WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 70 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 20 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: 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: 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(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 (innermost) 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: 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: 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: 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: 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: 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. "[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] {(125,126,[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]), (125,127,[0_1|1, 2_1|1, 3_1|1, 4_1|1, 1_1|1, 5_1|1]), (125,128,[1_1|2]), (125,133,[2_1|2]), (125,138,[2_1|2]), (125,143,[4_1|2]), (125,148,[2_1|2]), (125,153,[2_1|2]), (125,158,[1_1|2]), (125,163,[3_1|2]), (125,168,[0_1|2]), (125,173,[0_1|2]), (125,178,[2_1|2]), (125,183,[0_1|2]), (125,188,[2_1|2]), (125,193,[2_1|2]), (125,198,[0_1|2]), (125,203,[0_1|2]), (125,208,[2_1|2]), (125,213,[0_1|2]), (125,218,[0_1|2]), (125,223,[0_1|2]), (125,228,[3_1|2]), (125,233,[3_1|2]), (125,238,[2_1|2]), (125,243,[3_1|2]), (125,248,[2_1|2]), (125,253,[0_1|2]), (125,258,[2_1|2]), (125,263,[3_1|2]), (125,268,[1_1|2]), (125,273,[1_1|2]), (125,278,[2_1|2]), (125,283,[1_1|2]), (125,288,[5_1|2]), (125,293,[5_1|2]), (126,126,[0_1|0, cons_2_1|0, cons_3_1|0, cons_4_1|0, cons_1_1|0, cons_5_1|0]), (127,126,[encArg_1|1]), (127,127,[0_1|1, 2_1|1, 3_1|1, 4_1|1, 1_1|1, 5_1|1]), (127,128,[1_1|2]), (127,133,[2_1|2]), (127,138,[2_1|2]), (127,143,[4_1|2]), (127,148,[2_1|2]), (127,153,[2_1|2]), (127,158,[1_1|2]), (127,163,[3_1|2]), (127,168,[0_1|2]), (127,173,[0_1|2]), (127,178,[2_1|2]), (127,183,[0_1|2]), (127,188,[2_1|2]), (127,193,[2_1|2]), (127,198,[0_1|2]), (127,203,[0_1|2]), (127,208,[2_1|2]), (127,213,[0_1|2]), (127,218,[0_1|2]), (127,223,[0_1|2]), (127,228,[3_1|2]), (127,233,[3_1|2]), (127,238,[2_1|2]), (127,243,[3_1|2]), (127,248,[2_1|2]), (127,253,[0_1|2]), (127,258,[2_1|2]), (127,263,[3_1|2]), (127,268,[1_1|2]), (127,273,[1_1|2]), (127,278,[2_1|2]), (127,283,[1_1|2]), (127,288,[5_1|2]), (127,293,[5_1|2]), (128,129,[3_1|2]), (129,130,[3_1|2]), (130,131,[0_1|2]), (131,132,[1_1|2]), (132,127,[0_1|2]), (132,288,[0_1|2]), (132,293,[0_1|2]), (133,134,[2_1|2]), (134,135,[0_1|2]), (135,136,[5_1|2]), (136,137,[0_1|2]), (137,127,[1_1|2]), (137,288,[1_1|2]), (137,293,[1_1|2]), (137,268,[1_1|2]), (137,273,[1_1|2]), (137,278,[2_1|2]), (137,283,[1_1|2]), (138,139,[2_1|2]), (139,140,[2_1|2]), (140,141,[1_1|2]), (141,142,[2_1|2]), (142,127,[3_1|2]), (142,128,[3_1|2]), (142,158,[3_1|2, 1_1|2]), (142,268,[3_1|2]), (142,273,[3_1|2]), (142,283,[3_1|2]), (142,289,[3_1|2]), (142,294,[3_1|2]), (142,163,[3_1|2]), (142,168,[0_1|2]), (142,173,[0_1|2]), (142,178,[2_1|2]), (142,183,[0_1|2]), (142,188,[2_1|2]), (142,193,[2_1|2]), (142,198,[0_1|2]), (142,203,[0_1|2]), (142,208,[2_1|2]), (142,213,[0_1|2]), (142,218,[0_1|2]), (142,223,[0_1|2]), (142,228,[3_1|2]), (142,233,[3_1|2]), (142,298,[1_1|3]), (142,303,[3_1|3]), (142,308,[0_1|3]), (142,313,[0_1|3]), (142,318,[2_1|3]), (143,144,[0_1|2]), (144,145,[2_1|2]), (145,146,[2_1|2]), (146,147,[3_1|2]), (147,127,[3_1|2]), (147,133,[3_1|2]), (147,138,[3_1|2]), (147,148,[3_1|2]), (147,153,[3_1|2]), (147,178,[3_1|2, 2_1|2]), (147,188,[3_1|2, 2_1|2]), (147,193,[3_1|2, 2_1|2]), (147,208,[3_1|2, 2_1|2]), (147,238,[3_1|2]), (147,248,[3_1|2]), (147,258,[3_1|2]), (147,278,[3_1|2]), (147,158,[1_1|2]), (147,163,[3_1|2]), (147,168,[0_1|2]), (147,173,[0_1|2]), (147,183,[0_1|2]), (147,198,[0_1|2]), (147,203,[0_1|2]), (147,213,[0_1|2]), (147,218,[0_1|2]), (147,223,[0_1|2]), (147,228,[3_1|2]), (147,233,[3_1|2]), (147,298,[1_1|3]), (147,303,[3_1|3]), (147,308,[0_1|3]), (147,313,[0_1|3]), (147,318,[2_1|3]), (148,149,[0_1|2]), (149,150,[4_1|2]), (150,151,[1_1|2]), (151,152,[3_1|2]), (152,127,[3_1|2]), (152,163,[3_1|2]), (152,228,[3_1|2]), (152,233,[3_1|2]), (152,243,[3_1|2]), (152,263,[3_1|2]), (152,158,[1_1|2]), (152,168,[0_1|2]), (152,173,[0_1|2]), (152,178,[2_1|2]), (152,183,[0_1|2]), (152,188,[2_1|2]), (152,193,[2_1|2]), (152,198,[0_1|2]), (152,203,[0_1|2]), (152,208,[2_1|2]), (152,213,[0_1|2]), (152,218,[0_1|2]), (152,223,[0_1|2]), (152,298,[1_1|3]), (152,303,[3_1|3]), (152,308,[0_1|3]), (152,313,[0_1|3]), (152,318,[2_1|3]), (153,154,[0_1|2]), (154,155,[5_1|2]), (155,156,[1_1|2]), (156,157,[0_1|2]), (157,127,[1_1|2]), (157,143,[1_1|2]), (157,268,[1_1|2]), (157,273,[1_1|2]), (157,278,[2_1|2]), (157,283,[1_1|2]), (158,159,[3_1|2]), (159,160,[2_1|2]), (160,161,[0_1|2]), (161,162,[0_1|2]), (162,127,[1_1|2]), (162,288,[1_1|2]), (162,293,[1_1|2]), (162,268,[1_1|2]), (162,273,[1_1|2]), (162,278,[2_1|2]), (162,283,[1_1|2]), (163,164,[2_1|2]), (164,165,[0_1|2]), (165,166,[5_1|2]), (166,167,[3_1|2]), (167,127,[0_1|2]), (167,288,[0_1|2]), (167,293,[0_1|2]), (168,169,[4_1|2]), (169,170,[2_1|2]), (170,171,[0_1|2]), (171,172,[0_1|2]), (172,127,[5_1|2]), (172,128,[5_1|2]), (172,158,[5_1|2]), (172,268,[5_1|2]), (172,273,[5_1|2]), (172,283,[5_1|2]), (172,289,[5_1|2]), (172,294,[5_1|2]), (172,288,[5_1|2]), (172,293,[5_1|2]), (173,174,[4_1|2]), (174,175,[2_1|2]), (175,176,[2_1|2]), (176,177,[3_1|2]), (176,233,[3_1|2]), (176,323,[3_1|3]), (177,127,[4_1|2]), (177,128,[4_1|2]), (177,158,[4_1|2]), (177,268,[4_1|2]), (177,273,[4_1|2]), (177,283,[4_1|2]), (177,289,[4_1|2]), (177,294,[4_1|2]), (177,238,[2_1|2]), (177,243,[3_1|2]), (177,248,[2_1|2]), (177,253,[0_1|2]), (177,258,[2_1|2]), (177,263,[3_1|2]), (177,328,[2_1|3]), (177,333,[3_1|3]), (177,338,[2_1|3]), (178,179,[1_1|2]), (179,180,[4_1|2]), (180,181,[1_1|2]), (181,182,[0_1|2]), (182,127,[1_1|2]), (182,128,[1_1|2]), (182,158,[1_1|2]), (182,268,[1_1|2]), (182,273,[1_1|2]), (182,283,[1_1|2]), (182,289,[1_1|2]), (182,294,[1_1|2]), (182,278,[2_1|2]), (183,184,[4_1|2]), (184,185,[3_1|2]), (185,186,[2_1|2]), (186,187,[2_1|2]), (187,127,[2_1|2]), (187,133,[2_1|2]), (187,138,[2_1|2]), (187,148,[2_1|2]), (187,153,[2_1|2]), (187,178,[2_1|2]), (187,188,[2_1|2]), (187,193,[2_1|2]), (187,208,[2_1|2]), (187,238,[2_1|2]), (187,248,[2_1|2]), (187,258,[2_1|2]), (187,278,[2_1|2]), (187,128,[1_1|2]), (187,143,[4_1|2]), (187,343,[1_1|3]), (187,348,[2_1|3]), (187,353,[2_1|3]), (188,189,[0_1|2]), (189,190,[2_1|2]), (190,191,[2_1|2]), (191,192,[3_1|2]), (192,127,[0_1|2]), (192,133,[0_1|2]), (192,138,[0_1|2]), (192,148,[0_1|2]), (192,153,[0_1|2]), (192,178,[0_1|2]), (192,188,[0_1|2]), (192,193,[0_1|2]), (192,208,[0_1|2]), (192,238,[0_1|2]), (192,248,[0_1|2]), (192,258,[0_1|2]), (192,278,[0_1|2]), (193,194,[3_1|2]), (194,195,[3_1|2]), (195,196,[2_1|2]), (196,197,[1_1|2]), (196,268,[1_1|2]), (196,273,[1_1|2]), (196,278,[2_1|2]), (196,358,[1_1|3]), (196,363,[1_1|3]), (196,368,[2_1|3]), (197,127,[2_1|2]), (197,133,[2_1|2]), (197,138,[2_1|2]), (197,148,[2_1|2]), (197,153,[2_1|2]), (197,178,[2_1|2]), (197,188,[2_1|2]), (197,193,[2_1|2]), (197,208,[2_1|2]), (197,238,[2_1|2]), (197,248,[2_1|2]), (197,258,[2_1|2]), (197,278,[2_1|2]), (197,128,[1_1|2]), (197,143,[4_1|2]), (197,343,[1_1|3]), (197,348,[2_1|3]), (197,353,[2_1|3]), (198,199,[2_1|2]), (199,200,[4_1|2]), (200,201,[3_1|2]), (201,202,[3_1|2]), (202,127,[0_1|2]), (202,163,[0_1|2]), (202,228,[0_1|2]), (202,233,[0_1|2]), (202,243,[0_1|2]), (202,263,[0_1|2]), (203,204,[5_1|2]), (204,205,[4_1|2]), (205,206,[3_1|2]), (206,207,[3_1|2]), (207,127,[0_1|2]), (207,163,[0_1|2]), (207,228,[0_1|2]), (207,233,[0_1|2]), (207,243,[0_1|2]), (207,263,[0_1|2]), (208,209,[3_1|2]), (209,210,[4_1|2]), (210,211,[0_1|2]), (211,212,[4_1|2]), (212,127,[2_1|2]), (212,163,[2_1|2]), (212,228,[2_1|2]), (212,233,[2_1|2]), (212,243,[2_1|2]), (212,263,[2_1|2]), (212,128,[1_1|2]), (212,133,[2_1|2]), (212,138,[2_1|2]), (212,143,[4_1|2]), (212,148,[2_1|2]), (212,153,[2_1|2]), (212,343,[1_1|3]), (212,348,[2_1|3]), (212,353,[2_1|3]), (213,214,[2_1|2]), (214,215,[0_1|2]), (215,216,[5_1|2]), (216,217,[0_1|2]), (217,127,[0_1|2]), (217,143,[0_1|2]), (218,219,[5_1|2]), (219,220,[0_1|2]), (220,221,[0_1|2]), (221,222,[1_1|2]), (221,268,[1_1|2]), (221,273,[1_1|2]), (221,278,[2_1|2]), (221,358,[1_1|3]), (221,363,[1_1|3]), (221,368,[2_1|3]), (222,127,[2_1|2]), (222,143,[2_1|2, 4_1|2]), (222,128,[1_1|2]), (222,133,[2_1|2]), (222,138,[2_1|2]), (222,148,[2_1|2]), (222,153,[2_1|2]), (222,343,[1_1|3]), (222,348,[2_1|3]), (222,353,[2_1|3]), (223,224,[5_1|2]), (224,225,[4_1|2]), (225,226,[1_1|2]), (226,227,[0_1|2]), (227,127,[5_1|2]), (227,288,[5_1|2]), (227,293,[5_1|2]), (228,229,[2_1|2]), (229,230,[0_1|2]), (230,231,[1_1|2]), (231,232,[0_1|2]), (232,127,[5_1|2]), (232,288,[5_1|2]), (232,293,[5_1|2]), (233,234,[4_1|2]), (234,235,[0_1|2]), (235,236,[2_1|2]), (236,237,[2_1|2]), (237,127,[2_1|2]), (237,133,[2_1|2]), (237,138,[2_1|2]), (237,148,[2_1|2]), (237,153,[2_1|2]), (237,178,[2_1|2]), (237,188,[2_1|2]), (237,193,[2_1|2]), (237,208,[2_1|2]), (237,238,[2_1|2]), (237,248,[2_1|2]), (237,258,[2_1|2]), (237,278,[2_1|2]), (237,128,[1_1|2]), (237,143,[4_1|2]), (237,343,[1_1|3]), (237,348,[2_1|3]), (237,353,[2_1|3]), (238,239,[2_1|2]), (239,240,[1_1|2]), (240,241,[3_1|2]), (241,242,[2_1|2]), (242,127,[1_1|2]), (242,288,[1_1|2]), (242,293,[1_1|2]), (242,268,[1_1|2]), (242,273,[1_1|2]), (242,278,[2_1|2]), (242,283,[1_1|2]), (243,244,[2_1|2]), (244,245,[0_1|2]), (245,246,[5_1|2]), (246,247,[0_1|2]), (247,127,[0_1|2]), (247,288,[0_1|2]), (247,293,[0_1|2]), (248,249,[1_1|2]), (249,250,[0_1|2]), (250,251,[5_1|2]), (251,252,[3_1|2]), (252,127,[3_1|2]), (252,128,[3_1|2]), (252,158,[3_1|2, 1_1|2]), (252,268,[3_1|2]), (252,273,[3_1|2]), (252,283,[3_1|2]), (252,289,[3_1|2]), (252,294,[3_1|2]), (252,163,[3_1|2]), (252,168,[0_1|2]), (252,173,[0_1|2]), (252,178,[2_1|2]), (252,183,[0_1|2]), (252,188,[2_1|2]), (252,193,[2_1|2]), (252,198,[0_1|2]), (252,203,[0_1|2]), (252,208,[2_1|2]), (252,213,[0_1|2]), (252,218,[0_1|2]), (252,223,[0_1|2]), (252,228,[3_1|2]), (252,233,[3_1|2]), (252,298,[1_1|3]), (252,303,[3_1|3]), (252,308,[0_1|3]), (252,313,[0_1|3]), (252,318,[2_1|3]), (253,254,[5_1|2]), (254,255,[1_1|2]), (255,256,[0_1|2]), (256,257,[0_1|2]), (257,127,[4_1|2]), (257,133,[4_1|2]), (257,138,[4_1|2]), (257,148,[4_1|2]), (257,153,[4_1|2]), (257,178,[4_1|2]), (257,188,[4_1|2]), (257,193,[4_1|2]), (257,208,[4_1|2]), (257,238,[4_1|2, 2_1|2]), (257,248,[4_1|2, 2_1|2]), (257,258,[4_1|2, 2_1|2]), (257,278,[4_1|2]), (257,243,[3_1|2]), (257,253,[0_1|2]), (257,263,[3_1|2]), (257,328,[2_1|3]), (257,333,[3_1|3]), (257,338,[2_1|3]), (258,259,[2_1|2]), (259,260,[1_1|2]), (260,261,[0_1|2]), (261,262,[4_1|2]), (262,127,[2_1|2]), (262,143,[2_1|2, 4_1|2]), (262,128,[1_1|2]), (262,133,[2_1|2]), (262,138,[2_1|2]), (262,148,[2_1|2]), (262,153,[2_1|2]), (262,343,[1_1|3]), (262,348,[2_1|3]), (262,353,[2_1|3]), (263,264,[2_1|2]), (264,265,[0_1|2]), (265,266,[3_1|2]), (266,267,[2_1|2]), (267,127,[0_1|2]), (267,143,[0_1|2]), (268,269,[0_1|2]), (269,270,[5_1|2]), (270,271,[0_1|2]), (271,272,[5_1|2]), (272,127,[4_1|2]), (272,288,[4_1|2]), (272,293,[4_1|2]), (272,238,[2_1|2]), (272,243,[3_1|2]), (272,248,[2_1|2]), (272,253,[0_1|2]), (272,258,[2_1|2]), (272,263,[3_1|2]), (272,328,[2_1|3]), (272,333,[3_1|3]), (272,338,[2_1|3]), (273,274,[2_1|2]), (274,275,[2_1|2]), (275,276,[1_1|2]), (276,277,[0_1|2]), (277,127,[1_1|2]), (277,288,[1_1|2]), (277,293,[1_1|2]), (277,268,[1_1|2]), (277,273,[1_1|2]), (277,278,[2_1|2]), (277,283,[1_1|2]), (278,279,[0_1|2]), (279,280,[1_1|2]), (280,281,[3_1|2]), (281,282,[1_1|2]), (282,127,[0_1|2]), (282,288,[0_1|2]), (282,293,[0_1|2]), (283,284,[2_1|2]), (284,285,[4_1|2]), (285,286,[0_1|2]), (286,287,[2_1|2]), (287,127,[1_1|2]), (287,288,[1_1|2]), (287,293,[1_1|2]), (287,268,[1_1|2]), (287,273,[1_1|2]), (287,278,[2_1|2]), (287,283,[1_1|2]), (288,289,[1_1|2]), (289,290,[0_1|2]), (290,291,[1_1|2]), (291,292,[2_1|2]), (292,127,[2_1|2]), (292,163,[2_1|2]), (292,228,[2_1|2]), (292,233,[2_1|2]), (292,243,[2_1|2]), (292,263,[2_1|2]), (292,128,[1_1|2]), (292,133,[2_1|2]), (292,138,[2_1|2]), (292,143,[4_1|2]), (292,148,[2_1|2]), (292,153,[2_1|2]), (292,343,[1_1|3]), (292,348,[2_1|3]), (292,353,[2_1|3]), (293,294,[1_1|2]), (294,295,[0_1|2]), (295,296,[4_1|2]), (296,297,[2_1|2]), (297,127,[2_1|2]), (297,143,[2_1|2, 4_1|2]), (297,128,[1_1|2]), (297,133,[2_1|2]), (297,138,[2_1|2]), (297,148,[2_1|2]), (297,153,[2_1|2]), (297,343,[1_1|3]), (297,348,[2_1|3]), (297,353,[2_1|3]), (298,299,[3_1|3]), (299,300,[2_1|3]), (300,301,[0_1|3]), (301,302,[0_1|3]), (302,288,[1_1|3]), (302,293,[1_1|3]), (303,304,[2_1|3]), (304,305,[0_1|3]), (305,306,[5_1|3]), (306,307,[3_1|3]), (307,288,[0_1|3]), (307,293,[0_1|3]), (308,309,[4_1|3]), (309,310,[2_1|3]), (310,311,[0_1|3]), (311,312,[0_1|3]), (312,289,[5_1|3]), (312,294,[5_1|3]), (313,314,[4_1|3]), (314,315,[2_1|3]), (315,316,[2_1|3]), (316,317,[3_1|3]), (317,289,[4_1|3]), (317,294,[4_1|3]), (318,319,[1_1|3]), (319,320,[4_1|3]), (320,321,[1_1|3]), (321,322,[0_1|3]), (322,289,[1_1|3]), (322,294,[1_1|3]), (323,324,[4_1|3]), (324,325,[0_1|3]), (325,326,[2_1|3]), (326,327,[2_1|3]), (327,133,[2_1|3]), (327,138,[2_1|3]), (327,148,[2_1|3]), (327,153,[2_1|3]), (327,178,[2_1|3]), (327,188,[2_1|3]), (327,193,[2_1|3]), (327,208,[2_1|3]), (327,238,[2_1|3]), (327,248,[2_1|3]), (327,258,[2_1|3]), (327,278,[2_1|3]), (327,274,[2_1|3]), (327,284,[2_1|3]), (328,329,[2_1|3]), (329,330,[1_1|3]), (330,331,[3_1|3]), (331,332,[2_1|3]), (332,288,[1_1|3]), (332,293,[1_1|3]), (333,334,[2_1|3]), (334,335,[0_1|3]), (335,336,[5_1|3]), (336,337,[0_1|3]), (337,288,[0_1|3]), (337,293,[0_1|3]), (338,339,[1_1|3]), (339,340,[0_1|3]), (340,341,[5_1|3]), (341,342,[3_1|3]), (342,289,[3_1|3]), (342,294,[3_1|3]), (343,344,[3_1|3]), (344,345,[3_1|3]), (345,346,[0_1|3]), (346,347,[1_1|3]), (347,288,[0_1|3]), (347,293,[0_1|3]), (348,349,[2_1|3]), (349,350,[0_1|3]), (350,351,[5_1|3]), (351,352,[0_1|3]), (352,288,[1_1|3]), (352,293,[1_1|3]), (353,354,[2_1|3]), (354,355,[2_1|3]), (355,356,[1_1|3]), (356,357,[2_1|3]), (357,289,[3_1|3]), (357,294,[3_1|3]), (358,359,[0_1|3]), (359,360,[5_1|3]), (360,361,[0_1|3]), (361,362,[5_1|3]), (362,288,[4_1|3]), (362,293,[4_1|3]), (363,364,[2_1|3]), (364,365,[2_1|3]), (365,366,[1_1|3]), (366,367,[0_1|3]), (367,288,[1_1|3]), (367,293,[1_1|3]), (368,369,[0_1|3]), (369,370,[1_1|3]), (370,371,[3_1|3]), (371,372,[1_1|3]), (372,288,[0_1|3]), (372,293,[0_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)