/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 50 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 102 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(3(x1)))) -> 2(0(3(1(2(x1))))) 0(1(2(3(x1)))) -> 2(0(3(1(3(x1))))) 0(1(2(3(x1)))) -> 2(0(3(2(1(x1))))) 0(1(2(3(x1)))) -> 2(1(0(3(0(x1))))) 0(1(2(3(x1)))) -> 2(1(3(0(2(x1))))) 0(1(2(3(x1)))) -> 2(1(4(3(0(x1))))) 0(1(2(3(x1)))) -> 2(3(0(2(1(x1))))) 0(1(2(3(x1)))) -> 2(0(3(2(1(1(x1)))))) 0(1(2(3(x1)))) -> 2(0(3(3(2(1(x1)))))) 0(1(2(3(x1)))) -> 2(1(3(0(3(0(x1)))))) 0(1(5(3(x1)))) -> 2(1(0(3(3(5(x1)))))) 0(1(5(3(x1)))) -> 2(1(0(3(4(5(x1)))))) 0(5(2(3(x1)))) -> 2(0(3(3(5(x1))))) 0(5(2(3(x1)))) -> 2(0(0(3(5(3(x1)))))) 0(0(1(2(3(x1))))) -> 0(2(0(3(1(0(x1)))))) 0(0(1(2(3(x1))))) -> 2(1(1(3(0(0(x1)))))) 0(0(4(2(3(x1))))) -> 0(3(4(0(3(2(x1)))))) 0(0(4(2(3(x1))))) -> 3(0(0(2(4(4(x1)))))) 0(0(5(2(3(x1))))) -> 0(3(5(2(4(0(x1)))))) 0(1(0(2(3(x1))))) -> 3(2(4(1(0(0(x1)))))) 0(1(0(5(3(x1))))) -> 0(1(1(5(0(3(x1)))))) 0(1(0(5(3(x1))))) -> 1(5(0(0(3(4(x1)))))) 0(1(2(1(3(x1))))) -> 2(1(0(0(3(1(x1)))))) 0(1(2(2(3(x1))))) -> 2(0(3(3(1(2(x1)))))) 0(1(2(3(3(x1))))) -> 2(0(3(3(4(1(x1)))))) 0(1(2(5(3(x1))))) -> 2(5(0(3(1(0(x1)))))) 0(4(5(5(3(x1))))) -> 5(0(3(4(1(5(x1)))))) 0(4(5(5(3(x1))))) -> 5(4(0(3(3(5(x1)))))) 0(5(2(1(3(x1))))) -> 2(1(0(3(3(5(x1)))))) 0(5(4(2(3(x1))))) -> 2(0(3(4(5(1(x1)))))) 1(0(0(5(3(x1))))) -> 0(3(1(3(5(0(x1)))))) 1(0(1(2(3(x1))))) -> 1(1(1(2(3(0(x1)))))) 1(0(1(2(3(x1))))) -> 1(2(0(3(5(1(x1)))))) 1(5(3(5(3(x1))))) -> 5(5(0(3(3(1(x1)))))) 4(0(1(2(3(x1))))) -> 2(1(4(4(0(3(x1)))))) 4(0(1(2(3(x1))))) -> 4(3(2(1(0(0(x1)))))) 5(0(0(5(3(x1))))) -> 3(0(3(5(5(0(x1)))))) 5(0(1(2(3(x1))))) -> 3(0(3(1(2(5(x1)))))) 5(0(1(2(3(x1))))) -> 4(5(3(0(2(1(x1)))))) 5(0(1(2(3(x1))))) -> 5(1(0(3(0(2(x1)))))) 5(0(1(2(3(x1))))) -> 5(1(0(3(1(2(x1)))))) 5(0(4(2(3(x1))))) -> 0(2(4(1(5(3(x1)))))) 5(0(4(2(3(x1))))) -> 0(3(3(5(2(4(x1)))))) 5(0(4(2(3(x1))))) -> 2(4(4(0(3(5(x1)))))) 5(0(5(2(3(x1))))) -> 5(0(3(5(4(2(x1)))))) 5(3(0(5(3(x1))))) -> 5(5(3(0(0(3(x1)))))) 5(3(1(2(3(x1))))) -> 2(0(3(1(5(3(x1)))))) 5(3(1(2(3(x1))))) -> 3(3(0(2(1(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(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(3(x1)))) -> 2(0(3(1(2(x1))))) 0(1(2(3(x1)))) -> 2(0(3(1(3(x1))))) 0(1(2(3(x1)))) -> 2(0(3(2(1(x1))))) 0(1(2(3(x1)))) -> 2(1(0(3(0(x1))))) 0(1(2(3(x1)))) -> 2(1(3(0(2(x1))))) 0(1(2(3(x1)))) -> 2(1(4(3(0(x1))))) 0(1(2(3(x1)))) -> 2(3(0(2(1(x1))))) 0(1(2(3(x1)))) -> 2(0(3(2(1(1(x1)))))) 0(1(2(3(x1)))) -> 2(0(3(3(2(1(x1)))))) 0(1(2(3(x1)))) -> 2(1(3(0(3(0(x1)))))) 0(1(5(3(x1)))) -> 2(1(0(3(3(5(x1)))))) 0(1(5(3(x1)))) -> 2(1(0(3(4(5(x1)))))) 0(5(2(3(x1)))) -> 2(0(3(3(5(x1))))) 0(5(2(3(x1)))) -> 2(0(0(3(5(3(x1)))))) 0(0(1(2(3(x1))))) -> 0(2(0(3(1(0(x1)))))) 0(0(1(2(3(x1))))) -> 2(1(1(3(0(0(x1)))))) 0(0(4(2(3(x1))))) -> 0(3(4(0(3(2(x1)))))) 0(0(4(2(3(x1))))) -> 3(0(0(2(4(4(x1)))))) 0(0(5(2(3(x1))))) -> 0(3(5(2(4(0(x1)))))) 0(1(0(2(3(x1))))) -> 3(2(4(1(0(0(x1)))))) 0(1(0(5(3(x1))))) -> 0(1(1(5(0(3(x1)))))) 0(1(0(5(3(x1))))) -> 1(5(0(0(3(4(x1)))))) 0(1(2(1(3(x1))))) -> 2(1(0(0(3(1(x1)))))) 0(1(2(2(3(x1))))) -> 2(0(3(3(1(2(x1)))))) 0(1(2(3(3(x1))))) -> 2(0(3(3(4(1(x1)))))) 0(1(2(5(3(x1))))) -> 2(5(0(3(1(0(x1)))))) 0(4(5(5(3(x1))))) -> 5(0(3(4(1(5(x1)))))) 0(4(5(5(3(x1))))) -> 5(4(0(3(3(5(x1)))))) 0(5(2(1(3(x1))))) -> 2(1(0(3(3(5(x1)))))) 0(5(4(2(3(x1))))) -> 2(0(3(4(5(1(x1)))))) 1(0(0(5(3(x1))))) -> 0(3(1(3(5(0(x1)))))) 1(0(1(2(3(x1))))) -> 1(1(1(2(3(0(x1)))))) 1(0(1(2(3(x1))))) -> 1(2(0(3(5(1(x1)))))) 1(5(3(5(3(x1))))) -> 5(5(0(3(3(1(x1)))))) 4(0(1(2(3(x1))))) -> 2(1(4(4(0(3(x1)))))) 4(0(1(2(3(x1))))) -> 4(3(2(1(0(0(x1)))))) 5(0(0(5(3(x1))))) -> 3(0(3(5(5(0(x1)))))) 5(0(1(2(3(x1))))) -> 3(0(3(1(2(5(x1)))))) 5(0(1(2(3(x1))))) -> 4(5(3(0(2(1(x1)))))) 5(0(1(2(3(x1))))) -> 5(1(0(3(0(2(x1)))))) 5(0(1(2(3(x1))))) -> 5(1(0(3(1(2(x1)))))) 5(0(4(2(3(x1))))) -> 0(2(4(1(5(3(x1)))))) 5(0(4(2(3(x1))))) -> 0(3(3(5(2(4(x1)))))) 5(0(4(2(3(x1))))) -> 2(4(4(0(3(5(x1)))))) 5(0(5(2(3(x1))))) -> 5(0(3(5(4(2(x1)))))) 5(3(0(5(3(x1))))) -> 5(5(3(0(0(3(x1)))))) 5(3(1(2(3(x1))))) -> 2(0(3(1(5(3(x1)))))) 5(3(1(2(3(x1))))) -> 3(3(0(2(1(5(x1)))))) The (relative) TRS S consists of the following rules: encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(3(x1)))) -> 2(0(3(1(2(x1))))) 0(1(2(3(x1)))) -> 2(0(3(1(3(x1))))) 0(1(2(3(x1)))) -> 2(0(3(2(1(x1))))) 0(1(2(3(x1)))) -> 2(1(0(3(0(x1))))) 0(1(2(3(x1)))) -> 2(1(3(0(2(x1))))) 0(1(2(3(x1)))) -> 2(1(4(3(0(x1))))) 0(1(2(3(x1)))) -> 2(3(0(2(1(x1))))) 0(1(2(3(x1)))) -> 2(0(3(2(1(1(x1)))))) 0(1(2(3(x1)))) -> 2(0(3(3(2(1(x1)))))) 0(1(2(3(x1)))) -> 2(1(3(0(3(0(x1)))))) 0(1(5(3(x1)))) -> 2(1(0(3(3(5(x1)))))) 0(1(5(3(x1)))) -> 2(1(0(3(4(5(x1)))))) 0(5(2(3(x1)))) -> 2(0(3(3(5(x1))))) 0(5(2(3(x1)))) -> 2(0(0(3(5(3(x1)))))) 0(0(1(2(3(x1))))) -> 0(2(0(3(1(0(x1)))))) 0(0(1(2(3(x1))))) -> 2(1(1(3(0(0(x1)))))) 0(0(4(2(3(x1))))) -> 0(3(4(0(3(2(x1)))))) 0(0(4(2(3(x1))))) -> 3(0(0(2(4(4(x1)))))) 0(0(5(2(3(x1))))) -> 0(3(5(2(4(0(x1)))))) 0(1(0(2(3(x1))))) -> 3(2(4(1(0(0(x1)))))) 0(1(0(5(3(x1))))) -> 0(1(1(5(0(3(x1)))))) 0(1(0(5(3(x1))))) -> 1(5(0(0(3(4(x1)))))) 0(1(2(1(3(x1))))) -> 2(1(0(0(3(1(x1)))))) 0(1(2(2(3(x1))))) -> 2(0(3(3(1(2(x1)))))) 0(1(2(3(3(x1))))) -> 2(0(3(3(4(1(x1)))))) 0(1(2(5(3(x1))))) -> 2(5(0(3(1(0(x1)))))) 0(4(5(5(3(x1))))) -> 5(0(3(4(1(5(x1)))))) 0(4(5(5(3(x1))))) -> 5(4(0(3(3(5(x1)))))) 0(5(2(1(3(x1))))) -> 2(1(0(3(3(5(x1)))))) 0(5(4(2(3(x1))))) -> 2(0(3(4(5(1(x1)))))) 1(0(0(5(3(x1))))) -> 0(3(1(3(5(0(x1)))))) 1(0(1(2(3(x1))))) -> 1(1(1(2(3(0(x1)))))) 1(0(1(2(3(x1))))) -> 1(2(0(3(5(1(x1)))))) 1(5(3(5(3(x1))))) -> 5(5(0(3(3(1(x1)))))) 4(0(1(2(3(x1))))) -> 2(1(4(4(0(3(x1)))))) 4(0(1(2(3(x1))))) -> 4(3(2(1(0(0(x1)))))) 5(0(0(5(3(x1))))) -> 3(0(3(5(5(0(x1)))))) 5(0(1(2(3(x1))))) -> 3(0(3(1(2(5(x1)))))) 5(0(1(2(3(x1))))) -> 4(5(3(0(2(1(x1)))))) 5(0(1(2(3(x1))))) -> 5(1(0(3(0(2(x1)))))) 5(0(1(2(3(x1))))) -> 5(1(0(3(1(2(x1)))))) 5(0(4(2(3(x1))))) -> 0(2(4(1(5(3(x1)))))) 5(0(4(2(3(x1))))) -> 0(3(3(5(2(4(x1)))))) 5(0(4(2(3(x1))))) -> 2(4(4(0(3(5(x1)))))) 5(0(5(2(3(x1))))) -> 5(0(3(5(4(2(x1)))))) 5(3(0(5(3(x1))))) -> 5(5(3(0(0(3(x1)))))) 5(3(1(2(3(x1))))) -> 2(0(3(1(5(3(x1)))))) 5(3(1(2(3(x1))))) -> 3(3(0(2(1(5(x1)))))) The (relative) TRS S consists of the following rules: encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(3(x1)))) -> 2(0(3(1(2(x1))))) 0(1(2(3(x1)))) -> 2(0(3(1(3(x1))))) 0(1(2(3(x1)))) -> 2(0(3(2(1(x1))))) 0(1(2(3(x1)))) -> 2(1(0(3(0(x1))))) 0(1(2(3(x1)))) -> 2(1(3(0(2(x1))))) 0(1(2(3(x1)))) -> 2(1(4(3(0(x1))))) 0(1(2(3(x1)))) -> 2(3(0(2(1(x1))))) 0(1(2(3(x1)))) -> 2(0(3(2(1(1(x1)))))) 0(1(2(3(x1)))) -> 2(0(3(3(2(1(x1)))))) 0(1(2(3(x1)))) -> 2(1(3(0(3(0(x1)))))) 0(1(5(3(x1)))) -> 2(1(0(3(3(5(x1)))))) 0(1(5(3(x1)))) -> 2(1(0(3(4(5(x1)))))) 0(5(2(3(x1)))) -> 2(0(3(3(5(x1))))) 0(5(2(3(x1)))) -> 2(0(0(3(5(3(x1)))))) 0(0(1(2(3(x1))))) -> 0(2(0(3(1(0(x1)))))) 0(0(1(2(3(x1))))) -> 2(1(1(3(0(0(x1)))))) 0(0(4(2(3(x1))))) -> 0(3(4(0(3(2(x1)))))) 0(0(4(2(3(x1))))) -> 3(0(0(2(4(4(x1)))))) 0(0(5(2(3(x1))))) -> 0(3(5(2(4(0(x1)))))) 0(1(0(2(3(x1))))) -> 3(2(4(1(0(0(x1)))))) 0(1(0(5(3(x1))))) -> 0(1(1(5(0(3(x1)))))) 0(1(0(5(3(x1))))) -> 1(5(0(0(3(4(x1)))))) 0(1(2(1(3(x1))))) -> 2(1(0(0(3(1(x1)))))) 0(1(2(2(3(x1))))) -> 2(0(3(3(1(2(x1)))))) 0(1(2(3(3(x1))))) -> 2(0(3(3(4(1(x1)))))) 0(1(2(5(3(x1))))) -> 2(5(0(3(1(0(x1)))))) 0(4(5(5(3(x1))))) -> 5(0(3(4(1(5(x1)))))) 0(4(5(5(3(x1))))) -> 5(4(0(3(3(5(x1)))))) 0(5(2(1(3(x1))))) -> 2(1(0(3(3(5(x1)))))) 0(5(4(2(3(x1))))) -> 2(0(3(4(5(1(x1)))))) 1(0(0(5(3(x1))))) -> 0(3(1(3(5(0(x1)))))) 1(0(1(2(3(x1))))) -> 1(1(1(2(3(0(x1)))))) 1(0(1(2(3(x1))))) -> 1(2(0(3(5(1(x1)))))) 1(5(3(5(3(x1))))) -> 5(5(0(3(3(1(x1)))))) 4(0(1(2(3(x1))))) -> 2(1(4(4(0(3(x1)))))) 4(0(1(2(3(x1))))) -> 4(3(2(1(0(0(x1)))))) 5(0(0(5(3(x1))))) -> 3(0(3(5(5(0(x1)))))) 5(0(1(2(3(x1))))) -> 3(0(3(1(2(5(x1)))))) 5(0(1(2(3(x1))))) -> 4(5(3(0(2(1(x1)))))) 5(0(1(2(3(x1))))) -> 5(1(0(3(0(2(x1)))))) 5(0(1(2(3(x1))))) -> 5(1(0(3(1(2(x1)))))) 5(0(4(2(3(x1))))) -> 0(2(4(1(5(3(x1)))))) 5(0(4(2(3(x1))))) -> 0(3(3(5(2(4(x1)))))) 5(0(4(2(3(x1))))) -> 2(4(4(0(3(5(x1)))))) 5(0(5(2(3(x1))))) -> 5(0(3(5(4(2(x1)))))) 5(3(0(5(3(x1))))) -> 5(5(3(0(0(3(x1)))))) 5(3(1(2(3(x1))))) -> 2(0(3(1(5(3(x1)))))) 5(3(1(2(3(x1))))) -> 3(3(0(2(1(5(x1)))))) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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. "[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] {(73,74,[0_1|0, 1_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]), (73,75,[2_1|1, 3_1|1, 0_1|1, 1_1|1, 4_1|1, 5_1|1]), (73,76,[2_1|2]), (73,80,[2_1|2]), (73,84,[2_1|2]), (73,88,[2_1|2]), (73,92,[2_1|2]), (73,96,[2_1|2]), (73,100,[2_1|2]), (73,104,[2_1|2]), (73,109,[2_1|2]), (73,114,[2_1|2]), (73,119,[2_1|2]), (73,124,[2_1|2]), (73,129,[2_1|2]), (73,134,[2_1|2]), (73,139,[2_1|2]), (73,144,[2_1|2]), (73,149,[3_1|2]), (73,154,[0_1|2]), (73,159,[1_1|2]), (73,164,[2_1|2]), (73,168,[2_1|2]), (73,173,[2_1|2]), (73,178,[0_1|2]), (73,183,[2_1|2]), (73,188,[0_1|2]), (73,193,[3_1|2]), (73,198,[0_1|2]), (73,203,[5_1|2]), (73,208,[5_1|2]), (73,213,[0_1|2]), (73,218,[1_1|2]), (73,223,[1_1|2]), (73,228,[5_1|2]), (73,233,[2_1|2]), (73,238,[4_1|2]), (73,243,[3_1|2]), (73,248,[3_1|2]), 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(187,144,[2_1|2]), (187,154,[0_1|2]), (187,159,[1_1|2]), (187,164,[2_1|2]), (187,168,[2_1|2]), (187,173,[2_1|2]), (187,303,[2_1|2]), (187,178,[0_1|2]), (187,183,[2_1|2]), (187,188,[0_1|2]), (187,198,[0_1|2]), (187,203,[5_1|2]), (187,208,[5_1|2]), (188,189,[3_1|2]), (189,190,[4_1|2]), (190,191,[0_1|2]), (191,192,[3_1|2]), (192,75,[2_1|2]), (192,149,[2_1|2]), (192,193,[2_1|2]), (192,243,[2_1|2]), (192,248,[2_1|2]), (192,298,[2_1|2]), (192,101,[2_1|2]), (193,194,[0_1|2]), (194,195,[0_1|2]), (195,196,[2_1|2]), (196,197,[4_1|2]), (197,75,[4_1|2]), (197,149,[4_1|2]), (197,193,[4_1|2]), (197,243,[4_1|2]), (197,248,[4_1|2]), (197,298,[4_1|2]), (197,101,[4_1|2]), (197,233,[2_1|2]), (197,238,[4_1|2]), (198,199,[3_1|2]), (199,200,[5_1|2]), (200,201,[2_1|2]), (201,202,[4_1|2]), (201,233,[2_1|2]), (201,238,[4_1|2]), (202,75,[0_1|2]), (202,149,[0_1|2, 3_1|2]), (202,193,[0_1|2, 3_1|2]), (202,243,[0_1|2]), (202,248,[0_1|2]), (202,298,[0_1|2]), (202,101,[0_1|2]), (202,76,[2_1|2]), (202,80,[2_1|2]), (202,84,[2_1|2]), (202,88,[2_1|2]), (202,92,[2_1|2]), (202,96,[2_1|2]), (202,100,[2_1|2]), (202,104,[2_1|2]), (202,109,[2_1|2]), (202,114,[2_1|2]), (202,119,[2_1|2]), (202,124,[2_1|2]), (202,129,[2_1|2]), (202,134,[2_1|2]), (202,139,[2_1|2]), (202,144,[2_1|2]), (202,154,[0_1|2]), (202,159,[1_1|2]), (202,164,[2_1|2]), (202,168,[2_1|2]), (202,173,[2_1|2]), (202,303,[2_1|2]), (202,178,[0_1|2]), (202,183,[2_1|2]), (202,188,[0_1|2]), (202,198,[0_1|2]), (202,203,[5_1|2]), (202,208,[5_1|2]), (203,204,[0_1|2]), (204,205,[3_1|2]), (205,206,[4_1|2]), (206,207,[1_1|2]), (206,228,[5_1|2]), (207,75,[5_1|2]), (207,149,[5_1|2]), (207,193,[5_1|2]), (207,243,[5_1|2, 3_1|2]), (207,248,[5_1|2, 3_1|2]), (207,298,[5_1|2, 3_1|2]), (207,290,[5_1|2]), (207,253,[4_1|2]), (207,258,[5_1|2]), (207,263,[5_1|2]), (207,268,[0_1|2]), (207,273,[0_1|2]), (207,278,[2_1|2]), (207,283,[5_1|2]), (207,288,[5_1|2]), (207,293,[2_1|2]), (208,209,[4_1|2]), (209,210,[0_1|2]), (210,211,[3_1|2]), (211,212,[3_1|2]), (212,75,[5_1|2]), (212,149,[5_1|2]), (212,193,[5_1|2]), (212,243,[5_1|2, 3_1|2]), (212,248,[5_1|2, 3_1|2]), (212,298,[5_1|2, 3_1|2]), (212,290,[5_1|2]), (212,253,[4_1|2]), (212,258,[5_1|2]), (212,263,[5_1|2]), (212,268,[0_1|2]), (212,273,[0_1|2]), (212,278,[2_1|2]), (212,283,[5_1|2]), (212,288,[5_1|2]), (212,293,[2_1|2]), (213,214,[3_1|2]), (214,215,[1_1|2]), (215,216,[3_1|2]), (216,217,[5_1|2]), (216,243,[3_1|2]), (216,248,[3_1|2]), (216,253,[4_1|2]), (216,258,[5_1|2]), (216,263,[5_1|2]), (216,268,[0_1|2]), (216,273,[0_1|2]), (216,278,[2_1|2]), (216,283,[5_1|2]), (217,75,[0_1|2]), (217,149,[0_1|2, 3_1|2]), (217,193,[0_1|2, 3_1|2]), (217,243,[0_1|2]), (217,248,[0_1|2]), (217,298,[0_1|2]), (217,76,[2_1|2]), (217,80,[2_1|2]), (217,84,[2_1|2]), (217,88,[2_1|2]), (217,92,[2_1|2]), (217,96,[2_1|2]), (217,100,[2_1|2]), (217,104,[2_1|2]), (217,109,[2_1|2]), (217,114,[2_1|2]), (217,119,[2_1|2]), (217,124,[2_1|2]), (217,129,[2_1|2]), (217,134,[2_1|2]), (217,139,[2_1|2]), (217,144,[2_1|2]), (217,154,[0_1|2]), (217,159,[1_1|2]), (217,164,[2_1|2]), (217,168,[2_1|2]), (217,173,[2_1|2]), (217,303,[2_1|2]), (217,178,[0_1|2]), (217,183,[2_1|2]), (217,188,[0_1|2]), (217,198,[0_1|2]), (217,203,[5_1|2]), (217,208,[5_1|2]), (218,219,[1_1|2]), (219,220,[1_1|2]), (220,221,[2_1|2]), (221,222,[3_1|2]), (222,75,[0_1|2]), (222,149,[0_1|2, 3_1|2]), (222,193,[0_1|2, 3_1|2]), (222,243,[0_1|2]), (222,248,[0_1|2]), (222,298,[0_1|2]), (222,101,[0_1|2]), (222,76,[2_1|2]), (222,80,[2_1|2]), (222,84,[2_1|2]), (222,88,[2_1|2]), (222,92,[2_1|2]), (222,96,[2_1|2]), (222,100,[2_1|2]), (222,104,[2_1|2]), (222,109,[2_1|2]), (222,114,[2_1|2]), (222,119,[2_1|2]), (222,124,[2_1|2]), (222,129,[2_1|2]), (222,134,[2_1|2]), (222,139,[2_1|2]), (222,144,[2_1|2]), (222,154,[0_1|2]), (222,159,[1_1|2]), (222,164,[2_1|2]), (222,168,[2_1|2]), (222,173,[2_1|2]), (222,303,[2_1|2]), (222,178,[0_1|2]), (222,183,[2_1|2]), (222,188,[0_1|2]), (222,198,[0_1|2]), (222,203,[5_1|2]), (222,208,[5_1|2]), (223,224,[2_1|2]), (224,225,[0_1|2]), (225,226,[3_1|2]), (226,227,[5_1|2]), (227,75,[1_1|2]), (227,149,[1_1|2]), (227,193,[1_1|2]), (227,243,[1_1|2]), (227,248,[1_1|2]), (227,298,[1_1|2]), (227,101,[1_1|2]), (227,213,[0_1|2]), (227,218,[1_1|2]), (227,223,[1_1|2]), (227,228,[5_1|2]), (228,229,[5_1|2]), (229,230,[0_1|2]), (230,231,[3_1|2]), (231,232,[3_1|2]), (232,75,[1_1|2]), (232,149,[1_1|2]), (232,193,[1_1|2]), (232,243,[1_1|2]), (232,248,[1_1|2]), (232,298,[1_1|2]), (232,213,[0_1|2]), (232,218,[1_1|2]), (232,223,[1_1|2]), (232,228,[5_1|2]), (233,234,[1_1|2]), (234,235,[4_1|2]), (235,236,[4_1|2]), (236,237,[0_1|2]), (237,75,[3_1|2]), (237,149,[3_1|2]), (237,193,[3_1|2]), (237,243,[3_1|2]), (237,248,[3_1|2]), (237,298,[3_1|2]), (237,101,[3_1|2]), (238,239,[3_1|2]), (239,240,[2_1|2]), (240,241,[1_1|2]), (240,213,[0_1|2]), (241,242,[0_1|2]), (241,178,[0_1|2]), (241,183,[2_1|2]), (241,188,[0_1|2]), (241,193,[3_1|2]), (241,198,[0_1|2]), (242,75,[0_1|2]), (242,149,[0_1|2, 3_1|2]), (242,193,[0_1|2, 3_1|2]), (242,243,[0_1|2]), (242,248,[0_1|2]), (242,298,[0_1|2]), (242,101,[0_1|2]), (242,76,[2_1|2]), (242,80,[2_1|2]), (242,84,[2_1|2]), (242,88,[2_1|2]), (242,92,[2_1|2]), (242,96,[2_1|2]), (242,100,[2_1|2]), (242,104,[2_1|2]), (242,109,[2_1|2]), (242,114,[2_1|2]), (242,119,[2_1|2]), (242,124,[2_1|2]), (242,129,[2_1|2]), (242,134,[2_1|2]), (242,139,[2_1|2]), (242,144,[2_1|2]), (242,154,[0_1|2]), (242,159,[1_1|2]), (242,164,[2_1|2]), (242,168,[2_1|2]), (242,173,[2_1|2]), (242,303,[2_1|2]), (242,178,[0_1|2]), (242,183,[2_1|2]), (242,188,[0_1|2]), (242,198,[0_1|2]), (242,203,[5_1|2]), (242,208,[5_1|2]), (243,244,[0_1|2]), (244,245,[3_1|2]), (245,246,[5_1|2]), (246,247,[5_1|2]), (246,243,[3_1|2]), (246,248,[3_1|2]), (246,253,[4_1|2]), (246,258,[5_1|2]), (246,263,[5_1|2]), (246,268,[0_1|2]), (246,273,[0_1|2]), (246,278,[2_1|2]), (246,283,[5_1|2]), (247,75,[0_1|2]), (247,149,[0_1|2, 3_1|2]), (247,193,[0_1|2, 3_1|2]), (247,243,[0_1|2]), (247,248,[0_1|2]), (247,298,[0_1|2]), (247,76,[2_1|2]), (247,80,[2_1|2]), (247,84,[2_1|2]), (247,88,[2_1|2]), (247,92,[2_1|2]), (247,96,[2_1|2]), (247,100,[2_1|2]), (247,104,[2_1|2]), (247,109,[2_1|2]), (247,114,[2_1|2]), (247,119,[2_1|2]), (247,124,[2_1|2]), (247,129,[2_1|2]), (247,134,[2_1|2]), (247,139,[2_1|2]), (247,144,[2_1|2]), (247,154,[0_1|2]), (247,159,[1_1|2]), (247,164,[2_1|2]), (247,168,[2_1|2]), (247,173,[2_1|2]), (247,303,[2_1|2]), (247,178,[0_1|2]), (247,183,[2_1|2]), (247,188,[0_1|2]), (247,198,[0_1|2]), (247,203,[5_1|2]), (247,208,[5_1|2]), (248,249,[0_1|2]), (249,250,[3_1|2]), (250,251,[1_1|2]), (251,252,[2_1|2]), (252,75,[5_1|2]), (252,149,[5_1|2]), (252,193,[5_1|2]), (252,243,[5_1|2, 3_1|2]), (252,248,[5_1|2, 3_1|2]), (252,298,[5_1|2, 3_1|2]), (252,101,[5_1|2]), (252,253,[4_1|2]), (252,258,[5_1|2]), (252,263,[5_1|2]), (252,268,[0_1|2]), (252,273,[0_1|2]), (252,278,[2_1|2]), (252,283,[5_1|2]), (252,288,[5_1|2]), (252,293,[2_1|2]), (253,254,[5_1|2]), (254,255,[3_1|2]), (255,256,[0_1|2]), (256,257,[2_1|2]), (257,75,[1_1|2]), (257,149,[1_1|2]), (257,193,[1_1|2]), (257,243,[1_1|2]), (257,248,[1_1|2]), (257,298,[1_1|2]), (257,101,[1_1|2]), (257,213,[0_1|2]), (257,218,[1_1|2]), (257,223,[1_1|2]), (257,228,[5_1|2]), (258,259,[1_1|2]), (259,260,[0_1|2]), (260,261,[3_1|2]), (261,262,[0_1|2]), (262,75,[2_1|2]), (262,149,[2_1|2]), (262,193,[2_1|2]), (262,243,[2_1|2]), (262,248,[2_1|2]), (262,298,[2_1|2]), (262,101,[2_1|2]), (263,264,[1_1|2]), (264,265,[0_1|2]), (265,266,[3_1|2]), (266,267,[1_1|2]), (267,75,[2_1|2]), (267,149,[2_1|2]), (267,193,[2_1|2]), (267,243,[2_1|2]), (267,248,[2_1|2]), (267,298,[2_1|2]), (267,101,[2_1|2]), (268,269,[2_1|2]), (269,270,[4_1|2]), (270,271,[1_1|2]), (270,228,[5_1|2]), (271,272,[5_1|2]), (271,288,[5_1|2]), (271,293,[2_1|2]), (271,298,[3_1|2]), (272,75,[3_1|2]), (272,149,[3_1|2]), (272,193,[3_1|2]), (272,243,[3_1|2]), (272,248,[3_1|2]), (272,298,[3_1|2]), (272,101,[3_1|2]), (273,274,[3_1|2]), (274,275,[3_1|2]), (275,276,[5_1|2]), (276,277,[2_1|2]), (277,75,[4_1|2]), (277,149,[4_1|2]), (277,193,[4_1|2]), (277,243,[4_1|2]), (277,248,[4_1|2]), (277,298,[4_1|2]), (277,101,[4_1|2]), (277,233,[2_1|2]), (277,238,[4_1|2]), (278,279,[4_1|2]), (279,280,[4_1|2]), (280,281,[0_1|2]), (281,282,[3_1|2]), (282,75,[5_1|2]), (282,149,[5_1|2]), (282,193,[5_1|2]), (282,243,[5_1|2, 3_1|2]), (282,248,[5_1|2, 3_1|2]), (282,298,[5_1|2, 3_1|2]), (282,101,[5_1|2]), (282,253,[4_1|2]), (282,258,[5_1|2]), (282,263,[5_1|2]), (282,268,[0_1|2]), (282,273,[0_1|2]), (282,278,[2_1|2]), (282,283,[5_1|2]), (282,288,[5_1|2]), (282,293,[2_1|2]), (283,284,[0_1|2]), (284,285,[3_1|2]), (285,286,[5_1|2]), (286,287,[4_1|2]), (287,75,[2_1|2]), (287,149,[2_1|2]), (287,193,[2_1|2]), (287,243,[2_1|2]), (287,248,[2_1|2]), (287,298,[2_1|2]), (287,101,[2_1|2]), (288,289,[5_1|2]), (289,290,[3_1|2]), (290,291,[0_1|2]), (291,292,[0_1|2]), (292,75,[3_1|2]), (292,149,[3_1|2]), (292,193,[3_1|2]), (292,243,[3_1|2]), (292,248,[3_1|2]), (292,298,[3_1|2]), (293,294,[0_1|2]), (294,295,[3_1|2]), (295,296,[1_1|2]), (295,228,[5_1|2]), (296,297,[5_1|2]), (296,288,[5_1|2]), (296,293,[2_1|2]), (296,298,[3_1|2]), (297,75,[3_1|2]), (297,149,[3_1|2]), (297,193,[3_1|2]), (297,243,[3_1|2]), (297,248,[3_1|2]), (297,298,[3_1|2]), (297,101,[3_1|2]), (298,299,[3_1|2]), (299,300,[0_1|2]), (300,301,[2_1|2]), (301,302,[1_1|2]), (301,228,[5_1|2]), (302,75,[5_1|2]), (302,149,[5_1|2]), (302,193,[5_1|2]), (302,243,[5_1|2, 3_1|2]), (302,248,[5_1|2, 3_1|2]), (302,298,[5_1|2, 3_1|2]), (302,101,[5_1|2]), (302,253,[4_1|2]), (302,258,[5_1|2]), (302,263,[5_1|2]), (302,268,[0_1|2]), (302,273,[0_1|2]), (302,278,[2_1|2]), (302,283,[5_1|2]), (302,288,[5_1|2]), (302,293,[2_1|2]), (303,304,[1_1|2]), (304,305,[0_1|2]), (305,306,[3_1|2]), (306,307,[3_1|2]), (307,94,[5_1|2]), (307,116,[5_1|2])}" ---------------------------------------- (8) BOUNDS(1, n^1)