/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 33 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 100 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(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: 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(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 (full) 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: 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(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: 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(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: 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. "[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] {(71,72,[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]), (71,73,[2_1|1, 3_1|1, 0_1|1, 1_1|1, 4_1|1, 5_1|1]), (71,74,[2_1|2]), (71,78,[2_1|2]), (71,82,[2_1|2]), (71,86,[2_1|2]), (71,90,[2_1|2]), (71,94,[2_1|2]), (71,98,[2_1|2]), (71,102,[2_1|2]), (71,107,[2_1|2]), (71,112,[2_1|2]), (71,117,[2_1|2]), (71,122,[2_1|2]), (71,127,[2_1|2]), (71,132,[2_1|2]), (71,137,[2_1|2]), (71,142,[2_1|2]), (71,147,[3_1|2]), (71,152,[0_1|2]), (71,157,[1_1|2]), (71,162,[2_1|2]), (71,166,[2_1|2]), (71,171,[2_1|2]), (71,176,[0_1|2]), (71,181,[2_1|2]), (71,186,[0_1|2]), (71,191,[3_1|2]), (71,196,[0_1|2]), (71,201,[5_1|2]), (71,206,[5_1|2]), (71,211,[0_1|2]), (71,216,[1_1|2]), (71,221,[1_1|2]), (71,226,[5_1|2]), (71,231,[2_1|2]), (71,236,[4_1|2]), (71,241,[3_1|2]), (71,246,[3_1|2]), 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(111,73,[1_1|2]), (111,147,[1_1|2]), (111,191,[1_1|2]), (111,241,[1_1|2]), (111,246,[1_1|2]), (111,296,[1_1|2]), (111,99,[1_1|2]), (111,211,[0_1|2]), (111,216,[1_1|2]), (111,221,[1_1|2]), (111,226,[5_1|2]), (112,113,[1_1|2]), (113,114,[3_1|2]), (114,115,[0_1|2]), (115,116,[3_1|2]), (116,73,[0_1|2]), (116,147,[0_1|2, 3_1|2]), (116,191,[0_1|2, 3_1|2]), (116,241,[0_1|2]), (116,246,[0_1|2]), (116,296,[0_1|2]), (116,99,[0_1|2]), (116,74,[2_1|2]), (116,78,[2_1|2]), (116,82,[2_1|2]), (116,86,[2_1|2]), (116,90,[2_1|2]), (116,94,[2_1|2]), (116,98,[2_1|2]), (116,102,[2_1|2]), (116,107,[2_1|2]), (116,112,[2_1|2]), (116,117,[2_1|2]), (116,122,[2_1|2]), (116,127,[2_1|2]), (116,132,[2_1|2]), (116,137,[2_1|2]), (116,142,[2_1|2]), (116,152,[0_1|2]), (116,157,[1_1|2]), (116,162,[2_1|2]), (116,166,[2_1|2]), (116,171,[2_1|2]), (116,301,[2_1|2]), (116,176,[0_1|2]), (116,181,[2_1|2]), (116,186,[0_1|2]), (116,196,[0_1|2]), (116,201,[5_1|2]), (116,206,[5_1|2]), (117,118,[0_1|2]), (118,119,[3_1|2]), 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(136,296,[0_1|2]), (136,74,[2_1|2]), (136,78,[2_1|2]), (136,82,[2_1|2]), (136,86,[2_1|2]), (136,90,[2_1|2]), (136,94,[2_1|2]), (136,98,[2_1|2]), (136,102,[2_1|2]), (136,107,[2_1|2]), (136,112,[2_1|2]), (136,117,[2_1|2]), (136,122,[2_1|2]), (136,127,[2_1|2]), (136,132,[2_1|2]), (136,137,[2_1|2]), (136,142,[2_1|2]), (136,152,[0_1|2]), (136,157,[1_1|2]), (136,162,[2_1|2]), (136,166,[2_1|2]), (136,171,[2_1|2]), (136,301,[2_1|2]), (136,176,[0_1|2]), (136,181,[2_1|2]), (136,186,[0_1|2]), (136,196,[0_1|2]), (136,201,[5_1|2]), (136,206,[5_1|2]), (137,138,[1_1|2]), (138,139,[0_1|2]), (139,140,[3_1|2]), (140,141,[3_1|2]), (141,73,[5_1|2]), (141,147,[5_1|2]), (141,191,[5_1|2]), (141,241,[5_1|2, 3_1|2]), (141,246,[5_1|2, 3_1|2]), (141,296,[5_1|2, 3_1|2]), (141,251,[4_1|2]), (141,256,[5_1|2]), (141,261,[5_1|2]), (141,266,[0_1|2]), (141,271,[0_1|2]), (141,276,[2_1|2]), (141,281,[5_1|2]), (141,286,[5_1|2]), (141,291,[2_1|2]), (142,143,[1_1|2]), (143,144,[0_1|2]), (144,145,[3_1|2]), (145,146,[4_1|2]), 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(167,168,[0_1|2]), (168,169,[3_1|2]), (169,170,[5_1|2]), (169,286,[5_1|2]), (169,291,[2_1|2]), (169,296,[3_1|2]), (170,73,[3_1|2]), (170,147,[3_1|2]), (170,191,[3_1|2]), (170,241,[3_1|2]), (170,246,[3_1|2]), (170,296,[3_1|2]), (170,99,[3_1|2]), (171,172,[0_1|2]), (172,173,[3_1|2]), (173,174,[4_1|2]), (174,175,[5_1|2]), (175,73,[1_1|2]), (175,147,[1_1|2]), (175,191,[1_1|2]), (175,241,[1_1|2]), (175,246,[1_1|2]), (175,296,[1_1|2]), (175,99,[1_1|2]), (175,211,[0_1|2]), (175,216,[1_1|2]), (175,221,[1_1|2]), (175,226,[5_1|2]), (176,177,[2_1|2]), (177,178,[0_1|2]), (178,179,[3_1|2]), (179,180,[1_1|2]), (179,211,[0_1|2]), (179,216,[1_1|2]), (179,221,[1_1|2]), (180,73,[0_1|2]), (180,147,[0_1|2, 3_1|2]), (180,191,[0_1|2, 3_1|2]), (180,241,[0_1|2]), (180,246,[0_1|2]), (180,296,[0_1|2]), (180,99,[0_1|2]), (180,74,[2_1|2]), (180,78,[2_1|2]), (180,82,[2_1|2]), (180,86,[2_1|2]), (180,90,[2_1|2]), (180,94,[2_1|2]), (180,98,[2_1|2]), (180,102,[2_1|2]), (180,107,[2_1|2]), (180,112,[2_1|2]), (180,117,[2_1|2]), (180,122,[2_1|2]), (180,127,[2_1|2]), (180,132,[2_1|2]), (180,137,[2_1|2]), (180,142,[2_1|2]), (180,152,[0_1|2]), (180,157,[1_1|2]), (180,162,[2_1|2]), (180,166,[2_1|2]), (180,171,[2_1|2]), (180,301,[2_1|2]), (180,176,[0_1|2]), (180,181,[2_1|2]), (180,186,[0_1|2]), (180,196,[0_1|2]), (180,201,[5_1|2]), (180,206,[5_1|2]), (181,182,[1_1|2]), (182,183,[1_1|2]), (183,184,[3_1|2]), (184,185,[0_1|2]), (184,176,[0_1|2]), (184,181,[2_1|2]), (184,186,[0_1|2]), (184,191,[3_1|2]), (184,196,[0_1|2]), (185,73,[0_1|2]), (185,147,[0_1|2, 3_1|2]), (185,191,[0_1|2, 3_1|2]), (185,241,[0_1|2]), (185,246,[0_1|2]), (185,296,[0_1|2]), (185,99,[0_1|2]), (185,74,[2_1|2]), (185,78,[2_1|2]), (185,82,[2_1|2]), (185,86,[2_1|2]), (185,90,[2_1|2]), (185,94,[2_1|2]), (185,98,[2_1|2]), (185,102,[2_1|2]), (185,107,[2_1|2]), (185,112,[2_1|2]), (185,117,[2_1|2]), (185,122,[2_1|2]), (185,127,[2_1|2]), (185,132,[2_1|2]), (185,137,[2_1|2]), (185,142,[2_1|2]), (185,152,[0_1|2]), (185,157,[1_1|2]), (185,162,[2_1|2]), (185,166,[2_1|2]), (185,171,[2_1|2]), (185,301,[2_1|2]), (185,176,[0_1|2]), (185,181,[2_1|2]), (185,186,[0_1|2]), (185,196,[0_1|2]), (185,201,[5_1|2]), (185,206,[5_1|2]), (186,187,[3_1|2]), (187,188,[4_1|2]), (188,189,[0_1|2]), (189,190,[3_1|2]), (190,73,[2_1|2]), (190,147,[2_1|2]), (190,191,[2_1|2]), (190,241,[2_1|2]), (190,246,[2_1|2]), (190,296,[2_1|2]), (190,99,[2_1|2]), (191,192,[0_1|2]), (192,193,[0_1|2]), (193,194,[2_1|2]), (194,195,[4_1|2]), (195,73,[4_1|2]), (195,147,[4_1|2]), (195,191,[4_1|2]), (195,241,[4_1|2]), (195,246,[4_1|2]), (195,296,[4_1|2]), (195,99,[4_1|2]), (195,231,[2_1|2]), (195,236,[4_1|2]), (196,197,[3_1|2]), (197,198,[5_1|2]), (198,199,[2_1|2]), (199,200,[4_1|2]), (199,231,[2_1|2]), (199,236,[4_1|2]), (200,73,[0_1|2]), (200,147,[0_1|2, 3_1|2]), (200,191,[0_1|2, 3_1|2]), (200,241,[0_1|2]), (200,246,[0_1|2]), (200,296,[0_1|2]), (200,99,[0_1|2]), (200,74,[2_1|2]), (200,78,[2_1|2]), (200,82,[2_1|2]), (200,86,[2_1|2]), (200,90,[2_1|2]), (200,94,[2_1|2]), (200,98,[2_1|2]), (200,102,[2_1|2]), (200,107,[2_1|2]), (200,112,[2_1|2]), (200,117,[2_1|2]), (200,122,[2_1|2]), (200,127,[2_1|2]), (200,132,[2_1|2]), (200,137,[2_1|2]), (200,142,[2_1|2]), (200,152,[0_1|2]), (200,157,[1_1|2]), (200,162,[2_1|2]), (200,166,[2_1|2]), (200,171,[2_1|2]), (200,301,[2_1|2]), (200,176,[0_1|2]), (200,181,[2_1|2]), (200,186,[0_1|2]), (200,196,[0_1|2]), (200,201,[5_1|2]), (200,206,[5_1|2]), (201,202,[0_1|2]), (202,203,[3_1|2]), (203,204,[4_1|2]), (204,205,[1_1|2]), (204,226,[5_1|2]), (205,73,[5_1|2]), (205,147,[5_1|2]), (205,191,[5_1|2]), (205,241,[5_1|2, 3_1|2]), (205,246,[5_1|2, 3_1|2]), (205,296,[5_1|2, 3_1|2]), (205,288,[5_1|2]), (205,251,[4_1|2]), (205,256,[5_1|2]), (205,261,[5_1|2]), (205,266,[0_1|2]), (205,271,[0_1|2]), (205,276,[2_1|2]), (205,281,[5_1|2]), (205,286,[5_1|2]), (205,291,[2_1|2]), (206,207,[4_1|2]), (207,208,[0_1|2]), (208,209,[3_1|2]), (209,210,[3_1|2]), (210,73,[5_1|2]), (210,147,[5_1|2]), (210,191,[5_1|2]), (210,241,[5_1|2, 3_1|2]), (210,246,[5_1|2, 3_1|2]), (210,296,[5_1|2, 3_1|2]), (210,288,[5_1|2]), (210,251,[4_1|2]), (210,256,[5_1|2]), (210,261,[5_1|2]), (210,266,[0_1|2]), (210,271,[0_1|2]), (210,276,[2_1|2]), (210,281,[5_1|2]), (210,286,[5_1|2]), (210,291,[2_1|2]), (211,212,[3_1|2]), (212,213,[1_1|2]), (213,214,[3_1|2]), (214,215,[5_1|2]), (214,241,[3_1|2]), (214,246,[3_1|2]), (214,251,[4_1|2]), (214,256,[5_1|2]), (214,261,[5_1|2]), (214,266,[0_1|2]), (214,271,[0_1|2]), (214,276,[2_1|2]), (214,281,[5_1|2]), (215,73,[0_1|2]), (215,147,[0_1|2, 3_1|2]), (215,191,[0_1|2, 3_1|2]), (215,241,[0_1|2]), (215,246,[0_1|2]), (215,296,[0_1|2]), (215,74,[2_1|2]), (215,78,[2_1|2]), (215,82,[2_1|2]), (215,86,[2_1|2]), (215,90,[2_1|2]), (215,94,[2_1|2]), (215,98,[2_1|2]), (215,102,[2_1|2]), (215,107,[2_1|2]), (215,112,[2_1|2]), (215,117,[2_1|2]), (215,122,[2_1|2]), (215,127,[2_1|2]), (215,132,[2_1|2]), (215,137,[2_1|2]), (215,142,[2_1|2]), (215,152,[0_1|2]), (215,157,[1_1|2]), (215,162,[2_1|2]), (215,166,[2_1|2]), (215,171,[2_1|2]), (215,301,[2_1|2]), (215,176,[0_1|2]), (215,181,[2_1|2]), (215,186,[0_1|2]), (215,196,[0_1|2]), (215,201,[5_1|2]), (215,206,[5_1|2]), (216,217,[1_1|2]), (217,218,[1_1|2]), (218,219,[2_1|2]), (219,220,[3_1|2]), (220,73,[0_1|2]), (220,147,[0_1|2, 3_1|2]), (220,191,[0_1|2, 3_1|2]), (220,241,[0_1|2]), (220,246,[0_1|2]), (220,296,[0_1|2]), (220,99,[0_1|2]), (220,74,[2_1|2]), (220,78,[2_1|2]), (220,82,[2_1|2]), (220,86,[2_1|2]), (220,90,[2_1|2]), (220,94,[2_1|2]), (220,98,[2_1|2]), (220,102,[2_1|2]), (220,107,[2_1|2]), (220,112,[2_1|2]), (220,117,[2_1|2]), (220,122,[2_1|2]), (220,127,[2_1|2]), (220,132,[2_1|2]), (220,137,[2_1|2]), (220,142,[2_1|2]), (220,152,[0_1|2]), (220,157,[1_1|2]), (220,162,[2_1|2]), (220,166,[2_1|2]), (220,171,[2_1|2]), (220,301,[2_1|2]), (220,176,[0_1|2]), (220,181,[2_1|2]), (220,186,[0_1|2]), (220,196,[0_1|2]), (220,201,[5_1|2]), (220,206,[5_1|2]), (221,222,[2_1|2]), (222,223,[0_1|2]), (223,224,[3_1|2]), (224,225,[5_1|2]), (225,73,[1_1|2]), (225,147,[1_1|2]), (225,191,[1_1|2]), (225,241,[1_1|2]), (225,246,[1_1|2]), (225,296,[1_1|2]), (225,99,[1_1|2]), (225,211,[0_1|2]), (225,216,[1_1|2]), (225,221,[1_1|2]), (225,226,[5_1|2]), (226,227,[5_1|2]), (227,228,[0_1|2]), (228,229,[3_1|2]), (229,230,[3_1|2]), (230,73,[1_1|2]), (230,147,[1_1|2]), (230,191,[1_1|2]), (230,241,[1_1|2]), (230,246,[1_1|2]), (230,296,[1_1|2]), (230,211,[0_1|2]), (230,216,[1_1|2]), (230,221,[1_1|2]), (230,226,[5_1|2]), (231,232,[1_1|2]), (232,233,[4_1|2]), (233,234,[4_1|2]), (234,235,[0_1|2]), (235,73,[3_1|2]), (235,147,[3_1|2]), (235,191,[3_1|2]), (235,241,[3_1|2]), (235,246,[3_1|2]), (235,296,[3_1|2]), (235,99,[3_1|2]), (236,237,[3_1|2]), (237,238,[2_1|2]), (238,239,[1_1|2]), (238,211,[0_1|2]), (239,240,[0_1|2]), (239,176,[0_1|2]), (239,181,[2_1|2]), (239,186,[0_1|2]), (239,191,[3_1|2]), (239,196,[0_1|2]), (240,73,[0_1|2]), (240,147,[0_1|2, 3_1|2]), (240,191,[0_1|2, 3_1|2]), (240,241,[0_1|2]), (240,246,[0_1|2]), (240,296,[0_1|2]), (240,99,[0_1|2]), (240,74,[2_1|2]), (240,78,[2_1|2]), (240,82,[2_1|2]), (240,86,[2_1|2]), (240,90,[2_1|2]), (240,94,[2_1|2]), (240,98,[2_1|2]), (240,102,[2_1|2]), (240,107,[2_1|2]), (240,112,[2_1|2]), (240,117,[2_1|2]), (240,122,[2_1|2]), (240,127,[2_1|2]), (240,132,[2_1|2]), (240,137,[2_1|2]), (240,142,[2_1|2]), (240,152,[0_1|2]), (240,157,[1_1|2]), (240,162,[2_1|2]), (240,166,[2_1|2]), (240,171,[2_1|2]), (240,301,[2_1|2]), (240,176,[0_1|2]), (240,181,[2_1|2]), (240,186,[0_1|2]), (240,196,[0_1|2]), (240,201,[5_1|2]), (240,206,[5_1|2]), (241,242,[0_1|2]), (242,243,[3_1|2]), (243,244,[5_1|2]), (244,245,[5_1|2]), (244,241,[3_1|2]), (244,246,[3_1|2]), (244,251,[4_1|2]), (244,256,[5_1|2]), (244,261,[5_1|2]), (244,266,[0_1|2]), (244,271,[0_1|2]), (244,276,[2_1|2]), (244,281,[5_1|2]), (245,73,[0_1|2]), (245,147,[0_1|2, 3_1|2]), (245,191,[0_1|2, 3_1|2]), (245,241,[0_1|2]), (245,246,[0_1|2]), (245,296,[0_1|2]), (245,74,[2_1|2]), (245,78,[2_1|2]), (245,82,[2_1|2]), (245,86,[2_1|2]), (245,90,[2_1|2]), (245,94,[2_1|2]), (245,98,[2_1|2]), (245,102,[2_1|2]), (245,107,[2_1|2]), (245,112,[2_1|2]), (245,117,[2_1|2]), (245,122,[2_1|2]), (245,127,[2_1|2]), (245,132,[2_1|2]), (245,137,[2_1|2]), (245,142,[2_1|2]), (245,152,[0_1|2]), (245,157,[1_1|2]), (245,162,[2_1|2]), (245,166,[2_1|2]), (245,171,[2_1|2]), (245,301,[2_1|2]), (245,176,[0_1|2]), (245,181,[2_1|2]), (245,186,[0_1|2]), (245,196,[0_1|2]), (245,201,[5_1|2]), (245,206,[5_1|2]), (246,247,[0_1|2]), (247,248,[3_1|2]), (248,249,[1_1|2]), (249,250,[2_1|2]), (250,73,[5_1|2]), (250,147,[5_1|2]), (250,191,[5_1|2]), (250,241,[5_1|2, 3_1|2]), (250,246,[5_1|2, 3_1|2]), (250,296,[5_1|2, 3_1|2]), (250,99,[5_1|2]), (250,251,[4_1|2]), (250,256,[5_1|2]), (250,261,[5_1|2]), (250,266,[0_1|2]), (250,271,[0_1|2]), (250,276,[2_1|2]), (250,281,[5_1|2]), (250,286,[5_1|2]), (250,291,[2_1|2]), (251,252,[5_1|2]), (252,253,[3_1|2]), (253,254,[0_1|2]), (254,255,[2_1|2]), (255,73,[1_1|2]), (255,147,[1_1|2]), (255,191,[1_1|2]), (255,241,[1_1|2]), (255,246,[1_1|2]), (255,296,[1_1|2]), (255,99,[1_1|2]), (255,211,[0_1|2]), (255,216,[1_1|2]), (255,221,[1_1|2]), (255,226,[5_1|2]), (256,257,[1_1|2]), (257,258,[0_1|2]), (258,259,[3_1|2]), (259,260,[0_1|2]), (260,73,[2_1|2]), (260,147,[2_1|2]), (260,191,[2_1|2]), (260,241,[2_1|2]), (260,246,[2_1|2]), (260,296,[2_1|2]), (260,99,[2_1|2]), (261,262,[1_1|2]), (262,263,[0_1|2]), (263,264,[3_1|2]), (264,265,[1_1|2]), (265,73,[2_1|2]), (265,147,[2_1|2]), (265,191,[2_1|2]), (265,241,[2_1|2]), (265,246,[2_1|2]), (265,296,[2_1|2]), (265,99,[2_1|2]), (266,267,[2_1|2]), (267,268,[4_1|2]), (268,269,[1_1|2]), (268,226,[5_1|2]), (269,270,[5_1|2]), (269,286,[5_1|2]), (269,291,[2_1|2]), (269,296,[3_1|2]), (270,73,[3_1|2]), (270,147,[3_1|2]), (270,191,[3_1|2]), (270,241,[3_1|2]), (270,246,[3_1|2]), (270,296,[3_1|2]), (270,99,[3_1|2]), (271,272,[3_1|2]), (272,273,[3_1|2]), (273,274,[5_1|2]), (274,275,[2_1|2]), (275,73,[4_1|2]), (275,147,[4_1|2]), (275,191,[4_1|2]), (275,241,[4_1|2]), (275,246,[4_1|2]), (275,296,[4_1|2]), (275,99,[4_1|2]), (275,231,[2_1|2]), (275,236,[4_1|2]), (276,277,[4_1|2]), (277,278,[4_1|2]), (278,279,[0_1|2]), (279,280,[3_1|2]), (280,73,[5_1|2]), (280,147,[5_1|2]), (280,191,[5_1|2]), (280,241,[5_1|2, 3_1|2]), (280,246,[5_1|2, 3_1|2]), (280,296,[5_1|2, 3_1|2]), (280,99,[5_1|2]), (280,251,[4_1|2]), (280,256,[5_1|2]), (280,261,[5_1|2]), (280,266,[0_1|2]), (280,271,[0_1|2]), (280,276,[2_1|2]), (280,281,[5_1|2]), (280,286,[5_1|2]), (280,291,[2_1|2]), (281,282,[0_1|2]), (282,283,[3_1|2]), (283,284,[5_1|2]), (284,285,[4_1|2]), (285,73,[2_1|2]), (285,147,[2_1|2]), (285,191,[2_1|2]), (285,241,[2_1|2]), (285,246,[2_1|2]), (285,296,[2_1|2]), (285,99,[2_1|2]), (286,287,[5_1|2]), (287,288,[3_1|2]), (288,289,[0_1|2]), (289,290,[0_1|2]), (290,73,[3_1|2]), (290,147,[3_1|2]), (290,191,[3_1|2]), (290,241,[3_1|2]), (290,246,[3_1|2]), (290,296,[3_1|2]), (291,292,[0_1|2]), (292,293,[3_1|2]), (293,294,[1_1|2]), (293,226,[5_1|2]), (294,295,[5_1|2]), (294,286,[5_1|2]), (294,291,[2_1|2]), (294,296,[3_1|2]), (295,73,[3_1|2]), (295,147,[3_1|2]), (295,191,[3_1|2]), (295,241,[3_1|2]), (295,246,[3_1|2]), (295,296,[3_1|2]), (295,99,[3_1|2]), (296,297,[3_1|2]), (297,298,[0_1|2]), (298,299,[2_1|2]), (299,300,[1_1|2]), (299,226,[5_1|2]), (300,73,[5_1|2]), (300,147,[5_1|2]), (300,191,[5_1|2]), (300,241,[5_1|2, 3_1|2]), (300,246,[5_1|2, 3_1|2]), (300,296,[5_1|2, 3_1|2]), (300,99,[5_1|2]), (300,251,[4_1|2]), (300,256,[5_1|2]), (300,261,[5_1|2]), (300,266,[0_1|2]), (300,271,[0_1|2]), (300,276,[2_1|2]), (300,281,[5_1|2]), (300,286,[5_1|2]), (300,291,[2_1|2]), (301,302,[1_1|2]), (302,303,[0_1|2]), (303,304,[3_1|2]), (304,305,[3_1|2]), (305,92,[5_1|2]), (305,114,[5_1|2])}" ---------------------------------------- (8) BOUNDS(1, n^1)