/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 56 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 40 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(x1))) -> 1(0(0(2(x1)))) 0(1(2(x1))) -> 1(0(3(2(x1)))) 0(1(2(x1))) -> 1(0(0(3(2(x1))))) 0(1(2(x1))) -> 4(5(1(0(2(x1))))) 0(5(2(x1))) -> 5(0(0(2(x1)))) 0(5(2(x1))) -> 5(5(0(2(x1)))) 0(5(2(x1))) -> 5(0(3(3(2(x1))))) 0(5(3(x1))) -> 5(0(0(3(x1)))) 0(5(3(x1))) -> 5(5(0(3(x1)))) 0(0(5(2(x1)))) -> 0(2(0(3(5(5(x1)))))) 0(1(2(3(x1)))) -> 1(3(2(0(3(x1))))) 0(1(2(4(x1)))) -> 4(5(1(0(2(x1))))) 0(1(4(2(x1)))) -> 4(4(1(0(2(x1))))) 0(4(1(2(x1)))) -> 0(4(5(5(1(2(x1)))))) 0(5(2(3(x1)))) -> 5(0(3(2(3(x1))))) 1(2(1(2(x1)))) -> 1(1(5(2(2(x1))))) 4(0(1(2(x1)))) -> 4(1(0(0(2(x1))))) 4(3(0(2(x1)))) -> 4(0(0(3(2(x1))))) 4(3(1(2(x1)))) -> 3(2(5(4(1(1(x1)))))) 0(0(1(2(3(x1))))) -> 3(2(1(0(0(3(x1)))))) 0(0(1(3(2(x1))))) -> 1(0(2(0(0(3(x1)))))) 0(0(1(3(3(x1))))) -> 0(0(3(1(0(3(x1)))))) 0(0(1(5(2(x1))))) -> 1(5(0(0(3(2(x1)))))) 0(1(2(1(2(x1))))) -> 1(1(0(2(2(2(x1)))))) 0(1(4(5(2(x1))))) -> 4(1(0(3(2(5(x1)))))) 0(5(0(1(2(x1))))) -> 1(2(0(1(5(0(x1)))))) 0(5(1(0(2(x1))))) -> 1(5(0(0(3(2(x1)))))) 0(5(1(4(3(x1))))) -> 1(0(3(5(4(5(x1)))))) 0(5(1(4(3(x1))))) -> 4(5(5(1(0(3(x1)))))) 0(5(3(1(2(x1))))) -> 0(1(5(0(2(3(x1)))))) 0(5(3(1(2(x1))))) -> 5(0(1(4(3(2(x1)))))) 0(5(3(4(2(x1))))) -> 3(2(0(3(5(4(x1)))))) 0(5(4(3(2(x1))))) -> 0(0(4(3(2(5(x1)))))) 1(2(5(2(3(x1))))) -> 5(1(2(3(3(2(x1)))))) 1(3(0(5(2(x1))))) -> 0(5(1(0(3(2(x1)))))) 1(3(0(5(2(x1))))) -> 1(3(0(0(2(5(x1)))))) 1(3(3(4(2(x1))))) -> 5(1(3(3(2(4(x1)))))) 4(3(0(2(3(x1))))) -> 0(3(3(3(2(4(x1)))))) 4(3(0(5(3(x1))))) -> 5(4(3(5(0(3(x1)))))) 4(3(3(1(2(x1))))) -> 1(3(0(4(3(2(x1)))))) 5(2(3(0(2(x1))))) -> 4(5(0(2(3(2(x1)))))) 5(2(3(1(2(x1))))) -> 2(3(2(4(1(5(x1)))))) 5(3(0(2(2(x1))))) -> 5(3(3(2(0(2(x1)))))) 5(3(0(5(2(x1))))) -> 5(5(3(0(2(4(x1)))))) 5(3(1(2(2(x1))))) -> 5(1(3(2(2(2(x1)))))) 5(3(1(5(2(x1))))) -> 2(5(5(1(5(3(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(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(x1))) -> 1(0(0(2(x1)))) 0(1(2(x1))) -> 1(0(3(2(x1)))) 0(1(2(x1))) -> 1(0(0(3(2(x1))))) 0(1(2(x1))) -> 4(5(1(0(2(x1))))) 0(5(2(x1))) -> 5(0(0(2(x1)))) 0(5(2(x1))) -> 5(5(0(2(x1)))) 0(5(2(x1))) -> 5(0(3(3(2(x1))))) 0(5(3(x1))) -> 5(0(0(3(x1)))) 0(5(3(x1))) -> 5(5(0(3(x1)))) 0(0(5(2(x1)))) -> 0(2(0(3(5(5(x1)))))) 0(1(2(3(x1)))) -> 1(3(2(0(3(x1))))) 0(1(2(4(x1)))) -> 4(5(1(0(2(x1))))) 0(1(4(2(x1)))) -> 4(4(1(0(2(x1))))) 0(4(1(2(x1)))) -> 0(4(5(5(1(2(x1)))))) 0(5(2(3(x1)))) -> 5(0(3(2(3(x1))))) 1(2(1(2(x1)))) -> 1(1(5(2(2(x1))))) 4(0(1(2(x1)))) -> 4(1(0(0(2(x1))))) 4(3(0(2(x1)))) -> 4(0(0(3(2(x1))))) 4(3(1(2(x1)))) -> 3(2(5(4(1(1(x1)))))) 0(0(1(2(3(x1))))) -> 3(2(1(0(0(3(x1)))))) 0(0(1(3(2(x1))))) -> 1(0(2(0(0(3(x1)))))) 0(0(1(3(3(x1))))) -> 0(0(3(1(0(3(x1)))))) 0(0(1(5(2(x1))))) -> 1(5(0(0(3(2(x1)))))) 0(1(2(1(2(x1))))) -> 1(1(0(2(2(2(x1)))))) 0(1(4(5(2(x1))))) -> 4(1(0(3(2(5(x1)))))) 0(5(0(1(2(x1))))) -> 1(2(0(1(5(0(x1)))))) 0(5(1(0(2(x1))))) -> 1(5(0(0(3(2(x1)))))) 0(5(1(4(3(x1))))) -> 1(0(3(5(4(5(x1)))))) 0(5(1(4(3(x1))))) -> 4(5(5(1(0(3(x1)))))) 0(5(3(1(2(x1))))) -> 0(1(5(0(2(3(x1)))))) 0(5(3(1(2(x1))))) -> 5(0(1(4(3(2(x1)))))) 0(5(3(4(2(x1))))) -> 3(2(0(3(5(4(x1)))))) 0(5(4(3(2(x1))))) -> 0(0(4(3(2(5(x1)))))) 1(2(5(2(3(x1))))) -> 5(1(2(3(3(2(x1)))))) 1(3(0(5(2(x1))))) -> 0(5(1(0(3(2(x1)))))) 1(3(0(5(2(x1))))) -> 1(3(0(0(2(5(x1)))))) 1(3(3(4(2(x1))))) -> 5(1(3(3(2(4(x1)))))) 4(3(0(2(3(x1))))) -> 0(3(3(3(2(4(x1)))))) 4(3(0(5(3(x1))))) -> 5(4(3(5(0(3(x1)))))) 4(3(3(1(2(x1))))) -> 1(3(0(4(3(2(x1)))))) 5(2(3(0(2(x1))))) -> 4(5(0(2(3(2(x1)))))) 5(2(3(1(2(x1))))) -> 2(3(2(4(1(5(x1)))))) 5(3(0(2(2(x1))))) -> 5(3(3(2(0(2(x1)))))) 5(3(0(5(2(x1))))) -> 5(5(3(0(2(4(x1)))))) 5(3(1(2(2(x1))))) -> 5(1(3(2(2(2(x1)))))) 5(3(1(5(2(x1))))) -> 2(5(5(1(5(3(x1)))))) The (relative) TRS S consists of the following rules: encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(x1))) -> 1(0(0(2(x1)))) 0(1(2(x1))) -> 1(0(3(2(x1)))) 0(1(2(x1))) -> 1(0(0(3(2(x1))))) 0(1(2(x1))) -> 4(5(1(0(2(x1))))) 0(5(2(x1))) -> 5(0(0(2(x1)))) 0(5(2(x1))) -> 5(5(0(2(x1)))) 0(5(2(x1))) -> 5(0(3(3(2(x1))))) 0(5(3(x1))) -> 5(0(0(3(x1)))) 0(5(3(x1))) -> 5(5(0(3(x1)))) 0(0(5(2(x1)))) -> 0(2(0(3(5(5(x1)))))) 0(1(2(3(x1)))) -> 1(3(2(0(3(x1))))) 0(1(2(4(x1)))) -> 4(5(1(0(2(x1))))) 0(1(4(2(x1)))) -> 4(4(1(0(2(x1))))) 0(4(1(2(x1)))) -> 0(4(5(5(1(2(x1)))))) 0(5(2(3(x1)))) -> 5(0(3(2(3(x1))))) 1(2(1(2(x1)))) -> 1(1(5(2(2(x1))))) 4(0(1(2(x1)))) -> 4(1(0(0(2(x1))))) 4(3(0(2(x1)))) -> 4(0(0(3(2(x1))))) 4(3(1(2(x1)))) -> 3(2(5(4(1(1(x1)))))) 0(0(1(2(3(x1))))) -> 3(2(1(0(0(3(x1)))))) 0(0(1(3(2(x1))))) -> 1(0(2(0(0(3(x1)))))) 0(0(1(3(3(x1))))) -> 0(0(3(1(0(3(x1)))))) 0(0(1(5(2(x1))))) -> 1(5(0(0(3(2(x1)))))) 0(1(2(1(2(x1))))) -> 1(1(0(2(2(2(x1)))))) 0(1(4(5(2(x1))))) -> 4(1(0(3(2(5(x1)))))) 0(5(0(1(2(x1))))) -> 1(2(0(1(5(0(x1)))))) 0(5(1(0(2(x1))))) -> 1(5(0(0(3(2(x1)))))) 0(5(1(4(3(x1))))) -> 1(0(3(5(4(5(x1)))))) 0(5(1(4(3(x1))))) -> 4(5(5(1(0(3(x1)))))) 0(5(3(1(2(x1))))) -> 0(1(5(0(2(3(x1)))))) 0(5(3(1(2(x1))))) -> 5(0(1(4(3(2(x1)))))) 0(5(3(4(2(x1))))) -> 3(2(0(3(5(4(x1)))))) 0(5(4(3(2(x1))))) -> 0(0(4(3(2(5(x1)))))) 1(2(5(2(3(x1))))) -> 5(1(2(3(3(2(x1)))))) 1(3(0(5(2(x1))))) -> 0(5(1(0(3(2(x1)))))) 1(3(0(5(2(x1))))) -> 1(3(0(0(2(5(x1)))))) 1(3(3(4(2(x1))))) -> 5(1(3(3(2(4(x1)))))) 4(3(0(2(3(x1))))) -> 0(3(3(3(2(4(x1)))))) 4(3(0(5(3(x1))))) -> 5(4(3(5(0(3(x1)))))) 4(3(3(1(2(x1))))) -> 1(3(0(4(3(2(x1)))))) 5(2(3(0(2(x1))))) -> 4(5(0(2(3(2(x1)))))) 5(2(3(1(2(x1))))) -> 2(3(2(4(1(5(x1)))))) 5(3(0(2(2(x1))))) -> 5(3(3(2(0(2(x1)))))) 5(3(0(5(2(x1))))) -> 5(5(3(0(2(4(x1)))))) 5(3(1(2(2(x1))))) -> 5(1(3(2(2(2(x1)))))) 5(3(1(5(2(x1))))) -> 2(5(5(1(5(3(x1)))))) The (relative) TRS S consists of the following rules: encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(2(x1))) -> 1(0(0(2(x1)))) 0(1(2(x1))) -> 1(0(3(2(x1)))) 0(1(2(x1))) -> 1(0(0(3(2(x1))))) 0(1(2(x1))) -> 4(5(1(0(2(x1))))) 0(5(2(x1))) -> 5(0(0(2(x1)))) 0(5(2(x1))) -> 5(5(0(2(x1)))) 0(5(2(x1))) -> 5(0(3(3(2(x1))))) 0(5(3(x1))) -> 5(0(0(3(x1)))) 0(5(3(x1))) -> 5(5(0(3(x1)))) 0(0(5(2(x1)))) -> 0(2(0(3(5(5(x1)))))) 0(1(2(3(x1)))) -> 1(3(2(0(3(x1))))) 0(1(2(4(x1)))) -> 4(5(1(0(2(x1))))) 0(1(4(2(x1)))) -> 4(4(1(0(2(x1))))) 0(4(1(2(x1)))) -> 0(4(5(5(1(2(x1)))))) 0(5(2(3(x1)))) -> 5(0(3(2(3(x1))))) 1(2(1(2(x1)))) -> 1(1(5(2(2(x1))))) 4(0(1(2(x1)))) -> 4(1(0(0(2(x1))))) 4(3(0(2(x1)))) -> 4(0(0(3(2(x1))))) 4(3(1(2(x1)))) -> 3(2(5(4(1(1(x1)))))) 0(0(1(2(3(x1))))) -> 3(2(1(0(0(3(x1)))))) 0(0(1(3(2(x1))))) -> 1(0(2(0(0(3(x1)))))) 0(0(1(3(3(x1))))) -> 0(0(3(1(0(3(x1)))))) 0(0(1(5(2(x1))))) -> 1(5(0(0(3(2(x1)))))) 0(1(2(1(2(x1))))) -> 1(1(0(2(2(2(x1)))))) 0(1(4(5(2(x1))))) -> 4(1(0(3(2(5(x1)))))) 0(5(0(1(2(x1))))) -> 1(2(0(1(5(0(x1)))))) 0(5(1(0(2(x1))))) -> 1(5(0(0(3(2(x1)))))) 0(5(1(4(3(x1))))) -> 1(0(3(5(4(5(x1)))))) 0(5(1(4(3(x1))))) -> 4(5(5(1(0(3(x1)))))) 0(5(3(1(2(x1))))) -> 0(1(5(0(2(3(x1)))))) 0(5(3(1(2(x1))))) -> 5(0(1(4(3(2(x1)))))) 0(5(3(4(2(x1))))) -> 3(2(0(3(5(4(x1)))))) 0(5(4(3(2(x1))))) -> 0(0(4(3(2(5(x1)))))) 1(2(5(2(3(x1))))) -> 5(1(2(3(3(2(x1)))))) 1(3(0(5(2(x1))))) -> 0(5(1(0(3(2(x1)))))) 1(3(0(5(2(x1))))) -> 1(3(0(0(2(5(x1)))))) 1(3(3(4(2(x1))))) -> 5(1(3(3(2(4(x1)))))) 4(3(0(2(3(x1))))) -> 0(3(3(3(2(4(x1)))))) 4(3(0(5(3(x1))))) -> 5(4(3(5(0(3(x1)))))) 4(3(3(1(2(x1))))) -> 1(3(0(4(3(2(x1)))))) 5(2(3(0(2(x1))))) -> 4(5(0(2(3(2(x1)))))) 5(2(3(1(2(x1))))) -> 2(3(2(4(1(5(x1)))))) 5(3(0(2(2(x1))))) -> 5(3(3(2(0(2(x1)))))) 5(3(0(5(2(x1))))) -> 5(5(3(0(2(4(x1)))))) 5(3(1(2(2(x1))))) -> 5(1(3(2(2(2(x1)))))) 5(3(1(5(2(x1))))) -> 2(5(5(1(5(3(x1)))))) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (7) CpxTrsMatchBoundsProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. The certificate found is represented by the following graph. "[97, 98, 99, 100, 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, 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] {(97,98,[0_1|0, 1_1|0, 4_1|0, 5_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (97,99,[2_1|1, 3_1|1, 0_1|1, 1_1|1, 4_1|1, 5_1|1]), (97,100,[1_1|2]), (97,103,[1_1|2]), (97,106,[1_1|2]), (97,110,[4_1|2]), (97,114,[1_1|2]), (97,118,[1_1|2]), (97,123,[4_1|2]), (97,127,[4_1|2]), (97,132,[5_1|2]), (97,135,[5_1|2]), (97,138,[5_1|2]), (97,142,[5_1|2]), (97,146,[5_1|2]), (97,149,[5_1|2]), (97,152,[0_1|2]), (97,157,[5_1|2]), (97,162,[3_1|2]), (97,167,[1_1|2]), (97,172,[1_1|2]), (97,177,[1_1|2]), (97,182,[4_1|2]), (97,187,[0_1|2]), (97,192,[0_1|2]), (97,197,[3_1|2]), (97,202,[1_1|2]), (97,207,[0_1|2]), (97,212,[0_1|2]), (97,217,[1_1|2]), (97,221,[5_1|2]), (97,226,[0_1|2]), (97,231,[1_1|2]), (97,236,[5_1|2]), (97,241,[4_1|2]), (97,245,[4_1|2]), (97,249,[0_1|2]), (97,254,[5_1|2]), (97,259,[3_1|2]), (97,264,[1_1|2]), (97,269,[4_1|2]), (97,274,[2_1|2]), (97,279,[5_1|2]), (97,284,[5_1|2]), (97,289,[5_1|2]), (97,294,[2_1|2]), (97,299,[4_1|2]), (98,98,[2_1|0, 3_1|0, cons_0_1|0, cons_1_1|0, cons_4_1|0, cons_5_1|0]), (99,98,[encArg_1|1]), (99,99,[2_1|1, 3_1|1, 0_1|1, 1_1|1, 4_1|1, 5_1|1]), (99,100,[1_1|2]), (99,103,[1_1|2]), (99,106,[1_1|2]), (99,110,[4_1|2]), (99,114,[1_1|2]), (99,118,[1_1|2]), (99,123,[4_1|2]), (99,127,[4_1|2]), (99,132,[5_1|2]), (99,135,[5_1|2]), (99,138,[5_1|2]), (99,142,[5_1|2]), (99,146,[5_1|2]), (99,149,[5_1|2]), (99,152,[0_1|2]), (99,157,[5_1|2]), (99,162,[3_1|2]), (99,167,[1_1|2]), (99,172,[1_1|2]), (99,177,[1_1|2]), (99,182,[4_1|2]), (99,187,[0_1|2]), (99,192,[0_1|2]), (99,197,[3_1|2]), (99,202,[1_1|2]), (99,207,[0_1|2]), (99,212,[0_1|2]), (99,217,[1_1|2]), (99,221,[5_1|2]), (99,226,[0_1|2]), (99,231,[1_1|2]), (99,236,[5_1|2]), (99,241,[4_1|2]), (99,245,[4_1|2]), (99,249,[0_1|2]), (99,254,[5_1|2]), (99,259,[3_1|2]), (99,264,[1_1|2]), (99,269,[4_1|2]), (99,274,[2_1|2]), (99,279,[5_1|2]), (99,284,[5_1|2]), (99,289,[5_1|2]), (99,294,[2_1|2]), (99,299,[4_1|2]), (100,101,[0_1|2]), (101,102,[0_1|2]), (102,99,[2_1|2]), (102,274,[2_1|2]), (102,294,[2_1|2]), (102,168,[2_1|2]), (103,104,[0_1|2]), (104,105,[3_1|2]), (105,99,[2_1|2]), (105,274,[2_1|2]), (105,294,[2_1|2]), (105,168,[2_1|2]), (106,107,[0_1|2]), (107,108,[0_1|2]), (108,109,[3_1|2]), (109,99,[2_1|2]), (109,274,[2_1|2]), (109,294,[2_1|2]), (109,168,[2_1|2]), (110,111,[5_1|2]), (111,112,[1_1|2]), (112,113,[0_1|2]), (113,99,[2_1|2]), (113,274,[2_1|2]), (113,294,[2_1|2]), (113,168,[2_1|2]), (114,115,[3_1|2]), (115,116,[2_1|2]), (116,117,[0_1|2]), (117,99,[3_1|2]), (117,162,[3_1|2]), (117,197,[3_1|2]), (117,259,[3_1|2]), (117,275,[3_1|2]), (118,119,[1_1|2]), (119,120,[0_1|2]), (120,121,[2_1|2]), (121,122,[2_1|2]), (122,99,[2_1|2]), (122,274,[2_1|2]), (122,294,[2_1|2]), (122,168,[2_1|2]), (123,124,[4_1|2]), (124,125,[1_1|2]), (125,126,[0_1|2]), (126,99,[2_1|2]), (126,274,[2_1|2]), (126,294,[2_1|2]), (127,128,[1_1|2]), (128,129,[0_1|2]), (129,130,[3_1|2]), (130,131,[2_1|2]), (131,99,[5_1|2]), (131,274,[5_1|2, 2_1|2]), (131,294,[5_1|2, 2_1|2]), (131,269,[4_1|2]), (131,279,[5_1|2]), (131,284,[5_1|2]), (131,289,[5_1|2]), (132,133,[0_1|2]), (133,134,[0_1|2]), (134,99,[2_1|2]), (134,274,[2_1|2]), (134,294,[2_1|2]), (135,136,[5_1|2]), (136,137,[0_1|2]), (137,99,[2_1|2]), (137,274,[2_1|2]), (137,294,[2_1|2]), (138,139,[0_1|2]), (139,140,[3_1|2]), (140,141,[3_1|2]), (141,99,[2_1|2]), (141,274,[2_1|2]), (141,294,[2_1|2]), (142,143,[0_1|2]), (143,144,[3_1|2]), (144,145,[2_1|2]), (145,99,[3_1|2]), (145,162,[3_1|2]), (145,197,[3_1|2]), (145,259,[3_1|2]), (145,275,[3_1|2]), (146,147,[0_1|2]), (147,148,[0_1|2]), (148,99,[3_1|2]), (148,162,[3_1|2]), (148,197,[3_1|2]), (148,259,[3_1|2]), (148,280,[3_1|2]), (149,150,[5_1|2]), (150,151,[0_1|2]), (151,99,[3_1|2]), (151,162,[3_1|2]), (151,197,[3_1|2]), (151,259,[3_1|2]), (151,280,[3_1|2]), (152,153,[1_1|2]), (153,154,[5_1|2]), (154,155,[0_1|2]), (155,156,[2_1|2]), (156,99,[3_1|2]), (156,274,[3_1|2]), (156,294,[3_1|2]), (156,168,[3_1|2]), (157,158,[0_1|2]), (158,159,[1_1|2]), (159,160,[4_1|2]), (160,161,[3_1|2]), (161,99,[2_1|2]), (161,274,[2_1|2]), (161,294,[2_1|2]), (161,168,[2_1|2]), (162,163,[2_1|2]), (163,164,[0_1|2]), (164,165,[3_1|2]), (165,166,[5_1|2]), (166,99,[4_1|2]), (166,274,[4_1|2]), (166,294,[4_1|2]), (166,241,[4_1|2]), (166,245,[4_1|2]), (166,249,[0_1|2]), (166,254,[5_1|2]), (166,259,[3_1|2]), (166,264,[1_1|2]), (167,168,[2_1|2]), (168,169,[0_1|2]), (169,170,[1_1|2]), (170,171,[5_1|2]), (171,99,[0_1|2]), (171,274,[0_1|2]), (171,294,[0_1|2]), (171,168,[0_1|2]), (171,100,[1_1|2]), (171,103,[1_1|2]), (171,106,[1_1|2]), (171,110,[4_1|2]), (171,114,[1_1|2]), (171,118,[1_1|2]), (171,299,[4_1|2]), (171,123,[4_1|2]), (171,127,[4_1|2]), (171,132,[5_1|2]), (171,135,[5_1|2]), (171,138,[5_1|2]), (171,142,[5_1|2]), (171,146,[5_1|2]), (171,149,[5_1|2]), (171,152,[0_1|2]), (171,157,[5_1|2]), (171,162,[3_1|2]), (171,167,[1_1|2]), (171,172,[1_1|2]), (171,177,[1_1|2]), (171,182,[4_1|2]), (171,187,[0_1|2]), (171,192,[0_1|2]), (171,197,[3_1|2]), (171,202,[1_1|2]), (171,207,[0_1|2]), (171,212,[0_1|2]), (171,303,[1_1|3]), (171,306,[1_1|3]), (171,309,[1_1|3]), (171,313,[4_1|3]), (171,317,[5_1|3]), (171,320,[5_1|3]), (172,173,[5_1|2]), (173,174,[0_1|2]), (174,175,[0_1|2]), (175,176,[3_1|2]), (176,99,[2_1|2]), (176,274,[2_1|2]), (176,294,[2_1|2]), (176,193,[2_1|2]), (176,204,[2_1|2]), (177,178,[0_1|2]), (178,179,[3_1|2]), (179,180,[5_1|2]), (180,181,[4_1|2]), (181,99,[5_1|2]), (181,162,[5_1|2]), (181,197,[5_1|2]), (181,259,[5_1|2]), (181,269,[4_1|2]), (181,274,[2_1|2]), (181,279,[5_1|2]), (181,284,[5_1|2]), (181,289,[5_1|2]), (181,294,[2_1|2]), (182,183,[5_1|2]), (183,184,[5_1|2]), (184,185,[1_1|2]), (185,186,[0_1|2]), (186,99,[3_1|2]), (186,162,[3_1|2]), (186,197,[3_1|2]), (186,259,[3_1|2]), (187,188,[0_1|2]), (188,189,[4_1|2]), (189,190,[3_1|2]), (190,191,[2_1|2]), (191,99,[5_1|2]), (191,274,[5_1|2, 2_1|2]), (191,294,[5_1|2, 2_1|2]), (191,163,[5_1|2]), (191,198,[5_1|2]), (191,260,[5_1|2]), (191,269,[4_1|2]), (191,279,[5_1|2]), (191,284,[5_1|2]), (191,289,[5_1|2]), (192,193,[2_1|2]), (193,194,[0_1|2]), (194,195,[3_1|2]), (195,196,[5_1|2]), (196,99,[5_1|2]), (196,274,[5_1|2, 2_1|2]), (196,294,[5_1|2, 2_1|2]), (196,269,[4_1|2]), (196,279,[5_1|2]), (196,284,[5_1|2]), (196,289,[5_1|2]), (197,198,[2_1|2]), (198,199,[1_1|2]), (199,200,[0_1|2]), (200,201,[0_1|2]), (201,99,[3_1|2]), (201,162,[3_1|2]), (201,197,[3_1|2]), (201,259,[3_1|2]), (201,275,[3_1|2]), (202,203,[0_1|2]), (203,204,[2_1|2]), (204,205,[0_1|2]), (205,206,[0_1|2]), (206,99,[3_1|2]), (206,274,[3_1|2]), (206,294,[3_1|2]), (206,163,[3_1|2]), (206,198,[3_1|2]), (206,260,[3_1|2]), (206,116,[3_1|2]), (207,208,[0_1|2]), (208,209,[3_1|2]), (209,210,[1_1|2]), (210,211,[0_1|2]), (211,99,[3_1|2]), (211,162,[3_1|2]), (211,197,[3_1|2]), (211,259,[3_1|2]), (212,213,[4_1|2]), (213,214,[5_1|2]), (214,215,[5_1|2]), (215,216,[1_1|2]), (215,217,[1_1|2]), (215,221,[5_1|2]), (215,323,[1_1|3]), (216,99,[2_1|2]), (216,274,[2_1|2]), (216,294,[2_1|2]), (216,168,[2_1|2]), (217,218,[1_1|2]), (218,219,[5_1|2]), (219,220,[2_1|2]), (220,99,[2_1|2]), (220,274,[2_1|2]), (220,294,[2_1|2]), (220,168,[2_1|2]), (221,222,[1_1|2]), (222,223,[2_1|2]), (223,224,[3_1|2]), (224,225,[3_1|2]), (225,99,[2_1|2]), (225,162,[2_1|2]), (225,197,[2_1|2]), (225,259,[2_1|2]), (225,275,[2_1|2]), (226,227,[5_1|2]), (227,228,[1_1|2]), (228,229,[0_1|2]), (229,230,[3_1|2]), (230,99,[2_1|2]), (230,274,[2_1|2]), (230,294,[2_1|2]), (231,232,[3_1|2]), (232,233,[0_1|2]), (233,234,[0_1|2]), (234,235,[2_1|2]), (235,99,[5_1|2]), (235,274,[5_1|2, 2_1|2]), (235,294,[5_1|2, 2_1|2]), (235,269,[4_1|2]), (235,279,[5_1|2]), (235,284,[5_1|2]), (235,289,[5_1|2]), (236,237,[1_1|2]), (237,238,[3_1|2]), (238,239,[3_1|2]), (239,240,[2_1|2]), (240,99,[4_1|2]), (240,274,[4_1|2]), (240,294,[4_1|2]), (240,241,[4_1|2]), (240,245,[4_1|2]), (240,249,[0_1|2]), (240,254,[5_1|2]), (240,259,[3_1|2]), (240,264,[1_1|2]), (241,242,[1_1|2]), (242,243,[0_1|2]), (243,244,[0_1|2]), (244,99,[2_1|2]), (244,274,[2_1|2]), (244,294,[2_1|2]), (244,168,[2_1|2]), (245,246,[0_1|2]), (246,247,[0_1|2]), (247,248,[3_1|2]), (248,99,[2_1|2]), (248,274,[2_1|2]), (248,294,[2_1|2]), (248,193,[2_1|2]), (249,250,[3_1|2]), (250,251,[3_1|2]), (251,252,[3_1|2]), (252,253,[2_1|2]), (253,99,[4_1|2]), (253,162,[4_1|2]), (253,197,[4_1|2]), (253,259,[4_1|2, 3_1|2]), (253,275,[4_1|2]), (253,241,[4_1|2]), (253,245,[4_1|2]), (253,249,[0_1|2]), (253,254,[5_1|2]), (253,264,[1_1|2]), (254,255,[4_1|2]), (255,256,[3_1|2]), (256,257,[5_1|2]), (257,258,[0_1|2]), (258,99,[3_1|2]), (258,162,[3_1|2]), (258,197,[3_1|2]), (258,259,[3_1|2]), (258,280,[3_1|2]), (259,260,[2_1|2]), (260,261,[5_1|2]), (261,262,[4_1|2]), (262,263,[1_1|2]), (263,99,[1_1|2]), (263,274,[1_1|2]), (263,294,[1_1|2]), (263,168,[1_1|2]), (263,217,[1_1|2]), (263,221,[5_1|2]), (263,226,[0_1|2]), (263,231,[1_1|2]), (263,236,[5_1|2]), (264,265,[3_1|2]), (265,266,[0_1|2]), (266,267,[4_1|2]), (267,268,[3_1|2]), (268,99,[2_1|2]), (268,274,[2_1|2]), (268,294,[2_1|2]), (268,168,[2_1|2]), (269,270,[5_1|2]), (270,271,[0_1|2]), (271,272,[2_1|2]), (272,273,[3_1|2]), (273,99,[2_1|2]), (273,274,[2_1|2]), (273,294,[2_1|2]), (273,193,[2_1|2]), (274,275,[3_1|2]), (275,276,[2_1|2]), (276,277,[4_1|2]), (277,278,[1_1|2]), (278,99,[5_1|2]), (278,274,[5_1|2, 2_1|2]), (278,294,[5_1|2, 2_1|2]), (278,168,[5_1|2]), (278,269,[4_1|2]), (278,279,[5_1|2]), (278,284,[5_1|2]), (278,289,[5_1|2]), (279,280,[3_1|2]), (280,281,[3_1|2]), (281,282,[2_1|2]), (282,283,[0_1|2]), (283,99,[2_1|2]), (283,274,[2_1|2]), (283,294,[2_1|2]), (284,285,[5_1|2]), (285,286,[3_1|2]), (286,287,[0_1|2]), (287,288,[2_1|2]), (288,99,[4_1|2]), (288,274,[4_1|2]), (288,294,[4_1|2]), (288,241,[4_1|2]), (288,245,[4_1|2]), (288,249,[0_1|2]), (288,254,[5_1|2]), (288,259,[3_1|2]), (288,264,[1_1|2]), (289,290,[1_1|2]), (290,291,[3_1|2]), (291,292,[2_1|2]), (292,293,[2_1|2]), (293,99,[2_1|2]), (293,274,[2_1|2]), (293,294,[2_1|2]), (294,295,[5_1|2]), (295,296,[5_1|2]), (296,297,[1_1|2]), (297,298,[5_1|2]), (297,279,[5_1|2]), (297,284,[5_1|2]), (297,289,[5_1|2]), (297,294,[2_1|2]), (298,99,[3_1|2]), (298,274,[3_1|2]), (298,294,[3_1|2]), (299,300,[5_1|2]), (300,301,[1_1|2]), (301,302,[0_1|2]), (302,110,[2_1|2]), (302,123,[2_1|2]), (302,127,[2_1|2]), (302,182,[2_1|2]), (302,241,[2_1|2]), (302,245,[2_1|2]), (302,269,[2_1|2]), (302,299,[2_1|2]), (303,304,[0_1|3]), (304,305,[0_1|3]), (305,168,[2_1|3]), (306,307,[0_1|3]), (307,308,[3_1|3]), (308,168,[2_1|3]), (309,310,[0_1|3]), (310,311,[0_1|3]), (311,312,[3_1|3]), (312,168,[2_1|3]), (313,314,[5_1|3]), (314,315,[1_1|3]), (315,316,[0_1|3]), (316,168,[2_1|3]), (317,318,[0_1|3]), (318,319,[0_1|3]), (319,280,[3_1|3]), (320,321,[5_1|3]), (321,322,[0_1|3]), (322,280,[3_1|3]), (323,324,[1_1|3]), (324,325,[5_1|3]), (325,326,[2_1|3]), (326,168,[2_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)