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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 52 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 53 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. "[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] {(78,79,[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]), (78,80,[2_1|1, 3_1|1, 5_1|1, 0_1|1, 4_1|1, 1_1|1]), (78,81,[1_1|2]), (78,84,[1_1|2]), (78,88,[1_1|2]), (78,93,[5_1|2]), (78,97,[1_1|2]), (78,101,[1_1|2]), (78,104,[4_1|2]), (78,107,[4_1|2]), (78,111,[1_1|2]), (78,115,[1_1|2]), (78,119,[0_1|2]), (78,124,[1_1|2]), (78,129,[0_1|2]), (78,132,[4_1|2]), (78,135,[1_1|2]), (78,139,[2_1|2]), (78,143,[2_1|2]), (78,147,[0_1|2]), (78,152,[0_1|2]), (78,157,[1_1|2]), (78,162,[4_1|2]), (78,167,[5_1|2]), (78,172,[4_1|2]), 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(210,231,[1_1|2]), (210,235,[4_1|2]), (210,240,[4_1|2]), (210,249,[0_1|2]), (210,254,[5_1|2]), (210,316,[4_1|3]), (210,319,[1_1|3]), (211,212,[5_1|2]), (212,213,[3_1|2]), (213,214,[0_1|2]), (214,215,[2_1|2]), (215,80,[5_1|2]), (215,139,[5_1|2]), (215,143,[5_1|2]), (215,232,[5_1|2]), (216,217,[0_1|2]), (217,218,[3_1|2]), (218,219,[0_1|2]), (219,220,[0_1|2]), (220,80,[2_1|2]), (220,206,[2_1|2]), (220,244,[2_1|2]), (221,222,[0_1|2]), (222,223,[2_1|2]), (223,224,[5_1|2]), (224,225,[0_1|2]), (224,81,[1_1|2]), (224,84,[1_1|2]), (224,88,[1_1|2]), (224,93,[5_1|2]), (224,97,[1_1|2]), (224,101,[1_1|2]), (224,104,[4_1|2]), (224,107,[4_1|2]), (224,111,[1_1|2]), (224,115,[1_1|2]), (224,284,[4_1|2]), (224,119,[0_1|2]), (224,124,[1_1|2]), (224,323,[1_1|3]), (224,326,[1_1|3]), (224,330,[1_1|3]), (224,335,[1_1|3]), (224,338,[4_1|3]), (224,341,[4_1|3]), (224,345,[1_1|3]), (224,349,[0_1|3]), (224,354,[1_1|3]), (224,358,[5_1|3]), (225,80,[1_1|2]), (225,139,[1_1|2]), (225,143,[1_1|2]), (225,232,[1_1|2]), (225,259,[1_1|2]), (225,264,[5_1|2]), (225,269,[1_1|2]), (225,274,[4_1|2]), (225,279,[0_1|2]), (226,227,[5_1|2]), (227,228,[0_1|2]), (228,229,[0_1|2]), (229,230,[3_1|2]), (230,80,[1_1|2]), (230,206,[1_1|2]), (230,244,[1_1|2]), (230,125,[1_1|2]), (230,259,[1_1|2]), (230,264,[5_1|2]), (230,269,[1_1|2]), (230,274,[4_1|2]), (230,279,[0_1|2]), (231,232,[2_1|2]), (232,233,[4_1|2]), (233,234,[0_1|2]), (234,80,[2_1|2]), (234,81,[2_1|2]), (234,84,[2_1|2]), (234,88,[2_1|2]), (234,97,[2_1|2]), (234,101,[2_1|2]), (234,111,[2_1|2]), (234,115,[2_1|2]), (234,124,[2_1|2]), (234,135,[2_1|2]), (234,157,[2_1|2]), (234,182,[2_1|2]), (234,187,[2_1|2]), (234,211,[2_1|2]), (234,216,[2_1|2]), (234,231,[2_1|2]), (234,259,[2_1|2]), (234,269,[2_1|2]), (234,140,[2_1|2]), (235,236,[4_1|2]), (236,237,[1_1|2]), (237,238,[5_1|2]), (238,239,[3_1|2]), (239,80,[2_1|2]), (239,81,[2_1|2]), (239,84,[2_1|2]), (239,88,[2_1|2]), (239,97,[2_1|2]), (239,101,[2_1|2]), (239,111,[2_1|2]), (239,115,[2_1|2]), (239,124,[2_1|2]), (239,135,[2_1|2]), (239,157,[2_1|2]), (239,182,[2_1|2]), (239,187,[2_1|2]), (239,211,[2_1|2]), (239,216,[2_1|2]), (239,231,[2_1|2]), (239,259,[2_1|2]), (239,269,[2_1|2]), (239,173,[2_1|2]), (239,241,[2_1|2]), (240,241,[1_1|2]), (241,242,[0_1|2]), (242,243,[2_1|2]), (243,80,[1_1|2]), (243,81,[1_1|2]), (243,84,[1_1|2]), (243,88,[1_1|2]), (243,97,[1_1|2]), (243,101,[1_1|2]), (243,111,[1_1|2]), (243,115,[1_1|2]), (243,124,[1_1|2]), (243,135,[1_1|2]), (243,157,[1_1|2]), (243,182,[1_1|2]), (243,187,[1_1|2]), (243,211,[1_1|2]), (243,216,[1_1|2]), (243,231,[1_1|2]), (243,259,[1_1|2]), (243,269,[1_1|2]), (243,140,[1_1|2]), (243,264,[5_1|2]), (243,274,[4_1|2]), (243,279,[0_1|2]), (244,245,[4_1|2]), (245,246,[0_1|2]), (246,247,[2_1|2]), (247,248,[1_1|2]), (248,80,[1_1|2]), (248,81,[1_1|2]), (248,84,[1_1|2]), (248,88,[1_1|2]), (248,97,[1_1|2]), (248,101,[1_1|2]), (248,111,[1_1|2]), (248,115,[1_1|2]), (248,124,[1_1|2]), (248,135,[1_1|2]), (248,157,[1_1|2]), (248,182,[1_1|2]), (248,187,[1_1|2]), (248,211,[1_1|2]), (248,216,[1_1|2]), (248,231,[1_1|2]), (248,259,[1_1|2]), (248,269,[1_1|2]), (248,140,[1_1|2]), (248,264,[5_1|2]), (248,274,[4_1|2]), (248,279,[0_1|2]), (249,250,[3_1|2]), (250,251,[4_1|2]), (251,252,[0_1|2]), (252,253,[2_1|2]), (253,80,[1_1|2]), (253,81,[1_1|2]), (253,84,[1_1|2]), (253,88,[1_1|2]), (253,97,[1_1|2]), (253,101,[1_1|2]), (253,111,[1_1|2]), (253,115,[1_1|2]), (253,124,[1_1|2]), (253,135,[1_1|2]), (253,157,[1_1|2]), (253,182,[1_1|2]), (253,187,[1_1|2]), (253,211,[1_1|2]), (253,216,[1_1|2]), (253,231,[1_1|2]), (253,259,[1_1|2]), (253,269,[1_1|2]), (253,140,[1_1|2]), (253,264,[5_1|2]), (253,274,[4_1|2]), (253,279,[0_1|2]), (254,255,[0_1|2]), (255,256,[0_1|2]), (256,257,[4_1|2]), (257,258,[4_1|2]), (258,80,[5_1|2]), (258,104,[5_1|2]), (258,107,[5_1|2]), (258,132,[5_1|2]), (258,162,[5_1|2]), (258,172,[5_1|2]), (258,226,[5_1|2]), (258,235,[5_1|2]), (258,240,[5_1|2]), (258,274,[5_1|2]), (258,284,[5_1|2]), (258,288,[5_1|2]), (258,291,[5_1|2]), (259,260,[4_1|2]), (260,261,[5_1|2]), (261,262,[0_1|2]), (262,263,[3_1|2]), (263,80,[3_1|2]), (263,104,[3_1|2]), (263,107,[3_1|2]), (263,132,[3_1|2]), (263,162,[3_1|2]), (263,172,[3_1|2]), (263,226,[3_1|2]), (263,235,[3_1|2]), (263,240,[3_1|2]), (263,274,[3_1|2]), (263,284,[3_1|2]), (263,288,[3_1|2]), (263,291,[3_1|2]), (264,265,[5_1|2]), (265,266,[1_1|2]), (266,267,[0_1|2]), (267,268,[2_1|2]), (268,80,[4_1|2]), (268,104,[4_1|2]), (268,107,[4_1|2]), (268,132,[4_1|2]), (268,162,[4_1|2]), (268,172,[4_1|2]), (268,226,[4_1|2]), (268,235,[4_1|2]), (268,240,[4_1|2]), (268,274,[4_1|2]), (268,313,[4_1|2]), (268,231,[1_1|2]), (268,244,[3_1|2]), (268,249,[0_1|2]), (268,254,[5_1|2]), (268,316,[4_1|3]), (268,319,[1_1|3]), (268,284,[4_1|2]), (268,288,[4_1|2]), (268,291,[4_1|2]), (269,270,[1_1|2]), (270,271,[0_1|2]), (271,272,[2_1|2]), (272,273,[3_1|2]), (273,80,[4_1|2]), (273,104,[4_1|2]), (273,107,[4_1|2]), (273,132,[4_1|2]), (273,162,[4_1|2]), (273,172,[4_1|2]), (273,226,[4_1|2]), (273,235,[4_1|2]), (273,240,[4_1|2]), (273,274,[4_1|2]), (273,233,[4_1|2]), (273,313,[4_1|2]), (273,231,[1_1|2]), (273,244,[3_1|2]), (273,249,[0_1|2]), (273,254,[5_1|2]), (273,316,[4_1|3]), (273,319,[1_1|3]), (273,284,[4_1|2]), (273,288,[4_1|2]), (273,291,[4_1|2]), (274,275,[0_1|2]), (275,276,[2_1|2]), (276,277,[1_1|2]), (277,278,[2_1|2]), (278,80,[1_1|2]), (278,81,[1_1|2]), (278,84,[1_1|2]), (278,88,[1_1|2]), (278,97,[1_1|2]), (278,101,[1_1|2]), (278,111,[1_1|2]), (278,115,[1_1|2]), (278,124,[1_1|2]), (278,135,[1_1|2]), (278,157,[1_1|2]), (278,182,[1_1|2]), (278,187,[1_1|2]), (278,211,[1_1|2]), (278,216,[1_1|2]), (278,231,[1_1|2]), (278,259,[1_1|2]), (278,269,[1_1|2]), (278,140,[1_1|2]), (278,264,[5_1|2]), (278,274,[4_1|2]), (278,279,[0_1|2]), (279,280,[2_1|2]), (280,281,[2_1|2]), (281,282,[1_1|2]), (282,283,[1_1|2]), (282,274,[4_1|2]), (282,279,[0_1|2]), (282,308,[4_1|3]), (283,80,[4_1|2]), (283,139,[4_1|2]), (283,143,[4_1|2]), (283,232,[4_1|2]), (283,313,[4_1|2]), (283,231,[1_1|2]), (283,235,[4_1|2]), (283,240,[4_1|2]), (283,244,[3_1|2]), (283,249,[0_1|2]), (283,254,[5_1|2]), (283,316,[4_1|3]), (283,319,[1_1|3]), (284,285,[0_1|2]), (285,286,[2_1|2]), (286,287,[1_1|2]), (287,206,[3_1|2]), (287,244,[3_1|2]), (288,289,[0_1|2]), (289,290,[2_1|2]), (290,81,[1_1|2]), (290,84,[1_1|2]), (290,88,[1_1|2]), (290,97,[1_1|2]), (290,101,[1_1|2]), (290,111,[1_1|2]), (290,115,[1_1|2]), (290,124,[1_1|2]), (290,135,[1_1|2]), (290,157,[1_1|2]), (290,182,[1_1|2]), (290,187,[1_1|2]), (290,211,[1_1|2]), (290,216,[1_1|2]), (290,231,[1_1|2]), (290,259,[1_1|2]), (290,269,[1_1|2]), (290,173,[1_1|2]), (290,241,[1_1|2]), (291,292,[0_1|2]), (292,293,[2_1|2]), (293,140,[1_1|2]), (294,295,[1_1|3]), (295,296,[0_1|3]), (296,297,[2_1|3]), (297,140,[1_1|3]), (298,299,[4_1|3]), (299,300,[0_1|3]), (300,301,[2_1|3]), (301,302,[1_1|3]), (302,140,[1_1|3]), (303,304,[3_1|3]), (304,305,[4_1|3]), (305,306,[0_1|3]), (306,307,[2_1|3]), (307,140,[1_1|3]), (308,309,[0_1|3]), (309,310,[2_1|3]), (310,311,[1_1|3]), (311,312,[2_1|3]), (312,140,[1_1|3]), (313,314,[0_1|2]), (314,315,[2_1|2]), (315,80,[1_1|2]), (315,81,[1_1|2]), (315,84,[1_1|2]), (315,88,[1_1|2]), (315,97,[1_1|2]), (315,101,[1_1|2]), (315,111,[1_1|2]), (315,115,[1_1|2]), (315,124,[1_1|2]), (315,135,[1_1|2]), (315,157,[1_1|2]), (315,182,[1_1|2]), (315,187,[1_1|2]), (315,211,[1_1|2]), (315,216,[1_1|2]), (315,231,[1_1|2]), (315,259,[1_1|2]), (315,269,[1_1|2]), (315,264,[5_1|2]), (315,274,[4_1|2]), (315,279,[0_1|2]), (316,317,[0_1|3]), (317,318,[2_1|3]), (318,140,[1_1|3]), (319,320,[2_1|3]), (320,321,[4_1|3]), (321,322,[0_1|3]), (322,140,[2_1|3]), (323,324,[0_1|3]), (324,325,[2_1|3]), (325,81,[1_1|3]), (325,84,[1_1|3]), (325,88,[1_1|3]), (325,97,[1_1|3]), (325,101,[1_1|3]), (325,111,[1_1|3]), (325,115,[1_1|3]), (325,124,[1_1|3]), (325,135,[1_1|3]), (325,157,[1_1|3]), (325,182,[1_1|3]), (325,187,[1_1|3]), (325,211,[1_1|3]), (325,216,[1_1|3]), (325,231,[1_1|3]), (325,259,[1_1|3]), (325,269,[1_1|3]), (325,140,[1_1|3]), (325,270,[1_1|3]), (326,327,[1_1|3]), (327,328,[0_1|3]), (328,329,[3_1|3]), (329,81,[2_1|3]), (329,84,[2_1|3]), (329,88,[2_1|3]), (329,97,[2_1|3]), (329,101,[2_1|3]), (329,111,[2_1|3]), (329,115,[2_1|3]), (329,124,[2_1|3]), (329,135,[2_1|3]), (329,157,[2_1|3]), (329,182,[2_1|3]), (329,187,[2_1|3]), (329,211,[2_1|3]), (329,216,[2_1|3]), (329,231,[2_1|3]), (329,259,[2_1|3]), (329,269,[2_1|3]), (329,140,[2_1|3]), (329,270,[2_1|3]), (330,331,[4_1|3]), (331,332,[0_1|3]), (332,333,[0_1|3]), (333,334,[2_1|3]), (334,81,[1_1|3]), (334,84,[1_1|3]), (334,88,[1_1|3]), (334,97,[1_1|3]), (334,101,[1_1|3]), (334,111,[1_1|3]), (334,115,[1_1|3]), (334,124,[1_1|3]), (334,135,[1_1|3]), (334,157,[1_1|3]), (334,182,[1_1|3]), (334,187,[1_1|3]), (334,211,[1_1|3]), (334,216,[1_1|3]), (334,231,[1_1|3]), (334,259,[1_1|3]), (334,269,[1_1|3]), (334,140,[1_1|3]), (334,270,[1_1|3]), (335,336,[4_1|3]), (336,337,[0_1|3]), (337,104,[3_1|3]), (337,107,[3_1|3]), (337,132,[3_1|3]), (337,162,[3_1|3]), (337,172,[3_1|3]), (337,226,[3_1|3]), (337,235,[3_1|3]), (337,240,[3_1|3]), (337,274,[3_1|3]), (337,284,[3_1|3]), (337,288,[3_1|3]), (337,291,[3_1|3]), (337,233,[3_1|3]), (337,260,[3_1|3]), (338,339,[0_1|3]), (339,340,[2_1|3]), (340,104,[1_1|3]), (340,107,[1_1|3]), (340,132,[1_1|3]), (340,162,[1_1|3]), (340,172,[1_1|3]), (340,226,[1_1|3]), (340,235,[1_1|3]), (340,240,[1_1|3]), (340,274,[1_1|3]), (340,284,[1_1|3]), (340,288,[1_1|3]), (340,291,[1_1|3]), (340,233,[1_1|3]), (340,260,[1_1|3]), (341,342,[0_1|3]), (342,343,[2_1|3]), (343,344,[1_1|3]), (344,104,[3_1|3]), (344,107,[3_1|3]), (344,132,[3_1|3]), (344,162,[3_1|3]), (344,172,[3_1|3]), (344,226,[3_1|3]), (344,235,[3_1|3]), (344,240,[3_1|3]), (344,274,[3_1|3]), (344,284,[3_1|3]), (344,288,[3_1|3]), (344,291,[3_1|3]), (344,233,[3_1|3]), (344,260,[3_1|3]), (345,346,[1_1|3]), (346,347,[5_1|3]), (347,348,[0_1|3]), (348,125,[3_1|3]), (349,350,[0_1|3]), (350,351,[2_1|3]), (351,352,[2_1|3]), (352,353,[1_1|3]), (353,148,[4_1|3]), (354,355,[0_1|3]), (355,356,[2_1|3]), (356,357,[4_1|3]), (357,173,[1_1|3]), (357,241,[1_1|3]), (358,359,[1_1|3]), (359,360,[0_1|3]), (360,361,[2_1|3]), (361,232,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)