/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 225 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 115 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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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, 682, 683, 684] {(151,152,[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]), (151,153,[0_1|1, 4_1|1, 1_1|1, 5_1|1, 3_1|1, 2_1|1]), (151,154,[0_1|2]), (151,163,[0_1|2]), (151,172,[2_1|2]), (151,181,[3_1|2]), (151,190,[0_1|2]), (151,199,[2_1|2]), 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(369,532,[0_1|3]), (370,371,[5_1|2]), (371,372,[3_1|2]), (372,373,[4_1|2]), (373,374,[4_1|2]), (374,375,[3_1|2]), (375,376,[2_1|2]), (376,377,[2_1|2]), (377,378,[1_1|2]), (377,334,[4_1|2]), (378,153,[5_1|2]), (378,352,[5_1|2]), (378,343,[2_1|2]), (378,361,[4_1|2]), (378,370,[3_1|2]), (379,380,[3_1|2]), (380,381,[3_1|2]), (381,382,[4_1|2]), (382,383,[5_1|2]), (383,384,[2_1|2]), (384,385,[3_1|2]), (385,386,[3_1|2]), (386,387,[2_1|2]), (386,442,[1_1|2]), (387,153,[4_1|2]), (387,352,[4_1|2]), (387,308,[4_1|2]), (387,371,[4_1|2]), (387,217,[4_1|2]), (387,226,[2_1|2]), (387,235,[2_1|2]), (387,244,[3_1|2]), (387,253,[2_1|2]), (387,262,[4_1|2]), (387,271,[2_1|2]), (387,280,[4_1|2]), (387,478,[4_1|3]), (388,389,[3_1|2]), (389,390,[0_1|2]), (390,391,[5_1|2]), (391,392,[5_1|2]), (392,393,[3_1|2]), (393,394,[2_1|2]), (394,395,[2_1|2]), (395,396,[5_1|2]), (395,343,[2_1|2]), (395,352,[5_1|2]), (395,361,[4_1|2]), (395,370,[3_1|2]), (395,550,[2_1|3]), (396,153,[0_1|2]), (396,154,[0_1|2]), (396,163,[0_1|2]), (396,190,[0_1|2]), (396,208,[0_1|2]), (396,325,[0_1|2]), (396,172,[2_1|2]), (396,181,[3_1|2]), (396,199,[2_1|2]), (396,532,[0_1|3]), (397,398,[4_1|2]), (398,399,[5_1|2]), (399,400,[2_1|2]), (400,401,[4_1|2]), (401,402,[4_1|2]), (402,403,[2_1|2]), (403,404,[0_1|2]), (403,640,[0_1|3]), (404,405,[0_1|2]), (404,190,[0_1|2]), (404,199,[2_1|2]), (405,153,[3_1|2]), (405,181,[3_1|2]), (405,244,[3_1|2]), (405,307,[3_1|2]), (405,316,[3_1|2]), (405,370,[3_1|2]), (405,379,[3_1|2]), (405,388,[3_1|2]), (405,290,[3_1|2]), (405,397,[2_1|2]), (405,406,[2_1|2]), (406,407,[1_1|2]), (407,408,[3_1|2]), (408,409,[4_1|2]), (409,410,[5_1|2]), (410,411,[1_1|2]), (411,412,[4_1|2]), (411,649,[4_1|3]), (412,413,[0_1|2]), (413,414,[4_1|2]), (413,262,[4_1|2]), (413,478,[4_1|3]), (414,153,[1_1|2]), (414,289,[1_1|2]), (414,298,[1_1|2]), (414,424,[1_1|2]), (414,442,[1_1|2]), (414,353,[1_1|2]), (414,454,[1_1|2]), (414,307,[3_1|2]), (414,316,[3_1|2]), (414,325,[0_1|2]), (414,334,[4_1|2]), (415,416,[4_1|2]), (416,417,[4_1|2]), (417,418,[1_1|2]), (418,419,[0_1|2]), (419,420,[5_1|2]), (420,421,[5_1|2]), (421,422,[2_1|2]), (422,423,[1_1|2]), (422,289,[1_1|2]), (423,153,[1_1|2]), (423,154,[1_1|2]), (423,163,[1_1|2]), (423,190,[1_1|2]), (423,208,[1_1|2]), (423,325,[1_1|2, 0_1|2]), (423,289,[1_1|2]), (423,298,[1_1|2]), (423,307,[3_1|2]), (423,316,[3_1|2]), (423,334,[4_1|2]), (424,425,[0_1|2]), (425,426,[2_1|2]), (426,427,[1_1|2]), (427,428,[4_1|2]), (428,429,[3_1|2]), (429,430,[0_1|2]), (430,431,[4_1|2]), (431,432,[4_1|2]), (431,271,[2_1|2]), (432,153,[2_1|2]), (432,181,[2_1|2]), (432,244,[2_1|2]), (432,307,[2_1|2]), (432,316,[2_1|2]), (432,370,[2_1|2]), (432,379,[2_1|2]), (432,388,[2_1|2]), (432,290,[2_1|2]), (432,415,[2_1|2]), (432,424,[1_1|2]), (432,433,[2_1|2]), (432,442,[1_1|2]), (432,451,[2_1|2]), (433,434,[3_1|2]), (434,435,[1_1|2]), (435,436,[4_1|2]), (436,437,[3_1|2]), (437,438,[1_1|2]), (438,439,[3_1|2]), (439,440,[3_1|2]), (440,441,[5_1|2]), (441,153,[1_1|2]), (441,289,[1_1|2]), (441,298,[1_1|2]), (441,424,[1_1|2]), (441,442,[1_1|2]), (441,307,[3_1|2]), (441,316,[3_1|2]), (441,325,[0_1|2]), (441,334,[4_1|2]), (442,443,[0_1|2]), (443,444,[3_1|2]), (444,445,[1_1|2]), (445,446,[4_1|2]), (446,447,[5_1|2]), (447,448,[0_1|2]), (448,449,[5_1|2]), (449,450,[4_1|2]), (450,153,[4_1|2]), (450,154,[4_1|2]), (450,163,[4_1|2]), (450,190,[4_1|2]), (450,208,[4_1|2]), (450,325,[4_1|2]), (450,425,[4_1|2]), (450,443,[4_1|2]), (450,217,[4_1|2]), (450,226,[2_1|2]), (450,235,[2_1|2]), (450,244,[3_1|2]), (450,253,[2_1|2]), (450,262,[4_1|2]), (450,271,[2_1|2]), (450,280,[4_1|2]), (450,478,[4_1|3]), (451,452,[5_1|2]), (452,453,[5_1|2]), (453,454,[1_1|2]), (454,455,[1_1|2]), (455,456,[1_1|2]), (456,457,[4_1|2]), (457,458,[2_1|2]), (458,459,[3_1|2]), (458,379,[3_1|2]), (458,388,[3_1|2]), (458,397,[2_1|2]), (459,153,[0_1|2]), (459,154,[0_1|2]), (459,163,[0_1|2]), (459,190,[0_1|2]), (459,208,[0_1|2]), (459,325,[0_1|2]), (459,425,[0_1|2]), (459,443,[0_1|2]), (459,172,[2_1|2]), (459,181,[3_1|2]), (459,199,[2_1|2]), (459,532,[0_1|3]), (460,461,[5_1|3]), (461,462,[3_1|3]), (462,463,[4_1|3]), (463,464,[4_1|3]), (464,465,[3_1|3]), (465,466,[2_1|3]), (466,467,[2_1|3]), (467,468,[1_1|3]), (468,352,[5_1|3]), (469,470,[4_1|3]), (470,471,[2_1|3]), (471,472,[3_1|3]), (472,473,[0_1|3]), (473,474,[2_1|3]), (474,475,[4_1|3]), (475,476,[2_1|3]), (476,477,[3_1|3]), (477,189,[4_1|3]), (477,271,[2_1|2]), (478,479,[4_1|3]), (479,480,[2_1|3]), (480,481,[3_1|3]), (481,482,[0_1|3]), (482,483,[2_1|3]), (483,484,[4_1|3]), (484,485,[2_1|3]), (485,486,[3_1|3]), (486,154,[4_1|3]), (486,163,[4_1|3]), (486,190,[4_1|3]), (486,208,[4_1|3]), (486,325,[4_1|3]), (487,488,[4_1|3]), (488,489,[2_1|3]), (489,490,[3_1|3]), (490,491,[0_1|3]), (491,492,[2_1|3]), (492,493,[4_1|3]), (493,494,[2_1|3]), (494,495,[3_1|3]), (495,212,[4_1|3]), (496,497,[4_1|3]), (497,498,[4_1|3]), (498,499,[5_1|3]), (499,500,[1_1|3]), (500,501,[1_1|3]), (501,502,[3_1|3]), (502,503,[1_1|3]), (503,504,[2_1|3]), (504,231,[1_1|3]), (505,506,[4_1|3]), (506,507,[2_1|3]), (507,508,[3_1|3]), (508,509,[0_1|3]), (509,510,[2_1|3]), (510,511,[4_1|3]), (511,512,[2_1|3]), (512,513,[3_1|3]), (513,252,[4_1|3]), (513,208,[4_1|3]), (514,515,[4_1|3]), (515,516,[2_1|3]), (516,517,[3_1|3]), (517,518,[0_1|3]), (518,519,[2_1|3]), (519,520,[4_1|3]), (520,521,[2_1|3]), (521,522,[3_1|3]), (522,153,[4_1|3]), (522,154,[4_1|3]), (522,163,[4_1|3]), (522,190,[4_1|3]), (522,208,[4_1|3]), (522,325,[4_1|3]), (522,532,[4_1|3]), (522,217,[4_1|2]), (522,226,[2_1|2]), (522,235,[2_1|2]), (522,244,[3_1|2]), (522,253,[2_1|2]), (522,262,[4_1|2]), (522,271,[2_1|2]), (522,280,[4_1|2]), (522,478,[4_1|3]), (523,524,[2_1|3]), (524,525,[2_1|3]), (525,526,[3_1|3]), (526,527,[0_1|3]), (526,658,[0_1|4]), (527,528,[0_1|3]), (528,529,[4_1|3]), (529,530,[4_1|3]), (530,531,[2_1|3]), (531,154,[1_1|3]), (531,163,[1_1|3]), (531,190,[1_1|3]), (531,208,[1_1|3]), (531,325,[1_1|3]), (532,533,[4_1|3]), (533,534,[4_1|3]), (534,535,[5_1|3]), (535,536,[1_1|3]), (536,537,[1_1|3]), (537,538,[3_1|3]), (538,539,[1_1|3]), (539,540,[2_1|3]), (540,154,[1_1|3]), (540,163,[1_1|3]), (540,190,[1_1|3]), (540,208,[1_1|3]), (540,325,[1_1|3]), (541,542,[4_1|3]), (542,543,[2_1|3]), (543,544,[3_1|3]), (544,545,[0_1|3]), (545,546,[2_1|3]), (546,547,[4_1|3]), (547,548,[2_1|3]), (548,549,[3_1|3]), (549,286,[4_1|3]), (549,280,[4_1|2]), (550,551,[5_1|3]), (551,552,[4_1|3]), (552,553,[5_1|3]), (553,554,[2_1|3]), (554,555,[1_1|3]), (555,556,[2_1|3]), (556,557,[3_1|3]), (557,558,[0_1|3]), (558,155,[4_1|3]), (558,164,[4_1|3]), (558,209,[4_1|3]), (558,326,[4_1|3]), (559,560,[4_1|3]), (560,561,[2_1|3]), (561,562,[3_1|3]), (562,563,[0_1|3]), (563,564,[2_1|3]), (564,565,[4_1|3]), (565,566,[2_1|3]), (566,567,[3_1|3]), (567,324,[4_1|3]), (567,262,[4_1|2]), (567,478,[4_1|3]), (567,532,[4_1|3]), (568,569,[4_1|3]), (569,570,[2_1|3]), (570,571,[3_1|3]), (571,572,[0_1|3]), (572,573,[2_1|3]), (573,574,[4_1|3]), (574,575,[2_1|3]), (575,576,[3_1|3]), (576,339,[4_1|3]), (577,578,[4_1|3]), (578,579,[4_1|3]), (579,580,[5_1|3]), (580,581,[1_1|3]), (581,582,[1_1|3]), (582,583,[3_1|3]), (583,584,[1_1|3]), (584,585,[2_1|3]), (585,358,[1_1|3]), (586,587,[4_1|3]), (587,588,[2_1|3]), (588,589,[3_1|3]), (589,590,[0_1|3]), (590,591,[2_1|3]), (591,592,[4_1|3]), (592,593,[2_1|3]), (593,594,[3_1|3]), (594,365,[4_1|3]), (595,596,[4_1|3]), (596,597,[2_1|3]), (597,598,[3_1|3]), (598,599,[0_1|3]), (599,600,[2_1|3]), (600,601,[4_1|3]), (601,602,[2_1|3]), (602,603,[3_1|3]), (603,369,[4_1|3]), (603,622,[4_1|3]), (603,163,[4_1|3]), (603,631,[4_1|3]), (603,514,[4_1|3]), (603,226,[2_1|2]), (603,235,[2_1|2]), (603,244,[3_1|2]), (603,253,[2_1|2]), (603,523,[2_1|3]), (603,667,[4_1|4]), (604,605,[2_1|3]), (605,606,[2_1|3]), (606,607,[3_1|3]), (607,608,[0_1|3]), (607,676,[0_1|4]), (608,609,[0_1|3]), (609,610,[4_1|3]), (610,611,[4_1|3]), (611,612,[2_1|3]), (612,153,[1_1|3]), (612,154,[1_1|3]), (612,163,[1_1|3]), (612,190,[1_1|3]), (612,208,[1_1|3]), (612,325,[1_1|3, 0_1|2]), (612,532,[1_1|3]), (612,289,[1_1|2]), (612,298,[1_1|2]), (612,307,[3_1|2]), (612,316,[3_1|2]), (612,334,[4_1|2]), (613,614,[2_1|3]), (614,615,[2_1|3]), (615,616,[3_1|3]), (616,617,[3_1|3]), (617,618,[0_1|3]), (618,619,[2_1|3]), (619,620,[3_1|3]), (620,621,[5_1|3]), (621,289,[1_1|3]), (621,298,[1_1|3]), (621,424,[1_1|3]), (621,442,[1_1|3]), (622,623,[4_1|3]), (623,624,[4_1|3]), (624,625,[5_1|3]), (625,626,[1_1|3]), (626,627,[1_1|3]), (627,628,[3_1|3]), (628,629,[1_1|3]), (629,630,[2_1|3]), (630,153,[1_1|3]), (630,154,[1_1|3]), (630,163,[1_1|3]), (630,190,[1_1|3]), (630,208,[1_1|3]), (630,325,[1_1|3, 0_1|2]), (630,532,[1_1|3]), (630,289,[1_1|2]), (630,298,[1_1|2]), (630,307,[3_1|2]), (630,316,[3_1|2]), (630,334,[4_1|2]), (631,632,[4_1|3]), (632,633,[1_1|3]), (633,634,[3_1|3]), (634,635,[0_1|3]), (635,636,[2_1|3]), (636,637,[1_1|3]), (637,638,[5_1|3]), (638,639,[0_1|3]), (639,289,[1_1|3]), (639,298,[1_1|3]), (639,424,[1_1|3]), (639,442,[1_1|3]), (640,641,[4_1|3]), (641,642,[4_1|3]), (642,643,[5_1|3]), (643,644,[1_1|3]), (644,645,[1_1|3]), (645,646,[3_1|3]), (646,647,[1_1|3]), (647,648,[2_1|3]), (648,405,[1_1|3]), (648,190,[1_1|3]), (649,650,[4_1|3]), (650,651,[2_1|3]), (651,652,[3_1|3]), (652,653,[0_1|3]), (653,654,[2_1|3]), (654,655,[4_1|3]), (655,656,[2_1|3]), (656,657,[3_1|3]), (657,413,[4_1|3]), (658,659,[4_1|4]), (659,660,[4_1|4]), (660,661,[5_1|4]), (661,662,[1_1|4]), (662,663,[1_1|4]), (663,664,[3_1|4]), (664,665,[1_1|4]), (665,666,[2_1|4]), (666,528,[1_1|4]), (667,668,[4_1|4]), (668,669,[2_1|4]), (669,670,[3_1|4]), (670,671,[0_1|4]), (671,672,[2_1|4]), (672,673,[4_1|4]), (673,674,[2_1|4]), (674,675,[3_1|4]), (675,532,[4_1|4]), (676,677,[4_1|4]), (677,678,[4_1|4]), (678,679,[5_1|4]), (679,680,[1_1|4]), (680,681,[1_1|4]), (681,682,[3_1|4]), (682,683,[1_1|4]), (683,684,[2_1|4]), (684,609,[1_1|4])}" ---------------------------------------- (8) BOUNDS(1, n^1)