/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 42 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 30 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. "[101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 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] {(101,102,[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]), (101,103,[0_1|1, 2_1|1, 3_1|1, 4_1|1, 1_1|1, 5_1|1]), (101,104,[1_1|2]), (101,109,[2_1|2]), (101,114,[2_1|2]), (101,119,[4_1|2]), (101,124,[2_1|2]), (101,129,[2_1|2]), (101,134,[1_1|2]), (101,139,[3_1|2]), (101,144,[0_1|2]), (101,149,[0_1|2]), (101,154,[2_1|2]), (101,159,[0_1|2]), (101,164,[2_1|2]), (101,169,[2_1|2]), (101,174,[0_1|2]), (101,179,[0_1|2]), (101,184,[2_1|2]), (101,189,[0_1|2]), (101,194,[0_1|2]), (101,199,[0_1|2]), (101,204,[3_1|2]), (101,209,[3_1|2]), (101,214,[2_1|2]), (101,219,[3_1|2]), (101,224,[2_1|2]), (101,229,[0_1|2]), (101,234,[2_1|2]), (101,239,[3_1|2]), (101,244,[1_1|2]), (101,249,[1_1|2]), (101,254,[2_1|2]), (101,259,[1_1|2]), (101,264,[5_1|2]), (101,269,[5_1|2]), (102,102,[0_1|0, cons_2_1|0, cons_3_1|0, cons_4_1|0, cons_1_1|0, cons_5_1|0]), (103,102,[encArg_1|1]), (103,103,[0_1|1, 2_1|1, 3_1|1, 4_1|1, 1_1|1, 5_1|1]), (103,104,[1_1|2]), (103,109,[2_1|2]), (103,114,[2_1|2]), (103,119,[4_1|2]), (103,124,[2_1|2]), (103,129,[2_1|2]), (103,134,[1_1|2]), (103,139,[3_1|2]), (103,144,[0_1|2]), (103,149,[0_1|2]), (103,154,[2_1|2]), (103,159,[0_1|2]), (103,164,[2_1|2]), (103,169,[2_1|2]), (103,174,[0_1|2]), (103,179,[0_1|2]), (103,184,[2_1|2]), (103,189,[0_1|2]), (103,194,[0_1|2]), (103,199,[0_1|2]), (103,204,[3_1|2]), (103,209,[3_1|2]), (103,214,[2_1|2]), (103,219,[3_1|2]), (103,224,[2_1|2]), (103,229,[0_1|2]), (103,234,[2_1|2]), (103,239,[3_1|2]), (103,244,[1_1|2]), (103,249,[1_1|2]), (103,254,[2_1|2]), (103,259,[1_1|2]), (103,264,[5_1|2]), (103,269,[5_1|2]), (104,105,[3_1|2]), (105,106,[3_1|2]), (106,107,[0_1|2]), (107,108,[1_1|2]), (108,103,[0_1|2]), (108,264,[0_1|2]), (108,269,[0_1|2]), (109,110,[2_1|2]), (110,111,[0_1|2]), (111,112,[5_1|2]), (112,113,[0_1|2]), (113,103,[1_1|2]), (113,264,[1_1|2]), (113,269,[1_1|2]), (113,244,[1_1|2]), (113,249,[1_1|2]), (113,254,[2_1|2]), (113,259,[1_1|2]), (114,115,[2_1|2]), (115,116,[2_1|2]), (116,117,[1_1|2]), (117,118,[2_1|2]), (118,103,[3_1|2]), (118,104,[3_1|2]), (118,134,[3_1|2, 1_1|2]), (118,244,[3_1|2]), (118,249,[3_1|2]), (118,259,[3_1|2]), (118,265,[3_1|2]), (118,270,[3_1|2]), (118,139,[3_1|2]), (118,144,[0_1|2]), (118,149,[0_1|2]), (118,154,[2_1|2]), (118,159,[0_1|2]), (118,164,[2_1|2]), (118,169,[2_1|2]), (118,174,[0_1|2]), (118,179,[0_1|2]), (118,184,[2_1|2]), (118,189,[0_1|2]), (118,194,[0_1|2]), (118,199,[0_1|2]), (118,204,[3_1|2]), (118,209,[3_1|2]), (118,298,[1_1|3]), (118,303,[3_1|3]), (118,308,[0_1|3]), (118,313,[0_1|3]), (118,318,[2_1|3]), (119,120,[0_1|2]), (120,121,[2_1|2]), (121,122,[2_1|2]), (122,123,[3_1|2]), (123,103,[3_1|2]), (123,109,[3_1|2]), (123,114,[3_1|2]), (123,124,[3_1|2]), (123,129,[3_1|2]), (123,154,[3_1|2, 2_1|2]), (123,164,[3_1|2, 2_1|2]), (123,169,[3_1|2, 2_1|2]), (123,184,[3_1|2, 2_1|2]), (123,214,[3_1|2]), (123,224,[3_1|2]), (123,234,[3_1|2]), (123,254,[3_1|2]), (123,134,[1_1|2]), (123,139,[3_1|2]), (123,144,[0_1|2]), (123,149,[0_1|2]), (123,159,[0_1|2]), (123,174,[0_1|2]), (123,179,[0_1|2]), (123,189,[0_1|2]), (123,194,[0_1|2]), (123,199,[0_1|2]), (123,204,[3_1|2]), (123,209,[3_1|2]), (123,298,[1_1|3]), (123,303,[3_1|3]), (123,308,[0_1|3]), (123,313,[0_1|3]), (123,318,[2_1|3]), (124,125,[0_1|2]), (125,126,[4_1|2]), (126,127,[1_1|2]), (127,128,[3_1|2]), (128,103,[3_1|2]), (128,139,[3_1|2]), (128,204,[3_1|2]), (128,209,[3_1|2]), (128,219,[3_1|2]), (128,239,[3_1|2]), (128,134,[1_1|2]), (128,144,[0_1|2]), (128,149,[0_1|2]), (128,154,[2_1|2]), (128,159,[0_1|2]), (128,164,[2_1|2]), (128,169,[2_1|2]), (128,174,[0_1|2]), (128,179,[0_1|2]), (128,184,[2_1|2]), (128,189,[0_1|2]), (128,194,[0_1|2]), (128,199,[0_1|2]), (128,298,[1_1|3]), (128,303,[3_1|3]), (128,308,[0_1|3]), (128,313,[0_1|3]), (128,318,[2_1|3]), (129,130,[0_1|2]), (130,131,[5_1|2]), (131,132,[1_1|2]), (132,133,[0_1|2]), (133,103,[1_1|2]), (133,119,[1_1|2]), (133,244,[1_1|2]), (133,249,[1_1|2]), (133,254,[2_1|2]), (133,259,[1_1|2]), (134,135,[3_1|2]), (135,136,[2_1|2]), (136,137,[0_1|2]), (137,138,[0_1|2]), (138,103,[1_1|2]), (138,264,[1_1|2]), (138,269,[1_1|2]), (138,244,[1_1|2]), (138,249,[1_1|2]), (138,254,[2_1|2]), (138,259,[1_1|2]), (139,140,[2_1|2]), (140,141,[0_1|2]), (141,142,[5_1|2]), (142,143,[3_1|2]), (143,103,[0_1|2]), (143,264,[0_1|2]), (143,269,[0_1|2]), (144,145,[4_1|2]), (145,146,[2_1|2]), (146,147,[0_1|2]), (147,148,[0_1|2]), (148,103,[5_1|2]), (148,104,[5_1|2]), (148,134,[5_1|2]), (148,244,[5_1|2]), (148,249,[5_1|2]), (148,259,[5_1|2]), (148,265,[5_1|2]), (148,270,[5_1|2]), (148,264,[5_1|2]), (148,269,[5_1|2]), (149,150,[4_1|2]), (150,151,[2_1|2]), (151,152,[2_1|2]), (152,153,[3_1|2]), (152,209,[3_1|2]), (152,323,[3_1|3]), (153,103,[4_1|2]), (153,104,[4_1|2]), (153,134,[4_1|2]), (153,244,[4_1|2]), (153,249,[4_1|2]), (153,259,[4_1|2]), (153,265,[4_1|2]), (153,270,[4_1|2]), (153,214,[2_1|2]), (153,219,[3_1|2]), (153,224,[2_1|2]), (153,229,[0_1|2]), (153,234,[2_1|2]), (153,239,[3_1|2]), (153,328,[2_1|3]), (153,333,[3_1|3]), (153,338,[2_1|3]), (154,155,[1_1|2]), (155,156,[4_1|2]), (156,157,[1_1|2]), (157,158,[0_1|2]), (158,103,[1_1|2]), (158,104,[1_1|2]), (158,134,[1_1|2]), (158,244,[1_1|2]), (158,249,[1_1|2]), (158,259,[1_1|2]), (158,265,[1_1|2]), (158,270,[1_1|2]), (158,254,[2_1|2]), (159,160,[4_1|2]), (160,161,[3_1|2]), (161,162,[2_1|2]), (162,163,[2_1|2]), (163,103,[2_1|2]), (163,109,[2_1|2]), (163,114,[2_1|2]), (163,124,[2_1|2]), (163,129,[2_1|2]), (163,154,[2_1|2]), (163,164,[2_1|2]), (163,169,[2_1|2]), (163,184,[2_1|2]), (163,214,[2_1|2]), (163,224,[2_1|2]), (163,234,[2_1|2]), (163,254,[2_1|2]), (163,104,[1_1|2]), (163,119,[4_1|2]), (163,343,[1_1|3]), (163,348,[2_1|3]), (163,353,[2_1|3]), (164,165,[0_1|2]), (165,166,[2_1|2]), (166,167,[2_1|2]), (167,168,[3_1|2]), (168,103,[0_1|2]), (168,109,[0_1|2]), (168,114,[0_1|2]), (168,124,[0_1|2]), (168,129,[0_1|2]), (168,154,[0_1|2]), (168,164,[0_1|2]), (168,169,[0_1|2]), (168,184,[0_1|2]), (168,214,[0_1|2]), (168,224,[0_1|2]), (168,234,[0_1|2]), (168,254,[0_1|2]), (169,170,[3_1|2]), (170,171,[3_1|2]), (171,172,[2_1|2]), (172,173,[1_1|2]), (172,244,[1_1|2]), (172,249,[1_1|2]), (172,254,[2_1|2]), (172,358,[1_1|3]), (172,363,[1_1|3]), (172,368,[2_1|3]), (173,103,[2_1|2]), (173,109,[2_1|2]), (173,114,[2_1|2]), (173,124,[2_1|2]), (173,129,[2_1|2]), (173,154,[2_1|2]), (173,164,[2_1|2]), (173,169,[2_1|2]), (173,184,[2_1|2]), (173,214,[2_1|2]), (173,224,[2_1|2]), (173,234,[2_1|2]), (173,254,[2_1|2]), (173,104,[1_1|2]), (173,119,[4_1|2]), (173,343,[1_1|3]), (173,348,[2_1|3]), (173,353,[2_1|3]), (174,175,[2_1|2]), (175,176,[4_1|2]), (176,177,[3_1|2]), (177,178,[3_1|2]), (178,103,[0_1|2]), (178,139,[0_1|2]), (178,204,[0_1|2]), (178,209,[0_1|2]), (178,219,[0_1|2]), (178,239,[0_1|2]), (179,180,[5_1|2]), (180,181,[4_1|2]), (181,182,[3_1|2]), (182,183,[3_1|2]), (183,103,[0_1|2]), (183,139,[0_1|2]), (183,204,[0_1|2]), (183,209,[0_1|2]), (183,219,[0_1|2]), (183,239,[0_1|2]), (184,185,[3_1|2]), (185,186,[4_1|2]), (186,187,[0_1|2]), (187,188,[4_1|2]), (188,103,[2_1|2]), (188,139,[2_1|2]), (188,204,[2_1|2]), (188,209,[2_1|2]), (188,219,[2_1|2]), (188,239,[2_1|2]), (188,104,[1_1|2]), (188,109,[2_1|2]), (188,114,[2_1|2]), (188,119,[4_1|2]), (188,124,[2_1|2]), (188,129,[2_1|2]), (188,343,[1_1|3]), (188,348,[2_1|3]), (188,353,[2_1|3]), (189,190,[2_1|2]), (190,191,[0_1|2]), (191,192,[5_1|2]), (192,193,[0_1|2]), (193,103,[0_1|2]), (193,119,[0_1|2]), (194,195,[5_1|2]), (195,196,[0_1|2]), (196,197,[0_1|2]), (197,198,[1_1|2]), (197,244,[1_1|2]), (197,249,[1_1|2]), (197,254,[2_1|2]), (197,358,[1_1|3]), (197,363,[1_1|3]), (197,368,[2_1|3]), (198,103,[2_1|2]), (198,119,[2_1|2, 4_1|2]), (198,104,[1_1|2]), (198,109,[2_1|2]), (198,114,[2_1|2]), (198,124,[2_1|2]), (198,129,[2_1|2]), (198,343,[1_1|3]), (198,348,[2_1|3]), (198,353,[2_1|3]), (199,200,[5_1|2]), (200,201,[4_1|2]), (201,202,[1_1|2]), (202,203,[0_1|2]), (203,103,[5_1|2]), (203,264,[5_1|2]), (203,269,[5_1|2]), (204,205,[2_1|2]), (205,206,[0_1|2]), (206,207,[1_1|2]), (207,208,[0_1|2]), (208,103,[5_1|2]), (208,264,[5_1|2]), (208,269,[5_1|2]), (209,210,[4_1|2]), (210,211,[0_1|2]), (211,212,[2_1|2]), (212,213,[2_1|2]), (213,103,[2_1|2]), (213,109,[2_1|2]), (213,114,[2_1|2]), (213,124,[2_1|2]), (213,129,[2_1|2]), (213,154,[2_1|2]), (213,164,[2_1|2]), (213,169,[2_1|2]), (213,184,[2_1|2]), (213,214,[2_1|2]), (213,224,[2_1|2]), (213,234,[2_1|2]), (213,254,[2_1|2]), (213,104,[1_1|2]), (213,119,[4_1|2]), (213,343,[1_1|3]), (213,348,[2_1|3]), (213,353,[2_1|3]), (214,215,[2_1|2]), (215,216,[1_1|2]), (216,217,[3_1|2]), (217,218,[2_1|2]), (218,103,[1_1|2]), (218,264,[1_1|2]), (218,269,[1_1|2]), (218,244,[1_1|2]), (218,249,[1_1|2]), (218,254,[2_1|2]), (218,259,[1_1|2]), (219,220,[2_1|2]), (220,221,[0_1|2]), (221,222,[5_1|2]), (222,223,[0_1|2]), (223,103,[0_1|2]), (223,264,[0_1|2]), (223,269,[0_1|2]), (224,225,[1_1|2]), (225,226,[0_1|2]), (226,227,[5_1|2]), (227,228,[3_1|2]), (228,103,[3_1|2]), (228,104,[3_1|2]), (228,134,[3_1|2, 1_1|2]), (228,244,[3_1|2]), (228,249,[3_1|2]), (228,259,[3_1|2]), (228,265,[3_1|2]), (228,270,[3_1|2]), (228,139,[3_1|2]), (228,144,[0_1|2]), (228,149,[0_1|2]), (228,154,[2_1|2]), (228,159,[0_1|2]), (228,164,[2_1|2]), (228,169,[2_1|2]), (228,174,[0_1|2]), (228,179,[0_1|2]), (228,184,[2_1|2]), (228,189,[0_1|2]), (228,194,[0_1|2]), (228,199,[0_1|2]), (228,204,[3_1|2]), (228,209,[3_1|2]), (228,298,[1_1|3]), (228,303,[3_1|3]), (228,308,[0_1|3]), (228,313,[0_1|3]), (228,318,[2_1|3]), (229,230,[5_1|2]), (230,231,[1_1|2]), (231,232,[0_1|2]), (232,233,[0_1|2]), (233,103,[4_1|2]), (233,109,[4_1|2]), (233,114,[4_1|2]), (233,124,[4_1|2]), (233,129,[4_1|2]), (233,154,[4_1|2]), (233,164,[4_1|2]), (233,169,[4_1|2]), (233,184,[4_1|2]), (233,214,[4_1|2, 2_1|2]), (233,224,[4_1|2, 2_1|2]), (233,234,[4_1|2, 2_1|2]), (233,254,[4_1|2]), (233,219,[3_1|2]), (233,229,[0_1|2]), (233,239,[3_1|2]), (233,328,[2_1|3]), (233,333,[3_1|3]), (233,338,[2_1|3]), (234,235,[2_1|2]), (235,236,[1_1|2]), (236,237,[0_1|2]), (237,238,[4_1|2]), (238,103,[2_1|2]), (238,119,[2_1|2, 4_1|2]), (238,104,[1_1|2]), (238,109,[2_1|2]), (238,114,[2_1|2]), (238,124,[2_1|2]), (238,129,[2_1|2]), (238,343,[1_1|3]), (238,348,[2_1|3]), (238,353,[2_1|3]), (239,240,[2_1|2]), (240,241,[0_1|2]), (241,242,[3_1|2]), (242,243,[2_1|2]), (243,103,[0_1|2]), (243,119,[0_1|2]), (244,245,[0_1|2]), (245,246,[5_1|2]), (246,247,[0_1|2]), (247,248,[5_1|2]), (248,103,[4_1|2]), (248,264,[4_1|2]), (248,269,[4_1|2]), (248,214,[2_1|2]), (248,219,[3_1|2]), (248,224,[2_1|2]), (248,229,[0_1|2]), (248,234,[2_1|2]), (248,239,[3_1|2]), (248,328,[2_1|3]), (248,333,[3_1|3]), (248,338,[2_1|3]), (249,250,[2_1|2]), (250,251,[2_1|2]), (251,252,[1_1|2]), (252,253,[0_1|2]), (253,103,[1_1|2]), (253,264,[1_1|2]), (253,269,[1_1|2]), (253,244,[1_1|2]), (253,249,[1_1|2]), (253,254,[2_1|2]), (253,259,[1_1|2]), (254,255,[0_1|2]), (255,256,[1_1|2]), (256,257,[3_1|2]), (257,258,[1_1|2]), (258,103,[0_1|2]), (258,264,[0_1|2]), (258,269,[0_1|2]), (259,260,[2_1|2]), (260,261,[4_1|2]), (261,262,[0_1|2]), (262,263,[2_1|2]), (263,103,[1_1|2]), (263,264,[1_1|2]), (263,269,[1_1|2]), (263,244,[1_1|2]), (263,249,[1_1|2]), (263,254,[2_1|2]), (263,259,[1_1|2]), (264,265,[1_1|2]), (265,266,[0_1|2]), (266,267,[1_1|2]), (267,268,[2_1|2]), (268,103,[2_1|2]), (268,139,[2_1|2]), (268,204,[2_1|2]), (268,209,[2_1|2]), (268,219,[2_1|2]), (268,239,[2_1|2]), (268,104,[1_1|2]), (268,109,[2_1|2]), (268,114,[2_1|2]), (268,119,[4_1|2]), (268,124,[2_1|2]), (268,129,[2_1|2]), (268,343,[1_1|3]), (268,348,[2_1|3]), (268,353,[2_1|3]), (269,270,[1_1|2]), (270,271,[0_1|2]), (271,272,[4_1|2]), (272,273,[2_1|2]), (273,103,[2_1|2]), (273,119,[2_1|2, 4_1|2]), (273,104,[1_1|2]), (273,109,[2_1|2]), (273,114,[2_1|2]), (273,124,[2_1|2]), (273,129,[2_1|2]), (273,343,[1_1|3]), (273,348,[2_1|3]), (273,353,[2_1|3]), (298,299,[3_1|3]), (299,300,[2_1|3]), (300,301,[0_1|3]), (301,302,[0_1|3]), (302,264,[1_1|3]), (302,269,[1_1|3]), (303,304,[2_1|3]), (304,305,[0_1|3]), (305,306,[5_1|3]), (306,307,[3_1|3]), (307,264,[0_1|3]), (307,269,[0_1|3]), (308,309,[4_1|3]), (309,310,[2_1|3]), (310,311,[0_1|3]), (311,312,[0_1|3]), (312,265,[5_1|3]), (312,270,[5_1|3]), (313,314,[4_1|3]), (314,315,[2_1|3]), (315,316,[2_1|3]), (316,317,[3_1|3]), (317,265,[4_1|3]), (317,270,[4_1|3]), (318,319,[1_1|3]), (319,320,[4_1|3]), (320,321,[1_1|3]), (321,322,[0_1|3]), (322,265,[1_1|3]), (322,270,[1_1|3]), (323,324,[4_1|3]), (324,325,[0_1|3]), (325,326,[2_1|3]), (326,327,[2_1|3]), (327,109,[2_1|3]), (327,114,[2_1|3]), (327,124,[2_1|3]), (327,129,[2_1|3]), (327,154,[2_1|3]), (327,164,[2_1|3]), (327,169,[2_1|3]), (327,184,[2_1|3]), (327,214,[2_1|3]), (327,224,[2_1|3]), (327,234,[2_1|3]), (327,254,[2_1|3]), (327,250,[2_1|3]), (327,260,[2_1|3]), (328,329,[2_1|3]), (329,330,[1_1|3]), (330,331,[3_1|3]), (331,332,[2_1|3]), (332,264,[1_1|3]), (332,269,[1_1|3]), (333,334,[2_1|3]), (334,335,[0_1|3]), (335,336,[5_1|3]), (336,337,[0_1|3]), (337,264,[0_1|3]), (337,269,[0_1|3]), (338,339,[1_1|3]), (339,340,[0_1|3]), (340,341,[5_1|3]), (341,342,[3_1|3]), (342,265,[3_1|3]), (342,270,[3_1|3]), (343,344,[3_1|3]), (344,345,[3_1|3]), (345,346,[0_1|3]), (346,347,[1_1|3]), (347,264,[0_1|3]), (347,269,[0_1|3]), (348,349,[2_1|3]), (349,350,[0_1|3]), (350,351,[5_1|3]), (351,352,[0_1|3]), (352,264,[1_1|3]), (352,269,[1_1|3]), (353,354,[2_1|3]), (354,355,[2_1|3]), (355,356,[1_1|3]), (356,357,[2_1|3]), (357,265,[3_1|3]), (357,270,[3_1|3]), (358,359,[0_1|3]), (359,360,[5_1|3]), (360,361,[0_1|3]), (361,362,[5_1|3]), (362,264,[4_1|3]), (362,269,[4_1|3]), (363,364,[2_1|3]), (364,365,[2_1|3]), (365,366,[1_1|3]), (366,367,[0_1|3]), (367,264,[1_1|3]), (367,269,[1_1|3]), (368,369,[0_1|3]), (369,370,[1_1|3]), (370,371,[3_1|3]), (371,372,[1_1|3]), (372,264,[0_1|3]), (372,269,[0_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)