/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 45 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 62 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(1(x1))) -> 1(0(2(1(x1)))) 0(1(1(x1))) -> 1(1(0(3(2(x1))))) 0(1(1(x1))) -> 1(4(0(0(2(1(x1)))))) 0(1(4(x1))) -> 1(4(0(3(x1)))) 0(1(4(x1))) -> 4(0(2(1(x1)))) 0(1(4(x1))) -> 4(0(2(1(3(x1))))) 0(4(1(x1))) -> 0(2(4(1(x1)))) 0(4(1(x1))) -> 4(0(2(1(x1)))) 0(4(1(x1))) -> 4(0(3(1(x1)))) 0(4(1(x1))) -> 1(4(4(0(2(x1))))) 0(4(1(x1))) -> 2(1(4(0(2(x1))))) 0(5(4(x1))) -> 1(4(0(0(2(5(x1)))))) 0(5(4(x1))) -> 4(0(2(5(2(5(x1)))))) 0(5(4(x1))) -> 5(0(4(0(3(3(x1)))))) 4(2(1(x1))) -> 4(0(2(1(x1)))) 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 0(1(0(4(x1)))) -> 0(0(2(2(1(4(x1)))))) 0(1(1(2(x1)))) -> 5(1(0(2(1(x1))))) 0(1(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(1(4(1(x1)))) -> 1(0(2(4(1(x1))))) 0(1(4(3(x1)))) -> 1(0(2(4(3(x1))))) 0(1(4(3(x1)))) -> 4(0(2(1(3(x1))))) 0(4(1(2(x1)))) -> 2(0(3(1(4(x1))))) 0(4(2(1(x1)))) -> 0(4(3(0(2(1(x1)))))) 0(5(0(4(x1)))) -> 1(5(4(0(0(2(x1)))))) 0(5(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(5(1(3(x1)))) -> 5(3(1(0(3(x1))))) 0(5(4(1(x1)))) -> 4(1(5(4(0(2(x1)))))) 0(5(4(3(x1)))) -> 0(2(5(0(3(4(x1)))))) 0(5(4(3(x1)))) -> 1(5(3(4(0(3(x1)))))) 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 0(0(1(2(3(x1))))) -> 1(0(3(0(0(2(x1)))))) 0(0(5(1(2(x1))))) -> 0(0(2(5(0(1(x1)))))) 0(0(5(1(3(x1))))) -> 4(5(0(0(3(1(x1)))))) 0(1(3(4(2(x1))))) -> 1(3(4(3(0(2(x1)))))) 0(4(5(3(4(x1))))) -> 0(3(2(5(4(4(x1)))))) 0(5(0(2(2(x1))))) -> 0(0(2(5(2(4(x1)))))) 0(5(1(1(3(x1))))) -> 0(3(2(1(1(5(x1)))))) 0(5(1(4(3(x1))))) -> 3(0(2(1(5(4(x1)))))) 0(5(5(1(2(x1))))) -> 1(5(3(0(2(5(x1)))))) 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 4(2(5(4(1(x1))))) -> 4(4(1(5(3(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(2(x_1)) -> 2(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_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(1(x1))) -> 1(0(2(1(x1)))) 0(1(1(x1))) -> 1(1(0(3(2(x1))))) 0(1(1(x1))) -> 1(4(0(0(2(1(x1)))))) 0(1(4(x1))) -> 1(4(0(3(x1)))) 0(1(4(x1))) -> 4(0(2(1(x1)))) 0(1(4(x1))) -> 4(0(2(1(3(x1))))) 0(4(1(x1))) -> 0(2(4(1(x1)))) 0(4(1(x1))) -> 4(0(2(1(x1)))) 0(4(1(x1))) -> 4(0(3(1(x1)))) 0(4(1(x1))) -> 1(4(4(0(2(x1))))) 0(4(1(x1))) -> 2(1(4(0(2(x1))))) 0(5(4(x1))) -> 1(4(0(0(2(5(x1)))))) 0(5(4(x1))) -> 4(0(2(5(2(5(x1)))))) 0(5(4(x1))) -> 5(0(4(0(3(3(x1)))))) 4(2(1(x1))) -> 4(0(2(1(x1)))) 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 0(1(0(4(x1)))) -> 0(0(2(2(1(4(x1)))))) 0(1(1(2(x1)))) -> 5(1(0(2(1(x1))))) 0(1(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(1(4(1(x1)))) -> 1(0(2(4(1(x1))))) 0(1(4(3(x1)))) -> 1(0(2(4(3(x1))))) 0(1(4(3(x1)))) -> 4(0(2(1(3(x1))))) 0(4(1(2(x1)))) -> 2(0(3(1(4(x1))))) 0(4(2(1(x1)))) -> 0(4(3(0(2(1(x1)))))) 0(5(0(4(x1)))) -> 1(5(4(0(0(2(x1)))))) 0(5(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(5(1(3(x1)))) -> 5(3(1(0(3(x1))))) 0(5(4(1(x1)))) -> 4(1(5(4(0(2(x1)))))) 0(5(4(3(x1)))) -> 0(2(5(0(3(4(x1)))))) 0(5(4(3(x1)))) -> 1(5(3(4(0(3(x1)))))) 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 0(0(1(2(3(x1))))) -> 1(0(3(0(0(2(x1)))))) 0(0(5(1(2(x1))))) -> 0(0(2(5(0(1(x1)))))) 0(0(5(1(3(x1))))) -> 4(5(0(0(3(1(x1)))))) 0(1(3(4(2(x1))))) -> 1(3(4(3(0(2(x1)))))) 0(4(5(3(4(x1))))) -> 0(3(2(5(4(4(x1)))))) 0(5(0(2(2(x1))))) -> 0(0(2(5(2(4(x1)))))) 0(5(1(1(3(x1))))) -> 0(3(2(1(1(5(x1)))))) 0(5(1(4(3(x1))))) -> 3(0(2(1(5(4(x1)))))) 0(5(5(1(2(x1))))) -> 1(5(3(0(2(5(x1)))))) 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(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(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(1(x1))) -> 1(0(2(1(x1)))) 0(1(1(x1))) -> 1(1(0(3(2(x1))))) 0(1(1(x1))) -> 1(4(0(0(2(1(x1)))))) 0(1(4(x1))) -> 1(4(0(3(x1)))) 0(1(4(x1))) -> 4(0(2(1(x1)))) 0(1(4(x1))) -> 4(0(2(1(3(x1))))) 0(4(1(x1))) -> 0(2(4(1(x1)))) 0(4(1(x1))) -> 4(0(2(1(x1)))) 0(4(1(x1))) -> 4(0(3(1(x1)))) 0(4(1(x1))) -> 1(4(4(0(2(x1))))) 0(4(1(x1))) -> 2(1(4(0(2(x1))))) 0(5(4(x1))) -> 1(4(0(0(2(5(x1)))))) 0(5(4(x1))) -> 4(0(2(5(2(5(x1)))))) 0(5(4(x1))) -> 5(0(4(0(3(3(x1)))))) 4(2(1(x1))) -> 4(0(2(1(x1)))) 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 0(1(0(4(x1)))) -> 0(0(2(2(1(4(x1)))))) 0(1(1(2(x1)))) -> 5(1(0(2(1(x1))))) 0(1(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(1(4(1(x1)))) -> 1(0(2(4(1(x1))))) 0(1(4(3(x1)))) -> 1(0(2(4(3(x1))))) 0(1(4(3(x1)))) -> 4(0(2(1(3(x1))))) 0(4(1(2(x1)))) -> 2(0(3(1(4(x1))))) 0(4(2(1(x1)))) -> 0(4(3(0(2(1(x1)))))) 0(5(0(4(x1)))) -> 1(5(4(0(0(2(x1)))))) 0(5(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(5(1(3(x1)))) -> 5(3(1(0(3(x1))))) 0(5(4(1(x1)))) -> 4(1(5(4(0(2(x1)))))) 0(5(4(3(x1)))) -> 0(2(5(0(3(4(x1)))))) 0(5(4(3(x1)))) -> 1(5(3(4(0(3(x1)))))) 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 0(0(1(2(3(x1))))) -> 1(0(3(0(0(2(x1)))))) 0(0(5(1(2(x1))))) -> 0(0(2(5(0(1(x1)))))) 0(0(5(1(3(x1))))) -> 4(5(0(0(3(1(x1)))))) 0(1(3(4(2(x1))))) -> 1(3(4(3(0(2(x1)))))) 0(4(5(3(4(x1))))) -> 0(3(2(5(4(4(x1)))))) 0(5(0(2(2(x1))))) -> 0(0(2(5(2(4(x1)))))) 0(5(1(1(3(x1))))) -> 0(3(2(1(1(5(x1)))))) 0(5(1(4(3(x1))))) -> 3(0(2(1(5(4(x1)))))) 0(5(5(1(2(x1))))) -> 1(5(3(0(2(5(x1)))))) 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(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(5(x_1)) -> 5(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(1(x1))) -> 1(0(2(1(x1)))) 0(1(1(x1))) -> 1(1(0(3(2(x1))))) 0(1(1(x1))) -> 1(4(0(0(2(1(x1)))))) 0(1(4(x1))) -> 1(4(0(3(x1)))) 0(1(4(x1))) -> 4(0(2(1(x1)))) 0(1(4(x1))) -> 4(0(2(1(3(x1))))) 0(4(1(x1))) -> 0(2(4(1(x1)))) 0(4(1(x1))) -> 4(0(2(1(x1)))) 0(4(1(x1))) -> 4(0(3(1(x1)))) 0(4(1(x1))) -> 1(4(4(0(2(x1))))) 0(4(1(x1))) -> 2(1(4(0(2(x1))))) 0(5(4(x1))) -> 1(4(0(0(2(5(x1)))))) 0(5(4(x1))) -> 4(0(2(5(2(5(x1)))))) 0(5(4(x1))) -> 5(0(4(0(3(3(x1)))))) 4(2(1(x1))) -> 4(0(2(1(x1)))) 4(2(1(x1))) -> 1(2(4(0(2(x1))))) 0(1(0(4(x1)))) -> 0(0(2(2(1(4(x1)))))) 0(1(1(2(x1)))) -> 5(1(0(2(1(x1))))) 0(1(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(1(4(1(x1)))) -> 1(0(2(4(1(x1))))) 0(1(4(3(x1)))) -> 1(0(2(4(3(x1))))) 0(1(4(3(x1)))) -> 4(0(2(1(3(x1))))) 0(4(1(2(x1)))) -> 2(0(3(1(4(x1))))) 0(4(2(1(x1)))) -> 0(4(3(0(2(1(x1)))))) 0(5(0(4(x1)))) -> 1(5(4(0(0(2(x1)))))) 0(5(1(3(x1)))) -> 1(1(5(0(3(x1))))) 0(5(1(3(x1)))) -> 5(3(1(0(3(x1))))) 0(5(4(1(x1)))) -> 4(1(5(4(0(2(x1)))))) 0(5(4(3(x1)))) -> 0(2(5(0(3(4(x1)))))) 0(5(4(3(x1)))) -> 1(5(3(4(0(3(x1)))))) 1(0(5(4(x1)))) -> 1(4(5(0(3(3(x1)))))) 1(0(5(4(x1)))) -> 5(5(1(0(2(4(x1)))))) 1(4(2(1(x1)))) -> 4(0(2(1(2(1(x1)))))) 4(1(2(1(x1)))) -> 4(1(0(2(1(x1))))) 4(1(2(1(x1)))) -> 3(4(0(2(1(1(x1)))))) 4(3(2(1(x1)))) -> 0(3(4(0(2(1(x1)))))) 0(0(1(2(3(x1))))) -> 1(0(3(0(0(2(x1)))))) 0(0(5(1(2(x1))))) -> 0(0(2(5(0(1(x1)))))) 0(0(5(1(3(x1))))) -> 4(5(0(0(3(1(x1)))))) 0(1(3(4(2(x1))))) -> 1(3(4(3(0(2(x1)))))) 0(4(5(3(4(x1))))) -> 0(3(2(5(4(4(x1)))))) 0(5(0(2(2(x1))))) -> 0(0(2(5(2(4(x1)))))) 0(5(1(1(3(x1))))) -> 0(3(2(1(1(5(x1)))))) 0(5(1(4(3(x1))))) -> 3(0(2(1(5(4(x1)))))) 0(5(5(1(2(x1))))) -> 1(5(3(0(2(5(x1)))))) 1(0(1(2(4(x1))))) -> 1(1(0(2(3(4(x1)))))) 1(4(2(1(2(x1))))) -> 0(2(2(1(1(4(x1)))))) 4(0(0(5(4(x1))))) -> 5(0(0(4(4(5(x1)))))) 4(2(5(4(1(x1))))) -> 4(4(1(5(3(2(x1)))))) encArg(2(x_1)) -> 2(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_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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. "[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, 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] {(75,76,[0_1|0, 4_1|0, 1_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]), (75,77,[2_1|1, 3_1|1, 5_1|1, 0_1|1, 4_1|1, 1_1|1]), (75,78,[1_1|2]), (75,81,[1_1|2]), (75,85,[1_1|2]), (75,90,[5_1|2]), (75,94,[1_1|2]), (75,98,[1_1|2]), (75,101,[4_1|2]), (75,104,[4_1|2]), (75,108,[1_1|2]), (75,112,[1_1|2]), (75,116,[0_1|2]), (75,121,[1_1|2]), (75,126,[0_1|2]), (75,129,[4_1|2]), (75,132,[1_1|2]), (75,136,[2_1|2]), (75,140,[2_1|2]), (75,144,[0_1|2]), (75,149,[0_1|2]), (75,154,[1_1|2]), (75,159,[4_1|2]), (75,164,[5_1|2]), (75,169,[4_1|2]), 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(207,228,[1_1|2]), (207,232,[4_1|2]), (207,237,[4_1|2]), (207,246,[0_1|2]), (207,251,[5_1|2]), (207,313,[4_1|3]), (207,316,[1_1|3]), (208,209,[5_1|2]), (209,210,[3_1|2]), (210,211,[0_1|2]), (211,212,[2_1|2]), (212,77,[5_1|2]), (212,136,[5_1|2]), (212,140,[5_1|2]), (212,229,[5_1|2]), (213,214,[0_1|2]), (214,215,[3_1|2]), (215,216,[0_1|2]), (216,217,[0_1|2]), (217,77,[2_1|2]), (217,203,[2_1|2]), (217,241,[2_1|2]), (218,219,[0_1|2]), (219,220,[2_1|2]), (220,221,[5_1|2]), (221,222,[0_1|2]), (221,78,[1_1|2]), (221,81,[1_1|2]), (221,85,[1_1|2]), (221,90,[5_1|2]), (221,94,[1_1|2]), (221,98,[1_1|2]), (221,101,[4_1|2]), (221,104,[4_1|2]), (221,108,[1_1|2]), (221,112,[1_1|2]), (221,281,[4_1|2]), (221,116,[0_1|2]), (221,121,[1_1|2]), (221,320,[1_1|3]), (221,323,[1_1|3]), (221,327,[1_1|3]), (221,332,[1_1|3]), (221,335,[4_1|3]), (221,338,[4_1|3]), (221,342,[1_1|3]), (221,346,[0_1|3]), (221,351,[1_1|3]), (221,355,[5_1|3]), (222,77,[1_1|2]), (222,136,[1_1|2]), (222,140,[1_1|2]), (222,229,[1_1|2]), (222,256,[1_1|2]), (222,261,[5_1|2]), (222,266,[1_1|2]), (222,271,[4_1|2]), (222,276,[0_1|2]), (223,224,[5_1|2]), (224,225,[0_1|2]), (225,226,[0_1|2]), (226,227,[3_1|2]), (227,77,[1_1|2]), (227,203,[1_1|2]), (227,241,[1_1|2]), (227,122,[1_1|2]), (227,256,[1_1|2]), (227,261,[5_1|2]), (227,266,[1_1|2]), (227,271,[4_1|2]), (227,276,[0_1|2]), (228,229,[2_1|2]), (229,230,[4_1|2]), (230,231,[0_1|2]), (231,77,[2_1|2]), (231,78,[2_1|2]), (231,81,[2_1|2]), (231,85,[2_1|2]), (231,94,[2_1|2]), (231,98,[2_1|2]), (231,108,[2_1|2]), (231,112,[2_1|2]), (231,121,[2_1|2]), (231,132,[2_1|2]), (231,154,[2_1|2]), (231,179,[2_1|2]), (231,184,[2_1|2]), (231,208,[2_1|2]), (231,213,[2_1|2]), (231,228,[2_1|2]), (231,256,[2_1|2]), (231,266,[2_1|2]), (231,137,[2_1|2]), (232,233,[4_1|2]), (233,234,[1_1|2]), (234,235,[5_1|2]), (235,236,[3_1|2]), (236,77,[2_1|2]), (236,78,[2_1|2]), (236,81,[2_1|2]), (236,85,[2_1|2]), (236,94,[2_1|2]), (236,98,[2_1|2]), (236,108,[2_1|2]), (236,112,[2_1|2]), (236,121,[2_1|2]), (236,132,[2_1|2]), (236,154,[2_1|2]), (236,179,[2_1|2]), (236,184,[2_1|2]), (236,208,[2_1|2]), (236,213,[2_1|2]), (236,228,[2_1|2]), (236,256,[2_1|2]), (236,266,[2_1|2]), (236,170,[2_1|2]), (236,238,[2_1|2]), (237,238,[1_1|2]), (238,239,[0_1|2]), (239,240,[2_1|2]), (240,77,[1_1|2]), (240,78,[1_1|2]), (240,81,[1_1|2]), (240,85,[1_1|2]), (240,94,[1_1|2]), (240,98,[1_1|2]), (240,108,[1_1|2]), (240,112,[1_1|2]), (240,121,[1_1|2]), (240,132,[1_1|2]), (240,154,[1_1|2]), (240,179,[1_1|2]), (240,184,[1_1|2]), (240,208,[1_1|2]), (240,213,[1_1|2]), (240,228,[1_1|2]), (240,256,[1_1|2]), (240,266,[1_1|2]), (240,137,[1_1|2]), (240,261,[5_1|2]), (240,271,[4_1|2]), (240,276,[0_1|2]), (241,242,[4_1|2]), (242,243,[0_1|2]), (243,244,[2_1|2]), (244,245,[1_1|2]), (245,77,[1_1|2]), (245,78,[1_1|2]), (245,81,[1_1|2]), (245,85,[1_1|2]), (245,94,[1_1|2]), (245,98,[1_1|2]), (245,108,[1_1|2]), (245,112,[1_1|2]), (245,121,[1_1|2]), (245,132,[1_1|2]), (245,154,[1_1|2]), (245,179,[1_1|2]), (245,184,[1_1|2]), (245,208,[1_1|2]), (245,213,[1_1|2]), (245,228,[1_1|2]), (245,256,[1_1|2]), (245,266,[1_1|2]), (245,137,[1_1|2]), (245,261,[5_1|2]), (245,271,[4_1|2]), (245,276,[0_1|2]), (246,247,[3_1|2]), (247,248,[4_1|2]), (248,249,[0_1|2]), (249,250,[2_1|2]), (250,77,[1_1|2]), (250,78,[1_1|2]), (250,81,[1_1|2]), (250,85,[1_1|2]), (250,94,[1_1|2]), (250,98,[1_1|2]), (250,108,[1_1|2]), (250,112,[1_1|2]), (250,121,[1_1|2]), (250,132,[1_1|2]), (250,154,[1_1|2]), (250,179,[1_1|2]), (250,184,[1_1|2]), (250,208,[1_1|2]), (250,213,[1_1|2]), (250,228,[1_1|2]), (250,256,[1_1|2]), (250,266,[1_1|2]), (250,137,[1_1|2]), (250,261,[5_1|2]), (250,271,[4_1|2]), (250,276,[0_1|2]), (251,252,[0_1|2]), (252,253,[0_1|2]), (253,254,[4_1|2]), (254,255,[4_1|2]), (255,77,[5_1|2]), (255,101,[5_1|2]), (255,104,[5_1|2]), (255,129,[5_1|2]), (255,159,[5_1|2]), (255,169,[5_1|2]), (255,223,[5_1|2]), (255,232,[5_1|2]), (255,237,[5_1|2]), (255,271,[5_1|2]), (255,281,[5_1|2]), (255,285,[5_1|2]), (255,288,[5_1|2]), (256,257,[4_1|2]), (257,258,[5_1|2]), (258,259,[0_1|2]), (259,260,[3_1|2]), (260,77,[3_1|2]), (260,101,[3_1|2]), (260,104,[3_1|2]), (260,129,[3_1|2]), (260,159,[3_1|2]), (260,169,[3_1|2]), (260,223,[3_1|2]), (260,232,[3_1|2]), (260,237,[3_1|2]), (260,271,[3_1|2]), (260,281,[3_1|2]), (260,285,[3_1|2]), (260,288,[3_1|2]), (261,262,[5_1|2]), (262,263,[1_1|2]), (263,264,[0_1|2]), (264,265,[2_1|2]), (265,77,[4_1|2]), (265,101,[4_1|2]), (265,104,[4_1|2]), (265,129,[4_1|2]), (265,159,[4_1|2]), (265,169,[4_1|2]), (265,223,[4_1|2]), (265,232,[4_1|2]), (265,237,[4_1|2]), (265,271,[4_1|2]), (265,310,[4_1|2]), (265,228,[1_1|2]), (265,241,[3_1|2]), (265,246,[0_1|2]), (265,251,[5_1|2]), (265,313,[4_1|3]), (265,316,[1_1|3]), (265,281,[4_1|2]), (265,285,[4_1|2]), (265,288,[4_1|2]), (266,267,[1_1|2]), (267,268,[0_1|2]), (268,269,[2_1|2]), (269,270,[3_1|2]), (270,77,[4_1|2]), (270,101,[4_1|2]), (270,104,[4_1|2]), (270,129,[4_1|2]), (270,159,[4_1|2]), (270,169,[4_1|2]), (270,223,[4_1|2]), (270,232,[4_1|2]), (270,237,[4_1|2]), (270,271,[4_1|2]), (270,230,[4_1|2]), (270,310,[4_1|2]), (270,228,[1_1|2]), (270,241,[3_1|2]), (270,246,[0_1|2]), (270,251,[5_1|2]), (270,313,[4_1|3]), (270,316,[1_1|3]), (270,281,[4_1|2]), (270,285,[4_1|2]), (270,288,[4_1|2]), (271,272,[0_1|2]), (272,273,[2_1|2]), (273,274,[1_1|2]), (274,275,[2_1|2]), (275,77,[1_1|2]), (275,78,[1_1|2]), (275,81,[1_1|2]), (275,85,[1_1|2]), (275,94,[1_1|2]), (275,98,[1_1|2]), (275,108,[1_1|2]), (275,112,[1_1|2]), (275,121,[1_1|2]), (275,132,[1_1|2]), (275,154,[1_1|2]), (275,179,[1_1|2]), (275,184,[1_1|2]), (275,208,[1_1|2]), (275,213,[1_1|2]), (275,228,[1_1|2]), (275,256,[1_1|2]), (275,266,[1_1|2]), (275,137,[1_1|2]), (275,261,[5_1|2]), (275,271,[4_1|2]), (275,276,[0_1|2]), (276,277,[2_1|2]), (277,278,[2_1|2]), (278,279,[1_1|2]), (279,280,[1_1|2]), (279,271,[4_1|2]), (279,276,[0_1|2]), (279,305,[4_1|3]), (280,77,[4_1|2]), (280,136,[4_1|2]), (280,140,[4_1|2]), (280,229,[4_1|2]), (280,310,[4_1|2]), (280,228,[1_1|2]), (280,232,[4_1|2]), (280,237,[4_1|2]), (280,241,[3_1|2]), (280,246,[0_1|2]), (280,251,[5_1|2]), (280,313,[4_1|3]), (280,316,[1_1|3]), (281,282,[0_1|2]), (282,283,[2_1|2]), (283,284,[1_1|2]), (284,203,[3_1|2]), (284,241,[3_1|2]), (285,286,[0_1|2]), (286,287,[2_1|2]), (287,78,[1_1|2]), (287,81,[1_1|2]), (287,85,[1_1|2]), (287,94,[1_1|2]), (287,98,[1_1|2]), (287,108,[1_1|2]), (287,112,[1_1|2]), (287,121,[1_1|2]), (287,132,[1_1|2]), (287,154,[1_1|2]), (287,179,[1_1|2]), (287,184,[1_1|2]), (287,208,[1_1|2]), (287,213,[1_1|2]), (287,228,[1_1|2]), (287,256,[1_1|2]), (287,266,[1_1|2]), (287,170,[1_1|2]), (287,238,[1_1|2]), (288,289,[0_1|2]), (289,290,[2_1|2]), (290,137,[1_1|2]), (291,292,[1_1|3]), (292,293,[0_1|3]), (293,294,[2_1|3]), (294,137,[1_1|3]), (295,296,[4_1|3]), (296,297,[0_1|3]), (297,298,[2_1|3]), (298,299,[1_1|3]), (299,137,[1_1|3]), (300,301,[3_1|3]), (301,302,[4_1|3]), (302,303,[0_1|3]), (303,304,[2_1|3]), (304,137,[1_1|3]), (305,306,[0_1|3]), (306,307,[2_1|3]), (307,308,[1_1|3]), (308,309,[2_1|3]), (309,137,[1_1|3]), (310,311,[0_1|2]), (311,312,[2_1|2]), (312,77,[1_1|2]), (312,78,[1_1|2]), (312,81,[1_1|2]), (312,85,[1_1|2]), (312,94,[1_1|2]), (312,98,[1_1|2]), (312,108,[1_1|2]), (312,112,[1_1|2]), (312,121,[1_1|2]), (312,132,[1_1|2]), (312,154,[1_1|2]), (312,179,[1_1|2]), (312,184,[1_1|2]), (312,208,[1_1|2]), (312,213,[1_1|2]), (312,228,[1_1|2]), (312,256,[1_1|2]), (312,266,[1_1|2]), (312,261,[5_1|2]), (312,271,[4_1|2]), (312,276,[0_1|2]), (313,314,[0_1|3]), (314,315,[2_1|3]), (315,137,[1_1|3]), (316,317,[2_1|3]), (317,318,[4_1|3]), (318,319,[0_1|3]), (319,137,[2_1|3]), (320,321,[0_1|3]), (321,322,[2_1|3]), (322,78,[1_1|3]), (322,81,[1_1|3]), (322,85,[1_1|3]), (322,94,[1_1|3]), (322,98,[1_1|3]), (322,108,[1_1|3]), (322,112,[1_1|3]), (322,121,[1_1|3]), (322,132,[1_1|3]), (322,154,[1_1|3]), (322,179,[1_1|3]), (322,184,[1_1|3]), (322,208,[1_1|3]), (322,213,[1_1|3]), (322,228,[1_1|3]), (322,256,[1_1|3]), (322,266,[1_1|3]), (322,137,[1_1|3]), (322,267,[1_1|3]), (323,324,[1_1|3]), (324,325,[0_1|3]), (325,326,[3_1|3]), (326,78,[2_1|3]), (326,81,[2_1|3]), (326,85,[2_1|3]), (326,94,[2_1|3]), (326,98,[2_1|3]), (326,108,[2_1|3]), (326,112,[2_1|3]), (326,121,[2_1|3]), (326,132,[2_1|3]), (326,154,[2_1|3]), (326,179,[2_1|3]), (326,184,[2_1|3]), (326,208,[2_1|3]), (326,213,[2_1|3]), (326,228,[2_1|3]), (326,256,[2_1|3]), (326,266,[2_1|3]), (326,137,[2_1|3]), (326,267,[2_1|3]), (327,328,[4_1|3]), (328,329,[0_1|3]), (329,330,[0_1|3]), (330,331,[2_1|3]), (331,78,[1_1|3]), (331,81,[1_1|3]), (331,85,[1_1|3]), (331,94,[1_1|3]), (331,98,[1_1|3]), (331,108,[1_1|3]), (331,112,[1_1|3]), (331,121,[1_1|3]), (331,132,[1_1|3]), (331,154,[1_1|3]), (331,179,[1_1|3]), (331,184,[1_1|3]), (331,208,[1_1|3]), (331,213,[1_1|3]), (331,228,[1_1|3]), (331,256,[1_1|3]), (331,266,[1_1|3]), (331,137,[1_1|3]), (331,267,[1_1|3]), (332,333,[4_1|3]), (333,334,[0_1|3]), (334,101,[3_1|3]), (334,104,[3_1|3]), (334,129,[3_1|3]), (334,159,[3_1|3]), (334,169,[3_1|3]), (334,223,[3_1|3]), (334,232,[3_1|3]), (334,237,[3_1|3]), (334,271,[3_1|3]), (334,281,[3_1|3]), (334,285,[3_1|3]), (334,288,[3_1|3]), (334,230,[3_1|3]), (334,257,[3_1|3]), (335,336,[0_1|3]), (336,337,[2_1|3]), (337,101,[1_1|3]), (337,104,[1_1|3]), (337,129,[1_1|3]), (337,159,[1_1|3]), (337,169,[1_1|3]), (337,223,[1_1|3]), (337,232,[1_1|3]), (337,237,[1_1|3]), (337,271,[1_1|3]), (337,281,[1_1|3]), (337,285,[1_1|3]), (337,288,[1_1|3]), (337,230,[1_1|3]), (337,257,[1_1|3]), (338,339,[0_1|3]), (339,340,[2_1|3]), (340,341,[1_1|3]), (341,101,[3_1|3]), (341,104,[3_1|3]), (341,129,[3_1|3]), (341,159,[3_1|3]), (341,169,[3_1|3]), (341,223,[3_1|3]), (341,232,[3_1|3]), (341,237,[3_1|3]), (341,271,[3_1|3]), (341,281,[3_1|3]), (341,285,[3_1|3]), (341,288,[3_1|3]), (341,230,[3_1|3]), (341,257,[3_1|3]), (342,343,[1_1|3]), (343,344,[5_1|3]), (344,345,[0_1|3]), (345,122,[3_1|3]), (346,347,[0_1|3]), (347,348,[2_1|3]), (348,349,[2_1|3]), (349,350,[1_1|3]), (350,145,[4_1|3]), (351,352,[0_1|3]), (352,353,[2_1|3]), (353,354,[4_1|3]), (354,170,[1_1|3]), (354,238,[1_1|3]), (355,356,[1_1|3]), (356,357,[0_1|3]), (357,358,[2_1|3]), (358,229,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)