/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 84 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 117 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(x1)) -> 0(1(0(2(x1)))) 0(0(x1)) -> 1(0(2(0(x1)))) 0(0(x1)) -> 1(0(1(0(1(x1))))) 0(0(x1)) -> 1(0(1(2(0(x1))))) 0(0(x1)) -> 1(0(2(0(3(x1))))) 0(0(x1)) -> 1(0(2(2(0(x1))))) 0(0(x1)) -> 2(1(0(2(0(x1))))) 0(0(x1)) -> 0(1(0(2(1(2(x1)))))) 0(0(x1)) -> 1(0(1(0(2(2(x1)))))) 0(0(x1)) -> 1(0(1(3(0(1(x1)))))) 0(0(x1)) -> 1(0(4(1(0(2(x1)))))) 0(0(x1)) -> 1(1(1(0(2(0(x1)))))) 0(0(x1)) -> 3(0(4(0(2(2(x1)))))) 0(0(x1)) -> 3(1(0(1(0(4(x1)))))) 0(0(0(x1))) -> 0(1(0(4(0(4(x1)))))) 0(0(0(x1))) -> 3(0(0(1(0(2(x1)))))) 3(0(0(x1))) -> 3(0(2(0(3(x1))))) 3(0(0(x1))) -> 3(0(2(4(0(2(x1)))))) 5(2(0(x1))) -> 0(2(3(5(x1)))) 5(2(0(x1))) -> 3(5(0(2(x1)))) 5(2(0(x1))) -> 0(2(3(3(5(x1))))) 5(2(0(x1))) -> 1(0(2(3(5(x1))))) 5(2(0(x1))) -> 5(1(0(2(4(x1))))) 5(2(0(x1))) -> 5(0(1(2(2(2(x1)))))) 5(2(0(x1))) -> 5(3(5(1(0(2(x1)))))) 0(5(2(0(x1)))) -> 0(5(0(2(2(x1))))) 3(4(0(0(x1)))) -> 0(3(3(0(4(5(x1)))))) 3(4(0(0(x1)))) -> 3(0(4(5(3(0(x1)))))) 5(1(0(0(x1)))) -> 0(3(1(0(1(5(x1)))))) 5(1(4(0(x1)))) -> 0(1(5(2(4(x1))))) 5(1(5(0(x1)))) -> 5(1(0(3(5(x1))))) 5(2(2(0(x1)))) -> 0(2(1(2(4(5(x1)))))) 5(3(2(0(x1)))) -> 5(3(0(1(2(x1))))) 5(3(2(0(x1)))) -> 3(3(5(3(0(2(x1)))))) 5(4(0(0(x1)))) -> 0(4(5(5(0(2(x1)))))) 5(4(2(0(x1)))) -> 2(4(3(5(0(x1))))) 5(4(2(0(x1)))) -> 5(0(2(2(4(x1))))) 5(4(2(0(x1)))) -> 5(4(5(0(2(x1))))) 0(3(5(2(0(x1))))) -> 3(0(2(5(3(0(x1)))))) 3(3(5(2(0(x1))))) -> 3(5(2(3(0(2(x1)))))) 3(3(5(2(0(x1))))) -> 4(3(3(5(0(2(x1)))))) 5(0(5(2(0(x1))))) -> 0(3(5(5(0(2(x1)))))) 5(1(4(0(0(x1))))) -> 0(2(5(0(1(4(x1)))))) 5(3(3(2(0(x1))))) -> 5(2(3(3(0(2(x1)))))) 5(4(3(0(0(x1))))) -> 1(0(4(0(3(5(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(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(x1)) -> 0(1(0(2(x1)))) 0(0(x1)) -> 1(0(2(0(x1)))) 0(0(x1)) -> 1(0(1(0(1(x1))))) 0(0(x1)) -> 1(0(1(2(0(x1))))) 0(0(x1)) -> 1(0(2(0(3(x1))))) 0(0(x1)) -> 1(0(2(2(0(x1))))) 0(0(x1)) -> 2(1(0(2(0(x1))))) 0(0(x1)) -> 0(1(0(2(1(2(x1)))))) 0(0(x1)) -> 1(0(1(0(2(2(x1)))))) 0(0(x1)) -> 1(0(1(3(0(1(x1)))))) 0(0(x1)) -> 1(0(4(1(0(2(x1)))))) 0(0(x1)) -> 1(1(1(0(2(0(x1)))))) 0(0(x1)) -> 3(0(4(0(2(2(x1)))))) 0(0(x1)) -> 3(1(0(1(0(4(x1)))))) 0(0(0(x1))) -> 0(1(0(4(0(4(x1)))))) 0(0(0(x1))) -> 3(0(0(1(0(2(x1)))))) 3(0(0(x1))) -> 3(0(2(0(3(x1))))) 3(0(0(x1))) -> 3(0(2(4(0(2(x1)))))) 5(2(0(x1))) -> 0(2(3(5(x1)))) 5(2(0(x1))) -> 3(5(0(2(x1)))) 5(2(0(x1))) -> 0(2(3(3(5(x1))))) 5(2(0(x1))) -> 1(0(2(3(5(x1))))) 5(2(0(x1))) -> 5(1(0(2(4(x1))))) 5(2(0(x1))) -> 5(0(1(2(2(2(x1)))))) 5(2(0(x1))) -> 5(3(5(1(0(2(x1)))))) 0(5(2(0(x1)))) -> 0(5(0(2(2(x1))))) 3(4(0(0(x1)))) -> 0(3(3(0(4(5(x1)))))) 3(4(0(0(x1)))) -> 3(0(4(5(3(0(x1)))))) 5(1(0(0(x1)))) -> 0(3(1(0(1(5(x1)))))) 5(1(4(0(x1)))) -> 0(1(5(2(4(x1))))) 5(1(5(0(x1)))) -> 5(1(0(3(5(x1))))) 5(2(2(0(x1)))) -> 0(2(1(2(4(5(x1)))))) 5(3(2(0(x1)))) -> 5(3(0(1(2(x1))))) 5(3(2(0(x1)))) -> 3(3(5(3(0(2(x1)))))) 5(4(0(0(x1)))) -> 0(4(5(5(0(2(x1)))))) 5(4(2(0(x1)))) -> 2(4(3(5(0(x1))))) 5(4(2(0(x1)))) -> 5(0(2(2(4(x1))))) 5(4(2(0(x1)))) -> 5(4(5(0(2(x1))))) 0(3(5(2(0(x1))))) -> 3(0(2(5(3(0(x1)))))) 3(3(5(2(0(x1))))) -> 3(5(2(3(0(2(x1)))))) 3(3(5(2(0(x1))))) -> 4(3(3(5(0(2(x1)))))) 5(0(5(2(0(x1))))) -> 0(3(5(5(0(2(x1)))))) 5(1(4(0(0(x1))))) -> 0(2(5(0(1(4(x1)))))) 5(3(3(2(0(x1))))) -> 5(2(3(3(0(2(x1)))))) 5(4(3(0(0(x1))))) -> 1(0(4(0(3(5(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(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(x1)) -> 0(1(0(2(x1)))) 0(0(x1)) -> 1(0(2(0(x1)))) 0(0(x1)) -> 1(0(1(0(1(x1))))) 0(0(x1)) -> 1(0(1(2(0(x1))))) 0(0(x1)) -> 1(0(2(0(3(x1))))) 0(0(x1)) -> 1(0(2(2(0(x1))))) 0(0(x1)) -> 2(1(0(2(0(x1))))) 0(0(x1)) -> 0(1(0(2(1(2(x1)))))) 0(0(x1)) -> 1(0(1(0(2(2(x1)))))) 0(0(x1)) -> 1(0(1(3(0(1(x1)))))) 0(0(x1)) -> 1(0(4(1(0(2(x1)))))) 0(0(x1)) -> 1(1(1(0(2(0(x1)))))) 0(0(x1)) -> 3(0(4(0(2(2(x1)))))) 0(0(x1)) -> 3(1(0(1(0(4(x1)))))) 0(0(0(x1))) -> 0(1(0(4(0(4(x1)))))) 0(0(0(x1))) -> 3(0(0(1(0(2(x1)))))) 3(0(0(x1))) -> 3(0(2(0(3(x1))))) 3(0(0(x1))) -> 3(0(2(4(0(2(x1)))))) 5(2(0(x1))) -> 0(2(3(5(x1)))) 5(2(0(x1))) -> 3(5(0(2(x1)))) 5(2(0(x1))) -> 0(2(3(3(5(x1))))) 5(2(0(x1))) -> 1(0(2(3(5(x1))))) 5(2(0(x1))) -> 5(1(0(2(4(x1))))) 5(2(0(x1))) -> 5(0(1(2(2(2(x1)))))) 5(2(0(x1))) -> 5(3(5(1(0(2(x1)))))) 0(5(2(0(x1)))) -> 0(5(0(2(2(x1))))) 3(4(0(0(x1)))) -> 0(3(3(0(4(5(x1)))))) 3(4(0(0(x1)))) -> 3(0(4(5(3(0(x1)))))) 5(1(0(0(x1)))) -> 0(3(1(0(1(5(x1)))))) 5(1(4(0(x1)))) -> 0(1(5(2(4(x1))))) 5(1(5(0(x1)))) -> 5(1(0(3(5(x1))))) 5(2(2(0(x1)))) -> 0(2(1(2(4(5(x1)))))) 5(3(2(0(x1)))) -> 5(3(0(1(2(x1))))) 5(3(2(0(x1)))) -> 3(3(5(3(0(2(x1)))))) 5(4(0(0(x1)))) -> 0(4(5(5(0(2(x1)))))) 5(4(2(0(x1)))) -> 2(4(3(5(0(x1))))) 5(4(2(0(x1)))) -> 5(0(2(2(4(x1))))) 5(4(2(0(x1)))) -> 5(4(5(0(2(x1))))) 0(3(5(2(0(x1))))) -> 3(0(2(5(3(0(x1)))))) 3(3(5(2(0(x1))))) -> 3(5(2(3(0(2(x1)))))) 3(3(5(2(0(x1))))) -> 4(3(3(5(0(2(x1)))))) 5(0(5(2(0(x1))))) -> 0(3(5(5(0(2(x1)))))) 5(1(4(0(0(x1))))) -> 0(2(5(0(1(4(x1)))))) 5(3(3(2(0(x1))))) -> 5(2(3(3(0(2(x1)))))) 5(4(3(0(0(x1))))) -> 1(0(4(0(3(5(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(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(x1)) -> 0(1(0(2(x1)))) 0(0(x1)) -> 1(0(2(0(x1)))) 0(0(x1)) -> 1(0(1(0(1(x1))))) 0(0(x1)) -> 1(0(1(2(0(x1))))) 0(0(x1)) -> 1(0(2(0(3(x1))))) 0(0(x1)) -> 1(0(2(2(0(x1))))) 0(0(x1)) -> 2(1(0(2(0(x1))))) 0(0(x1)) -> 0(1(0(2(1(2(x1)))))) 0(0(x1)) -> 1(0(1(0(2(2(x1)))))) 0(0(x1)) -> 1(0(1(3(0(1(x1)))))) 0(0(x1)) -> 1(0(4(1(0(2(x1)))))) 0(0(x1)) -> 1(1(1(0(2(0(x1)))))) 0(0(x1)) -> 3(0(4(0(2(2(x1)))))) 0(0(x1)) -> 3(1(0(1(0(4(x1)))))) 0(0(0(x1))) -> 0(1(0(4(0(4(x1)))))) 0(0(0(x1))) -> 3(0(0(1(0(2(x1)))))) 3(0(0(x1))) -> 3(0(2(0(3(x1))))) 3(0(0(x1))) -> 3(0(2(4(0(2(x1)))))) 5(2(0(x1))) -> 0(2(3(5(x1)))) 5(2(0(x1))) -> 3(5(0(2(x1)))) 5(2(0(x1))) -> 0(2(3(3(5(x1))))) 5(2(0(x1))) -> 1(0(2(3(5(x1))))) 5(2(0(x1))) -> 5(1(0(2(4(x1))))) 5(2(0(x1))) -> 5(0(1(2(2(2(x1)))))) 5(2(0(x1))) -> 5(3(5(1(0(2(x1)))))) 0(5(2(0(x1)))) -> 0(5(0(2(2(x1))))) 3(4(0(0(x1)))) -> 0(3(3(0(4(5(x1)))))) 3(4(0(0(x1)))) -> 3(0(4(5(3(0(x1)))))) 5(1(0(0(x1)))) -> 0(3(1(0(1(5(x1)))))) 5(1(4(0(x1)))) -> 0(1(5(2(4(x1))))) 5(1(5(0(x1)))) -> 5(1(0(3(5(x1))))) 5(2(2(0(x1)))) -> 0(2(1(2(4(5(x1)))))) 5(3(2(0(x1)))) -> 5(3(0(1(2(x1))))) 5(3(2(0(x1)))) -> 3(3(5(3(0(2(x1)))))) 5(4(0(0(x1)))) -> 0(4(5(5(0(2(x1)))))) 5(4(2(0(x1)))) -> 2(4(3(5(0(x1))))) 5(4(2(0(x1)))) -> 5(0(2(2(4(x1))))) 5(4(2(0(x1)))) -> 5(4(5(0(2(x1))))) 0(3(5(2(0(x1))))) -> 3(0(2(5(3(0(x1)))))) 3(3(5(2(0(x1))))) -> 3(5(2(3(0(2(x1)))))) 3(3(5(2(0(x1))))) -> 4(3(3(5(0(2(x1)))))) 5(0(5(2(0(x1))))) -> 0(3(5(5(0(2(x1)))))) 5(1(4(0(0(x1))))) -> 0(2(5(0(1(4(x1)))))) 5(3(3(2(0(x1))))) -> 5(2(3(3(0(2(x1)))))) 5(4(3(0(0(x1))))) -> 1(0(4(0(3(5(x1)))))) encArg(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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. "[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, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420] {(77,78,[0_1|0, 3_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]), (77,79,[1_1|1, 2_1|1, 4_1|1, 0_1|1, 3_1|1, 5_1|1]), (77,80,[0_1|2]), (77,83,[1_1|2]), (77,86,[1_1|2]), (77,90,[1_1|2]), (77,94,[1_1|2]), (77,98,[1_1|2]), (77,102,[2_1|2]), (77,106,[0_1|2]), (77,111,[1_1|2]), (77,116,[1_1|2]), (77,121,[1_1|2]), (77,126,[1_1|2]), (77,131,[3_1|2]), (77,136,[3_1|2]), (77,141,[0_1|2]), (77,146,[3_1|2]), (77,151,[0_1|2]), (77,155,[3_1|2]), (77,160,[3_1|2]), (77,164,[3_1|2]), (77,169,[0_1|2]), (77,174,[3_1|2]), (77,179,[3_1|2]), (77,184,[4_1|2]), (77,189,[0_1|2]), (77,192,[3_1|2]), (77,195,[0_1|2]), (77,199,[1_1|2]), (77,203,[5_1|2]), (77,207,[5_1|2]), (77,212,[5_1|2]), (77,217,[0_1|2]), (77,222,[0_1|2]), (77,227,[0_1|2]), (77,231,[0_1|2]), (77,236,[5_1|2]), (77,240,[5_1|2]), (77,244,[3_1|2]), (77,249,[5_1|2]), (77,254,[0_1|2]), (77,259,[2_1|2]), (77,263,[5_1|2]), (77,267,[5_1|2]), (77,271,[1_1|2]), (77,276,[0_1|2]), (77,281,[3_1|3]), (77,285,[3_1|3]), (78,78,[1_1|0, 2_1|0, 4_1|0, cons_0_1|0, cons_3_1|0, cons_5_1|0]), (79,78,[encArg_1|1]), (79,79,[1_1|1, 2_1|1, 4_1|1, 0_1|1, 3_1|1, 5_1|1]), (79,80,[0_1|2]), (79,83,[1_1|2]), (79,86,[1_1|2]), (79,90,[1_1|2]), (79,94,[1_1|2]), (79,98,[1_1|2]), (79,102,[2_1|2]), (79,106,[0_1|2]), 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(262,316,[0_1|3]), (262,321,[1_1|3]), (262,326,[1_1|3]), (262,331,[1_1|3]), (262,336,[1_1|3]), (262,341,[3_1|3]), (262,346,[3_1|3]), (262,281,[3_1|3]), (262,285,[3_1|3]), (263,264,[0_1|2]), (264,265,[2_1|2]), (265,266,[2_1|2]), (266,79,[4_1|2]), (266,80,[4_1|2]), (266,106,[4_1|2]), (266,141,[4_1|2]), (266,151,[4_1|2]), (266,169,[4_1|2]), (266,189,[4_1|2]), (266,195,[4_1|2]), (266,217,[4_1|2]), (266,222,[4_1|2]), (266,227,[4_1|2]), (266,231,[4_1|2]), (266,254,[4_1|2]), (266,276,[4_1|2]), (267,268,[4_1|2]), (268,269,[5_1|2]), (269,270,[0_1|2]), (270,79,[2_1|2]), (270,80,[2_1|2]), (270,106,[2_1|2]), (270,141,[2_1|2]), (270,151,[2_1|2]), (270,169,[2_1|2]), (270,189,[2_1|2]), (270,195,[2_1|2]), (270,217,[2_1|2]), (270,222,[2_1|2]), (270,227,[2_1|2]), (270,231,[2_1|2]), (270,254,[2_1|2]), (270,276,[2_1|2]), (271,272,[0_1|2]), (272,273,[4_1|2]), (273,274,[0_1|2]), (273,155,[3_1|2]), (274,275,[3_1|2]), (275,79,[5_1|2]), (275,80,[5_1|2]), (275,106,[5_1|2]), (275,141,[5_1|2]), (275,151,[5_1|2]), (275,169,[5_1|2]), (275,189,[5_1|2, 0_1|2]), (275,195,[5_1|2, 0_1|2]), (275,217,[5_1|2, 0_1|2]), (275,222,[5_1|2, 0_1|2]), (275,227,[5_1|2, 0_1|2]), (275,231,[5_1|2, 0_1|2]), (275,254,[5_1|2, 0_1|2]), (275,276,[5_1|2, 0_1|2]), (275,148,[5_1|2]), (275,192,[3_1|2]), (275,199,[1_1|2]), (275,203,[5_1|2]), (275,207,[5_1|2]), (275,212,[5_1|2]), (275,236,[5_1|2]), (275,240,[5_1|2]), (275,244,[3_1|2]), (275,249,[5_1|2]), (275,259,[2_1|2]), (275,263,[5_1|2]), (275,267,[5_1|2]), (275,271,[1_1|2]), (276,277,[3_1|2]), (277,278,[5_1|2]), (278,279,[5_1|2]), (279,280,[0_1|2]), (280,79,[2_1|2]), (280,80,[2_1|2]), (280,106,[2_1|2]), (280,141,[2_1|2]), (280,151,[2_1|2]), (280,169,[2_1|2]), (280,189,[2_1|2]), (280,195,[2_1|2]), (280,217,[2_1|2]), (280,222,[2_1|2]), (280,227,[2_1|2]), (280,231,[2_1|2]), (280,254,[2_1|2]), (280,276,[2_1|2]), (281,282,[0_1|3]), (282,283,[2_1|3]), (283,284,[0_1|3]), (284,148,[3_1|3]), (285,286,[0_1|3]), (286,287,[2_1|3]), (287,288,[4_1|3]), (288,289,[0_1|3]), (289,148,[2_1|3]), (290,291,[1_1|3]), (291,292,[0_1|3]), (292,80,[2_1|3]), (292,106,[2_1|3]), (292,141,[2_1|3]), (292,151,[2_1|3]), (292,169,[2_1|3]), (292,189,[2_1|3]), (292,195,[2_1|3]), (292,217,[2_1|3]), (292,222,[2_1|3]), (292,227,[2_1|3]), (292,231,[2_1|3]), (292,254,[2_1|3]), (292,276,[2_1|3]), (293,294,[0_1|3]), (294,295,[2_1|3]), (295,80,[0_1|3]), (295,106,[0_1|3]), (295,141,[0_1|3]), (295,151,[0_1|3]), (295,169,[0_1|3]), (295,189,[0_1|3]), (295,195,[0_1|3]), (295,217,[0_1|3]), (295,222,[0_1|3]), (295,227,[0_1|3]), (295,231,[0_1|3]), (295,254,[0_1|3]), (295,276,[0_1|3]), (296,297,[0_1|3]), (297,298,[1_1|3]), (298,299,[0_1|3]), (299,80,[1_1|3]), (299,106,[1_1|3]), (299,141,[1_1|3]), (299,151,[1_1|3]), (299,169,[1_1|3]), (299,189,[1_1|3]), (299,195,[1_1|3]), (299,217,[1_1|3]), (299,222,[1_1|3]), (299,227,[1_1|3]), (299,231,[1_1|3]), (299,254,[1_1|3]), (299,276,[1_1|3]), (300,301,[0_1|3]), (301,302,[1_1|3]), (302,303,[2_1|3]), (303,80,[0_1|3]), (303,106,[0_1|3]), (303,141,[0_1|3]), (303,151,[0_1|3]), (303,169,[0_1|3]), (303,189,[0_1|3]), (303,195,[0_1|3]), (303,217,[0_1|3]), (303,222,[0_1|3]), (303,227,[0_1|3]), (303,231,[0_1|3]), (303,254,[0_1|3]), (303,276,[0_1|3]), (304,305,[0_1|3]), (305,306,[2_1|3]), (306,307,[0_1|3]), (307,80,[3_1|3]), (307,106,[3_1|3]), (307,141,[3_1|3]), (307,151,[3_1|3]), (307,169,[3_1|3]), (307,189,[3_1|3]), (307,195,[3_1|3]), (307,217,[3_1|3]), (307,222,[3_1|3]), (307,227,[3_1|3]), (307,231,[3_1|3]), (307,254,[3_1|3]), (307,276,[3_1|3]), (308,309,[0_1|3]), (309,310,[2_1|3]), (310,311,[2_1|3]), (311,80,[0_1|3]), (311,106,[0_1|3]), (311,141,[0_1|3]), (311,151,[0_1|3]), (311,169,[0_1|3]), (311,189,[0_1|3]), (311,195,[0_1|3]), (311,217,[0_1|3]), (311,222,[0_1|3]), (311,227,[0_1|3]), (311,231,[0_1|3]), (311,254,[0_1|3]), (311,276,[0_1|3]), (312,313,[1_1|3]), (313,314,[0_1|3]), (314,315,[2_1|3]), (315,80,[0_1|3]), (315,106,[0_1|3]), (315,141,[0_1|3]), (315,151,[0_1|3]), (315,169,[0_1|3]), (315,189,[0_1|3]), (315,195,[0_1|3]), (315,217,[0_1|3]), (315,222,[0_1|3]), (315,227,[0_1|3]), (315,231,[0_1|3]), (315,254,[0_1|3]), (315,276,[0_1|3]), (316,317,[1_1|3]), (317,318,[0_1|3]), (318,319,[2_1|3]), (319,320,[1_1|3]), (320,80,[2_1|3]), (320,106,[2_1|3]), (320,141,[2_1|3]), (320,151,[2_1|3]), (320,169,[2_1|3]), (320,189,[2_1|3]), (320,195,[2_1|3]), (320,217,[2_1|3]), (320,222,[2_1|3]), (320,227,[2_1|3]), (320,231,[2_1|3]), (320,254,[2_1|3]), (320,276,[2_1|3]), (321,322,[0_1|3]), (322,323,[1_1|3]), (323,324,[0_1|3]), (324,325,[2_1|3]), (325,80,[2_1|3]), (325,106,[2_1|3]), (325,141,[2_1|3]), (325,151,[2_1|3]), (325,169,[2_1|3]), (325,189,[2_1|3]), (325,195,[2_1|3]), (325,217,[2_1|3]), (325,222,[2_1|3]), (325,227,[2_1|3]), (325,231,[2_1|3]), (325,254,[2_1|3]), (325,276,[2_1|3]), (326,327,[0_1|3]), (327,328,[1_1|3]), (328,329,[3_1|3]), (329,330,[0_1|3]), (330,80,[1_1|3]), (330,106,[1_1|3]), (330,141,[1_1|3]), (330,151,[1_1|3]), (330,169,[1_1|3]), (330,189,[1_1|3]), (330,195,[1_1|3]), (330,217,[1_1|3]), (330,222,[1_1|3]), (330,227,[1_1|3]), (330,231,[1_1|3]), (330,254,[1_1|3]), (330,276,[1_1|3]), (331,332,[0_1|3]), (332,333,[4_1|3]), (333,334,[1_1|3]), (334,335,[0_1|3]), (335,80,[2_1|3]), (335,106,[2_1|3]), (335,141,[2_1|3]), (335,151,[2_1|3]), (335,169,[2_1|3]), (335,189,[2_1|3]), (335,195,[2_1|3]), (335,217,[2_1|3]), (335,222,[2_1|3]), (335,227,[2_1|3]), (335,231,[2_1|3]), (335,254,[2_1|3]), (335,276,[2_1|3]), (336,337,[1_1|3]), (337,338,[1_1|3]), (338,339,[0_1|3]), (339,340,[2_1|3]), (340,80,[0_1|3]), (340,106,[0_1|3]), (340,141,[0_1|3]), (340,151,[0_1|3]), (340,169,[0_1|3]), (340,189,[0_1|3]), (340,195,[0_1|3]), (340,217,[0_1|3]), (340,222,[0_1|3]), (340,227,[0_1|3]), (340,231,[0_1|3]), (340,254,[0_1|3]), (340,276,[0_1|3]), (341,342,[0_1|3]), (342,343,[4_1|3]), (343,344,[0_1|3]), (344,345,[2_1|3]), (345,80,[2_1|3]), (345,106,[2_1|3]), (345,141,[2_1|3]), (345,151,[2_1|3]), (345,169,[2_1|3]), (345,189,[2_1|3]), (345,195,[2_1|3]), (345,217,[2_1|3]), (345,222,[2_1|3]), (345,227,[2_1|3]), (345,231,[2_1|3]), (345,254,[2_1|3]), (345,276,[2_1|3]), (346,347,[1_1|3]), (347,348,[0_1|3]), (348,349,[1_1|3]), (349,350,[0_1|3]), (350,80,[4_1|3]), (350,106,[4_1|3]), (350,141,[4_1|3]), (350,151,[4_1|3]), (350,169,[4_1|3]), (350,189,[4_1|3]), (350,195,[4_1|3]), (350,217,[4_1|3]), (350,222,[4_1|3]), (350,227,[4_1|3]), (350,231,[4_1|3]), (350,254,[4_1|3]), (350,276,[4_1|3]), (351,352,[1_1|3]), (352,353,[0_1|3]), (353,148,[2_1|3]), (354,355,[0_1|3]), (355,356,[2_1|3]), (356,148,[0_1|3]), (357,358,[0_1|3]), (358,359,[1_1|3]), (359,360,[0_1|3]), (360,148,[1_1|3]), (361,362,[0_1|3]), (362,363,[1_1|3]), (363,364,[2_1|3]), (364,148,[0_1|3]), (365,366,[0_1|3]), (366,367,[2_1|3]), (367,368,[0_1|3]), (368,148,[3_1|3]), (369,370,[0_1|3]), (370,371,[2_1|3]), (371,372,[2_1|3]), (372,148,[0_1|3]), (373,374,[1_1|3]), (374,375,[0_1|3]), (375,376,[2_1|3]), (376,148,[0_1|3]), (377,378,[1_1|3]), (378,379,[0_1|3]), (379,380,[2_1|3]), (380,381,[1_1|3]), (381,148,[2_1|3]), (382,383,[0_1|3]), (383,384,[1_1|3]), (384,385,[0_1|3]), (385,386,[2_1|3]), (386,148,[2_1|3]), (387,388,[0_1|3]), (388,389,[1_1|3]), (389,390,[3_1|3]), (390,391,[0_1|3]), (391,148,[1_1|3]), (392,393,[0_1|3]), (393,394,[4_1|3]), (394,395,[1_1|3]), (395,396,[0_1|3]), (396,148,[2_1|3]), (397,398,[1_1|3]), (398,399,[1_1|3]), (399,400,[0_1|3]), (400,401,[2_1|3]), (401,148,[0_1|3]), (402,403,[0_1|3]), (403,404,[4_1|3]), (404,405,[0_1|3]), (405,406,[2_1|3]), (406,148,[2_1|3]), (407,408,[1_1|3]), (408,409,[0_1|3]), (409,410,[1_1|3]), (410,411,[0_1|3]), (411,148,[4_1|3]), (412,413,[0_1|3]), (413,414,[2_1|3]), (414,415,[0_1|3]), (415,80,[3_1|3]), (415,106,[3_1|3]), (415,141,[3_1|3]), (415,151,[3_1|3]), (415,169,[3_1|3]), (415,189,[3_1|3]), (415,195,[3_1|3]), (415,217,[3_1|3]), (415,222,[3_1|3]), (415,227,[3_1|3]), (415,231,[3_1|3]), (415,254,[3_1|3]), (415,276,[3_1|3]), (416,417,[0_1|3]), (417,418,[2_1|3]), (418,419,[4_1|3]), (419,420,[0_1|3]), (420,80,[2_1|3]), (420,106,[2_1|3]), (420,141,[2_1|3]), (420,151,[2_1|3]), (420,169,[2_1|3]), (420,189,[2_1|3]), (420,195,[2_1|3]), (420,217,[2_1|3]), (420,222,[2_1|3]), (420,227,[2_1|3]), (420,231,[2_1|3]), (420,254,[2_1|3]), (420,276,[2_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)