/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 81 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: 0(1(2(x1))) -> 0(0(2(1(x1)))) 0(1(2(x1))) -> 0(2(1(3(x1)))) 0(1(2(x1))) -> 0(2(3(1(x1)))) 0(1(4(x1))) -> 0(4(1(1(0(0(x1)))))) 0(3(2(x1))) -> 0(0(2(3(x1)))) 0(3(2(x1))) -> 0(2(3(1(x1)))) 0(3(4(x1))) -> 0(0(4(3(x1)))) 0(4(5(x1))) -> 0(0(4(1(5(x1))))) 2(0(1(x1))) -> 0(2(1(1(x1)))) 2(4(1(x1))) -> 0(4(2(3(1(x1))))) 4(3(2(x1))) -> 4(2(3(1(x1)))) 0(1(0(1(x1)))) -> 0(0(3(1(1(x1))))) 0(1(0(2(x1)))) -> 0(0(2(1(1(1(x1)))))) 0(1(4(2(x1)))) -> 0(4(2(1(1(x1))))) 0(3(2(4(x1)))) -> 0(4(2(3(0(x1))))) 0(3(4(2(x1)))) -> 0(4(2(3(1(x1))))) 0(3(5(2(x1)))) -> 0(2(1(3(5(x1))))) 0(4(5(3(x1)))) -> 0(0(4(3(5(x1))))) 0(5(3(4(x1)))) -> 0(4(3(3(5(x1))))) 0(5(4(2(x1)))) -> 0(4(2(1(5(x1))))) 2(0(3(1(x1)))) -> 0(3(2(1(1(x1))))) 2(2(4(1(x1)))) -> 4(2(2(3(1(x1))))) 2(3(4(3(x1)))) -> 2(3(0(4(3(3(x1)))))) 2(4(1(1(x1)))) -> 2(0(4(1(1(x1))))) 2(4(1(3(x1)))) -> 0(4(3(2(1(x1))))) 2(4(3(2(x1)))) -> 2(0(4(2(3(x1))))) 2(5(4(3(x1)))) -> 0(4(2(3(5(x1))))) 4(2(0(3(x1)))) -> 2(3(0(4(3(x1))))) 4(3(4(3(x1)))) -> 4(3(0(4(3(x1))))) 0(1(5(3(2(x1))))) -> 0(5(0(3(2(1(x1)))))) 0(1(5(4(2(x1))))) -> 5(2(1(0(4(3(x1)))))) 0(1(5(4(5(x1))))) -> 0(4(1(2(5(5(x1)))))) 0(2(2(4(3(x1))))) -> 2(0(4(3(0(2(x1)))))) 0(3(0(4(5(x1))))) -> 5(0(0(4(3(2(x1)))))) 0(3(2(4(3(x1))))) -> 0(4(3(3(4(2(x1)))))) 0(4(2(5(4(x1))))) -> 0(4(2(1(5(4(x1)))))) 0(5(3(2(1(x1))))) -> 0(2(3(1(3(5(x1)))))) 0(5(4(1(4(x1))))) -> 4(0(4(1(5(0(x1)))))) 2(4(1(5(3(x1))))) -> 0(4(1(3(5(2(x1)))))) 2(4(2(0(1(x1))))) -> 2(1(1(2(0(4(x1)))))) 2(5(3(4(1(x1))))) -> 5(1(0(4(3(2(x1)))))) 4(0(1(5(4(x1))))) -> 4(0(0(4(1(5(x1)))))) 4(3(0(2(3(x1))))) -> 0(4(2(3(1(3(x1)))))) 4(4(1(2(3(x1))))) -> 0(4(4(2(3(1(x1)))))) 4(5(1(0(2(x1))))) -> 1(0(4(2(1(5(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(1(x_1)) -> 1(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_4(x_1)) -> 4(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))) -> 0(0(2(1(x1)))) 0(1(2(x1))) -> 0(2(1(3(x1)))) 0(1(2(x1))) -> 0(2(3(1(x1)))) 0(1(4(x1))) -> 0(4(1(1(0(0(x1)))))) 0(3(2(x1))) -> 0(0(2(3(x1)))) 0(3(2(x1))) -> 0(2(3(1(x1)))) 0(3(4(x1))) -> 0(0(4(3(x1)))) 0(4(5(x1))) -> 0(0(4(1(5(x1))))) 2(0(1(x1))) -> 0(2(1(1(x1)))) 2(4(1(x1))) -> 0(4(2(3(1(x1))))) 4(3(2(x1))) -> 4(2(3(1(x1)))) 0(1(0(1(x1)))) -> 0(0(3(1(1(x1))))) 0(1(0(2(x1)))) -> 0(0(2(1(1(1(x1)))))) 0(1(4(2(x1)))) -> 0(4(2(1(1(x1))))) 0(3(2(4(x1)))) -> 0(4(2(3(0(x1))))) 0(3(4(2(x1)))) -> 0(4(2(3(1(x1))))) 0(3(5(2(x1)))) -> 0(2(1(3(5(x1))))) 0(4(5(3(x1)))) -> 0(0(4(3(5(x1))))) 0(5(3(4(x1)))) -> 0(4(3(3(5(x1))))) 0(5(4(2(x1)))) -> 0(4(2(1(5(x1))))) 2(0(3(1(x1)))) -> 0(3(2(1(1(x1))))) 2(2(4(1(x1)))) -> 4(2(2(3(1(x1))))) 2(3(4(3(x1)))) -> 2(3(0(4(3(3(x1)))))) 2(4(1(1(x1)))) -> 2(0(4(1(1(x1))))) 2(4(1(3(x1)))) -> 0(4(3(2(1(x1))))) 2(4(3(2(x1)))) -> 2(0(4(2(3(x1))))) 2(5(4(3(x1)))) -> 0(4(2(3(5(x1))))) 4(2(0(3(x1)))) -> 2(3(0(4(3(x1))))) 4(3(4(3(x1)))) -> 4(3(0(4(3(x1))))) 0(1(5(3(2(x1))))) -> 0(5(0(3(2(1(x1)))))) 0(1(5(4(2(x1))))) -> 5(2(1(0(4(3(x1)))))) 0(1(5(4(5(x1))))) -> 0(4(1(2(5(5(x1)))))) 0(2(2(4(3(x1))))) -> 2(0(4(3(0(2(x1)))))) 0(3(0(4(5(x1))))) -> 5(0(0(4(3(2(x1)))))) 0(3(2(4(3(x1))))) -> 0(4(3(3(4(2(x1)))))) 0(4(2(5(4(x1))))) -> 0(4(2(1(5(4(x1)))))) 0(5(3(2(1(x1))))) -> 0(2(3(1(3(5(x1)))))) 0(5(4(1(4(x1))))) -> 4(0(4(1(5(0(x1)))))) 2(4(1(5(3(x1))))) -> 0(4(1(3(5(2(x1)))))) 2(4(2(0(1(x1))))) -> 2(1(1(2(0(4(x1)))))) 2(5(3(4(1(x1))))) -> 5(1(0(4(3(2(x1)))))) 4(0(1(5(4(x1))))) -> 4(0(0(4(1(5(x1)))))) 4(3(0(2(3(x1))))) -> 0(4(2(3(1(3(x1)))))) 4(4(1(2(3(x1))))) -> 0(4(4(2(3(1(x1)))))) 4(5(1(0(2(x1))))) -> 1(0(4(2(1(5(x1)))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_4(x_1)) -> 4(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))) -> 0(0(2(1(x1)))) 0(1(2(x1))) -> 0(2(1(3(x1)))) 0(1(2(x1))) -> 0(2(3(1(x1)))) 0(1(4(x1))) -> 0(4(1(1(0(0(x1)))))) 0(3(2(x1))) -> 0(0(2(3(x1)))) 0(3(2(x1))) -> 0(2(3(1(x1)))) 0(3(4(x1))) -> 0(0(4(3(x1)))) 0(4(5(x1))) -> 0(0(4(1(5(x1))))) 2(0(1(x1))) -> 0(2(1(1(x1)))) 2(4(1(x1))) -> 0(4(2(3(1(x1))))) 4(3(2(x1))) -> 4(2(3(1(x1)))) 0(1(0(1(x1)))) -> 0(0(3(1(1(x1))))) 0(1(0(2(x1)))) -> 0(0(2(1(1(1(x1)))))) 0(1(4(2(x1)))) -> 0(4(2(1(1(x1))))) 0(3(2(4(x1)))) -> 0(4(2(3(0(x1))))) 0(3(4(2(x1)))) -> 0(4(2(3(1(x1))))) 0(3(5(2(x1)))) -> 0(2(1(3(5(x1))))) 0(4(5(3(x1)))) -> 0(0(4(3(5(x1))))) 0(5(3(4(x1)))) -> 0(4(3(3(5(x1))))) 0(5(4(2(x1)))) -> 0(4(2(1(5(x1))))) 2(0(3(1(x1)))) -> 0(3(2(1(1(x1))))) 2(2(4(1(x1)))) -> 4(2(2(3(1(x1))))) 2(3(4(3(x1)))) -> 2(3(0(4(3(3(x1)))))) 2(4(1(1(x1)))) -> 2(0(4(1(1(x1))))) 2(4(1(3(x1)))) -> 0(4(3(2(1(x1))))) 2(4(3(2(x1)))) -> 2(0(4(2(3(x1))))) 2(5(4(3(x1)))) -> 0(4(2(3(5(x1))))) 4(2(0(3(x1)))) -> 2(3(0(4(3(x1))))) 4(3(4(3(x1)))) -> 4(3(0(4(3(x1))))) 0(1(5(3(2(x1))))) -> 0(5(0(3(2(1(x1)))))) 0(1(5(4(2(x1))))) -> 5(2(1(0(4(3(x1)))))) 0(1(5(4(5(x1))))) -> 0(4(1(2(5(5(x1)))))) 0(2(2(4(3(x1))))) -> 2(0(4(3(0(2(x1)))))) 0(3(0(4(5(x1))))) -> 5(0(0(4(3(2(x1)))))) 0(3(2(4(3(x1))))) -> 0(4(3(3(4(2(x1)))))) 0(4(2(5(4(x1))))) -> 0(4(2(1(5(4(x1)))))) 0(5(3(2(1(x1))))) -> 0(2(3(1(3(5(x1)))))) 0(5(4(1(4(x1))))) -> 4(0(4(1(5(0(x1)))))) 2(4(1(5(3(x1))))) -> 0(4(1(3(5(2(x1)))))) 2(4(2(0(1(x1))))) -> 2(1(1(2(0(4(x1)))))) 2(5(3(4(1(x1))))) -> 5(1(0(4(3(2(x1)))))) 4(0(1(5(4(x1))))) -> 4(0(0(4(1(5(x1)))))) 4(3(0(2(3(x1))))) -> 0(4(2(3(1(3(x1)))))) 4(4(1(2(3(x1))))) -> 0(4(4(2(3(1(x1)))))) 4(5(1(0(2(x1))))) -> 1(0(4(2(1(5(x1)))))) The (relative) TRS S consists of the following rules: encArg(1(x_1)) -> 1(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_4(x_1)) -> 4(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))) -> 0(0(2(1(x1)))) 0(1(2(x1))) -> 0(2(1(3(x1)))) 0(1(2(x1))) -> 0(2(3(1(x1)))) 0(1(4(x1))) -> 0(4(1(1(0(0(x1)))))) 0(3(2(x1))) -> 0(0(2(3(x1)))) 0(3(2(x1))) -> 0(2(3(1(x1)))) 0(3(4(x1))) -> 0(0(4(3(x1)))) 0(4(5(x1))) -> 0(0(4(1(5(x1))))) 2(0(1(x1))) -> 0(2(1(1(x1)))) 2(4(1(x1))) -> 0(4(2(3(1(x1))))) 4(3(2(x1))) -> 4(2(3(1(x1)))) 0(1(0(1(x1)))) -> 0(0(3(1(1(x1))))) 0(1(0(2(x1)))) -> 0(0(2(1(1(1(x1)))))) 0(1(4(2(x1)))) -> 0(4(2(1(1(x1))))) 0(3(2(4(x1)))) -> 0(4(2(3(0(x1))))) 0(3(4(2(x1)))) -> 0(4(2(3(1(x1))))) 0(3(5(2(x1)))) -> 0(2(1(3(5(x1))))) 0(4(5(3(x1)))) -> 0(0(4(3(5(x1))))) 0(5(3(4(x1)))) -> 0(4(3(3(5(x1))))) 0(5(4(2(x1)))) -> 0(4(2(1(5(x1))))) 2(0(3(1(x1)))) -> 0(3(2(1(1(x1))))) 2(2(4(1(x1)))) -> 4(2(2(3(1(x1))))) 2(3(4(3(x1)))) -> 2(3(0(4(3(3(x1)))))) 2(4(1(1(x1)))) -> 2(0(4(1(1(x1))))) 2(4(1(3(x1)))) -> 0(4(3(2(1(x1))))) 2(4(3(2(x1)))) -> 2(0(4(2(3(x1))))) 2(5(4(3(x1)))) -> 0(4(2(3(5(x1))))) 4(2(0(3(x1)))) -> 2(3(0(4(3(x1))))) 4(3(4(3(x1)))) -> 4(3(0(4(3(x1))))) 0(1(5(3(2(x1))))) -> 0(5(0(3(2(1(x1)))))) 0(1(5(4(2(x1))))) -> 5(2(1(0(4(3(x1)))))) 0(1(5(4(5(x1))))) -> 0(4(1(2(5(5(x1)))))) 0(2(2(4(3(x1))))) -> 2(0(4(3(0(2(x1)))))) 0(3(0(4(5(x1))))) -> 5(0(0(4(3(2(x1)))))) 0(3(2(4(3(x1))))) -> 0(4(3(3(4(2(x1)))))) 0(4(2(5(4(x1))))) -> 0(4(2(1(5(4(x1)))))) 0(5(3(2(1(x1))))) -> 0(2(3(1(3(5(x1)))))) 0(5(4(1(4(x1))))) -> 4(0(4(1(5(0(x1)))))) 2(4(1(5(3(x1))))) -> 0(4(1(3(5(2(x1)))))) 2(4(2(0(1(x1))))) -> 2(1(1(2(0(4(x1)))))) 2(5(3(4(1(x1))))) -> 5(1(0(4(3(2(x1)))))) 4(0(1(5(4(x1))))) -> 4(0(0(4(1(5(x1)))))) 4(3(0(2(3(x1))))) -> 0(4(2(3(1(3(x1)))))) 4(4(1(2(3(x1))))) -> 0(4(4(2(3(1(x1)))))) 4(5(1(0(2(x1))))) -> 1(0(4(2(1(5(x1)))))) encArg(1(x_1)) -> 1(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_4(x_1)) -> 4(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. "[55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 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] {(55,56,[0_1|0, 2_1|0, 4_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]), (55,57,[1_1|1, 3_1|1, 5_1|1, 0_1|1, 2_1|1, 4_1|1]), (55,58,[0_1|2]), (55,61,[0_1|2]), (55,64,[0_1|2]), (55,67,[0_1|2]), (55,72,[0_1|2]), (55,76,[0_1|2]), (55,80,[0_1|2]), (55,85,[0_1|2]), (55,90,[5_1|2]), (55,95,[0_1|2]), (55,100,[0_1|2]), (55,103,[0_1|2]), (55,107,[0_1|2]), (55,112,[0_1|2]), (55,115,[0_1|2]), (55,119,[0_1|2]), (55,123,[5_1|2]), (55,128,[0_1|2]), (55,132,[0_1|2]), (55,136,[0_1|2]), (55,141,[0_1|2]), (55,145,[0_1|2]), (55,150,[0_1|2]), (55,154,[4_1|2]), (55,159,[2_1|2]), (55,164,[0_1|2]), (55,167,[0_1|2]), (55,171,[2_1|2]), (55,175,[0_1|2]), (55,179,[0_1|2]), (55,184,[2_1|2]), (55,188,[2_1|2]), (55,193,[4_1|2]), (55,197,[2_1|2]), (55,202,[0_1|2]), 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(210,197,[2_1|2]), (210,202,[0_1|2]), (210,206,[5_1|2]), (210,246,[0_1|3]), (210,249,[0_1|3]), (211,212,[2_1|2]), (212,213,[3_1|2]), (213,57,[1_1|2]), (213,159,[1_1|2]), (213,171,[1_1|2]), (213,184,[1_1|2]), (213,188,[1_1|2]), (213,197,[1_1|2]), (213,223,[1_1|2]), (214,215,[3_1|2]), (215,216,[0_1|2]), (216,217,[4_1|2]), (216,211,[4_1|2]), (216,214,[4_1|2]), (216,218,[0_1|2]), (216,258,[0_1|3]), (216,263,[4_1|3]), (216,266,[4_1|3]), (217,57,[3_1|2]), (217,215,[3_1|2]), (218,219,[4_1|2]), (219,220,[2_1|2]), (220,221,[3_1|2]), (221,222,[1_1|2]), (222,57,[3_1|2]), (222,198,[3_1|2]), (222,224,[3_1|2]), (222,66,[3_1|2]), (222,147,[3_1|2]), (222,251,[3_1|2]), (223,224,[3_1|2]), (224,225,[0_1|2]), (225,226,[4_1|2]), (225,211,[4_1|2]), (225,214,[4_1|2]), (225,218,[0_1|2]), (225,258,[0_1|3]), (225,263,[4_1|3]), (225,266,[4_1|3]), (226,57,[3_1|2]), (226,168,[3_1|2]), (227,228,[0_1|2]), (228,229,[0_1|2]), (229,230,[4_1|2]), (230,231,[1_1|2]), (231,57,[5_1|2]), (231,154,[5_1|2]), (231,193,[5_1|2]), (231,211,[5_1|2]), (231,214,[5_1|2]), (231,227,[5_1|2]), (232,233,[4_1|2]), (233,234,[4_1|2]), (234,235,[2_1|2]), (235,236,[3_1|2]), (236,57,[1_1|2]), (236,198,[1_1|2]), (236,224,[1_1|2]), (237,238,[0_1|2]), (238,239,[4_1|2]), (239,240,[2_1|2]), (240,241,[1_1|2]), (241,57,[5_1|2]), (241,159,[5_1|2]), (241,171,[5_1|2]), (241,184,[5_1|2]), (241,188,[5_1|2]), (241,197,[5_1|2]), (241,223,[5_1|2]), (241,62,[5_1|2]), (241,65,[5_1|2]), (241,120,[5_1|2]), (241,146,[5_1|2]), (241,165,[5_1|2]), (241,250,[5_1|2]), (242,243,[4_1|2]), (243,244,[2_1|2]), (244,245,[3_1|2]), (245,237,[1_1|2]), (246,247,[0_1|3]), (247,248,[2_1|3]), (248,169,[3_1|3]), (249,250,[2_1|3]), (250,251,[3_1|3]), (251,169,[1_1|3]), (252,253,[0_1|3]), (253,254,[2_1|3]), (254,89,[3_1|3]), (255,256,[2_1|3]), (256,257,[3_1|3]), (257,89,[1_1|3]), (258,259,[4_1|3]), (259,260,[2_1|3]), (260,261,[3_1|3]), (261,262,[1_1|3]), (262,66,[3_1|3]), (262,147,[3_1|3]), (262,251,[3_1|3]), (263,264,[2_1|3]), (264,265,[3_1|3]), (265,159,[1_1|3]), (265,171,[1_1|3]), (265,184,[1_1|3]), (265,188,[1_1|3]), (265,197,[1_1|3]), (265,223,[1_1|3]), (265,195,[1_1|3]), (265,194,[1_1|3]), (265,212,[1_1|3]), (265,169,[1_1|3]), (266,267,[3_1|3]), (267,268,[0_1|3]), (268,269,[4_1|3]), (269,215,[3_1|3]), (270,271,[3_1|3]), (271,272,[0_1|3]), (272,273,[4_1|3]), (273,274,[3_1|3]), (274,215,[3_1|3]), (275,276,[3_1|3]), (276,277,[0_1|3]), (277,278,[4_1|3]), (277,263,[4_1|3]), (278,168,[3_1|3]), (279,280,[4_1|2]), (280,281,[2_1|2]), (281,282,[3_1|2]), (282,57,[1_1|2]), (282,237,[1_1|2]), (283,284,[2_1|3]), (284,285,[3_1|3]), (285,57,[1_1|3]), (285,90,[1_1|3]), (285,123,[1_1|3]), (285,206,[1_1|3]), (285,171,[1_1|3]), (285,184,[1_1|3]), (285,188,[1_1|3]), (285,197,[1_1|3]), (285,237,[1_1|3]), (286,287,[2_1|3]), (287,288,[3_1|3]), (288,178,[1_1|3]), (289,290,[0_1|3]), (290,291,[4_1|3]), (291,292,[1_1|3]), (292,90,[5_1|3]), (292,123,[5_1|3]), (292,206,[5_1|3]), (293,294,[4_1|3]), (294,295,[2_1|3]), (295,296,[3_1|3]), (296,297,[1_1|3]), (297,198,[3_1|3]), (298,299,[2_1|3]), (299,300,[1_1|3]), (300,237,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)