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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 46 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 73 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(1(2(x1)))) -> 0(1(0(x1))) 0(3(4(4(x1)))) -> 0(3(2(x1))) 3(0(4(3(4(x1))))) -> 5(1(0(3(4(x1))))) 3(1(1(1(4(x1))))) -> 3(2(0(4(x1)))) 3(3(1(2(2(1(x1)))))) -> 0(0(0(3(5(1(x1)))))) 4(1(4(0(0(3(x1)))))) -> 4(4(0(2(2(x1))))) 2(4(3(5(4(3(1(x1))))))) -> 5(1(2(0(4(1(x1)))))) 5(2(2(0(1(3(4(x1))))))) -> 5(2(5(3(4(0(0(x1))))))) 5(5(3(0(0(3(1(x1))))))) -> 5(4(4(1(4(2(3(x1))))))) 0(5(1(0(3(1(3(3(x1)))))))) -> 3(3(4(2(5(3(3(x1))))))) 1(2(2(2(4(5(3(0(3(0(x1)))))))))) -> 1(0(1(3(0(2(3(4(0(x1))))))))) 4(3(5(2(1(0(4(0(2(5(x1)))))))))) -> 1(0(1(1(1(4(3(4(5(5(x1)))))))))) 1(4(3(3(5(1(0(5(4(4(5(x1))))))))))) -> 4(2(5(5(3(0(3(3(1(5(x1)))))))))) 2(1(4(3(4(5(4(0(2(0(0(3(x1)))))))))))) -> 3(2(4(1(5(2(5(2(1(1(1(x1))))))))))) 3(2(3(3(2(4(2(4(2(4(0(1(x1)))))))))))) -> 2(0(3(0(3(0(0(0(2(2(0(1(x1)))))))))))) 4(1(5(3(4(4(2(4(4(5(2(4(x1)))))))))))) -> 4(3(5(3(1(0(0(4(5(4(4(x1))))))))))) 0(2(0(4(0(4(2(4(4(3(5(2(5(x1))))))))))))) -> 0(1(5(4(0(1(5(3(4(3(3(5(x1)))))))))))) 3(3(5(3(2(0(4(5(2(4(0(3(2(2(x1)))))))))))))) -> 3(3(5(3(5(3(3(5(1(3(3(5(0(2(x1)))))))))))))) 1(4(2(5(5(0(1(3(1(0(1(0(1(2(2(3(x1)))))))))))))))) -> 2(2(4(1(1(0(1(0(1(4(4(5(2(1(3(1(3(x1))))))))))))))))) 5(3(5(1(3(3(2(5(3(5(4(1(5(2(0(3(x1)))))))))))))))) -> 5(3(5(4(4(5(2(1(4(4(1(3(2(4(3(1(x1)))))))))))))))) 5(5(3(2(5(1(3(4(1(0(1(0(3(3(5(4(4(x1))))))))))))))))) -> 5(3(2(1(4(1(5(0(5(5(5(3(1(2(4(1(2(x1))))))))))))))))) 0(3(4(4(5(4(4(5(0(1(5(5(5(5(0(3(3(1(x1)))))))))))))))))) -> 0(2(1(1(5(3(5(2(4(4(0(2(3(2(3(0(1(1(x1)))))))))))))))))) 3(5(0(3(5(4(2(5(3(4(2(3(3(4(2(5(0(0(x1)))))))))))))))))) -> 0(1(2(1(4(0(5(2(0(2(5(3(5(1(3(2(0(x1))))))))))))))))) 0(3(4(1(2(4(5(1(3(2(2(1(3(1(5(5(1(5(0(x1))))))))))))))))))) -> 3(0(4(1(5(1(3(3(4(0(1(0(0(1(0(2(0(x1))))))))))))))))) 2(4(2(1(1(4(3(2(1(1(4(4(0(3(3(4(1(5(3(4(x1)))))))))))))))))))) -> 0(2(5(5(3(2(3(3(5(3(0(0(0(0(3(2(1(3(2(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_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(1(2(x1)))) -> 0(1(0(x1))) 0(3(4(4(x1)))) -> 0(3(2(x1))) 3(0(4(3(4(x1))))) -> 5(1(0(3(4(x1))))) 3(1(1(1(4(x1))))) -> 3(2(0(4(x1)))) 3(3(1(2(2(1(x1)))))) -> 0(0(0(3(5(1(x1)))))) 4(1(4(0(0(3(x1)))))) -> 4(4(0(2(2(x1))))) 2(4(3(5(4(3(1(x1))))))) -> 5(1(2(0(4(1(x1)))))) 5(2(2(0(1(3(4(x1))))))) -> 5(2(5(3(4(0(0(x1))))))) 5(5(3(0(0(3(1(x1))))))) -> 5(4(4(1(4(2(3(x1))))))) 0(5(1(0(3(1(3(3(x1)))))))) -> 3(3(4(2(5(3(3(x1))))))) 1(2(2(2(4(5(3(0(3(0(x1)))))))))) -> 1(0(1(3(0(2(3(4(0(x1))))))))) 4(3(5(2(1(0(4(0(2(5(x1)))))))))) -> 1(0(1(1(1(4(3(4(5(5(x1)))))))))) 1(4(3(3(5(1(0(5(4(4(5(x1))))))))))) -> 4(2(5(5(3(0(3(3(1(5(x1)))))))))) 2(1(4(3(4(5(4(0(2(0(0(3(x1)))))))))))) -> 3(2(4(1(5(2(5(2(1(1(1(x1))))))))))) 3(2(3(3(2(4(2(4(2(4(0(1(x1)))))))))))) -> 2(0(3(0(3(0(0(0(2(2(0(1(x1)))))))))))) 4(1(5(3(4(4(2(4(4(5(2(4(x1)))))))))))) -> 4(3(5(3(1(0(0(4(5(4(4(x1))))))))))) 0(2(0(4(0(4(2(4(4(3(5(2(5(x1))))))))))))) -> 0(1(5(4(0(1(5(3(4(3(3(5(x1)))))))))))) 3(3(5(3(2(0(4(5(2(4(0(3(2(2(x1)))))))))))))) -> 3(3(5(3(5(3(3(5(1(3(3(5(0(2(x1)))))))))))))) 1(4(2(5(5(0(1(3(1(0(1(0(1(2(2(3(x1)))))))))))))))) -> 2(2(4(1(1(0(1(0(1(4(4(5(2(1(3(1(3(x1))))))))))))))))) 5(3(5(1(3(3(2(5(3(5(4(1(5(2(0(3(x1)))))))))))))))) -> 5(3(5(4(4(5(2(1(4(4(1(3(2(4(3(1(x1)))))))))))))))) 5(5(3(2(5(1(3(4(1(0(1(0(3(3(5(4(4(x1))))))))))))))))) -> 5(3(2(1(4(1(5(0(5(5(5(3(1(2(4(1(2(x1))))))))))))))))) 0(3(4(4(5(4(4(5(0(1(5(5(5(5(0(3(3(1(x1)))))))))))))))))) -> 0(2(1(1(5(3(5(2(4(4(0(2(3(2(3(0(1(1(x1)))))))))))))))))) 3(5(0(3(5(4(2(5(3(4(2(3(3(4(2(5(0(0(x1)))))))))))))))))) -> 0(1(2(1(4(0(5(2(0(2(5(3(5(1(3(2(0(x1))))))))))))))))) 0(3(4(1(2(4(5(1(3(2(2(1(3(1(5(5(1(5(0(x1))))))))))))))))))) -> 3(0(4(1(5(1(3(3(4(0(1(0(0(1(0(2(0(x1))))))))))))))))) 2(4(2(1(1(4(3(2(1(1(4(4(0(3(3(4(1(5(3(4(x1)))))))))))))))))))) -> 0(2(5(5(3(2(3(3(5(3(0(0(0(0(3(2(1(3(2(x1))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(1(2(x1)))) -> 0(1(0(x1))) 0(3(4(4(x1)))) -> 0(3(2(x1))) 3(0(4(3(4(x1))))) -> 5(1(0(3(4(x1))))) 3(1(1(1(4(x1))))) -> 3(2(0(4(x1)))) 3(3(1(2(2(1(x1)))))) -> 0(0(0(3(5(1(x1)))))) 4(1(4(0(0(3(x1)))))) -> 4(4(0(2(2(x1))))) 2(4(3(5(4(3(1(x1))))))) -> 5(1(2(0(4(1(x1)))))) 5(2(2(0(1(3(4(x1))))))) -> 5(2(5(3(4(0(0(x1))))))) 5(5(3(0(0(3(1(x1))))))) -> 5(4(4(1(4(2(3(x1))))))) 0(5(1(0(3(1(3(3(x1)))))))) -> 3(3(4(2(5(3(3(x1))))))) 1(2(2(2(4(5(3(0(3(0(x1)))))))))) -> 1(0(1(3(0(2(3(4(0(x1))))))))) 4(3(5(2(1(0(4(0(2(5(x1)))))))))) -> 1(0(1(1(1(4(3(4(5(5(x1)))))))))) 1(4(3(3(5(1(0(5(4(4(5(x1))))))))))) -> 4(2(5(5(3(0(3(3(1(5(x1)))))))))) 2(1(4(3(4(5(4(0(2(0(0(3(x1)))))))))))) -> 3(2(4(1(5(2(5(2(1(1(1(x1))))))))))) 3(2(3(3(2(4(2(4(2(4(0(1(x1)))))))))))) -> 2(0(3(0(3(0(0(0(2(2(0(1(x1)))))))))))) 4(1(5(3(4(4(2(4(4(5(2(4(x1)))))))))))) -> 4(3(5(3(1(0(0(4(5(4(4(x1))))))))))) 0(2(0(4(0(4(2(4(4(3(5(2(5(x1))))))))))))) -> 0(1(5(4(0(1(5(3(4(3(3(5(x1)))))))))))) 3(3(5(3(2(0(4(5(2(4(0(3(2(2(x1)))))))))))))) -> 3(3(5(3(5(3(3(5(1(3(3(5(0(2(x1)))))))))))))) 1(4(2(5(5(0(1(3(1(0(1(0(1(2(2(3(x1)))))))))))))))) -> 2(2(4(1(1(0(1(0(1(4(4(5(2(1(3(1(3(x1))))))))))))))))) 5(3(5(1(3(3(2(5(3(5(4(1(5(2(0(3(x1)))))))))))))))) -> 5(3(5(4(4(5(2(1(4(4(1(3(2(4(3(1(x1)))))))))))))))) 5(5(3(2(5(1(3(4(1(0(1(0(3(3(5(4(4(x1))))))))))))))))) -> 5(3(2(1(4(1(5(0(5(5(5(3(1(2(4(1(2(x1))))))))))))))))) 0(3(4(4(5(4(4(5(0(1(5(5(5(5(0(3(3(1(x1)))))))))))))))))) -> 0(2(1(1(5(3(5(2(4(4(0(2(3(2(3(0(1(1(x1)))))))))))))))))) 3(5(0(3(5(4(2(5(3(4(2(3(3(4(2(5(0(0(x1)))))))))))))))))) -> 0(1(2(1(4(0(5(2(0(2(5(3(5(1(3(2(0(x1))))))))))))))))) 0(3(4(1(2(4(5(1(3(2(2(1(3(1(5(5(1(5(0(x1))))))))))))))))))) -> 3(0(4(1(5(1(3(3(4(0(1(0(0(1(0(2(0(x1))))))))))))))))) 2(4(2(1(1(4(3(2(1(1(4(4(0(3(3(4(1(5(3(4(x1)))))))))))))))))))) -> 0(2(5(5(3(2(3(3(5(3(0(0(0(0(3(2(1(3(2(x1))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(1(2(x1)))) -> 0(1(0(x1))) 0(3(4(4(x1)))) -> 0(3(2(x1))) 3(0(4(3(4(x1))))) -> 5(1(0(3(4(x1))))) 3(1(1(1(4(x1))))) -> 3(2(0(4(x1)))) 3(3(1(2(2(1(x1)))))) -> 0(0(0(3(5(1(x1)))))) 4(1(4(0(0(3(x1)))))) -> 4(4(0(2(2(x1))))) 2(4(3(5(4(3(1(x1))))))) -> 5(1(2(0(4(1(x1)))))) 5(2(2(0(1(3(4(x1))))))) -> 5(2(5(3(4(0(0(x1))))))) 5(5(3(0(0(3(1(x1))))))) -> 5(4(4(1(4(2(3(x1))))))) 0(5(1(0(3(1(3(3(x1)))))))) -> 3(3(4(2(5(3(3(x1))))))) 1(2(2(2(4(5(3(0(3(0(x1)))))))))) -> 1(0(1(3(0(2(3(4(0(x1))))))))) 4(3(5(2(1(0(4(0(2(5(x1)))))))))) -> 1(0(1(1(1(4(3(4(5(5(x1)))))))))) 1(4(3(3(5(1(0(5(4(4(5(x1))))))))))) -> 4(2(5(5(3(0(3(3(1(5(x1)))))))))) 2(1(4(3(4(5(4(0(2(0(0(3(x1)))))))))))) -> 3(2(4(1(5(2(5(2(1(1(1(x1))))))))))) 3(2(3(3(2(4(2(4(2(4(0(1(x1)))))))))))) -> 2(0(3(0(3(0(0(0(2(2(0(1(x1)))))))))))) 4(1(5(3(4(4(2(4(4(5(2(4(x1)))))))))))) -> 4(3(5(3(1(0(0(4(5(4(4(x1))))))))))) 0(2(0(4(0(4(2(4(4(3(5(2(5(x1))))))))))))) -> 0(1(5(4(0(1(5(3(4(3(3(5(x1)))))))))))) 3(3(5(3(2(0(4(5(2(4(0(3(2(2(x1)))))))))))))) -> 3(3(5(3(5(3(3(5(1(3(3(5(0(2(x1)))))))))))))) 1(4(2(5(5(0(1(3(1(0(1(0(1(2(2(3(x1)))))))))))))))) -> 2(2(4(1(1(0(1(0(1(4(4(5(2(1(3(1(3(x1))))))))))))))))) 5(3(5(1(3(3(2(5(3(5(4(1(5(2(0(3(x1)))))))))))))))) -> 5(3(5(4(4(5(2(1(4(4(1(3(2(4(3(1(x1)))))))))))))))) 5(5(3(2(5(1(3(4(1(0(1(0(3(3(5(4(4(x1))))))))))))))))) -> 5(3(2(1(4(1(5(0(5(5(5(3(1(2(4(1(2(x1))))))))))))))))) 0(3(4(4(5(4(4(5(0(1(5(5(5(5(0(3(3(1(x1)))))))))))))))))) -> 0(2(1(1(5(3(5(2(4(4(0(2(3(2(3(0(1(1(x1)))))))))))))))))) 3(5(0(3(5(4(2(5(3(4(2(3(3(4(2(5(0(0(x1)))))))))))))))))) -> 0(1(2(1(4(0(5(2(0(2(5(3(5(1(3(2(0(x1))))))))))))))))) 0(3(4(1(2(4(5(1(3(2(2(1(3(1(5(5(1(5(0(x1))))))))))))))))))) -> 3(0(4(1(5(1(3(3(4(0(1(0(0(1(0(2(0(x1))))))))))))))))) 2(4(2(1(1(4(3(2(1(1(4(4(0(3(3(4(1(5(3(4(x1)))))))))))))))))))) -> 0(2(5(5(3(2(3(3(5(3(0(0(0(0(3(2(1(3(2(x1))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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. "[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] {(148,149,[0_1|0, 3_1|0, 4_1|0, 2_1|0, 5_1|0, 1_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, 3_1|1, 4_1|1, 2_1|1, 5_1|1, 1_1|1]), (148,151,[0_1|2]), (148,153,[0_1|2]), (148,155,[0_1|2]), (148,172,[3_1|2]), (148,188,[3_1|2]), (148,194,[0_1|2]), (148,205,[5_1|2]), (148,209,[3_1|2]), (148,212,[0_1|2]), (148,217,[3_1|2]), (148,230,[2_1|2]), (148,241,[0_1|2]), (148,257,[4_1|2]), (148,261,[4_1|2]), (148,271,[1_1|2]), (148,280,[5_1|2]), (148,285,[0_1|2]), (148,303,[3_1|2]), (148,313,[5_1|2]), (148,319,[5_1|2]), (148,325,[5_1|2]), (148,341,[5_1|2]), (148,356,[1_1|2]), (148,364,[4_1|2]), (148,373,[2_1|2]), (149,149,[cons_0_1|0, cons_3_1|0, cons_4_1|0, cons_2_1|0, cons_5_1|0, cons_1_1|0]), (150,149,[encArg_1|1]), (150,150,[0_1|1, 3_1|1, 4_1|1, 2_1|1, 5_1|1, 1_1|1]), (150,151,[0_1|2]), (150,153,[0_1|2]), (150,155,[0_1|2]), (150,172,[3_1|2]), (150,188,[3_1|2]), (150,194,[0_1|2]), (150,205,[5_1|2]), (150,209,[3_1|2]), (150,212,[0_1|2]), (150,217,[3_1|2]), (150,230,[2_1|2]), (150,241,[0_1|2]), (150,257,[4_1|2]), (150,261,[4_1|2]), (150,271,[1_1|2]), (150,280,[5_1|2]), (150,285,[0_1|2]), (150,303,[3_1|2]), (150,313,[5_1|2]), (150,319,[5_1|2]), (150,325,[5_1|2]), (150,341,[5_1|2]), (150,356,[1_1|2]), (150,364,[4_1|2]), (150,373,[2_1|2]), (151,152,[1_1|2]), (152,150,[0_1|2]), (152,230,[0_1|2]), (152,373,[0_1|2]), (152,151,[0_1|2]), (152,153,[0_1|2]), (152,155,[0_1|2]), (152,172,[3_1|2]), (152,188,[3_1|2]), (152,194,[0_1|2]), (153,154,[3_1|2]), (153,230,[2_1|2]), (154,150,[2_1|2]), (154,257,[2_1|2]), (154,261,[2_1|2]), (154,364,[2_1|2]), (154,258,[2_1|2]), (154,280,[5_1|2]), (154,285,[0_1|2]), (154,303,[3_1|2]), (155,156,[2_1|2]), (156,157,[1_1|2]), (157,158,[1_1|2]), (158,159,[5_1|2]), (159,160,[3_1|2]), (160,161,[5_1|2]), (161,162,[2_1|2]), (162,163,[4_1|2]), (163,164,[4_1|2]), (164,165,[0_1|2]), (165,166,[2_1|2]), (166,167,[3_1|2]), (167,168,[2_1|2]), (168,169,[3_1|2]), (169,170,[0_1|2]), (169,151,[0_1|2]), (169,389,[0_1|3]), (170,171,[1_1|2]), (171,150,[1_1|2]), (171,271,[1_1|2]), (171,356,[1_1|2]), (171,364,[4_1|2]), (171,373,[2_1|2]), (172,173,[0_1|2]), (173,174,[4_1|2]), (174,175,[1_1|2]), (175,176,[5_1|2]), (176,177,[1_1|2]), (177,178,[3_1|2]), (178,179,[3_1|2]), (179,180,[4_1|2]), (180,181,[0_1|2]), (181,182,[1_1|2]), (182,183,[0_1|2]), (183,184,[0_1|2]), (184,185,[1_1|2]), (185,186,[0_1|2]), (185,194,[0_1|2]), (186,187,[2_1|2]), (187,150,[0_1|2]), (187,151,[0_1|2]), (187,153,[0_1|2]), (187,155,[0_1|2]), (187,194,[0_1|2]), (187,212,[0_1|2]), (187,241,[0_1|2]), (187,285,[0_1|2]), (187,172,[3_1|2]), (187,188,[3_1|2]), (188,189,[3_1|2]), (189,190,[4_1|2]), (190,191,[2_1|2]), (191,192,[5_1|2]), (192,193,[3_1|2]), (192,212,[0_1|2]), (192,217,[3_1|2]), (193,150,[3_1|2]), (193,172,[3_1|2]), (193,188,[3_1|2]), (193,209,[3_1|2]), (193,217,[3_1|2]), (193,303,[3_1|2]), (193,189,[3_1|2]), (193,218,[3_1|2]), (193,205,[5_1|2]), (193,212,[0_1|2]), (193,230,[2_1|2]), (193,241,[0_1|2]), (194,195,[1_1|2]), (195,196,[5_1|2]), (196,197,[4_1|2]), (197,198,[0_1|2]), (198,199,[1_1|2]), (199,200,[5_1|2]), (200,201,[3_1|2]), (201,202,[4_1|2]), (202,203,[3_1|2]), (202,217,[3_1|2]), (203,204,[3_1|2]), (203,241,[0_1|2]), (204,150,[5_1|2]), (204,205,[5_1|2]), (204,280,[5_1|2]), (204,313,[5_1|2]), (204,319,[5_1|2]), (204,325,[5_1|2]), (204,341,[5_1|2]), (204,315,[5_1|2]), (205,206,[1_1|2]), (206,207,[0_1|2]), (206,153,[0_1|2]), (206,155,[0_1|2]), (206,172,[3_1|2]), (206,391,[0_1|3]), (207,208,[3_1|2]), (208,150,[4_1|2]), (208,257,[4_1|2]), (208,261,[4_1|2]), (208,364,[4_1|2]), (208,271,[1_1|2]), (209,210,[2_1|2]), (210,211,[0_1|2]), (211,150,[4_1|2]), (211,257,[4_1|2]), (211,261,[4_1|2]), (211,364,[4_1|2]), (211,271,[1_1|2]), (212,213,[0_1|2]), (213,214,[0_1|2]), (214,215,[3_1|2]), (215,216,[5_1|2]), (216,150,[1_1|2]), (216,271,[1_1|2]), (216,356,[1_1|2]), (216,364,[4_1|2]), (216,373,[2_1|2]), (217,218,[3_1|2]), (218,219,[5_1|2]), (219,220,[3_1|2]), (220,221,[5_1|2]), (221,222,[3_1|2]), (222,223,[3_1|2]), (223,224,[5_1|2]), (224,225,[1_1|2]), (225,226,[3_1|2]), (226,227,[3_1|2]), (227,228,[5_1|2]), (228,229,[0_1|2]), (228,194,[0_1|2]), (229,150,[2_1|2]), (229,230,[2_1|2]), (229,373,[2_1|2]), (229,374,[2_1|2]), (229,280,[5_1|2]), (229,285,[0_1|2]), (229,303,[3_1|2]), (229,365,[2_1|2]), (230,231,[0_1|2]), (231,232,[3_1|2]), (232,233,[0_1|2]), (233,234,[3_1|2]), (234,235,[0_1|2]), (235,236,[0_1|2]), (236,237,[0_1|2]), (237,238,[2_1|2]), (238,239,[2_1|2]), (239,240,[0_1|2]), (239,151,[0_1|2]), (240,150,[1_1|2]), (240,271,[1_1|2]), (240,356,[1_1|2]), (240,152,[1_1|2]), (240,195,[1_1|2]), (240,242,[1_1|2]), (240,364,[4_1|2]), (240,373,[2_1|2]), (241,242,[1_1|2]), (242,243,[2_1|2]), (243,244,[1_1|2]), (244,245,[4_1|2]), (245,246,[0_1|2]), (246,247,[5_1|2]), (247,248,[2_1|2]), (248,249,[0_1|2]), (249,250,[2_1|2]), (250,251,[5_1|2]), (251,252,[3_1|2]), (252,253,[5_1|2]), (253,254,[1_1|2]), (254,255,[3_1|2]), (255,256,[2_1|2]), (256,150,[0_1|2]), (256,151,[0_1|2]), (256,153,[0_1|2]), (256,155,[0_1|2]), (256,194,[0_1|2]), (256,212,[0_1|2]), (256,241,[0_1|2]), (256,285,[0_1|2]), (256,213,[0_1|2]), (256,172,[3_1|2]), (256,188,[3_1|2]), (257,258,[4_1|2]), (258,259,[0_1|2]), (259,260,[2_1|2]), (260,150,[2_1|2]), (260,172,[2_1|2]), (260,188,[2_1|2]), (260,209,[2_1|2]), (260,217,[2_1|2]), (260,303,[2_1|2, 3_1|2]), (260,154,[2_1|2]), (260,280,[5_1|2]), (260,285,[0_1|2]), (261,262,[3_1|2]), (262,263,[5_1|2]), (263,264,[3_1|2]), (264,265,[1_1|2]), (265,266,[0_1|2]), (266,267,[0_1|2]), (267,268,[4_1|2]), (268,269,[5_1|2]), (269,270,[4_1|2]), (270,150,[4_1|2]), (270,257,[4_1|2]), (270,261,[4_1|2]), (270,364,[4_1|2]), (270,271,[1_1|2]), (271,272,[0_1|2]), (272,273,[1_1|2]), (273,274,[1_1|2]), (274,275,[1_1|2]), (275,276,[4_1|2]), (276,277,[3_1|2]), (277,278,[4_1|2]), (278,279,[5_1|2]), (278,319,[5_1|2]), (278,325,[5_1|2]), (279,150,[5_1|2]), (279,205,[5_1|2]), (279,280,[5_1|2]), (279,313,[5_1|2]), (279,319,[5_1|2]), (279,325,[5_1|2]), (279,341,[5_1|2]), (279,287,[5_1|2]), (280,281,[1_1|2]), (281,282,[2_1|2]), (282,283,[0_1|2]), (283,284,[4_1|2]), (283,257,[4_1|2]), (283,261,[4_1|2]), (284,150,[1_1|2]), (284,271,[1_1|2]), (284,356,[1_1|2]), (284,364,[4_1|2]), (284,373,[2_1|2]), (285,286,[2_1|2]), (286,287,[5_1|2]), (287,288,[5_1|2]), (288,289,[3_1|2]), (289,290,[2_1|2]), (290,291,[3_1|2]), (291,292,[3_1|2]), (292,293,[5_1|2]), (293,294,[3_1|2]), (294,295,[0_1|2]), (295,296,[0_1|2]), (296,297,[0_1|2]), (297,298,[0_1|2]), (298,299,[3_1|2]), (299,300,[2_1|2]), (300,301,[1_1|2]), (301,302,[3_1|2]), (301,230,[2_1|2]), (302,150,[2_1|2]), (302,257,[2_1|2]), (302,261,[2_1|2]), (302,364,[2_1|2]), (302,280,[5_1|2]), (302,285,[0_1|2]), (302,303,[3_1|2]), (303,304,[2_1|2]), (304,305,[4_1|2]), (305,306,[1_1|2]), (306,307,[5_1|2]), (307,308,[2_1|2]), (308,309,[5_1|2]), (309,310,[2_1|2]), (310,311,[1_1|2]), (311,312,[1_1|2]), (312,150,[1_1|2]), (312,172,[1_1|2]), (312,188,[1_1|2]), (312,209,[1_1|2]), (312,217,[1_1|2]), (312,303,[1_1|2]), (312,154,[1_1|2]), (312,356,[1_1|2]), (312,364,[4_1|2]), (312,373,[2_1|2]), (313,314,[2_1|2]), (314,315,[5_1|2]), (315,316,[3_1|2]), (316,317,[4_1|2]), (317,318,[0_1|2]), (318,150,[0_1|2]), (318,257,[0_1|2]), (318,261,[0_1|2]), (318,364,[0_1|2]), (318,151,[0_1|2]), (318,153,[0_1|2]), (318,155,[0_1|2]), (318,172,[3_1|2]), (318,188,[3_1|2]), (318,194,[0_1|2]), (319,320,[4_1|2]), (320,321,[4_1|2]), (321,322,[1_1|2]), (322,323,[4_1|2]), (323,324,[2_1|2]), (324,150,[3_1|2]), (324,271,[3_1|2]), (324,356,[3_1|2]), (324,205,[5_1|2]), (324,209,[3_1|2]), (324,212,[0_1|2]), (324,217,[3_1|2]), (324,230,[2_1|2]), (324,241,[0_1|2]), (325,326,[3_1|2]), (326,327,[2_1|2]), (327,328,[1_1|2]), (328,329,[4_1|2]), (329,330,[1_1|2]), (330,331,[5_1|2]), (331,332,[0_1|2]), (332,333,[5_1|2]), (333,334,[5_1|2]), (334,335,[5_1|2]), (335,336,[3_1|2]), (336,337,[1_1|2]), (337,338,[2_1|2]), (338,339,[4_1|2]), (339,340,[1_1|2]), (339,356,[1_1|2]), (340,150,[2_1|2]), (340,257,[2_1|2]), (340,261,[2_1|2]), (340,364,[2_1|2]), (340,258,[2_1|2]), (340,321,[2_1|2]), (340,280,[5_1|2]), (340,285,[0_1|2]), (340,303,[3_1|2]), (341,342,[3_1|2]), (342,343,[5_1|2]), (343,344,[4_1|2]), (344,345,[4_1|2]), (345,346,[5_1|2]), (346,347,[2_1|2]), (347,348,[1_1|2]), (348,349,[4_1|2]), (349,350,[4_1|2]), (350,351,[1_1|2]), (351,352,[3_1|2]), (352,353,[2_1|2]), (353,354,[4_1|2]), (354,355,[3_1|2]), (354,209,[3_1|2]), (355,150,[1_1|2]), (355,172,[1_1|2]), (355,188,[1_1|2]), (355,209,[1_1|2]), (355,217,[1_1|2]), (355,303,[1_1|2]), (355,154,[1_1|2]), (355,232,[1_1|2]), (355,356,[1_1|2]), (355,364,[4_1|2]), (355,373,[2_1|2]), (356,357,[0_1|2]), (357,358,[1_1|2]), (358,359,[3_1|2]), (359,360,[0_1|2]), (360,361,[2_1|2]), (361,362,[3_1|2]), (362,363,[4_1|2]), (363,150,[0_1|2]), (363,151,[0_1|2]), (363,153,[0_1|2]), (363,155,[0_1|2]), (363,194,[0_1|2]), (363,212,[0_1|2]), (363,241,[0_1|2]), (363,285,[0_1|2]), (363,173,[0_1|2]), (363,172,[3_1|2]), (363,188,[3_1|2]), (364,365,[2_1|2]), (365,366,[5_1|2]), (366,367,[5_1|2]), (367,368,[3_1|2]), (368,369,[0_1|2]), (369,370,[3_1|2]), (370,371,[3_1|2]), (371,372,[1_1|2]), (372,150,[5_1|2]), (372,205,[5_1|2]), (372,280,[5_1|2]), (372,313,[5_1|2]), (372,319,[5_1|2]), (372,325,[5_1|2]), (372,341,[5_1|2]), (373,374,[2_1|2]), (374,375,[4_1|2]), (375,376,[1_1|2]), (376,377,[1_1|2]), (377,378,[0_1|2]), (378,379,[1_1|2]), (379,380,[0_1|2]), (380,381,[1_1|2]), (381,382,[4_1|2]), (382,383,[4_1|2]), (383,384,[5_1|2]), (384,385,[2_1|2]), (385,386,[1_1|2]), (386,387,[3_1|2]), (387,388,[1_1|2]), (388,150,[3_1|2]), (388,172,[3_1|2]), (388,188,[3_1|2]), (388,209,[3_1|2]), (388,217,[3_1|2]), (388,303,[3_1|2]), (388,205,[5_1|2]), (388,212,[0_1|2]), (388,230,[2_1|2]), (388,241,[0_1|2]), (389,390,[1_1|3]), (390,230,[0_1|3]), (390,373,[0_1|3]), (391,392,[3_1|3]), (392,257,[2_1|3]), (392,261,[2_1|3]), (392,364,[2_1|3]), (392,258,[2_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)