/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 44 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 38 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: 2(5(x1)) -> 1(3(3(0(1(0(x1)))))) 2(5(x1)) -> 2(2(0(5(0(1(x1)))))) 3(5(x1)) -> 1(3(2(0(0(1(x1)))))) 3(5(x1)) -> 3(2(0(5(3(0(x1)))))) 4(5(x1)) -> 2(2(1(3(2(1(x1)))))) 4(5(x1)) -> 3(2(0(5(0(0(x1)))))) 1(2(5(x1))) -> 1(0(5(0(5(4(x1)))))) 1(2(5(x1))) -> 1(2(2(1(0(1(x1)))))) 1(2(5(x1))) -> 2(0(1(3(1(0(x1)))))) 1(4(5(x1))) -> 1(2(4(0(2(1(x1)))))) 2(5(1(x1))) -> 2(2(2(1(2(3(x1)))))) 2(5(2(x1))) -> 4(0(2(2(3(3(x1)))))) 2(5(3(x1))) -> 2(0(4(1(3(3(x1)))))) 2(5(4(x1))) -> 2(0(5(1(0(1(x1)))))) 3(2(5(x1))) -> 3(2(0(1(0(5(x1)))))) 3(4(2(x1))) -> 3(4(0(2(2(2(x1)))))) 3(5(1(x1))) -> 0(4(2(0(0(5(x1)))))) 3(5(1(x1))) -> 0(4(2(2(3(4(x1)))))) 3(5(1(x1))) -> 2(1(4(1(0(1(x1)))))) 3(5(2(x1))) -> 0(4(3(2(2(2(x1)))))) 3(5(2(x1))) -> 2(0(2(2(3(0(x1)))))) 3(5(2(x1))) -> 2(3(3(2(1(2(x1)))))) 3(5(3(x1))) -> 0(2(4(3(3(0(x1)))))) 3(5(3(x1))) -> 0(5(4(3(3(0(x1)))))) 3(5(3(x1))) -> 2(3(4(0(4(2(x1)))))) 3(5(4(x1))) -> 0(2(0(5(0(0(x1)))))) 3(5(4(x1))) -> 0(5(0(0(1(2(x1)))))) 3(5(5(x1))) -> 0(5(4(1(0(5(x1)))))) 4(5(1(x1))) -> 2(1(0(5(3(3(x1)))))) 4(5(2(x1))) -> 0(5(1(0(0(4(x1)))))) 4(5(4(x1))) -> 2(2(1(0(4(2(x1)))))) 4(5(4(x1))) -> 3(2(0(3(2(0(x1)))))) 5(5(3(x1))) -> 5(1(0(1(2(2(x1)))))) 5(5(4(x1))) -> 5(1(0(4(2(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(0(x_1)) -> 0(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_1(x_1)) -> 1(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_4(x_1) -> 4(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: 2(5(x1)) -> 1(3(3(0(1(0(x1)))))) 2(5(x1)) -> 2(2(0(5(0(1(x1)))))) 3(5(x1)) -> 1(3(2(0(0(1(x1)))))) 3(5(x1)) -> 3(2(0(5(3(0(x1)))))) 4(5(x1)) -> 2(2(1(3(2(1(x1)))))) 4(5(x1)) -> 3(2(0(5(0(0(x1)))))) 1(2(5(x1))) -> 1(0(5(0(5(4(x1)))))) 1(2(5(x1))) -> 1(2(2(1(0(1(x1)))))) 1(2(5(x1))) -> 2(0(1(3(1(0(x1)))))) 1(4(5(x1))) -> 1(2(4(0(2(1(x1)))))) 2(5(1(x1))) -> 2(2(2(1(2(3(x1)))))) 2(5(2(x1))) -> 4(0(2(2(3(3(x1)))))) 2(5(3(x1))) -> 2(0(4(1(3(3(x1)))))) 2(5(4(x1))) -> 2(0(5(1(0(1(x1)))))) 3(2(5(x1))) -> 3(2(0(1(0(5(x1)))))) 3(4(2(x1))) -> 3(4(0(2(2(2(x1)))))) 3(5(1(x1))) -> 0(4(2(0(0(5(x1)))))) 3(5(1(x1))) -> 0(4(2(2(3(4(x1)))))) 3(5(1(x1))) -> 2(1(4(1(0(1(x1)))))) 3(5(2(x1))) -> 0(4(3(2(2(2(x1)))))) 3(5(2(x1))) -> 2(0(2(2(3(0(x1)))))) 3(5(2(x1))) -> 2(3(3(2(1(2(x1)))))) 3(5(3(x1))) -> 0(2(4(3(3(0(x1)))))) 3(5(3(x1))) -> 0(5(4(3(3(0(x1)))))) 3(5(3(x1))) -> 2(3(4(0(4(2(x1)))))) 3(5(4(x1))) -> 0(2(0(5(0(0(x1)))))) 3(5(4(x1))) -> 0(5(0(0(1(2(x1)))))) 3(5(5(x1))) -> 0(5(4(1(0(5(x1)))))) 4(5(1(x1))) -> 2(1(0(5(3(3(x1)))))) 4(5(2(x1))) -> 0(5(1(0(0(4(x1)))))) 4(5(4(x1))) -> 2(2(1(0(4(2(x1)))))) 4(5(4(x1))) -> 3(2(0(3(2(0(x1)))))) 5(5(3(x1))) -> 5(1(0(1(2(2(x1)))))) 5(5(4(x1))) -> 5(1(0(4(2(2(x1)))))) The (relative) TRS S consists of the following rules: encArg(0(x_1)) -> 0(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_1(x_1)) -> 1(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_4(x_1) -> 4(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: 2(5(x1)) -> 1(3(3(0(1(0(x1)))))) 2(5(x1)) -> 2(2(0(5(0(1(x1)))))) 3(5(x1)) -> 1(3(2(0(0(1(x1)))))) 3(5(x1)) -> 3(2(0(5(3(0(x1)))))) 4(5(x1)) -> 2(2(1(3(2(1(x1)))))) 4(5(x1)) -> 3(2(0(5(0(0(x1)))))) 1(2(5(x1))) -> 1(0(5(0(5(4(x1)))))) 1(2(5(x1))) -> 1(2(2(1(0(1(x1)))))) 1(2(5(x1))) -> 2(0(1(3(1(0(x1)))))) 1(4(5(x1))) -> 1(2(4(0(2(1(x1)))))) 2(5(1(x1))) -> 2(2(2(1(2(3(x1)))))) 2(5(2(x1))) -> 4(0(2(2(3(3(x1)))))) 2(5(3(x1))) -> 2(0(4(1(3(3(x1)))))) 2(5(4(x1))) -> 2(0(5(1(0(1(x1)))))) 3(2(5(x1))) -> 3(2(0(1(0(5(x1)))))) 3(4(2(x1))) -> 3(4(0(2(2(2(x1)))))) 3(5(1(x1))) -> 0(4(2(0(0(5(x1)))))) 3(5(1(x1))) -> 0(4(2(2(3(4(x1)))))) 3(5(1(x1))) -> 2(1(4(1(0(1(x1)))))) 3(5(2(x1))) -> 0(4(3(2(2(2(x1)))))) 3(5(2(x1))) -> 2(0(2(2(3(0(x1)))))) 3(5(2(x1))) -> 2(3(3(2(1(2(x1)))))) 3(5(3(x1))) -> 0(2(4(3(3(0(x1)))))) 3(5(3(x1))) -> 0(5(4(3(3(0(x1)))))) 3(5(3(x1))) -> 2(3(4(0(4(2(x1)))))) 3(5(4(x1))) -> 0(2(0(5(0(0(x1)))))) 3(5(4(x1))) -> 0(5(0(0(1(2(x1)))))) 3(5(5(x1))) -> 0(5(4(1(0(5(x1)))))) 4(5(1(x1))) -> 2(1(0(5(3(3(x1)))))) 4(5(2(x1))) -> 0(5(1(0(0(4(x1)))))) 4(5(4(x1))) -> 2(2(1(0(4(2(x1)))))) 4(5(4(x1))) -> 3(2(0(3(2(0(x1)))))) 5(5(3(x1))) -> 5(1(0(1(2(2(x1)))))) 5(5(4(x1))) -> 5(1(0(4(2(2(x1)))))) The (relative) TRS S consists of the following rules: encArg(0(x_1)) -> 0(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_1(x_1)) -> 1(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_4(x_1) -> 4(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: 2(5(x1)) -> 1(3(3(0(1(0(x1)))))) 2(5(x1)) -> 2(2(0(5(0(1(x1)))))) 3(5(x1)) -> 1(3(2(0(0(1(x1)))))) 3(5(x1)) -> 3(2(0(5(3(0(x1)))))) 4(5(x1)) -> 2(2(1(3(2(1(x1)))))) 4(5(x1)) -> 3(2(0(5(0(0(x1)))))) 1(2(5(x1))) -> 1(0(5(0(5(4(x1)))))) 1(2(5(x1))) -> 1(2(2(1(0(1(x1)))))) 1(2(5(x1))) -> 2(0(1(3(1(0(x1)))))) 1(4(5(x1))) -> 1(2(4(0(2(1(x1)))))) 2(5(1(x1))) -> 2(2(2(1(2(3(x1)))))) 2(5(2(x1))) -> 4(0(2(2(3(3(x1)))))) 2(5(3(x1))) -> 2(0(4(1(3(3(x1)))))) 2(5(4(x1))) -> 2(0(5(1(0(1(x1)))))) 3(2(5(x1))) -> 3(2(0(1(0(5(x1)))))) 3(4(2(x1))) -> 3(4(0(2(2(2(x1)))))) 3(5(1(x1))) -> 0(4(2(0(0(5(x1)))))) 3(5(1(x1))) -> 0(4(2(2(3(4(x1)))))) 3(5(1(x1))) -> 2(1(4(1(0(1(x1)))))) 3(5(2(x1))) -> 0(4(3(2(2(2(x1)))))) 3(5(2(x1))) -> 2(0(2(2(3(0(x1)))))) 3(5(2(x1))) -> 2(3(3(2(1(2(x1)))))) 3(5(3(x1))) -> 0(2(4(3(3(0(x1)))))) 3(5(3(x1))) -> 0(5(4(3(3(0(x1)))))) 3(5(3(x1))) -> 2(3(4(0(4(2(x1)))))) 3(5(4(x1))) -> 0(2(0(5(0(0(x1)))))) 3(5(4(x1))) -> 0(5(0(0(1(2(x1)))))) 3(5(5(x1))) -> 0(5(4(1(0(5(x1)))))) 4(5(1(x1))) -> 2(1(0(5(3(3(x1)))))) 4(5(2(x1))) -> 0(5(1(0(0(4(x1)))))) 4(5(4(x1))) -> 2(2(1(0(4(2(x1)))))) 4(5(4(x1))) -> 3(2(0(3(2(0(x1)))))) 5(5(3(x1))) -> 5(1(0(1(2(2(x1)))))) 5(5(4(x1))) -> 5(1(0(4(2(2(x1)))))) encArg(0(x_1)) -> 0(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_1(x_1)) -> 1(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_4(x_1) -> 4(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. "[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, 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] {(115,116,[2_1|0, 3_1|0, 4_1|0, 1_1|0, 5_1|0, encArg_1|0, encode_2_1|0, encode_5_1|0, encode_1_1|0, encode_3_1|0, encode_0_1|0, encode_4_1|0]), (115,117,[0_1|1, 2_1|1, 3_1|1, 4_1|1, 1_1|1, 5_1|1]), (115,118,[1_1|2]), (115,123,[2_1|2]), (115,128,[2_1|2]), (115,133,[4_1|2]), (115,138,[2_1|2]), (115,143,[2_1|2]), (115,148,[1_1|2]), (115,153,[3_1|2]), (115,158,[0_1|2]), (115,163,[0_1|2]), (115,168,[2_1|2]), (115,173,[0_1|2]), (115,178,[2_1|2]), (115,183,[2_1|2]), (115,188,[0_1|2]), (115,193,[0_1|2]), (115,198,[2_1|2]), (115,203,[0_1|2]), (115,208,[0_1|2]), (115,213,[0_1|2]), (115,218,[3_1|2]), (115,223,[3_1|2]), (115,228,[2_1|2]), (115,233,[3_1|2]), (115,238,[2_1|2]), (115,243,[0_1|2]), (115,248,[2_1|2]), (115,253,[3_1|2]), (115,258,[1_1|2]), (115,263,[1_1|2]), (115,268,[2_1|2]), (115,273,[1_1|2]), (115,278,[5_1|2]), (115,283,[5_1|2]), (116,116,[0_1|0, cons_2_1|0, cons_3_1|0, cons_4_1|0, cons_1_1|0, cons_5_1|0]), (117,116,[encArg_1|1]), (117,117,[0_1|1, 2_1|1, 3_1|1, 4_1|1, 1_1|1, 5_1|1]), (117,118,[1_1|2]), (117,123,[2_1|2]), (117,128,[2_1|2]), (117,133,[4_1|2]), (117,138,[2_1|2]), (117,143,[2_1|2]), (117,148,[1_1|2]), (117,153,[3_1|2]), (117,158,[0_1|2]), (117,163,[0_1|2]), (117,168,[2_1|2]), (117,173,[0_1|2]), (117,178,[2_1|2]), (117,183,[2_1|2]), (117,188,[0_1|2]), (117,193,[0_1|2]), (117,198,[2_1|2]), (117,203,[0_1|2]), (117,208,[0_1|2]), (117,213,[0_1|2]), (117,218,[3_1|2]), (117,223,[3_1|2]), (117,228,[2_1|2]), (117,233,[3_1|2]), (117,238,[2_1|2]), (117,243,[0_1|2]), (117,248,[2_1|2]), (117,253,[3_1|2]), (117,258,[1_1|2]), (117,263,[1_1|2]), (117,268,[2_1|2]), (117,273,[1_1|2]), (117,278,[5_1|2]), (117,283,[5_1|2]), (118,119,[3_1|2]), (119,120,[3_1|2]), (120,121,[0_1|2]), (121,122,[1_1|2]), (122,117,[0_1|2]), (122,278,[0_1|2]), (122,283,[0_1|2]), (123,124,[2_1|2]), (124,125,[0_1|2]), (125,126,[5_1|2]), (126,127,[0_1|2]), (127,117,[1_1|2]), (127,278,[1_1|2]), (127,283,[1_1|2]), (127,258,[1_1|2]), (127,263,[1_1|2]), (127,268,[2_1|2]), (127,273,[1_1|2]), (128,129,[2_1|2]), (129,130,[2_1|2]), (130,131,[1_1|2]), (131,132,[2_1|2]), (132,117,[3_1|2]), (132,118,[3_1|2]), (132,148,[3_1|2, 1_1|2]), (132,258,[3_1|2]), (132,263,[3_1|2]), (132,273,[3_1|2]), (132,279,[3_1|2]), (132,284,[3_1|2]), (132,153,[3_1|2]), (132,158,[0_1|2]), (132,163,[0_1|2]), (132,168,[2_1|2]), (132,173,[0_1|2]), (132,178,[2_1|2]), (132,183,[2_1|2]), (132,188,[0_1|2]), (132,193,[0_1|2]), (132,198,[2_1|2]), (132,203,[0_1|2]), (132,208,[0_1|2]), (132,213,[0_1|2]), (132,218,[3_1|2]), (132,223,[3_1|2]), (132,300,[1_1|3]), (132,305,[3_1|3]), (132,310,[0_1|3]), (132,315,[0_1|3]), (132,320,[2_1|3]), (133,134,[0_1|2]), (134,135,[2_1|2]), (135,136,[2_1|2]), (136,137,[3_1|2]), (137,117,[3_1|2]), (137,123,[3_1|2]), (137,128,[3_1|2]), (137,138,[3_1|2]), (137,143,[3_1|2]), (137,168,[3_1|2, 2_1|2]), (137,178,[3_1|2, 2_1|2]), (137,183,[3_1|2, 2_1|2]), (137,198,[3_1|2, 2_1|2]), (137,228,[3_1|2]), (137,238,[3_1|2]), (137,248,[3_1|2]), (137,268,[3_1|2]), (137,148,[1_1|2]), (137,153,[3_1|2]), (137,158,[0_1|2]), (137,163,[0_1|2]), (137,173,[0_1|2]), (137,188,[0_1|2]), (137,193,[0_1|2]), (137,203,[0_1|2]), (137,208,[0_1|2]), (137,213,[0_1|2]), (137,218,[3_1|2]), (137,223,[3_1|2]), (137,300,[1_1|3]), (137,305,[3_1|3]), (137,310,[0_1|3]), (137,315,[0_1|3]), (137,320,[2_1|3]), (138,139,[0_1|2]), (139,140,[4_1|2]), (140,141,[1_1|2]), (141,142,[3_1|2]), (142,117,[3_1|2]), (142,153,[3_1|2]), (142,218,[3_1|2]), (142,223,[3_1|2]), (142,233,[3_1|2]), (142,253,[3_1|2]), (142,148,[1_1|2]), (142,158,[0_1|2]), (142,163,[0_1|2]), (142,168,[2_1|2]), (142,173,[0_1|2]), (142,178,[2_1|2]), (142,183,[2_1|2]), (142,188,[0_1|2]), (142,193,[0_1|2]), (142,198,[2_1|2]), (142,203,[0_1|2]), (142,208,[0_1|2]), (142,213,[0_1|2]), (142,300,[1_1|3]), (142,305,[3_1|3]), (142,310,[0_1|3]), (142,315,[0_1|3]), (142,320,[2_1|3]), (143,144,[0_1|2]), (144,145,[5_1|2]), (145,146,[1_1|2]), (146,147,[0_1|2]), (147,117,[1_1|2]), (147,133,[1_1|2]), (147,258,[1_1|2]), (147,263,[1_1|2]), (147,268,[2_1|2]), (147,273,[1_1|2]), (148,149,[3_1|2]), (149,150,[2_1|2]), (150,151,[0_1|2]), (151,152,[0_1|2]), (152,117,[1_1|2]), (152,278,[1_1|2]), (152,283,[1_1|2]), (152,258,[1_1|2]), (152,263,[1_1|2]), (152,268,[2_1|2]), (152,273,[1_1|2]), (153,154,[2_1|2]), (154,155,[0_1|2]), (155,156,[5_1|2]), (156,157,[3_1|2]), (157,117,[0_1|2]), (157,278,[0_1|2]), (157,283,[0_1|2]), (158,159,[4_1|2]), (159,160,[2_1|2]), (160,161,[0_1|2]), (161,162,[0_1|2]), (162,117,[5_1|2]), (162,118,[5_1|2]), (162,148,[5_1|2]), (162,258,[5_1|2]), (162,263,[5_1|2]), (162,273,[5_1|2]), (162,279,[5_1|2]), (162,284,[5_1|2]), (162,278,[5_1|2]), (162,283,[5_1|2]), (163,164,[4_1|2]), (164,165,[2_1|2]), (165,166,[2_1|2]), (166,167,[3_1|2]), (166,223,[3_1|2]), (166,325,[3_1|3]), (167,117,[4_1|2]), (167,118,[4_1|2]), (167,148,[4_1|2]), (167,258,[4_1|2]), (167,263,[4_1|2]), (167,273,[4_1|2]), (167,279,[4_1|2]), (167,284,[4_1|2]), (167,228,[2_1|2]), (167,233,[3_1|2]), (167,238,[2_1|2]), (167,243,[0_1|2]), (167,248,[2_1|2]), (167,253,[3_1|2]), (167,330,[2_1|3]), (167,335,[3_1|3]), (167,340,[2_1|3]), (168,169,[1_1|2]), (169,170,[4_1|2]), (170,171,[1_1|2]), (171,172,[0_1|2]), (172,117,[1_1|2]), (172,118,[1_1|2]), (172,148,[1_1|2]), (172,258,[1_1|2]), (172,263,[1_1|2]), (172,273,[1_1|2]), (172,279,[1_1|2]), (172,284,[1_1|2]), (172,268,[2_1|2]), (173,174,[4_1|2]), (174,175,[3_1|2]), (175,176,[2_1|2]), (176,177,[2_1|2]), (177,117,[2_1|2]), (177,123,[2_1|2]), (177,128,[2_1|2]), (177,138,[2_1|2]), (177,143,[2_1|2]), (177,168,[2_1|2]), (177,178,[2_1|2]), (177,183,[2_1|2]), (177,198,[2_1|2]), (177,228,[2_1|2]), (177,238,[2_1|2]), (177,248,[2_1|2]), (177,268,[2_1|2]), (177,118,[1_1|2]), (177,133,[4_1|2]), (177,345,[1_1|3]), (177,350,[2_1|3]), (177,355,[2_1|3]), (178,179,[0_1|2]), (179,180,[2_1|2]), (180,181,[2_1|2]), (181,182,[3_1|2]), (182,117,[0_1|2]), (182,123,[0_1|2]), (182,128,[0_1|2]), (182,138,[0_1|2]), (182,143,[0_1|2]), (182,168,[0_1|2]), (182,178,[0_1|2]), (182,183,[0_1|2]), (182,198,[0_1|2]), (182,228,[0_1|2]), (182,238,[0_1|2]), (182,248,[0_1|2]), (182,268,[0_1|2]), (183,184,[3_1|2]), (184,185,[3_1|2]), (185,186,[2_1|2]), (186,187,[1_1|2]), (186,258,[1_1|2]), (186,263,[1_1|2]), (186,268,[2_1|2]), (186,360,[1_1|3]), (186,365,[1_1|3]), (186,370,[2_1|3]), (187,117,[2_1|2]), (187,123,[2_1|2]), (187,128,[2_1|2]), (187,138,[2_1|2]), (187,143,[2_1|2]), (187,168,[2_1|2]), (187,178,[2_1|2]), (187,183,[2_1|2]), (187,198,[2_1|2]), (187,228,[2_1|2]), (187,238,[2_1|2]), (187,248,[2_1|2]), (187,268,[2_1|2]), (187,118,[1_1|2]), (187,133,[4_1|2]), (187,345,[1_1|3]), (187,350,[2_1|3]), (187,355,[2_1|3]), (188,189,[2_1|2]), (189,190,[4_1|2]), (190,191,[3_1|2]), (191,192,[3_1|2]), (192,117,[0_1|2]), (192,153,[0_1|2]), (192,218,[0_1|2]), (192,223,[0_1|2]), (192,233,[0_1|2]), (192,253,[0_1|2]), (193,194,[5_1|2]), (194,195,[4_1|2]), (195,196,[3_1|2]), (196,197,[3_1|2]), (197,117,[0_1|2]), (197,153,[0_1|2]), (197,218,[0_1|2]), (197,223,[0_1|2]), (197,233,[0_1|2]), (197,253,[0_1|2]), (198,199,[3_1|2]), (199,200,[4_1|2]), (200,201,[0_1|2]), (201,202,[4_1|2]), (202,117,[2_1|2]), (202,153,[2_1|2]), (202,218,[2_1|2]), (202,223,[2_1|2]), (202,233,[2_1|2]), (202,253,[2_1|2]), (202,118,[1_1|2]), (202,123,[2_1|2]), (202,128,[2_1|2]), (202,133,[4_1|2]), (202,138,[2_1|2]), (202,143,[2_1|2]), (202,345,[1_1|3]), (202,350,[2_1|3]), (202,355,[2_1|3]), (203,204,[2_1|2]), (204,205,[0_1|2]), (205,206,[5_1|2]), (206,207,[0_1|2]), (207,117,[0_1|2]), (207,133,[0_1|2]), (208,209,[5_1|2]), (209,210,[0_1|2]), (210,211,[0_1|2]), (211,212,[1_1|2]), (211,258,[1_1|2]), (211,263,[1_1|2]), (211,268,[2_1|2]), (211,360,[1_1|3]), (211,365,[1_1|3]), (211,370,[2_1|3]), (212,117,[2_1|2]), (212,133,[2_1|2, 4_1|2]), (212,118,[1_1|2]), (212,123,[2_1|2]), (212,128,[2_1|2]), (212,138,[2_1|2]), (212,143,[2_1|2]), (212,345,[1_1|3]), (212,350,[2_1|3]), (212,355,[2_1|3]), (213,214,[5_1|2]), (214,215,[4_1|2]), (215,216,[1_1|2]), (216,217,[0_1|2]), (217,117,[5_1|2]), (217,278,[5_1|2]), (217,283,[5_1|2]), (218,219,[2_1|2]), (219,220,[0_1|2]), (220,221,[1_1|2]), (221,222,[0_1|2]), (222,117,[5_1|2]), (222,278,[5_1|2]), (222,283,[5_1|2]), (223,224,[4_1|2]), (224,225,[0_1|2]), (225,226,[2_1|2]), (226,227,[2_1|2]), (227,117,[2_1|2]), (227,123,[2_1|2]), (227,128,[2_1|2]), (227,138,[2_1|2]), (227,143,[2_1|2]), (227,168,[2_1|2]), (227,178,[2_1|2]), (227,183,[2_1|2]), (227,198,[2_1|2]), (227,228,[2_1|2]), (227,238,[2_1|2]), (227,248,[2_1|2]), (227,268,[2_1|2]), (227,118,[1_1|2]), (227,133,[4_1|2]), (227,345,[1_1|3]), (227,350,[2_1|3]), (227,355,[2_1|3]), (228,229,[2_1|2]), (229,230,[1_1|2]), (230,231,[3_1|2]), (231,232,[2_1|2]), (232,117,[1_1|2]), (232,278,[1_1|2]), (232,283,[1_1|2]), (232,258,[1_1|2]), (232,263,[1_1|2]), (232,268,[2_1|2]), (232,273,[1_1|2]), (233,234,[2_1|2]), (234,235,[0_1|2]), (235,236,[5_1|2]), (236,237,[0_1|2]), (237,117,[0_1|2]), (237,278,[0_1|2]), (237,283,[0_1|2]), (238,239,[1_1|2]), (239,240,[0_1|2]), (240,241,[5_1|2]), (241,242,[3_1|2]), (242,117,[3_1|2]), (242,118,[3_1|2]), (242,148,[3_1|2, 1_1|2]), (242,258,[3_1|2]), (242,263,[3_1|2]), (242,273,[3_1|2]), (242,279,[3_1|2]), (242,284,[3_1|2]), (242,153,[3_1|2]), (242,158,[0_1|2]), (242,163,[0_1|2]), (242,168,[2_1|2]), (242,173,[0_1|2]), (242,178,[2_1|2]), (242,183,[2_1|2]), (242,188,[0_1|2]), (242,193,[0_1|2]), (242,198,[2_1|2]), (242,203,[0_1|2]), (242,208,[0_1|2]), (242,213,[0_1|2]), (242,218,[3_1|2]), (242,223,[3_1|2]), (242,300,[1_1|3]), (242,305,[3_1|3]), (242,310,[0_1|3]), (242,315,[0_1|3]), (242,320,[2_1|3]), (243,244,[5_1|2]), (244,245,[1_1|2]), (245,246,[0_1|2]), (246,247,[0_1|2]), (247,117,[4_1|2]), (247,123,[4_1|2]), (247,128,[4_1|2]), (247,138,[4_1|2]), (247,143,[4_1|2]), (247,168,[4_1|2]), (247,178,[4_1|2]), (247,183,[4_1|2]), (247,198,[4_1|2]), (247,228,[4_1|2, 2_1|2]), (247,238,[4_1|2, 2_1|2]), (247,248,[4_1|2, 2_1|2]), (247,268,[4_1|2]), (247,233,[3_1|2]), (247,243,[0_1|2]), (247,253,[3_1|2]), (247,330,[2_1|3]), (247,335,[3_1|3]), (247,340,[2_1|3]), (248,249,[2_1|2]), (249,250,[1_1|2]), (250,251,[0_1|2]), (251,252,[4_1|2]), (252,117,[2_1|2]), (252,133,[2_1|2, 4_1|2]), (252,118,[1_1|2]), (252,123,[2_1|2]), (252,128,[2_1|2]), (252,138,[2_1|2]), (252,143,[2_1|2]), (252,345,[1_1|3]), (252,350,[2_1|3]), (252,355,[2_1|3]), (253,254,[2_1|2]), (254,255,[0_1|2]), (255,256,[3_1|2]), (256,257,[2_1|2]), (257,117,[0_1|2]), (257,133,[0_1|2]), (258,259,[0_1|2]), (259,260,[5_1|2]), (260,261,[0_1|2]), (261,262,[5_1|2]), (262,117,[4_1|2]), (262,278,[4_1|2]), (262,283,[4_1|2]), (262,228,[2_1|2]), (262,233,[3_1|2]), (262,238,[2_1|2]), (262,243,[0_1|2]), (262,248,[2_1|2]), (262,253,[3_1|2]), (262,330,[2_1|3]), (262,335,[3_1|3]), (262,340,[2_1|3]), (263,264,[2_1|2]), (264,265,[2_1|2]), (265,266,[1_1|2]), (266,267,[0_1|2]), (267,117,[1_1|2]), (267,278,[1_1|2]), (267,283,[1_1|2]), (267,258,[1_1|2]), (267,263,[1_1|2]), (267,268,[2_1|2]), (267,273,[1_1|2]), (268,269,[0_1|2]), (269,270,[1_1|2]), (270,271,[3_1|2]), (271,272,[1_1|2]), (272,117,[0_1|2]), (272,278,[0_1|2]), (272,283,[0_1|2]), (273,274,[2_1|2]), (274,275,[4_1|2]), (275,276,[0_1|2]), (276,277,[2_1|2]), (277,117,[1_1|2]), (277,278,[1_1|2]), (277,283,[1_1|2]), (277,258,[1_1|2]), (277,263,[1_1|2]), (277,268,[2_1|2]), (277,273,[1_1|2]), (278,279,[1_1|2]), (279,280,[0_1|2]), (280,281,[1_1|2]), (281,282,[2_1|2]), (282,117,[2_1|2]), (282,153,[2_1|2]), (282,218,[2_1|2]), (282,223,[2_1|2]), (282,233,[2_1|2]), (282,253,[2_1|2]), (282,118,[1_1|2]), (282,123,[2_1|2]), (282,128,[2_1|2]), (282,133,[4_1|2]), (282,138,[2_1|2]), (282,143,[2_1|2]), (282,345,[1_1|3]), (282,350,[2_1|3]), (282,355,[2_1|3]), (283,284,[1_1|2]), (284,285,[0_1|2]), (285,286,[4_1|2]), (286,287,[2_1|2]), (287,117,[2_1|2]), (287,133,[2_1|2, 4_1|2]), (287,118,[1_1|2]), (287,123,[2_1|2]), (287,128,[2_1|2]), (287,138,[2_1|2]), (287,143,[2_1|2]), (287,345,[1_1|3]), (287,350,[2_1|3]), (287,355,[2_1|3]), (300,301,[3_1|3]), (301,302,[2_1|3]), (302,303,[0_1|3]), (303,304,[0_1|3]), (304,278,[1_1|3]), (304,283,[1_1|3]), (305,306,[2_1|3]), (306,307,[0_1|3]), (307,308,[5_1|3]), (308,309,[3_1|3]), (309,278,[0_1|3]), (309,283,[0_1|3]), (310,311,[4_1|3]), (311,312,[2_1|3]), (312,313,[0_1|3]), (313,314,[0_1|3]), (314,279,[5_1|3]), (314,284,[5_1|3]), (315,316,[4_1|3]), (316,317,[2_1|3]), (317,318,[2_1|3]), (318,319,[3_1|3]), (319,279,[4_1|3]), (319,284,[4_1|3]), (320,321,[1_1|3]), (321,322,[4_1|3]), (322,323,[1_1|3]), (323,324,[0_1|3]), (324,279,[1_1|3]), (324,284,[1_1|3]), (325,326,[4_1|3]), (326,327,[0_1|3]), (327,328,[2_1|3]), (328,329,[2_1|3]), (329,123,[2_1|3]), (329,128,[2_1|3]), (329,138,[2_1|3]), (329,143,[2_1|3]), (329,168,[2_1|3]), (329,178,[2_1|3]), (329,183,[2_1|3]), (329,198,[2_1|3]), (329,228,[2_1|3]), (329,238,[2_1|3]), (329,248,[2_1|3]), (329,268,[2_1|3]), (329,264,[2_1|3]), (329,274,[2_1|3]), (330,331,[2_1|3]), (331,332,[1_1|3]), (332,333,[3_1|3]), (333,334,[2_1|3]), (334,278,[1_1|3]), (334,283,[1_1|3]), (335,336,[2_1|3]), (336,337,[0_1|3]), (337,338,[5_1|3]), (338,339,[0_1|3]), (339,278,[0_1|3]), (339,283,[0_1|3]), (340,341,[1_1|3]), (341,342,[0_1|3]), (342,343,[5_1|3]), (343,344,[3_1|3]), (344,279,[3_1|3]), (344,284,[3_1|3]), (345,346,[3_1|3]), (346,347,[3_1|3]), (347,348,[0_1|3]), (348,349,[1_1|3]), (349,278,[0_1|3]), (349,283,[0_1|3]), (350,351,[2_1|3]), (351,352,[0_1|3]), (352,353,[5_1|3]), (353,354,[0_1|3]), (354,278,[1_1|3]), (354,283,[1_1|3]), (355,356,[2_1|3]), (356,357,[2_1|3]), (357,358,[1_1|3]), (358,359,[2_1|3]), (359,279,[3_1|3]), (359,284,[3_1|3]), (360,361,[0_1|3]), (361,362,[5_1|3]), (362,363,[0_1|3]), (363,364,[5_1|3]), (364,278,[4_1|3]), (364,283,[4_1|3]), (365,366,[2_1|3]), (366,367,[2_1|3]), (367,368,[1_1|3]), (368,369,[0_1|3]), (369,278,[1_1|3]), (369,283,[1_1|3]), (370,371,[0_1|3]), (371,372,[1_1|3]), (372,373,[3_1|3]), (373,374,[1_1|3]), (374,278,[0_1|3]), (374,283,[0_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)