), (754,293,[1_1|3]), (754,279,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)