/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 46 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 98 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). The TRS R consists of the following rules: 0(1(0(2(x1)))) -> 3(0(1(2(0(x1))))) 1(0(0(2(x1)))) -> 2(3(0(0(1(x1))))) 1(0(0(2(x1)))) -> 1(0(1(1(2(0(x1)))))) 1(0(0(2(x1)))) -> 1(3(3(0(2(0(x1)))))) 1(0(0(2(x1)))) -> 3(0(0(1(1(2(x1)))))) 1(0(2(2(x1)))) -> 2(1(2(3(0(x1))))) 1(0(2(2(x1)))) -> 1(1(1(2(2(0(x1)))))) 1(3(4(2(x1)))) -> 1(1(2(3(4(x1))))) 1(3(4(2(x1)))) -> 1(2(3(3(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(4(4(4(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(4(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(5(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(5(5(4(x1)))))) 1(3(5(2(x1)))) -> 2(3(1(0(5(x1))))) 1(3(5(2(x1)))) -> 4(5(1(2(3(x1))))) 3(1(0(2(x1)))) -> 3(0(1(2(0(x1))))) 3(4(0(2(x1)))) -> 3(0(0(2(4(x1))))) 3(4(0(2(x1)))) -> 3(0(1(2(4(x1))))) 3(4(0(2(x1)))) -> 3(0(5(2(4(x1))))) 3(4(0(2(x1)))) -> 3(1(0(2(4(x1))))) 3(4(0(2(x1)))) -> 4(1(2(3(0(x1))))) 3(4(0(2(x1)))) -> 2(0(4(3(3(0(x1)))))) 3(4(0(2(x1)))) -> 3(0(2(1(1(4(x1)))))) 3(4(0(2(x1)))) -> 3(3(0(5(2(4(x1)))))) 3(4(0(2(x1)))) -> 4(2(3(3(3(0(x1)))))) 3(5(0(2(x1)))) -> 3(0(3(2(5(x1))))) 3(5(0(2(x1)))) -> 2(5(3(0(0(0(x1)))))) 3(5(0(2(x1)))) -> 3(0(0(2(5(4(x1)))))) 3(5(0(2(x1)))) -> 5(5(2(3(0(3(x1)))))) 0(2(3(4(2(x1))))) -> 3(0(2(2(4(5(x1)))))) 0(3(4(0(2(x1))))) -> 0(3(1(0(4(2(x1)))))) 0(3(5(0(2(x1))))) -> 2(1(0(5(3(0(x1)))))) 1(0(0(4(2(x1))))) -> 0(4(5(1(0(2(x1)))))) 1(0(3(5(2(x1))))) -> 4(5(3(1(2(0(x1)))))) 1(1(0(2(2(x1))))) -> 1(1(2(0(1(2(x1)))))) 1(3(4(0(2(x1))))) -> 1(2(3(0(1(4(x1)))))) 1(3(5(0(2(x1))))) -> 1(0(2(5(2(3(x1)))))) 3(1(0(0(2(x1))))) -> 3(0(1(2(2(0(x1)))))) 3(1(3(5(2(x1))))) -> 3(0(3(5(1(2(x1)))))) 3(3(4(0(2(x1))))) -> 3(0(0(4(2(3(x1)))))) 3(4(0(0(2(x1))))) -> 3(0(0(4(4(2(x1)))))) 3(4(1(0(2(x1))))) -> 3(1(2(3(0(4(x1)))))) 3(4(1(5(2(x1))))) -> 2(3(0(1(4(5(x1)))))) 3(4(2(0(2(x1))))) -> 3(2(0(4(2(3(x1)))))) 3(4(2(0(2(x1))))) -> 4(2(2(3(0(3(x1)))))) 3(5(0(0(2(x1))))) -> 0(3(0(2(4(5(x1)))))) 3(5(0(4(2(x1))))) -> 2(0(4(4(5(3(x1)))))) 3(5(0(4(2(x1))))) -> 2(5(4(3(0(0(x1)))))) 3(5(3(4(2(x1))))) -> 0(5(4(2(3(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(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) 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). The TRS R consists of the following rules: 0(1(0(2(x1)))) -> 3(0(1(2(0(x1))))) 1(0(0(2(x1)))) -> 2(3(0(0(1(x1))))) 1(0(0(2(x1)))) -> 1(0(1(1(2(0(x1)))))) 1(0(0(2(x1)))) -> 1(3(3(0(2(0(x1)))))) 1(0(0(2(x1)))) -> 3(0(0(1(1(2(x1)))))) 1(0(2(2(x1)))) -> 2(1(2(3(0(x1))))) 1(0(2(2(x1)))) -> 1(1(1(2(2(0(x1)))))) 1(3(4(2(x1)))) -> 1(1(2(3(4(x1))))) 1(3(4(2(x1)))) -> 1(2(3(3(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(4(4(4(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(4(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(5(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(5(5(4(x1)))))) 1(3(5(2(x1)))) -> 2(3(1(0(5(x1))))) 1(3(5(2(x1)))) -> 4(5(1(2(3(x1))))) 3(1(0(2(x1)))) -> 3(0(1(2(0(x1))))) 3(4(0(2(x1)))) -> 3(0(0(2(4(x1))))) 3(4(0(2(x1)))) -> 3(0(1(2(4(x1))))) 3(4(0(2(x1)))) -> 3(0(5(2(4(x1))))) 3(4(0(2(x1)))) -> 3(1(0(2(4(x1))))) 3(4(0(2(x1)))) -> 4(1(2(3(0(x1))))) 3(4(0(2(x1)))) -> 2(0(4(3(3(0(x1)))))) 3(4(0(2(x1)))) -> 3(0(2(1(1(4(x1)))))) 3(4(0(2(x1)))) -> 3(3(0(5(2(4(x1)))))) 3(4(0(2(x1)))) -> 4(2(3(3(3(0(x1)))))) 3(5(0(2(x1)))) -> 3(0(3(2(5(x1))))) 3(5(0(2(x1)))) -> 2(5(3(0(0(0(x1)))))) 3(5(0(2(x1)))) -> 3(0(0(2(5(4(x1)))))) 3(5(0(2(x1)))) -> 5(5(2(3(0(3(x1)))))) 0(2(3(4(2(x1))))) -> 3(0(2(2(4(5(x1)))))) 0(3(4(0(2(x1))))) -> 0(3(1(0(4(2(x1)))))) 0(3(5(0(2(x1))))) -> 2(1(0(5(3(0(x1)))))) 1(0(0(4(2(x1))))) -> 0(4(5(1(0(2(x1)))))) 1(0(3(5(2(x1))))) -> 4(5(3(1(2(0(x1)))))) 1(1(0(2(2(x1))))) -> 1(1(2(0(1(2(x1)))))) 1(3(4(0(2(x1))))) -> 1(2(3(0(1(4(x1)))))) 1(3(5(0(2(x1))))) -> 1(0(2(5(2(3(x1)))))) 3(1(0(0(2(x1))))) -> 3(0(1(2(2(0(x1)))))) 3(1(3(5(2(x1))))) -> 3(0(3(5(1(2(x1)))))) 3(3(4(0(2(x1))))) -> 3(0(0(4(2(3(x1)))))) 3(4(0(0(2(x1))))) -> 3(0(0(4(4(2(x1)))))) 3(4(1(0(2(x1))))) -> 3(1(2(3(0(4(x1)))))) 3(4(1(5(2(x1))))) -> 2(3(0(1(4(5(x1)))))) 3(4(2(0(2(x1))))) -> 3(2(0(4(2(3(x1)))))) 3(4(2(0(2(x1))))) -> 4(2(2(3(0(3(x1)))))) 3(5(0(0(2(x1))))) -> 0(3(0(2(4(5(x1)))))) 3(5(0(4(2(x1))))) -> 2(0(4(4(5(3(x1)))))) 3(5(0(4(2(x1))))) -> 2(5(4(3(0(0(x1)))))) 3(5(3(4(2(x1))))) -> 0(5(4(2(3(3(x1)))))) The (relative) TRS S consists of the following rules: encArg(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) 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(1(0(2(x1)))) -> 3(0(1(2(0(x1))))) 1(0(0(2(x1)))) -> 2(3(0(0(1(x1))))) 1(0(0(2(x1)))) -> 1(0(1(1(2(0(x1)))))) 1(0(0(2(x1)))) -> 1(3(3(0(2(0(x1)))))) 1(0(0(2(x1)))) -> 3(0(0(1(1(2(x1)))))) 1(0(2(2(x1)))) -> 2(1(2(3(0(x1))))) 1(0(2(2(x1)))) -> 1(1(1(2(2(0(x1)))))) 1(3(4(2(x1)))) -> 1(1(2(3(4(x1))))) 1(3(4(2(x1)))) -> 1(2(3(3(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(4(4(4(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(4(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(5(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(5(5(4(x1)))))) 1(3(5(2(x1)))) -> 2(3(1(0(5(x1))))) 1(3(5(2(x1)))) -> 4(5(1(2(3(x1))))) 3(1(0(2(x1)))) -> 3(0(1(2(0(x1))))) 3(4(0(2(x1)))) -> 3(0(0(2(4(x1))))) 3(4(0(2(x1)))) -> 3(0(1(2(4(x1))))) 3(4(0(2(x1)))) -> 3(0(5(2(4(x1))))) 3(4(0(2(x1)))) -> 3(1(0(2(4(x1))))) 3(4(0(2(x1)))) -> 4(1(2(3(0(x1))))) 3(4(0(2(x1)))) -> 2(0(4(3(3(0(x1)))))) 3(4(0(2(x1)))) -> 3(0(2(1(1(4(x1)))))) 3(4(0(2(x1)))) -> 3(3(0(5(2(4(x1)))))) 3(4(0(2(x1)))) -> 4(2(3(3(3(0(x1)))))) 3(5(0(2(x1)))) -> 3(0(3(2(5(x1))))) 3(5(0(2(x1)))) -> 2(5(3(0(0(0(x1)))))) 3(5(0(2(x1)))) -> 3(0(0(2(5(4(x1)))))) 3(5(0(2(x1)))) -> 5(5(2(3(0(3(x1)))))) 0(2(3(4(2(x1))))) -> 3(0(2(2(4(5(x1)))))) 0(3(4(0(2(x1))))) -> 0(3(1(0(4(2(x1)))))) 0(3(5(0(2(x1))))) -> 2(1(0(5(3(0(x1)))))) 1(0(0(4(2(x1))))) -> 0(4(5(1(0(2(x1)))))) 1(0(3(5(2(x1))))) -> 4(5(3(1(2(0(x1)))))) 1(1(0(2(2(x1))))) -> 1(1(2(0(1(2(x1)))))) 1(3(4(0(2(x1))))) -> 1(2(3(0(1(4(x1)))))) 1(3(5(0(2(x1))))) -> 1(0(2(5(2(3(x1)))))) 3(1(0(0(2(x1))))) -> 3(0(1(2(2(0(x1)))))) 3(1(3(5(2(x1))))) -> 3(0(3(5(1(2(x1)))))) 3(3(4(0(2(x1))))) -> 3(0(0(4(2(3(x1)))))) 3(4(0(0(2(x1))))) -> 3(0(0(4(4(2(x1)))))) 3(4(1(0(2(x1))))) -> 3(1(2(3(0(4(x1)))))) 3(4(1(5(2(x1))))) -> 2(3(0(1(4(5(x1)))))) 3(4(2(0(2(x1))))) -> 3(2(0(4(2(3(x1)))))) 3(4(2(0(2(x1))))) -> 4(2(2(3(0(3(x1)))))) 3(5(0(0(2(x1))))) -> 0(3(0(2(4(5(x1)))))) 3(5(0(4(2(x1))))) -> 2(0(4(4(5(3(x1)))))) 3(5(0(4(2(x1))))) -> 2(5(4(3(0(0(x1)))))) 3(5(3(4(2(x1))))) -> 0(5(4(2(3(3(x1)))))) The (relative) TRS S consists of the following rules: encArg(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) 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). The TRS R consists of the following rules: 0(1(0(2(x1)))) -> 3(0(1(2(0(x1))))) 1(0(0(2(x1)))) -> 2(3(0(0(1(x1))))) 1(0(0(2(x1)))) -> 1(0(1(1(2(0(x1)))))) 1(0(0(2(x1)))) -> 1(3(3(0(2(0(x1)))))) 1(0(0(2(x1)))) -> 3(0(0(1(1(2(x1)))))) 1(0(2(2(x1)))) -> 2(1(2(3(0(x1))))) 1(0(2(2(x1)))) -> 1(1(1(2(2(0(x1)))))) 1(3(4(2(x1)))) -> 1(1(2(3(4(x1))))) 1(3(4(2(x1)))) -> 1(2(3(3(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(4(4(4(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(4(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(5(4(5(x1)))))) 1(3(4(2(x1)))) -> 1(2(3(5(5(4(x1)))))) 1(3(5(2(x1)))) -> 2(3(1(0(5(x1))))) 1(3(5(2(x1)))) -> 4(5(1(2(3(x1))))) 3(1(0(2(x1)))) -> 3(0(1(2(0(x1))))) 3(4(0(2(x1)))) -> 3(0(0(2(4(x1))))) 3(4(0(2(x1)))) -> 3(0(1(2(4(x1))))) 3(4(0(2(x1)))) -> 3(0(5(2(4(x1))))) 3(4(0(2(x1)))) -> 3(1(0(2(4(x1))))) 3(4(0(2(x1)))) -> 4(1(2(3(0(x1))))) 3(4(0(2(x1)))) -> 2(0(4(3(3(0(x1)))))) 3(4(0(2(x1)))) -> 3(0(2(1(1(4(x1)))))) 3(4(0(2(x1)))) -> 3(3(0(5(2(4(x1)))))) 3(4(0(2(x1)))) -> 4(2(3(3(3(0(x1)))))) 3(5(0(2(x1)))) -> 3(0(3(2(5(x1))))) 3(5(0(2(x1)))) -> 2(5(3(0(0(0(x1)))))) 3(5(0(2(x1)))) -> 3(0(0(2(5(4(x1)))))) 3(5(0(2(x1)))) -> 5(5(2(3(0(3(x1)))))) 0(2(3(4(2(x1))))) -> 3(0(2(2(4(5(x1)))))) 0(3(4(0(2(x1))))) -> 0(3(1(0(4(2(x1)))))) 0(3(5(0(2(x1))))) -> 2(1(0(5(3(0(x1)))))) 1(0(0(4(2(x1))))) -> 0(4(5(1(0(2(x1)))))) 1(0(3(5(2(x1))))) -> 4(5(3(1(2(0(x1)))))) 1(1(0(2(2(x1))))) -> 1(1(2(0(1(2(x1)))))) 1(3(4(0(2(x1))))) -> 1(2(3(0(1(4(x1)))))) 1(3(5(0(2(x1))))) -> 1(0(2(5(2(3(x1)))))) 3(1(0(0(2(x1))))) -> 3(0(1(2(2(0(x1)))))) 3(1(3(5(2(x1))))) -> 3(0(3(5(1(2(x1)))))) 3(3(4(0(2(x1))))) -> 3(0(0(4(2(3(x1)))))) 3(4(0(0(2(x1))))) -> 3(0(0(4(4(2(x1)))))) 3(4(1(0(2(x1))))) -> 3(1(2(3(0(4(x1)))))) 3(4(1(5(2(x1))))) -> 2(3(0(1(4(5(x1)))))) 3(4(2(0(2(x1))))) -> 3(2(0(4(2(3(x1)))))) 3(4(2(0(2(x1))))) -> 4(2(2(3(0(3(x1)))))) 3(5(0(0(2(x1))))) -> 0(3(0(2(4(5(x1)))))) 3(5(0(4(2(x1))))) -> 2(0(4(4(5(3(x1)))))) 3(5(0(4(2(x1))))) -> 2(5(4(3(0(0(x1)))))) 3(5(3(4(2(x1))))) -> 0(5(4(2(3(3(x1)))))) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) 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 3. The certificate found is represented by the following graph. "[57, 58, 59, 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] {(57,58,[0_1|0, 1_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]), (57,59,[2_1|1, 4_1|1, 5_1|1, 0_1|1, 1_1|1, 3_1|1]), (57,60,[3_1|2]), (57,64,[3_1|2]), (57,69,[0_1|2]), (57,74,[2_1|2]), (57,79,[2_1|2]), (57,83,[1_1|2]), (57,88,[1_1|2]), (57,93,[3_1|2]), (57,98,[0_1|2]), (57,103,[2_1|2]), (57,107,[1_1|2]), (57,112,[4_1|2]), (57,117,[1_1|2]), (57,121,[1_1|2]), (57,126,[1_1|2]), (57,131,[1_1|2]), (57,136,[1_1|2]), (57,141,[1_1|2]), (57,146,[1_1|2]), (57,151,[2_1|2]), (57,155,[4_1|2]), (57,159,[1_1|2]), (57,164,[1_1|2]), (57,169,[3_1|2]), (57,174,[3_1|2]), (57,179,[3_1|2]), (57,183,[3_1|2]), (57,187,[3_1|2]), (57,191,[3_1|2]), (57,195,[4_1|2]), (57,199,[2_1|2]), 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(59,199,[2_1|2]), (59,204,[3_1|2]), (59,209,[3_1|2]), (59,214,[4_1|2]), (59,219,[3_1|2]), (59,224,[3_1|2]), (59,229,[2_1|2]), (59,234,[3_1|2]), (59,239,[4_1|2]), (59,244,[3_1|2]), (59,248,[2_1|2]), (59,253,[3_1|2]), (59,258,[5_1|2]), (59,263,[0_1|2]), (59,268,[2_1|2]), (59,273,[2_1|2]), (59,278,[0_1|2]), (59,283,[3_1|2]), (59,288,[3_1|3]), (60,61,[0_1|2]), (61,62,[1_1|2]), (62,63,[2_1|2]), (63,59,[0_1|2]), (63,74,[0_1|2, 2_1|2]), (63,79,[0_1|2]), (63,103,[0_1|2]), (63,151,[0_1|2]), (63,199,[0_1|2]), (63,229,[0_1|2]), (63,248,[0_1|2]), (63,268,[0_1|2]), (63,273,[0_1|2]), (63,161,[0_1|2]), (63,60,[3_1|2]), (63,64,[3_1|2]), (63,69,[0_1|2]), (63,292,[3_1|3]), (64,65,[0_1|2]), (65,66,[2_1|2]), (66,67,[2_1|2]), (67,68,[4_1|2]), (68,59,[5_1|2]), (68,74,[5_1|2]), (68,79,[5_1|2]), (68,103,[5_1|2]), (68,151,[5_1|2]), (68,199,[5_1|2]), (68,229,[5_1|2]), (68,248,[5_1|2]), (68,268,[5_1|2]), (68,273,[5_1|2]), (68,215,[5_1|2]), (68,240,[5_1|2]), (69,70,[3_1|2]), (70,71,[1_1|2]), (71,72,[0_1|2]), 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(111,64,[3_1|2]), (111,69,[0_1|2]), (111,292,[3_1|3]), (112,113,[5_1|2]), (113,114,[3_1|2]), (114,115,[1_1|2]), (115,116,[2_1|2]), (116,59,[0_1|2]), (116,74,[0_1|2, 2_1|2]), (116,79,[0_1|2]), (116,103,[0_1|2]), (116,151,[0_1|2]), (116,199,[0_1|2]), (116,229,[0_1|2]), (116,248,[0_1|2]), (116,268,[0_1|2]), (116,273,[0_1|2]), (116,60,[3_1|2]), (116,64,[3_1|2]), (116,69,[0_1|2]), (116,292,[3_1|3]), (117,118,[1_1|2]), (118,119,[2_1|2]), (119,120,[3_1|2]), (119,179,[3_1|2]), (119,183,[3_1|2]), (119,187,[3_1|2]), (119,191,[3_1|2]), (119,195,[4_1|2]), (119,199,[2_1|2]), (119,204,[3_1|2]), (119,209,[3_1|2]), (119,214,[4_1|2]), (119,219,[3_1|2]), (119,224,[3_1|2]), (119,229,[2_1|2]), (119,234,[3_1|2]), (119,239,[4_1|2]), (119,305,[3_1|3]), (119,288,[3_1|3]), (120,59,[4_1|2]), (120,74,[4_1|2]), (120,79,[4_1|2]), (120,103,[4_1|2]), (120,151,[4_1|2]), (120,199,[4_1|2]), (120,229,[4_1|2]), (120,248,[4_1|2]), (120,268,[4_1|2]), (120,273,[4_1|2]), (120,215,[4_1|2]), (120,240,[4_1|2]), 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(190,248,[4_1|2]), (190,268,[4_1|2]), (190,273,[4_1|2]), (191,192,[1_1|2]), (192,193,[0_1|2]), (193,194,[2_1|2]), (194,59,[4_1|2]), (194,74,[4_1|2]), (194,79,[4_1|2]), (194,103,[4_1|2]), (194,151,[4_1|2]), (194,199,[4_1|2]), (194,229,[4_1|2]), (194,248,[4_1|2]), (194,268,[4_1|2]), (194,273,[4_1|2]), (195,196,[1_1|2]), (196,197,[2_1|2]), (197,198,[3_1|2]), (198,59,[0_1|2]), (198,74,[0_1|2, 2_1|2]), (198,79,[0_1|2]), (198,103,[0_1|2]), (198,151,[0_1|2]), (198,199,[0_1|2]), (198,229,[0_1|2]), (198,248,[0_1|2]), (198,268,[0_1|2]), (198,273,[0_1|2]), (198,60,[3_1|2]), (198,64,[3_1|2]), (198,69,[0_1|2]), (198,292,[3_1|3]), (199,200,[0_1|2]), (200,201,[4_1|2]), (201,202,[3_1|2]), (202,203,[3_1|2]), (203,59,[0_1|2]), (203,74,[0_1|2, 2_1|2]), (203,79,[0_1|2]), (203,103,[0_1|2]), (203,151,[0_1|2]), (203,199,[0_1|2]), (203,229,[0_1|2]), (203,248,[0_1|2]), (203,268,[0_1|2]), (203,273,[0_1|2]), (203,60,[3_1|2]), (203,64,[3_1|2]), (203,69,[0_1|2]), (203,292,[3_1|3]), (204,205,[0_1|2]), (205,206,[2_1|2]), (206,207,[1_1|2]), (207,208,[1_1|2]), (208,59,[4_1|2]), (208,74,[4_1|2]), (208,79,[4_1|2]), (208,103,[4_1|2]), (208,151,[4_1|2]), (208,199,[4_1|2]), (208,229,[4_1|2]), (208,248,[4_1|2]), (208,268,[4_1|2]), (208,273,[4_1|2]), (209,210,[3_1|2]), (210,211,[0_1|2]), (211,212,[5_1|2]), (212,213,[2_1|2]), (213,59,[4_1|2]), (213,74,[4_1|2]), (213,79,[4_1|2]), (213,103,[4_1|2]), (213,151,[4_1|2]), (213,199,[4_1|2]), (213,229,[4_1|2]), (213,248,[4_1|2]), (213,268,[4_1|2]), (213,273,[4_1|2]), (214,215,[2_1|2]), (215,216,[3_1|2]), (216,217,[3_1|2]), (217,218,[3_1|2]), (218,59,[0_1|2]), (218,74,[0_1|2, 2_1|2]), (218,79,[0_1|2]), (218,103,[0_1|2]), (218,151,[0_1|2]), (218,199,[0_1|2]), (218,229,[0_1|2]), (218,248,[0_1|2]), (218,268,[0_1|2]), (218,273,[0_1|2]), (218,60,[3_1|2]), (218,64,[3_1|2]), (218,69,[0_1|2]), (218,292,[3_1|3]), (219,220,[0_1|2]), (220,221,[0_1|2]), (221,222,[4_1|2]), (222,223,[4_1|2]), (223,59,[2_1|2]), (223,74,[2_1|2]), (223,79,[2_1|2]), (223,103,[2_1|2]), (223,151,[2_1|2]), (223,199,[2_1|2]), (223,229,[2_1|2]), (223,248,[2_1|2]), (223,268,[2_1|2]), (223,273,[2_1|2]), (224,225,[1_1|2]), (225,226,[2_1|2]), (226,227,[3_1|2]), (227,228,[0_1|2]), (228,59,[4_1|2]), (228,74,[4_1|2]), (228,79,[4_1|2]), (228,103,[4_1|2]), (228,151,[4_1|2]), (228,199,[4_1|2]), (228,229,[4_1|2]), (228,248,[4_1|2]), (228,268,[4_1|2]), (228,273,[4_1|2]), (228,161,[4_1|2]), (229,230,[3_1|2]), (230,231,[0_1|2]), (231,232,[1_1|2]), (232,233,[4_1|2]), (233,59,[5_1|2]), (233,74,[5_1|2]), (233,79,[5_1|2]), (233,103,[5_1|2]), (233,151,[5_1|2]), (233,199,[5_1|2]), (233,229,[5_1|2]), (233,248,[5_1|2]), (233,268,[5_1|2]), (233,273,[5_1|2]), (234,235,[2_1|2]), (235,236,[0_1|2]), (236,237,[4_1|2]), (237,238,[2_1|2]), (238,59,[3_1|2]), (238,74,[3_1|2]), (238,79,[3_1|2]), (238,103,[3_1|2]), (238,151,[3_1|2]), (238,199,[3_1|2, 2_1|2]), (238,229,[3_1|2, 2_1|2]), (238,248,[3_1|2, 2_1|2]), (238,268,[3_1|2, 2_1|2]), (238,273,[3_1|2, 2_1|2]), (238,310,[3_1|2]), (238,169,[3_1|2]), (238,174,[3_1|2]), (238,179,[3_1|2]), (238,183,[3_1|2]), (238,187,[3_1|2]), (238,191,[3_1|2]), (238,195,[4_1|2]), (238,204,[3_1|2]), (238,209,[3_1|2]), (238,214,[4_1|2]), (238,219,[3_1|2]), (238,224,[3_1|2]), (238,234,[3_1|2]), (238,239,[4_1|2]), (238,244,[3_1|2]), (238,253,[3_1|2]), (238,258,[5_1|2]), (238,263,[0_1|2]), (238,278,[0_1|2]), (238,283,[3_1|2]), (238,314,[3_1|3]), (239,240,[2_1|2]), (240,241,[2_1|2]), (241,242,[3_1|2]), (242,243,[0_1|2]), (242,69,[0_1|2]), (242,74,[2_1|2]), (243,59,[3_1|2]), (243,74,[3_1|2]), (243,79,[3_1|2]), (243,103,[3_1|2]), (243,151,[3_1|2]), (243,199,[3_1|2, 2_1|2]), (243,229,[3_1|2, 2_1|2]), (243,248,[3_1|2, 2_1|2]), (243,268,[3_1|2, 2_1|2]), (243,273,[3_1|2, 2_1|2]), (243,310,[3_1|2]), (243,169,[3_1|2]), (243,174,[3_1|2]), (243,179,[3_1|2]), (243,183,[3_1|2]), (243,187,[3_1|2]), (243,191,[3_1|2]), (243,195,[4_1|2]), (243,204,[3_1|2]), (243,209,[3_1|2]), (243,214,[4_1|2]), (243,219,[3_1|2]), (243,224,[3_1|2]), (243,234,[3_1|2]), (243,239,[4_1|2]), (243,244,[3_1|2]), (243,253,[3_1|2]), (243,258,[5_1|2]), (243,263,[0_1|2]), (243,278,[0_1|2]), (243,283,[3_1|2]), (243,314,[3_1|3]), (244,245,[0_1|2]), (245,246,[3_1|2]), (246,247,[2_1|2]), (247,59,[5_1|2]), (247,74,[5_1|2]), (247,79,[5_1|2]), (247,103,[5_1|2]), (247,151,[5_1|2]), (247,199,[5_1|2]), (247,229,[5_1|2]), (247,248,[5_1|2]), (247,268,[5_1|2]), (247,273,[5_1|2]), (248,249,[5_1|2]), (249,250,[3_1|2]), (250,251,[0_1|2]), (251,252,[0_1|2]), (252,59,[0_1|2]), (252,74,[0_1|2, 2_1|2]), (252,79,[0_1|2]), (252,103,[0_1|2]), (252,151,[0_1|2]), (252,199,[0_1|2]), (252,229,[0_1|2]), (252,248,[0_1|2]), (252,268,[0_1|2]), (252,273,[0_1|2]), (252,60,[3_1|2]), (252,64,[3_1|2]), (252,69,[0_1|2]), (252,292,[3_1|3]), (253,254,[0_1|2]), (254,255,[0_1|2]), (255,256,[2_1|2]), (256,257,[5_1|2]), (257,59,[4_1|2]), (257,74,[4_1|2]), (257,79,[4_1|2]), (257,103,[4_1|2]), (257,151,[4_1|2]), (257,199,[4_1|2]), (257,229,[4_1|2]), (257,248,[4_1|2]), (257,268,[4_1|2]), (257,273,[4_1|2]), (258,259,[5_1|2]), (259,260,[2_1|2]), (260,261,[3_1|2]), (261,262,[0_1|2]), (261,69,[0_1|2]), (261,74,[2_1|2]), (262,59,[3_1|2]), (262,74,[3_1|2]), (262,79,[3_1|2]), (262,103,[3_1|2]), (262,151,[3_1|2]), (262,199,[3_1|2, 2_1|2]), (262,229,[3_1|2, 2_1|2]), (262,248,[3_1|2, 2_1|2]), (262,268,[3_1|2, 2_1|2]), (262,273,[3_1|2, 2_1|2]), (262,310,[3_1|2]), (262,169,[3_1|2]), (262,174,[3_1|2]), (262,179,[3_1|2]), (262,183,[3_1|2]), (262,187,[3_1|2]), (262,191,[3_1|2]), (262,195,[4_1|2]), (262,204,[3_1|2]), (262,209,[3_1|2]), (262,214,[4_1|2]), (262,219,[3_1|2]), (262,224,[3_1|2]), (262,234,[3_1|2]), (262,239,[4_1|2]), (262,244,[3_1|2]), (262,253,[3_1|2]), (262,258,[5_1|2]), (262,263,[0_1|2]), (262,278,[0_1|2]), (262,283,[3_1|2]), (262,314,[3_1|3]), (263,264,[3_1|2]), (264,265,[0_1|2]), (265,266,[2_1|2]), (266,267,[4_1|2]), (267,59,[5_1|2]), (267,74,[5_1|2]), (267,79,[5_1|2]), (267,103,[5_1|2]), (267,151,[5_1|2]), (267,199,[5_1|2]), (267,229,[5_1|2]), (267,248,[5_1|2]), (267,268,[5_1|2]), (267,273,[5_1|2]), (268,269,[0_1|2]), (269,270,[4_1|2]), (270,271,[4_1|2]), (271,272,[5_1|2]), (272,59,[3_1|2]), (272,74,[3_1|2]), (272,79,[3_1|2]), (272,103,[3_1|2]), (272,151,[3_1|2]), (272,199,[3_1|2, 2_1|2]), (272,229,[3_1|2, 2_1|2]), (272,248,[3_1|2, 2_1|2]), (272,268,[3_1|2, 2_1|2]), (272,273,[3_1|2, 2_1|2]), (272,215,[3_1|2]), (272,240,[3_1|2]), (272,310,[3_1|2]), (272,169,[3_1|2]), (272,174,[3_1|2]), (272,179,[3_1|2]), (272,183,[3_1|2]), (272,187,[3_1|2]), (272,191,[3_1|2]), (272,195,[4_1|2]), (272,204,[3_1|2]), (272,209,[3_1|2]), (272,214,[4_1|2]), (272,219,[3_1|2]), (272,224,[3_1|2]), (272,234,[3_1|2]), (272,239,[4_1|2]), (272,244,[3_1|2]), (272,253,[3_1|2]), (272,258,[5_1|2]), (272,263,[0_1|2]), (272,278,[0_1|2]), (272,283,[3_1|2]), (272,314,[3_1|3]), (273,274,[5_1|2]), (274,275,[4_1|2]), (275,276,[3_1|2]), (276,277,[0_1|2]), (277,59,[0_1|2]), (277,74,[0_1|2, 2_1|2]), (277,79,[0_1|2]), (277,103,[0_1|2]), (277,151,[0_1|2]), (277,199,[0_1|2]), (277,229,[0_1|2]), (277,248,[0_1|2]), (277,268,[0_1|2]), (277,273,[0_1|2]), (277,215,[0_1|2]), (277,240,[0_1|2]), (277,60,[3_1|2]), (277,64,[3_1|2]), (277,69,[0_1|2]), (277,292,[3_1|3]), (278,279,[5_1|2]), (279,280,[4_1|2]), (280,281,[2_1|2]), (281,282,[3_1|2]), (281,283,[3_1|2]), (282,59,[3_1|2]), (282,74,[3_1|2]), (282,79,[3_1|2]), (282,103,[3_1|2]), (282,151,[3_1|2]), (282,199,[3_1|2, 2_1|2]), (282,229,[3_1|2, 2_1|2]), (282,248,[3_1|2, 2_1|2]), (282,268,[3_1|2, 2_1|2]), (282,273,[3_1|2, 2_1|2]), (282,215,[3_1|2]), (282,240,[3_1|2]), (282,310,[3_1|2]), (282,169,[3_1|2]), (282,174,[3_1|2]), (282,179,[3_1|2]), (282,183,[3_1|2]), (282,187,[3_1|2]), (282,191,[3_1|2]), (282,195,[4_1|2]), (282,204,[3_1|2]), (282,209,[3_1|2]), (282,214,[4_1|2]), (282,219,[3_1|2]), (282,224,[3_1|2]), (282,234,[3_1|2]), (282,239,[4_1|2]), (282,244,[3_1|2]), (282,253,[3_1|2]), (282,258,[5_1|2]), (282,263,[0_1|2]), (282,278,[0_1|2]), (282,283,[3_1|2]), (282,314,[3_1|3]), (283,284,[0_1|2]), (284,285,[0_1|2]), (285,286,[4_1|2]), (286,287,[2_1|2]), (287,59,[3_1|2]), (287,74,[3_1|2]), (287,79,[3_1|2]), (287,103,[3_1|2]), (287,151,[3_1|2]), (287,199,[3_1|2, 2_1|2]), (287,229,[3_1|2, 2_1|2]), (287,248,[3_1|2, 2_1|2]), (287,268,[3_1|2, 2_1|2]), (287,273,[3_1|2, 2_1|2]), (287,310,[3_1|2]), (287,169,[3_1|2]), (287,174,[3_1|2]), (287,179,[3_1|2]), (287,183,[3_1|2]), (287,187,[3_1|2]), (287,191,[3_1|2]), (287,195,[4_1|2]), (287,204,[3_1|2]), (287,209,[3_1|2]), (287,214,[4_1|2]), (287,219,[3_1|2]), (287,224,[3_1|2]), (287,234,[3_1|2]), (287,239,[4_1|2]), (287,244,[3_1|2]), (287,253,[3_1|2]), (287,258,[5_1|2]), (287,263,[0_1|2]), (287,278,[0_1|2]), (287,283,[3_1|2]), (287,314,[3_1|3]), (288,289,[0_1|3]), (289,290,[1_1|3]), (290,291,[2_1|3]), (291,194,[0_1|3]), (292,293,[0_1|3]), (293,294,[1_1|3]), (294,295,[2_1|3]), (295,161,[0_1|3]), (296,297,[1_1|3]), (297,298,[2_1|3]), (298,299,[3_1|3]), (299,74,[0_1|3]), (299,79,[0_1|3]), (299,103,[0_1|3]), (299,151,[0_1|3]), (299,199,[0_1|3]), (299,229,[0_1|3]), (299,248,[0_1|3]), (299,268,[0_1|3]), (299,273,[0_1|3]), (299,241,[0_1|3]), (300,301,[1_1|3]), (301,302,[1_1|3]), (302,303,[2_1|3]), (303,304,[2_1|3]), (304,74,[0_1|3]), (304,79,[0_1|3]), (304,103,[0_1|3]), (304,151,[0_1|3]), (304,199,[0_1|3]), (304,229,[0_1|3]), (304,248,[0_1|3]), (304,268,[0_1|3]), (304,273,[0_1|3]), (304,241,[0_1|3]), (305,306,[1_1|3]), (306,307,[2_1|3]), (307,308,[3_1|3]), (308,309,[0_1|3]), (309,161,[4_1|3]), (310,311,[0_1|2]), (311,312,[1_1|2]), (312,313,[2_1|2]), (313,59,[0_1|2]), (313,74,[0_1|2, 2_1|2]), (313,79,[0_1|2]), (313,103,[0_1|2]), (313,151,[0_1|2]), (313,199,[0_1|2]), (313,229,[0_1|2]), (313,248,[0_1|2]), (313,268,[0_1|2]), (313,273,[0_1|2]), (313,60,[3_1|2]), (313,64,[3_1|2]), (313,69,[0_1|2]), (313,292,[3_1|3]), (314,315,[0_1|3]), (315,316,[1_1|3]), (316,317,[2_1|3]), (317,161,[0_1|3]), (317,194,[0_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)