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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 62 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 97 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(0(0(x1))) -> 0(0(1(0(2(x1))))) 0(3(2(x1))) -> 4(3(0(2(x1)))) 0(0(4(2(x1)))) -> 0(4(1(0(2(x1))))) 0(0(5(2(x1)))) -> 5(0(2(3(0(x1))))) 0(1(3(2(x1)))) -> 0(3(1(0(2(x1))))) 0(1(3(2(x1)))) -> 3(1(1(0(2(x1))))) 0(1(3(2(x1)))) -> 0(1(4(3(1(2(x1)))))) 0(4(1(3(x1)))) -> 1(4(3(0(2(2(x1)))))) 0(4(2(3(x1)))) -> 5(4(3(0(2(x1))))) 0(4(5(2(x1)))) -> 5(0(2(2(4(2(x1)))))) 0(5(1(3(x1)))) -> 3(0(1(5(1(2(x1)))))) 0(5(3(0(x1)))) -> 5(0(1(4(3(0(x1)))))) 0(5(3(2(x1)))) -> 5(1(5(0(2(3(x1)))))) 4(0(2(3(x1)))) -> 3(4(3(0(2(x1))))) 4(0(2(3(x1)))) -> 4(3(5(0(2(x1))))) 4(4(1(3(x1)))) -> 4(3(4(1(2(2(x1)))))) 4(5(2(0(x1)))) -> 4(2(1(5(0(2(x1)))))) 4(5(2(0(x1)))) -> 5(1(0(2(2(4(x1)))))) 5(1(0(0(x1)))) -> 5(1(0(2(0(x1))))) 5(1(0(0(x1)))) -> 5(2(1(0(2(0(x1)))))) 5(1(3(0(x1)))) -> 5(0(2(1(3(x1))))) 5(1(3(2(x1)))) -> 3(0(1(5(1(2(x1)))))) 5(1(3(2(x1)))) -> 3(1(1(5(2(2(x1)))))) 5(3(0(0(x1)))) -> 5(0(4(3(0(2(x1)))))) 0(0(4(1(3(x1))))) -> 4(0(1(0(2(3(x1)))))) 0(0(4(5(2(x1))))) -> 5(0(1(0(2(4(x1)))))) 0(0(5(3(2(x1))))) -> 0(1(5(0(2(3(x1)))))) 0(1(0(5(2(x1))))) -> 1(0(2(5(1(0(x1)))))) 0(1(4(5(2(x1))))) -> 2(1(5(0(2(4(x1)))))) 0(3(1(4(0(x1))))) -> 4(1(0(1(0(3(x1)))))) 0(3(2(0(0(x1))))) -> 0(0(1(0(2(3(x1)))))) 0(3(4(0(2(x1))))) -> 4(3(0(2(1(0(x1)))))) 0(3(4(0(2(x1))))) -> 4(3(0(2(3(0(x1)))))) 0(3(4(4(2(x1))))) -> 4(0(3(4(2(2(x1)))))) 0(4(2(5(3(x1))))) -> 0(4(3(5(1(2(x1)))))) 0(5(1(2(0(x1))))) -> 3(0(1(5(0(2(x1)))))) 4(4(2(2(0(x1))))) -> 4(1(0(2(2(4(x1)))))) 4(5(1(2(0(x1))))) -> 5(0(4(1(2(2(x1)))))) 4(5(2(3(2(x1))))) -> 5(4(3(5(2(2(x1)))))) 5(1(0(3(2(x1))))) -> 5(0(3(1(0(2(x1)))))) 5(1(0(5(3(x1))))) -> 5(5(0(1(3(1(x1)))))) 5(1(3(0(0(x1))))) -> 3(5(0(1(2(0(x1)))))) 5(1(3(0(2(x1))))) -> 3(0(2(1(5(2(x1)))))) 5(1(3(0(2(x1))))) -> 5(0(1(0(3(2(x1)))))) 5(1(3(0(2(x1))))) -> 5(0(1(1(2(3(x1)))))) 5(1(3(2(0(x1))))) -> 5(3(1(5(2(0(x1)))))) 5(1(3(2(3(x1))))) -> 3(4(3(5(1(2(x1)))))) 5(1(4(5(2(x1))))) -> 5(1(4(1(5(2(x1)))))) 5(5(1(3(2(x1))))) -> 3(5(5(4(1(2(x1)))))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(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_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(0(0(x1))) -> 0(0(1(0(2(x1))))) 0(3(2(x1))) -> 4(3(0(2(x1)))) 0(0(4(2(x1)))) -> 0(4(1(0(2(x1))))) 0(0(5(2(x1)))) -> 5(0(2(3(0(x1))))) 0(1(3(2(x1)))) -> 0(3(1(0(2(x1))))) 0(1(3(2(x1)))) -> 3(1(1(0(2(x1))))) 0(1(3(2(x1)))) -> 0(1(4(3(1(2(x1)))))) 0(4(1(3(x1)))) -> 1(4(3(0(2(2(x1)))))) 0(4(2(3(x1)))) -> 5(4(3(0(2(x1))))) 0(4(5(2(x1)))) -> 5(0(2(2(4(2(x1)))))) 0(5(1(3(x1)))) -> 3(0(1(5(1(2(x1)))))) 0(5(3(0(x1)))) -> 5(0(1(4(3(0(x1)))))) 0(5(3(2(x1)))) -> 5(1(5(0(2(3(x1)))))) 4(0(2(3(x1)))) -> 3(4(3(0(2(x1))))) 4(0(2(3(x1)))) -> 4(3(5(0(2(x1))))) 4(4(1(3(x1)))) -> 4(3(4(1(2(2(x1)))))) 4(5(2(0(x1)))) -> 4(2(1(5(0(2(x1)))))) 4(5(2(0(x1)))) -> 5(1(0(2(2(4(x1)))))) 5(1(0(0(x1)))) -> 5(1(0(2(0(x1))))) 5(1(0(0(x1)))) -> 5(2(1(0(2(0(x1)))))) 5(1(3(0(x1)))) -> 5(0(2(1(3(x1))))) 5(1(3(2(x1)))) -> 3(0(1(5(1(2(x1)))))) 5(1(3(2(x1)))) -> 3(1(1(5(2(2(x1)))))) 5(3(0(0(x1)))) -> 5(0(4(3(0(2(x1)))))) 0(0(4(1(3(x1))))) -> 4(0(1(0(2(3(x1)))))) 0(0(4(5(2(x1))))) -> 5(0(1(0(2(4(x1)))))) 0(0(5(3(2(x1))))) -> 0(1(5(0(2(3(x1)))))) 0(1(0(5(2(x1))))) -> 1(0(2(5(1(0(x1)))))) 0(1(4(5(2(x1))))) -> 2(1(5(0(2(4(x1)))))) 0(3(1(4(0(x1))))) -> 4(1(0(1(0(3(x1)))))) 0(3(2(0(0(x1))))) -> 0(0(1(0(2(3(x1)))))) 0(3(4(0(2(x1))))) -> 4(3(0(2(1(0(x1)))))) 0(3(4(0(2(x1))))) -> 4(3(0(2(3(0(x1)))))) 0(3(4(4(2(x1))))) -> 4(0(3(4(2(2(x1)))))) 0(4(2(5(3(x1))))) -> 0(4(3(5(1(2(x1)))))) 0(5(1(2(0(x1))))) -> 3(0(1(5(0(2(x1)))))) 4(4(2(2(0(x1))))) -> 4(1(0(2(2(4(x1)))))) 4(5(1(2(0(x1))))) -> 5(0(4(1(2(2(x1)))))) 4(5(2(3(2(x1))))) -> 5(4(3(5(2(2(x1)))))) 5(1(0(3(2(x1))))) -> 5(0(3(1(0(2(x1)))))) 5(1(0(5(3(x1))))) -> 5(5(0(1(3(1(x1)))))) 5(1(3(0(0(x1))))) -> 3(5(0(1(2(0(x1)))))) 5(1(3(0(2(x1))))) -> 3(0(2(1(5(2(x1)))))) 5(1(3(0(2(x1))))) -> 5(0(1(0(3(2(x1)))))) 5(1(3(0(2(x1))))) -> 5(0(1(1(2(3(x1)))))) 5(1(3(2(0(x1))))) -> 5(3(1(5(2(0(x1)))))) 5(1(3(2(3(x1))))) -> 3(4(3(5(1(2(x1)))))) 5(1(4(5(2(x1))))) -> 5(1(4(1(5(2(x1)))))) 5(5(1(3(2(x1))))) -> 3(5(5(4(1(2(x1)))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) 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_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(0(0(x1))) -> 0(0(1(0(2(x1))))) 0(3(2(x1))) -> 4(3(0(2(x1)))) 0(0(4(2(x1)))) -> 0(4(1(0(2(x1))))) 0(0(5(2(x1)))) -> 5(0(2(3(0(x1))))) 0(1(3(2(x1)))) -> 0(3(1(0(2(x1))))) 0(1(3(2(x1)))) -> 3(1(1(0(2(x1))))) 0(1(3(2(x1)))) -> 0(1(4(3(1(2(x1)))))) 0(4(1(3(x1)))) -> 1(4(3(0(2(2(x1)))))) 0(4(2(3(x1)))) -> 5(4(3(0(2(x1))))) 0(4(5(2(x1)))) -> 5(0(2(2(4(2(x1)))))) 0(5(1(3(x1)))) -> 3(0(1(5(1(2(x1)))))) 0(5(3(0(x1)))) -> 5(0(1(4(3(0(x1)))))) 0(5(3(2(x1)))) -> 5(1(5(0(2(3(x1)))))) 4(0(2(3(x1)))) -> 3(4(3(0(2(x1))))) 4(0(2(3(x1)))) -> 4(3(5(0(2(x1))))) 4(4(1(3(x1)))) -> 4(3(4(1(2(2(x1)))))) 4(5(2(0(x1)))) -> 4(2(1(5(0(2(x1)))))) 4(5(2(0(x1)))) -> 5(1(0(2(2(4(x1)))))) 5(1(0(0(x1)))) -> 5(1(0(2(0(x1))))) 5(1(0(0(x1)))) -> 5(2(1(0(2(0(x1)))))) 5(1(3(0(x1)))) -> 5(0(2(1(3(x1))))) 5(1(3(2(x1)))) -> 3(0(1(5(1(2(x1)))))) 5(1(3(2(x1)))) -> 3(1(1(5(2(2(x1)))))) 5(3(0(0(x1)))) -> 5(0(4(3(0(2(x1)))))) 0(0(4(1(3(x1))))) -> 4(0(1(0(2(3(x1)))))) 0(0(4(5(2(x1))))) -> 5(0(1(0(2(4(x1)))))) 0(0(5(3(2(x1))))) -> 0(1(5(0(2(3(x1)))))) 0(1(0(5(2(x1))))) -> 1(0(2(5(1(0(x1)))))) 0(1(4(5(2(x1))))) -> 2(1(5(0(2(4(x1)))))) 0(3(1(4(0(x1))))) -> 4(1(0(1(0(3(x1)))))) 0(3(2(0(0(x1))))) -> 0(0(1(0(2(3(x1)))))) 0(3(4(0(2(x1))))) -> 4(3(0(2(1(0(x1)))))) 0(3(4(0(2(x1))))) -> 4(3(0(2(3(0(x1)))))) 0(3(4(4(2(x1))))) -> 4(0(3(4(2(2(x1)))))) 0(4(2(5(3(x1))))) -> 0(4(3(5(1(2(x1)))))) 0(5(1(2(0(x1))))) -> 3(0(1(5(0(2(x1)))))) 4(4(2(2(0(x1))))) -> 4(1(0(2(2(4(x1)))))) 4(5(1(2(0(x1))))) -> 5(0(4(1(2(2(x1)))))) 4(5(2(3(2(x1))))) -> 5(4(3(5(2(2(x1)))))) 5(1(0(3(2(x1))))) -> 5(0(3(1(0(2(x1)))))) 5(1(0(5(3(x1))))) -> 5(5(0(1(3(1(x1)))))) 5(1(3(0(0(x1))))) -> 3(5(0(1(2(0(x1)))))) 5(1(3(0(2(x1))))) -> 3(0(2(1(5(2(x1)))))) 5(1(3(0(2(x1))))) -> 5(0(1(0(3(2(x1)))))) 5(1(3(0(2(x1))))) -> 5(0(1(1(2(3(x1)))))) 5(1(3(2(0(x1))))) -> 5(3(1(5(2(0(x1)))))) 5(1(3(2(3(x1))))) -> 3(4(3(5(1(2(x1)))))) 5(1(4(5(2(x1))))) -> 5(1(4(1(5(2(x1)))))) 5(5(1(3(2(x1))))) -> 3(5(5(4(1(2(x1)))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) 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_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(0(0(x1))) -> 0(0(1(0(2(x1))))) 0(3(2(x1))) -> 4(3(0(2(x1)))) 0(0(4(2(x1)))) -> 0(4(1(0(2(x1))))) 0(0(5(2(x1)))) -> 5(0(2(3(0(x1))))) 0(1(3(2(x1)))) -> 0(3(1(0(2(x1))))) 0(1(3(2(x1)))) -> 3(1(1(0(2(x1))))) 0(1(3(2(x1)))) -> 0(1(4(3(1(2(x1)))))) 0(4(1(3(x1)))) -> 1(4(3(0(2(2(x1)))))) 0(4(2(3(x1)))) -> 5(4(3(0(2(x1))))) 0(4(5(2(x1)))) -> 5(0(2(2(4(2(x1)))))) 0(5(1(3(x1)))) -> 3(0(1(5(1(2(x1)))))) 0(5(3(0(x1)))) -> 5(0(1(4(3(0(x1)))))) 0(5(3(2(x1)))) -> 5(1(5(0(2(3(x1)))))) 4(0(2(3(x1)))) -> 3(4(3(0(2(x1))))) 4(0(2(3(x1)))) -> 4(3(5(0(2(x1))))) 4(4(1(3(x1)))) -> 4(3(4(1(2(2(x1)))))) 4(5(2(0(x1)))) -> 4(2(1(5(0(2(x1)))))) 4(5(2(0(x1)))) -> 5(1(0(2(2(4(x1)))))) 5(1(0(0(x1)))) -> 5(1(0(2(0(x1))))) 5(1(0(0(x1)))) -> 5(2(1(0(2(0(x1)))))) 5(1(3(0(x1)))) -> 5(0(2(1(3(x1))))) 5(1(3(2(x1)))) -> 3(0(1(5(1(2(x1)))))) 5(1(3(2(x1)))) -> 3(1(1(5(2(2(x1)))))) 5(3(0(0(x1)))) -> 5(0(4(3(0(2(x1)))))) 0(0(4(1(3(x1))))) -> 4(0(1(0(2(3(x1)))))) 0(0(4(5(2(x1))))) -> 5(0(1(0(2(4(x1)))))) 0(0(5(3(2(x1))))) -> 0(1(5(0(2(3(x1)))))) 0(1(0(5(2(x1))))) -> 1(0(2(5(1(0(x1)))))) 0(1(4(5(2(x1))))) -> 2(1(5(0(2(4(x1)))))) 0(3(1(4(0(x1))))) -> 4(1(0(1(0(3(x1)))))) 0(3(2(0(0(x1))))) -> 0(0(1(0(2(3(x1)))))) 0(3(4(0(2(x1))))) -> 4(3(0(2(1(0(x1)))))) 0(3(4(0(2(x1))))) -> 4(3(0(2(3(0(x1)))))) 0(3(4(4(2(x1))))) -> 4(0(3(4(2(2(x1)))))) 0(4(2(5(3(x1))))) -> 0(4(3(5(1(2(x1)))))) 0(5(1(2(0(x1))))) -> 3(0(1(5(0(2(x1)))))) 4(4(2(2(0(x1))))) -> 4(1(0(2(2(4(x1)))))) 4(5(1(2(0(x1))))) -> 5(0(4(1(2(2(x1)))))) 4(5(2(3(2(x1))))) -> 5(4(3(5(2(2(x1)))))) 5(1(0(3(2(x1))))) -> 5(0(3(1(0(2(x1)))))) 5(1(0(5(3(x1))))) -> 5(5(0(1(3(1(x1)))))) 5(1(3(0(0(x1))))) -> 3(5(0(1(2(0(x1)))))) 5(1(3(0(2(x1))))) -> 3(0(2(1(5(2(x1)))))) 5(1(3(0(2(x1))))) -> 5(0(1(0(3(2(x1)))))) 5(1(3(0(2(x1))))) -> 5(0(1(1(2(3(x1)))))) 5(1(3(2(0(x1))))) -> 5(3(1(5(2(0(x1)))))) 5(1(3(2(3(x1))))) -> 3(4(3(5(1(2(x1)))))) 5(1(4(5(2(x1))))) -> 5(1(4(1(5(2(x1)))))) 5(5(1(3(2(x1))))) -> 3(5(5(4(1(2(x1)))))) encArg(1(x_1)) -> 1(encArg(x_1)) 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_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 3. The certificate found is represented by the following graph. "[65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364] {(65,66,[0_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]), (65,67,[4_1|1]), (65,70,[0_1|1]), (65,74,[3_1|1]), (65,78,[0_1|1]), (65,83,[3_1|1]), (65,88,[3_1|1]), (65,93,[3_1|1]), (65,98,[1_1|1, 2_1|1, 3_1|1, 0_1|1, 4_1|1, 5_1|1]), (65,99,[0_1|2]), (65,103,[0_1|2]), (65,107,[4_1|2]), (65,112,[5_1|2]), (65,117,[5_1|2]), (65,121,[0_1|2]), (65,126,[4_1|2]), (65,129,[0_1|2]), (65,134,[4_1|2]), (65,139,[4_1|2]), (65,144,[4_1|2]), (65,149,[4_1|2]), 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(223,201,[2_1|2]), (223,216,[2_1|2]), (223,277,[2_1|2]), (223,282,[2_1|2]), (223,297,[2_1|2]), (223,307,[2_1|2]), (223,322,[2_1|2]), (223,327,[2_1|2]), (224,225,[3_1|2]), (225,226,[4_1|2]), (226,227,[1_1|2]), (227,228,[2_1|2]), (228,98,[2_1|2]), (228,158,[2_1|2]), (228,196,[2_1|2]), (228,201,[2_1|2]), (228,216,[2_1|2]), (228,277,[2_1|2]), (228,282,[2_1|2]), (228,297,[2_1|2]), (228,307,[2_1|2]), (228,322,[2_1|2]), (228,327,[2_1|2]), (229,230,[1_1|2]), (230,231,[0_1|2]), (231,232,[2_1|2]), (232,233,[2_1|2]), (233,98,[4_1|2]), (233,99,[4_1|2]), (233,103,[4_1|2]), (233,121,[4_1|2]), (233,129,[4_1|2]), (233,154,[4_1|2]), (233,162,[4_1|2]), (233,186,[4_1|2]), (233,216,[3_1|2]), (233,220,[4_1|2]), (233,224,[4_1|2]), (233,229,[4_1|2]), (233,234,[4_1|2]), (233,239,[5_1|2]), (233,244,[5_1|2]), (233,249,[5_1|2]), (234,235,[2_1|2]), (235,236,[1_1|2]), (236,237,[5_1|2]), (237,238,[0_1|2]), (238,98,[2_1|2]), (238,99,[2_1|2]), (238,103,[2_1|2]), (238,121,[2_1|2]), (238,129,[2_1|2]), (238,154,[2_1|2]), (238,162,[2_1|2]), (238,186,[2_1|2]), (239,240,[1_1|2]), (240,241,[0_1|2]), (241,242,[2_1|2]), (242,243,[2_1|2]), (243,98,[4_1|2]), (243,99,[4_1|2]), (243,103,[4_1|2]), (243,121,[4_1|2]), (243,129,[4_1|2]), (243,154,[4_1|2]), (243,162,[4_1|2]), (243,186,[4_1|2]), (243,216,[3_1|2]), (243,220,[4_1|2]), (243,224,[4_1|2]), (243,229,[4_1|2]), (243,234,[4_1|2]), (243,239,[5_1|2]), (243,244,[5_1|2]), (243,249,[5_1|2]), (244,245,[4_1|2]), (245,246,[3_1|2]), (246,247,[5_1|2]), (247,248,[2_1|2]), (248,98,[2_1|2]), (248,172,[2_1|2]), (249,250,[0_1|2]), (250,251,[4_1|2]), (251,252,[1_1|2]), (252,253,[2_1|2]), (253,98,[2_1|2]), (253,99,[2_1|2]), (253,103,[2_1|2]), (253,121,[2_1|2]), (253,129,[2_1|2]), (253,154,[2_1|2]), (253,162,[2_1|2]), (253,186,[2_1|2]), (254,255,[1_1|2]), (255,256,[0_1|2]), (256,257,[2_1|2]), (257,98,[0_1|2]), (257,99,[0_1|2]), (257,103,[0_1|2]), (257,121,[0_1|2]), (257,129,[0_1|2]), (257,154,[0_1|2]), (257,162,[0_1|2]), (257,186,[0_1|2]), (257,100,[0_1|2]), (257,130,[0_1|2]), (257,107,[4_1|2]), (257,112,[5_1|2]), (257,117,[5_1|2]), (257,126,[4_1|2]), (257,134,[4_1|2]), (257,139,[4_1|2]), (257,144,[4_1|2]), (257,149,[4_1|2]), (257,158,[3_1|2]), (257,167,[1_1|2]), (257,172,[2_1|2]), (257,177,[1_1|2]), (257,182,[5_1|2]), (257,191,[5_1|2]), (257,196,[3_1|2]), (257,201,[3_1|2]), (257,206,[5_1|2]), (257,211,[5_1|2]), (257,332,[0_1|3]), (258,259,[2_1|2]), (259,260,[1_1|2]), (260,261,[0_1|2]), (261,262,[2_1|2]), (262,98,[0_1|2]), (262,99,[0_1|2]), (262,103,[0_1|2]), (262,121,[0_1|2]), (262,129,[0_1|2]), (262,154,[0_1|2]), (262,162,[0_1|2]), (262,186,[0_1|2]), (262,100,[0_1|2]), (262,130,[0_1|2]), (262,107,[4_1|2]), (262,112,[5_1|2]), (262,117,[5_1|2]), (262,126,[4_1|2]), (262,134,[4_1|2]), (262,139,[4_1|2]), (262,144,[4_1|2]), (262,149,[4_1|2]), (262,158,[3_1|2]), (262,167,[1_1|2]), (262,172,[2_1|2]), (262,177,[1_1|2]), (262,182,[5_1|2]), (262,191,[5_1|2]), (262,196,[3_1|2]), (262,201,[3_1|2]), (262,206,[5_1|2]), (262,211,[5_1|2]), (262,332,[0_1|3]), (263,264,[0_1|2]), (264,265,[3_1|2]), (265,266,[1_1|2]), (266,267,[0_1|2]), (267,98,[2_1|2]), (267,172,[2_1|2]), (268,269,[5_1|2]), (269,270,[0_1|2]), (270,271,[1_1|2]), (271,272,[3_1|2]), (272,98,[1_1|2]), (272,158,[1_1|2]), (272,196,[1_1|2]), (272,201,[1_1|2]), (272,216,[1_1|2]), (272,277,[1_1|2]), (272,282,[1_1|2]), (272,297,[1_1|2]), (272,307,[1_1|2]), (272,322,[1_1|2]), (272,303,[1_1|2]), (272,327,[1_1|2]), (273,274,[0_1|2]), (274,275,[2_1|2]), (275,276,[1_1|2]), (276,98,[3_1|2]), (276,99,[3_1|2]), (276,103,[3_1|2]), (276,121,[3_1|2]), (276,129,[3_1|2]), (276,154,[3_1|2]), (276,162,[3_1|2]), (276,186,[3_1|2]), (276,197,[3_1|2]), (276,202,[3_1|2]), (276,283,[3_1|2]), (276,328,[3_1|2]), (277,278,[5_1|2]), (278,279,[0_1|2]), (279,280,[1_1|2]), (280,281,[2_1|2]), (281,98,[0_1|2]), (281,99,[0_1|2]), (281,103,[0_1|2]), (281,121,[0_1|2]), (281,129,[0_1|2]), (281,154,[0_1|2]), (281,162,[0_1|2]), (281,186,[0_1|2]), (281,100,[0_1|2]), (281,130,[0_1|2]), (281,107,[4_1|2]), (281,112,[5_1|2]), (281,117,[5_1|2]), (281,126,[4_1|2]), (281,134,[4_1|2]), (281,139,[4_1|2]), (281,144,[4_1|2]), (281,149,[4_1|2]), (281,158,[3_1|2]), (281,167,[1_1|2]), (281,172,[2_1|2]), (281,177,[1_1|2]), (281,182,[5_1|2]), (281,191,[5_1|2]), (281,196,[3_1|2]), (281,201,[3_1|2]), (281,206,[5_1|2]), (281,211,[5_1|2]), (281,332,[0_1|3]), (282,283,[0_1|2]), (283,284,[2_1|2]), (284,285,[1_1|2]), (285,286,[5_1|2]), (286,98,[2_1|2]), (286,172,[2_1|2]), (286,284,[2_1|2]), (287,288,[0_1|2]), (288,289,[1_1|2]), (289,290,[0_1|2]), (289,353,[4_1|3]), (289,129,[0_1|2]), (289,356,[0_1|3]), (290,291,[3_1|2]), (291,98,[2_1|2]), (291,172,[2_1|2]), (291,284,[2_1|2]), (292,293,[0_1|2]), (293,294,[1_1|2]), (294,295,[1_1|2]), (295,296,[2_1|2]), (296,98,[3_1|2]), (296,172,[3_1|2]), (296,284,[3_1|2]), (297,298,[1_1|2]), (298,299,[1_1|2]), (299,300,[5_1|2]), (300,301,[2_1|2]), (301,98,[2_1|2]), (301,172,[2_1|2]), (302,303,[3_1|2]), (303,304,[1_1|2]), (304,305,[5_1|2]), (305,306,[2_1|2]), (306,98,[0_1|2]), (306,99,[0_1|2]), (306,103,[0_1|2]), (306,121,[0_1|2]), (306,129,[0_1|2]), (306,154,[0_1|2]), (306,162,[0_1|2]), (306,186,[0_1|2]), (306,107,[4_1|2]), (306,112,[5_1|2]), (306,117,[5_1|2]), (306,126,[4_1|2]), (306,134,[4_1|2]), (306,139,[4_1|2]), (306,144,[4_1|2]), (306,149,[4_1|2]), (306,158,[3_1|2]), (306,167,[1_1|2]), (306,172,[2_1|2]), (306,177,[1_1|2]), (306,182,[5_1|2]), (306,191,[5_1|2]), (306,196,[3_1|2]), (306,201,[3_1|2]), (306,206,[5_1|2]), (306,211,[5_1|2]), (306,332,[0_1|3]), (307,308,[4_1|2]), (308,309,[3_1|2]), (309,310,[5_1|2]), (310,311,[1_1|2]), (311,98,[2_1|2]), (311,158,[2_1|2]), (311,196,[2_1|2]), (311,201,[2_1|2]), (311,216,[2_1|2]), (311,277,[2_1|2]), (311,282,[2_1|2]), (311,297,[2_1|2]), (311,307,[2_1|2]), (311,322,[2_1|2]), (311,327,[2_1|2]), (312,313,[1_1|2]), (313,314,[4_1|2]), (314,315,[1_1|2]), (315,316,[5_1|2]), (316,98,[2_1|2]), (316,172,[2_1|2]), (316,259,[2_1|2]), (317,318,[0_1|2]), (318,319,[4_1|2]), (319,320,[3_1|2]), (320,321,[0_1|2]), (321,98,[2_1|2]), (321,99,[2_1|2]), (321,103,[2_1|2]), (321,121,[2_1|2]), (321,129,[2_1|2]), (321,154,[2_1|2]), (321,162,[2_1|2]), (321,186,[2_1|2]), (321,100,[2_1|2]), (321,130,[2_1|2]), (322,323,[5_1|2]), (323,324,[5_1|2]), (324,325,[4_1|2]), (325,326,[1_1|2]), (326,98,[2_1|2]), (326,172,[2_1|2]), (327,328,[0_1|2]), (328,329,[1_1|2]), (329,330,[5_1|2]), (330,331,[1_1|2]), (331,172,[2_1|2]), (332,333,[0_1|3]), (333,334,[1_1|3]), (334,335,[0_1|3]), (335,100,[2_1|3]), (335,130,[2_1|3]), (336,337,[3_1|3]), (337,338,[0_1|3]), (338,172,[2_1|3]), (339,340,[1_1|3]), (340,341,[0_1|3]), (341,342,[2_1|3]), (342,99,[0_1|3]), (342,103,[0_1|3]), (342,121,[0_1|3]), (342,129,[0_1|3]), (342,154,[0_1|3]), (342,162,[0_1|3]), (342,186,[0_1|3]), (342,100,[0_1|3]), (342,130,[0_1|3]), (342,333,[0_1|3]), (343,344,[2_1|3]), (344,345,[1_1|3]), (345,346,[0_1|3]), (346,347,[2_1|3]), (347,99,[0_1|3]), (347,103,[0_1|3]), (347,121,[0_1|3]), (347,129,[0_1|3]), (347,154,[0_1|3]), (347,162,[0_1|3]), (347,186,[0_1|3]), (347,100,[0_1|3]), (347,130,[0_1|3]), (347,333,[0_1|3]), (348,349,[5_1|3]), (349,350,[0_1|3]), (350,351,[1_1|3]), (351,352,[3_1|3]), (352,303,[1_1|3]), (353,354,[3_1|3]), (354,355,[0_1|3]), (355,98,[2_1|3]), (355,172,[2_1|3]), (355,284,[2_1|3]), (356,357,[0_1|3]), (357,358,[1_1|3]), (358,359,[0_1|3]), (359,360,[2_1|3]), (360,100,[3_1|3]), (360,130,[3_1|3]), (361,362,[0_1|3]), (362,363,[2_1|3]), (363,364,[1_1|3]), (364,197,[3_1|3]), (364,202,[3_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)