WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 72 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 336 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(1(0(x1))) -> 2(0(0(1(x1)))) 0(1(0(x1))) -> 0(1(2(2(0(x1))))) 0(1(0(x1))) -> 2(0(0(3(1(x1))))) 0(1(0(x1))) -> 0(1(2(4(0(3(x1)))))) 0(1(0(x1))) -> 1(2(2(0(0(4(x1)))))) 0(1(0(x1))) -> 1(2(3(4(0(0(x1)))))) 0(1(0(x1))) -> 1(3(2(0(0(0(x1)))))) 0(1(0(x1))) -> 1(3(4(0(2(0(x1)))))) 0(1(0(x1))) -> 1(3(4(4(0(0(x1)))))) 0(1(0(x1))) -> 2(0(0(1(2(2(x1)))))) 0(1(0(x1))) -> 2(0(0(2(0(1(x1)))))) 0(1(0(x1))) -> 2(0(0(3(0(1(x1)))))) 0(1(0(x1))) -> 2(0(2(0(4(1(x1)))))) 0(1(0(x1))) -> 2(1(2(2(0(0(x1)))))) 0(1(0(x1))) -> 2(4(0(4(0(1(x1)))))) 0(1(0(x1))) -> 4(1(2(2(0(0(x1)))))) 0(1(1(0(x1)))) -> 2(2(0(0(1(1(x1)))))) 0(1(5(0(x1)))) -> 0(3(5(1(0(x1))))) 0(1(5(0(x1)))) -> 0(3(3(5(1(0(x1)))))) 0(5(5(0(x1)))) -> 2(2(0(0(5(5(x1)))))) 1(0(1(0(x1)))) -> 1(1(3(5(0(0(x1)))))) 1(3(0(1(x1)))) -> 1(1(0(3(4(1(x1)))))) 1(3(0(1(x1)))) -> 5(1(1(3(4(0(x1)))))) 3(0(1(0(x1)))) -> 0(1(3(2(0(4(x1)))))) 3(0(1(0(x1)))) -> 2(0(4(3(0(1(x1)))))) 3(0(1(0(x1)))) -> 2(2(3(0(0(1(x1)))))) 3(0(1(0(x1)))) -> 3(0(2(2(0(1(x1)))))) 3(1(0(0(x1)))) -> 1(0(3(4(0(x1))))) 3(1(0(0(x1)))) -> 2(0(3(1(0(x1))))) 3(1(0(0(x1)))) -> 3(0(0(5(1(x1))))) 3(1(0(0(x1)))) -> 1(2(0(3(0(2(x1)))))) 3(1(0(0(x1)))) -> 3(1(3(0(2(0(x1)))))) 3(1(5(0(x1)))) -> 1(1(3(5(0(x1))))) 3(1(5(0(x1)))) -> 0(2(5(1(3(5(x1)))))) 3(1(5(0(x1)))) -> 0(3(1(3(4(5(x1)))))) 3(1(5(0(x1)))) -> 1(5(2(3(5(0(x1)))))) 3(1(5(0(x1)))) -> 3(1(4(0(2(5(x1)))))) 3(1(5(0(x1)))) -> 4(0(5(1(3(5(x1)))))) 0(0(2(1(0(x1))))) -> 2(0(0(0(3(1(x1)))))) 0(1(2(0(1(x1))))) -> 0(0(1(3(2(1(x1)))))) 0(1(2(0(1(x1))))) -> 0(2(0(3(1(1(x1)))))) 1(3(0(2(1(x1))))) -> 0(2(1(1(3(2(x1)))))) 1(3(0(2(1(x1))))) -> 0(3(2(2(1(1(x1)))))) 1(3(0(5(5(x1))))) -> 0(5(4(3(5(1(x1)))))) 1(3(1(5(0(x1))))) -> 1(3(1(5(2(0(x1)))))) 3(0(5(0(0(x1))))) -> 3(0(0(3(5(0(x1)))))) 3(0(5(5(0(x1))))) -> 5(0(2(3(5(0(x1)))))) 3(1(4(0(0(x1))))) -> 1(0(0(3(4(0(x1)))))) 3(1(4(5(0(x1))))) -> 0(5(1(3(5(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(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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 (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(0(x1))) -> 2(0(0(1(x1)))) 0(1(0(x1))) -> 0(1(2(2(0(x1))))) 0(1(0(x1))) -> 2(0(0(3(1(x1))))) 0(1(0(x1))) -> 0(1(2(4(0(3(x1)))))) 0(1(0(x1))) -> 1(2(2(0(0(4(x1)))))) 0(1(0(x1))) -> 1(2(3(4(0(0(x1)))))) 0(1(0(x1))) -> 1(3(2(0(0(0(x1)))))) 0(1(0(x1))) -> 1(3(4(0(2(0(x1)))))) 0(1(0(x1))) -> 1(3(4(4(0(0(x1)))))) 0(1(0(x1))) -> 2(0(0(1(2(2(x1)))))) 0(1(0(x1))) -> 2(0(0(2(0(1(x1)))))) 0(1(0(x1))) -> 2(0(0(3(0(1(x1)))))) 0(1(0(x1))) -> 2(0(2(0(4(1(x1)))))) 0(1(0(x1))) -> 2(1(2(2(0(0(x1)))))) 0(1(0(x1))) -> 2(4(0(4(0(1(x1)))))) 0(1(0(x1))) -> 4(1(2(2(0(0(x1)))))) 0(1(1(0(x1)))) -> 2(2(0(0(1(1(x1)))))) 0(1(5(0(x1)))) -> 0(3(5(1(0(x1))))) 0(1(5(0(x1)))) -> 0(3(3(5(1(0(x1)))))) 0(5(5(0(x1)))) -> 2(2(0(0(5(5(x1)))))) 1(0(1(0(x1)))) -> 1(1(3(5(0(0(x1)))))) 1(3(0(1(x1)))) -> 1(1(0(3(4(1(x1)))))) 1(3(0(1(x1)))) -> 5(1(1(3(4(0(x1)))))) 3(0(1(0(x1)))) -> 0(1(3(2(0(4(x1)))))) 3(0(1(0(x1)))) -> 2(0(4(3(0(1(x1)))))) 3(0(1(0(x1)))) -> 2(2(3(0(0(1(x1)))))) 3(0(1(0(x1)))) -> 3(0(2(2(0(1(x1)))))) 3(1(0(0(x1)))) -> 1(0(3(4(0(x1))))) 3(1(0(0(x1)))) -> 2(0(3(1(0(x1))))) 3(1(0(0(x1)))) -> 3(0(0(5(1(x1))))) 3(1(0(0(x1)))) -> 1(2(0(3(0(2(x1)))))) 3(1(0(0(x1)))) -> 3(1(3(0(2(0(x1)))))) 3(1(5(0(x1)))) -> 1(1(3(5(0(x1))))) 3(1(5(0(x1)))) -> 0(2(5(1(3(5(x1)))))) 3(1(5(0(x1)))) -> 0(3(1(3(4(5(x1)))))) 3(1(5(0(x1)))) -> 1(5(2(3(5(0(x1)))))) 3(1(5(0(x1)))) -> 3(1(4(0(2(5(x1)))))) 3(1(5(0(x1)))) -> 4(0(5(1(3(5(x1)))))) 0(0(2(1(0(x1))))) -> 2(0(0(0(3(1(x1)))))) 0(1(2(0(1(x1))))) -> 0(0(1(3(2(1(x1)))))) 0(1(2(0(1(x1))))) -> 0(2(0(3(1(1(x1)))))) 1(3(0(2(1(x1))))) -> 0(2(1(1(3(2(x1)))))) 1(3(0(2(1(x1))))) -> 0(3(2(2(1(1(x1)))))) 1(3(0(5(5(x1))))) -> 0(5(4(3(5(1(x1)))))) 1(3(1(5(0(x1))))) -> 1(3(1(5(2(0(x1)))))) 3(0(5(0(0(x1))))) -> 3(0(0(3(5(0(x1)))))) 3(0(5(5(0(x1))))) -> 5(0(2(3(5(0(x1)))))) 3(1(4(0(0(x1))))) -> 1(0(0(3(4(0(x1)))))) 3(1(4(5(0(x1))))) -> 0(5(1(3(5(4(x1)))))) The (relative) TRS S consists of the following rules: encArg(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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: 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(1(0(x1))) -> 2(0(0(1(x1)))) 0(1(0(x1))) -> 0(1(2(2(0(x1))))) 0(1(0(x1))) -> 2(0(0(3(1(x1))))) 0(1(0(x1))) -> 0(1(2(4(0(3(x1)))))) 0(1(0(x1))) -> 1(2(2(0(0(4(x1)))))) 0(1(0(x1))) -> 1(2(3(4(0(0(x1)))))) 0(1(0(x1))) -> 1(3(2(0(0(0(x1)))))) 0(1(0(x1))) -> 1(3(4(0(2(0(x1)))))) 0(1(0(x1))) -> 1(3(4(4(0(0(x1)))))) 0(1(0(x1))) -> 2(0(0(1(2(2(x1)))))) 0(1(0(x1))) -> 2(0(0(2(0(1(x1)))))) 0(1(0(x1))) -> 2(0(0(3(0(1(x1)))))) 0(1(0(x1))) -> 2(0(2(0(4(1(x1)))))) 0(1(0(x1))) -> 2(1(2(2(0(0(x1)))))) 0(1(0(x1))) -> 2(4(0(4(0(1(x1)))))) 0(1(0(x1))) -> 4(1(2(2(0(0(x1)))))) 0(1(1(0(x1)))) -> 2(2(0(0(1(1(x1)))))) 0(1(5(0(x1)))) -> 0(3(5(1(0(x1))))) 0(1(5(0(x1)))) -> 0(3(3(5(1(0(x1)))))) 0(5(5(0(x1)))) -> 2(2(0(0(5(5(x1)))))) 1(0(1(0(x1)))) -> 1(1(3(5(0(0(x1)))))) 1(3(0(1(x1)))) -> 1(1(0(3(4(1(x1)))))) 1(3(0(1(x1)))) -> 5(1(1(3(4(0(x1)))))) 3(0(1(0(x1)))) -> 0(1(3(2(0(4(x1)))))) 3(0(1(0(x1)))) -> 2(0(4(3(0(1(x1)))))) 3(0(1(0(x1)))) -> 2(2(3(0(0(1(x1)))))) 3(0(1(0(x1)))) -> 3(0(2(2(0(1(x1)))))) 3(1(0(0(x1)))) -> 1(0(3(4(0(x1))))) 3(1(0(0(x1)))) -> 2(0(3(1(0(x1))))) 3(1(0(0(x1)))) -> 3(0(0(5(1(x1))))) 3(1(0(0(x1)))) -> 1(2(0(3(0(2(x1)))))) 3(1(0(0(x1)))) -> 3(1(3(0(2(0(x1)))))) 3(1(5(0(x1)))) -> 1(1(3(5(0(x1))))) 3(1(5(0(x1)))) -> 0(2(5(1(3(5(x1)))))) 3(1(5(0(x1)))) -> 0(3(1(3(4(5(x1)))))) 3(1(5(0(x1)))) -> 1(5(2(3(5(0(x1)))))) 3(1(5(0(x1)))) -> 3(1(4(0(2(5(x1)))))) 3(1(5(0(x1)))) -> 4(0(5(1(3(5(x1)))))) 0(0(2(1(0(x1))))) -> 2(0(0(0(3(1(x1)))))) 0(1(2(0(1(x1))))) -> 0(0(1(3(2(1(x1)))))) 0(1(2(0(1(x1))))) -> 0(2(0(3(1(1(x1)))))) 1(3(0(2(1(x1))))) -> 0(2(1(1(3(2(x1)))))) 1(3(0(2(1(x1))))) -> 0(3(2(2(1(1(x1)))))) 1(3(0(5(5(x1))))) -> 0(5(4(3(5(1(x1)))))) 1(3(1(5(0(x1))))) -> 1(3(1(5(2(0(x1)))))) 3(0(5(0(0(x1))))) -> 3(0(0(3(5(0(x1)))))) 3(0(5(5(0(x1))))) -> 5(0(2(3(5(0(x1)))))) 3(1(4(0(0(x1))))) -> 1(0(0(3(4(0(x1)))))) 3(1(4(5(0(x1))))) -> 0(5(1(3(5(4(x1)))))) The (relative) TRS S consists of the following rules: encArg(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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: 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(1(0(x1))) -> 2(0(0(1(x1)))) 0(1(0(x1))) -> 0(1(2(2(0(x1))))) 0(1(0(x1))) -> 2(0(0(3(1(x1))))) 0(1(0(x1))) -> 0(1(2(4(0(3(x1)))))) 0(1(0(x1))) -> 1(2(2(0(0(4(x1)))))) 0(1(0(x1))) -> 1(2(3(4(0(0(x1)))))) 0(1(0(x1))) -> 1(3(2(0(0(0(x1)))))) 0(1(0(x1))) -> 1(3(4(0(2(0(x1)))))) 0(1(0(x1))) -> 1(3(4(4(0(0(x1)))))) 0(1(0(x1))) -> 2(0(0(1(2(2(x1)))))) 0(1(0(x1))) -> 2(0(0(2(0(1(x1)))))) 0(1(0(x1))) -> 2(0(0(3(0(1(x1)))))) 0(1(0(x1))) -> 2(0(2(0(4(1(x1)))))) 0(1(0(x1))) -> 2(1(2(2(0(0(x1)))))) 0(1(0(x1))) -> 2(4(0(4(0(1(x1)))))) 0(1(0(x1))) -> 4(1(2(2(0(0(x1)))))) 0(1(1(0(x1)))) -> 2(2(0(0(1(1(x1)))))) 0(1(5(0(x1)))) -> 0(3(5(1(0(x1))))) 0(1(5(0(x1)))) -> 0(3(3(5(1(0(x1)))))) 0(5(5(0(x1)))) -> 2(2(0(0(5(5(x1)))))) 1(0(1(0(x1)))) -> 1(1(3(5(0(0(x1)))))) 1(3(0(1(x1)))) -> 1(1(0(3(4(1(x1)))))) 1(3(0(1(x1)))) -> 5(1(1(3(4(0(x1)))))) 3(0(1(0(x1)))) -> 0(1(3(2(0(4(x1)))))) 3(0(1(0(x1)))) -> 2(0(4(3(0(1(x1)))))) 3(0(1(0(x1)))) -> 2(2(3(0(0(1(x1)))))) 3(0(1(0(x1)))) -> 3(0(2(2(0(1(x1)))))) 3(1(0(0(x1)))) -> 1(0(3(4(0(x1))))) 3(1(0(0(x1)))) -> 2(0(3(1(0(x1))))) 3(1(0(0(x1)))) -> 3(0(0(5(1(x1))))) 3(1(0(0(x1)))) -> 1(2(0(3(0(2(x1)))))) 3(1(0(0(x1)))) -> 3(1(3(0(2(0(x1)))))) 3(1(5(0(x1)))) -> 1(1(3(5(0(x1))))) 3(1(5(0(x1)))) -> 0(2(5(1(3(5(x1)))))) 3(1(5(0(x1)))) -> 0(3(1(3(4(5(x1)))))) 3(1(5(0(x1)))) -> 1(5(2(3(5(0(x1)))))) 3(1(5(0(x1)))) -> 3(1(4(0(2(5(x1)))))) 3(1(5(0(x1)))) -> 4(0(5(1(3(5(x1)))))) 0(0(2(1(0(x1))))) -> 2(0(0(0(3(1(x1)))))) 0(1(2(0(1(x1))))) -> 0(0(1(3(2(1(x1)))))) 0(1(2(0(1(x1))))) -> 0(2(0(3(1(1(x1)))))) 1(3(0(2(1(x1))))) -> 0(2(1(1(3(2(x1)))))) 1(3(0(2(1(x1))))) -> 0(3(2(2(1(1(x1)))))) 1(3(0(5(5(x1))))) -> 0(5(4(3(5(1(x1)))))) 1(3(1(5(0(x1))))) -> 1(3(1(5(2(0(x1)))))) 3(0(5(0(0(x1))))) -> 3(0(0(3(5(0(x1)))))) 3(0(5(5(0(x1))))) -> 5(0(2(3(5(0(x1)))))) 3(1(4(0(0(x1))))) -> 1(0(0(3(4(0(x1)))))) 3(1(4(5(0(x1))))) -> 0(5(1(3(5(4(x1)))))) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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: 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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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, 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, 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, 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, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 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(580,349,[2_1|3]), (580,354,[2_1|3]), (580,359,[2_1|3]), (580,364,[2_1|3]), (580,369,[2_1|3]), (580,374,[2_1|3]), (580,379,[4_1|3]), (581,75,[1_1|3]), (581,83,[1_1|3]), (581,153,[1_1|3]), (581,157,[1_1|3]), (581,162,[1_1|3]), (581,167,[1_1|3]), (581,197,[1_1|3]), (581,202,[1_1|3]), (581,207,[1_1|3]), (581,217,[1_1|3]), (581,273,[1_1|3]), (581,278,[1_1|3]), (581,303,[1_1|3]), (581,163,[1_1|3]), (581,300,[1_1|3]), (582,583,[2_1|3]), (583,584,[0_1|3]), (584,585,[0_1|3]), (584,582,[2_1|3]), (585,586,[1_1|3]), (586,75,[1_1|3]), (586,83,[1_1|3]), (586,153,[1_1|3]), (586,157,[1_1|3]), (586,162,[1_1|3]), (586,167,[1_1|3]), (586,197,[1_1|3]), (586,202,[1_1|3]), (586,207,[1_1|3]), (586,217,[1_1|3]), (586,273,[1_1|3]), (586,278,[1_1|3]), (586,303,[1_1|3]), (586,163,[1_1|3]), (586,300,[1_1|3]), (587,588,[1_1|3]), (588,589,[3_1|3]), (589,590,[5_1|3]), (590,591,[0_1|3]), (591,248,[0_1|3]), (591,299,[0_1|3]), (592,593,[2_1|3]), (593,594,[0_1|3]), (594,595,[0_1|3]), (594,592,[2_1|3]), (595,596,[5_1|3]), (596,75,[5_1|3]), (596,83,[5_1|3]), (596,153,[5_1|3]), (596,157,[5_1|3]), (596,162,[5_1|3]), (596,167,[5_1|3]), (596,197,[5_1|3]), (596,202,[5_1|3]), (596,207,[5_1|3]), (596,217,[5_1|3]), (596,273,[5_1|3]), (596,278,[5_1|3]), (596,303,[5_1|3]), (596,163,[5_1|3]), (607,608,[0_1|3]), (608,609,[3_1|3]), (609,610,[4_1|3]), (610,75,[0_1|3]), (610,83,[0_1|3]), (610,153,[0_1|3]), (610,157,[0_1|3]), (610,162,[0_1|3]), (610,167,[0_1|3]), (610,197,[0_1|3]), (610,202,[0_1|3]), (610,207,[0_1|3]), (610,217,[0_1|3]), (610,273,[0_1|3]), (610,278,[0_1|3]), (610,303,[0_1|3]), (610,163,[0_1|3]), (611,612,[0_1|3]), (611,659,[2_1|4]), (611,662,[0_1|4]), (611,666,[2_1|4]), (611,670,[0_1|4]), (611,675,[1_1|4]), (611,680,[1_1|4]), (611,685,[1_1|4]), (611,690,[1_1|4]), (611,695,[1_1|4]), (611,700,[2_1|4]), (611,705,[2_1|4]), (611,710,[2_1|4]), (611,715,[2_1|4]), (611,720,[2_1|4]), (611,725,[2_1|4]), (611,730,[4_1|4]), (612,613,[3_1|3]), (612,479,[1_1|3]), (612,483,[2_1|3]), (612,487,[3_1|3]), (612,491,[1_1|3]), (612,496,[3_1|3]), (613,614,[1_1|3]), (614,75,[0_1|3]), (614,83,[0_1|3]), (614,153,[0_1|3]), (614,157,[0_1|3]), (614,162,[0_1|3]), (614,167,[0_1|3]), (614,197,[0_1|3]), (614,202,[0_1|3]), (614,207,[0_1|3]), (614,217,[0_1|3]), (614,273,[0_1|3]), (614,278,[0_1|3]), (614,303,[0_1|3]), (614,163,[0_1|3]), (615,616,[0_1|3]), (616,617,[0_1|3]), (617,618,[5_1|3]), (618,75,[1_1|3]), (618,83,[1_1|3]), (618,153,[1_1|3]), (618,157,[1_1|3]), (618,162,[1_1|3]), (618,167,[1_1|3]), (618,197,[1_1|3]), (618,202,[1_1|3]), (618,207,[1_1|3]), (618,217,[1_1|3]), (618,273,[1_1|3]), (618,278,[1_1|3]), (618,303,[1_1|3]), (618,163,[1_1|3]), (619,620,[2_1|3]), (620,621,[0_1|3]), (621,622,[3_1|3]), (622,623,[0_1|3]), (623,75,[2_1|3]), (623,83,[2_1|3]), (623,153,[2_1|3]), (623,157,[2_1|3]), (623,162,[2_1|3]), (623,167,[2_1|3]), (623,197,[2_1|3]), (623,202,[2_1|3]), (623,207,[2_1|3]), (623,217,[2_1|3]), (623,273,[2_1|3]), (623,278,[2_1|3]), (623,303,[2_1|3]), (623,163,[2_1|3]), (624,625,[1_1|3]), (625,626,[3_1|3]), (626,627,[0_1|3]), (627,628,[2_1|3]), (628,75,[0_1|3]), (628,83,[0_1|3]), (628,153,[0_1|3]), (628,157,[0_1|3]), (628,162,[0_1|3]), (628,167,[0_1|3]), (628,197,[0_1|3]), (628,202,[0_1|3]), (628,207,[0_1|3]), (628,217,[0_1|3]), (628,273,[0_1|3]), (628,278,[0_1|3]), (628,303,[0_1|3]), (628,163,[0_1|3]), (629,630,[0_1|3]), (630,631,[1_1|3]), (631,632,[3_1|3]), (632,633,[2_1|3]), (633,88,[1_1|3]), (633,93,[1_1|3]), (633,98,[1_1|3]), (633,103,[1_1|3]), (633,108,[1_1|3]), (633,324,[1_1|3]), (633,329,[1_1|3]), (633,334,[1_1|3]), (633,339,[1_1|3]), (633,344,[1_1|3]), (633,247,[1_1|3]), (633,259,[1_1|3]), (633,607,[1_1|3]), (633,619,[1_1|3]), (633,419,[1_1|3]), (633,424,[1_1|3]), (633,429,[1_1|3]), (633,434,[1_1|3]), (633,439,[1_1|3]), (633,407,[1_1|3]), (633,415,[1_1|3]), (634,635,[2_1|3]), (635,636,[0_1|3]), (636,637,[3_1|3]), (637,638,[1_1|3]), (638,88,[1_1|3]), (638,93,[1_1|3]), (638,98,[1_1|3]), (638,103,[1_1|3]), (638,108,[1_1|3]), (638,324,[1_1|3]), (638,329,[1_1|3]), (638,334,[1_1|3]), (638,339,[1_1|3]), (638,344,[1_1|3]), (638,247,[1_1|3]), (638,259,[1_1|3]), (638,607,[1_1|3]), (638,619,[1_1|3]), (638,419,[1_1|3]), (638,424,[1_1|3]), (638,429,[1_1|3]), (638,434,[1_1|3]), (638,439,[1_1|3]), (638,407,[1_1|3]), (638,415,[1_1|3]), (639,640,[2_1|3]), (640,641,[1_1|3]), (641,642,[1_1|3]), (642,643,[3_1|3]), (643,88,[2_1|3]), (643,93,[2_1|3]), (643,98,[2_1|3]), (643,103,[2_1|3]), (643,108,[2_1|3]), (643,419,[2_1|3]), (643,424,[2_1|3]), (643,429,[2_1|3]), (643,434,[2_1|3]), (643,439,[2_1|3]), (644,645,[3_1|3]), (645,646,[2_1|3]), (646,647,[2_1|3]), (647,648,[1_1|3]), (648,88,[1_1|3]), (648,93,[1_1|3]), (648,98,[1_1|3]), (648,103,[1_1|3]), (648,108,[1_1|3]), (648,419,[1_1|3]), (648,424,[1_1|3]), (648,429,[1_1|3]), (648,434,[1_1|3]), (648,439,[1_1|3]), (649,650,[2_1|3]), (650,651,[1_1|3]), (651,652,[1_1|3]), (652,653,[3_1|3]), (653,641,[2_1|3]), (654,655,[3_1|3]), (655,656,[2_1|3]), (656,657,[2_1|3]), (657,658,[1_1|3]), (658,641,[1_1|3]), (659,660,[0_1|4]), (660,661,[0_1|4]), (661,480,[1_1|4]), (662,663,[1_1|4]), (663,664,[2_1|4]), (664,665,[2_1|4]), (665,480,[0_1|4]), (666,667,[0_1|4]), (667,668,[0_1|4]), (668,669,[3_1|4]), (669,480,[1_1|4]), (670,671,[1_1|4]), (671,672,[2_1|4]), (672,673,[4_1|4]), (673,674,[0_1|4]), (674,480,[3_1|4]), (675,676,[2_1|4]), (676,677,[2_1|4]), (677,678,[0_1|4]), (678,679,[0_1|4]), (679,480,[4_1|4]), (680,681,[2_1|4]), (681,682,[3_1|4]), (682,683,[4_1|4]), (683,684,[0_1|4]), (684,480,[0_1|4]), (685,686,[3_1|4]), (686,687,[2_1|4]), (687,688,[0_1|4]), (688,689,[0_1|4]), (689,480,[0_1|4]), (690,691,[3_1|4]), (691,692,[4_1|4]), (692,693,[0_1|4]), (693,694,[2_1|4]), (694,480,[0_1|4]), (695,696,[3_1|4]), (696,697,[4_1|4]), (697,698,[4_1|4]), (698,699,[0_1|4]), (699,480,[0_1|4]), (700,701,[0_1|4]), (701,702,[0_1|4]), (702,703,[1_1|4]), (703,704,[2_1|4]), (704,480,[2_1|4]), (705,706,[0_1|4]), (706,707,[0_1|4]), (707,708,[2_1|4]), (708,709,[0_1|4]), (709,480,[1_1|4]), (710,711,[0_1|4]), (711,712,[0_1|4]), (712,713,[3_1|4]), (713,714,[0_1|4]), (714,480,[1_1|4]), (715,716,[0_1|4]), (716,717,[2_1|4]), (717,718,[0_1|4]), (718,719,[4_1|4]), (719,480,[1_1|4]), (720,721,[1_1|4]), (721,722,[2_1|4]), (722,723,[2_1|4]), (723,724,[0_1|4]), (724,480,[0_1|4]), (725,726,[4_1|4]), (726,727,[0_1|4]), (727,728,[4_1|4]), (728,729,[0_1|4]), (729,480,[1_1|4]), (730,731,[1_1|4]), (731,732,[2_1|4]), (732,733,[2_1|4]), (733,734,[0_1|4]), (734,480,[0_1|4])}" ---------------------------------------- (8) BOUNDS(1, n^1)