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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 56 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 165 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(1(2(1(1(2(0(1(3(4(2(0(3(0(2(0(4(0(1(3(4(4(0(5(3(2(1(2(5(3(2(0(5(3(1(5(1(1(2(1(1(2(4(2(4(1(5(2(2(4(1(3(5(5(0(0(3(4(2(4(0(5(4(5(4(4(2(1(3(5(4(2(4(0(4(5(2(0(5(1(4(5(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(5(1(4(0(0(4(4(2(5(4(1(3(3(5(2(3(5(3(3(1(4(3(2(2(2(3(5(0(0(1(1(0(5(0(0(1(0(5(2(1(2(1(5(3(2(1(0(1(0(2(0(0(3(0(3(0(1(3(4(0(2(4(5(1(5(5(2(5(1(3(5(0(2(4(2(1(3(5(2(3(0(0(2(0(3(2(3(0(1(0(0(1(1(2(4(0(2(5(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(3(3(1(1(5(5(2(2(2(5(5(5(0(1(3(4(5(5(2(2(1(3(3(5(1(5(5(0(4(3(0(0(1(3(4(0(1(5(3(4(3(2(2(0(1(4(4(3(5(2(0(2(0(5(2(1(3(2(0(4(1(4(5(2(0(0(0(4(5(1(2(2(3(5(2(1(2(3(0(0(3(5(3(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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0(0(1(4(5(0(0(5(2(0(3(1(1(0(2(2(4(5(4(4(1(1(0(0(2(0(5(0(0(0(3(2(0(0(1(4(2(3(5(3(4(5(5(4(0(4(2(2(3(0(3(2(5(1(5(3(2(3(5(4(1(1(1(3(2(0(5(5(4(3(5(4(3(5(3(5(2(3(5(2(4(3(0(4(0(0(5(0(3(2(5(2(0(1(1(5(0(4(4(5(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(4(3(4(3(1(3(0(1(2(5(4(4(4(2(0(1(1(5(5(5(0(5(1(0(0(4(4(2(1(1(1(5(4(2(2(2(1(3(3(1(5(4(4(4(1(1(3(2(1(3(2(4(4(3(4(4(0(3(2(4(5(2(2(5(1(2(4(1(3(4(1(2(5(2(1(4(3(3(1(2(1(3(3(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(4(5(4(1(2(2(2(0(4(2(2(0(5(0(2(5(5(1(0(3(2(3(0(4(2(0(2(5(3(4(0(2(0(1(3(1(2(3(0(1(3(4(3(5(0(2(1(4(2(2(5(1(1(2(2(0(5(4(0(2(2(4(0(2(0(4(3(5(3(1(4(3(0(1(1(3(2(2(2(4(3(2(1(3(0(2(3(0(2(1(3(0(1(1(0(5(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(4(5(2(1(4(0(4(5(5(4(0(5(3(1(3(3(5(0(4(1(2(1(4(3(3(2(5(1(2(0(3(0(2(1(3(4(4(3(1(4(0(3(1(3(1(0(3(1(3(5(4(0(2(0(4(0(3(3(1(3(2(0(5(4(1(0(2(2(4(4(1(2(2(2(1(5(0(2(1(4(1(3(4(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(4(5(0(0(5(2(0(3(1(1(0(2(2(4(5(4(4(1(1(0(0(2(0(5(0(0(0(3(2(0(0(1(4(2(3(5(3(4(5(5(4(0(4(2(2(3(0(3(2(5(1(5(3(2(3(5(4(1(1(1(3(2(0(5(5(4(3(5(4(3(5(3(5(2(3(5(2(4(3(0(4(0(0(5(0(3(2(5(2(0(1(1(5(0(4(4(5(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(1(2(1(1(2(0(1(3(4(2(0(3(0(2(0(4(0(1(3(4(4(0(5(3(2(1(2(5(3(2(0(5(3(1(5(1(1(2(1(1(2(4(2(4(1(5(2(2(4(1(3(5(5(0(0(3(4(2(4(0(5(4(5(4(4(2(1(3(5(4(2(4(0(4(5(2(0(5(1(4(5(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(5(1(4(0(0(4(4(2(5(4(1(3(3(5(2(3(5(3(3(1(4(3(2(2(2(3(5(0(0(1(1(0(5(0(0(1(0(5(2(1(2(1(5(3(2(1(0(1(0(2(0(0(3(0(3(0(1(3(4(0(2(4(5(1(5(5(2(5(1(3(5(0(2(4(2(1(3(5(2(3(0(0(2(0(3(2(3(0(1(0(0(1(1(2(4(0(2(5(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(3(3(1(1(5(5(2(2(2(5(5(5(0(1(3(4(5(5(2(2(1(3(3(5(1(5(5(0(4(3(0(0(1(3(4(0(1(5(3(4(3(2(2(0(1(4(4(3(5(2(0(2(0(5(2(1(3(2(0(4(1(4(5(2(0(0(0(4(5(1(2(2(3(5(2(1(2(3(0(0(3(5(3(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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5(4(3(4(3(1(3(0(1(2(5(4(4(4(2(0(1(1(5(5(5(0(5(1(0(0(4(4(2(1(1(1(5(4(2(2(2(1(3(3(1(5(4(4(4(1(1(3(2(1(3(2(4(4(3(4(4(0(3(2(4(5(2(2(5(1(2(4(1(3(4(1(2(5(2(1(4(3(3(1(2(1(3(3(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(4(5(4(1(2(2(2(0(4(2(2(0(5(0(2(5(5(1(0(3(2(3(0(4(2(0(2(5(3(4(0(2(0(1(3(1(2(3(0(1(3(4(3(5(0(2(1(4(2(2(5(1(1(2(2(0(5(4(0(2(2(4(0(2(0(4(3(5(3(1(4(3(0(1(1(3(2(2(2(4(3(2(1(3(0(2(3(0(2(1(3(0(1(1(0(5(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 5(4(5(2(1(4(0(4(5(5(4(0(5(3(1(3(3(5(0(4(1(2(1(4(3(3(2(5(1(2(0(3(0(2(1(3(4(4(3(1(4(0(3(1(3(1(0(3(1(3(5(4(0(2(0(4(0(3(3(1(3(2(0(5(4(1(0(2(2(4(4(1(2(2(2(1(5(0(2(1(4(1(3(4(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(1(4(5(0(0(5(2(0(3(1(1(0(2(2(4(5(4(4(1(1(0(0(2(0(5(0(0(0(3(2(0(0(1(4(2(3(5(3(4(5(5(4(0(4(2(2(3(0(3(2(5(1(5(3(2(3(5(4(1(1(1(3(2(0(5(5(4(3(5(4(3(5(3(5(2(3(5(2(4(3(0(4(0(0(5(0(3(2(5(2(0(1(1(5(0(4(4(5(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(1(2(1(1(2(0(1(3(4(2(0(3(0(2(0(4(0(1(3(4(4(0(5(3(2(1(2(5(3(2(0(5(3(1(5(1(1(2(1(1(2(4(2(4(1(5(2(2(4(1(3(5(5(0(0(3(4(2(4(0(5(4(5(4(4(2(1(3(5(4(2(4(0(4(5(2(0(5(1(4(5(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(5(1(4(0(0(4(4(2(5(4(1(3(3(5(2(3(5(3(3(1(4(3(2(2(2(3(5(0(0(1(1(0(5(0(0(1(0(5(2(1(2(1(5(3(2(1(0(1(0(2(0(0(3(0(3(0(1(3(4(0(2(4(5(1(5(5(2(5(1(3(5(0(2(4(2(1(3(5(2(3(0(0(2(0(3(2(3(0(1(0(0(1(1(2(4(0(2(5(5(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(3(3(1(1(5(5(2(2(2(5(5(5(0(1(3(4(5(5(2(2(1(3(3(5(1(5(5(0(4(3(0(0(1(3(4(0(1(5(3(4(3(2(2(0(1(4(4(3(5(2(0(2(0(5(2(1(3(2(0(4(1(4(5(2(0(0(0(4(5(1(2(2(3(5(2(1(2(3(0(0(3(5(3(4(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 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0(0(1(4(5(0(0(5(2(0(3(1(1(0(2(2(4(5(4(4(1(1(0(0(2(0(5(0(0(0(3(2(0(0(1(4(2(3(5(3(4(5(5(4(0(4(2(2(3(0(3(2(5(1(5(3(2(3(5(4(1(1(1(3(2(0(5(5(4(3(5(4(3(5(3(5(2(3(5(2(4(3(0(4(0(0(5(0(3(2(5(2(0(1(1(5(0(4(4(5(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,[0_1|2]), (148,349,[5_1|2]), (148,448,[2_1|2]), (148,547,[5_1|2]), (148,646,[4_1|2]), (148,745,[0_1|2]), (148,844,[0_1|2]), (148,943,[1_1|2]), (148,1042,[3_1|2]), (148,1141,[3_1|2]), (148,1240,[5_1|2]), (148,1339,[5_1|2]), (148,1438,[3_1|2]), (148,1537,[0_1|2]), (148,1636,[2_1|2]), (148,1735,[5_1|2]), (148,1834,[5_1|2]), (148,1933,[4_1|2]), (148,2032,[0_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,[0_1|2]), (150,349,[5_1|2]), (150,448,[2_1|2]), (150,547,[5_1|2]), (150,646,[4_1|2]), (150,745,[0_1|2]), (150,844,[0_1|2]), (150,943,[1_1|2]), (150,1042,[3_1|2]), (150,1141,[3_1|2]), (150,1240,[5_1|2]), (150,1339,[5_1|2]), (150,1438,[3_1|2]), (150,1537,[0_1|2]), (150,1636,[2_1|2]), (150,1735,[5_1|2]), (150,1834,[5_1|2]), (150,1933,[4_1|2]), (150,2032,[0_1|2]), (151,152,[5_1|2]), (152,153,[1_1|2]), (153,154,[4_1|2]), (154,155,[0_1|2]), (155,156,[0_1|2]), (156,157,[4_1|2]), (157,158,[4_1|2]), (158,159,[2_1|2]), (159,160,[5_1|2]), (160,161,[4_1|2]), (161,162,[1_1|2]), (162,163,[3_1|2]), (163,164,[3_1|2]), (164,165,[5_1|2]), (165,166,[2_1|2]), (166,167,[3_1|2]), (167,168,[5_1|2]), (168,169,[3_1|2]), (169,170,[3_1|2]), (170,171,[1_1|2]), (171,172,[4_1|2]), (172,173,[3_1|2]), (173,174,[2_1|2]), (174,175,[2_1|2]), (175,176,[2_1|2]), (176,177,[3_1|2]), (177,178,[5_1|2]), (178,179,[0_1|2]), (179,180,[0_1|2]), (180,181,[1_1|2]), (181,182,[1_1|2]), (182,183,[0_1|2]), (183,184,[5_1|2]), (184,185,[0_1|2]), (185,186,[0_1|2]), (186,187,[1_1|2]), (187,188,[0_1|2]), (188,189,[5_1|2]), (189,190,[2_1|2]), (190,191,[1_1|2]), 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(1826,1827,[0_1|2]), (1827,1828,[3_1|2]), (1828,1829,[0_1|2]), (1829,1830,[0_1|2]), (1830,1831,[5_1|2]), (1831,1832,[3_1|2]), (1832,1833,[5_1|2]), (1833,150,[5_1|2]), (1833,943,[5_1|2]), (1833,153,[5_1|2]), (1833,1735,[5_1|2]), (1833,1834,[5_1|2]), (1833,1933,[4_1|2]), (1833,2032,[0_1|2]), (1834,1835,[3_1|2]), (1835,1836,[3_1|2]), (1836,1837,[0_1|2]), (1837,1838,[5_1|2]), (1838,1839,[0_1|2]), (1839,1840,[5_1|2]), (1840,1841,[1_1|2]), (1841,1842,[2_1|2]), (1842,1843,[3_1|2]), (1843,1844,[5_1|2]), (1844,1845,[0_1|2]), (1845,1846,[2_1|2]), (1846,1847,[5_1|2]), (1847,1848,[5_1|2]), (1848,1849,[0_1|2]), (1849,1850,[0_1|2]), (1850,1851,[0_1|2]), (1851,1852,[5_1|2]), (1852,1853,[5_1|2]), (1853,1854,[2_1|2]), (1854,1855,[0_1|2]), (1855,1856,[5_1|2]), (1856,1857,[5_1|2]), (1857,1858,[4_1|2]), (1858,1859,[5_1|2]), (1859,1860,[2_1|2]), (1860,1861,[0_1|2]), (1861,1862,[5_1|2]), (1862,1863,[5_1|2]), (1863,1864,[0_1|2]), (1864,1865,[0_1|2]), (1865,1866,[5_1|2]), (1866,1867,[1_1|2]), (1867,1868,[2_1|2]), (1868,1869,[5_1|2]), (1869,1870,[1_1|2]), (1870,1871,[1_1|2]), (1871,1872,[1_1|2]), (1872,1873,[0_1|2]), (1873,1874,[3_1|2]), (1874,1875,[3_1|2]), (1875,1876,[5_1|2]), (1876,1877,[5_1|2]), (1877,1878,[2_1|2]), (1878,1879,[5_1|2]), (1879,1880,[1_1|2]), (1880,1881,[0_1|2]), (1881,1882,[0_1|2]), (1882,1883,[1_1|2]), (1883,1884,[2_1|2]), (1884,1885,[5_1|2]), (1885,1886,[0_1|2]), (1886,1887,[1_1|2]), (1887,1888,[2_1|2]), (1888,1889,[2_1|2]), (1889,1890,[0_1|2]), (1890,1891,[0_1|2]), (1891,1892,[4_1|2]), (1892,1893,[5_1|2]), (1893,1894,[2_1|2]), (1894,1895,[1_1|2]), (1895,1896,[2_1|2]), (1896,1897,[1_1|2]), (1897,1898,[5_1|2]), (1898,1899,[0_1|2]), (1899,1900,[0_1|2]), (1900,1901,[5_1|2]), (1901,1902,[3_1|2]), (1902,1903,[2_1|2]), (1903,1904,[0_1|2]), (1904,1905,[0_1|2]), (1905,1906,[0_1|2]), (1906,1907,[1_1|2]), (1907,1908,[1_1|2]), (1908,1909,[2_1|2]), (1909,1910,[3_1|2]), (1910,1911,[0_1|2]), (1911,1912,[4_1|2]), (1912,1913,[0_1|2]), (1913,1914,[4_1|2]), (1914,1915,[2_1|2]), (1915,1916,[3_1|2]), (1916,1917,[3_1|2]), (1917,1918,[0_1|2]), (1918,1919,[0_1|2]), (1919,1920,[1_1|2]), (1920,1921,[0_1|2]), (1921,1922,[5_1|2]), (1922,1923,[4_1|2]), (1923,1924,[1_1|2]), (1924,1925,[3_1|2]), (1925,1926,[2_1|2]), (1926,1927,[5_1|2]), (1927,1928,[0_1|2]), (1928,1929,[1_1|2]), (1929,1930,[4_1|2]), (1930,1931,[0_1|2]), (1930,250,[0_1|2]), (1930,349,[5_1|2]), (1931,1932,[3_1|2]), (1932,150,[3_1|2]), (1932,1042,[3_1|2]), (1932,1141,[3_1|2]), (1932,1438,[3_1|2]), (1933,1934,[0_1|2]), (1934,1935,[4_1|2]), (1935,1936,[5_1|2]), (1936,1937,[4_1|2]), (1937,1938,[1_1|2]), (1938,1939,[2_1|2]), (1939,1940,[2_1|2]), (1940,1941,[2_1|2]), (1941,1942,[0_1|2]), (1942,1943,[4_1|2]), (1943,1944,[2_1|2]), (1944,1945,[2_1|2]), (1945,1946,[0_1|2]), (1946,1947,[5_1|2]), (1947,1948,[0_1|2]), (1948,1949,[2_1|2]), (1949,1950,[5_1|2]), (1950,1951,[5_1|2]), (1951,1952,[1_1|2]), (1952,1953,[0_1|2]), (1953,1954,[3_1|2]), (1954,1955,[2_1|2]), (1955,1956,[3_1|2]), (1956,1957,[0_1|2]), (1957,1958,[4_1|2]), (1958,1959,[2_1|2]), (1959,1960,[0_1|2]), (1960,1961,[2_1|2]), (1961,1962,[5_1|2]), (1962,1963,[3_1|2]), (1963,1964,[4_1|2]), (1964,1965,[0_1|2]), (1965,1966,[2_1|2]), (1966,1967,[0_1|2]), (1967,1968,[1_1|2]), (1968,1969,[3_1|2]), (1969,1970,[1_1|2]), (1970,1971,[2_1|2]), (1971,1972,[3_1|2]), (1972,1973,[0_1|2]), (1973,1974,[1_1|2]), (1974,1975,[3_1|2]), (1975,1976,[4_1|2]), (1976,1977,[3_1|2]), (1977,1978,[5_1|2]), (1978,1979,[0_1|2]), (1979,1980,[2_1|2]), (1980,1981,[1_1|2]), (1981,1982,[4_1|2]), (1982,1983,[2_1|2]), (1983,1984,[2_1|2]), (1984,1985,[5_1|2]), (1985,1986,[1_1|2]), (1986,1987,[1_1|2]), (1987,1988,[2_1|2]), (1988,1989,[2_1|2]), (1989,1990,[0_1|2]), (1990,1991,[5_1|2]), (1991,1992,[4_1|2]), (1992,1993,[0_1|2]), (1993,1994,[2_1|2]), (1994,1995,[2_1|2]), (1995,1996,[4_1|2]), (1996,1997,[0_1|2]), (1997,1998,[2_1|2]), (1998,1999,[0_1|2]), (1999,2000,[4_1|2]), (2000,2001,[3_1|2]), (2001,2002,[5_1|2]), (2002,2003,[3_1|2]), (2003,2004,[1_1|2]), (2004,2005,[4_1|2]), (2005,2006,[3_1|2]), (2006,2007,[0_1|2]), (2007,2008,[1_1|2]), (2008,2009,[1_1|2]), (2009,2010,[3_1|2]), (2010,2011,[2_1|2]), (2011,2012,[2_1|2]), (2012,2013,[2_1|2]), (2013,2014,[4_1|2]), (2014,2015,[3_1|2]), (2015,2016,[2_1|2]), (2016,2017,[1_1|2]), (2017,2018,[3_1|2]), (2018,2019,[0_1|2]), (2019,2020,[2_1|2]), (2020,2021,[3_1|2]), (2021,2022,[0_1|2]), (2022,2023,[2_1|2]), (2023,2024,[1_1|2]), (2024,2025,[3_1|2]), (2025,2026,[0_1|2]), (2026,2027,[1_1|2]), (2027,2028,[1_1|2]), (2028,2029,[0_1|2]), (2029,2030,[5_1|2]), (2030,2031,[0_1|2]), (2030,151,[0_1|2]), (2031,150,[0_1|2]), (2031,646,[0_1|2]), (2031,1933,[0_1|2]), (2031,151,[0_1|2]), (2031,250,[0_1|2]), (2031,349,[5_1|2]), (2031,448,[2_1|2]), (2031,547,[5_1|2]), (2032,2033,[0_1|2]), (2033,2034,[1_1|2]), (2034,2035,[4_1|2]), (2035,2036,[5_1|2]), (2036,2037,[0_1|2]), (2037,2038,[0_1|2]), (2038,2039,[5_1|2]), (2039,2040,[2_1|2]), (2040,2041,[0_1|2]), (2041,2042,[3_1|2]), (2042,2043,[1_1|2]), (2043,2044,[1_1|2]), (2044,2045,[0_1|2]), (2045,2046,[2_1|2]), (2046,2047,[2_1|2]), (2047,2048,[4_1|2]), (2048,2049,[5_1|2]), (2049,2050,[4_1|2]), (2050,2051,[4_1|2]), (2051,2052,[1_1|2]), (2052,2053,[1_1|2]), (2053,2054,[0_1|2]), (2054,2055,[0_1|2]), (2055,2056,[2_1|2]), (2056,2057,[0_1|2]), (2057,2058,[5_1|2]), (2058,2059,[0_1|2]), (2059,2060,[0_1|2]), (2060,2061,[0_1|2]), (2061,2062,[3_1|2]), (2062,2063,[2_1|2]), (2063,2064,[0_1|2]), (2064,2065,[0_1|2]), (2065,2066,[1_1|2]), (2066,2067,[4_1|2]), (2067,2068,[2_1|2]), (2068,2069,[3_1|2]), (2069,2070,[5_1|2]), (2070,2071,[3_1|2]), (2071,2072,[4_1|2]), (2072,2073,[5_1|2]), (2073,2074,[5_1|2]), (2074,2075,[4_1|2]), (2075,2076,[0_1|2]), (2076,2077,[4_1|2]), (2077,2078,[2_1|2]), (2078,2079,[2_1|2]), (2079,2080,[3_1|2]), (2080,2081,[0_1|2]), (2081,2082,[3_1|2]), (2082,2083,[2_1|2]), (2083,2084,[5_1|2]), (2084,2085,[1_1|2]), (2085,2086,[5_1|2]), (2086,2087,[3_1|2]), (2087,2088,[2_1|2]), (2088,2089,[3_1|2]), (2089,2090,[5_1|2]), (2090,2091,[4_1|2]), (2091,2092,[1_1|2]), (2092,2093,[1_1|2]), (2093,2094,[1_1|2]), (2094,2095,[3_1|2]), (2095,2096,[2_1|2]), (2096,2097,[0_1|2]), (2097,2098,[5_1|2]), (2098,2099,[5_1|2]), (2099,2100,[4_1|2]), (2100,2101,[3_1|2]), (2101,2102,[5_1|2]), (2102,2103,[4_1|2]), (2103,2104,[3_1|2]), (2104,2105,[5_1|2]), (2105,2106,[3_1|2]), (2106,2107,[5_1|2]), (2107,2108,[2_1|2]), (2108,2109,[3_1|2]), (2109,2110,[5_1|2]), (2110,2111,[2_1|2]), (2111,2112,[4_1|2]), (2112,2113,[3_1|2]), (2113,2114,[0_1|2]), (2114,2115,[4_1|2]), (2115,2116,[0_1|2]), (2116,2117,[0_1|2]), (2117,2118,[5_1|2]), (2118,2119,[0_1|2]), (2119,2120,[3_1|2]), (2120,2121,[2_1|2]), (2121,2122,[5_1|2]), (2122,2123,[2_1|2]), (2123,2124,[0_1|2]), (2124,2125,[1_1|2]), (2125,2126,[1_1|2]), (2126,2127,[5_1|2]), (2127,2128,[0_1|2]), (2128,2129,[4_1|2]), (2129,2130,[4_1|2]), (2130,150,[5_1|2]), (2130,646,[5_1|2]), (2130,1933,[5_1|2, 4_1|2]), (2130,1735,[5_1|2]), (2130,1834,[5_1|2]), (2130,2032,[0_1|2])}" ---------------------------------------- (8) BOUNDS(1, n^1)