/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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, 162 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). 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5(2(2(1(3(4(4(0(5(2(5(0(1(1(1(0(2(1(3(3(0(4(5(5(1(5(5(1(3(2(1(1(4(3(4(3(4(1(4(4(2(4(0(2(3(2(0(4(5(4(2(2(0(4(2(4(3(1(1(5(4(4(5(2(2(4(5(3(3(3(4(1(4(2(4(5(5(5(2(2(3(3(1(0(3(3(3(1(3(4(2(2(1(0(4(5(2(1(5(0(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_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(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 (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). 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5(0(0(0(0(5(4(5(3(2(0(5(0(5(5(1(1(0(2(1(3(5(5(3(2(0(2(4(0(2(4(5(2(4(3(5(2(5(3(2(0(1(4(0(0(5(1(1(0(5(0(1(1(3(5(1(2(1(1(4(2(0(4(0(0(3(0(0(5(1(4(1(1(5(0(4(5(2(0(0(0(1(5(4(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(4(4(2(2(4(5(3(2(3(3(4(4(0(4(4(2(1(0(0(2(2(3(5(4(5(1(0(3(4(4(2(2(3(5(5(2(3(0(1(3(2(1(3(2(4(5(3(2(1(2(3(3(5(5(1(1(2(3(4(2(3(3(2(5(0(0(2(1(0(4(0(0(4(1(4(5(0(3(2(3(4(0(3(2(2(1(4(1(3(2(1(2(0(0(0(2(2(3(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(0(0(3(3(5(4(3(5(5(1(5(2(4(0(3(4(2(2(4(0(5(1(0(0(0(5(3(5(1(0(1(4(1(5(0(1(0(4(0(1(2(1(2(2(3(1(5(3(0(0(0(2(3(1(0(5(3(4(2(5(1(5(4(5(4(1(2(5(3(4(5(1(0(4(2(0(5(5(4(2(4(3(1(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(2(2(1(3(4(4(0(5(2(5(0(1(1(1(0(2(1(3(3(0(4(5(5(1(5(5(1(3(2(1(1(4(3(4(3(4(1(4(4(2(4(0(2(3(2(0(4(5(4(2(2(0(4(2(4(3(1(1(5(4(4(5(2(2(4(5(3(3(3(4(1(4(2(4(5(5(5(2(2(3(3(1(0(3(3(3(1(3(4(2(2(1(0(4(5(2(1(5(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(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: 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(0(0(1(1(2(2(0(3(2(4(0(5(0(1(1(5(3(1(0(3(0(0(4(5(2(4(0(4(2(1(4(3(3(3(2(5(0(0(1(5(0(3(4(0(4(5(0(2(0(5(5(4(1(0(0(4(5(4(4(4(1(3(0(0(0(4(3(5(2(2(3(1(3(5(3(1(0(3(4(4(4(4(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(4(4(0(4(2(4(0(2(1(1(0(0(5(4(5(2(2(0(1(0(5(2(4(4(1(0(4(0(0(0(5(4(5(0(4(2(1(3(3(0(1(3(0(3(2(1(2(3(5(5(2(1(4(4(4(0(3(4(4(0(2(5(4(1(0(4(2(1(4(2(4(0(3(3(2(1(2(4(3(3(5(4(2(4(3(0(3(1(5(1(4(3(3(3(1(5(1(2(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(3(1(3(4(1(4(0(0(5(2(0(3(0(0(2(4(0(0(4(5(5(0(1(3(4(5(0(3(3(0(5(3(0(4(0(4(4(3(4(0(0(0(4(5(0(3(5(2(4(1(0(2(1(0(2(0(5(0(4(0(4(3(5(0(0(2(4(3(3(1(1(4(5(4(0(0(1(5(1(1(5(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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5(0(0(0(0(5(4(5(3(2(0(5(0(5(5(1(1(0(2(1(3(5(5(3(2(0(2(4(0(2(4(5(2(4(3(5(2(5(3(2(0(1(4(0(0(5(1(1(0(5(0(1(1(3(5(1(2(1(1(4(2(0(4(0(0(3(0(0(5(1(4(1(1(5(0(4(5(2(0(0(0(1(5(4(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(4(4(2(2(4(5(3(2(3(3(4(4(0(4(4(2(1(0(0(2(2(3(5(4(5(1(0(3(4(4(2(2(3(5(5(2(3(0(1(3(2(1(3(2(4(5(3(2(1(2(3(3(5(5(1(1(2(3(4(2(3(3(2(5(0(0(2(1(0(4(0(0(4(1(4(5(0(3(2(3(4(0(3(2(2(1(4(1(3(2(1(2(0(0(0(2(2(3(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(0(0(3(3(5(4(3(5(5(1(5(2(4(0(3(4(2(2(4(0(5(1(0(0(0(5(3(5(1(0(1(4(1(5(0(1(0(4(0(1(2(1(2(2(3(1(5(3(0(0(0(2(3(1(0(5(3(4(2(5(1(5(4(5(4(1(2(5(3(4(5(1(0(4(2(0(5(5(4(2(4(3(1(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 5(2(2(1(3(4(4(0(5(2(5(0(1(1(1(0(2(1(3(3(0(4(5(5(1(5(5(1(3(2(1(1(4(3(4(3(4(1(4(4(2(4(0(2(3(2(0(4(5(4(2(2(0(4(2(4(3(1(1(5(4(4(5(2(2(4(5(3(3(3(4(1(4(2(4(5(5(5(2(2(3(3(1(0(3(3(3(1(3(4(2(2(1(0(4(5(2(1(5(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(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: 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(0(0(1(1(2(2(0(3(2(4(0(5(0(1(1(5(3(1(0(3(0(0(4(5(2(4(0(4(2(1(4(3(3(3(2(5(0(0(1(5(0(3(4(0(4(5(0(2(0(5(5(4(1(0(0(4(5(4(4(4(1(3(0(0(0(4(3(5(2(2(3(1(3(5(3(1(0(3(4(4(4(4(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(4(4(0(4(2(4(0(2(1(1(0(0(5(4(5(2(2(0(1(0(5(2(4(4(1(0(4(0(0(0(5(4(5(0(4(2(1(3(3(0(1(3(0(3(2(1(2(3(5(5(2(1(4(4(4(0(3(4(4(0(2(5(4(1(0(4(2(1(4(2(4(0(3(3(2(1(2(4(3(3(5(4(2(4(3(0(3(1(5(1(4(3(3(3(1(5(1(2(3(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(3(1(3(4(1(4(0(0(5(2(0(3(0(0(2(4(0(0(4(5(5(0(1(3(4(5(0(3(3(0(5(3(0(4(0(4(4(3(4(0(0(0(4(5(0(3(5(2(4(1(0(2(1(0(2(0(5(0(4(0(4(3(5(0(0(2(4(3(3(1(1(4(5(4(0(0(1(5(1(1(5(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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5(2(2(1(3(4(4(0(5(2(5(0(1(1(1(0(2(1(3(3(0(4(5(5(1(5(5(1(3(2(1(1(4(3(4(3(4(1(4(4(2(4(0(2(3(2(0(4(5(4(2(2(0(4(2(4(3(1(1(5(4(4(5(2(2(4(5(3(3(3(4(1(4(2(4(5(5(5(2(2(3(3(1(0(3(3(3(1(3(4(2(2(1(0(4(5(2(1(5(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(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: 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 2. The certificate found is represented by the following graph. "[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, 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, 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1952, 1953, 1954, 1955, 1956, 1957, 1958, 1959, 1960, 1961, 1962, 1963, 1964, 1965, 1966, 1967, 1968, 1969, 1970, 1971, 1972, 1973, 1974, 1975, 1976, 1977, 1978, 1979, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990, 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023, 2024, 2025, 2026, 2027, 2028, 2029, 2030, 2031, 2032, 2033, 2034, 2035, 2036, 2037, 2038, 2039, 2040, 2041, 2042, 2043, 2044, 2045, 2046, 2047, 2048, 2049, 2050, 2051, 2052, 2053, 2054, 2055, 2056, 2057, 2058, 2059, 2060, 2061, 2062, 2063, 2064, 2065, 2066, 2067, 2068, 2069, 2070, 2071, 2072, 2073, 2074, 2075, 2076, 2077, 2078, 2079, 2080, 2081, 2082, 2083, 2084, 2085, 2086, 2087, 2088, 2089, 2090, 2091, 2092, 2093, 2094, 2095, 2096, 2097, 2098, 2099, 2100, 2101, 2102, 2103, 2104, 2105, 2106, 2107, 2108, 2109, 2110, 2111, 2112, 2113, 2114, 2115, 2116, 2117, 2118, 2119, 2120, 2121, 2122, 2123, 2124, 2125, 2126, 2127, 2128, 2129, 2130] {(148,149,[0_1|0, 1_1|0, 2_1|0, 3_1|0, 4_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]), (148,150,[0_1|1, 1_1|1, 2_1|1, 3_1|1, 4_1|1, 5_1|1]), (148,151,[0_1|2]), (148,250,[1_1|2]), (148,349,[5_1|2]), (148,448,[3_1|2]), (148,547,[4_1|2]), (148,646,[3_1|2]), (148,745,[2_1|2]), (148,844,[1_1|2]), (148,943,[2_1|2]), (148,1042,[1_1|2]), (148,1141,[4_1|2]), (148,1240,[1_1|2]), (148,1339,[3_1|2]), (148,1438,[4_1|2]), (148,1537,[4_1|2]), (148,1636,[5_1|2]), (148,1735,[4_1|2]), (148,1834,[1_1|2]), (148,1933,[2_1|2]), (148,2032,[5_1|2]), (149,149,[cons_0_1|0, cons_1_1|0, cons_2_1|0, cons_3_1|0, cons_4_1|0, cons_5_1|0]), (150,149,[encArg_1|1]), (150,150,[0_1|1, 1_1|1, 2_1|1, 3_1|1, 4_1|1, 5_1|1]), (150,151,[0_1|2]), (150,250,[1_1|2]), (150,349,[5_1|2]), (150,448,[3_1|2]), (150,547,[4_1|2]), (150,646,[3_1|2]), (150,745,[2_1|2]), (150,844,[1_1|2]), (150,943,[2_1|2]), (150,1042,[1_1|2]), (150,1141,[4_1|2]), (150,1240,[1_1|2]), (150,1339,[3_1|2]), (150,1438,[4_1|2]), (150,1537,[4_1|2]), (150,1636,[5_1|2]), (150,1735,[4_1|2]), (150,1834,[1_1|2]), (150,1933,[2_1|2]), (150,2032,[5_1|2]), (151,152,[4_1|2]), (152,153,[4_1|2]), (153,154,[0_1|2]), (154,155,[4_1|2]), (155,156,[2_1|2]), (156,157,[4_1|2]), (157,158,[0_1|2]), (158,159,[2_1|2]), (159,160,[1_1|2]), (160,161,[1_1|2]), (161,162,[0_1|2]), (162,163,[0_1|2]), (163,164,[5_1|2]), (164,165,[4_1|2]), (165,166,[5_1|2]), (166,167,[2_1|2]), (167,168,[2_1|2]), (168,169,[0_1|2]), (169,170,[1_1|2]), (170,171,[0_1|2]), (171,172,[5_1|2]), (172,173,[2_1|2]), (173,174,[4_1|2]), (174,175,[4_1|2]), (175,176,[1_1|2]), (176,177,[0_1|2]), (177,178,[4_1|2]), (178,179,[0_1|2]), (179,180,[0_1|2]), (180,181,[0_1|2]), (181,182,[5_1|2]), (182,183,[4_1|2]), (183,184,[5_1|2]), (184,185,[0_1|2]), (185,186,[4_1|2]), (186,187,[2_1|2]), (187,188,[1_1|2]), (188,189,[3_1|2]), (189,190,[3_1|2]), (190,191,[0_1|2]), 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(1713,1714,[0_1|2]), (1714,1715,[2_1|2]), (1715,1716,[5_1|2]), (1716,1717,[3_1|2]), (1717,1718,[4_1|2]), (1718,1719,[1_1|2]), (1719,1720,[1_1|2]), (1720,1721,[5_1|2]), (1721,1722,[2_1|2]), (1722,1723,[3_1|2]), (1723,1724,[2_1|2]), (1724,1725,[2_1|2]), (1725,1726,[4_1|2]), (1726,1727,[4_1|2]), (1727,1728,[4_1|2]), (1728,1729,[1_1|2]), (1729,1730,[5_1|2]), (1730,1731,[2_1|2]), (1731,1732,[5_1|2]), (1732,1733,[1_1|2]), (1733,1734,[1_1|2]), (1733,1141,[4_1|2]), (1734,150,[5_1|2]), (1734,448,[5_1|2]), (1734,646,[5_1|2]), (1734,1339,[5_1|2]), (1734,1639,[5_1|2]), (1734,1933,[2_1|2]), (1734,2032,[5_1|2]), (1735,1736,[4_1|2]), (1736,1737,[2_1|2]), (1737,1738,[2_1|2]), (1738,1739,[2_1|2]), (1739,1740,[0_1|2]), (1740,1741,[4_1|2]), (1741,1742,[2_1|2]), (1742,1743,[4_1|2]), (1743,1744,[5_1|2]), (1744,1745,[1_1|2]), (1745,1746,[1_1|2]), (1746,1747,[0_1|2]), (1747,1748,[5_1|2]), (1748,1749,[4_1|2]), (1749,1750,[4_1|2]), (1750,1751,[5_1|2]), (1751,1752,[4_1|2]), (1752,1753,[5_1|2]), (1753,1754,[5_1|2]), (1754,1755,[5_1|2]), (1755,1756,[5_1|2]), (1756,1757,[4_1|2]), (1757,1758,[2_1|2]), (1758,1759,[4_1|2]), (1759,1760,[3_1|2]), (1760,1761,[5_1|2]), (1761,1762,[2_1|2]), (1762,1763,[4_1|2]), (1763,1764,[0_1|2]), (1764,1765,[5_1|2]), (1765,1766,[5_1|2]), (1766,1767,[4_1|2]), (1767,1768,[3_1|2]), (1768,1769,[3_1|2]), (1769,1770,[3_1|2]), (1770,1771,[0_1|2]), (1771,1772,[3_1|2]), (1772,1773,[2_1|2]), (1773,1774,[5_1|2]), (1774,1775,[2_1|2]), (1775,1776,[1_1|2]), (1776,1777,[4_1|2]), (1777,1778,[1_1|2]), (1778,1779,[1_1|2]), (1779,1780,[0_1|2]), (1780,1781,[4_1|2]), (1781,1782,[3_1|2]), (1782,1783,[5_1|2]), (1783,1784,[2_1|2]), (1784,1785,[3_1|2]), (1785,1786,[2_1|2]), (1786,1787,[2_1|2]), (1787,1788,[5_1|2]), (1788,1789,[2_1|2]), (1789,1790,[2_1|2]), (1790,1791,[2_1|2]), (1791,1792,[5_1|2]), (1792,1793,[1_1|2]), (1793,1794,[2_1|2]), (1794,1795,[2_1|2]), (1795,1796,[0_1|2]), (1796,1797,[0_1|2]), (1797,1798,[2_1|2]), (1798,1799,[5_1|2]), (1799,1800,[5_1|2]), (1800,1801,[2_1|2]), (1801,1802,[4_1|2]), (1802,1803,[1_1|2]), (1803,1804,[2_1|2]), (1804,1805,[1_1|2]), (1805,1806,[4_1|2]), (1806,1807,[2_1|2]), (1807,1808,[1_1|2]), (1808,1809,[4_1|2]), (1809,1810,[3_1|2]), (1810,1811,[5_1|2]), (1811,1812,[5_1|2]), (1812,1813,[1_1|2]), (1813,1814,[1_1|2]), (1814,1815,[3_1|2]), (1815,1816,[3_1|2]), (1816,1817,[2_1|2]), (1817,1818,[1_1|2]), (1818,1819,[4_1|2]), (1819,1820,[4_1|2]), (1820,1821,[5_1|2]), (1821,1822,[5_1|2]), (1822,1823,[3_1|2]), (1823,1824,[1_1|2]), (1824,1825,[3_1|2]), (1825,1826,[4_1|2]), (1826,1827,[1_1|2]), (1827,1828,[1_1|2]), (1828,1829,[4_1|2]), (1829,1830,[5_1|2]), (1830,1831,[4_1|2]), (1831,1832,[1_1|2]), (1832,1833,[4_1|2]), (1833,150,[5_1|2]), (1833,250,[5_1|2]), (1833,844,[5_1|2]), (1833,1042,[5_1|2]), (1833,1240,[5_1|2]), (1833,1834,[5_1|2]), (1833,1933,[2_1|2]), (1833,2032,[5_1|2]), (1834,1835,[2_1|2]), (1835,1836,[4_1|2]), (1836,1837,[3_1|2]), (1837,1838,[0_1|2]), (1838,1839,[4_1|2]), (1839,1840,[0_1|2]), (1840,1841,[1_1|2]), (1841,1842,[5_1|2]), (1842,1843,[3_1|2]), (1843,1844,[2_1|2]), (1844,1845,[5_1|2]), (1845,1846,[3_1|2]), (1846,1847,[3_1|2]), (1847,1848,[4_1|2]), (1848,1849,[0_1|2]), (1849,1850,[1_1|2]), (1850,1851,[2_1|2]), (1851,1852,[2_1|2]), (1852,1853,[3_1|2]), (1853,1854,[1_1|2]), (1854,1855,[0_1|2]), (1855,1856,[4_1|2]), (1856,1857,[5_1|2]), (1857,1858,[1_1|2]), (1858,1859,[5_1|2]), (1859,1860,[4_1|2]), (1860,1861,[3_1|2]), (1861,1862,[4_1|2]), (1862,1863,[0_1|2]), (1863,1864,[3_1|2]), (1864,1865,[5_1|2]), (1865,1866,[2_1|2]), (1866,1867,[1_1|2]), (1867,1868,[2_1|2]), (1868,1869,[0_1|2]), (1869,1870,[2_1|2]), (1870,1871,[1_1|2]), (1871,1872,[1_1|2]), (1872,1873,[2_1|2]), (1873,1874,[1_1|2]), (1874,1875,[3_1|2]), (1875,1876,[0_1|2]), (1876,1877,[2_1|2]), (1877,1878,[1_1|2]), (1878,1879,[5_1|2]), (1879,1880,[2_1|2]), (1880,1881,[1_1|2]), (1881,1882,[1_1|2]), (1882,1883,[2_1|2]), (1883,1884,[2_1|2]), (1884,1885,[2_1|2]), (1885,1886,[1_1|2]), (1886,1887,[3_1|2]), (1887,1888,[1_1|2]), (1888,1889,[1_1|2]), (1889,1890,[3_1|2]), (1890,1891,[5_1|2]), (1891,1892,[4_1|2]), (1892,1893,[2_1|2]), (1893,1894,[4_1|2]), (1894,1895,[4_1|2]), (1895,1896,[3_1|2]), (1896,1897,[2_1|2]), (1897,1898,[1_1|2]), (1898,1899,[1_1|2]), (1899,1900,[2_1|2]), (1900,1901,[2_1|2]), (1901,1902,[3_1|2]), (1902,1903,[4_1|2]), (1903,1904,[5_1|2]), (1904,1905,[2_1|2]), (1905,1906,[4_1|2]), (1906,1907,[2_1|2]), (1907,1908,[0_1|2]), (1908,1909,[5_1|2]), (1909,1910,[3_1|2]), (1910,1911,[1_1|2]), (1911,1912,[0_1|2]), (1912,1913,[4_1|2]), (1913,1914,[3_1|2]), (1914,1915,[3_1|2]), (1915,1916,[0_1|2]), (1916,1917,[2_1|2]), (1917,1918,[3_1|2]), (1918,1919,[5_1|2]), (1919,1920,[3_1|2]), (1920,1921,[5_1|2]), (1921,1922,[1_1|2]), (1922,1923,[3_1|2]), (1923,1924,[4_1|2]), (1924,1925,[2_1|2]), (1925,1926,[2_1|2]), (1926,1927,[5_1|2]), (1927,1928,[0_1|2]), (1928,1929,[4_1|2]), (1929,1930,[4_1|2]), (1930,1931,[5_1|2]), (1931,1932,[1_1|2]), (1931,844,[1_1|2]), (1931,943,[2_1|2]), (1932,150,[2_1|2]), (1932,151,[2_1|2]), (1932,1240,[1_1|2]), (1932,1339,[3_1|2]), (1933,1934,[4_1|2]), (1934,1935,[4_1|2]), (1935,1936,[2_1|2]), (1936,1937,[2_1|2]), (1937,1938,[4_1|2]), (1938,1939,[5_1|2]), (1939,1940,[3_1|2]), (1940,1941,[2_1|2]), (1941,1942,[3_1|2]), (1942,1943,[3_1|2]), (1943,1944,[4_1|2]), (1944,1945,[4_1|2]), (1945,1946,[0_1|2]), (1946,1947,[4_1|2]), (1947,1948,[4_1|2]), (1948,1949,[2_1|2]), (1949,1950,[1_1|2]), (1950,1951,[0_1|2]), (1951,1952,[0_1|2]), (1952,1953,[2_1|2]), (1953,1954,[2_1|2]), (1954,1955,[3_1|2]), (1955,1956,[5_1|2]), (1956,1957,[4_1|2]), (1957,1958,[5_1|2]), (1958,1959,[1_1|2]), (1959,1960,[0_1|2]), (1960,1961,[3_1|2]), (1961,1962,[4_1|2]), (1962,1963,[4_1|2]), (1963,1964,[2_1|2]), (1964,1965,[2_1|2]), (1965,1966,[3_1|2]), (1966,1967,[5_1|2]), (1967,1968,[5_1|2]), (1968,1969,[2_1|2]), (1969,1970,[3_1|2]), (1970,1971,[0_1|2]), (1971,1972,[1_1|2]), (1972,1973,[3_1|2]), (1973,1974,[2_1|2]), (1974,1975,[1_1|2]), (1975,1976,[3_1|2]), (1976,1977,[2_1|2]), (1977,1978,[4_1|2]), (1978,1979,[5_1|2]), (1979,1980,[3_1|2]), (1980,1981,[2_1|2]), (1981,1982,[1_1|2]), (1982,1983,[2_1|2]), (1983,1984,[3_1|2]), (1984,1985,[3_1|2]), (1985,1986,[5_1|2]), (1986,1987,[5_1|2]), (1987,1988,[1_1|2]), (1988,1989,[1_1|2]), (1989,1990,[2_1|2]), (1990,1991,[3_1|2]), (1991,1992,[4_1|2]), (1992,1993,[2_1|2]), (1993,1994,[3_1|2]), (1994,1995,[3_1|2]), (1995,1996,[2_1|2]), (1996,1997,[5_1|2]), (1997,1998,[0_1|2]), (1998,1999,[0_1|2]), (1999,2000,[2_1|2]), (2000,2001,[1_1|2]), (2001,2002,[0_1|2]), (2002,2003,[4_1|2]), (2003,2004,[0_1|2]), (2004,2005,[0_1|2]), (2005,2006,[4_1|2]), (2006,2007,[1_1|2]), (2007,2008,[4_1|2]), (2008,2009,[5_1|2]), (2009,2010,[0_1|2]), (2010,2011,[3_1|2]), (2011,2012,[2_1|2]), (2012,2013,[3_1|2]), (2013,2014,[4_1|2]), (2014,2015,[0_1|2]), (2015,2016,[3_1|2]), (2016,2017,[2_1|2]), (2017,2018,[2_1|2]), (2018,2019,[1_1|2]), (2019,2020,[4_1|2]), (2020,2021,[1_1|2]), (2021,2022,[3_1|2]), (2022,2023,[2_1|2]), (2023,2024,[1_1|2]), (2024,2025,[2_1|2]), (2025,2026,[0_1|2]), (2026,2027,[0_1|2]), (2027,2028,[0_1|2]), (2028,2029,[2_1|2]), (2029,2030,[2_1|2]), (2030,2031,[3_1|2]), (2031,150,[3_1|2]), (2031,547,[3_1|2]), (2031,1141,[3_1|2]), (2031,1438,[3_1|2, 4_1|2]), (2031,1537,[3_1|2, 4_1|2]), (2031,1735,[3_1|2]), (2031,1439,[3_1|2]), (2031,1736,[3_1|2]), (2031,1636,[5_1|2]), (2032,2033,[2_1|2]), (2033,2034,[2_1|2]), (2034,2035,[1_1|2]), (2035,2036,[3_1|2]), (2036,2037,[4_1|2]), (2037,2038,[4_1|2]), (2038,2039,[0_1|2]), (2039,2040,[5_1|2]), (2040,2041,[2_1|2]), (2041,2042,[5_1|2]), (2042,2043,[0_1|2]), (2043,2044,[1_1|2]), (2044,2045,[1_1|2]), (2045,2046,[1_1|2]), (2046,2047,[0_1|2]), (2047,2048,[2_1|2]), (2048,2049,[1_1|2]), (2049,2050,[3_1|2]), (2050,2051,[3_1|2]), (2051,2052,[0_1|2]), (2052,2053,[4_1|2]), (2053,2054,[5_1|2]), (2054,2055,[5_1|2]), (2055,2056,[1_1|2]), (2056,2057,[5_1|2]), (2057,2058,[5_1|2]), (2058,2059,[1_1|2]), (2059,2060,[3_1|2]), (2060,2061,[2_1|2]), (2061,2062,[1_1|2]), (2062,2063,[1_1|2]), (2063,2064,[4_1|2]), (2064,2065,[3_1|2]), (2065,2066,[4_1|2]), (2066,2067,[3_1|2]), (2067,2068,[4_1|2]), (2068,2069,[1_1|2]), (2069,2070,[4_1|2]), (2070,2071,[4_1|2]), (2071,2072,[2_1|2]), (2072,2073,[4_1|2]), (2073,2074,[0_1|2]), (2074,2075,[2_1|2]), (2075,2076,[3_1|2]), (2076,2077,[2_1|2]), (2077,2078,[0_1|2]), (2078,2079,[4_1|2]), (2079,2080,[5_1|2]), (2080,2081,[4_1|2]), (2081,2082,[2_1|2]), (2082,2083,[2_1|2]), (2083,2084,[0_1|2]), (2084,2085,[4_1|2]), (2085,2086,[2_1|2]), (2086,2087,[4_1|2]), (2087,2088,[3_1|2]), (2088,2089,[1_1|2]), (2089,2090,[1_1|2]), (2090,2091,[5_1|2]), (2091,2092,[4_1|2]), (2092,2093,[4_1|2]), (2093,2094,[5_1|2]), (2094,2095,[2_1|2]), (2095,2096,[2_1|2]), (2096,2097,[4_1|2]), (2097,2098,[5_1|2]), (2098,2099,[3_1|2]), (2099,2100,[3_1|2]), (2100,2101,[3_1|2]), (2101,2102,[4_1|2]), (2102,2103,[1_1|2]), (2103,2104,[4_1|2]), (2104,2105,[2_1|2]), (2105,2106,[4_1|2]), (2106,2107,[5_1|2]), (2107,2108,[5_1|2]), (2108,2109,[5_1|2]), (2109,2110,[2_1|2]), (2110,2111,[2_1|2]), (2111,2112,[3_1|2]), (2112,2113,[3_1|2]), (2113,2114,[1_1|2]), (2114,2115,[0_1|2]), (2115,2116,[3_1|2]), (2116,2117,[3_1|2]), (2117,2118,[3_1|2]), (2118,2119,[1_1|2]), (2119,2120,[3_1|2]), (2120,2121,[4_1|2]), (2121,2122,[2_1|2]), (2122,2123,[2_1|2]), (2123,2124,[1_1|2]), (2124,2125,[0_1|2]), (2125,2126,[4_1|2]), (2126,2127,[5_1|2]), (2127,2128,[2_1|2]), (2128,2129,[1_1|2]), (2129,2130,[5_1|2]), (2129,1933,[2_1|2]), (2129,2032,[5_1|2]), (2130,150,[0_1|2]), (2130,547,[0_1|2, 4_1|2]), (2130,1141,[0_1|2]), (2130,1438,[0_1|2]), (2130,1537,[0_1|2]), (2130,1735,[0_1|2]), (2130,1043,[0_1|2]), (2130,151,[0_1|2]), (2130,250,[1_1|2]), (2130,349,[5_1|2]), (2130,448,[3_1|2])}" ---------------------------------------- (8) BOUNDS(1, n^1)