WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 69 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 90 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. "[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, 421, 422] {(79,80,[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]), (79,81,[1_1|1, 2_1|1, 4_1|1, 0_1|1, 3_1|1, 5_1|1]), (79,82,[0_1|2]), (79,85,[1_1|2]), (79,88,[1_1|2]), (79,92,[1_1|2]), (79,96,[1_1|2]), (79,100,[1_1|2]), (79,104,[2_1|2]), 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(264,318,[0_1|3]), (264,323,[1_1|3]), (264,328,[1_1|3]), (264,333,[1_1|3]), (264,338,[1_1|3]), (264,343,[3_1|3]), (264,348,[3_1|3]), (264,283,[3_1|3]), (264,287,[3_1|3]), (265,266,[0_1|2]), (266,267,[2_1|2]), (267,268,[2_1|2]), (268,81,[4_1|2]), (268,82,[4_1|2]), (268,108,[4_1|2]), (268,143,[4_1|2]), (268,153,[4_1|2]), (268,171,[4_1|2]), (268,191,[4_1|2]), (268,197,[4_1|2]), (268,219,[4_1|2]), (268,224,[4_1|2]), (268,229,[4_1|2]), (268,233,[4_1|2]), (268,256,[4_1|2]), (268,278,[4_1|2]), (269,270,[4_1|2]), (270,271,[5_1|2]), (271,272,[0_1|2]), (272,81,[2_1|2]), (272,82,[2_1|2]), (272,108,[2_1|2]), (272,143,[2_1|2]), (272,153,[2_1|2]), (272,171,[2_1|2]), (272,191,[2_1|2]), (272,197,[2_1|2]), (272,219,[2_1|2]), (272,224,[2_1|2]), (272,229,[2_1|2]), (272,233,[2_1|2]), (272,256,[2_1|2]), (272,278,[2_1|2]), (273,274,[0_1|2]), (274,275,[4_1|2]), (275,276,[0_1|2]), (275,157,[3_1|2]), (276,277,[3_1|2]), (277,81,[5_1|2]), (277,82,[5_1|2]), (277,108,[5_1|2]), (277,143,[5_1|2]), (277,153,[5_1|2]), (277,171,[5_1|2]), (277,191,[5_1|2, 0_1|2]), (277,197,[5_1|2, 0_1|2]), (277,219,[5_1|2, 0_1|2]), (277,224,[5_1|2, 0_1|2]), (277,229,[5_1|2, 0_1|2]), (277,233,[5_1|2, 0_1|2]), (277,256,[5_1|2, 0_1|2]), (277,278,[5_1|2, 0_1|2]), (277,150,[5_1|2]), (277,194,[3_1|2]), (277,201,[1_1|2]), (277,205,[5_1|2]), (277,209,[5_1|2]), (277,214,[5_1|2]), (277,238,[5_1|2]), (277,242,[5_1|2]), (277,246,[3_1|2]), (277,251,[5_1|2]), (277,261,[2_1|2]), (277,265,[5_1|2]), (277,269,[5_1|2]), (277,273,[1_1|2]), (278,279,[3_1|2]), (279,280,[5_1|2]), (280,281,[5_1|2]), (281,282,[0_1|2]), (282,81,[2_1|2]), (282,82,[2_1|2]), (282,108,[2_1|2]), (282,143,[2_1|2]), (282,153,[2_1|2]), (282,171,[2_1|2]), (282,191,[2_1|2]), (282,197,[2_1|2]), (282,219,[2_1|2]), (282,224,[2_1|2]), (282,229,[2_1|2]), (282,233,[2_1|2]), (282,256,[2_1|2]), (282,278,[2_1|2]), (283,284,[0_1|3]), (284,285,[2_1|3]), (285,286,[0_1|3]), (286,150,[3_1|3]), (287,288,[0_1|3]), (288,289,[2_1|3]), (289,290,[4_1|3]), (290,291,[0_1|3]), (291,150,[2_1|3]), (292,293,[1_1|3]), (293,294,[0_1|3]), (294,82,[2_1|3]), (294,108,[2_1|3]), (294,143,[2_1|3]), (294,153,[2_1|3]), (294,171,[2_1|3]), (294,191,[2_1|3]), (294,197,[2_1|3]), (294,219,[2_1|3]), (294,224,[2_1|3]), (294,229,[2_1|3]), (294,233,[2_1|3]), (294,256,[2_1|3]), (294,278,[2_1|3]), (295,296,[0_1|3]), (296,297,[2_1|3]), (297,82,[0_1|3]), (297,108,[0_1|3]), (297,143,[0_1|3]), (297,153,[0_1|3]), (297,171,[0_1|3]), (297,191,[0_1|3]), (297,197,[0_1|3]), (297,219,[0_1|3]), (297,224,[0_1|3]), (297,229,[0_1|3]), (297,233,[0_1|3]), (297,256,[0_1|3]), (297,278,[0_1|3]), (298,299,[0_1|3]), (299,300,[1_1|3]), (300,301,[0_1|3]), (301,82,[1_1|3]), (301,108,[1_1|3]), (301,143,[1_1|3]), (301,153,[1_1|3]), (301,171,[1_1|3]), (301,191,[1_1|3]), (301,197,[1_1|3]), (301,219,[1_1|3]), (301,224,[1_1|3]), (301,229,[1_1|3]), (301,233,[1_1|3]), (301,256,[1_1|3]), (301,278,[1_1|3]), (302,303,[0_1|3]), (303,304,[1_1|3]), (304,305,[2_1|3]), (305,82,[0_1|3]), (305,108,[0_1|3]), (305,143,[0_1|3]), (305,153,[0_1|3]), (305,171,[0_1|3]), (305,191,[0_1|3]), (305,197,[0_1|3]), (305,219,[0_1|3]), (305,224,[0_1|3]), (305,229,[0_1|3]), (305,233,[0_1|3]), (305,256,[0_1|3]), (305,278,[0_1|3]), (306,307,[0_1|3]), (307,308,[2_1|3]), (308,309,[0_1|3]), (309,82,[3_1|3]), (309,108,[3_1|3]), (309,143,[3_1|3]), (309,153,[3_1|3]), (309,171,[3_1|3]), (309,191,[3_1|3]), (309,197,[3_1|3]), (309,219,[3_1|3]), (309,224,[3_1|3]), (309,229,[3_1|3]), (309,233,[3_1|3]), (309,256,[3_1|3]), (309,278,[3_1|3]), (310,311,[0_1|3]), (311,312,[2_1|3]), (312,313,[2_1|3]), (313,82,[0_1|3]), (313,108,[0_1|3]), (313,143,[0_1|3]), (313,153,[0_1|3]), (313,171,[0_1|3]), (313,191,[0_1|3]), (313,197,[0_1|3]), (313,219,[0_1|3]), (313,224,[0_1|3]), (313,229,[0_1|3]), (313,233,[0_1|3]), (313,256,[0_1|3]), (313,278,[0_1|3]), (314,315,[1_1|3]), (315,316,[0_1|3]), (316,317,[2_1|3]), (317,82,[0_1|3]), (317,108,[0_1|3]), (317,143,[0_1|3]), (317,153,[0_1|3]), (317,171,[0_1|3]), (317,191,[0_1|3]), (317,197,[0_1|3]), (317,219,[0_1|3]), (317,224,[0_1|3]), (317,229,[0_1|3]), (317,233,[0_1|3]), (317,256,[0_1|3]), (317,278,[0_1|3]), (318,319,[1_1|3]), (319,320,[0_1|3]), (320,321,[2_1|3]), (321,322,[1_1|3]), (322,82,[2_1|3]), (322,108,[2_1|3]), (322,143,[2_1|3]), (322,153,[2_1|3]), (322,171,[2_1|3]), (322,191,[2_1|3]), (322,197,[2_1|3]), (322,219,[2_1|3]), (322,224,[2_1|3]), (322,229,[2_1|3]), (322,233,[2_1|3]), (322,256,[2_1|3]), (322,278,[2_1|3]), (323,324,[0_1|3]), (324,325,[1_1|3]), (325,326,[0_1|3]), (326,327,[2_1|3]), (327,82,[2_1|3]), (327,108,[2_1|3]), (327,143,[2_1|3]), (327,153,[2_1|3]), (327,171,[2_1|3]), (327,191,[2_1|3]), (327,197,[2_1|3]), (327,219,[2_1|3]), (327,224,[2_1|3]), (327,229,[2_1|3]), (327,233,[2_1|3]), (327,256,[2_1|3]), (327,278,[2_1|3]), (328,329,[0_1|3]), (329,330,[1_1|3]), (330,331,[3_1|3]), (331,332,[0_1|3]), (332,82,[1_1|3]), (332,108,[1_1|3]), (332,143,[1_1|3]), (332,153,[1_1|3]), (332,171,[1_1|3]), (332,191,[1_1|3]), (332,197,[1_1|3]), (332,219,[1_1|3]), (332,224,[1_1|3]), (332,229,[1_1|3]), (332,233,[1_1|3]), (332,256,[1_1|3]), (332,278,[1_1|3]), (333,334,[0_1|3]), (334,335,[4_1|3]), (335,336,[1_1|3]), (336,337,[0_1|3]), (337,82,[2_1|3]), (337,108,[2_1|3]), (337,143,[2_1|3]), (337,153,[2_1|3]), (337,171,[2_1|3]), (337,191,[2_1|3]), (337,197,[2_1|3]), (337,219,[2_1|3]), (337,224,[2_1|3]), (337,229,[2_1|3]), (337,233,[2_1|3]), (337,256,[2_1|3]), (337,278,[2_1|3]), (338,339,[1_1|3]), (339,340,[1_1|3]), (340,341,[0_1|3]), (341,342,[2_1|3]), (342,82,[0_1|3]), (342,108,[0_1|3]), (342,143,[0_1|3]), (342,153,[0_1|3]), (342,171,[0_1|3]), (342,191,[0_1|3]), (342,197,[0_1|3]), (342,219,[0_1|3]), (342,224,[0_1|3]), (342,229,[0_1|3]), (342,233,[0_1|3]), (342,256,[0_1|3]), (342,278,[0_1|3]), (343,344,[0_1|3]), (344,345,[4_1|3]), (345,346,[0_1|3]), (346,347,[2_1|3]), (347,82,[2_1|3]), (347,108,[2_1|3]), (347,143,[2_1|3]), (347,153,[2_1|3]), (347,171,[2_1|3]), (347,191,[2_1|3]), (347,197,[2_1|3]), (347,219,[2_1|3]), (347,224,[2_1|3]), (347,229,[2_1|3]), (347,233,[2_1|3]), (347,256,[2_1|3]), (347,278,[2_1|3]), (348,349,[1_1|3]), (349,350,[0_1|3]), (350,351,[1_1|3]), (351,352,[0_1|3]), (352,82,[4_1|3]), (352,108,[4_1|3]), (352,143,[4_1|3]), (352,153,[4_1|3]), (352,171,[4_1|3]), (352,191,[4_1|3]), (352,197,[4_1|3]), (352,219,[4_1|3]), (352,224,[4_1|3]), (352,229,[4_1|3]), (352,233,[4_1|3]), (352,256,[4_1|3]), (352,278,[4_1|3]), (353,354,[1_1|3]), (354,355,[0_1|3]), (355,150,[2_1|3]), (356,357,[0_1|3]), (357,358,[2_1|3]), (358,150,[0_1|3]), (359,360,[0_1|3]), (360,361,[1_1|3]), (361,362,[0_1|3]), (362,150,[1_1|3]), (363,364,[0_1|3]), (364,365,[1_1|3]), (365,366,[2_1|3]), (366,150,[0_1|3]), (367,368,[0_1|3]), (368,369,[2_1|3]), (369,370,[0_1|3]), (370,150,[3_1|3]), (371,372,[0_1|3]), (372,373,[2_1|3]), (373,374,[2_1|3]), (374,150,[0_1|3]), (375,376,[1_1|3]), (376,377,[0_1|3]), (377,378,[2_1|3]), (378,150,[0_1|3]), (379,380,[1_1|3]), (380,381,[0_1|3]), (381,382,[2_1|3]), (382,383,[1_1|3]), (383,150,[2_1|3]), (384,385,[0_1|3]), (385,386,[1_1|3]), (386,387,[0_1|3]), (387,388,[2_1|3]), (388,150,[2_1|3]), (389,390,[0_1|3]), (390,391,[1_1|3]), (391,392,[3_1|3]), (392,393,[0_1|3]), (393,150,[1_1|3]), (394,395,[0_1|3]), (395,396,[4_1|3]), (396,397,[1_1|3]), (397,398,[0_1|3]), (398,150,[2_1|3]), (399,400,[1_1|3]), (400,401,[1_1|3]), (401,402,[0_1|3]), (402,403,[2_1|3]), (403,150,[0_1|3]), (404,405,[0_1|3]), (405,406,[4_1|3]), (406,407,[0_1|3]), (407,408,[2_1|3]), (408,150,[2_1|3]), (409,410,[1_1|3]), (410,411,[0_1|3]), (411,412,[1_1|3]), (412,413,[0_1|3]), (413,150,[4_1|3]), (414,415,[0_1|3]), (415,416,[2_1|3]), (416,417,[0_1|3]), (417,82,[3_1|3]), (417,108,[3_1|3]), (417,143,[3_1|3]), (417,153,[3_1|3]), (417,171,[3_1|3]), (417,191,[3_1|3]), (417,197,[3_1|3]), (417,219,[3_1|3]), (417,224,[3_1|3]), (417,229,[3_1|3]), (417,233,[3_1|3]), (417,256,[3_1|3]), (417,278,[3_1|3]), (418,419,[0_1|3]), (419,420,[2_1|3]), (420,421,[4_1|3]), (421,422,[0_1|3]), (422,82,[2_1|3]), (422,108,[2_1|3]), (422,143,[2_1|3]), (422,153,[2_1|3]), (422,171,[2_1|3]), (422,191,[2_1|3]), (422,197,[2_1|3]), (422,219,[2_1|3]), (422,224,[2_1|3]), (422,229,[2_1|3]), (422,233,[2_1|3]), (422,256,[2_1|3]), (422,278,[2_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)