/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 169 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(1(1(x1))) -> 1(0(2(1(x1)))) 0(1(1(x1))) -> 1(1(0(3(2(x1))))) 0(1(1(x1))) -> 1(4(0(0(2(1(x1)))))) 0(1(4(x1))) -> 1(4(0(3(x1)))) 0(1(4(x1))) -> 4(0(2(1(x1)))) 0(1(4(x1))) -> 4(0(2(1(3(x1))))) 0(4(1(x1))) -> 0(2(4(1(x1)))) 0(4(1(x1))) -> 4(0(2(1(x1)))) 0(4(1(x1))) -> 4(0(3(1(x1)))) 0(4(1(x1))) -> 1(4(4(0(2(x1))))) 0(4(1(x1))) -> 2(1(4(0(2(x1))))) 0(5(4(x1))) -> 1(4(0(0(2(5(x1)))))) 0(5(4(x1))) -> 4(0(2(5(2(5(x1)))))) 0(5(4(x1))) -> 5(0(4(0(3(3(x1)))))) 4(2(1(x1))) -> 4(0(2(1(x1)))) 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 0(1(0(4(x1)))) -> 0(0(2(2(1(4(x1)))))) 0(1(1(2(x1)))) -> 5(1(0(2(1(x1))))) 0(1(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(1(4(1(x1)))) -> 1(0(2(4(1(x1))))) 0(1(4(3(x1)))) -> 1(0(2(4(3(x1))))) 0(1(4(3(x1)))) -> 4(0(2(1(3(x1))))) 0(4(1(2(x1)))) -> 2(0(3(1(4(x1))))) 0(4(2(1(x1)))) -> 0(4(3(0(2(1(x1)))))) 0(5(0(4(x1)))) -> 1(5(4(0(0(2(x1)))))) 0(5(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(5(1(3(x1)))) -> 5(3(1(0(3(x1))))) 0(5(4(1(x1)))) -> 4(1(5(4(0(2(x1)))))) 0(5(4(3(x1)))) -> 0(2(5(0(3(4(x1)))))) 0(5(4(3(x1)))) -> 1(5(3(4(0(3(x1)))))) 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 0(0(1(2(3(x1))))) -> 1(0(3(0(0(2(x1)))))) 0(0(5(1(2(x1))))) -> 0(0(2(5(0(1(x1)))))) 0(0(5(1(3(x1))))) -> 4(5(0(0(3(1(x1)))))) 0(1(3(4(2(x1))))) -> 1(3(4(3(0(2(x1)))))) 0(4(5(3(4(x1))))) -> 0(3(2(5(4(4(x1)))))) 0(5(0(2(2(x1))))) -> 0(0(2(5(2(4(x1)))))) 0(5(1(1(3(x1))))) -> 0(3(2(1(1(5(x1)))))) 0(5(1(4(3(x1))))) -> 3(0(2(1(5(4(x1)))))) 0(5(5(1(2(x1))))) -> 1(5(3(0(2(5(x1)))))) 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 4(2(5(4(1(x1))))) -> 4(4(1(5(3(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(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(1(x1))) -> 1(0(2(1(x1)))) 0(1(1(x1))) -> 1(1(0(3(2(x1))))) 0(1(1(x1))) -> 1(4(0(0(2(1(x1)))))) 0(1(4(x1))) -> 1(4(0(3(x1)))) 0(1(4(x1))) -> 4(0(2(1(x1)))) 0(1(4(x1))) -> 4(0(2(1(3(x1))))) 0(4(1(x1))) -> 0(2(4(1(x1)))) 0(4(1(x1))) -> 4(0(2(1(x1)))) 0(4(1(x1))) -> 4(0(3(1(x1)))) 0(4(1(x1))) -> 1(4(4(0(2(x1))))) 0(4(1(x1))) -> 2(1(4(0(2(x1))))) 0(5(4(x1))) -> 1(4(0(0(2(5(x1)))))) 0(5(4(x1))) -> 4(0(2(5(2(5(x1)))))) 0(5(4(x1))) -> 5(0(4(0(3(3(x1)))))) 4(2(1(x1))) -> 4(0(2(1(x1)))) 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 0(1(0(4(x1)))) -> 0(0(2(2(1(4(x1)))))) 0(1(1(2(x1)))) -> 5(1(0(2(1(x1))))) 0(1(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(1(4(1(x1)))) -> 1(0(2(4(1(x1))))) 0(1(4(3(x1)))) -> 1(0(2(4(3(x1))))) 0(1(4(3(x1)))) -> 4(0(2(1(3(x1))))) 0(4(1(2(x1)))) -> 2(0(3(1(4(x1))))) 0(4(2(1(x1)))) -> 0(4(3(0(2(1(x1)))))) 0(5(0(4(x1)))) -> 1(5(4(0(0(2(x1)))))) 0(5(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(5(1(3(x1)))) -> 5(3(1(0(3(x1))))) 0(5(4(1(x1)))) -> 4(1(5(4(0(2(x1)))))) 0(5(4(3(x1)))) -> 0(2(5(0(3(4(x1)))))) 0(5(4(3(x1)))) -> 1(5(3(4(0(3(x1)))))) 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 0(0(1(2(3(x1))))) -> 1(0(3(0(0(2(x1)))))) 0(0(5(1(2(x1))))) -> 0(0(2(5(0(1(x1)))))) 0(0(5(1(3(x1))))) -> 4(5(0(0(3(1(x1)))))) 0(1(3(4(2(x1))))) -> 1(3(4(3(0(2(x1)))))) 0(4(5(3(4(x1))))) -> 0(3(2(5(4(4(x1)))))) 0(5(0(2(2(x1))))) -> 0(0(2(5(2(4(x1)))))) 0(5(1(1(3(x1))))) -> 0(3(2(1(1(5(x1)))))) 0(5(1(4(3(x1))))) -> 3(0(2(1(5(4(x1)))))) 0(5(5(1(2(x1))))) -> 1(5(3(0(2(5(x1)))))) 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(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(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(1(x1))) -> 1(0(2(1(x1)))) 0(1(1(x1))) -> 1(1(0(3(2(x1))))) 0(1(1(x1))) -> 1(4(0(0(2(1(x1)))))) 0(1(4(x1))) -> 1(4(0(3(x1)))) 0(1(4(x1))) -> 4(0(2(1(x1)))) 0(1(4(x1))) -> 4(0(2(1(3(x1))))) 0(4(1(x1))) -> 0(2(4(1(x1)))) 0(4(1(x1))) -> 4(0(2(1(x1)))) 0(4(1(x1))) -> 4(0(3(1(x1)))) 0(4(1(x1))) -> 1(4(4(0(2(x1))))) 0(4(1(x1))) -> 2(1(4(0(2(x1))))) 0(5(4(x1))) -> 1(4(0(0(2(5(x1)))))) 0(5(4(x1))) -> 4(0(2(5(2(5(x1)))))) 0(5(4(x1))) -> 5(0(4(0(3(3(x1)))))) 4(2(1(x1))) -> 4(0(2(1(x1)))) 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 0(1(0(4(x1)))) -> 0(0(2(2(1(4(x1)))))) 0(1(1(2(x1)))) -> 5(1(0(2(1(x1))))) 0(1(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(1(4(1(x1)))) -> 1(0(2(4(1(x1))))) 0(1(4(3(x1)))) -> 1(0(2(4(3(x1))))) 0(1(4(3(x1)))) -> 4(0(2(1(3(x1))))) 0(4(1(2(x1)))) -> 2(0(3(1(4(x1))))) 0(4(2(1(x1)))) -> 0(4(3(0(2(1(x1)))))) 0(5(0(4(x1)))) -> 1(5(4(0(0(2(x1)))))) 0(5(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(5(1(3(x1)))) -> 5(3(1(0(3(x1))))) 0(5(4(1(x1)))) -> 4(1(5(4(0(2(x1)))))) 0(5(4(3(x1)))) -> 0(2(5(0(3(4(x1)))))) 0(5(4(3(x1)))) -> 1(5(3(4(0(3(x1)))))) 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 0(0(1(2(3(x1))))) -> 1(0(3(0(0(2(x1)))))) 0(0(5(1(2(x1))))) -> 0(0(2(5(0(1(x1)))))) 0(0(5(1(3(x1))))) -> 4(5(0(0(3(1(x1)))))) 0(1(3(4(2(x1))))) -> 1(3(4(3(0(2(x1)))))) 0(4(5(3(4(x1))))) -> 0(3(2(5(4(4(x1)))))) 0(5(0(2(2(x1))))) -> 0(0(2(5(2(4(x1)))))) 0(5(1(1(3(x1))))) -> 0(3(2(1(1(5(x1)))))) 0(5(1(4(3(x1))))) -> 3(0(2(1(5(4(x1)))))) 0(5(5(1(2(x1))))) -> 1(5(3(0(2(5(x1)))))) 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(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(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(1(x1))) -> 1(0(2(1(x1)))) 0(1(1(x1))) -> 1(1(0(3(2(x1))))) 0(1(1(x1))) -> 1(4(0(0(2(1(x1)))))) 0(1(4(x1))) -> 1(4(0(3(x1)))) 0(1(4(x1))) -> 4(0(2(1(x1)))) 0(1(4(x1))) -> 4(0(2(1(3(x1))))) 0(4(1(x1))) -> 0(2(4(1(x1)))) 0(4(1(x1))) -> 4(0(2(1(x1)))) 0(4(1(x1))) -> 4(0(3(1(x1)))) 0(4(1(x1))) -> 1(4(4(0(2(x1))))) 0(4(1(x1))) -> 2(1(4(0(2(x1))))) 0(5(4(x1))) -> 1(4(0(0(2(5(x1)))))) 0(5(4(x1))) -> 4(0(2(5(2(5(x1)))))) 0(5(4(x1))) -> 5(0(4(0(3(3(x1)))))) 4(2(1(x1))) -> 4(0(2(1(x1)))) 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 0(1(0(4(x1)))) -> 0(0(2(2(1(4(x1)))))) 0(1(1(2(x1)))) -> 5(1(0(2(1(x1))))) 0(1(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(1(4(1(x1)))) -> 1(0(2(4(1(x1))))) 0(1(4(3(x1)))) -> 1(0(2(4(3(x1))))) 0(1(4(3(x1)))) -> 4(0(2(1(3(x1))))) 0(4(1(2(x1)))) -> 2(0(3(1(4(x1))))) 0(4(2(1(x1)))) -> 0(4(3(0(2(1(x1)))))) 0(5(0(4(x1)))) -> 1(5(4(0(0(2(x1)))))) 0(5(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(5(1(3(x1)))) -> 5(3(1(0(3(x1))))) 0(5(4(1(x1)))) -> 4(1(5(4(0(2(x1)))))) 0(5(4(3(x1)))) -> 0(2(5(0(3(4(x1)))))) 0(5(4(3(x1)))) -> 1(5(3(4(0(3(x1)))))) 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 0(0(1(2(3(x1))))) -> 1(0(3(0(0(2(x1)))))) 0(0(5(1(2(x1))))) -> 0(0(2(5(0(1(x1)))))) 0(0(5(1(3(x1))))) -> 4(5(0(0(3(1(x1)))))) 0(1(3(4(2(x1))))) -> 1(3(4(3(0(2(x1)))))) 0(4(5(3(4(x1))))) -> 0(3(2(5(4(4(x1)))))) 0(5(0(2(2(x1))))) -> 0(0(2(5(2(4(x1)))))) 0(5(1(1(3(x1))))) -> 0(3(2(1(1(5(x1)))))) 0(5(1(4(3(x1))))) -> 3(0(2(1(5(4(x1)))))) 0(5(5(1(2(x1))))) -> 1(5(3(0(2(5(x1)))))) 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(x1)))))) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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. "[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] {(79,80,[0_1|0, 4_1|0, 1_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]), (79,81,[2_1|1, 3_1|1, 5_1|1, 0_1|1, 4_1|1, 1_1|1]), (79,82,[1_1|2]), (79,85,[1_1|2]), (79,89,[1_1|2]), (79,94,[5_1|2]), (79,98,[1_1|2]), (79,102,[1_1|2]), (79,105,[4_1|2]), (79,108,[4_1|2]), (79,112,[1_1|2]), (79,116,[1_1|2]), (79,120,[0_1|2]), (79,125,[1_1|2]), (79,130,[0_1|2]), (79,133,[4_1|2]), (79,136,[1_1|2]), (79,140,[2_1|2]), (79,144,[2_1|2]), (79,148,[0_1|2]), (79,153,[0_1|2]), (79,158,[1_1|2]), (79,163,[4_1|2]), (79,168,[5_1|2]), (79,173,[4_1|2]), 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(211,314,[4_1|2]), (211,232,[1_1|2]), (211,236,[4_1|2]), (211,241,[4_1|2]), (211,250,[0_1|2]), (211,255,[5_1|2]), (211,317,[4_1|3]), (211,320,[1_1|3]), (212,213,[5_1|2]), (213,214,[3_1|2]), (214,215,[0_1|2]), (215,216,[2_1|2]), (216,81,[5_1|2]), (216,140,[5_1|2]), (216,144,[5_1|2]), (216,233,[5_1|2]), (217,218,[0_1|2]), (218,219,[3_1|2]), (219,220,[0_1|2]), (220,221,[0_1|2]), (221,81,[2_1|2]), (221,207,[2_1|2]), (221,245,[2_1|2]), (222,223,[0_1|2]), (223,224,[2_1|2]), (224,225,[5_1|2]), (225,226,[0_1|2]), (225,82,[1_1|2]), (225,85,[1_1|2]), (225,89,[1_1|2]), (225,94,[5_1|2]), (225,98,[1_1|2]), (225,102,[1_1|2]), (225,105,[4_1|2]), (225,108,[4_1|2]), (225,112,[1_1|2]), (225,116,[1_1|2]), (225,285,[4_1|2]), (225,120,[0_1|2]), (225,125,[1_1|2]), (225,324,[1_1|3]), (225,327,[1_1|3]), (225,331,[1_1|3]), (225,336,[1_1|3]), (225,339,[4_1|3]), (225,342,[4_1|3]), (225,346,[1_1|3]), (225,350,[0_1|3]), (225,355,[1_1|3]), (225,359,[5_1|3]), (226,81,[1_1|2]), (226,140,[1_1|2]), (226,144,[1_1|2]), (226,233,[1_1|2]), (226,260,[1_1|2]), (226,265,[5_1|2]), (226,270,[1_1|2]), (226,275,[4_1|2]), (226,280,[0_1|2]), (227,228,[5_1|2]), (228,229,[0_1|2]), (229,230,[0_1|2]), (230,231,[3_1|2]), (231,81,[1_1|2]), (231,207,[1_1|2]), (231,245,[1_1|2]), (231,126,[1_1|2]), (231,260,[1_1|2]), (231,265,[5_1|2]), (231,270,[1_1|2]), (231,275,[4_1|2]), (231,280,[0_1|2]), (232,233,[2_1|2]), (233,234,[4_1|2]), (234,235,[0_1|2]), (235,81,[2_1|2]), (235,82,[2_1|2]), (235,85,[2_1|2]), (235,89,[2_1|2]), (235,98,[2_1|2]), (235,102,[2_1|2]), (235,112,[2_1|2]), (235,116,[2_1|2]), (235,125,[2_1|2]), (235,136,[2_1|2]), (235,158,[2_1|2]), (235,183,[2_1|2]), (235,188,[2_1|2]), (235,212,[2_1|2]), (235,217,[2_1|2]), (235,232,[2_1|2]), (235,260,[2_1|2]), (235,270,[2_1|2]), (235,141,[2_1|2]), (236,237,[4_1|2]), (237,238,[1_1|2]), (238,239,[5_1|2]), (239,240,[3_1|2]), (240,81,[2_1|2]), (240,82,[2_1|2]), (240,85,[2_1|2]), (240,89,[2_1|2]), (240,98,[2_1|2]), (240,102,[2_1|2]), (240,112,[2_1|2]), (240,116,[2_1|2]), (240,125,[2_1|2]), (240,136,[2_1|2]), (240,158,[2_1|2]), (240,183,[2_1|2]), (240,188,[2_1|2]), (240,212,[2_1|2]), (240,217,[2_1|2]), (240,232,[2_1|2]), (240,260,[2_1|2]), (240,270,[2_1|2]), (240,174,[2_1|2]), (240,242,[2_1|2]), (241,242,[1_1|2]), (242,243,[0_1|2]), (243,244,[2_1|2]), (244,81,[1_1|2]), (244,82,[1_1|2]), (244,85,[1_1|2]), (244,89,[1_1|2]), (244,98,[1_1|2]), (244,102,[1_1|2]), (244,112,[1_1|2]), (244,116,[1_1|2]), (244,125,[1_1|2]), (244,136,[1_1|2]), (244,158,[1_1|2]), (244,183,[1_1|2]), (244,188,[1_1|2]), (244,212,[1_1|2]), (244,217,[1_1|2]), (244,232,[1_1|2]), (244,260,[1_1|2]), (244,270,[1_1|2]), (244,141,[1_1|2]), (244,265,[5_1|2]), (244,275,[4_1|2]), (244,280,[0_1|2]), (245,246,[4_1|2]), (246,247,[0_1|2]), (247,248,[2_1|2]), (248,249,[1_1|2]), (249,81,[1_1|2]), (249,82,[1_1|2]), (249,85,[1_1|2]), (249,89,[1_1|2]), (249,98,[1_1|2]), (249,102,[1_1|2]), (249,112,[1_1|2]), (249,116,[1_1|2]), (249,125,[1_1|2]), (249,136,[1_1|2]), (249,158,[1_1|2]), (249,183,[1_1|2]), (249,188,[1_1|2]), (249,212,[1_1|2]), (249,217,[1_1|2]), (249,232,[1_1|2]), (249,260,[1_1|2]), (249,270,[1_1|2]), (249,141,[1_1|2]), (249,265,[5_1|2]), (249,275,[4_1|2]), (249,280,[0_1|2]), (250,251,[3_1|2]), (251,252,[4_1|2]), (252,253,[0_1|2]), (253,254,[2_1|2]), (254,81,[1_1|2]), (254,82,[1_1|2]), (254,85,[1_1|2]), (254,89,[1_1|2]), (254,98,[1_1|2]), (254,102,[1_1|2]), (254,112,[1_1|2]), (254,116,[1_1|2]), (254,125,[1_1|2]), (254,136,[1_1|2]), (254,158,[1_1|2]), (254,183,[1_1|2]), (254,188,[1_1|2]), (254,212,[1_1|2]), (254,217,[1_1|2]), (254,232,[1_1|2]), (254,260,[1_1|2]), (254,270,[1_1|2]), (254,141,[1_1|2]), (254,265,[5_1|2]), (254,275,[4_1|2]), (254,280,[0_1|2]), (255,256,[0_1|2]), (256,257,[0_1|2]), (257,258,[4_1|2]), (258,259,[4_1|2]), (259,81,[5_1|2]), (259,105,[5_1|2]), (259,108,[5_1|2]), (259,133,[5_1|2]), (259,163,[5_1|2]), (259,173,[5_1|2]), (259,227,[5_1|2]), (259,236,[5_1|2]), (259,241,[5_1|2]), (259,275,[5_1|2]), (259,285,[5_1|2]), (259,289,[5_1|2]), (259,292,[5_1|2]), (260,261,[4_1|2]), (261,262,[5_1|2]), (262,263,[0_1|2]), (263,264,[3_1|2]), (264,81,[3_1|2]), (264,105,[3_1|2]), (264,108,[3_1|2]), (264,133,[3_1|2]), (264,163,[3_1|2]), (264,173,[3_1|2]), (264,227,[3_1|2]), (264,236,[3_1|2]), (264,241,[3_1|2]), (264,275,[3_1|2]), (264,285,[3_1|2]), (264,289,[3_1|2]), (264,292,[3_1|2]), (265,266,[5_1|2]), (266,267,[1_1|2]), (267,268,[0_1|2]), (268,269,[2_1|2]), (269,81,[4_1|2]), (269,105,[4_1|2]), (269,108,[4_1|2]), (269,133,[4_1|2]), (269,163,[4_1|2]), (269,173,[4_1|2]), (269,227,[4_1|2]), (269,236,[4_1|2]), (269,241,[4_1|2]), (269,275,[4_1|2]), (269,314,[4_1|2]), (269,232,[1_1|2]), (269,245,[3_1|2]), (269,250,[0_1|2]), (269,255,[5_1|2]), (269,317,[4_1|3]), (269,320,[1_1|3]), (269,285,[4_1|2]), (269,289,[4_1|2]), (269,292,[4_1|2]), (270,271,[1_1|2]), (271,272,[0_1|2]), (272,273,[2_1|2]), (273,274,[3_1|2]), (274,81,[4_1|2]), (274,105,[4_1|2]), (274,108,[4_1|2]), (274,133,[4_1|2]), (274,163,[4_1|2]), (274,173,[4_1|2]), (274,227,[4_1|2]), (274,236,[4_1|2]), (274,241,[4_1|2]), (274,275,[4_1|2]), (274,234,[4_1|2]), (274,314,[4_1|2]), (274,232,[1_1|2]), (274,245,[3_1|2]), (274,250,[0_1|2]), (274,255,[5_1|2]), (274,317,[4_1|3]), (274,320,[1_1|3]), (274,285,[4_1|2]), (274,289,[4_1|2]), (274,292,[4_1|2]), (275,276,[0_1|2]), (276,277,[2_1|2]), (277,278,[1_1|2]), (278,279,[2_1|2]), (279,81,[1_1|2]), (279,82,[1_1|2]), (279,85,[1_1|2]), (279,89,[1_1|2]), (279,98,[1_1|2]), (279,102,[1_1|2]), (279,112,[1_1|2]), (279,116,[1_1|2]), (279,125,[1_1|2]), (279,136,[1_1|2]), (279,158,[1_1|2]), (279,183,[1_1|2]), (279,188,[1_1|2]), (279,212,[1_1|2]), (279,217,[1_1|2]), (279,232,[1_1|2]), (279,260,[1_1|2]), (279,270,[1_1|2]), (279,141,[1_1|2]), (279,265,[5_1|2]), (279,275,[4_1|2]), (279,280,[0_1|2]), (280,281,[2_1|2]), (281,282,[2_1|2]), (282,283,[1_1|2]), (283,284,[1_1|2]), (283,275,[4_1|2]), (283,280,[0_1|2]), (283,309,[4_1|3]), (284,81,[4_1|2]), (284,140,[4_1|2]), (284,144,[4_1|2]), (284,233,[4_1|2]), (284,314,[4_1|2]), (284,232,[1_1|2]), (284,236,[4_1|2]), (284,241,[4_1|2]), (284,245,[3_1|2]), (284,250,[0_1|2]), (284,255,[5_1|2]), (284,317,[4_1|3]), (284,320,[1_1|3]), (285,286,[0_1|2]), (286,287,[2_1|2]), (287,288,[1_1|2]), (288,207,[3_1|2]), (288,245,[3_1|2]), (289,290,[0_1|2]), (290,291,[2_1|2]), (291,82,[1_1|2]), (291,85,[1_1|2]), (291,89,[1_1|2]), (291,98,[1_1|2]), (291,102,[1_1|2]), (291,112,[1_1|2]), (291,116,[1_1|2]), (291,125,[1_1|2]), (291,136,[1_1|2]), (291,158,[1_1|2]), (291,183,[1_1|2]), (291,188,[1_1|2]), (291,212,[1_1|2]), (291,217,[1_1|2]), (291,232,[1_1|2]), (291,260,[1_1|2]), (291,270,[1_1|2]), (291,174,[1_1|2]), (291,242,[1_1|2]), (292,293,[0_1|2]), (293,294,[2_1|2]), (294,141,[1_1|2]), (295,296,[1_1|3]), (296,297,[0_1|3]), (297,298,[2_1|3]), (298,141,[1_1|3]), (299,300,[4_1|3]), (300,301,[0_1|3]), (301,302,[2_1|3]), (302,303,[1_1|3]), (303,141,[1_1|3]), (304,305,[3_1|3]), (305,306,[4_1|3]), (306,307,[0_1|3]), (307,308,[2_1|3]), (308,141,[1_1|3]), (309,310,[0_1|3]), (310,311,[2_1|3]), (311,312,[1_1|3]), (312,313,[2_1|3]), (313,141,[1_1|3]), (314,315,[0_1|2]), (315,316,[2_1|2]), (316,81,[1_1|2]), (316,82,[1_1|2]), (316,85,[1_1|2]), (316,89,[1_1|2]), (316,98,[1_1|2]), (316,102,[1_1|2]), (316,112,[1_1|2]), (316,116,[1_1|2]), (316,125,[1_1|2]), (316,136,[1_1|2]), (316,158,[1_1|2]), (316,183,[1_1|2]), (316,188,[1_1|2]), (316,212,[1_1|2]), (316,217,[1_1|2]), (316,232,[1_1|2]), (316,260,[1_1|2]), (316,270,[1_1|2]), (316,265,[5_1|2]), (316,275,[4_1|2]), (316,280,[0_1|2]), (317,318,[0_1|3]), (318,319,[2_1|3]), (319,141,[1_1|3]), (320,321,[2_1|3]), (321,322,[4_1|3]), (322,323,[0_1|3]), (323,141,[2_1|3]), (324,325,[0_1|3]), (325,326,[2_1|3]), (326,82,[1_1|3]), (326,85,[1_1|3]), (326,89,[1_1|3]), (326,98,[1_1|3]), (326,102,[1_1|3]), (326,112,[1_1|3]), (326,116,[1_1|3]), (326,125,[1_1|3]), (326,136,[1_1|3]), (326,158,[1_1|3]), (326,183,[1_1|3]), (326,188,[1_1|3]), (326,212,[1_1|3]), (326,217,[1_1|3]), (326,232,[1_1|3]), (326,260,[1_1|3]), (326,270,[1_1|3]), (326,141,[1_1|3]), (326,271,[1_1|3]), (327,328,[1_1|3]), (328,329,[0_1|3]), (329,330,[3_1|3]), (330,82,[2_1|3]), (330,85,[2_1|3]), (330,89,[2_1|3]), (330,98,[2_1|3]), (330,102,[2_1|3]), (330,112,[2_1|3]), (330,116,[2_1|3]), (330,125,[2_1|3]), (330,136,[2_1|3]), (330,158,[2_1|3]), (330,183,[2_1|3]), (330,188,[2_1|3]), (330,212,[2_1|3]), (330,217,[2_1|3]), (330,232,[2_1|3]), (330,260,[2_1|3]), (330,270,[2_1|3]), (330,141,[2_1|3]), (330,271,[2_1|3]), (331,332,[4_1|3]), (332,333,[0_1|3]), (333,334,[0_1|3]), (334,335,[2_1|3]), (335,82,[1_1|3]), (335,85,[1_1|3]), (335,89,[1_1|3]), (335,98,[1_1|3]), (335,102,[1_1|3]), (335,112,[1_1|3]), (335,116,[1_1|3]), (335,125,[1_1|3]), (335,136,[1_1|3]), (335,158,[1_1|3]), (335,183,[1_1|3]), (335,188,[1_1|3]), (335,212,[1_1|3]), (335,217,[1_1|3]), (335,232,[1_1|3]), (335,260,[1_1|3]), (335,270,[1_1|3]), (335,141,[1_1|3]), (335,271,[1_1|3]), (336,337,[4_1|3]), (337,338,[0_1|3]), (338,105,[3_1|3]), (338,108,[3_1|3]), (338,133,[3_1|3]), (338,163,[3_1|3]), (338,173,[3_1|3]), (338,227,[3_1|3]), (338,236,[3_1|3]), (338,241,[3_1|3]), (338,275,[3_1|3]), (338,285,[3_1|3]), (338,289,[3_1|3]), (338,292,[3_1|3]), (338,234,[3_1|3]), (338,261,[3_1|3]), (339,340,[0_1|3]), (340,341,[2_1|3]), (341,105,[1_1|3]), (341,108,[1_1|3]), (341,133,[1_1|3]), (341,163,[1_1|3]), (341,173,[1_1|3]), (341,227,[1_1|3]), (341,236,[1_1|3]), (341,241,[1_1|3]), (341,275,[1_1|3]), (341,285,[1_1|3]), (341,289,[1_1|3]), (341,292,[1_1|3]), (341,234,[1_1|3]), (341,261,[1_1|3]), (342,343,[0_1|3]), (343,344,[2_1|3]), (344,345,[1_1|3]), (345,105,[3_1|3]), (345,108,[3_1|3]), (345,133,[3_1|3]), (345,163,[3_1|3]), (345,173,[3_1|3]), (345,227,[3_1|3]), (345,236,[3_1|3]), (345,241,[3_1|3]), (345,275,[3_1|3]), (345,285,[3_1|3]), (345,289,[3_1|3]), (345,292,[3_1|3]), (345,234,[3_1|3]), (345,261,[3_1|3]), (346,347,[1_1|3]), (347,348,[5_1|3]), (348,349,[0_1|3]), (349,126,[3_1|3]), (350,351,[0_1|3]), (351,352,[2_1|3]), (352,353,[2_1|3]), (353,354,[1_1|3]), (354,149,[4_1|3]), (355,356,[0_1|3]), (356,357,[2_1|3]), (357,358,[4_1|3]), (358,174,[1_1|3]), (358,242,[1_1|3]), (359,360,[1_1|3]), (360,361,[0_1|3]), (361,362,[2_1|3]), (362,233,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)