/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 48 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 376 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(x1))) -> 0(2(1(0(x1)))) 0(1(1(x1))) -> 0(3(1(4(1(x1))))) 0(1(1(x1))) -> 0(5(1(3(2(5(1(x1))))))) 0(1(1(x1))) -> 3(5(5(1(0(2(1(x1))))))) 0(1(4(x1))) -> 0(5(1(4(5(x1))))) 4(0(1(x1))) -> 3(5(1(4(1(2(0(x1))))))) 0(0(1(1(x1)))) -> 2(0(5(1(4(1(0(x1))))))) 0(0(3(4(x1)))) -> 0(3(2(1(4(5(5(0(x1)))))))) 0(1(1(0(x1)))) -> 2(1(0(3(1(0(x1)))))) 0(1(1(4(x1)))) -> 3(1(4(1(0(3(5(x1))))))) 0(1(3(0(x1)))) -> 0(0(3(2(1(x1))))) 0(1(3(4(x1)))) -> 3(1(4(2(5(0(5(x1))))))) 0(1(4(0(x1)))) -> 0(5(0(4(1(3(1(x1))))))) 0(3(4(1(x1)))) -> 4(3(0(3(1(x1))))) 2(0(1(0(x1)))) -> 2(0(5(1(0(x1))))) 2(0(1(1(x1)))) -> 2(0(2(1(3(1(x1)))))) 2(3(1(1(x1)))) -> 2(3(1(4(1(x1))))) 2(3(1(1(x1)))) -> 3(1(3(2(1(x1))))) 2(4(1(1(x1)))) -> 2(4(2(1(4(1(x1)))))) 3(0(1(0(x1)))) -> 3(1(2(2(0(0(x1)))))) 3(3(1(1(x1)))) -> 5(3(5(1(3(2(2(1(x1)))))))) 3(4(0(1(x1)))) -> 0(3(1(4(1(x1))))) 3(4(1(1(x1)))) -> 3(4(1(3(1(x1))))) 3(4(5(4(x1)))) -> 5(1(4(1(4(5(3(x1))))))) 4(0(0(1(x1)))) -> 4(0(0(3(1(x1))))) 4(3(0(1(x1)))) -> 3(5(0(4(2(1(x1)))))) 4(3(0(1(x1)))) -> 3(1(4(2(5(5(2(0(x1)))))))) 4(3(1(1(x1)))) -> 4(3(1(3(1(x1))))) 0(0(0(1(1(x1))))) -> 0(0(0(3(5(1(1(x1))))))) 0(0(0(3(4(x1))))) -> 0(0(3(1(0(4(5(x1))))))) 0(0(1(3(0(x1))))) -> 0(3(1(0(5(0(5(x1))))))) 0(0(2(0(1(x1))))) -> 0(0(0(3(2(1(x1)))))) 0(1(1(3(4(x1))))) -> 0(5(4(1(3(1(x1)))))) 0(1(1(3(4(x1))))) -> 4(1(0(3(5(5(2(1(x1)))))))) 0(1(2(5(4(x1))))) -> 3(2(1(0(4(5(x1)))))) 0(5(5(0(1(x1))))) -> 0(5(5(5(1(0(2(x1))))))) 2(0(1(4(1(x1))))) -> 5(5(1(0(4(2(1(x1))))))) 2(2(3(1(1(x1))))) -> 3(2(2(1(4(1(x1)))))) 2(3(4(1(1(x1))))) -> 2(1(3(5(4(1(x1)))))) 2(4(4(0(1(x1))))) -> 4(5(2(1(4(5(5(0(x1)))))))) 3(0(4(0(1(x1))))) -> 4(0(3(1(2(2(0(x1))))))) 3(2(3(1(1(x1))))) -> 3(5(1(3(2(1(x1)))))) 3(3(0(1(0(x1))))) -> 3(2(5(2(1(3(0(0(x1)))))))) 3(3(4(0(1(x1))))) -> 3(5(0(3(1(2(4(1(x1)))))))) 3(4(2(0(1(x1))))) -> 0(3(1(4(2(1(x1)))))) 3(4(3(0(1(x1))))) -> 0(3(1(3(5(4(x1)))))) 4(0(1(1(4(x1))))) -> 4(0(1(3(1(4(5(5(x1)))))))) 4(3(2(0(1(x1))))) -> 3(1(2(2(4(0(x1)))))) 4(3(4(1(1(x1))))) -> 3(1(4(1(4(2(x1)))))) 0(0(2(1(1(1(x1)))))) -> 5(1(0(4(1(0(2(1(x1)))))))) 0(1(1(2(5(4(x1)))))) -> 0(2(3(1(4(5(1(x1))))))) 0(1(5(1(4(0(x1)))))) -> 0(5(1(4(2(1(0(5(x1)))))))) 0(2(5(3(1(1(x1)))))) -> 3(0(2(1(3(5(1(x1))))))) 0(3(0(5(4(1(x1)))))) -> 3(2(1(0(4(5(0(x1))))))) 0(5(5(3(3(4(x1)))))) -> 3(5(5(0(4(5(5(3(x1)))))))) 2(0(4(4(1(1(x1)))))) -> 4(0(0(2(1(4(5(1(x1)))))))) 2(2(3(1(0(1(x1)))))) -> 0(2(5(2(1(3(1(x1))))))) 2(3(0(1(1(1(x1)))))) -> 3(1(4(1(0(2(5(1(x1)))))))) 2(3(2(3(0(1(x1)))))) -> 2(3(5(1(3(1(2(0(x1)))))))) 2(3(4(1(0(1(x1)))))) -> 3(3(2(1(4(5(1(0(x1)))))))) 3(0(1(4(1(1(x1)))))) -> 3(1(2(2(1(4(1(0(x1)))))))) 3(0(5(2(5(4(x1)))))) -> 4(3(5(2(1(0(5(x1))))))) 3(3(0(2(5(0(x1)))))) -> 3(2(5(0(0(3(1(x1))))))) 3(3(1(4(0(0(x1)))))) -> 4(0(3(1(3(5(0(x1))))))) 3(4(1(2(5(0(x1)))))) -> 4(4(5(0(3(2(1(x1))))))) 3(4(2(2(0(1(x1)))))) -> 3(2(2(3(1(4(5(0(x1)))))))) 3(4(5(3(0(1(x1)))))) -> 5(1(0(3(2(5(3(4(x1)))))))) 4(0(1(3(0(1(x1)))))) -> 0(3(1(4(1(0(3(x1))))))) 4(0(3(4(1(1(x1)))))) -> 0(1(4(3(1(4(5(4(x1)))))))) 4(2(0(5(1(1(x1)))))) -> 3(5(0(2(1(4(2(1(x1)))))))) 4(3(0(1(0(4(x1)))))) -> 2(0(4(5(1(3(0(4(x1)))))))) 0(1(2(3(4(0(1(x1))))))) -> 2(0(4(5(1(3(1(0(x1)))))))) 2(3(4(5(4(1(1(x1))))))) -> 2(1(3(4(3(5(4(1(x1)))))))) 2(4(0(2(1(0(1(x1))))))) -> 0(2(2(1(4(5(0(1(x1)))))))) 2(4(3(4(2(1(1(x1))))))) -> 2(5(1(2(4(4(3(1(x1)))))))) 2(4(5(0(3(0(1(x1))))))) -> 2(0(0(4(3(2(5(1(x1)))))))) 3(0(0(4(0(1(1(x1))))))) -> 3(2(1(0(0(0(4(1(x1)))))))) 3(2(4(5(1(0(1(x1))))))) -> 1(3(5(2(1(4(1(0(x1)))))))) 4(0(3(2(0(0(1(x1))))))) -> 0(0(5(1(4(2(3(0(x1)))))))) 4(3(0(5(0(1(4(x1))))))) -> 5(0(4(1(0(3(1(4(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(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(x1))) -> 0(2(1(0(x1)))) 0(1(1(x1))) -> 0(3(1(4(1(x1))))) 0(1(1(x1))) -> 0(5(1(3(2(5(1(x1))))))) 0(1(1(x1))) -> 3(5(5(1(0(2(1(x1))))))) 0(1(4(x1))) -> 0(5(1(4(5(x1))))) 4(0(1(x1))) -> 3(5(1(4(1(2(0(x1))))))) 0(0(1(1(x1)))) -> 2(0(5(1(4(1(0(x1))))))) 0(0(3(4(x1)))) -> 0(3(2(1(4(5(5(0(x1)))))))) 0(1(1(0(x1)))) -> 2(1(0(3(1(0(x1)))))) 0(1(1(4(x1)))) -> 3(1(4(1(0(3(5(x1))))))) 0(1(3(0(x1)))) -> 0(0(3(2(1(x1))))) 0(1(3(4(x1)))) -> 3(1(4(2(5(0(5(x1))))))) 0(1(4(0(x1)))) -> 0(5(0(4(1(3(1(x1))))))) 0(3(4(1(x1)))) -> 4(3(0(3(1(x1))))) 2(0(1(0(x1)))) -> 2(0(5(1(0(x1))))) 2(0(1(1(x1)))) -> 2(0(2(1(3(1(x1)))))) 2(3(1(1(x1)))) -> 2(3(1(4(1(x1))))) 2(3(1(1(x1)))) -> 3(1(3(2(1(x1))))) 2(4(1(1(x1)))) -> 2(4(2(1(4(1(x1)))))) 3(0(1(0(x1)))) -> 3(1(2(2(0(0(x1)))))) 3(3(1(1(x1)))) -> 5(3(5(1(3(2(2(1(x1)))))))) 3(4(0(1(x1)))) -> 0(3(1(4(1(x1))))) 3(4(1(1(x1)))) -> 3(4(1(3(1(x1))))) 3(4(5(4(x1)))) -> 5(1(4(1(4(5(3(x1))))))) 4(0(0(1(x1)))) -> 4(0(0(3(1(x1))))) 4(3(0(1(x1)))) -> 3(5(0(4(2(1(x1)))))) 4(3(0(1(x1)))) -> 3(1(4(2(5(5(2(0(x1)))))))) 4(3(1(1(x1)))) -> 4(3(1(3(1(x1))))) 0(0(0(1(1(x1))))) -> 0(0(0(3(5(1(1(x1))))))) 0(0(0(3(4(x1))))) -> 0(0(3(1(0(4(5(x1))))))) 0(0(1(3(0(x1))))) -> 0(3(1(0(5(0(5(x1))))))) 0(0(2(0(1(x1))))) -> 0(0(0(3(2(1(x1)))))) 0(1(1(3(4(x1))))) -> 0(5(4(1(3(1(x1)))))) 0(1(1(3(4(x1))))) -> 4(1(0(3(5(5(2(1(x1)))))))) 0(1(2(5(4(x1))))) -> 3(2(1(0(4(5(x1)))))) 0(5(5(0(1(x1))))) -> 0(5(5(5(1(0(2(x1))))))) 2(0(1(4(1(x1))))) -> 5(5(1(0(4(2(1(x1))))))) 2(2(3(1(1(x1))))) -> 3(2(2(1(4(1(x1)))))) 2(3(4(1(1(x1))))) -> 2(1(3(5(4(1(x1)))))) 2(4(4(0(1(x1))))) -> 4(5(2(1(4(5(5(0(x1)))))))) 3(0(4(0(1(x1))))) -> 4(0(3(1(2(2(0(x1))))))) 3(2(3(1(1(x1))))) -> 3(5(1(3(2(1(x1)))))) 3(3(0(1(0(x1))))) -> 3(2(5(2(1(3(0(0(x1)))))))) 3(3(4(0(1(x1))))) -> 3(5(0(3(1(2(4(1(x1)))))))) 3(4(2(0(1(x1))))) -> 0(3(1(4(2(1(x1)))))) 3(4(3(0(1(x1))))) -> 0(3(1(3(5(4(x1)))))) 4(0(1(1(4(x1))))) -> 4(0(1(3(1(4(5(5(x1)))))))) 4(3(2(0(1(x1))))) -> 3(1(2(2(4(0(x1)))))) 4(3(4(1(1(x1))))) -> 3(1(4(1(4(2(x1)))))) 0(0(2(1(1(1(x1)))))) -> 5(1(0(4(1(0(2(1(x1)))))))) 0(1(1(2(5(4(x1)))))) -> 0(2(3(1(4(5(1(x1))))))) 0(1(5(1(4(0(x1)))))) -> 0(5(1(4(2(1(0(5(x1)))))))) 0(2(5(3(1(1(x1)))))) -> 3(0(2(1(3(5(1(x1))))))) 0(3(0(5(4(1(x1)))))) -> 3(2(1(0(4(5(0(x1))))))) 0(5(5(3(3(4(x1)))))) -> 3(5(5(0(4(5(5(3(x1)))))))) 2(0(4(4(1(1(x1)))))) -> 4(0(0(2(1(4(5(1(x1)))))))) 2(2(3(1(0(1(x1)))))) -> 0(2(5(2(1(3(1(x1))))))) 2(3(0(1(1(1(x1)))))) -> 3(1(4(1(0(2(5(1(x1)))))))) 2(3(2(3(0(1(x1)))))) -> 2(3(5(1(3(1(2(0(x1)))))))) 2(3(4(1(0(1(x1)))))) -> 3(3(2(1(4(5(1(0(x1)))))))) 3(0(1(4(1(1(x1)))))) -> 3(1(2(2(1(4(1(0(x1)))))))) 3(0(5(2(5(4(x1)))))) -> 4(3(5(2(1(0(5(x1))))))) 3(3(0(2(5(0(x1)))))) -> 3(2(5(0(0(3(1(x1))))))) 3(3(1(4(0(0(x1)))))) -> 4(0(3(1(3(5(0(x1))))))) 3(4(1(2(5(0(x1)))))) -> 4(4(5(0(3(2(1(x1))))))) 3(4(2(2(0(1(x1)))))) -> 3(2(2(3(1(4(5(0(x1)))))))) 3(4(5(3(0(1(x1)))))) -> 5(1(0(3(2(5(3(4(x1)))))))) 4(0(1(3(0(1(x1)))))) -> 0(3(1(4(1(0(3(x1))))))) 4(0(3(4(1(1(x1)))))) -> 0(1(4(3(1(4(5(4(x1)))))))) 4(2(0(5(1(1(x1)))))) -> 3(5(0(2(1(4(2(1(x1)))))))) 4(3(0(1(0(4(x1)))))) -> 2(0(4(5(1(3(0(4(x1)))))))) 0(1(2(3(4(0(1(x1))))))) -> 2(0(4(5(1(3(1(0(x1)))))))) 2(3(4(5(4(1(1(x1))))))) -> 2(1(3(4(3(5(4(1(x1)))))))) 2(4(0(2(1(0(1(x1))))))) -> 0(2(2(1(4(5(0(1(x1)))))))) 2(4(3(4(2(1(1(x1))))))) -> 2(5(1(2(4(4(3(1(x1)))))))) 2(4(5(0(3(0(1(x1))))))) -> 2(0(0(4(3(2(5(1(x1)))))))) 3(0(0(4(0(1(1(x1))))))) -> 3(2(1(0(0(0(4(1(x1)))))))) 3(2(4(5(1(0(1(x1))))))) -> 1(3(5(2(1(4(1(0(x1)))))))) 4(0(3(2(0(0(1(x1))))))) -> 0(0(5(1(4(2(3(0(x1)))))))) 4(3(0(5(0(1(4(x1))))))) -> 5(0(4(1(0(3(1(4(x1)))))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(x1))) -> 0(2(1(0(x1)))) 0(1(1(x1))) -> 0(3(1(4(1(x1))))) 0(1(1(x1))) -> 0(5(1(3(2(5(1(x1))))))) 0(1(1(x1))) -> 3(5(5(1(0(2(1(x1))))))) 0(1(4(x1))) -> 0(5(1(4(5(x1))))) 4(0(1(x1))) -> 3(5(1(4(1(2(0(x1))))))) 0(0(1(1(x1)))) -> 2(0(5(1(4(1(0(x1))))))) 0(0(3(4(x1)))) -> 0(3(2(1(4(5(5(0(x1)))))))) 0(1(1(0(x1)))) -> 2(1(0(3(1(0(x1)))))) 0(1(1(4(x1)))) -> 3(1(4(1(0(3(5(x1))))))) 0(1(3(0(x1)))) -> 0(0(3(2(1(x1))))) 0(1(3(4(x1)))) -> 3(1(4(2(5(0(5(x1))))))) 0(1(4(0(x1)))) -> 0(5(0(4(1(3(1(x1))))))) 0(3(4(1(x1)))) -> 4(3(0(3(1(x1))))) 2(0(1(0(x1)))) -> 2(0(5(1(0(x1))))) 2(0(1(1(x1)))) -> 2(0(2(1(3(1(x1)))))) 2(3(1(1(x1)))) -> 2(3(1(4(1(x1))))) 2(3(1(1(x1)))) -> 3(1(3(2(1(x1))))) 2(4(1(1(x1)))) -> 2(4(2(1(4(1(x1)))))) 3(0(1(0(x1)))) -> 3(1(2(2(0(0(x1)))))) 3(3(1(1(x1)))) -> 5(3(5(1(3(2(2(1(x1)))))))) 3(4(0(1(x1)))) -> 0(3(1(4(1(x1))))) 3(4(1(1(x1)))) -> 3(4(1(3(1(x1))))) 3(4(5(4(x1)))) -> 5(1(4(1(4(5(3(x1))))))) 4(0(0(1(x1)))) -> 4(0(0(3(1(x1))))) 4(3(0(1(x1)))) -> 3(5(0(4(2(1(x1)))))) 4(3(0(1(x1)))) -> 3(1(4(2(5(5(2(0(x1)))))))) 4(3(1(1(x1)))) -> 4(3(1(3(1(x1))))) 0(0(0(1(1(x1))))) -> 0(0(0(3(5(1(1(x1))))))) 0(0(0(3(4(x1))))) -> 0(0(3(1(0(4(5(x1))))))) 0(0(1(3(0(x1))))) -> 0(3(1(0(5(0(5(x1))))))) 0(0(2(0(1(x1))))) -> 0(0(0(3(2(1(x1)))))) 0(1(1(3(4(x1))))) -> 0(5(4(1(3(1(x1)))))) 0(1(1(3(4(x1))))) -> 4(1(0(3(5(5(2(1(x1)))))))) 0(1(2(5(4(x1))))) -> 3(2(1(0(4(5(x1)))))) 0(5(5(0(1(x1))))) -> 0(5(5(5(1(0(2(x1))))))) 2(0(1(4(1(x1))))) -> 5(5(1(0(4(2(1(x1))))))) 2(2(3(1(1(x1))))) -> 3(2(2(1(4(1(x1)))))) 2(3(4(1(1(x1))))) -> 2(1(3(5(4(1(x1)))))) 2(4(4(0(1(x1))))) -> 4(5(2(1(4(5(5(0(x1)))))))) 3(0(4(0(1(x1))))) -> 4(0(3(1(2(2(0(x1))))))) 3(2(3(1(1(x1))))) -> 3(5(1(3(2(1(x1)))))) 3(3(0(1(0(x1))))) -> 3(2(5(2(1(3(0(0(x1)))))))) 3(3(4(0(1(x1))))) -> 3(5(0(3(1(2(4(1(x1)))))))) 3(4(2(0(1(x1))))) -> 0(3(1(4(2(1(x1)))))) 3(4(3(0(1(x1))))) -> 0(3(1(3(5(4(x1)))))) 4(0(1(1(4(x1))))) -> 4(0(1(3(1(4(5(5(x1)))))))) 4(3(2(0(1(x1))))) -> 3(1(2(2(4(0(x1)))))) 4(3(4(1(1(x1))))) -> 3(1(4(1(4(2(x1)))))) 0(0(2(1(1(1(x1)))))) -> 5(1(0(4(1(0(2(1(x1)))))))) 0(1(1(2(5(4(x1)))))) -> 0(2(3(1(4(5(1(x1))))))) 0(1(5(1(4(0(x1)))))) -> 0(5(1(4(2(1(0(5(x1)))))))) 0(2(5(3(1(1(x1)))))) -> 3(0(2(1(3(5(1(x1))))))) 0(3(0(5(4(1(x1)))))) -> 3(2(1(0(4(5(0(x1))))))) 0(5(5(3(3(4(x1)))))) -> 3(5(5(0(4(5(5(3(x1)))))))) 2(0(4(4(1(1(x1)))))) -> 4(0(0(2(1(4(5(1(x1)))))))) 2(2(3(1(0(1(x1)))))) -> 0(2(5(2(1(3(1(x1))))))) 2(3(0(1(1(1(x1)))))) -> 3(1(4(1(0(2(5(1(x1)))))))) 2(3(2(3(0(1(x1)))))) -> 2(3(5(1(3(1(2(0(x1)))))))) 2(3(4(1(0(1(x1)))))) -> 3(3(2(1(4(5(1(0(x1)))))))) 3(0(1(4(1(1(x1)))))) -> 3(1(2(2(1(4(1(0(x1)))))))) 3(0(5(2(5(4(x1)))))) -> 4(3(5(2(1(0(5(x1))))))) 3(3(0(2(5(0(x1)))))) -> 3(2(5(0(0(3(1(x1))))))) 3(3(1(4(0(0(x1)))))) -> 4(0(3(1(3(5(0(x1))))))) 3(4(1(2(5(0(x1)))))) -> 4(4(5(0(3(2(1(x1))))))) 3(4(2(2(0(1(x1)))))) -> 3(2(2(3(1(4(5(0(x1)))))))) 3(4(5(3(0(1(x1)))))) -> 5(1(0(3(2(5(3(4(x1)))))))) 4(0(1(3(0(1(x1)))))) -> 0(3(1(4(1(0(3(x1))))))) 4(0(3(4(1(1(x1)))))) -> 0(1(4(3(1(4(5(4(x1)))))))) 4(2(0(5(1(1(x1)))))) -> 3(5(0(2(1(4(2(1(x1)))))))) 4(3(0(1(0(4(x1)))))) -> 2(0(4(5(1(3(0(4(x1)))))))) 0(1(2(3(4(0(1(x1))))))) -> 2(0(4(5(1(3(1(0(x1)))))))) 2(3(4(5(4(1(1(x1))))))) -> 2(1(3(4(3(5(4(1(x1)))))))) 2(4(0(2(1(0(1(x1))))))) -> 0(2(2(1(4(5(0(1(x1)))))))) 2(4(3(4(2(1(1(x1))))))) -> 2(5(1(2(4(4(3(1(x1)))))))) 2(4(5(0(3(0(1(x1))))))) -> 2(0(0(4(3(2(5(1(x1)))))))) 3(0(0(4(0(1(1(x1))))))) -> 3(2(1(0(0(0(4(1(x1)))))))) 3(2(4(5(1(0(1(x1))))))) -> 1(3(5(2(1(4(1(0(x1)))))))) 4(0(3(2(0(0(1(x1))))))) -> 0(0(5(1(4(2(3(0(x1)))))))) 4(3(0(5(0(1(4(x1))))))) -> 5(0(4(1(0(3(1(4(x1)))))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(x1))) -> 0(2(1(0(x1)))) 0(1(1(x1))) -> 0(3(1(4(1(x1))))) 0(1(1(x1))) -> 0(5(1(3(2(5(1(x1))))))) 0(1(1(x1))) -> 3(5(5(1(0(2(1(x1))))))) 0(1(4(x1))) -> 0(5(1(4(5(x1))))) 4(0(1(x1))) -> 3(5(1(4(1(2(0(x1))))))) 0(0(1(1(x1)))) -> 2(0(5(1(4(1(0(x1))))))) 0(0(3(4(x1)))) -> 0(3(2(1(4(5(5(0(x1)))))))) 0(1(1(0(x1)))) -> 2(1(0(3(1(0(x1)))))) 0(1(1(4(x1)))) -> 3(1(4(1(0(3(5(x1))))))) 0(1(3(0(x1)))) -> 0(0(3(2(1(x1))))) 0(1(3(4(x1)))) -> 3(1(4(2(5(0(5(x1))))))) 0(1(4(0(x1)))) -> 0(5(0(4(1(3(1(x1))))))) 0(3(4(1(x1)))) -> 4(3(0(3(1(x1))))) 2(0(1(0(x1)))) -> 2(0(5(1(0(x1))))) 2(0(1(1(x1)))) -> 2(0(2(1(3(1(x1)))))) 2(3(1(1(x1)))) -> 2(3(1(4(1(x1))))) 2(3(1(1(x1)))) -> 3(1(3(2(1(x1))))) 2(4(1(1(x1)))) -> 2(4(2(1(4(1(x1)))))) 3(0(1(0(x1)))) -> 3(1(2(2(0(0(x1)))))) 3(3(1(1(x1)))) -> 5(3(5(1(3(2(2(1(x1)))))))) 3(4(0(1(x1)))) -> 0(3(1(4(1(x1))))) 3(4(1(1(x1)))) -> 3(4(1(3(1(x1))))) 3(4(5(4(x1)))) -> 5(1(4(1(4(5(3(x1))))))) 4(0(0(1(x1)))) -> 4(0(0(3(1(x1))))) 4(3(0(1(x1)))) -> 3(5(0(4(2(1(x1)))))) 4(3(0(1(x1)))) -> 3(1(4(2(5(5(2(0(x1)))))))) 4(3(1(1(x1)))) -> 4(3(1(3(1(x1))))) 0(0(0(1(1(x1))))) -> 0(0(0(3(5(1(1(x1))))))) 0(0(0(3(4(x1))))) -> 0(0(3(1(0(4(5(x1))))))) 0(0(1(3(0(x1))))) -> 0(3(1(0(5(0(5(x1))))))) 0(0(2(0(1(x1))))) -> 0(0(0(3(2(1(x1)))))) 0(1(1(3(4(x1))))) -> 0(5(4(1(3(1(x1)))))) 0(1(1(3(4(x1))))) -> 4(1(0(3(5(5(2(1(x1)))))))) 0(1(2(5(4(x1))))) -> 3(2(1(0(4(5(x1)))))) 0(5(5(0(1(x1))))) -> 0(5(5(5(1(0(2(x1))))))) 2(0(1(4(1(x1))))) -> 5(5(1(0(4(2(1(x1))))))) 2(2(3(1(1(x1))))) -> 3(2(2(1(4(1(x1)))))) 2(3(4(1(1(x1))))) -> 2(1(3(5(4(1(x1)))))) 2(4(4(0(1(x1))))) -> 4(5(2(1(4(5(5(0(x1)))))))) 3(0(4(0(1(x1))))) -> 4(0(3(1(2(2(0(x1))))))) 3(2(3(1(1(x1))))) -> 3(5(1(3(2(1(x1)))))) 3(3(0(1(0(x1))))) -> 3(2(5(2(1(3(0(0(x1)))))))) 3(3(4(0(1(x1))))) -> 3(5(0(3(1(2(4(1(x1)))))))) 3(4(2(0(1(x1))))) -> 0(3(1(4(2(1(x1)))))) 3(4(3(0(1(x1))))) -> 0(3(1(3(5(4(x1)))))) 4(0(1(1(4(x1))))) -> 4(0(1(3(1(4(5(5(x1)))))))) 4(3(2(0(1(x1))))) -> 3(1(2(2(4(0(x1)))))) 4(3(4(1(1(x1))))) -> 3(1(4(1(4(2(x1)))))) 0(0(2(1(1(1(x1)))))) -> 5(1(0(4(1(0(2(1(x1)))))))) 0(1(1(2(5(4(x1)))))) -> 0(2(3(1(4(5(1(x1))))))) 0(1(5(1(4(0(x1)))))) -> 0(5(1(4(2(1(0(5(x1)))))))) 0(2(5(3(1(1(x1)))))) -> 3(0(2(1(3(5(1(x1))))))) 0(3(0(5(4(1(x1)))))) -> 3(2(1(0(4(5(0(x1))))))) 0(5(5(3(3(4(x1)))))) -> 3(5(5(0(4(5(5(3(x1)))))))) 2(0(4(4(1(1(x1)))))) -> 4(0(0(2(1(4(5(1(x1)))))))) 2(2(3(1(0(1(x1)))))) -> 0(2(5(2(1(3(1(x1))))))) 2(3(0(1(1(1(x1)))))) -> 3(1(4(1(0(2(5(1(x1)))))))) 2(3(2(3(0(1(x1)))))) -> 2(3(5(1(3(1(2(0(x1)))))))) 2(3(4(1(0(1(x1)))))) -> 3(3(2(1(4(5(1(0(x1)))))))) 3(0(1(4(1(1(x1)))))) -> 3(1(2(2(1(4(1(0(x1)))))))) 3(0(5(2(5(4(x1)))))) -> 4(3(5(2(1(0(5(x1))))))) 3(3(0(2(5(0(x1)))))) -> 3(2(5(0(0(3(1(x1))))))) 3(3(1(4(0(0(x1)))))) -> 4(0(3(1(3(5(0(x1))))))) 3(4(1(2(5(0(x1)))))) -> 4(4(5(0(3(2(1(x1))))))) 3(4(2(2(0(1(x1)))))) -> 3(2(2(3(1(4(5(0(x1)))))))) 3(4(5(3(0(1(x1)))))) -> 5(1(0(3(2(5(3(4(x1)))))))) 4(0(1(3(0(1(x1)))))) -> 0(3(1(4(1(0(3(x1))))))) 4(0(3(4(1(1(x1)))))) -> 0(1(4(3(1(4(5(4(x1)))))))) 4(2(0(5(1(1(x1)))))) -> 3(5(0(2(1(4(2(1(x1)))))))) 4(3(0(1(0(4(x1)))))) -> 2(0(4(5(1(3(0(4(x1)))))))) 0(1(2(3(4(0(1(x1))))))) -> 2(0(4(5(1(3(1(0(x1)))))))) 2(3(4(5(4(1(1(x1))))))) -> 2(1(3(4(3(5(4(1(x1)))))))) 2(4(0(2(1(0(1(x1))))))) -> 0(2(2(1(4(5(0(1(x1)))))))) 2(4(3(4(2(1(1(x1))))))) -> 2(5(1(2(4(4(3(1(x1)))))))) 2(4(5(0(3(0(1(x1))))))) -> 2(0(0(4(3(2(5(1(x1)))))))) 3(0(0(4(0(1(1(x1))))))) -> 3(2(1(0(0(0(4(1(x1)))))))) 3(2(4(5(1(0(1(x1))))))) -> 1(3(5(2(1(4(1(0(x1)))))))) 4(0(3(2(0(0(1(x1))))))) -> 0(0(5(1(4(2(3(0(x1)))))))) 4(3(0(5(0(1(4(x1))))))) -> 5(0(4(1(0(3(1(4(x1)))))))) encArg(1(x_1)) -> 1(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (7) CpxTrsMatchBoundsProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. The certificate found is represented by the following graph. "[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, 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671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681] {(64,65,[0_1|0, 4_1|0, 2_1|0, 3_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (64,66,[0_1|1]), (64,70,[0_1|1]), (64,76,[3_1|1]), (64,82,[1_1|1, 5_1|1, 0_1|1, 4_1|1, 2_1|1, 3_1|1]), (64,83,[0_1|2]), (64,86,[0_1|2]), (64,90,[0_1|2]), (64,96,[3_1|2]), (64,102,[2_1|2]), (64,107,[3_1|2]), (64,113,[0_1|2]), (64,118,[4_1|2]), (64,125,[0_1|2]), (64,131,[0_1|2]), (64,135,[0_1|2]), (64,141,[0_1|2]), (64,145,[3_1|2]), (64,151,[3_1|2]), (64,156,[2_1|2]), (64,163,[0_1|2]), (64,170,[2_1|2]), (64,176,[0_1|2]), (64,182,[0_1|2]), (64,189,[0_1|2]), (64,195,[0_1|2]), (64,201,[0_1|2]), (64,206,[5_1|2]), (64,213,[4_1|2]), (64,217,[3_1|2]), (64,223,[0_1|2]), (64,229,[3_1|2]), (64,236,[3_1|2]), (64,242,[3_1|2]), (64,248,[4_1|2]), (64,255,[0_1|2]), (64,261,[4_1|2]), (64,265,[0_1|2]), (64,272,[0_1|2]), (64,279,[3_1|2]), (64,284,[3_1|2]), (64,291,[2_1|2]), (64,298,[5_1|2]), (64,305,[4_1|2]), 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(519,291,[2_1|2]), (519,298,[5_1|2]), (519,305,[4_1|2]), (519,309,[3_1|2]), (519,314,[3_1|2]), (519,319,[3_1|2]), (519,585,[3_1|3]), (519,559,[0_1|3]), (520,521,[3_1|2]), (521,522,[1_1|2]), (522,523,[4_1|2]), (523,524,[2_1|2]), (524,82,[1_1|2]), (524,542,[1_1|2]), (524,266,[1_1|2]), (525,526,[2_1|2]), (526,527,[2_1|2]), (527,528,[3_1|2]), (528,529,[1_1|2]), (529,530,[4_1|2]), (530,531,[5_1|2]), (531,82,[0_1|2]), (531,542,[0_1|2]), (531,266,[0_1|2]), (531,83,[0_1|2]), (531,86,[0_1|2]), (531,90,[0_1|2]), (531,96,[3_1|2]), (531,102,[2_1|2]), (531,107,[3_1|2]), (531,113,[0_1|2]), (531,118,[4_1|2]), (531,125,[0_1|2]), (531,131,[0_1|2]), (531,135,[0_1|2]), (531,141,[0_1|2]), (531,145,[3_1|2]), (531,151,[3_1|2]), (531,156,[2_1|2]), (531,163,[0_1|2]), (531,170,[2_1|2]), (531,176,[0_1|2]), (531,182,[0_1|2]), (531,189,[0_1|2]), (531,195,[0_1|2]), (531,201,[0_1|2]), (531,206,[5_1|2]), (531,213,[4_1|2]), (531,217,[3_1|2]), (531,223,[0_1|2]), (531,229,[3_1|2]), (531,236,[3_1|2]), (531,563,[4_1|3]), (532,533,[3_1|2]), (533,534,[1_1|2]), (534,535,[3_1|2]), (535,536,[5_1|2]), (536,82,[4_1|2]), (536,542,[4_1|2]), (536,266,[4_1|2]), (536,242,[3_1|2]), (536,248,[4_1|2]), (536,255,[0_1|2]), (536,261,[4_1|2]), (536,265,[0_1|2]), (536,272,[0_1|2]), (536,279,[3_1|2]), (536,284,[3_1|2]), (536,291,[2_1|2]), (536,298,[5_1|2]), (536,305,[4_1|2]), (536,309,[3_1|2]), (536,314,[3_1|2]), (536,319,[3_1|2]), (536,585,[3_1|3]), (536,559,[0_1|3]), (537,538,[5_1|2]), (538,539,[1_1|2]), (539,540,[3_1|2]), (540,541,[2_1|2]), (541,82,[1_1|2]), (541,542,[1_1|2]), (542,543,[3_1|2]), (543,544,[5_1|2]), (544,545,[2_1|2]), (545,546,[1_1|2]), (546,547,[4_1|2]), (547,548,[1_1|2]), (548,82,[0_1|2]), (548,542,[0_1|2]), (548,266,[0_1|2]), (548,83,[0_1|2]), (548,86,[0_1|2]), (548,90,[0_1|2]), (548,96,[3_1|2]), (548,102,[2_1|2]), (548,107,[3_1|2]), (548,113,[0_1|2]), (548,118,[4_1|2]), (548,125,[0_1|2]), (548,131,[0_1|2]), (548,135,[0_1|2]), (548,141,[0_1|2]), (548,145,[3_1|2]), (548,151,[3_1|2]), (548,156,[2_1|2]), (548,163,[0_1|2]), (548,170,[2_1|2]), (548,176,[0_1|2]), (548,182,[0_1|2]), (548,189,[0_1|2]), (548,195,[0_1|2]), (548,201,[0_1|2]), (548,206,[5_1|2]), (548,213,[4_1|2]), (548,217,[3_1|2]), (548,223,[0_1|2]), (548,229,[3_1|2]), (548,236,[3_1|2]), (548,563,[4_1|3]), (549,550,[3_1|2]), (550,551,[1_1|2]), (551,552,[4_1|2]), (552,266,[1_1|2]), (552,250,[1_1|2]), (553,554,[5_1|3]), (554,555,[1_1|3]), (555,556,[4_1|3]), (556,557,[1_1|3]), (557,558,[2_1|3]), (558,250,[0_1|3]), (559,560,[5_1|3]), (560,561,[1_1|3]), (561,562,[4_1|3]), (562,267,[5_1|3]), (563,564,[3_1|3]), (564,565,[0_1|3]), (565,566,[3_1|3]), (566,499,[1_1|3]), (567,568,[3_1|2]), (568,569,[1_1|2]), (569,570,[4_1|2]), (570,82,[1_1|2]), (570,542,[1_1|2]), (570,266,[1_1|2]), (571,572,[3_1|3]), (572,573,[1_1|3]), (573,574,[4_1|3]), (574,250,[1_1|3]), (575,576,[2_1|3]), (576,577,[1_1|3]), (577,578,[0_1|3]), (578,579,[4_1|3]), (579,580,[5_1|3]), (580,116,[0_1|3]), (581,582,[3_1|3]), (582,583,[0_1|3]), (583,584,[3_1|3]), (584,119,[1_1|3]), (584,499,[1_1|3]), (585,586,[5_1|3]), (586,587,[1_1|3]), (587,588,[4_1|3]), (588,589,[1_1|3]), (589,590,[2_1|3]), (590,266,[0_1|3]), (590,250,[0_1|3]), (591,592,[0_1|3]), (592,593,[3_1|3]), (593,594,[1_1|3]), (594,595,[2_1|3]), (595,596,[2_1|3]), (596,250,[0_1|3]), (597,598,[0_1|3]), (598,599,[3_1|3]), (599,600,[1_1|3]), (600,601,[2_1|3]), (601,602,[2_1|3]), (602,266,[0_1|3]), (602,250,[0_1|3]), (603,604,[0_1|3]), (604,605,[0_1|3]), (605,606,[3_1|3]), (606,266,[1_1|3]), (607,608,[5_1|3]), (608,609,[1_1|3]), (609,610,[4_1|3]), (610,611,[1_1|3]), (611,612,[2_1|3]), (612,542,[0_1|3]), (612,250,[0_1|3]), (613,614,[2_1|3]), (614,615,[1_1|3]), (615,83,[0_1|3]), (615,86,[0_1|3]), (615,90,[0_1|3]), (615,113,[0_1|3]), (615,125,[0_1|3]), (615,131,[0_1|3]), (615,135,[0_1|3]), (615,141,[0_1|3]), (615,163,[0_1|3]), (615,176,[0_1|3]), (615,182,[0_1|3]), (615,189,[0_1|3]), (615,195,[0_1|3]), (615,201,[0_1|3]), (615,223,[0_1|3]), (615,255,[0_1|3]), (615,265,[0_1|3]), (615,272,[0_1|3]), (615,401,[0_1|3]), (615,427,[0_1|3]), (615,520,[0_1|3]), (615,532,[0_1|3]), (615,549,[0_1|3]), (615,559,[0_1|3]), (616,617,[5_1|3]), (617,618,[1_1|3]), (618,619,[4_1|3]), (619,118,[5_1|3]), (619,213,[5_1|3]), (619,248,[5_1|3]), (619,261,[5_1|3]), (619,305,[5_1|3]), (619,341,[5_1|3]), (619,394,[5_1|3]), (619,445,[5_1|3]), (619,451,[5_1|3]), (619,471,[5_1|3]), (619,501,[5_1|3]), (619,267,[5_1|3]), (620,621,[0_1|3]), (621,622,[3_1|3]), (622,623,[2_1|3]), (623,237,[1_1|3]), (624,625,[5_1|3]), (625,626,[0_1|3]), (626,627,[4_1|3]), (627,628,[1_1|3]), (628,629,[3_1|3]), (629,249,[1_1|3]), (629,262,[1_1|3]), (629,342,[1_1|3]), (629,446,[1_1|3]), (629,472,[1_1|3]), (630,631,[1_1|3]), (631,632,[4_1|3]), (632,633,[2_1|3]), (633,634,[5_1|3]), (634,635,[0_1|3]), (635,498,[5_1|3]), (636,637,[3_1|3]), (637,638,[1_1|3]), (638,639,[4_1|3]), (639,542,[1_1|3]), (640,641,[5_1|3]), (641,642,[1_1|3]), (642,643,[3_1|3]), (643,644,[2_1|3]), (644,645,[5_1|3]), (645,542,[1_1|3]), (646,647,[5_1|3]), (647,648,[5_1|3]), (648,649,[1_1|3]), (649,650,[0_1|3]), (650,651,[2_1|3]), (651,542,[1_1|3]), (652,653,[3_1|3]), (653,654,[1_1|3]), (654,655,[3_1|3]), (655,542,[1_1|3]), (656,657,[3_1|3]), (657,658,[2_1|3]), (658,659,[1_1|3]), (659,660,[4_1|3]), (660,661,[5_1|3]), (661,662,[5_1|3]), (662,498,[0_1|3]), (663,664,[4_1|3]), (664,665,[2_1|3]), (665,666,[1_1|3]), (666,667,[4_1|3]), (667,542,[1_1|3]), (668,669,[3_1|3]), (669,670,[1_1|3]), (670,671,[4_1|3]), (671,266,[1_1|3]), (671,250,[1_1|3]), (672,673,[2_1|3]), (673,674,[1_1|3]), (674,120,[0_1|3]), (675,676,[2_1|3]), (676,677,[2_1|3]), (677,678,[1_1|3]), (678,679,[4_1|3]), (679,680,[5_1|3]), (680,681,[0_1|3]), (680,559,[0_1|3]), (681,542,[1_1|3]), (681,266,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)