/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 51 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 45 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 1(2(0(x1))) -> 4(0(3(3(5(4(5(1(4(3(x1)))))))))) 1(0(0(4(5(x1))))) -> 1(4(3(1(3(1(4(5(2(3(x1)))))))))) 2(0(3(0(2(x1))))) -> 3(3(1(2(2(4(5(0(4(3(x1)))))))))) 2(1(0(1(0(x1))))) -> 3(5(4(5(4(3(3(1(1(2(x1)))))))))) 3(4(2(0(2(x1))))) -> 3(5(3(0(3(3(2(5(3(2(x1)))))))))) 0(3(5(2(4(0(x1)))))) -> 4(4(0(2(3(2(2(5(3(2(x1)))))))))) 1(1(2(0(4(5(x1)))))) -> 3(0(5(4(2(1(0(2(3(3(x1)))))))))) 2(1(1(0(1(2(x1)))))) -> 3(4(4(1(3(2(2(2(5(5(x1)))))))))) 2(2(0(1(1(1(x1)))))) -> 2(3(4(1(5(2(2(2(5(4(x1)))))))))) 2(4(1(0(4(2(x1)))))) -> 1(5(1(3(2(3(4(4(4(0(x1)))))))))) 2(4(2(1(1(1(x1)))))) -> 1(3(5(4(3(4(3(1(4(4(x1)))))))))) 3(0(1(0(0(2(x1)))))) -> 2(4(2(5(3(5(0(3(3(2(x1)))))))))) 3(0(1(1(1(1(x1)))))) -> 3(2(2(4(4(5(2(4(5(1(x1)))))))))) 4(1(1(2(0(2(x1)))))) -> 4(0(3(4(4(4(2(3(2(3(x1)))))))))) 0(2(1(1(1(1(0(x1))))))) -> 0(1(5(5(3(5(2(5(5(5(x1)))))))))) 0(2(4(1(1(1(5(x1))))))) -> 4(4(3(4(3(2(3(0(2(2(x1)))))))))) 0(4(2(0(0(4(1(x1))))))) -> 4(2(5(4(1(0(4(3(3(1(x1)))))))))) 0(4(3(0(5(4(1(x1))))))) -> 0(3(1(5(3(1(2(5(4(1(x1)))))))))) 1(0(5(2(2(0(0(x1))))))) -> 1(5(4(4(3(4(5(4(5(2(x1)))))))))) 1(1(3(4(5(0(0(x1))))))) -> 1(3(1(5(3(4(1(4(5(3(x1)))))))))) 1(4(3(1(5(0(5(x1))))))) -> 5(0(3(3(2(4(1(3(3(2(x1)))))))))) 1(5(0(2(0(5(5(x1))))))) -> 2(5(2(5(4(2(0(0(5(5(x1)))))))))) 2(0(1(5(2(0(5(x1))))))) -> 4(3(3(5(5(3(1(3(5(5(x1)))))))))) 2(4(0(5(4(1(4(x1))))))) -> 3(4(5(5(1(5(3(5(1(4(x1)))))))))) 3(4(1(4(0(4(5(x1))))))) -> 3(2(2(1(3(4(3(3(0(3(x1)))))))))) 4(1(0(4(2(0(0(x1))))))) -> 4(2(2(3(1(0(0(3(4(0(x1)))))))))) 4(1(0(4(2(0(3(x1))))))) -> 0(4(3(0(0(1(5(4(3(2(x1)))))))))) 4(1(1(1(0(1(2(x1))))))) -> 3(3(2(3(3(0(1(5(5(2(x1)))))))))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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(5(x_1)) -> 5(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_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 1(2(0(x1))) -> 4(0(3(3(5(4(5(1(4(3(x1)))))))))) 1(0(0(4(5(x1))))) -> 1(4(3(1(3(1(4(5(2(3(x1)))))))))) 2(0(3(0(2(x1))))) -> 3(3(1(2(2(4(5(0(4(3(x1)))))))))) 2(1(0(1(0(x1))))) -> 3(5(4(5(4(3(3(1(1(2(x1)))))))))) 3(4(2(0(2(x1))))) -> 3(5(3(0(3(3(2(5(3(2(x1)))))))))) 0(3(5(2(4(0(x1)))))) -> 4(4(0(2(3(2(2(5(3(2(x1)))))))))) 1(1(2(0(4(5(x1)))))) -> 3(0(5(4(2(1(0(2(3(3(x1)))))))))) 2(1(1(0(1(2(x1)))))) -> 3(4(4(1(3(2(2(2(5(5(x1)))))))))) 2(2(0(1(1(1(x1)))))) -> 2(3(4(1(5(2(2(2(5(4(x1)))))))))) 2(4(1(0(4(2(x1)))))) -> 1(5(1(3(2(3(4(4(4(0(x1)))))))))) 2(4(2(1(1(1(x1)))))) -> 1(3(5(4(3(4(3(1(4(4(x1)))))))))) 3(0(1(0(0(2(x1)))))) -> 2(4(2(5(3(5(0(3(3(2(x1)))))))))) 3(0(1(1(1(1(x1)))))) -> 3(2(2(4(4(5(2(4(5(1(x1)))))))))) 4(1(1(2(0(2(x1)))))) -> 4(0(3(4(4(4(2(3(2(3(x1)))))))))) 0(2(1(1(1(1(0(x1))))))) -> 0(1(5(5(3(5(2(5(5(5(x1)))))))))) 0(2(4(1(1(1(5(x1))))))) -> 4(4(3(4(3(2(3(0(2(2(x1)))))))))) 0(4(2(0(0(4(1(x1))))))) -> 4(2(5(4(1(0(4(3(3(1(x1)))))))))) 0(4(3(0(5(4(1(x1))))))) -> 0(3(1(5(3(1(2(5(4(1(x1)))))))))) 1(0(5(2(2(0(0(x1))))))) -> 1(5(4(4(3(4(5(4(5(2(x1)))))))))) 1(1(3(4(5(0(0(x1))))))) -> 1(3(1(5(3(4(1(4(5(3(x1)))))))))) 1(4(3(1(5(0(5(x1))))))) -> 5(0(3(3(2(4(1(3(3(2(x1)))))))))) 1(5(0(2(0(5(5(x1))))))) -> 2(5(2(5(4(2(0(0(5(5(x1)))))))))) 2(0(1(5(2(0(5(x1))))))) -> 4(3(3(5(5(3(1(3(5(5(x1)))))))))) 2(4(0(5(4(1(4(x1))))))) -> 3(4(5(5(1(5(3(5(1(4(x1)))))))))) 3(4(1(4(0(4(5(x1))))))) -> 3(2(2(1(3(4(3(3(0(3(x1)))))))))) 4(1(0(4(2(0(0(x1))))))) -> 4(2(2(3(1(0(0(3(4(0(x1)))))))))) 4(1(0(4(2(0(3(x1))))))) -> 0(4(3(0(0(1(5(4(3(2(x1)))))))))) 4(1(1(1(0(1(2(x1))))))) -> 3(3(2(3(3(0(1(5(5(2(x1)))))))))) The (relative) TRS S consists of the following rules: encArg(5(x_1)) -> 5(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_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 1(2(0(x1))) -> 4(0(3(3(5(4(5(1(4(3(x1)))))))))) 1(0(0(4(5(x1))))) -> 1(4(3(1(3(1(4(5(2(3(x1)))))))))) 2(0(3(0(2(x1))))) -> 3(3(1(2(2(4(5(0(4(3(x1)))))))))) 2(1(0(1(0(x1))))) -> 3(5(4(5(4(3(3(1(1(2(x1)))))))))) 3(4(2(0(2(x1))))) -> 3(5(3(0(3(3(2(5(3(2(x1)))))))))) 0(3(5(2(4(0(x1)))))) -> 4(4(0(2(3(2(2(5(3(2(x1)))))))))) 1(1(2(0(4(5(x1)))))) -> 3(0(5(4(2(1(0(2(3(3(x1)))))))))) 2(1(1(0(1(2(x1)))))) -> 3(4(4(1(3(2(2(2(5(5(x1)))))))))) 2(2(0(1(1(1(x1)))))) -> 2(3(4(1(5(2(2(2(5(4(x1)))))))))) 2(4(1(0(4(2(x1)))))) -> 1(5(1(3(2(3(4(4(4(0(x1)))))))))) 2(4(2(1(1(1(x1)))))) -> 1(3(5(4(3(4(3(1(4(4(x1)))))))))) 3(0(1(0(0(2(x1)))))) -> 2(4(2(5(3(5(0(3(3(2(x1)))))))))) 3(0(1(1(1(1(x1)))))) -> 3(2(2(4(4(5(2(4(5(1(x1)))))))))) 4(1(1(2(0(2(x1)))))) -> 4(0(3(4(4(4(2(3(2(3(x1)))))))))) 0(2(1(1(1(1(0(x1))))))) -> 0(1(5(5(3(5(2(5(5(5(x1)))))))))) 0(2(4(1(1(1(5(x1))))))) -> 4(4(3(4(3(2(3(0(2(2(x1)))))))))) 0(4(2(0(0(4(1(x1))))))) -> 4(2(5(4(1(0(4(3(3(1(x1)))))))))) 0(4(3(0(5(4(1(x1))))))) -> 0(3(1(5(3(1(2(5(4(1(x1)))))))))) 1(0(5(2(2(0(0(x1))))))) -> 1(5(4(4(3(4(5(4(5(2(x1)))))))))) 1(1(3(4(5(0(0(x1))))))) -> 1(3(1(5(3(4(1(4(5(3(x1)))))))))) 1(4(3(1(5(0(5(x1))))))) -> 5(0(3(3(2(4(1(3(3(2(x1)))))))))) 1(5(0(2(0(5(5(x1))))))) -> 2(5(2(5(4(2(0(0(5(5(x1)))))))))) 2(0(1(5(2(0(5(x1))))))) -> 4(3(3(5(5(3(1(3(5(5(x1)))))))))) 2(4(0(5(4(1(4(x1))))))) -> 3(4(5(5(1(5(3(5(1(4(x1)))))))))) 3(4(1(4(0(4(5(x1))))))) -> 3(2(2(1(3(4(3(3(0(3(x1)))))))))) 4(1(0(4(2(0(0(x1))))))) -> 4(2(2(3(1(0(0(3(4(0(x1)))))))))) 4(1(0(4(2(0(3(x1))))))) -> 0(4(3(0(0(1(5(4(3(2(x1)))))))))) 4(1(1(1(0(1(2(x1))))))) -> 3(3(2(3(3(0(1(5(5(2(x1)))))))))) The (relative) TRS S consists of the following rules: encArg(5(x_1)) -> 5(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_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 1(2(0(x1))) -> 4(0(3(3(5(4(5(1(4(3(x1)))))))))) 1(0(0(4(5(x1))))) -> 1(4(3(1(3(1(4(5(2(3(x1)))))))))) 2(0(3(0(2(x1))))) -> 3(3(1(2(2(4(5(0(4(3(x1)))))))))) 2(1(0(1(0(x1))))) -> 3(5(4(5(4(3(3(1(1(2(x1)))))))))) 3(4(2(0(2(x1))))) -> 3(5(3(0(3(3(2(5(3(2(x1)))))))))) 0(3(5(2(4(0(x1)))))) -> 4(4(0(2(3(2(2(5(3(2(x1)))))))))) 1(1(2(0(4(5(x1)))))) -> 3(0(5(4(2(1(0(2(3(3(x1)))))))))) 2(1(1(0(1(2(x1)))))) -> 3(4(4(1(3(2(2(2(5(5(x1)))))))))) 2(2(0(1(1(1(x1)))))) -> 2(3(4(1(5(2(2(2(5(4(x1)))))))))) 2(4(1(0(4(2(x1)))))) -> 1(5(1(3(2(3(4(4(4(0(x1)))))))))) 2(4(2(1(1(1(x1)))))) -> 1(3(5(4(3(4(3(1(4(4(x1)))))))))) 3(0(1(0(0(2(x1)))))) -> 2(4(2(5(3(5(0(3(3(2(x1)))))))))) 3(0(1(1(1(1(x1)))))) -> 3(2(2(4(4(5(2(4(5(1(x1)))))))))) 4(1(1(2(0(2(x1)))))) -> 4(0(3(4(4(4(2(3(2(3(x1)))))))))) 0(2(1(1(1(1(0(x1))))))) -> 0(1(5(5(3(5(2(5(5(5(x1)))))))))) 0(2(4(1(1(1(5(x1))))))) -> 4(4(3(4(3(2(3(0(2(2(x1)))))))))) 0(4(2(0(0(4(1(x1))))))) -> 4(2(5(4(1(0(4(3(3(1(x1)))))))))) 0(4(3(0(5(4(1(x1))))))) -> 0(3(1(5(3(1(2(5(4(1(x1)))))))))) 1(0(5(2(2(0(0(x1))))))) -> 1(5(4(4(3(4(5(4(5(2(x1)))))))))) 1(1(3(4(5(0(0(x1))))))) -> 1(3(1(5(3(4(1(4(5(3(x1)))))))))) 1(4(3(1(5(0(5(x1))))))) -> 5(0(3(3(2(4(1(3(3(2(x1)))))))))) 1(5(0(2(0(5(5(x1))))))) -> 2(5(2(5(4(2(0(0(5(5(x1)))))))))) 2(0(1(5(2(0(5(x1))))))) -> 4(3(3(5(5(3(1(3(5(5(x1)))))))))) 2(4(0(5(4(1(4(x1))))))) -> 3(4(5(5(1(5(3(5(1(4(x1)))))))))) 3(4(1(4(0(4(5(x1))))))) -> 3(2(2(1(3(4(3(3(0(3(x1)))))))))) 4(1(0(4(2(0(0(x1))))))) -> 4(2(2(3(1(0(0(3(4(0(x1)))))))))) 4(1(0(4(2(0(3(x1))))))) -> 0(4(3(0(0(1(5(4(3(2(x1)))))))))) 4(1(1(1(0(1(2(x1))))))) -> 3(3(2(3(3(0(1(5(5(2(x1)))))))))) encArg(5(x_1)) -> 5(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_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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. "[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] {(129,130,[1_1|0, 2_1|0, 3_1|0, 0_1|0, 4_1|0, encArg_1|0, encode_1_1|0, encode_2_1|0, encode_0_1|0, encode_4_1|0, encode_3_1|0, encode_5_1|0]), (129,131,[5_1|1, 1_1|1, 2_1|1, 3_1|1, 0_1|1, 4_1|1]), (129,132,[4_1|2]), (129,141,[1_1|2]), (129,150,[1_1|2]), (129,159,[3_1|2]), (129,168,[1_1|2]), (129,177,[5_1|2]), (129,186,[2_1|2]), (129,195,[3_1|2]), (129,204,[4_1|2]), (129,213,[3_1|2]), (129,222,[3_1|2]), (129,231,[2_1|2]), (129,240,[1_1|2]), (129,249,[1_1|2]), (129,258,[3_1|2]), (129,267,[3_1|2]), (129,276,[3_1|2]), (129,285,[2_1|2]), (129,294,[3_1|2]), (129,303,[4_1|2]), (129,312,[0_1|2]), (129,321,[4_1|2]), (129,330,[4_1|2]), (129,339,[0_1|2]), (129,348,[4_1|2]), (129,357,[3_1|2]), (129,366,[4_1|2]), (129,375,[0_1|2]), (130,130,[5_1|0, cons_1_1|0, cons_2_1|0, cons_3_1|0, cons_0_1|0, cons_4_1|0]), (131,130,[encArg_1|1]), (131,131,[5_1|1, 1_1|1, 2_1|1, 3_1|1, 0_1|1, 4_1|1]), (131,132,[4_1|2]), (131,141,[1_1|2]), (131,150,[1_1|2]), (131,159,[3_1|2]), (131,168,[1_1|2]), (131,177,[5_1|2]), (131,186,[2_1|2]), (131,195,[3_1|2]), (131,204,[4_1|2]), (131,213,[3_1|2]), (131,222,[3_1|2]), (131,231,[2_1|2]), (131,240,[1_1|2]), (131,249,[1_1|2]), (131,258,[3_1|2]), (131,267,[3_1|2]), (131,276,[3_1|2]), (131,285,[2_1|2]), (131,294,[3_1|2]), (131,303,[4_1|2]), (131,312,[0_1|2]), (131,321,[4_1|2]), (131,330,[4_1|2]), (131,339,[0_1|2]), (131,348,[4_1|2]), (131,357,[3_1|2]), (131,366,[4_1|2]), (131,375,[0_1|2]), (132,133,[0_1|2]), (133,134,[3_1|2]), (134,135,[3_1|2]), (135,136,[5_1|2]), (136,137,[4_1|2]), (137,138,[5_1|2]), (138,139,[1_1|2]), (138,177,[5_1|2]), (139,140,[4_1|2]), (140,131,[3_1|2]), (140,312,[3_1|2]), (140,339,[3_1|2]), (140,375,[3_1|2]), (140,267,[3_1|2]), (140,276,[3_1|2]), (140,285,[2_1|2]), (140,294,[3_1|2]), (141,142,[4_1|2]), (142,143,[3_1|2]), (143,144,[1_1|2]), (144,145,[3_1|2]), (145,146,[1_1|2]), (146,147,[4_1|2]), (147,148,[5_1|2]), (148,149,[2_1|2]), (149,131,[3_1|2]), (149,177,[3_1|2]), (149,267,[3_1|2]), (149,276,[3_1|2]), (149,285,[2_1|2]), (149,294,[3_1|2]), (150,151,[5_1|2]), (151,152,[4_1|2]), (152,153,[4_1|2]), (153,154,[3_1|2]), (154,155,[4_1|2]), (155,156,[5_1|2]), (156,157,[4_1|2]), (157,158,[5_1|2]), (158,131,[2_1|2]), (158,312,[2_1|2]), (158,339,[2_1|2]), (158,375,[2_1|2]), (158,195,[3_1|2]), (158,204,[4_1|2]), (158,213,[3_1|2]), (158,222,[3_1|2]), (158,231,[2_1|2]), (158,240,[1_1|2]), (158,249,[1_1|2]), (158,258,[3_1|2]), (159,160,[0_1|2]), (160,161,[5_1|2]), (161,162,[4_1|2]), (162,163,[2_1|2]), (163,164,[1_1|2]), (164,165,[0_1|2]), (165,166,[2_1|2]), (166,167,[3_1|2]), (167,131,[3_1|2]), (167,177,[3_1|2]), (167,267,[3_1|2]), (167,276,[3_1|2]), (167,285,[2_1|2]), (167,294,[3_1|2]), (168,169,[3_1|2]), (169,170,[1_1|2]), (170,171,[5_1|2]), (171,172,[3_1|2]), (172,173,[4_1|2]), (173,174,[1_1|2]), (174,175,[4_1|2]), (175,176,[5_1|2]), (176,131,[3_1|2]), (176,312,[3_1|2]), (176,339,[3_1|2]), (176,375,[3_1|2]), (176,267,[3_1|2]), (176,276,[3_1|2]), (176,285,[2_1|2]), (176,294,[3_1|2]), (177,178,[0_1|2]), (178,179,[3_1|2]), (179,180,[3_1|2]), (180,181,[2_1|2]), (181,182,[4_1|2]), (182,183,[1_1|2]), (183,184,[3_1|2]), (184,185,[3_1|2]), (185,131,[2_1|2]), (185,177,[2_1|2]), (185,195,[3_1|2]), (185,204,[4_1|2]), (185,213,[3_1|2]), (185,222,[3_1|2]), (185,231,[2_1|2]), (185,240,[1_1|2]), (185,249,[1_1|2]), (185,258,[3_1|2]), (186,187,[5_1|2]), (187,188,[2_1|2]), (188,189,[5_1|2]), (189,190,[4_1|2]), (190,191,[2_1|2]), (191,192,[0_1|2]), (192,193,[0_1|2]), (193,194,[5_1|2]), (194,131,[5_1|2]), (194,177,[5_1|2]), (195,196,[3_1|2]), (196,197,[1_1|2]), (197,198,[2_1|2]), (198,199,[2_1|2]), (199,200,[4_1|2]), (200,201,[5_1|2]), (201,202,[0_1|2]), (201,339,[0_1|2]), (202,203,[4_1|2]), (203,131,[3_1|2]), (203,186,[3_1|2]), (203,231,[3_1|2]), (203,285,[3_1|2, 2_1|2]), (203,267,[3_1|2]), (203,276,[3_1|2]), (203,294,[3_1|2]), (204,205,[3_1|2]), (205,206,[3_1|2]), (206,207,[5_1|2]), (207,208,[5_1|2]), (208,209,[3_1|2]), (209,210,[1_1|2]), (210,211,[3_1|2]), (211,212,[5_1|2]), (212,131,[5_1|2]), (212,177,[5_1|2]), (213,214,[5_1|2]), (214,215,[4_1|2]), (215,216,[5_1|2]), (216,217,[4_1|2]), (217,218,[3_1|2]), (218,219,[3_1|2]), (219,220,[1_1|2]), (219,159,[3_1|2]), (220,221,[1_1|2]), (220,132,[4_1|2]), (220,384,[4_1|3]), (221,131,[2_1|2]), (221,312,[2_1|2]), (221,339,[2_1|2]), (221,375,[2_1|2]), (221,195,[3_1|2]), (221,204,[4_1|2]), (221,213,[3_1|2]), (221,222,[3_1|2]), (221,231,[2_1|2]), (221,240,[1_1|2]), (221,249,[1_1|2]), (221,258,[3_1|2]), (222,223,[4_1|2]), (223,224,[4_1|2]), (224,225,[1_1|2]), (225,226,[3_1|2]), (226,227,[2_1|2]), (227,228,[2_1|2]), (228,229,[2_1|2]), (229,230,[5_1|2]), (230,131,[5_1|2]), (230,186,[5_1|2]), (230,231,[5_1|2]), (230,285,[5_1|2]), (231,232,[3_1|2]), (232,233,[4_1|2]), (233,234,[1_1|2]), (234,235,[5_1|2]), (235,236,[2_1|2]), (236,237,[2_1|2]), (237,238,[2_1|2]), (238,239,[5_1|2]), (239,131,[4_1|2]), (239,141,[4_1|2]), (239,150,[4_1|2]), (239,168,[4_1|2]), (239,240,[4_1|2]), (239,249,[4_1|2]), (239,348,[4_1|2]), (239,357,[3_1|2]), (239,366,[4_1|2]), (239,375,[0_1|2]), (240,241,[5_1|2]), (241,242,[1_1|2]), (242,243,[3_1|2]), (243,244,[2_1|2]), (244,245,[3_1|2]), (245,246,[4_1|2]), (246,247,[4_1|2]), (247,248,[4_1|2]), (248,131,[0_1|2]), (248,186,[0_1|2]), (248,231,[0_1|2]), (248,285,[0_1|2]), (248,331,[0_1|2]), (248,367,[0_1|2]), (248,303,[4_1|2]), (248,312,[0_1|2]), (248,321,[4_1|2]), (248,330,[4_1|2]), (248,339,[0_1|2]), (249,250,[3_1|2]), (250,251,[5_1|2]), (251,252,[4_1|2]), (252,253,[3_1|2]), (253,254,[4_1|2]), (254,255,[3_1|2]), (255,256,[1_1|2]), (256,257,[4_1|2]), (257,131,[4_1|2]), (257,141,[4_1|2]), (257,150,[4_1|2]), (257,168,[4_1|2]), (257,240,[4_1|2]), (257,249,[4_1|2]), (257,348,[4_1|2]), (257,357,[3_1|2]), (257,366,[4_1|2]), (257,375,[0_1|2]), (258,259,[4_1|2]), (259,260,[5_1|2]), (260,261,[5_1|2]), (261,262,[1_1|2]), (262,263,[5_1|2]), (263,264,[3_1|2]), (264,265,[5_1|2]), (265,266,[1_1|2]), (265,177,[5_1|2]), (266,131,[4_1|2]), (266,132,[4_1|2]), (266,204,[4_1|2]), (266,303,[4_1|2]), (266,321,[4_1|2]), (266,330,[4_1|2]), (266,348,[4_1|2]), (266,366,[4_1|2]), (266,142,[4_1|2]), (266,357,[3_1|2]), (266,375,[0_1|2]), (267,268,[5_1|2]), (268,269,[3_1|2]), (269,270,[0_1|2]), (270,271,[3_1|2]), (271,272,[3_1|2]), (272,273,[2_1|2]), (273,274,[5_1|2]), (274,275,[3_1|2]), (275,131,[2_1|2]), (275,186,[2_1|2]), (275,231,[2_1|2]), (275,285,[2_1|2]), (275,195,[3_1|2]), (275,204,[4_1|2]), (275,213,[3_1|2]), (275,222,[3_1|2]), (275,240,[1_1|2]), (275,249,[1_1|2]), (275,258,[3_1|2]), (276,277,[2_1|2]), (277,278,[2_1|2]), (278,279,[1_1|2]), (279,280,[3_1|2]), (280,281,[4_1|2]), (281,282,[3_1|2]), (282,283,[3_1|2]), (283,284,[0_1|2]), (283,303,[4_1|2]), (284,131,[3_1|2]), (284,177,[3_1|2]), (284,267,[3_1|2]), (284,276,[3_1|2]), (284,285,[2_1|2]), (284,294,[3_1|2]), (285,286,[4_1|2]), (286,287,[2_1|2]), (287,288,[5_1|2]), (288,289,[3_1|2]), (289,290,[5_1|2]), (290,291,[0_1|2]), (291,292,[3_1|2]), (292,293,[3_1|2]), (293,131,[2_1|2]), (293,186,[2_1|2]), (293,231,[2_1|2]), (293,285,[2_1|2]), (293,195,[3_1|2]), (293,204,[4_1|2]), (293,213,[3_1|2]), (293,222,[3_1|2]), (293,240,[1_1|2]), (293,249,[1_1|2]), (293,258,[3_1|2]), (294,295,[2_1|2]), (295,296,[2_1|2]), (296,297,[4_1|2]), (297,298,[4_1|2]), (298,299,[5_1|2]), (299,300,[2_1|2]), (300,301,[4_1|2]), (301,302,[5_1|2]), (302,131,[1_1|2]), (302,141,[1_1|2]), (302,150,[1_1|2]), (302,168,[1_1|2]), (302,240,[1_1|2]), (302,249,[1_1|2]), (302,132,[4_1|2]), (302,159,[3_1|2]), (302,177,[5_1|2]), (302,186,[2_1|2]), (303,304,[4_1|2]), (304,305,[0_1|2]), (305,306,[2_1|2]), (306,307,[3_1|2]), (307,308,[2_1|2]), (308,309,[2_1|2]), (309,310,[5_1|2]), (310,311,[3_1|2]), (311,131,[2_1|2]), (311,312,[2_1|2]), (311,339,[2_1|2]), (311,375,[2_1|2]), (311,133,[2_1|2]), (311,349,[2_1|2]), (311,195,[3_1|2]), (311,204,[4_1|2]), (311,213,[3_1|2]), (311,222,[3_1|2]), (311,231,[2_1|2]), (311,240,[1_1|2]), (311,249,[1_1|2]), (311,258,[3_1|2]), (312,313,[1_1|2]), (313,314,[5_1|2]), (314,315,[5_1|2]), (315,316,[3_1|2]), (316,317,[5_1|2]), (317,318,[2_1|2]), (318,319,[5_1|2]), (319,320,[5_1|2]), (320,131,[5_1|2]), (320,312,[5_1|2]), (320,339,[5_1|2]), (320,375,[5_1|2]), (321,322,[4_1|2]), (322,323,[3_1|2]), (323,324,[4_1|2]), (324,325,[3_1|2]), (325,326,[2_1|2]), (326,327,[3_1|2]), (327,328,[0_1|2]), (328,329,[2_1|2]), (328,231,[2_1|2]), (329,131,[2_1|2]), (329,177,[2_1|2]), (329,151,[2_1|2]), (329,241,[2_1|2]), (329,195,[3_1|2]), (329,204,[4_1|2]), (329,213,[3_1|2]), (329,222,[3_1|2]), (329,231,[2_1|2]), (329,240,[1_1|2]), (329,249,[1_1|2]), (329,258,[3_1|2]), (330,331,[2_1|2]), (331,332,[5_1|2]), (332,333,[4_1|2]), (333,334,[1_1|2]), (334,335,[0_1|2]), (335,336,[4_1|2]), (336,337,[3_1|2]), (337,338,[3_1|2]), (338,131,[1_1|2]), (338,141,[1_1|2]), (338,150,[1_1|2]), (338,168,[1_1|2]), (338,240,[1_1|2]), (338,249,[1_1|2]), (338,132,[4_1|2]), (338,159,[3_1|2]), (338,177,[5_1|2]), (338,186,[2_1|2]), (339,340,[3_1|2]), (340,341,[1_1|2]), (341,342,[5_1|2]), (342,343,[3_1|2]), (343,344,[1_1|2]), (344,345,[2_1|2]), (345,346,[5_1|2]), (346,347,[4_1|2]), (346,348,[4_1|2]), (346,357,[3_1|2]), (346,366,[4_1|2]), (346,375,[0_1|2]), (347,131,[1_1|2]), (347,141,[1_1|2]), (347,150,[1_1|2]), (347,168,[1_1|2]), (347,240,[1_1|2]), (347,249,[1_1|2]), (347,132,[4_1|2]), (347,159,[3_1|2]), (347,177,[5_1|2]), (347,186,[2_1|2]), (348,349,[0_1|2]), (349,350,[3_1|2]), (350,351,[4_1|2]), (351,352,[4_1|2]), (352,353,[4_1|2]), (353,354,[2_1|2]), (354,355,[3_1|2]), (355,356,[2_1|2]), (356,131,[3_1|2]), (356,186,[3_1|2]), (356,231,[3_1|2]), (356,285,[3_1|2, 2_1|2]), (356,267,[3_1|2]), (356,276,[3_1|2]), (356,294,[3_1|2]), (357,358,[3_1|2]), (358,359,[2_1|2]), (359,360,[3_1|2]), (360,361,[3_1|2]), (361,362,[0_1|2]), (362,363,[1_1|2]), (363,364,[5_1|2]), (364,365,[5_1|2]), (365,131,[2_1|2]), (365,186,[2_1|2]), (365,231,[2_1|2]), (365,285,[2_1|2]), (365,195,[3_1|2]), (365,204,[4_1|2]), (365,213,[3_1|2]), (365,222,[3_1|2]), (365,240,[1_1|2]), (365,249,[1_1|2]), (365,258,[3_1|2]), (366,367,[2_1|2]), (367,368,[2_1|2]), (368,369,[3_1|2]), (369,370,[1_1|2]), (370,371,[0_1|2]), (371,372,[0_1|2]), (372,373,[3_1|2]), (373,374,[4_1|2]), (374,131,[0_1|2]), (374,312,[0_1|2]), (374,339,[0_1|2]), (374,375,[0_1|2]), (374,303,[4_1|2]), (374,321,[4_1|2]), (374,330,[4_1|2]), (375,376,[4_1|2]), (376,377,[3_1|2]), (377,378,[0_1|2]), (378,379,[0_1|2]), (379,380,[1_1|2]), (380,381,[5_1|2]), (381,382,[4_1|2]), (382,383,[3_1|2]), (383,131,[2_1|2]), (383,159,[2_1|2]), (383,195,[2_1|2, 3_1|2]), (383,213,[2_1|2, 3_1|2]), (383,222,[2_1|2, 3_1|2]), (383,258,[2_1|2, 3_1|2]), (383,267,[2_1|2]), (383,276,[2_1|2]), (383,294,[2_1|2]), (383,357,[2_1|2]), (383,340,[2_1|2]), (383,204,[4_1|2]), (383,231,[2_1|2]), (383,240,[1_1|2]), (383,249,[1_1|2]), (384,385,[0_1|3]), (385,386,[3_1|3]), (386,387,[3_1|3]), (387,388,[5_1|3]), (388,389,[4_1|3]), (389,390,[5_1|3]), (390,391,[1_1|3]), (391,392,[4_1|3]), (392,312,[3_1|3]), (392,339,[3_1|3]), (392,375,[3_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)