/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 84 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 165 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). 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4(0(1(5(3(1(0(3(2(2(2(4(5(5(3(2(4(3(0(2(2(5(2(3(0(2(2(2(4(1(2(0(3(5(5(1(3(4(4(2(1(1(4(1(1(0(1(5(5(1(1(1(5(2(2(4(4(1(4(2(2(1(1(3(1(2(2(2(3(1(1(4(5(5(3(4(0(5(4(0(5(3(2(0(0(1(4(4(5(1(1(4(2(1(1(2(0(5(4(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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 (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). 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4(0(1(5(3(1(0(3(2(2(2(4(5(5(3(2(4(3(0(2(2(5(2(3(0(2(2(2(4(1(2(0(3(5(5(1(3(4(4(2(1(1(4(1(1(0(1(5(5(1(1(1(5(2(2(4(4(1(4(2(2(1(1(3(1(2(2(2(3(1(1(4(5(5(3(4(0(5(4(0(5(3(2(0(0(1(4(4(5(1(1(4(2(1(1(2(0(5(4(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_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(0(1(2(3(1(4(4(1(0(5(4(4(2(3(5(5(3(2(3(4(0(4(0(4(3(5(4(2(4(0(1(4(2(1(1(2(4(4(4(0(2(5(1(3(0(0(0(2(4(3(2(1(4(1(4(5(2(4(0(2(5(1(2(3(3(4(5(0(0(0(1(1(0(0(4(3(4(4(3(0(3(5(0(4(3(2(5(2(3(2(4(1(4(5(5(2(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(2(3(5(1(0(3(1(0(5(1(5(1(5(2(2(2(1(4(1(4(1(3(0(1(0(4(0(3(3(4(5(5(5(1(5(4(3(5(1(4(0(5(5(3(3(3(4(4(0(5(2(3(5(1(3(2(3(4(5(4(2(5(4(0(0(3(2(3(4(4(0(4(2(0(1(3(3(5(2(2(4(0(1(4(3(2(4(1(4(0(1(3(1(3(4(3(2(0(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(2(3(1(5(1(5(5(2(0(0(0(3(0(2(2(5(5(5(0(1(0(1(3(3(1(4(4(1(2(3(5(1(3(2(1(2(2(4(5(1(3(4(1(0(3(1(2(4(2(4(1(1(4(1(2(5(1(0(1(5(0(2(1(2(4(5(3(1(4(4(1(2(1(2(2(1(1(5(4(5(0(1(0(3(3(3(5(0(0(1(5(4(4(5(0(1(3(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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5(5(2(5(0(3(3(5(1(1(1(1(4(4(0(5(1(0(1(5(2(4(2(4(3(2(5(3(3(5(1(0(0(3(0(4(1(3(0(2(5(2(3(1(5(0(2(0(1(5(5(4(0(5(3(1(0(2(1(2(3(3(1(4(5(5(5(2(3(5(3(5(2(1(2(5(3(3(0(3(3(3(4(0(3(3(4(4(5(3(3(0(0(3(5(3(3(1(5(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(1(1(3(2(4(5(2(0(3(0(1(4(5(0(4(2(0(2(3(1(3(4(0(2(3(4(1(0(4(4(1(0(5(2(0(3(0(5(5(4(3(3(2(2(5(1(2(1(1(5(2(5(0(4(2(1(0(0(5(3(0(0(4(5(2(0(2(0(2(2(2(1(4(0(1(1(5(1(1(2(1(0(3(1(3(1(3(3(3(0(1(2(5(2(3(4(1(1(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(5(4(5(0(3(5(3(0(4(1(5(2(2(5(1(5(1(1(4(2(0(3(1(3(4(0(1(5(2(4(5(5(0(5(0(5(5(4(5(3(1(4(3(3(3(1(1(5(0(0(4(5(5(2(3(4(4(1(3(4(0(0(1(5(3(1(3(1(5(5(1(2(5(1(2(4(3(3(5(4(1(1(2(4(2(1(4(4(1(0(0(4(5(4(3(2(5(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(1(5(3(1(0(3(2(2(2(4(5(5(3(2(4(3(0(2(2(5(2(3(0(2(2(2(4(1(2(0(3(5(5(1(3(4(4(2(1(1(4(1(1(0(1(5(5(1(1(1(5(2(2(4(4(1(4(2(2(1(1(3(1(2(2(2(3(1(1(4(5(5(3(4(0(5(4(0(5(3(2(0(0(1(4(4(5(1(1(4(2(1(1(2(0(5(4(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_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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: FULL ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). 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3(3(1(5(5(4(4(2(2(4(1(0(4(4(5(1(3(0(1(0(0(3(3(2(4(0(0(3(3(4(3(3(2(0(1(2(5(2(0(2(2(1(1(5(3(4(0(2(0(1(3(2(1(1(4(5(1(2(1(5(0(3(4(5(1(2(5(3(3(0(1(5(2(4(5(2(0(2(2(4(2(1(4(4(1(5(4(2(2(0(4(2(1(0(4(0(3(3(2(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(1(1(0(3(3(5(2(5(5(3(4(1(3(4(5(3(5(2(3(4(3(5(1(3(0(4(3(3(1(0(1(0(1(1(1(4(3(5(2(5(1(2(1(4(3(0(0(5(4(0(1(2(1(3(3(1(2(4(3(2(3(1(5(1(2(4(3(1(3(5(3(1(0(4(4(3(1(2(0(4(5(2(1(1(2(4(1(0(2(0(0(1(4(1(2(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 3(4(0(2(5(5(5(0(1(5(2(2(2(3(3(3(5(1(4(4(2(3(3(2(4(1(2(0(0(4(5(1(3(1(0(5(1(0(1(4(1(3(4(2(2(2(0(5(3(1(3(0(0(5(4(4(5(0(4(2(5(2(2(2(2(4(5(4(1(0(0(4(5(4(4(1(1(5(2(1(3(3(0(5(0(3(1(4(4(4(2(4(5(2(5(1(5(3(5(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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3(5(3(4(1(4(4(2(5(5(0(1(4(2(1(4(1(3(5(2(2(0(5(0(0(0(0(2(3(0(0(0(3(5(2(1(5(5(4(4(0(0(4(2(1(1(0(2(0(5(2(2(0(5(1(1(3(0(5(5(2(0(1(4(2(4(4(3(3(4(5(2(3(5(5(4(2(2(4(5(3(5(5(2(5(3(2(1(3(5(2(2(5(3(2(1(3(0(4(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(0(3(4(0(3(5(4(3(5(4(5(1(4(4(2(3(2(4(3(0(0(2(5(5(2(5(1(3(3(1(2(4(5(0(0(3(1(2(5(3(1(3(4(1(1(3(5(4(4(3(1(5(3(3(1(0(3(1(3(1(4(4(0(4(2(1(2(2(5(3(2(3(4(5(5(0(1(0(0(3(2(4(0(2(4(1(5(5(3(1(1(5(5(0(3(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 4(4(1(4(4(1(4(4(4(2(0(3(1(1(2(5(5(3(4(2(0(2(4(3(1(4(0(2(4(1(0(5(4(3(3(1(1(1(3(3(0(5(4(4(0(5(3(2(4(0(2(2(5(0(3(0(2(1(3(2(3(0(2(1(4(1(3(0(2(4(5(0(4(1(2(3(0(4(1(1(5(4(5(4(4(0(5(0(2(4(1(5(3(0(5(5(5(0(2(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(2(0(3(0(2(1(1(0(2(4(4(2(2(3(2(4(3(0(1(1(0(2(2(4(0(2(2(4(3(2(3(0(3(2(4(5(5(2(4(3(3(5(1(4(2(0(3(3(4(4(5(2(3(2(0(4(5(1(4(4(5(4(3(5(2(0(4(2(4(2(0(2(4(2(2(0(0(4(5(4(3(1(4(3(0(0(1(3(4(5(1(5(0(0(1(2(5(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 4(4(2(4(5(4(2(4(3(1(5(5(4(4(0(2(1(0(5(4(3(3(1(5(5(3(5(4(5(1(1(3(1(3(1(2(5(5(1(1(4(4(3(1(4(3(1(5(0(3(5(4(1(4(0(2(2(1(1(5(4(5(3(5(3(1(5(2(2(2(5(3(4(1(0(4(0(1(4(2(5(5(5(0(3(0(2(0(0(5(4(2(1(0(3(1(5(4(5(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(0(0(5(3(5(5(1(4(3(1(5(1(3(1(2(2(1(5(1(4(0(5(5(4(5(5(5(0(4(0(2(0(1(5(2(5(1(1(0(5(4(5(5(5(2(4(3(2(0(4(1(2(1(5(1(0(0(1(1(2(1(0(4(1(3(1(3(5(4(2(0(4(0(5(2(5(3(5(5(1(0(5(5(0(2(0(2(3(3(2(1(1(3(5(5(2(2(2(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(0(5(1(2(2(5(5(1(4(3(4(5(1(5(4(3(4(5(2(3(1(4(2(3(0(1(5(0(0(1(1(0(3(1(1(5(5(4(1(5(0(5(0(0(5(3(3(2(3(3(5(4(1(3(3(3(3(1(4(1(3(2(5(4(2(0(4(5(3(0(0(3(3(3(5(1(4(3(1(1(4(1(5(5(4(2(1(3(5(5(4(4(1(3(3(1(1(0(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(5(4(0(2(5(5(1(4(1(2(0(1(4(0(4(2(2(2(5(0(2(2(0(3(0(4(4(5(0(2(2(0(2(0(3(4(3(5(3(2(2(0(1(5(3(1(2(5(3(5(2(1(2(3(5(0(1(0(4(1(3(1(3(5(0(5(3(4(3(0(2(0(0(2(4(5(5(2(0(2(4(2(3(5(5(3(0(2(2(3(2(3(5(3(1(1(1(5(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(1(3(3(0(5(1(4(1(2(2(4(1(1(0(5(4(2(0(5(2(3(4(4(3(5(2(1(1(5(5(4(4(1(2(2(5(2(5(3(4(2(1(0(4(4(1(0(3(0(2(5(3(2(5(0(0(2(1(4(3(1(0(3(5(4(0(5(4(5(0(4(0(3(2(4(3(5(3(0(2(2(1(2(3(5(1(3(4(5(5(0(4(2(4(2(4(5(5(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 1(2(1(3(0(0(2(0(0(3(1(2(3(2(0(4(0(1(0(2(3(4(1(5(3(4(5(1(1(3(4(2(0(4(2(1(2(3(2(1(0(1(4(4(3(5(0(0(3(2(5(3(3(3(2(3(4(2(1(4(5(5(5(4(3(5(3(5(3(4(5(0(0(4(2(5(1(5(5(2(3(3(0(2(5(3(1(4(5(0(0(0(1(1(3(1(2(5(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(1(5(5(2(1(5(4(0(3(2(5(2(3(0(4(2(3(2(0(3(4(1(1(5(3(3(0(4(3(4(5(4(2(2(4(1(0(3(1(0(2(4(4(3(1(0(2(3(1(1(4(4(4(0(0(4(2(4(0(1(3(4(5(1(3(3(5(4(0(5(4(2(3(3(1(4(5(0(4(5(0(5(3(4(0(0(0(2(3(4(4(1(4(5(1(4(0(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(2(3(4(5(2(4(0(5(5(0(3(1(2(4(2(5(5(1(2(4(5(1(4(1(5(4(5(2(2(5(3(1(3(2(0(1(0(1(5(4(4(0(5(5(4(1(3(5(2(3(4(0(4(3(2(0(5(0(3(0(4(5(0(4(4(3(1(2(3(5(2(5(2(1(0(2(0(0(1(3(5(1(4(3(3(2(2(0(3(3(1(0(4(4(4(2(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(5(2(5(0(3(3(5(1(1(1(1(4(4(0(5(1(0(1(5(2(4(2(4(3(2(5(3(3(5(1(0(0(3(0(4(1(3(0(2(5(2(3(1(5(0(2(0(1(5(5(4(0(5(3(1(0(2(1(2(3(3(1(4(5(5(5(2(3(5(3(5(2(1(2(5(3(3(0(3(3(3(4(0(3(3(4(4(5(3(3(0(0(3(5(3(3(1(5(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 3(1(1(3(2(4(5(2(0(3(0(1(4(5(0(4(2(0(2(3(1(3(4(0(2(3(4(1(0(4(4(1(0(5(2(0(3(0(5(5(4(3(3(2(2(5(1(2(1(1(5(2(5(0(4(2(1(0(0(5(3(0(0(4(5(2(0(2(0(2(2(2(1(4(0(1(1(5(1(1(2(1(0(3(1(3(1(3(3(3(0(1(2(5(2(3(4(1(1(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(5(4(5(0(3(5(3(0(4(1(5(2(2(5(1(5(1(1(4(2(0(3(1(3(4(0(1(5(2(4(5(5(0(5(0(5(5(4(5(3(1(4(3(3(3(1(1(5(0(0(4(5(5(2(3(4(4(1(3(4(0(0(1(5(3(1(3(1(5(5(1(2(5(1(2(4(3(3(5(4(1(1(2(4(2(1(4(4(1(0(0(4(5(4(3(2(5(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(1(5(3(1(0(3(2(2(2(4(5(5(3(2(4(3(0(2(2(5(2(3(0(2(2(2(4(1(2(0(3(5(5(1(3(4(4(2(1(1(4(1(1(0(1(5(5(1(1(1(5(2(2(4(4(1(4(2(2(1(1(3(1(2(2(2(3(1(1(4(5(5(3(4(0(5(4(0(5(3(2(0(0(1(4(4(5(1(1(4(2(1(1(2(0(5(4(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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: FULL ---------------------------------------- (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. 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2118, 2119, 2120, 2121, 2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 2130] {(148,149,[0_1|0, 1_1|0, 2_1|0, 3_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]), (148,150,[0_1|1, 1_1|1, 2_1|1, 3_1|1, 4_1|1, 5_1|1]), (148,151,[5_1|2]), (148,250,[5_1|2]), (148,349,[3_1|2]), (148,448,[3_1|2]), (148,547,[0_1|2]), (148,646,[1_1|2]), (148,745,[1_1|2]), (148,844,[4_1|2]), (148,943,[1_1|2]), (148,1042,[4_1|2]), (148,1141,[2_1|2]), (148,1240,[1_1|2]), (148,1339,[1_1|2]), (148,1438,[3_1|2]), (148,1537,[2_1|2]), (148,1636,[0_1|2]), (148,1735,[1_1|2]), (148,1834,[4_1|2]), (148,1933,[3_1|2]), (148,2032,[4_1|2]), (149,149,[cons_0_1|0, cons_1_1|0, cons_2_1|0, cons_3_1|0, cons_4_1|0, cons_5_1|0]), (150,149,[encArg_1|1]), (150,150,[0_1|1, 1_1|1, 2_1|1, 3_1|1, 4_1|1, 5_1|1]), (150,151,[5_1|2]), (150,250,[5_1|2]), (150,349,[3_1|2]), (150,448,[3_1|2]), (150,547,[0_1|2]), (150,646,[1_1|2]), (150,745,[1_1|2]), (150,844,[4_1|2]), 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(1837,1838,[4_1|2]), (1838,1839,[5_1|2]), (1839,1840,[2_1|2]), (1840,1841,[4_1|2]), (1841,1842,[0_1|2]), (1842,1843,[5_1|2]), (1843,1844,[5_1|2]), (1844,1845,[0_1|2]), (1845,1846,[3_1|2]), (1846,1847,[1_1|2]), (1847,1848,[2_1|2]), (1848,1849,[4_1|2]), (1849,1850,[2_1|2]), (1850,1851,[5_1|2]), (1851,1852,[5_1|2]), (1852,1853,[1_1|2]), (1853,1854,[2_1|2]), (1854,1855,[4_1|2]), (1855,1856,[5_1|2]), (1856,1857,[1_1|2]), (1857,1858,[4_1|2]), (1858,1859,[1_1|2]), (1859,1860,[5_1|2]), (1860,1861,[4_1|2]), (1861,1862,[5_1|2]), (1862,1863,[2_1|2]), (1863,1864,[2_1|2]), (1864,1865,[5_1|2]), (1865,1866,[3_1|2]), (1866,1867,[1_1|2]), (1867,1868,[3_1|2]), (1868,1869,[2_1|2]), (1869,1870,[0_1|2]), (1870,1871,[1_1|2]), (1871,1872,[0_1|2]), (1872,1873,[1_1|2]), (1873,1874,[5_1|2]), (1874,1875,[4_1|2]), (1875,1876,[4_1|2]), (1876,1877,[0_1|2]), (1877,1878,[5_1|2]), (1878,1879,[5_1|2]), (1879,1880,[4_1|2]), (1880,1881,[1_1|2]), (1881,1882,[3_1|2]), (1882,1883,[5_1|2]), (1883,1884,[2_1|2]), (1884,1885,[3_1|2]), (1885,1886,[4_1|2]), (1886,1887,[0_1|2]), (1887,1888,[4_1|2]), (1888,1889,[3_1|2]), (1889,1890,[2_1|2]), (1890,1891,[0_1|2]), (1891,1892,[5_1|2]), (1892,1893,[0_1|2]), (1893,1894,[3_1|2]), (1894,1895,[0_1|2]), (1895,1896,[4_1|2]), (1896,1897,[5_1|2]), (1897,1898,[0_1|2]), (1898,1899,[4_1|2]), (1899,1900,[4_1|2]), (1900,1901,[3_1|2]), (1901,1902,[1_1|2]), (1902,1903,[2_1|2]), (1903,1904,[3_1|2]), (1904,1905,[5_1|2]), (1905,1906,[2_1|2]), (1906,1907,[5_1|2]), (1907,1908,[2_1|2]), (1908,1909,[1_1|2]), (1909,1910,[0_1|2]), (1910,1911,[2_1|2]), (1911,1912,[0_1|2]), (1912,1913,[0_1|2]), (1913,1914,[1_1|2]), (1914,1915,[3_1|2]), (1915,1916,[5_1|2]), (1916,1917,[1_1|2]), (1917,1918,[4_1|2]), (1918,1919,[3_1|2]), (1919,1920,[3_1|2]), (1920,1921,[2_1|2]), (1921,1922,[2_1|2]), (1922,1923,[0_1|2]), (1923,1924,[3_1|2]), (1924,1925,[3_1|2]), (1925,1926,[1_1|2]), (1926,1927,[0_1|2]), (1927,1928,[4_1|2]), (1928,1929,[4_1|2]), (1929,1930,[4_1|2]), (1930,1931,[2_1|2]), (1931,1932,[2_1|2]), (1931,646,[1_1|2]), (1931,745,[1_1|2]), (1932,150,[1_1|2]), (1932,844,[1_1|2]), (1932,1042,[1_1|2]), (1932,1834,[1_1|2]), (1932,2032,[1_1|2]), (1932,547,[0_1|2]), (1933,1934,[1_1|2]), (1934,1935,[1_1|2]), (1935,1936,[3_1|2]), (1936,1937,[2_1|2]), (1937,1938,[4_1|2]), (1938,1939,[5_1|2]), (1939,1940,[2_1|2]), (1940,1941,[0_1|2]), (1941,1942,[3_1|2]), (1942,1943,[0_1|2]), (1943,1944,[1_1|2]), (1944,1945,[4_1|2]), (1945,1946,[5_1|2]), (1946,1947,[0_1|2]), (1947,1948,[4_1|2]), (1948,1949,[2_1|2]), (1949,1950,[0_1|2]), (1950,1951,[2_1|2]), (1951,1952,[3_1|2]), (1952,1953,[1_1|2]), (1953,1954,[3_1|2]), (1954,1955,[4_1|2]), (1955,1956,[0_1|2]), (1956,1957,[2_1|2]), (1957,1958,[3_1|2]), (1958,1959,[4_1|2]), (1959,1960,[1_1|2]), (1960,1961,[0_1|2]), (1961,1962,[4_1|2]), (1962,1963,[4_1|2]), (1963,1964,[1_1|2]), (1964,1965,[0_1|2]), (1965,1966,[5_1|2]), (1966,1967,[2_1|2]), (1967,1968,[0_1|2]), (1968,1969,[3_1|2]), (1969,1970,[0_1|2]), (1970,1971,[5_1|2]), (1971,1972,[5_1|2]), (1972,1973,[4_1|2]), (1973,1974,[3_1|2]), (1974,1975,[3_1|2]), (1975,1976,[2_1|2]), (1976,1977,[2_1|2]), (1977,1978,[5_1|2]), (1978,1979,[1_1|2]), (1979,1980,[2_1|2]), (1980,1981,[1_1|2]), (1981,1982,[1_1|2]), (1982,1983,[5_1|2]), (1983,1984,[2_1|2]), (1984,1985,[5_1|2]), (1985,1986,[0_1|2]), (1986,1987,[4_1|2]), (1987,1988,[2_1|2]), (1988,1989,[1_1|2]), (1989,1990,[0_1|2]), (1990,1991,[0_1|2]), (1991,1992,[5_1|2]), (1992,1993,[3_1|2]), (1993,1994,[0_1|2]), (1994,1995,[0_1|2]), (1995,1996,[4_1|2]), (1996,1997,[5_1|2]), (1997,1998,[2_1|2]), (1998,1999,[0_1|2]), (1999,2000,[2_1|2]), (2000,2001,[0_1|2]), (2001,2002,[2_1|2]), (2002,2003,[2_1|2]), (2003,2004,[2_1|2]), (2004,2005,[1_1|2]), (2005,2006,[4_1|2]), (2006,2007,[0_1|2]), (2007,2008,[1_1|2]), (2008,2009,[1_1|2]), (2009,2010,[5_1|2]), (2010,2011,[1_1|2]), (2011,2012,[1_1|2]), (2012,2013,[2_1|2]), (2013,2014,[1_1|2]), (2014,2015,[0_1|2]), (2015,2016,[3_1|2]), (2016,2017,[1_1|2]), (2017,2018,[3_1|2]), (2018,2019,[1_1|2]), (2019,2020,[3_1|2]), (2020,2021,[3_1|2]), (2021,2022,[3_1|2]), (2022,2023,[0_1|2]), (2023,2024,[1_1|2]), (2024,2025,[2_1|2]), (2025,2026,[5_1|2]), (2026,2027,[2_1|2]), (2027,2028,[3_1|2]), (2028,2029,[4_1|2]), (2029,2030,[1_1|2]), (2030,2031,[1_1|2]), (2031,150,[3_1|2]), (2031,547,[3_1|2]), (2031,1636,[3_1|2]), (2031,943,[1_1|2]), (2031,1042,[4_1|2]), (2031,1141,[2_1|2]), (2031,1240,[1_1|2]), (2031,1339,[1_1|2]), (2032,2033,[0_1|2]), (2033,2034,[1_1|2]), (2034,2035,[5_1|2]), (2035,2036,[3_1|2]), (2036,2037,[1_1|2]), (2037,2038,[0_1|2]), (2038,2039,[3_1|2]), (2039,2040,[2_1|2]), (2040,2041,[2_1|2]), (2041,2042,[2_1|2]), (2042,2043,[4_1|2]), (2043,2044,[5_1|2]), (2044,2045,[5_1|2]), (2045,2046,[3_1|2]), (2046,2047,[2_1|2]), (2047,2048,[4_1|2]), (2048,2049,[3_1|2]), (2049,2050,[0_1|2]), (2050,2051,[2_1|2]), (2051,2052,[2_1|2]), (2052,2053,[5_1|2]), (2053,2054,[2_1|2]), (2054,2055,[3_1|2]), (2055,2056,[0_1|2]), (2056,2057,[2_1|2]), (2057,2058,[2_1|2]), (2058,2059,[2_1|2]), (2059,2060,[4_1|2]), (2060,2061,[1_1|2]), (2061,2062,[2_1|2]), (2062,2063,[0_1|2]), (2063,2064,[3_1|2]), (2064,2065,[5_1|2]), (2065,2066,[5_1|2]), (2066,2067,[1_1|2]), (2067,2068,[3_1|2]), (2068,2069,[4_1|2]), (2069,2070,[4_1|2]), (2070,2071,[2_1|2]), (2071,2072,[1_1|2]), (2072,2073,[1_1|2]), (2073,2074,[4_1|2]), (2074,2075,[1_1|2]), (2075,2076,[1_1|2]), (2076,2077,[0_1|2]), (2077,2078,[1_1|2]), (2078,2079,[5_1|2]), (2079,2080,[5_1|2]), (2080,2081,[1_1|2]), (2081,2082,[1_1|2]), (2082,2083,[1_1|2]), (2083,2084,[5_1|2]), (2084,2085,[2_1|2]), (2085,2086,[2_1|2]), (2086,2087,[4_1|2]), (2087,2088,[4_1|2]), (2088,2089,[1_1|2]), (2089,2090,[4_1|2]), (2090,2091,[2_1|2]), (2091,2092,[2_1|2]), (2092,2093,[1_1|2]), (2093,2094,[1_1|2]), (2094,2095,[3_1|2]), (2095,2096,[1_1|2]), (2096,2097,[2_1|2]), (2097,2098,[2_1|2]), (2098,2099,[2_1|2]), (2099,2100,[3_1|2]), (2100,2101,[1_1|2]), (2101,2102,[1_1|2]), (2102,2103,[4_1|2]), (2103,2104,[5_1|2]), (2104,2105,[5_1|2]), (2105,2106,[3_1|2]), (2106,2107,[4_1|2]), (2107,2108,[0_1|2]), (2108,2109,[5_1|2]), (2109,2110,[4_1|2]), (2110,2111,[0_1|2]), (2111,2112,[5_1|2]), (2112,2113,[3_1|2]), (2113,2114,[2_1|2]), (2114,2115,[0_1|2]), (2115,2116,[0_1|2]), (2116,2117,[1_1|2]), (2117,2118,[4_1|2]), (2118,2119,[4_1|2]), (2119,2120,[5_1|2]), (2120,2121,[1_1|2]), (2121,2122,[1_1|2]), (2122,2123,[4_1|2]), (2123,2124,[2_1|2]), (2124,2125,[1_1|2]), (2125,2126,[1_1|2]), (2126,2127,[2_1|2]), (2127,2128,[0_1|2]), (2128,2129,[5_1|2]), (2129,2130,[4_1|2]), (2130,150,[3_1|2]), (2130,646,[3_1|2]), (2130,745,[3_1|2]), (2130,943,[3_1|2, 1_1|2]), (2130,1240,[3_1|2, 1_1|2]), (2130,1339,[3_1|2, 1_1|2]), (2130,1735,[3_1|2]), (2130,1042,[4_1|2]), (2130,1141,[2_1|2])}" ---------------------------------------- (8) BOUNDS(1, n^1)