WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 44 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 84 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) 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(4(4(5(1(1(3(1(2(1(x1)))))))))) 4(0(x1)) -> 4(4(2(3(0(2(4(2(3(4(x1)))))))))) 0(0(1(x1))) -> 0(4(1(3(0(2(1(5(0(1(x1)))))))))) 4(0(0(x1))) -> 2(2(2(3(0(0(4(4(2(1(x1)))))))))) 0(0(5(2(x1)))) -> 2(3(4(3(0(2(3(0(5(3(x1)))))))))) 1(1(0(0(x1)))) -> 1(3(3(3(4(4(3(2(5(0(x1)))))))))) 4(0(0(1(x1)))) -> 2(2(2(3(3(0(2(3(5(1(x1)))))))))) 5(0(0(4(x1)))) -> 2(5(4(5(2(1(2(3(0(4(x1)))))))))) 5(0(1(5(x1)))) -> 3(5(3(4(4(3(2(2(1(5(x1)))))))))) 0(3(3(5(4(x1))))) -> 0(3(3(2(4(3(3(0(3(4(x1)))))))))) 1(0(0(0(0(x1))))) -> 1(2(0(1(0(2(3(2(1(0(x1)))))))))) 1(0(1(0(1(x1))))) -> 3(5(5(4(4(1(3(1(3(2(x1)))))))))) 3(0(0(3(5(x1))))) -> 3(3(3(4(5(2(3(3(2(4(x1)))))))))) 3(0(0(4(0(x1))))) -> 3(3(0(5(5(3(2(2(5(0(x1)))))))))) 4(0(3(4(0(x1))))) -> 2(3(0(3(2(3(5(5(4(0(x1)))))))))) 5(0(0(0(3(x1))))) -> 5(1(4(2(3(0(0(2(1(3(x1)))))))))) 1(2(0(0(1(3(x1)))))) -> 0(4(2(5(2(2(3(4(4(3(x1)))))))))) 2(0(0(1(0(0(x1)))))) -> 2(4(4(1(0(5(5(2(1(1(x1)))))))))) 2(0(5(5(0(1(x1)))))) -> 2(3(1(4(3(1(3(3(5(1(x1)))))))))) 2(4(1(5(1(0(x1)))))) -> 1(0(3(1(4(5(0(5(4(4(x1)))))))))) 2(5(5(4(1(0(x1)))))) -> 2(5(5(1(1(1(4(2(3(0(x1)))))))))) 3(5(2(5(5(1(x1)))))) -> 2(1(3(4(5(1(4(0(4(1(x1)))))))))) 4(1(0(3(4(3(x1)))))) -> 4(1(4(5(4(1(2(0(1(3(x1)))))))))) 5(0(0(0(0(0(x1)))))) -> 4(5(3(4(0(4(1(4(0(0(x1)))))))))) 0(0(0(0(5(1(0(x1))))))) -> 3(0(5(0(5(5(0(4(0(2(x1)))))))))) 0(3(5(0(0(5(2(x1))))))) -> 2(1(4(4(3(2(5(1(4(3(x1)))))))))) 0(4(5(2(5(5(5(x1))))))) -> 0(4(1(4(0(1(3(2(2(3(x1)))))))))) 1(0(1(4(3(5(5(x1))))))) -> 3(3(0(3(5(4(3(4(0(1(x1)))))))))) 1(5(1(0(0(4(3(x1))))))) -> 4(4(1(1(4(0(4(3(0(3(x1)))))))))) 2(0(0(4(5(1(3(x1))))))) -> 1(0(2(1(4(3(0(4(4(2(x1)))))))))) 3(0(0(5(5(1(3(x1))))))) -> 2(4(5(2(4(4(2(0(0(3(x1)))))))))) 4(0(0(4(0(3(4(x1))))))) -> 3(3(3(3(0(1(5(4(0(4(x1)))))))))) 4(2(4(0(0(1(5(x1))))))) -> 2(3(4(1(3(0(1(2(3(2(x1)))))))))) 4(3(0(4(0(3(4(x1))))))) -> 4(2(4(2(4(4(0(3(0(4(x1)))))))))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (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(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)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) 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(4(4(5(1(1(3(1(2(1(x1)))))))))) 4(0(x1)) -> 4(4(2(3(0(2(4(2(3(4(x1)))))))))) 0(0(1(x1))) -> 0(4(1(3(0(2(1(5(0(1(x1)))))))))) 4(0(0(x1))) -> 2(2(2(3(0(0(4(4(2(1(x1)))))))))) 0(0(5(2(x1)))) -> 2(3(4(3(0(2(3(0(5(3(x1)))))))))) 1(1(0(0(x1)))) -> 1(3(3(3(4(4(3(2(5(0(x1)))))))))) 4(0(0(1(x1)))) -> 2(2(2(3(3(0(2(3(5(1(x1)))))))))) 5(0(0(4(x1)))) -> 2(5(4(5(2(1(2(3(0(4(x1)))))))))) 5(0(1(5(x1)))) -> 3(5(3(4(4(3(2(2(1(5(x1)))))))))) 0(3(3(5(4(x1))))) -> 0(3(3(2(4(3(3(0(3(4(x1)))))))))) 1(0(0(0(0(x1))))) -> 1(2(0(1(0(2(3(2(1(0(x1)))))))))) 1(0(1(0(1(x1))))) -> 3(5(5(4(4(1(3(1(3(2(x1)))))))))) 3(0(0(3(5(x1))))) -> 3(3(3(4(5(2(3(3(2(4(x1)))))))))) 3(0(0(4(0(x1))))) -> 3(3(0(5(5(3(2(2(5(0(x1)))))))))) 4(0(3(4(0(x1))))) -> 2(3(0(3(2(3(5(5(4(0(x1)))))))))) 5(0(0(0(3(x1))))) -> 5(1(4(2(3(0(0(2(1(3(x1)))))))))) 1(2(0(0(1(3(x1)))))) -> 0(4(2(5(2(2(3(4(4(3(x1)))))))))) 2(0(0(1(0(0(x1)))))) -> 2(4(4(1(0(5(5(2(1(1(x1)))))))))) 2(0(5(5(0(1(x1)))))) -> 2(3(1(4(3(1(3(3(5(1(x1)))))))))) 2(4(1(5(1(0(x1)))))) -> 1(0(3(1(4(5(0(5(4(4(x1)))))))))) 2(5(5(4(1(0(x1)))))) -> 2(5(5(1(1(1(4(2(3(0(x1)))))))))) 3(5(2(5(5(1(x1)))))) -> 2(1(3(4(5(1(4(0(4(1(x1)))))))))) 4(1(0(3(4(3(x1)))))) -> 4(1(4(5(4(1(2(0(1(3(x1)))))))))) 5(0(0(0(0(0(x1)))))) -> 4(5(3(4(0(4(1(4(0(0(x1)))))))))) 0(0(0(0(5(1(0(x1))))))) -> 3(0(5(0(5(5(0(4(0(2(x1)))))))))) 0(3(5(0(0(5(2(x1))))))) -> 2(1(4(4(3(2(5(1(4(3(x1)))))))))) 0(4(5(2(5(5(5(x1))))))) -> 0(4(1(4(0(1(3(2(2(3(x1)))))))))) 1(0(1(4(3(5(5(x1))))))) -> 3(3(0(3(5(4(3(4(0(1(x1)))))))))) 1(5(1(0(0(4(3(x1))))))) -> 4(4(1(1(4(0(4(3(0(3(x1)))))))))) 2(0(0(4(5(1(3(x1))))))) -> 1(0(2(1(4(3(0(4(4(2(x1)))))))))) 3(0(0(5(5(1(3(x1))))))) -> 2(4(5(2(4(4(2(0(0(3(x1)))))))))) 4(0(0(4(0(3(4(x1))))))) -> 3(3(3(3(0(1(5(4(0(4(x1)))))))))) 4(2(4(0(0(1(5(x1))))))) -> 2(3(4(1(3(0(1(2(3(2(x1)))))))))) 4(3(0(4(0(3(4(x1))))))) -> 4(2(4(2(4(4(0(3(0(4(x1)))))))))) The (relative) TRS S consists of the following rules: 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)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (full) 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(4(4(5(1(1(3(1(2(1(x1)))))))))) 4(0(x1)) -> 4(4(2(3(0(2(4(2(3(4(x1)))))))))) 0(0(1(x1))) -> 0(4(1(3(0(2(1(5(0(1(x1)))))))))) 4(0(0(x1))) -> 2(2(2(3(0(0(4(4(2(1(x1)))))))))) 0(0(5(2(x1)))) -> 2(3(4(3(0(2(3(0(5(3(x1)))))))))) 1(1(0(0(x1)))) -> 1(3(3(3(4(4(3(2(5(0(x1)))))))))) 4(0(0(1(x1)))) -> 2(2(2(3(3(0(2(3(5(1(x1)))))))))) 5(0(0(4(x1)))) -> 2(5(4(5(2(1(2(3(0(4(x1)))))))))) 5(0(1(5(x1)))) -> 3(5(3(4(4(3(2(2(1(5(x1)))))))))) 0(3(3(5(4(x1))))) -> 0(3(3(2(4(3(3(0(3(4(x1)))))))))) 1(0(0(0(0(x1))))) -> 1(2(0(1(0(2(3(2(1(0(x1)))))))))) 1(0(1(0(1(x1))))) -> 3(5(5(4(4(1(3(1(3(2(x1)))))))))) 3(0(0(3(5(x1))))) -> 3(3(3(4(5(2(3(3(2(4(x1)))))))))) 3(0(0(4(0(x1))))) -> 3(3(0(5(5(3(2(2(5(0(x1)))))))))) 4(0(3(4(0(x1))))) -> 2(3(0(3(2(3(5(5(4(0(x1)))))))))) 5(0(0(0(3(x1))))) -> 5(1(4(2(3(0(0(2(1(3(x1)))))))))) 1(2(0(0(1(3(x1)))))) -> 0(4(2(5(2(2(3(4(4(3(x1)))))))))) 2(0(0(1(0(0(x1)))))) -> 2(4(4(1(0(5(5(2(1(1(x1)))))))))) 2(0(5(5(0(1(x1)))))) -> 2(3(1(4(3(1(3(3(5(1(x1)))))))))) 2(4(1(5(1(0(x1)))))) -> 1(0(3(1(4(5(0(5(4(4(x1)))))))))) 2(5(5(4(1(0(x1)))))) -> 2(5(5(1(1(1(4(2(3(0(x1)))))))))) 3(5(2(5(5(1(x1)))))) -> 2(1(3(4(5(1(4(0(4(1(x1)))))))))) 4(1(0(3(4(3(x1)))))) -> 4(1(4(5(4(1(2(0(1(3(x1)))))))))) 5(0(0(0(0(0(x1)))))) -> 4(5(3(4(0(4(1(4(0(0(x1)))))))))) 0(0(0(0(5(1(0(x1))))))) -> 3(0(5(0(5(5(0(4(0(2(x1)))))))))) 0(3(5(0(0(5(2(x1))))))) -> 2(1(4(4(3(2(5(1(4(3(x1)))))))))) 0(4(5(2(5(5(5(x1))))))) -> 0(4(1(4(0(1(3(2(2(3(x1)))))))))) 1(0(1(4(3(5(5(x1))))))) -> 3(3(0(3(5(4(3(4(0(1(x1)))))))))) 1(5(1(0(0(4(3(x1))))))) -> 4(4(1(1(4(0(4(3(0(3(x1)))))))))) 2(0(0(4(5(1(3(x1))))))) -> 1(0(2(1(4(3(0(4(4(2(x1)))))))))) 3(0(0(5(5(1(3(x1))))))) -> 2(4(5(2(4(4(2(0(0(3(x1)))))))))) 4(0(0(4(0(3(4(x1))))))) -> 3(3(3(3(0(1(5(4(0(4(x1)))))))))) 4(2(4(0(0(1(5(x1))))))) -> 2(3(4(1(3(0(1(2(3(2(x1)))))))))) 4(3(0(4(0(3(4(x1))))))) -> 4(2(4(2(4(4(0(3(0(4(x1)))))))))) The (relative) TRS S consists of the following rules: 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)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (full) 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(4(4(5(1(1(3(1(2(1(x1)))))))))) 4(0(x1)) -> 4(4(2(3(0(2(4(2(3(4(x1)))))))))) 0(0(1(x1))) -> 0(4(1(3(0(2(1(5(0(1(x1)))))))))) 4(0(0(x1))) -> 2(2(2(3(0(0(4(4(2(1(x1)))))))))) 0(0(5(2(x1)))) -> 2(3(4(3(0(2(3(0(5(3(x1)))))))))) 1(1(0(0(x1)))) -> 1(3(3(3(4(4(3(2(5(0(x1)))))))))) 4(0(0(1(x1)))) -> 2(2(2(3(3(0(2(3(5(1(x1)))))))))) 5(0(0(4(x1)))) -> 2(5(4(5(2(1(2(3(0(4(x1)))))))))) 5(0(1(5(x1)))) -> 3(5(3(4(4(3(2(2(1(5(x1)))))))))) 0(3(3(5(4(x1))))) -> 0(3(3(2(4(3(3(0(3(4(x1)))))))))) 1(0(0(0(0(x1))))) -> 1(2(0(1(0(2(3(2(1(0(x1)))))))))) 1(0(1(0(1(x1))))) -> 3(5(5(4(4(1(3(1(3(2(x1)))))))))) 3(0(0(3(5(x1))))) -> 3(3(3(4(5(2(3(3(2(4(x1)))))))))) 3(0(0(4(0(x1))))) -> 3(3(0(5(5(3(2(2(5(0(x1)))))))))) 4(0(3(4(0(x1))))) -> 2(3(0(3(2(3(5(5(4(0(x1)))))))))) 5(0(0(0(3(x1))))) -> 5(1(4(2(3(0(0(2(1(3(x1)))))))))) 1(2(0(0(1(3(x1)))))) -> 0(4(2(5(2(2(3(4(4(3(x1)))))))))) 2(0(0(1(0(0(x1)))))) -> 2(4(4(1(0(5(5(2(1(1(x1)))))))))) 2(0(5(5(0(1(x1)))))) -> 2(3(1(4(3(1(3(3(5(1(x1)))))))))) 2(4(1(5(1(0(x1)))))) -> 1(0(3(1(4(5(0(5(4(4(x1)))))))))) 2(5(5(4(1(0(x1)))))) -> 2(5(5(1(1(1(4(2(3(0(x1)))))))))) 3(5(2(5(5(1(x1)))))) -> 2(1(3(4(5(1(4(0(4(1(x1)))))))))) 4(1(0(3(4(3(x1)))))) -> 4(1(4(5(4(1(2(0(1(3(x1)))))))))) 5(0(0(0(0(0(x1)))))) -> 4(5(3(4(0(4(1(4(0(0(x1)))))))))) 0(0(0(0(5(1(0(x1))))))) -> 3(0(5(0(5(5(0(4(0(2(x1)))))))))) 0(3(5(0(0(5(2(x1))))))) -> 2(1(4(4(3(2(5(1(4(3(x1)))))))))) 0(4(5(2(5(5(5(x1))))))) -> 0(4(1(4(0(1(3(2(2(3(x1)))))))))) 1(0(1(4(3(5(5(x1))))))) -> 3(3(0(3(5(4(3(4(0(1(x1)))))))))) 1(5(1(0(0(4(3(x1))))))) -> 4(4(1(1(4(0(4(3(0(3(x1)))))))))) 2(0(0(4(5(1(3(x1))))))) -> 1(0(2(1(4(3(0(4(4(2(x1)))))))))) 3(0(0(5(5(1(3(x1))))))) -> 2(4(5(2(4(4(2(0(0(3(x1)))))))))) 4(0(0(4(0(3(4(x1))))))) -> 3(3(3(3(0(1(5(4(0(4(x1)))))))))) 4(2(4(0(0(1(5(x1))))))) -> 2(3(4(1(3(0(1(2(3(2(x1)))))))))) 4(3(0(4(0(3(4(x1))))))) -> 4(2(4(2(4(4(0(3(0(4(x1)))))))))) 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)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (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 4. The certificate found is represented by the following graph. 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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, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681] {(148,149,[0_1|0, 4_1|0, 1_1|0, 5_1|0, 3_1|0, 2_1|0, encArg_1|0, encode_0_1|0, encode_4_1|0, encode_5_1|0, encode_1_1|0, encode_3_1|0, encode_2_1|0]), (148,150,[0_1|1, 4_1|1, 1_1|1, 5_1|1, 3_1|1, 2_1|1]), (148,151,[0_1|2]), (148,160,[0_1|2]), (148,169,[2_1|2]), (148,178,[3_1|2]), (148,187,[0_1|2]), (148,196,[2_1|2]), 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(366,529,[0_1|3]), (367,368,[5_1|2]), (368,369,[3_1|2]), (369,370,[4_1|2]), (370,371,[4_1|2]), (371,372,[3_1|2]), (372,373,[2_1|2]), (373,374,[2_1|2]), (374,375,[1_1|2]), (374,331,[4_1|2]), (375,150,[5_1|2]), (375,349,[5_1|2]), (375,340,[2_1|2]), (375,358,[4_1|2]), (375,367,[3_1|2]), (376,377,[3_1|2]), (377,378,[3_1|2]), (378,379,[4_1|2]), (379,380,[5_1|2]), (380,381,[2_1|2]), (381,382,[3_1|2]), (382,383,[3_1|2]), (383,384,[2_1|2]), (383,439,[1_1|2]), (384,150,[4_1|2]), (384,349,[4_1|2]), (384,305,[4_1|2]), (384,368,[4_1|2]), (384,214,[4_1|2]), (384,223,[2_1|2]), (384,232,[2_1|2]), (384,241,[3_1|2]), (384,250,[2_1|2]), (384,259,[4_1|2]), (384,268,[2_1|2]), (384,277,[4_1|2]), (384,475,[4_1|3]), (385,386,[3_1|2]), (386,387,[0_1|2]), (387,388,[5_1|2]), (388,389,[5_1|2]), (389,390,[3_1|2]), (390,391,[2_1|2]), (391,392,[2_1|2]), (392,393,[5_1|2]), (392,340,[2_1|2]), (392,349,[5_1|2]), (392,358,[4_1|2]), (392,367,[3_1|2]), (392,547,[2_1|3]), (393,150,[0_1|2]), (393,151,[0_1|2]), (393,160,[0_1|2]), (393,187,[0_1|2]), (393,205,[0_1|2]), (393,322,[0_1|2]), (393,169,[2_1|2]), (393,178,[3_1|2]), (393,196,[2_1|2]), (393,529,[0_1|3]), (394,395,[4_1|2]), (395,396,[5_1|2]), (396,397,[2_1|2]), (397,398,[4_1|2]), (398,399,[4_1|2]), (399,400,[2_1|2]), (400,401,[0_1|2]), (400,637,[0_1|3]), (401,402,[0_1|2]), (401,187,[0_1|2]), (401,196,[2_1|2]), (402,150,[3_1|2]), (402,178,[3_1|2]), (402,241,[3_1|2]), (402,304,[3_1|2]), (402,313,[3_1|2]), (402,367,[3_1|2]), (402,376,[3_1|2]), (402,385,[3_1|2]), (402,287,[3_1|2]), (402,394,[2_1|2]), (402,403,[2_1|2]), (403,404,[1_1|2]), (404,405,[3_1|2]), (405,406,[4_1|2]), (406,407,[5_1|2]), (407,408,[1_1|2]), (408,409,[4_1|2]), (408,646,[4_1|3]), (409,410,[0_1|2]), (410,411,[4_1|2]), (410,259,[4_1|2]), (410,475,[4_1|3]), (411,150,[1_1|2]), (411,286,[1_1|2]), (411,295,[1_1|2]), (411,421,[1_1|2]), (411,439,[1_1|2]), (411,350,[1_1|2]), (411,451,[1_1|2]), (411,304,[3_1|2]), (411,313,[3_1|2]), (411,322,[0_1|2]), (411,331,[4_1|2]), (412,413,[4_1|2]), (413,414,[4_1|2]), (414,415,[1_1|2]), (415,416,[0_1|2]), (416,417,[5_1|2]), (417,418,[5_1|2]), (418,419,[2_1|2]), (419,420,[1_1|2]), (419,286,[1_1|2]), (420,150,[1_1|2]), (420,151,[1_1|2]), (420,160,[1_1|2]), (420,187,[1_1|2]), (420,205,[1_1|2]), (420,322,[1_1|2, 0_1|2]), (420,286,[1_1|2]), (420,295,[1_1|2]), (420,304,[3_1|2]), (420,313,[3_1|2]), (420,331,[4_1|2]), (421,422,[0_1|2]), (422,423,[2_1|2]), (423,424,[1_1|2]), (424,425,[4_1|2]), (425,426,[3_1|2]), (426,427,[0_1|2]), (427,428,[4_1|2]), (428,429,[4_1|2]), (428,268,[2_1|2]), (429,150,[2_1|2]), (429,178,[2_1|2]), (429,241,[2_1|2]), (429,304,[2_1|2]), (429,313,[2_1|2]), (429,367,[2_1|2]), (429,376,[2_1|2]), (429,385,[2_1|2]), (429,287,[2_1|2]), (429,412,[2_1|2]), (429,421,[1_1|2]), (429,430,[2_1|2]), (429,439,[1_1|2]), (429,448,[2_1|2]), (430,431,[3_1|2]), (431,432,[1_1|2]), (432,433,[4_1|2]), (433,434,[3_1|2]), (434,435,[1_1|2]), (435,436,[3_1|2]), (436,437,[3_1|2]), (437,438,[5_1|2]), (438,150,[1_1|2]), (438,286,[1_1|2]), (438,295,[1_1|2]), (438,421,[1_1|2]), (438,439,[1_1|2]), (438,304,[3_1|2]), (438,313,[3_1|2]), (438,322,[0_1|2]), (438,331,[4_1|2]), (439,440,[0_1|2]), (440,441,[3_1|2]), (441,442,[1_1|2]), (442,443,[4_1|2]), (443,444,[5_1|2]), (444,445,[0_1|2]), (445,446,[5_1|2]), (446,447,[4_1|2]), (447,150,[4_1|2]), (447,151,[4_1|2]), (447,160,[4_1|2]), (447,187,[4_1|2]), (447,205,[4_1|2]), (447,322,[4_1|2]), (447,422,[4_1|2]), (447,440,[4_1|2]), (447,214,[4_1|2]), (447,223,[2_1|2]), (447,232,[2_1|2]), (447,241,[3_1|2]), (447,250,[2_1|2]), (447,259,[4_1|2]), (447,268,[2_1|2]), (447,277,[4_1|2]), (447,475,[4_1|3]), (448,449,[5_1|2]), (449,450,[5_1|2]), (450,451,[1_1|2]), (451,452,[1_1|2]), (452,453,[1_1|2]), (453,454,[4_1|2]), (454,455,[2_1|2]), (455,456,[3_1|2]), (455,376,[3_1|2]), (455,385,[3_1|2]), (455,394,[2_1|2]), (456,150,[0_1|2]), (456,151,[0_1|2]), (456,160,[0_1|2]), (456,187,[0_1|2]), (456,205,[0_1|2]), (456,322,[0_1|2]), (456,422,[0_1|2]), (456,440,[0_1|2]), (456,169,[2_1|2]), (456,178,[3_1|2]), (456,196,[2_1|2]), (456,529,[0_1|3]), (457,458,[5_1|3]), (458,459,[3_1|3]), (459,460,[4_1|3]), (460,461,[4_1|3]), (461,462,[3_1|3]), (462,463,[2_1|3]), (463,464,[2_1|3]), (464,465,[1_1|3]), (465,349,[5_1|3]), (466,467,[4_1|3]), (467,468,[2_1|3]), (468,469,[3_1|3]), (469,470,[0_1|3]), (470,471,[2_1|3]), (471,472,[4_1|3]), (472,473,[2_1|3]), (473,474,[3_1|3]), (474,186,[4_1|3]), (474,268,[2_1|2]), (475,476,[4_1|3]), (476,477,[2_1|3]), (477,478,[3_1|3]), (478,479,[0_1|3]), (479,480,[2_1|3]), (480,481,[4_1|3]), (481,482,[2_1|3]), (482,483,[3_1|3]), (483,151,[4_1|3]), (483,160,[4_1|3]), (483,187,[4_1|3]), (483,205,[4_1|3]), (483,322,[4_1|3]), (484,485,[4_1|3]), (485,486,[2_1|3]), (486,487,[3_1|3]), (487,488,[0_1|3]), (488,489,[2_1|3]), (489,490,[4_1|3]), (490,491,[2_1|3]), (491,492,[3_1|3]), (492,209,[4_1|3]), (493,494,[4_1|3]), (494,495,[4_1|3]), (495,496,[5_1|3]), (496,497,[1_1|3]), (497,498,[1_1|3]), (498,499,[3_1|3]), (499,500,[1_1|3]), (500,501,[2_1|3]), (501,228,[1_1|3]), (502,503,[4_1|3]), (503,504,[2_1|3]), (504,505,[3_1|3]), (505,506,[0_1|3]), (506,507,[2_1|3]), (507,508,[4_1|3]), (508,509,[2_1|3]), (509,510,[3_1|3]), (510,249,[4_1|3]), (510,205,[4_1|3]), (511,512,[4_1|3]), (512,513,[2_1|3]), (513,514,[3_1|3]), (514,515,[0_1|3]), (515,516,[2_1|3]), (516,517,[4_1|3]), (517,518,[2_1|3]), (518,519,[3_1|3]), (519,150,[4_1|3]), (519,151,[4_1|3]), (519,160,[4_1|3]), (519,187,[4_1|3]), (519,205,[4_1|3]), (519,322,[4_1|3]), (519,529,[4_1|3]), (519,214,[4_1|2]), (519,223,[2_1|2]), (519,232,[2_1|2]), (519,241,[3_1|2]), (519,250,[2_1|2]), (519,259,[4_1|2]), (519,268,[2_1|2]), (519,277,[4_1|2]), (519,475,[4_1|3]), (520,521,[2_1|3]), (521,522,[2_1|3]), (522,523,[3_1|3]), (523,524,[0_1|3]), (523,655,[0_1|4]), (524,525,[0_1|3]), (525,526,[4_1|3]), (526,527,[4_1|3]), (527,528,[2_1|3]), (528,151,[1_1|3]), (528,160,[1_1|3]), (528,187,[1_1|3]), (528,205,[1_1|3]), (528,322,[1_1|3]), (529,530,[4_1|3]), (530,531,[4_1|3]), (531,532,[5_1|3]), (532,533,[1_1|3]), (533,534,[1_1|3]), (534,535,[3_1|3]), (535,536,[1_1|3]), (536,537,[2_1|3]), (537,151,[1_1|3]), (537,160,[1_1|3]), (537,187,[1_1|3]), (537,205,[1_1|3]), (537,322,[1_1|3]), (538,539,[4_1|3]), (539,540,[2_1|3]), (540,541,[3_1|3]), (541,542,[0_1|3]), (542,543,[2_1|3]), (543,544,[4_1|3]), (544,545,[2_1|3]), (545,546,[3_1|3]), (546,283,[4_1|3]), (546,277,[4_1|2]), (547,548,[5_1|3]), (548,549,[4_1|3]), (549,550,[5_1|3]), (550,551,[2_1|3]), (551,552,[1_1|3]), (552,553,[2_1|3]), (553,554,[3_1|3]), (554,555,[0_1|3]), (555,152,[4_1|3]), (555,161,[4_1|3]), (555,206,[4_1|3]), (555,323,[4_1|3]), (556,557,[4_1|3]), (557,558,[2_1|3]), (558,559,[3_1|3]), (559,560,[0_1|3]), (560,561,[2_1|3]), (561,562,[4_1|3]), (562,563,[2_1|3]), (563,564,[3_1|3]), (564,321,[4_1|3]), (564,259,[4_1|2]), (564,475,[4_1|3]), (564,529,[4_1|3]), (565,566,[4_1|3]), (566,567,[2_1|3]), (567,568,[3_1|3]), (568,569,[0_1|3]), (569,570,[2_1|3]), (570,571,[4_1|3]), (571,572,[2_1|3]), (572,573,[3_1|3]), (573,336,[4_1|3]), (574,575,[4_1|3]), (575,576,[4_1|3]), (576,577,[5_1|3]), (577,578,[1_1|3]), (578,579,[1_1|3]), (579,580,[3_1|3]), (580,581,[1_1|3]), (581,582,[2_1|3]), (582,355,[1_1|3]), (583,584,[4_1|3]), (584,585,[2_1|3]), (585,586,[3_1|3]), (586,587,[0_1|3]), (587,588,[2_1|3]), (588,589,[4_1|3]), (589,590,[2_1|3]), (590,591,[3_1|3]), (591,362,[4_1|3]), (592,593,[4_1|3]), (593,594,[2_1|3]), (594,595,[3_1|3]), (595,596,[0_1|3]), (596,597,[2_1|3]), (597,598,[4_1|3]), (598,599,[2_1|3]), (599,600,[3_1|3]), (600,366,[4_1|3]), (600,619,[4_1|3]), (600,160,[4_1|3]), (600,628,[4_1|3]), (600,511,[4_1|3]), (600,223,[2_1|2]), (600,232,[2_1|2]), (600,241,[3_1|2]), (600,250,[2_1|2]), (600,520,[2_1|3]), (600,664,[4_1|4]), (601,602,[2_1|3]), (602,603,[2_1|3]), (603,604,[3_1|3]), (604,605,[0_1|3]), (604,673,[0_1|4]), (605,606,[0_1|3]), (606,607,[4_1|3]), (607,608,[4_1|3]), (608,609,[2_1|3]), (609,150,[1_1|3]), (609,151,[1_1|3]), (609,160,[1_1|3]), (609,187,[1_1|3]), (609,205,[1_1|3]), (609,322,[1_1|3, 0_1|2]), (609,529,[1_1|3]), (609,286,[1_1|2]), (609,295,[1_1|2]), (609,304,[3_1|2]), (609,313,[3_1|2]), (609,331,[4_1|2]), (610,611,[2_1|3]), (611,612,[2_1|3]), (612,613,[3_1|3]), (613,614,[3_1|3]), (614,615,[0_1|3]), (615,616,[2_1|3]), (616,617,[3_1|3]), (617,618,[5_1|3]), (618,286,[1_1|3]), (618,295,[1_1|3]), (618,421,[1_1|3]), (618,439,[1_1|3]), (619,620,[4_1|3]), (620,621,[4_1|3]), (621,622,[5_1|3]), (622,623,[1_1|3]), (623,624,[1_1|3]), (624,625,[3_1|3]), (625,626,[1_1|3]), (626,627,[2_1|3]), (627,150,[1_1|3]), (627,151,[1_1|3]), (627,160,[1_1|3]), (627,187,[1_1|3]), (627,205,[1_1|3]), (627,322,[1_1|3, 0_1|2]), (627,529,[1_1|3]), (627,286,[1_1|2]), (627,295,[1_1|2]), (627,304,[3_1|2]), (627,313,[3_1|2]), (627,331,[4_1|2]), (628,629,[4_1|3]), (629,630,[1_1|3]), (630,631,[3_1|3]), (631,632,[0_1|3]), (632,633,[2_1|3]), (633,634,[1_1|3]), (634,635,[5_1|3]), (635,636,[0_1|3]), (636,286,[1_1|3]), (636,295,[1_1|3]), (636,421,[1_1|3]), (636,439,[1_1|3]), (637,638,[4_1|3]), (638,639,[4_1|3]), (639,640,[5_1|3]), (640,641,[1_1|3]), (641,642,[1_1|3]), (642,643,[3_1|3]), (643,644,[1_1|3]), (644,645,[2_1|3]), (645,402,[1_1|3]), (645,187,[1_1|3]), (646,647,[4_1|3]), (647,648,[2_1|3]), (648,649,[3_1|3]), (649,650,[0_1|3]), (650,651,[2_1|3]), (651,652,[4_1|3]), (652,653,[2_1|3]), (653,654,[3_1|3]), (654,410,[4_1|3]), (655,656,[4_1|4]), (656,657,[4_1|4]), (657,658,[5_1|4]), (658,659,[1_1|4]), (659,660,[1_1|4]), (660,661,[3_1|4]), (661,662,[1_1|4]), (662,663,[2_1|4]), (663,525,[1_1|4]), (664,665,[4_1|4]), (665,666,[2_1|4]), (666,667,[3_1|4]), (667,668,[0_1|4]), (668,669,[2_1|4]), (669,670,[4_1|4]), (670,671,[2_1|4]), (671,672,[3_1|4]), (672,529,[4_1|4]), (673,674,[4_1|4]), (674,675,[4_1|4]), (675,676,[5_1|4]), (676,677,[1_1|4]), (677,678,[1_1|4]), (678,679,[3_1|4]), (679,680,[1_1|4]), (680,681,[2_1|4]), (681,606,[1_1|4])}" ---------------------------------------- (8) BOUNDS(1, n^1)