/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 64 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 80 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(1(0(2(x1)))) 0(0(x1)) -> 1(0(2(0(x1)))) 0(0(x1)) -> 1(0(1(0(1(x1))))) 0(0(x1)) -> 1(0(1(2(0(x1))))) 0(0(x1)) -> 1(0(2(0(3(x1))))) 0(0(x1)) -> 1(0(2(2(0(x1))))) 0(0(x1)) -> 2(1(0(2(0(x1))))) 0(0(x1)) -> 0(1(0(2(1(2(x1)))))) 0(0(x1)) -> 1(0(1(0(2(2(x1)))))) 0(0(x1)) -> 1(0(1(3(0(1(x1)))))) 0(0(x1)) -> 1(0(4(1(0(2(x1)))))) 0(0(x1)) -> 1(1(1(0(2(0(x1)))))) 0(0(x1)) -> 3(0(4(0(2(2(x1)))))) 0(0(x1)) -> 3(1(0(1(0(4(x1)))))) 0(0(0(x1))) -> 0(1(0(4(0(4(x1)))))) 0(0(0(x1))) -> 3(0(0(1(0(2(x1)))))) 3(0(0(x1))) -> 3(0(2(0(3(x1))))) 3(0(0(x1))) -> 3(0(2(4(0(2(x1)))))) 5(2(0(x1))) -> 0(2(3(5(x1)))) 5(2(0(x1))) -> 3(5(0(2(x1)))) 5(2(0(x1))) -> 0(2(3(3(5(x1))))) 5(2(0(x1))) -> 1(0(2(3(5(x1))))) 5(2(0(x1))) -> 5(1(0(2(4(x1))))) 5(2(0(x1))) -> 5(0(1(2(2(2(x1)))))) 5(2(0(x1))) -> 5(3(5(1(0(2(x1)))))) 0(5(2(0(x1)))) -> 0(5(0(2(2(x1))))) 3(4(0(0(x1)))) -> 0(3(3(0(4(5(x1)))))) 3(4(0(0(x1)))) -> 3(0(4(5(3(0(x1)))))) 5(1(0(0(x1)))) -> 0(3(1(0(1(5(x1)))))) 5(1(4(0(x1)))) -> 0(1(5(2(4(x1))))) 5(1(5(0(x1)))) -> 5(1(0(3(5(x1))))) 5(2(2(0(x1)))) -> 0(2(1(2(4(5(x1)))))) 5(3(2(0(x1)))) -> 5(3(0(1(2(x1))))) 5(3(2(0(x1)))) -> 3(3(5(3(0(2(x1)))))) 5(4(0(0(x1)))) -> 0(4(5(5(0(2(x1)))))) 5(4(2(0(x1)))) -> 2(4(3(5(0(x1))))) 5(4(2(0(x1)))) -> 5(0(2(2(4(x1))))) 5(4(2(0(x1)))) -> 5(4(5(0(2(x1))))) 0(3(5(2(0(x1))))) -> 3(0(2(5(3(0(x1)))))) 3(3(5(2(0(x1))))) -> 3(5(2(3(0(2(x1)))))) 3(3(5(2(0(x1))))) -> 4(3(3(5(0(2(x1)))))) 5(0(5(2(0(x1))))) -> 0(3(5(5(0(2(x1)))))) 5(1(4(0(0(x1))))) -> 0(2(5(0(1(4(x1)))))) 5(3(3(2(0(x1))))) -> 5(2(3(3(0(2(x1)))))) 5(4(3(0(0(x1))))) -> 1(0(4(0(3(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(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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). The TRS R consists of the following rules: 0(0(x1)) -> 0(1(0(2(x1)))) 0(0(x1)) -> 1(0(2(0(x1)))) 0(0(x1)) -> 1(0(1(0(1(x1))))) 0(0(x1)) -> 1(0(1(2(0(x1))))) 0(0(x1)) -> 1(0(2(0(3(x1))))) 0(0(x1)) -> 1(0(2(2(0(x1))))) 0(0(x1)) -> 2(1(0(2(0(x1))))) 0(0(x1)) -> 0(1(0(2(1(2(x1)))))) 0(0(x1)) -> 1(0(1(0(2(2(x1)))))) 0(0(x1)) -> 1(0(1(3(0(1(x1)))))) 0(0(x1)) -> 1(0(4(1(0(2(x1)))))) 0(0(x1)) -> 1(1(1(0(2(0(x1)))))) 0(0(x1)) -> 3(0(4(0(2(2(x1)))))) 0(0(x1)) -> 3(1(0(1(0(4(x1)))))) 0(0(0(x1))) -> 0(1(0(4(0(4(x1)))))) 0(0(0(x1))) -> 3(0(0(1(0(2(x1)))))) 3(0(0(x1))) -> 3(0(2(0(3(x1))))) 3(0(0(x1))) -> 3(0(2(4(0(2(x1)))))) 5(2(0(x1))) -> 0(2(3(5(x1)))) 5(2(0(x1))) -> 3(5(0(2(x1)))) 5(2(0(x1))) -> 0(2(3(3(5(x1))))) 5(2(0(x1))) -> 1(0(2(3(5(x1))))) 5(2(0(x1))) -> 5(1(0(2(4(x1))))) 5(2(0(x1))) -> 5(0(1(2(2(2(x1)))))) 5(2(0(x1))) -> 5(3(5(1(0(2(x1)))))) 0(5(2(0(x1)))) -> 0(5(0(2(2(x1))))) 3(4(0(0(x1)))) -> 0(3(3(0(4(5(x1)))))) 3(4(0(0(x1)))) -> 3(0(4(5(3(0(x1)))))) 5(1(0(0(x1)))) -> 0(3(1(0(1(5(x1)))))) 5(1(4(0(x1)))) -> 0(1(5(2(4(x1))))) 5(1(5(0(x1)))) -> 5(1(0(3(5(x1))))) 5(2(2(0(x1)))) -> 0(2(1(2(4(5(x1)))))) 5(3(2(0(x1)))) -> 5(3(0(1(2(x1))))) 5(3(2(0(x1)))) -> 3(3(5(3(0(2(x1)))))) 5(4(0(0(x1)))) -> 0(4(5(5(0(2(x1)))))) 5(4(2(0(x1)))) -> 2(4(3(5(0(x1))))) 5(4(2(0(x1)))) -> 5(0(2(2(4(x1))))) 5(4(2(0(x1)))) -> 5(4(5(0(2(x1))))) 0(3(5(2(0(x1))))) -> 3(0(2(5(3(0(x1)))))) 3(3(5(2(0(x1))))) -> 3(5(2(3(0(2(x1)))))) 3(3(5(2(0(x1))))) -> 4(3(3(5(0(2(x1)))))) 5(0(5(2(0(x1))))) -> 0(3(5(5(0(2(x1)))))) 5(1(4(0(0(x1))))) -> 0(2(5(0(1(4(x1)))))) 5(3(3(2(0(x1))))) -> 5(2(3(3(0(2(x1)))))) 5(4(3(0(0(x1))))) -> 1(0(4(0(3(5(x1)))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(x1)) -> 0(1(0(2(x1)))) 0(0(x1)) -> 1(0(2(0(x1)))) 0(0(x1)) -> 1(0(1(0(1(x1))))) 0(0(x1)) -> 1(0(1(2(0(x1))))) 0(0(x1)) -> 1(0(2(0(3(x1))))) 0(0(x1)) -> 1(0(2(2(0(x1))))) 0(0(x1)) -> 2(1(0(2(0(x1))))) 0(0(x1)) -> 0(1(0(2(1(2(x1)))))) 0(0(x1)) -> 1(0(1(0(2(2(x1)))))) 0(0(x1)) -> 1(0(1(3(0(1(x1)))))) 0(0(x1)) -> 1(0(4(1(0(2(x1)))))) 0(0(x1)) -> 1(1(1(0(2(0(x1)))))) 0(0(x1)) -> 3(0(4(0(2(2(x1)))))) 0(0(x1)) -> 3(1(0(1(0(4(x1)))))) 0(0(0(x1))) -> 0(1(0(4(0(4(x1)))))) 0(0(0(x1))) -> 3(0(0(1(0(2(x1)))))) 3(0(0(x1))) -> 3(0(2(0(3(x1))))) 3(0(0(x1))) -> 3(0(2(4(0(2(x1)))))) 5(2(0(x1))) -> 0(2(3(5(x1)))) 5(2(0(x1))) -> 3(5(0(2(x1)))) 5(2(0(x1))) -> 0(2(3(3(5(x1))))) 5(2(0(x1))) -> 1(0(2(3(5(x1))))) 5(2(0(x1))) -> 5(1(0(2(4(x1))))) 5(2(0(x1))) -> 5(0(1(2(2(2(x1)))))) 5(2(0(x1))) -> 5(3(5(1(0(2(x1)))))) 0(5(2(0(x1)))) -> 0(5(0(2(2(x1))))) 3(4(0(0(x1)))) -> 0(3(3(0(4(5(x1)))))) 3(4(0(0(x1)))) -> 3(0(4(5(3(0(x1)))))) 5(1(0(0(x1)))) -> 0(3(1(0(1(5(x1)))))) 5(1(4(0(x1)))) -> 0(1(5(2(4(x1))))) 5(1(5(0(x1)))) -> 5(1(0(3(5(x1))))) 5(2(2(0(x1)))) -> 0(2(1(2(4(5(x1)))))) 5(3(2(0(x1)))) -> 5(3(0(1(2(x1))))) 5(3(2(0(x1)))) -> 3(3(5(3(0(2(x1)))))) 5(4(0(0(x1)))) -> 0(4(5(5(0(2(x1)))))) 5(4(2(0(x1)))) -> 2(4(3(5(0(x1))))) 5(4(2(0(x1)))) -> 5(0(2(2(4(x1))))) 5(4(2(0(x1)))) -> 5(4(5(0(2(x1))))) 0(3(5(2(0(x1))))) -> 3(0(2(5(3(0(x1)))))) 3(3(5(2(0(x1))))) -> 3(5(2(3(0(2(x1)))))) 3(3(5(2(0(x1))))) -> 4(3(3(5(0(2(x1)))))) 5(0(5(2(0(x1))))) -> 0(3(5(5(0(2(x1)))))) 5(1(4(0(0(x1))))) -> 0(2(5(0(1(4(x1)))))) 5(3(3(2(0(x1))))) -> 5(2(3(3(0(2(x1)))))) 5(4(3(0(0(x1))))) -> 1(0(4(0(3(5(x1)))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(x1)) -> 0(1(0(2(x1)))) 0(0(x1)) -> 1(0(2(0(x1)))) 0(0(x1)) -> 1(0(1(0(1(x1))))) 0(0(x1)) -> 1(0(1(2(0(x1))))) 0(0(x1)) -> 1(0(2(0(3(x1))))) 0(0(x1)) -> 1(0(2(2(0(x1))))) 0(0(x1)) -> 2(1(0(2(0(x1))))) 0(0(x1)) -> 0(1(0(2(1(2(x1)))))) 0(0(x1)) -> 1(0(1(0(2(2(x1)))))) 0(0(x1)) -> 1(0(1(3(0(1(x1)))))) 0(0(x1)) -> 1(0(4(1(0(2(x1)))))) 0(0(x1)) -> 1(1(1(0(2(0(x1)))))) 0(0(x1)) -> 3(0(4(0(2(2(x1)))))) 0(0(x1)) -> 3(1(0(1(0(4(x1)))))) 0(0(0(x1))) -> 0(1(0(4(0(4(x1)))))) 0(0(0(x1))) -> 3(0(0(1(0(2(x1)))))) 3(0(0(x1))) -> 3(0(2(0(3(x1))))) 3(0(0(x1))) -> 3(0(2(4(0(2(x1)))))) 5(2(0(x1))) -> 0(2(3(5(x1)))) 5(2(0(x1))) -> 3(5(0(2(x1)))) 5(2(0(x1))) -> 0(2(3(3(5(x1))))) 5(2(0(x1))) -> 1(0(2(3(5(x1))))) 5(2(0(x1))) -> 5(1(0(2(4(x1))))) 5(2(0(x1))) -> 5(0(1(2(2(2(x1)))))) 5(2(0(x1))) -> 5(3(5(1(0(2(x1)))))) 0(5(2(0(x1)))) -> 0(5(0(2(2(x1))))) 3(4(0(0(x1)))) -> 0(3(3(0(4(5(x1)))))) 3(4(0(0(x1)))) -> 3(0(4(5(3(0(x1)))))) 5(1(0(0(x1)))) -> 0(3(1(0(1(5(x1)))))) 5(1(4(0(x1)))) -> 0(1(5(2(4(x1))))) 5(1(5(0(x1)))) -> 5(1(0(3(5(x1))))) 5(2(2(0(x1)))) -> 0(2(1(2(4(5(x1)))))) 5(3(2(0(x1)))) -> 5(3(0(1(2(x1))))) 5(3(2(0(x1)))) -> 3(3(5(3(0(2(x1)))))) 5(4(0(0(x1)))) -> 0(4(5(5(0(2(x1)))))) 5(4(2(0(x1)))) -> 2(4(3(5(0(x1))))) 5(4(2(0(x1)))) -> 5(0(2(2(4(x1))))) 5(4(2(0(x1)))) -> 5(4(5(0(2(x1))))) 0(3(5(2(0(x1))))) -> 3(0(2(5(3(0(x1)))))) 3(3(5(2(0(x1))))) -> 3(5(2(3(0(2(x1)))))) 3(3(5(2(0(x1))))) -> 4(3(3(5(0(2(x1)))))) 5(0(5(2(0(x1))))) -> 0(3(5(5(0(2(x1)))))) 5(1(4(0(0(x1))))) -> 0(2(5(0(1(4(x1)))))) 5(3(3(2(0(x1))))) -> 5(2(3(3(0(2(x1)))))) 5(4(3(0(0(x1))))) -> 1(0(4(0(3(5(x1)))))) encArg(1(x_1)) -> 1(encArg(x_1)) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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 3. The certificate found is represented by the following graph. "[75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 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] {(75,76,[0_1|0, 3_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]), (75,77,[1_1|1, 2_1|1, 4_1|1, 0_1|1, 3_1|1, 5_1|1]), (75,78,[0_1|2]), (75,81,[1_1|2]), (75,84,[1_1|2]), (75,88,[1_1|2]), (75,92,[1_1|2]), (75,96,[1_1|2]), (75,100,[2_1|2]), (75,104,[0_1|2]), (75,109,[1_1|2]), (75,114,[1_1|2]), (75,119,[1_1|2]), (75,124,[1_1|2]), (75,129,[3_1|2]), (75,134,[3_1|2]), (75,139,[0_1|2]), (75,144,[3_1|2]), (75,149,[0_1|2]), (75,153,[3_1|2]), (75,158,[3_1|2]), (75,162,[3_1|2]), (75,167,[0_1|2]), (75,172,[3_1|2]), (75,177,[3_1|2]), (75,182,[4_1|2]), (75,187,[0_1|2]), (75,190,[3_1|2]), (75,193,[0_1|2]), (75,197,[1_1|2]), (75,201,[5_1|2]), (75,205,[5_1|2]), (75,210,[5_1|2]), (75,215,[0_1|2]), (75,220,[0_1|2]), (75,225,[0_1|2]), (75,229,[0_1|2]), (75,234,[5_1|2]), (75,238,[5_1|2]), (75,242,[3_1|2]), (75,247,[5_1|2]), (75,252,[0_1|2]), (75,257,[2_1|2]), (75,261,[5_1|2]), (75,265,[5_1|2]), (75,269,[1_1|2]), (75,274,[0_1|2]), (75,279,[3_1|3]), (75,283,[3_1|3]), (76,76,[1_1|0, 2_1|0, 4_1|0, cons_0_1|0, cons_3_1|0, cons_5_1|0]), (77,76,[encArg_1|1]), (77,77,[1_1|1, 2_1|1, 4_1|1, 0_1|1, 3_1|1, 5_1|1]), (77,78,[0_1|2]), (77,81,[1_1|2]), (77,84,[1_1|2]), (77,88,[1_1|2]), (77,92,[1_1|2]), (77,96,[1_1|2]), (77,100,[2_1|2]), (77,104,[0_1|2]), 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(260,329,[1_1|3]), (260,334,[1_1|3]), (260,339,[3_1|3]), (260,344,[3_1|3]), (260,279,[3_1|3]), (260,283,[3_1|3]), (261,262,[0_1|2]), (262,263,[2_1|2]), (263,264,[2_1|2]), (264,77,[4_1|2]), (264,78,[4_1|2]), (264,104,[4_1|2]), (264,139,[4_1|2]), (264,149,[4_1|2]), (264,167,[4_1|2]), (264,187,[4_1|2]), (264,193,[4_1|2]), (264,215,[4_1|2]), (264,220,[4_1|2]), (264,225,[4_1|2]), (264,229,[4_1|2]), (264,252,[4_1|2]), (264,274,[4_1|2]), (265,266,[4_1|2]), (266,267,[5_1|2]), (267,268,[0_1|2]), (268,77,[2_1|2]), (268,78,[2_1|2]), (268,104,[2_1|2]), (268,139,[2_1|2]), (268,149,[2_1|2]), (268,167,[2_1|2]), (268,187,[2_1|2]), (268,193,[2_1|2]), (268,215,[2_1|2]), (268,220,[2_1|2]), (268,225,[2_1|2]), (268,229,[2_1|2]), (268,252,[2_1|2]), (268,274,[2_1|2]), (269,270,[0_1|2]), (270,271,[4_1|2]), (271,272,[0_1|2]), (271,153,[3_1|2]), (272,273,[3_1|2]), (273,77,[5_1|2]), (273,78,[5_1|2]), (273,104,[5_1|2]), (273,139,[5_1|2]), (273,149,[5_1|2]), (273,167,[5_1|2]), (273,187,[5_1|2, 0_1|2]), (273,193,[5_1|2, 0_1|2]), (273,215,[5_1|2, 0_1|2]), (273,220,[5_1|2, 0_1|2]), (273,225,[5_1|2, 0_1|2]), (273,229,[5_1|2, 0_1|2]), (273,252,[5_1|2, 0_1|2]), (273,274,[5_1|2, 0_1|2]), (273,146,[5_1|2]), (273,190,[3_1|2]), (273,197,[1_1|2]), (273,201,[5_1|2]), (273,205,[5_1|2]), (273,210,[5_1|2]), (273,234,[5_1|2]), (273,238,[5_1|2]), (273,242,[3_1|2]), (273,247,[5_1|2]), (273,257,[2_1|2]), (273,261,[5_1|2]), (273,265,[5_1|2]), (273,269,[1_1|2]), (274,275,[3_1|2]), (275,276,[5_1|2]), (276,277,[5_1|2]), (277,278,[0_1|2]), (278,77,[2_1|2]), (278,78,[2_1|2]), (278,104,[2_1|2]), (278,139,[2_1|2]), (278,149,[2_1|2]), (278,167,[2_1|2]), (278,187,[2_1|2]), (278,193,[2_1|2]), (278,215,[2_1|2]), (278,220,[2_1|2]), (278,225,[2_1|2]), (278,229,[2_1|2]), (278,252,[2_1|2]), (278,274,[2_1|2]), (279,280,[0_1|3]), (280,281,[2_1|3]), (281,282,[0_1|3]), (282,146,[3_1|3]), (283,284,[0_1|3]), (284,285,[2_1|3]), (285,286,[4_1|3]), (286,287,[0_1|3]), (287,146,[2_1|3]), (288,289,[1_1|3]), (289,290,[0_1|3]), (290,78,[2_1|3]), (290,104,[2_1|3]), (290,139,[2_1|3]), (290,149,[2_1|3]), (290,167,[2_1|3]), (290,187,[2_1|3]), (290,193,[2_1|3]), (290,215,[2_1|3]), (290,220,[2_1|3]), (290,225,[2_1|3]), (290,229,[2_1|3]), (290,252,[2_1|3]), (290,274,[2_1|3]), (291,292,[0_1|3]), (292,293,[2_1|3]), (293,78,[0_1|3]), (293,104,[0_1|3]), (293,139,[0_1|3]), (293,149,[0_1|3]), (293,167,[0_1|3]), (293,187,[0_1|3]), (293,193,[0_1|3]), (293,215,[0_1|3]), (293,220,[0_1|3]), (293,225,[0_1|3]), (293,229,[0_1|3]), (293,252,[0_1|3]), (293,274,[0_1|3]), (294,295,[0_1|3]), (295,296,[1_1|3]), (296,297,[0_1|3]), (297,78,[1_1|3]), (297,104,[1_1|3]), (297,139,[1_1|3]), (297,149,[1_1|3]), (297,167,[1_1|3]), (297,187,[1_1|3]), (297,193,[1_1|3]), (297,215,[1_1|3]), (297,220,[1_1|3]), (297,225,[1_1|3]), (297,229,[1_1|3]), (297,252,[1_1|3]), (297,274,[1_1|3]), (298,299,[0_1|3]), (299,300,[1_1|3]), (300,301,[2_1|3]), (301,78,[0_1|3]), (301,104,[0_1|3]), (301,139,[0_1|3]), (301,149,[0_1|3]), (301,167,[0_1|3]), (301,187,[0_1|3]), (301,193,[0_1|3]), (301,215,[0_1|3]), (301,220,[0_1|3]), (301,225,[0_1|3]), (301,229,[0_1|3]), (301,252,[0_1|3]), (301,274,[0_1|3]), (302,303,[0_1|3]), (303,304,[2_1|3]), (304,305,[0_1|3]), (305,78,[3_1|3]), (305,104,[3_1|3]), (305,139,[3_1|3]), (305,149,[3_1|3]), (305,167,[3_1|3]), (305,187,[3_1|3]), (305,193,[3_1|3]), (305,215,[3_1|3]), (305,220,[3_1|3]), (305,225,[3_1|3]), (305,229,[3_1|3]), (305,252,[3_1|3]), (305,274,[3_1|3]), (306,307,[0_1|3]), (307,308,[2_1|3]), (308,309,[2_1|3]), (309,78,[0_1|3]), (309,104,[0_1|3]), (309,139,[0_1|3]), (309,149,[0_1|3]), (309,167,[0_1|3]), (309,187,[0_1|3]), (309,193,[0_1|3]), (309,215,[0_1|3]), (309,220,[0_1|3]), (309,225,[0_1|3]), (309,229,[0_1|3]), (309,252,[0_1|3]), (309,274,[0_1|3]), (310,311,[1_1|3]), (311,312,[0_1|3]), (312,313,[2_1|3]), (313,78,[0_1|3]), (313,104,[0_1|3]), (313,139,[0_1|3]), (313,149,[0_1|3]), (313,167,[0_1|3]), (313,187,[0_1|3]), (313,193,[0_1|3]), (313,215,[0_1|3]), (313,220,[0_1|3]), (313,225,[0_1|3]), (313,229,[0_1|3]), (313,252,[0_1|3]), (313,274,[0_1|3]), (314,315,[1_1|3]), (315,316,[0_1|3]), (316,317,[2_1|3]), (317,318,[1_1|3]), (318,78,[2_1|3]), (318,104,[2_1|3]), (318,139,[2_1|3]), (318,149,[2_1|3]), (318,167,[2_1|3]), (318,187,[2_1|3]), (318,193,[2_1|3]), (318,215,[2_1|3]), (318,220,[2_1|3]), (318,225,[2_1|3]), (318,229,[2_1|3]), (318,252,[2_1|3]), (318,274,[2_1|3]), (319,320,[0_1|3]), (320,321,[1_1|3]), (321,322,[0_1|3]), (322,323,[2_1|3]), (323,78,[2_1|3]), (323,104,[2_1|3]), (323,139,[2_1|3]), (323,149,[2_1|3]), (323,167,[2_1|3]), (323,187,[2_1|3]), (323,193,[2_1|3]), (323,215,[2_1|3]), (323,220,[2_1|3]), (323,225,[2_1|3]), (323,229,[2_1|3]), (323,252,[2_1|3]), (323,274,[2_1|3]), (324,325,[0_1|3]), (325,326,[1_1|3]), (326,327,[3_1|3]), (327,328,[0_1|3]), (328,78,[1_1|3]), (328,104,[1_1|3]), (328,139,[1_1|3]), (328,149,[1_1|3]), (328,167,[1_1|3]), (328,187,[1_1|3]), (328,193,[1_1|3]), (328,215,[1_1|3]), (328,220,[1_1|3]), (328,225,[1_1|3]), (328,229,[1_1|3]), (328,252,[1_1|3]), (328,274,[1_1|3]), (329,330,[0_1|3]), (330,331,[4_1|3]), (331,332,[1_1|3]), (332,333,[0_1|3]), (333,78,[2_1|3]), (333,104,[2_1|3]), (333,139,[2_1|3]), (333,149,[2_1|3]), (333,167,[2_1|3]), (333,187,[2_1|3]), (333,193,[2_1|3]), (333,215,[2_1|3]), (333,220,[2_1|3]), (333,225,[2_1|3]), (333,229,[2_1|3]), (333,252,[2_1|3]), (333,274,[2_1|3]), (334,335,[1_1|3]), (335,336,[1_1|3]), (336,337,[0_1|3]), (337,338,[2_1|3]), (338,78,[0_1|3]), (338,104,[0_1|3]), (338,139,[0_1|3]), (338,149,[0_1|3]), (338,167,[0_1|3]), (338,187,[0_1|3]), (338,193,[0_1|3]), (338,215,[0_1|3]), (338,220,[0_1|3]), (338,225,[0_1|3]), (338,229,[0_1|3]), (338,252,[0_1|3]), (338,274,[0_1|3]), (339,340,[0_1|3]), (340,341,[4_1|3]), (341,342,[0_1|3]), (342,343,[2_1|3]), (343,78,[2_1|3]), (343,104,[2_1|3]), (343,139,[2_1|3]), (343,149,[2_1|3]), (343,167,[2_1|3]), (343,187,[2_1|3]), (343,193,[2_1|3]), (343,215,[2_1|3]), (343,220,[2_1|3]), (343,225,[2_1|3]), (343,229,[2_1|3]), (343,252,[2_1|3]), (343,274,[2_1|3]), (344,345,[1_1|3]), (345,346,[0_1|3]), (346,347,[1_1|3]), (347,348,[0_1|3]), (348,78,[4_1|3]), (348,104,[4_1|3]), (348,139,[4_1|3]), (348,149,[4_1|3]), (348,167,[4_1|3]), (348,187,[4_1|3]), (348,193,[4_1|3]), (348,215,[4_1|3]), (348,220,[4_1|3]), (348,225,[4_1|3]), (348,229,[4_1|3]), (348,252,[4_1|3]), (348,274,[4_1|3]), (349,350,[1_1|3]), (350,351,[0_1|3]), (351,146,[2_1|3]), (352,353,[0_1|3]), (353,354,[2_1|3]), (354,146,[0_1|3]), (355,356,[0_1|3]), (356,357,[1_1|3]), (357,358,[0_1|3]), (358,146,[1_1|3]), (359,360,[0_1|3]), (360,361,[1_1|3]), (361,362,[2_1|3]), (362,146,[0_1|3]), (363,364,[0_1|3]), (364,365,[2_1|3]), (365,366,[0_1|3]), (366,146,[3_1|3]), (367,368,[0_1|3]), (368,369,[2_1|3]), (369,370,[2_1|3]), (370,146,[0_1|3]), (371,372,[1_1|3]), (372,373,[0_1|3]), (373,374,[2_1|3]), (374,146,[0_1|3]), (375,376,[1_1|3]), (376,377,[0_1|3]), (377,378,[2_1|3]), (378,379,[1_1|3]), (379,146,[2_1|3]), (380,381,[0_1|3]), (381,382,[1_1|3]), (382,383,[0_1|3]), (383,384,[2_1|3]), (384,146,[2_1|3]), (385,386,[0_1|3]), (386,387,[1_1|3]), (387,388,[3_1|3]), (388,389,[0_1|3]), (389,146,[1_1|3]), (390,391,[0_1|3]), (391,392,[4_1|3]), (392,393,[1_1|3]), (393,394,[0_1|3]), (394,146,[2_1|3]), (395,396,[1_1|3]), (396,397,[1_1|3]), (397,398,[0_1|3]), (398,399,[2_1|3]), (399,146,[0_1|3]), (400,401,[0_1|3]), (401,402,[4_1|3]), (402,403,[0_1|3]), (403,404,[2_1|3]), (404,146,[2_1|3]), (405,406,[1_1|3]), (406,407,[0_1|3]), (407,408,[1_1|3]), (408,409,[0_1|3]), (409,146,[4_1|3]), (410,411,[0_1|3]), (411,412,[2_1|3]), (412,413,[0_1|3]), (413,78,[3_1|3]), (413,104,[3_1|3]), (413,139,[3_1|3]), (413,149,[3_1|3]), (413,167,[3_1|3]), (413,187,[3_1|3]), (413,193,[3_1|3]), (413,215,[3_1|3]), (413,220,[3_1|3]), (413,225,[3_1|3]), (413,229,[3_1|3]), (413,252,[3_1|3]), (413,274,[3_1|3]), (414,415,[0_1|3]), (415,416,[2_1|3]), (416,417,[4_1|3]), (417,418,[0_1|3]), (418,78,[2_1|3]), (418,104,[2_1|3]), (418,139,[2_1|3]), (418,149,[2_1|3]), (418,167,[2_1|3]), (418,187,[2_1|3]), (418,193,[2_1|3]), (418,215,[2_1|3]), (418,220,[2_1|3]), (418,225,[2_1|3]), (418,229,[2_1|3]), (418,252,[2_1|3]), (418,274,[2_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)