/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 55 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 328 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(2(x1)))) -> 0(2(3(1(2(x1))))) 0(1(3(2(x1)))) -> 0(2(4(1(3(x1))))) 0(1(4(2(x1)))) -> 0(2(4(1(1(x1))))) 0(1(4(2(x1)))) -> 0(2(4(1(3(x1))))) 0(1(4(2(x1)))) -> 0(2(4(1(5(x1))))) 0(1(2(1(1(x1))))) -> 0(2(1(3(1(1(x1)))))) 0(1(3(2(2(x1))))) -> 0(2(3(1(3(2(x1)))))) 0(1(4(2(1(x1))))) -> 0(2(4(3(1(1(x1)))))) 0(1(4(2(5(x1))))) -> 0(2(4(5(4(1(x1)))))) 0(1(4(3(2(x1))))) -> 0(2(4(1(3(3(x1)))))) 0(3(2(1(4(x1))))) -> 0(2(4(3(1(3(x1)))))) 2(0(1(0(3(x1))))) -> 2(1(0(0(0(3(x1)))))) 2(4(0(1(3(x1))))) -> 0(2(4(3(1(3(x1)))))) 4(0(5(1(2(x1))))) -> 4(0(2(4(5(1(x1)))))) 4(2(4(0(1(x1))))) -> 4(0(2(4(3(1(x1)))))) 4(4(0(1(3(x1))))) -> 4(3(1(3(1(0(4(x1))))))) 5(2(0(1(4(x1))))) -> 5(0(2(4(1(3(x1)))))) 0(1(2(0(1(5(x1)))))) -> 0(2(4(1(1(0(0(5(x1)))))))) 0(1(2(0(2(2(x1)))))) -> 0(2(0(2(4(1(2(x1))))))) 0(1(4(0(2(2(x1)))))) -> 0(2(0(2(4(1(0(x1))))))) 0(1(4(2(5(4(x1)))))) -> 2(4(3(1(0(4(5(4(x1)))))))) 0(1(5(1(4(2(x1)))))) -> 0(4(5(3(1(1(2(x1))))))) 0(1(5(3(2(4(x1)))))) -> 5(0(2(3(1(3(4(x1))))))) 0(5(0(1(4(2(x1)))))) -> 0(2(1(3(0(4(5(x1))))))) 0(5(2(0(1(3(x1)))))) -> 0(0(2(1(5(5(3(x1))))))) 2(0(1(1(4(1(x1)))))) -> 2(1(0(4(3(1(1(x1))))))) 2(0(1(1(5(4(x1)))))) -> 5(4(1(3(1(0(2(x1))))))) 2(0(1(2(5(4(x1)))))) -> 2(4(1(5(0(2(4(x1))))))) 2(0(1(4(2(1(x1)))))) -> 0(2(3(4(1(2(1(x1))))))) 2(0(3(0(1(2(x1)))))) -> 2(0(0(2(1(3(1(x1))))))) 2(0(5(1(4(2(x1)))))) -> 2(4(1(0(2(3(5(x1))))))) 2(1(2(0(1(4(x1)))))) -> 3(4(1(0(2(1(2(x1))))))) 2(2(0(1(4(5(x1)))))) -> 2(3(0(2(4(5(1(x1))))))) 2(2(0(1(5(4(x1)))))) -> 2(0(4(3(5(1(2(x1))))))) 2(2(4(2(0(1(x1)))))) -> 2(2(4(1(3(2(0(x1))))))) 2(3(0(5(4(2(x1)))))) -> 2(2(5(3(1(0(4(x1))))))) 2(3(3(0(1(4(x1)))))) -> 3(1(0(4(2(3(1(x1))))))) 2(4(0(1(2(1(x1)))))) -> 2(0(0(2(4(1(1(x1))))))) 2(4(0(1(3(3(x1)))))) -> 0(2(4(3(1(3(3(x1))))))) 4(2(3(0(1(1(x1)))))) -> 1(3(5(0(2(4(1(x1))))))) 4(2(4(0(1(1(x1)))))) -> 4(0(2(3(1(4(1(x1))))))) 4(3(0(1(5(4(x1)))))) -> 4(0(4(5(3(1(1(x1))))))) 4(3(2(0(1(1(x1)))))) -> 3(4(1(0(2(4(1(x1))))))) 4(3(5(3(0(1(x1)))))) -> 4(5(3(3(3(1(3(0(x1)))))))) 4(4(0(3(1(5(x1)))))) -> 4(3(1(5(1(0(4(x1))))))) 5(0(1(4(3(2(x1)))))) -> 3(3(1(2(0(4(5(x1))))))) 5(0(1(5(3(2(x1)))))) -> 3(5(5(0(2(4(1(x1))))))) 5(2(2(4(0(1(x1)))))) -> 5(2(0(0(2(4(1(x1))))))) 5(4(3(4(0(1(x1)))))) -> 4(4(3(1(5(3(0(x1))))))) 0(1(1(5(4(5(2(x1))))))) -> 5(3(1(2(5(1(0(4(x1)))))))) 0(1(3(2(4(0(5(x1))))))) -> 3(5(0(2(4(1(0(4(x1)))))))) 0(1(4(0(5(2(2(x1))))))) -> 2(4(5(1(0(0(4(2(x1)))))))) 0(1(4(4(0(2(5(x1))))))) -> 0(0(2(4(5(1(0(4(x1)))))))) 0(1(5(1(4(0(5(x1))))))) -> 5(5(4(1(1(3(0(0(x1)))))))) 0(1(5(2(3(4(2(x1))))))) -> 2(0(0(2(3(5(4(1(x1)))))))) 0(1(5(4(4(2(4(x1))))))) -> 4(4(5(0(2(4(1(4(x1)))))))) 0(1(5(4(4(3(2(x1))))))) -> 0(2(5(4(3(4(4(1(x1)))))))) 0(3(0(1(5(2(4(x1))))))) -> 4(3(5(1(3(0(0(2(x1)))))))) 0(3(3(0(1(5(2(x1))))))) -> 5(0(0(2(3(5(1(3(x1)))))))) 0(5(0(1(4(2(4(x1))))))) -> 5(0(0(4(3(1(2(4(x1)))))))) 2(0(3(3(0(1(5(x1))))))) -> 2(3(5(4(1(3(0(0(x1)))))))) 2(0(3(5(2(1(5(x1))))))) -> 2(2(0(4(3(5(1(5(x1)))))))) 2(1(2(4(0(1(3(x1))))))) -> 2(1(2(1(5(0(4(3(x1)))))))) 2(3(2(4(0(1(4(x1))))))) -> 3(4(1(2(2(0(4(4(x1)))))))) 2(3(3(4(3(0(1(x1))))))) -> 2(3(3(4(1(3(3(0(x1)))))))) 2(3(4(0(5(1(4(x1))))))) -> 4(1(3(0(4(2(5(3(x1)))))))) 2(4(3(0(1(1(4(x1))))))) -> 1(4(3(1(3(0(2(4(x1)))))))) 2(5(2(3(0(1(1(x1))))))) -> 2(1(3(1(3(2(5(0(x1)))))))) 2(5(3(0(1(1(3(x1))))))) -> 0(2(4(3(1(3(5(1(x1)))))))) 4(0(1(5(3(2(1(x1))))))) -> 4(5(3(3(1(2(1(0(x1)))))))) 4(3(0(5(0(3(1(x1))))))) -> 0(0(4(3(3(5(1(3(x1)))))))) 4(4(0(5(1(0(1(x1))))))) -> 4(1(4(3(1(5(0(0(x1)))))))) 4(4(2(2(1(1(4(x1))))))) -> 4(1(4(4(1(2(1(2(x1)))))))) 4(4(3(1(4(1(4(x1))))))) -> 4(1(3(4(4(4(1(3(x1)))))))) 5(0(1(2(4(0(1(x1))))))) -> 5(0(4(1(3(0(2(1(x1)))))))) 5(2(1(5(4(5(3(x1))))))) -> 2(5(5(3(1(3(4(5(x1)))))))) 5(2(4(4(0(1(5(x1))))))) -> 2(5(0(4(0(4(5(1(x1)))))))) 5(4(0(1(3(2(4(x1))))))) -> 1(2(1(0(4(3(4(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(1(x_1)) -> 1(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(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(2(x1)))) -> 0(2(3(1(2(x1))))) 0(1(3(2(x1)))) -> 0(2(4(1(3(x1))))) 0(1(4(2(x1)))) -> 0(2(4(1(1(x1))))) 0(1(4(2(x1)))) -> 0(2(4(1(3(x1))))) 0(1(4(2(x1)))) -> 0(2(4(1(5(x1))))) 0(1(2(1(1(x1))))) -> 0(2(1(3(1(1(x1)))))) 0(1(3(2(2(x1))))) -> 0(2(3(1(3(2(x1)))))) 0(1(4(2(1(x1))))) -> 0(2(4(3(1(1(x1)))))) 0(1(4(2(5(x1))))) -> 0(2(4(5(4(1(x1)))))) 0(1(4(3(2(x1))))) -> 0(2(4(1(3(3(x1)))))) 0(3(2(1(4(x1))))) -> 0(2(4(3(1(3(x1)))))) 2(0(1(0(3(x1))))) -> 2(1(0(0(0(3(x1)))))) 2(4(0(1(3(x1))))) -> 0(2(4(3(1(3(x1)))))) 4(0(5(1(2(x1))))) -> 4(0(2(4(5(1(x1)))))) 4(2(4(0(1(x1))))) -> 4(0(2(4(3(1(x1)))))) 4(4(0(1(3(x1))))) -> 4(3(1(3(1(0(4(x1))))))) 5(2(0(1(4(x1))))) -> 5(0(2(4(1(3(x1)))))) 0(1(2(0(1(5(x1)))))) -> 0(2(4(1(1(0(0(5(x1)))))))) 0(1(2(0(2(2(x1)))))) -> 0(2(0(2(4(1(2(x1))))))) 0(1(4(0(2(2(x1)))))) -> 0(2(0(2(4(1(0(x1))))))) 0(1(4(2(5(4(x1)))))) -> 2(4(3(1(0(4(5(4(x1)))))))) 0(1(5(1(4(2(x1)))))) -> 0(4(5(3(1(1(2(x1))))))) 0(1(5(3(2(4(x1)))))) -> 5(0(2(3(1(3(4(x1))))))) 0(5(0(1(4(2(x1)))))) -> 0(2(1(3(0(4(5(x1))))))) 0(5(2(0(1(3(x1)))))) -> 0(0(2(1(5(5(3(x1))))))) 2(0(1(1(4(1(x1)))))) -> 2(1(0(4(3(1(1(x1))))))) 2(0(1(1(5(4(x1)))))) -> 5(4(1(3(1(0(2(x1))))))) 2(0(1(2(5(4(x1)))))) -> 2(4(1(5(0(2(4(x1))))))) 2(0(1(4(2(1(x1)))))) -> 0(2(3(4(1(2(1(x1))))))) 2(0(3(0(1(2(x1)))))) -> 2(0(0(2(1(3(1(x1))))))) 2(0(5(1(4(2(x1)))))) -> 2(4(1(0(2(3(5(x1))))))) 2(1(2(0(1(4(x1)))))) -> 3(4(1(0(2(1(2(x1))))))) 2(2(0(1(4(5(x1)))))) -> 2(3(0(2(4(5(1(x1))))))) 2(2(0(1(5(4(x1)))))) -> 2(0(4(3(5(1(2(x1))))))) 2(2(4(2(0(1(x1)))))) -> 2(2(4(1(3(2(0(x1))))))) 2(3(0(5(4(2(x1)))))) -> 2(2(5(3(1(0(4(x1))))))) 2(3(3(0(1(4(x1)))))) -> 3(1(0(4(2(3(1(x1))))))) 2(4(0(1(2(1(x1)))))) -> 2(0(0(2(4(1(1(x1))))))) 2(4(0(1(3(3(x1)))))) -> 0(2(4(3(1(3(3(x1))))))) 4(2(3(0(1(1(x1)))))) -> 1(3(5(0(2(4(1(x1))))))) 4(2(4(0(1(1(x1)))))) -> 4(0(2(3(1(4(1(x1))))))) 4(3(0(1(5(4(x1)))))) -> 4(0(4(5(3(1(1(x1))))))) 4(3(2(0(1(1(x1)))))) -> 3(4(1(0(2(4(1(x1))))))) 4(3(5(3(0(1(x1)))))) -> 4(5(3(3(3(1(3(0(x1)))))))) 4(4(0(3(1(5(x1)))))) -> 4(3(1(5(1(0(4(x1))))))) 5(0(1(4(3(2(x1)))))) -> 3(3(1(2(0(4(5(x1))))))) 5(0(1(5(3(2(x1)))))) -> 3(5(5(0(2(4(1(x1))))))) 5(2(2(4(0(1(x1)))))) -> 5(2(0(0(2(4(1(x1))))))) 5(4(3(4(0(1(x1)))))) -> 4(4(3(1(5(3(0(x1))))))) 0(1(1(5(4(5(2(x1))))))) -> 5(3(1(2(5(1(0(4(x1)))))))) 0(1(3(2(4(0(5(x1))))))) -> 3(5(0(2(4(1(0(4(x1)))))))) 0(1(4(0(5(2(2(x1))))))) -> 2(4(5(1(0(0(4(2(x1)))))))) 0(1(4(4(0(2(5(x1))))))) -> 0(0(2(4(5(1(0(4(x1)))))))) 0(1(5(1(4(0(5(x1))))))) -> 5(5(4(1(1(3(0(0(x1)))))))) 0(1(5(2(3(4(2(x1))))))) -> 2(0(0(2(3(5(4(1(x1)))))))) 0(1(5(4(4(2(4(x1))))))) -> 4(4(5(0(2(4(1(4(x1)))))))) 0(1(5(4(4(3(2(x1))))))) -> 0(2(5(4(3(4(4(1(x1)))))))) 0(3(0(1(5(2(4(x1))))))) -> 4(3(5(1(3(0(0(2(x1)))))))) 0(3(3(0(1(5(2(x1))))))) -> 5(0(0(2(3(5(1(3(x1)))))))) 0(5(0(1(4(2(4(x1))))))) -> 5(0(0(4(3(1(2(4(x1)))))))) 2(0(3(3(0(1(5(x1))))))) -> 2(3(5(4(1(3(0(0(x1)))))))) 2(0(3(5(2(1(5(x1))))))) -> 2(2(0(4(3(5(1(5(x1)))))))) 2(1(2(4(0(1(3(x1))))))) -> 2(1(2(1(5(0(4(3(x1)))))))) 2(3(2(4(0(1(4(x1))))))) -> 3(4(1(2(2(0(4(4(x1)))))))) 2(3(3(4(3(0(1(x1))))))) -> 2(3(3(4(1(3(3(0(x1)))))))) 2(3(4(0(5(1(4(x1))))))) -> 4(1(3(0(4(2(5(3(x1)))))))) 2(4(3(0(1(1(4(x1))))))) -> 1(4(3(1(3(0(2(4(x1)))))))) 2(5(2(3(0(1(1(x1))))))) -> 2(1(3(1(3(2(5(0(x1)))))))) 2(5(3(0(1(1(3(x1))))))) -> 0(2(4(3(1(3(5(1(x1)))))))) 4(0(1(5(3(2(1(x1))))))) -> 4(5(3(3(1(2(1(0(x1)))))))) 4(3(0(5(0(3(1(x1))))))) -> 0(0(4(3(3(5(1(3(x1)))))))) 4(4(0(5(1(0(1(x1))))))) -> 4(1(4(3(1(5(0(0(x1)))))))) 4(4(2(2(1(1(4(x1))))))) -> 4(1(4(4(1(2(1(2(x1)))))))) 4(4(3(1(4(1(4(x1))))))) -> 4(1(3(4(4(4(1(3(x1)))))))) 5(0(1(2(4(0(1(x1))))))) -> 5(0(4(1(3(0(2(1(x1)))))))) 5(2(1(5(4(5(3(x1))))))) -> 2(5(5(3(1(3(4(5(x1)))))))) 5(2(4(4(0(1(5(x1))))))) -> 2(5(0(4(0(4(5(1(x1)))))))) 5(4(0(1(3(2(4(x1))))))) -> 1(2(1(0(4(3(4(5(x1)))))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(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(2(x1)))) -> 0(2(3(1(2(x1))))) 0(1(3(2(x1)))) -> 0(2(4(1(3(x1))))) 0(1(4(2(x1)))) -> 0(2(4(1(1(x1))))) 0(1(4(2(x1)))) -> 0(2(4(1(3(x1))))) 0(1(4(2(x1)))) -> 0(2(4(1(5(x1))))) 0(1(2(1(1(x1))))) -> 0(2(1(3(1(1(x1)))))) 0(1(3(2(2(x1))))) -> 0(2(3(1(3(2(x1)))))) 0(1(4(2(1(x1))))) -> 0(2(4(3(1(1(x1)))))) 0(1(4(2(5(x1))))) -> 0(2(4(5(4(1(x1)))))) 0(1(4(3(2(x1))))) -> 0(2(4(1(3(3(x1)))))) 0(3(2(1(4(x1))))) -> 0(2(4(3(1(3(x1)))))) 2(0(1(0(3(x1))))) -> 2(1(0(0(0(3(x1)))))) 2(4(0(1(3(x1))))) -> 0(2(4(3(1(3(x1)))))) 4(0(5(1(2(x1))))) -> 4(0(2(4(5(1(x1)))))) 4(2(4(0(1(x1))))) -> 4(0(2(4(3(1(x1)))))) 4(4(0(1(3(x1))))) -> 4(3(1(3(1(0(4(x1))))))) 5(2(0(1(4(x1))))) -> 5(0(2(4(1(3(x1)))))) 0(1(2(0(1(5(x1)))))) -> 0(2(4(1(1(0(0(5(x1)))))))) 0(1(2(0(2(2(x1)))))) -> 0(2(0(2(4(1(2(x1))))))) 0(1(4(0(2(2(x1)))))) -> 0(2(0(2(4(1(0(x1))))))) 0(1(4(2(5(4(x1)))))) -> 2(4(3(1(0(4(5(4(x1)))))))) 0(1(5(1(4(2(x1)))))) -> 0(4(5(3(1(1(2(x1))))))) 0(1(5(3(2(4(x1)))))) -> 5(0(2(3(1(3(4(x1))))))) 0(5(0(1(4(2(x1)))))) -> 0(2(1(3(0(4(5(x1))))))) 0(5(2(0(1(3(x1)))))) -> 0(0(2(1(5(5(3(x1))))))) 2(0(1(1(4(1(x1)))))) -> 2(1(0(4(3(1(1(x1))))))) 2(0(1(1(5(4(x1)))))) -> 5(4(1(3(1(0(2(x1))))))) 2(0(1(2(5(4(x1)))))) -> 2(4(1(5(0(2(4(x1))))))) 2(0(1(4(2(1(x1)))))) -> 0(2(3(4(1(2(1(x1))))))) 2(0(3(0(1(2(x1)))))) -> 2(0(0(2(1(3(1(x1))))))) 2(0(5(1(4(2(x1)))))) -> 2(4(1(0(2(3(5(x1))))))) 2(1(2(0(1(4(x1)))))) -> 3(4(1(0(2(1(2(x1))))))) 2(2(0(1(4(5(x1)))))) -> 2(3(0(2(4(5(1(x1))))))) 2(2(0(1(5(4(x1)))))) -> 2(0(4(3(5(1(2(x1))))))) 2(2(4(2(0(1(x1)))))) -> 2(2(4(1(3(2(0(x1))))))) 2(3(0(5(4(2(x1)))))) -> 2(2(5(3(1(0(4(x1))))))) 2(3(3(0(1(4(x1)))))) -> 3(1(0(4(2(3(1(x1))))))) 2(4(0(1(2(1(x1)))))) -> 2(0(0(2(4(1(1(x1))))))) 2(4(0(1(3(3(x1)))))) -> 0(2(4(3(1(3(3(x1))))))) 4(2(3(0(1(1(x1)))))) -> 1(3(5(0(2(4(1(x1))))))) 4(2(4(0(1(1(x1)))))) -> 4(0(2(3(1(4(1(x1))))))) 4(3(0(1(5(4(x1)))))) -> 4(0(4(5(3(1(1(x1))))))) 4(3(2(0(1(1(x1)))))) -> 3(4(1(0(2(4(1(x1))))))) 4(3(5(3(0(1(x1)))))) -> 4(5(3(3(3(1(3(0(x1)))))))) 4(4(0(3(1(5(x1)))))) -> 4(3(1(5(1(0(4(x1))))))) 5(0(1(4(3(2(x1)))))) -> 3(3(1(2(0(4(5(x1))))))) 5(0(1(5(3(2(x1)))))) -> 3(5(5(0(2(4(1(x1))))))) 5(2(2(4(0(1(x1)))))) -> 5(2(0(0(2(4(1(x1))))))) 5(4(3(4(0(1(x1)))))) -> 4(4(3(1(5(3(0(x1))))))) 0(1(1(5(4(5(2(x1))))))) -> 5(3(1(2(5(1(0(4(x1)))))))) 0(1(3(2(4(0(5(x1))))))) -> 3(5(0(2(4(1(0(4(x1)))))))) 0(1(4(0(5(2(2(x1))))))) -> 2(4(5(1(0(0(4(2(x1)))))))) 0(1(4(4(0(2(5(x1))))))) -> 0(0(2(4(5(1(0(4(x1)))))))) 0(1(5(1(4(0(5(x1))))))) -> 5(5(4(1(1(3(0(0(x1)))))))) 0(1(5(2(3(4(2(x1))))))) -> 2(0(0(2(3(5(4(1(x1)))))))) 0(1(5(4(4(2(4(x1))))))) -> 4(4(5(0(2(4(1(4(x1)))))))) 0(1(5(4(4(3(2(x1))))))) -> 0(2(5(4(3(4(4(1(x1)))))))) 0(3(0(1(5(2(4(x1))))))) -> 4(3(5(1(3(0(0(2(x1)))))))) 0(3(3(0(1(5(2(x1))))))) -> 5(0(0(2(3(5(1(3(x1)))))))) 0(5(0(1(4(2(4(x1))))))) -> 5(0(0(4(3(1(2(4(x1)))))))) 2(0(3(3(0(1(5(x1))))))) -> 2(3(5(4(1(3(0(0(x1)))))))) 2(0(3(5(2(1(5(x1))))))) -> 2(2(0(4(3(5(1(5(x1)))))))) 2(1(2(4(0(1(3(x1))))))) -> 2(1(2(1(5(0(4(3(x1)))))))) 2(3(2(4(0(1(4(x1))))))) -> 3(4(1(2(2(0(4(4(x1)))))))) 2(3(3(4(3(0(1(x1))))))) -> 2(3(3(4(1(3(3(0(x1)))))))) 2(3(4(0(5(1(4(x1))))))) -> 4(1(3(0(4(2(5(3(x1)))))))) 2(4(3(0(1(1(4(x1))))))) -> 1(4(3(1(3(0(2(4(x1)))))))) 2(5(2(3(0(1(1(x1))))))) -> 2(1(3(1(3(2(5(0(x1)))))))) 2(5(3(0(1(1(3(x1))))))) -> 0(2(4(3(1(3(5(1(x1)))))))) 4(0(1(5(3(2(1(x1))))))) -> 4(5(3(3(1(2(1(0(x1)))))))) 4(3(0(5(0(3(1(x1))))))) -> 0(0(4(3(3(5(1(3(x1)))))))) 4(4(0(5(1(0(1(x1))))))) -> 4(1(4(3(1(5(0(0(x1)))))))) 4(4(2(2(1(1(4(x1))))))) -> 4(1(4(4(1(2(1(2(x1)))))))) 4(4(3(1(4(1(4(x1))))))) -> 4(1(3(4(4(4(1(3(x1)))))))) 5(0(1(2(4(0(1(x1))))))) -> 5(0(4(1(3(0(2(1(x1)))))))) 5(2(1(5(4(5(3(x1))))))) -> 2(5(5(3(1(3(4(5(x1)))))))) 5(2(4(4(0(1(5(x1))))))) -> 2(5(0(4(0(4(5(1(x1)))))))) 5(4(0(1(3(2(4(x1))))))) -> 1(2(1(0(4(3(4(5(x1)))))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(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(2(x1)))) -> 0(2(3(1(2(x1))))) 0(1(3(2(x1)))) -> 0(2(4(1(3(x1))))) 0(1(4(2(x1)))) -> 0(2(4(1(1(x1))))) 0(1(4(2(x1)))) -> 0(2(4(1(3(x1))))) 0(1(4(2(x1)))) -> 0(2(4(1(5(x1))))) 0(1(2(1(1(x1))))) -> 0(2(1(3(1(1(x1)))))) 0(1(3(2(2(x1))))) -> 0(2(3(1(3(2(x1)))))) 0(1(4(2(1(x1))))) -> 0(2(4(3(1(1(x1)))))) 0(1(4(2(5(x1))))) -> 0(2(4(5(4(1(x1)))))) 0(1(4(3(2(x1))))) -> 0(2(4(1(3(3(x1)))))) 0(3(2(1(4(x1))))) -> 0(2(4(3(1(3(x1)))))) 2(0(1(0(3(x1))))) -> 2(1(0(0(0(3(x1)))))) 2(4(0(1(3(x1))))) -> 0(2(4(3(1(3(x1)))))) 4(0(5(1(2(x1))))) -> 4(0(2(4(5(1(x1)))))) 4(2(4(0(1(x1))))) -> 4(0(2(4(3(1(x1)))))) 4(4(0(1(3(x1))))) -> 4(3(1(3(1(0(4(x1))))))) 5(2(0(1(4(x1))))) -> 5(0(2(4(1(3(x1)))))) 0(1(2(0(1(5(x1)))))) -> 0(2(4(1(1(0(0(5(x1)))))))) 0(1(2(0(2(2(x1)))))) -> 0(2(0(2(4(1(2(x1))))))) 0(1(4(0(2(2(x1)))))) -> 0(2(0(2(4(1(0(x1))))))) 0(1(4(2(5(4(x1)))))) -> 2(4(3(1(0(4(5(4(x1)))))))) 0(1(5(1(4(2(x1)))))) -> 0(4(5(3(1(1(2(x1))))))) 0(1(5(3(2(4(x1)))))) -> 5(0(2(3(1(3(4(x1))))))) 0(5(0(1(4(2(x1)))))) -> 0(2(1(3(0(4(5(x1))))))) 0(5(2(0(1(3(x1)))))) -> 0(0(2(1(5(5(3(x1))))))) 2(0(1(1(4(1(x1)))))) -> 2(1(0(4(3(1(1(x1))))))) 2(0(1(1(5(4(x1)))))) -> 5(4(1(3(1(0(2(x1))))))) 2(0(1(2(5(4(x1)))))) -> 2(4(1(5(0(2(4(x1))))))) 2(0(1(4(2(1(x1)))))) -> 0(2(3(4(1(2(1(x1))))))) 2(0(3(0(1(2(x1)))))) -> 2(0(0(2(1(3(1(x1))))))) 2(0(5(1(4(2(x1)))))) -> 2(4(1(0(2(3(5(x1))))))) 2(1(2(0(1(4(x1)))))) -> 3(4(1(0(2(1(2(x1))))))) 2(2(0(1(4(5(x1)))))) -> 2(3(0(2(4(5(1(x1))))))) 2(2(0(1(5(4(x1)))))) -> 2(0(4(3(5(1(2(x1))))))) 2(2(4(2(0(1(x1)))))) -> 2(2(4(1(3(2(0(x1))))))) 2(3(0(5(4(2(x1)))))) -> 2(2(5(3(1(0(4(x1))))))) 2(3(3(0(1(4(x1)))))) -> 3(1(0(4(2(3(1(x1))))))) 2(4(0(1(2(1(x1)))))) -> 2(0(0(2(4(1(1(x1))))))) 2(4(0(1(3(3(x1)))))) -> 0(2(4(3(1(3(3(x1))))))) 4(2(3(0(1(1(x1)))))) -> 1(3(5(0(2(4(1(x1))))))) 4(2(4(0(1(1(x1)))))) -> 4(0(2(3(1(4(1(x1))))))) 4(3(0(1(5(4(x1)))))) -> 4(0(4(5(3(1(1(x1))))))) 4(3(2(0(1(1(x1)))))) -> 3(4(1(0(2(4(1(x1))))))) 4(3(5(3(0(1(x1)))))) -> 4(5(3(3(3(1(3(0(x1)))))))) 4(4(0(3(1(5(x1)))))) -> 4(3(1(5(1(0(4(x1))))))) 5(0(1(4(3(2(x1)))))) -> 3(3(1(2(0(4(5(x1))))))) 5(0(1(5(3(2(x1)))))) -> 3(5(5(0(2(4(1(x1))))))) 5(2(2(4(0(1(x1)))))) -> 5(2(0(0(2(4(1(x1))))))) 5(4(3(4(0(1(x1)))))) -> 4(4(3(1(5(3(0(x1))))))) 0(1(1(5(4(5(2(x1))))))) -> 5(3(1(2(5(1(0(4(x1)))))))) 0(1(3(2(4(0(5(x1))))))) -> 3(5(0(2(4(1(0(4(x1)))))))) 0(1(4(0(5(2(2(x1))))))) -> 2(4(5(1(0(0(4(2(x1)))))))) 0(1(4(4(0(2(5(x1))))))) -> 0(0(2(4(5(1(0(4(x1)))))))) 0(1(5(1(4(0(5(x1))))))) -> 5(5(4(1(1(3(0(0(x1)))))))) 0(1(5(2(3(4(2(x1))))))) -> 2(0(0(2(3(5(4(1(x1)))))))) 0(1(5(4(4(2(4(x1))))))) -> 4(4(5(0(2(4(1(4(x1)))))))) 0(1(5(4(4(3(2(x1))))))) -> 0(2(5(4(3(4(4(1(x1)))))))) 0(3(0(1(5(2(4(x1))))))) -> 4(3(5(1(3(0(0(2(x1)))))))) 0(3(3(0(1(5(2(x1))))))) -> 5(0(0(2(3(5(1(3(x1)))))))) 0(5(0(1(4(2(4(x1))))))) -> 5(0(0(4(3(1(2(4(x1)))))))) 2(0(3(3(0(1(5(x1))))))) -> 2(3(5(4(1(3(0(0(x1)))))))) 2(0(3(5(2(1(5(x1))))))) -> 2(2(0(4(3(5(1(5(x1)))))))) 2(1(2(4(0(1(3(x1))))))) -> 2(1(2(1(5(0(4(3(x1)))))))) 2(3(2(4(0(1(4(x1))))))) -> 3(4(1(2(2(0(4(4(x1)))))))) 2(3(3(4(3(0(1(x1))))))) -> 2(3(3(4(1(3(3(0(x1)))))))) 2(3(4(0(5(1(4(x1))))))) -> 4(1(3(0(4(2(5(3(x1)))))))) 2(4(3(0(1(1(4(x1))))))) -> 1(4(3(1(3(0(2(4(x1)))))))) 2(5(2(3(0(1(1(x1))))))) -> 2(1(3(1(3(2(5(0(x1)))))))) 2(5(3(0(1(1(3(x1))))))) -> 0(2(4(3(1(3(5(1(x1)))))))) 4(0(1(5(3(2(1(x1))))))) -> 4(5(3(3(1(2(1(0(x1)))))))) 4(3(0(5(0(3(1(x1))))))) -> 0(0(4(3(3(5(1(3(x1)))))))) 4(4(0(5(1(0(1(x1))))))) -> 4(1(4(3(1(5(0(0(x1)))))))) 4(4(2(2(1(1(4(x1))))))) -> 4(1(4(4(1(2(1(2(x1)))))))) 4(4(3(1(4(1(4(x1))))))) -> 4(1(3(4(4(4(1(3(x1)))))))) 5(0(1(2(4(0(1(x1))))))) -> 5(0(4(1(3(0(2(1(x1)))))))) 5(2(1(5(4(5(3(x1))))))) -> 2(5(5(3(1(3(4(5(x1)))))))) 5(2(4(4(0(1(5(x1))))))) -> 2(5(0(4(0(4(5(1(x1)))))))) 5(4(0(1(3(2(4(x1))))))) -> 1(2(1(0(4(3(4(5(x1)))))))) encArg(1(x_1)) -> 1(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(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 2. The certificate found is represented by the following graph. "[60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 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] {(60,61,[0_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]), (60,62,[1_1|1, 3_1|1, 0_1|1, 2_1|1, 4_1|1, 5_1|1]), (60,63,[0_1|2]), (60,67,[0_1|2]), (60,72,[0_1|2]), (60,79,[0_1|2]), (60,85,[0_1|2]), (60,89,[0_1|2]), (60,94,[3_1|2]), (60,101,[0_1|2]), (60,105,[0_1|2]), (60,109,[0_1|2]), (60,114,[0_1|2]), (60,119,[2_1|2]), (60,126,[0_1|2]), (60,131,[0_1|2]), (60,137,[2_1|2]), (60,144,[0_1|2]), (60,151,[0_1|2]), (60,157,[5_1|2]), (60,164,[5_1|2]), (60,170,[2_1|2]), (60,177,[4_1|2]), (60,184,[0_1|2]), (60,191,[5_1|2]), (60,198,[0_1|2]), (60,203,[4_1|2]), (60,210,[5_1|2]), (60,217,[0_1|2]), (60,223,[5_1|2]), (60,230,[0_1|2]), (60,236,[2_1|2]), (60,241,[2_1|2]), (60,247,[5_1|2]), (60,253,[2_1|2]), (60,259,[0_1|2]), (60,265,[2_1|2]), (60,271,[2_1|2]), (60,278,[2_1|2]), (60,285,[2_1|2]), (60,291,[0_1|2]), (60,297,[2_1|2]), (60,303,[1_1|2]), (60,310,[3_1|2]), (60,316,[2_1|2]), (60,323,[2_1|2]), (60,329,[2_1|2]), (60,335,[2_1|2]), (60,341,[2_1|2]), (60,347,[3_1|2]), (60,353,[2_1|2]), (60,360,[3_1|2]), (60,367,[4_1|2]), (60,374,[2_1|2]), (60,381,[0_1|2]), (60,388,[4_1|2]), (60,393,[4_1|2]), (60,400,[4_1|2]), (60,405,[4_1|2]), (60,411,[1_1|2]), (60,417,[4_1|2]), (60,423,[4_1|2]), (60,429,[4_1|2]), (60,436,[4_1|2]), (60,443,[4_1|2]), (60,450,[4_1|2]), (60,456,[0_1|2]), (60,463,[3_1|2]), (60,469,[4_1|2]), (60,476,[5_1|2]), (60,481,[5_1|2]), (60,487,[2_1|2]), (60,494,[2_1|2]), (60,501,[3_1|2]), (60,507,[3_1|2]), (60,513,[5_1|2]), (60,520,[4_1|2]), (60,526,[1_1|2]), (60,533,[0_1|2]), (61,61,[1_1|0, 3_1|0, cons_0_1|0, cons_2_1|0, cons_4_1|0, cons_5_1|0]), (62,61,[encArg_1|1]), (62,62,[1_1|1, 3_1|1, 0_1|1, 2_1|1, 4_1|1, 5_1|1]), (62,63,[0_1|2]), (62,67,[0_1|2]), (62,72,[0_1|2]), (62,79,[0_1|2]), (62,85,[0_1|2]), (62,89,[0_1|2]), (62,94,[3_1|2]), (62,101,[0_1|2]), (62,105,[0_1|2]), (62,109,[0_1|2]), (62,114,[0_1|2]), (62,119,[2_1|2]), (62,126,[0_1|2]), (62,131,[0_1|2]), (62,137,[2_1|2]), (62,144,[0_1|2]), (62,151,[0_1|2]), (62,157,[5_1|2]), (62,164,[5_1|2]), (62,170,[2_1|2]), (62,177,[4_1|2]), (62,184,[0_1|2]), (62,191,[5_1|2]), (62,198,[0_1|2]), (62,203,[4_1|2]), (62,210,[5_1|2]), (62,217,[0_1|2]), (62,223,[5_1|2]), (62,230,[0_1|2]), (62,236,[2_1|2]), (62,241,[2_1|2]), (62,247,[5_1|2]), (62,253,[2_1|2]), (62,259,[0_1|2]), (62,265,[2_1|2]), (62,271,[2_1|2]), (62,278,[2_1|2]), (62,285,[2_1|2]), (62,291,[0_1|2]), (62,297,[2_1|2]), (62,303,[1_1|2]), (62,310,[3_1|2]), (62,316,[2_1|2]), (62,323,[2_1|2]), (62,329,[2_1|2]), (62,335,[2_1|2]), (62,341,[2_1|2]), (62,347,[3_1|2]), (62,353,[2_1|2]), (62,360,[3_1|2]), 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(439,440,[1_1|2]), (440,441,[2_1|2]), (440,310,[3_1|2]), (440,316,[2_1|2]), (441,442,[1_1|2]), (442,62,[2_1|2]), (442,177,[2_1|2]), (442,203,[2_1|2]), (442,367,[2_1|2, 4_1|2]), (442,388,[2_1|2]), (442,393,[2_1|2]), (442,400,[2_1|2]), (442,405,[2_1|2]), (442,417,[2_1|2]), (442,423,[2_1|2]), (442,429,[2_1|2]), (442,436,[2_1|2]), (442,443,[2_1|2]), (442,450,[2_1|2]), (442,469,[2_1|2]), (442,520,[2_1|2]), (442,304,[2_1|2]), (442,236,[2_1|2]), (442,241,[2_1|2]), (442,247,[5_1|2]), (442,253,[2_1|2]), (442,259,[0_1|2]), (442,265,[2_1|2]), (442,271,[2_1|2]), (442,278,[2_1|2]), (442,285,[2_1|2]), (442,538,[0_1|2]), (442,291,[0_1|2]), (442,297,[2_1|2]), (442,303,[1_1|2]), (442,310,[3_1|2]), (442,316,[2_1|2]), (442,323,[2_1|2]), (442,329,[2_1|2]), (442,335,[2_1|2]), (442,341,[2_1|2]), (442,347,[3_1|2]), (442,353,[2_1|2]), (442,360,[3_1|2]), (442,374,[2_1|2]), (442,381,[0_1|2]), (443,444,[1_1|2]), (444,445,[3_1|2]), (445,446,[4_1|2]), (446,447,[4_1|2]), (447,448,[4_1|2]), (448,449,[1_1|2]), (449,62,[3_1|2]), (449,177,[3_1|2]), (449,203,[3_1|2]), (449,367,[3_1|2]), (449,388,[3_1|2]), (449,393,[3_1|2]), (449,400,[3_1|2]), (449,405,[3_1|2]), (449,417,[3_1|2]), (449,423,[3_1|2]), (449,429,[3_1|2]), (449,436,[3_1|2]), (449,443,[3_1|2]), (449,450,[3_1|2]), (449,469,[3_1|2]), (449,520,[3_1|2]), (449,304,[3_1|2]), (449,431,[3_1|2]), (449,438,[3_1|2]), (450,451,[0_1|2]), (451,452,[4_1|2]), (452,453,[5_1|2]), (453,454,[3_1|2]), (454,455,[1_1|2]), (455,62,[1_1|2]), (455,177,[1_1|2]), (455,203,[1_1|2]), (455,367,[1_1|2]), (455,388,[1_1|2]), (455,393,[1_1|2]), (455,400,[1_1|2]), (455,405,[1_1|2]), (455,417,[1_1|2]), (455,423,[1_1|2]), (455,429,[1_1|2]), (455,436,[1_1|2]), (455,443,[1_1|2]), (455,450,[1_1|2]), (455,469,[1_1|2]), (455,520,[1_1|2]), (455,248,[1_1|2]), (456,457,[0_1|2]), (457,458,[4_1|2]), (458,459,[3_1|2]), (459,460,[3_1|2]), (460,461,[5_1|2]), (461,462,[1_1|2]), (462,62,[3_1|2]), (462,303,[3_1|2]), (462,411,[3_1|2]), (462,526,[3_1|2]), (462,348,[3_1|2]), (463,464,[4_1|2]), (464,465,[1_1|2]), (465,466,[0_1|2]), (466,467,[2_1|2]), (467,468,[4_1|2]), (468,62,[1_1|2]), (468,303,[1_1|2]), (468,411,[1_1|2]), (468,526,[1_1|2]), (469,470,[5_1|2]), (470,471,[3_1|2]), (471,472,[3_1|2]), (472,473,[3_1|2]), (473,474,[1_1|2]), (474,475,[3_1|2]), (475,62,[0_1|2]), (475,303,[0_1|2]), (475,411,[0_1|2]), (475,526,[0_1|2]), (475,63,[0_1|2]), (475,67,[0_1|2]), (475,72,[0_1|2]), (475,79,[0_1|2]), (475,85,[0_1|2]), (475,89,[0_1|2]), (475,94,[3_1|2]), (475,101,[0_1|2]), (475,105,[0_1|2]), (475,109,[0_1|2]), (475,114,[0_1|2]), (475,119,[2_1|2]), (475,126,[0_1|2]), (475,131,[0_1|2]), (475,137,[2_1|2]), (475,144,[0_1|2]), (475,151,[0_1|2]), (475,157,[5_1|2]), (475,164,[5_1|2]), (475,170,[2_1|2]), (475,177,[4_1|2]), (475,184,[0_1|2]), (475,191,[5_1|2]), (475,198,[0_1|2]), (475,203,[4_1|2]), (475,210,[5_1|2]), (475,217,[0_1|2]), (475,223,[5_1|2]), (475,230,[0_1|2]), (476,477,[0_1|2]), (477,478,[2_1|2]), (478,479,[4_1|2]), (479,480,[1_1|2]), (480,62,[3_1|2]), (480,177,[3_1|2]), (480,203,[3_1|2]), (480,367,[3_1|2]), (480,388,[3_1|2]), (480,393,[3_1|2]), (480,400,[3_1|2]), (480,405,[3_1|2]), (480,417,[3_1|2]), (480,423,[3_1|2]), (480,429,[3_1|2]), (480,436,[3_1|2]), (480,443,[3_1|2]), (480,450,[3_1|2]), (480,469,[3_1|2]), (480,520,[3_1|2]), (480,304,[3_1|2]), (481,482,[2_1|2]), (482,483,[0_1|2]), (483,484,[0_1|2]), (484,485,[2_1|2]), (485,486,[4_1|2]), (486,62,[1_1|2]), (486,303,[1_1|2]), (486,411,[1_1|2]), (486,526,[1_1|2]), (487,488,[5_1|2]), (488,489,[5_1|2]), (489,490,[3_1|2]), (490,491,[1_1|2]), (491,492,[3_1|2]), (492,493,[4_1|2]), (493,62,[5_1|2]), (493,94,[5_1|2]), (493,310,[5_1|2]), (493,347,[5_1|2]), (493,360,[5_1|2]), (493,463,[5_1|2]), (493,501,[5_1|2, 3_1|2]), (493,507,[5_1|2, 3_1|2]), (493,192,[5_1|2]), (493,395,[5_1|2]), (493,471,[5_1|2]), (493,476,[5_1|2]), (493,481,[5_1|2]), (493,487,[2_1|2]), (493,494,[2_1|2]), (493,513,[5_1|2]), (493,520,[4_1|2]), (493,526,[1_1|2]), (494,495,[5_1|2]), (495,496,[0_1|2]), (496,497,[4_1|2]), (497,498,[0_1|2]), (498,499,[4_1|2]), (499,500,[5_1|2]), (500,62,[1_1|2]), (500,157,[1_1|2]), (500,164,[1_1|2]), (500,191,[1_1|2]), (500,210,[1_1|2]), (500,223,[1_1|2]), (500,247,[1_1|2]), (500,476,[1_1|2]), (500,481,[1_1|2]), (500,513,[1_1|2]), (501,502,[3_1|2]), (502,503,[1_1|2]), (503,504,[2_1|2]), (504,505,[0_1|2]), (505,506,[4_1|2]), (506,62,[5_1|2]), (506,119,[5_1|2]), (506,137,[5_1|2]), (506,170,[5_1|2]), (506,236,[5_1|2]), (506,241,[5_1|2]), (506,253,[5_1|2]), (506,265,[5_1|2]), (506,271,[5_1|2]), (506,278,[5_1|2]), (506,285,[5_1|2]), (506,297,[5_1|2]), (506,316,[5_1|2]), (506,323,[5_1|2]), (506,329,[5_1|2]), (506,335,[5_1|2]), (506,341,[5_1|2]), (506,353,[5_1|2]), (506,374,[5_1|2]), (506,487,[5_1|2, 2_1|2]), (506,494,[5_1|2, 2_1|2]), (506,476,[5_1|2]), (506,481,[5_1|2]), (506,501,[3_1|2]), (506,507,[3_1|2]), (506,513,[5_1|2]), (506,520,[4_1|2]), (506,526,[1_1|2]), (507,508,[5_1|2]), (508,509,[5_1|2]), (509,510,[0_1|2]), (510,511,[2_1|2]), (511,512,[4_1|2]), (512,62,[1_1|2]), (512,119,[1_1|2]), (512,137,[1_1|2]), (512,170,[1_1|2]), (512,236,[1_1|2]), (512,241,[1_1|2]), (512,253,[1_1|2]), (512,265,[1_1|2]), (512,271,[1_1|2]), (512,278,[1_1|2]), (512,285,[1_1|2]), (512,297,[1_1|2]), (512,316,[1_1|2]), (512,323,[1_1|2]), (512,329,[1_1|2]), (512,335,[1_1|2]), (512,341,[1_1|2]), (512,353,[1_1|2]), (512,374,[1_1|2]), (512,487,[1_1|2]), (512,494,[1_1|2]), (513,514,[0_1|2]), (514,515,[4_1|2]), (515,516,[1_1|2]), (516,517,[3_1|2]), (517,518,[0_1|2]), (518,519,[2_1|2]), (518,310,[3_1|2]), (518,316,[2_1|2]), (519,62,[1_1|2]), (519,303,[1_1|2]), (519,411,[1_1|2]), (519,526,[1_1|2]), (520,521,[4_1|2]), (521,522,[3_1|2]), (522,523,[1_1|2]), (523,524,[5_1|2]), (524,525,[3_1|2]), (525,62,[0_1|2]), (525,303,[0_1|2]), (525,411,[0_1|2]), (525,526,[0_1|2]), (525,63,[0_1|2]), (525,67,[0_1|2]), (525,72,[0_1|2]), (525,79,[0_1|2]), (525,85,[0_1|2]), (525,89,[0_1|2]), (525,94,[3_1|2]), (525,101,[0_1|2]), (525,105,[0_1|2]), (525,109,[0_1|2]), (525,114,[0_1|2]), (525,119,[2_1|2]), (525,126,[0_1|2]), (525,131,[0_1|2]), (525,137,[2_1|2]), (525,144,[0_1|2]), (525,151,[0_1|2]), (525,157,[5_1|2]), (525,164,[5_1|2]), (525,170,[2_1|2]), (525,177,[4_1|2]), (525,184,[0_1|2]), (525,191,[5_1|2]), (525,198,[0_1|2]), (525,203,[4_1|2]), (525,210,[5_1|2]), (525,217,[0_1|2]), (525,223,[5_1|2]), (525,230,[0_1|2]), (526,527,[2_1|2]), (527,528,[1_1|2]), (528,529,[0_1|2]), (529,530,[4_1|2]), (530,531,[3_1|2]), (531,532,[4_1|2]), (532,62,[5_1|2]), (532,177,[5_1|2]), (532,203,[5_1|2]), (532,367,[5_1|2]), (532,388,[5_1|2]), (532,393,[5_1|2]), (532,400,[5_1|2]), (532,405,[5_1|2]), (532,417,[5_1|2]), (532,423,[5_1|2]), (532,429,[5_1|2]), (532,436,[5_1|2]), (532,443,[5_1|2]), (532,450,[5_1|2]), (532,469,[5_1|2]), (532,520,[5_1|2, 4_1|2]), (532,120,[5_1|2]), (532,138,[5_1|2]), (532,254,[5_1|2]), (532,286,[5_1|2]), (532,476,[5_1|2]), (532,481,[5_1|2]), (532,487,[2_1|2]), (532,494,[2_1|2]), (532,501,[3_1|2]), (532,507,[3_1|2]), (532,513,[5_1|2]), (532,526,[1_1|2]), (533,534,[2_1|2]), (534,535,[4_1|2]), (535,536,[3_1|2]), (536,537,[1_1|2]), (537,94,[3_1|2]), (537,310,[3_1|2]), (537,347,[3_1|2]), (537,360,[3_1|2]), (537,463,[3_1|2]), (537,501,[3_1|2]), (537,507,[3_1|2]), (537,412,[3_1|2]), (538,539,[2_1|2]), (539,540,[4_1|2]), (540,541,[3_1|2]), (541,542,[1_1|2]), (542,62,[3_1|2]), (542,94,[3_1|2]), (542,310,[3_1|2]), (542,347,[3_1|2]), (542,360,[3_1|2]), (542,463,[3_1|2]), (542,501,[3_1|2]), (542,507,[3_1|2]), (542,412,[3_1|2])}" ---------------------------------------- (8) BOUNDS(1, n^1)