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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 102 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 53 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(3(x1)))) -> 0(2(2(3(x1)))) 1(1(4(4(5(x1))))) -> 5(1(0(0(5(x1))))) 2(3(3(2(5(x1))))) -> 3(5(4(5(5(x1))))) 5(1(1(5(3(x1))))) -> 5(1(4(5(3(x1))))) 0(2(5(1(1(4(x1)))))) -> 0(3(2(2(4(5(x1)))))) 1(2(1(4(0(3(x1)))))) -> 4(2(5(4(5(3(x1)))))) 1(5(2(0(4(3(x1)))))) -> 5(0(1(1(1(x1))))) 2(2(1(5(4(0(x1)))))) -> 2(3(5(4(0(3(x1)))))) 4(0(2(3(1(4(4(x1))))))) -> 4(1(3(0(5(0(5(x1))))))) 4(3(5(4(3(2(2(2(x1)))))))) -> 4(1(2(3(4(1(4(x1))))))) 0(2(2(2(3(4(3(3(3(x1))))))))) -> 0(5(4(0(5(3(5(5(3(x1))))))))) 4(5(3(4(1(1(0(5(2(x1))))))))) -> 4(4(3(1(3(2(0(5(2(x1))))))))) 3(3(4(1(0(4(5(1(5(2(x1)))))))))) -> 3(3(4(1(5(0(3(0(2(4(x1)))))))))) 2(4(5(4(0(5(5(1(2(1(4(2(x1)))))))))))) -> 4(1(0(1(1(3(3(0(1(4(2(x1))))))))))) 1(0(0(4(5(4(3(4(5(1(5(4(0(x1))))))))))))) -> 5(3(3(1(2(1(1(0(3(1(3(x1))))))))))) 1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 4(4(4(3(2(0(1(3(1(2(2(4(5(x1))))))))))))) 4(1(5(4(5(3(3(3(1(2(0(2(0(x1))))))))))))) -> 4(1(4(3(4(4(0(1(3(1(1(5(x1)))))))))))) 2(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 5(5(5(2(0(2(5(0(0(4(3(2(1(4(3(3(1(x1))))))))))))))))) 1(5(1(1(3(0(3(3(3(3(1(1(5(1(5(2(5(2(x1)))))))))))))))))) -> 3(5(4(2(0(5(1(3(4(1(1(2(5(2(4(1(5(2(x1)))))))))))))))))) 2(4(3(3(4(2(3(5(4(0(4(0(2(3(0(3(3(0(x1)))))))))))))))))) -> 2(1(3(0(4(4(1(5(2(1(0(3(0(5(0(1(5(x1))))))))))))))))) 2(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 2(1(5(0(0(1(5(2(2(2(3(1(0(5(0(4(3(3(x1)))))))))))))))))) 2(3(5(1(3(0(0(5(0(2(2(4(5(4(0(3(1(4(2(x1))))))))))))))))))) -> 5(2(0(2(0(3(2(3(5(2(2(4(1(3(5(5(1(2(x1)))))))))))))))))) 3(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 3(2(0(1(5(0(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1)))))))))))))))))))) 3(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 3(1(3(3(0(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))))))))))) 4(5(1(4(5(3(1(5(5(3(5(0(2(1(2(4(4(5(1(0(4(x1))))))))))))))))))))) -> 4(4(0(2(1(5(2(0(4(5(2(2(3(5(5(2(2(0(3(5(4(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(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(3(x1)))) -> 0(2(2(3(x1)))) 1(1(4(4(5(x1))))) -> 5(1(0(0(5(x1))))) 2(3(3(2(5(x1))))) -> 3(5(4(5(5(x1))))) 5(1(1(5(3(x1))))) -> 5(1(4(5(3(x1))))) 0(2(5(1(1(4(x1)))))) -> 0(3(2(2(4(5(x1)))))) 1(2(1(4(0(3(x1)))))) -> 4(2(5(4(5(3(x1)))))) 1(5(2(0(4(3(x1)))))) -> 5(0(1(1(1(x1))))) 2(2(1(5(4(0(x1)))))) -> 2(3(5(4(0(3(x1)))))) 4(0(2(3(1(4(4(x1))))))) -> 4(1(3(0(5(0(5(x1))))))) 4(3(5(4(3(2(2(2(x1)))))))) -> 4(1(2(3(4(1(4(x1))))))) 0(2(2(2(3(4(3(3(3(x1))))))))) -> 0(5(4(0(5(3(5(5(3(x1))))))))) 4(5(3(4(1(1(0(5(2(x1))))))))) -> 4(4(3(1(3(2(0(5(2(x1))))))))) 3(3(4(1(0(4(5(1(5(2(x1)))))))))) -> 3(3(4(1(5(0(3(0(2(4(x1)))))))))) 2(4(5(4(0(5(5(1(2(1(4(2(x1)))))))))))) -> 4(1(0(1(1(3(3(0(1(4(2(x1))))))))))) 1(0(0(4(5(4(3(4(5(1(5(4(0(x1))))))))))))) -> 5(3(3(1(2(1(1(0(3(1(3(x1))))))))))) 1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 4(4(4(3(2(0(1(3(1(2(2(4(5(x1))))))))))))) 4(1(5(4(5(3(3(3(1(2(0(2(0(x1))))))))))))) -> 4(1(4(3(4(4(0(1(3(1(1(5(x1)))))))))))) 2(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 5(5(5(2(0(2(5(0(0(4(3(2(1(4(3(3(1(x1))))))))))))))))) 1(5(1(1(3(0(3(3(3(3(1(1(5(1(5(2(5(2(x1)))))))))))))))))) -> 3(5(4(2(0(5(1(3(4(1(1(2(5(2(4(1(5(2(x1)))))))))))))))))) 2(4(3(3(4(2(3(5(4(0(4(0(2(3(0(3(3(0(x1)))))))))))))))))) -> 2(1(3(0(4(4(1(5(2(1(0(3(0(5(0(1(5(x1))))))))))))))))) 2(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 2(1(5(0(0(1(5(2(2(2(3(1(0(5(0(4(3(3(x1)))))))))))))))))) 2(3(5(1(3(0(0(5(0(2(2(4(5(4(0(3(1(4(2(x1))))))))))))))))))) -> 5(2(0(2(0(3(2(3(5(2(2(4(1(3(5(5(1(2(x1)))))))))))))))))) 3(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 3(2(0(1(5(0(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1)))))))))))))))))))) 3(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 3(1(3(3(0(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))))))))))) 4(5(1(4(5(3(1(5(5(3(5(0(2(1(2(4(4(5(1(0(4(x1))))))))))))))))))))) -> 4(4(0(2(1(5(2(0(4(5(2(2(3(5(5(2(2(0(3(5(4(x1))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(3(x1)))) -> 0(2(2(3(x1)))) 1(1(4(4(5(x1))))) -> 5(1(0(0(5(x1))))) 2(3(3(2(5(x1))))) -> 3(5(4(5(5(x1))))) 5(1(1(5(3(x1))))) -> 5(1(4(5(3(x1))))) 0(2(5(1(1(4(x1)))))) -> 0(3(2(2(4(5(x1)))))) 1(2(1(4(0(3(x1)))))) -> 4(2(5(4(5(3(x1)))))) 1(5(2(0(4(3(x1)))))) -> 5(0(1(1(1(x1))))) 2(2(1(5(4(0(x1)))))) -> 2(3(5(4(0(3(x1)))))) 4(0(2(3(1(4(4(x1))))))) -> 4(1(3(0(5(0(5(x1))))))) 4(3(5(4(3(2(2(2(x1)))))))) -> 4(1(2(3(4(1(4(x1))))))) 0(2(2(2(3(4(3(3(3(x1))))))))) -> 0(5(4(0(5(3(5(5(3(x1))))))))) 4(5(3(4(1(1(0(5(2(x1))))))))) -> 4(4(3(1(3(2(0(5(2(x1))))))))) 3(3(4(1(0(4(5(1(5(2(x1)))))))))) -> 3(3(4(1(5(0(3(0(2(4(x1)))))))))) 2(4(5(4(0(5(5(1(2(1(4(2(x1)))))))))))) -> 4(1(0(1(1(3(3(0(1(4(2(x1))))))))))) 1(0(0(4(5(4(3(4(5(1(5(4(0(x1))))))))))))) -> 5(3(3(1(2(1(1(0(3(1(3(x1))))))))))) 1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 4(4(4(3(2(0(1(3(1(2(2(4(5(x1))))))))))))) 4(1(5(4(5(3(3(3(1(2(0(2(0(x1))))))))))))) -> 4(1(4(3(4(4(0(1(3(1(1(5(x1)))))))))))) 2(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 5(5(5(2(0(2(5(0(0(4(3(2(1(4(3(3(1(x1))))))))))))))))) 1(5(1(1(3(0(3(3(3(3(1(1(5(1(5(2(5(2(x1)))))))))))))))))) -> 3(5(4(2(0(5(1(3(4(1(1(2(5(2(4(1(5(2(x1)))))))))))))))))) 2(4(3(3(4(2(3(5(4(0(4(0(2(3(0(3(3(0(x1)))))))))))))))))) -> 2(1(3(0(4(4(1(5(2(1(0(3(0(5(0(1(5(x1))))))))))))))))) 2(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 2(1(5(0(0(1(5(2(2(2(3(1(0(5(0(4(3(3(x1)))))))))))))))))) 2(3(5(1(3(0(0(5(0(2(2(4(5(4(0(3(1(4(2(x1))))))))))))))))))) -> 5(2(0(2(0(3(2(3(5(2(2(4(1(3(5(5(1(2(x1)))))))))))))))))) 3(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 3(2(0(1(5(0(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1)))))))))))))))))))) 3(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 3(1(3(3(0(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))))))))))) 4(5(1(4(5(3(1(5(5(3(5(0(2(1(2(4(4(5(1(0(4(x1))))))))))))))))))))) -> 4(4(0(2(1(5(2(0(4(5(2(2(3(5(5(2(2(0(3(5(4(x1))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(3(x1)))) -> 0(2(2(3(x1)))) 1(1(4(4(5(x1))))) -> 5(1(0(0(5(x1))))) 2(3(3(2(5(x1))))) -> 3(5(4(5(5(x1))))) 5(1(1(5(3(x1))))) -> 5(1(4(5(3(x1))))) 0(2(5(1(1(4(x1)))))) -> 0(3(2(2(4(5(x1)))))) 1(2(1(4(0(3(x1)))))) -> 4(2(5(4(5(3(x1)))))) 1(5(2(0(4(3(x1)))))) -> 5(0(1(1(1(x1))))) 2(2(1(5(4(0(x1)))))) -> 2(3(5(4(0(3(x1)))))) 4(0(2(3(1(4(4(x1))))))) -> 4(1(3(0(5(0(5(x1))))))) 4(3(5(4(3(2(2(2(x1)))))))) -> 4(1(2(3(4(1(4(x1))))))) 0(2(2(2(3(4(3(3(3(x1))))))))) -> 0(5(4(0(5(3(5(5(3(x1))))))))) 4(5(3(4(1(1(0(5(2(x1))))))))) -> 4(4(3(1(3(2(0(5(2(x1))))))))) 3(3(4(1(0(4(5(1(5(2(x1)))))))))) -> 3(3(4(1(5(0(3(0(2(4(x1)))))))))) 2(4(5(4(0(5(5(1(2(1(4(2(x1)))))))))))) -> 4(1(0(1(1(3(3(0(1(4(2(x1))))))))))) 1(0(0(4(5(4(3(4(5(1(5(4(0(x1))))))))))))) -> 5(3(3(1(2(1(1(0(3(1(3(x1))))))))))) 1(2(2(1(2(3(2(4(4(0(0(3(2(x1))))))))))))) -> 4(4(4(3(2(0(1(3(1(2(2(4(5(x1))))))))))))) 4(1(5(4(5(3(3(3(1(2(0(2(0(x1))))))))))))) -> 4(1(4(3(4(4(0(1(3(1(1(5(x1)))))))))))) 2(2(3(3(0(2(0(2(5(0(5(5(5(1(0(3(1(x1))))))))))))))))) -> 5(5(5(2(0(2(5(0(0(4(3(2(1(4(3(3(1(x1))))))))))))))))) 1(5(1(1(3(0(3(3(3(3(1(1(5(1(5(2(5(2(x1)))))))))))))))))) -> 3(5(4(2(0(5(1(3(4(1(1(2(5(2(4(1(5(2(x1)))))))))))))))))) 2(4(3(3(4(2(3(5(4(0(4(0(2(3(0(3(3(0(x1)))))))))))))))))) -> 2(1(3(0(4(4(1(5(2(1(0(3(0(5(0(1(5(x1))))))))))))))))) 2(5(5(1(2(3(5(0(3(0(0(3(3(1(0(1(3(2(x1)))))))))))))))))) -> 2(1(5(0(0(1(5(2(2(2(3(1(0(5(0(4(3(3(x1)))))))))))))))))) 2(3(5(1(3(0(0(5(0(2(2(4(5(4(0(3(1(4(2(x1))))))))))))))))))) -> 5(2(0(2(0(3(2(3(5(2(2(4(1(3(5(5(1(2(x1)))))))))))))))))) 3(2(3(4(1(2(5(5(0(1(2(3(4(0(5(1(4(4(5(4(x1)))))))))))))))))))) -> 3(2(0(1(5(0(1(5(5(1(2(3(0(2(4(2(5(2(2(4(x1)))))))))))))))))))) 3(5(5(2(0(4(4(5(5(0(3(5(2(1(2(1(0(2(2(3(x1)))))))))))))))))))) -> 3(1(3(3(0(5(4(2(4(1(2(3(5(0(3(4(5(2(4(3(x1)))))))))))))))))))) 4(5(1(4(5(3(1(5(5(3(5(0(2(1(2(4(4(5(1(0(4(x1))))))))))))))))))))) -> 4(4(0(2(1(5(2(0(4(5(2(2(3(5(5(2(2(0(3(5(4(x1))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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 2. The certificate found is represented by the following graph. "[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, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405] {(148,149,[0_1|0, 1_1|0, 2_1|0, 5_1|0, 4_1|0, 3_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]), (148,150,[0_1|1, 1_1|1, 2_1|1, 5_1|1, 4_1|1, 3_1|1]), (148,151,[0_1|2]), (148,154,[0_1|2]), (148,159,[0_1|2]), (148,167,[5_1|2]), (148,171,[4_1|2]), (148,176,[4_1|2]), (148,188,[5_1|2]), (148,192,[3_1|2]), (148,209,[5_1|2]), (148,219,[3_1|2]), (148,223,[5_1|2]), (148,240,[2_1|2]), (148,245,[5_1|2]), (148,261,[4_1|2]), (148,271,[2_1|2]), (148,287,[2_1|2]), (148,304,[5_1|2]), (148,308,[4_1|2]), (148,314,[4_1|2]), (148,320,[4_1|2]), (148,328,[4_1|2]), (148,348,[4_1|2]), (148,359,[3_1|2]), (148,368,[3_1|2]), (148,387,[3_1|2]), (149,149,[cons_0_1|0, cons_1_1|0, cons_2_1|0, cons_5_1|0, cons_4_1|0, cons_3_1|0]), (150,149,[encArg_1|1]), (150,150,[0_1|1, 1_1|1, 2_1|1, 5_1|1, 4_1|1, 3_1|1]), (150,151,[0_1|2]), (150,154,[0_1|2]), (150,159,[0_1|2]), (150,167,[5_1|2]), (150,171,[4_1|2]), (150,176,[4_1|2]), (150,188,[5_1|2]), (150,192,[3_1|2]), (150,209,[5_1|2]), (150,219,[3_1|2]), (150,223,[5_1|2]), (150,240,[2_1|2]), (150,245,[5_1|2]), (150,261,[4_1|2]), (150,271,[2_1|2]), (150,287,[2_1|2]), (150,304,[5_1|2]), (150,308,[4_1|2]), (150,314,[4_1|2]), (150,320,[4_1|2]), (150,328,[4_1|2]), (150,348,[4_1|2]), (150,359,[3_1|2]), (150,368,[3_1|2]), (150,387,[3_1|2]), (151,152,[2_1|2]), (151,245,[5_1|2]), (152,153,[2_1|2]), (152,219,[3_1|2]), (152,223,[5_1|2]), (153,150,[3_1|2]), (153,192,[3_1|2]), (153,219,[3_1|2]), (153,359,[3_1|2]), (153,368,[3_1|2]), (153,387,[3_1|2]), (153,241,[3_1|2]), (154,155,[3_1|2]), (155,156,[2_1|2]), (156,157,[2_1|2]), (156,261,[4_1|2]), (157,158,[4_1|2]), (157,320,[4_1|2]), (157,328,[4_1|2]), (158,150,[5_1|2]), (158,171,[5_1|2]), (158,176,[5_1|2]), (158,261,[5_1|2]), (158,308,[5_1|2]), (158,314,[5_1|2]), (158,320,[5_1|2]), (158,328,[5_1|2]), (158,348,[5_1|2]), (158,304,[5_1|2]), (159,160,[5_1|2]), (160,161,[4_1|2]), (161,162,[0_1|2]), (162,163,[5_1|2]), (163,164,[3_1|2]), (164,165,[5_1|2]), (165,166,[5_1|2]), (166,150,[3_1|2]), (166,192,[3_1|2]), (166,219,[3_1|2]), (166,359,[3_1|2]), (166,368,[3_1|2]), (166,387,[3_1|2]), (166,360,[3_1|2]), (167,168,[1_1|2]), (168,169,[0_1|2]), (169,170,[0_1|2]), (170,150,[5_1|2]), (170,167,[5_1|2]), (170,188,[5_1|2]), (170,209,[5_1|2]), (170,223,[5_1|2]), (170,245,[5_1|2]), (170,304,[5_1|2]), (171,172,[2_1|2]), (172,173,[5_1|2]), (173,174,[4_1|2]), (173,320,[4_1|2]), (174,175,[5_1|2]), (175,150,[3_1|2]), (175,192,[3_1|2]), (175,219,[3_1|2]), (175,359,[3_1|2]), (175,368,[3_1|2]), (175,387,[3_1|2]), (175,155,[3_1|2]), (176,177,[4_1|2]), (177,178,[4_1|2]), (178,179,[3_1|2]), (179,180,[2_1|2]), (180,181,[0_1|2]), (181,182,[1_1|2]), (182,183,[3_1|2]), (183,184,[1_1|2]), (184,185,[2_1|2]), (185,186,[2_1|2]), (185,261,[4_1|2]), (186,187,[4_1|2]), (186,320,[4_1|2]), (186,328,[4_1|2]), (187,150,[5_1|2]), (187,240,[5_1|2]), (187,271,[5_1|2]), (187,287,[5_1|2]), (187,369,[5_1|2]), (187,156,[5_1|2]), (187,304,[5_1|2]), (188,189,[0_1|2]), (189,190,[1_1|2]), (190,191,[1_1|2]), (190,167,[5_1|2]), (191,150,[1_1|2]), (191,192,[1_1|2, 3_1|2]), (191,219,[1_1|2]), (191,359,[1_1|2]), (191,368,[1_1|2]), (191,387,[1_1|2]), (191,167,[5_1|2]), (191,171,[4_1|2]), (191,176,[4_1|2]), (191,188,[5_1|2]), (191,209,[5_1|2]), (192,193,[5_1|2]), (193,194,[4_1|2]), (194,195,[2_1|2]), (195,196,[0_1|2]), (196,197,[5_1|2]), (197,198,[1_1|2]), (198,199,[3_1|2]), (199,200,[4_1|2]), (200,201,[1_1|2]), (201,202,[1_1|2]), (202,203,[2_1|2]), (203,204,[5_1|2]), (204,205,[2_1|2]), (205,206,[4_1|2]), (206,207,[1_1|2]), (206,188,[5_1|2]), (207,208,[5_1|2]), (208,150,[2_1|2]), (208,240,[2_1|2]), (208,271,[2_1|2]), (208,287,[2_1|2]), (208,224,[2_1|2]), (208,219,[3_1|2]), (208,223,[5_1|2]), (208,245,[5_1|2]), (208,261,[4_1|2]), (209,210,[3_1|2]), (210,211,[3_1|2]), (211,212,[1_1|2]), (212,213,[2_1|2]), (213,214,[1_1|2]), (214,215,[1_1|2]), (215,216,[0_1|2]), (216,217,[3_1|2]), (217,218,[1_1|2]), (218,150,[3_1|2]), (218,151,[3_1|2]), (218,154,[3_1|2]), (218,159,[3_1|2]), (218,359,[3_1|2]), (218,368,[3_1|2]), (218,387,[3_1|2]), (219,220,[5_1|2]), (220,221,[4_1|2]), (221,222,[5_1|2]), (222,150,[5_1|2]), (222,167,[5_1|2]), (222,188,[5_1|2]), (222,209,[5_1|2]), (222,223,[5_1|2]), (222,245,[5_1|2]), (222,304,[5_1|2]), (223,224,[2_1|2]), (224,225,[0_1|2]), (225,226,[2_1|2]), (226,227,[0_1|2]), (227,228,[3_1|2]), (228,229,[2_1|2]), (229,230,[3_1|2]), (230,231,[5_1|2]), (231,232,[2_1|2]), (232,233,[2_1|2]), (233,234,[4_1|2]), (234,235,[1_1|2]), (235,236,[3_1|2]), (236,237,[5_1|2]), (237,238,[5_1|2]), (238,239,[1_1|2]), (238,171,[4_1|2]), (238,176,[4_1|2]), (239,150,[2_1|2]), (239,240,[2_1|2]), (239,271,[2_1|2]), (239,287,[2_1|2]), (239,172,[2_1|2]), (239,219,[3_1|2]), (239,223,[5_1|2]), (239,245,[5_1|2]), (239,261,[4_1|2]), (240,241,[3_1|2]), (241,242,[5_1|2]), (242,243,[4_1|2]), (243,244,[0_1|2]), (244,150,[3_1|2]), (244,151,[3_1|2]), (244,154,[3_1|2]), (244,159,[3_1|2]), (244,359,[3_1|2]), (244,368,[3_1|2]), (244,387,[3_1|2]), (245,246,[5_1|2]), (246,247,[5_1|2]), (247,248,[2_1|2]), (248,249,[0_1|2]), (249,250,[2_1|2]), (250,251,[5_1|2]), (251,252,[0_1|2]), (252,253,[0_1|2]), (253,254,[4_1|2]), (254,255,[3_1|2]), (255,256,[2_1|2]), (256,257,[1_1|2]), (257,258,[4_1|2]), (258,259,[3_1|2]), (259,260,[3_1|2]), (260,150,[1_1|2]), (260,388,[1_1|2]), (260,167,[5_1|2]), (260,171,[4_1|2]), (260,176,[4_1|2]), (260,188,[5_1|2]), (260,192,[3_1|2]), (260,209,[5_1|2]), (261,262,[1_1|2]), (262,263,[0_1|2]), (263,264,[1_1|2]), (264,265,[1_1|2]), (265,266,[3_1|2]), (266,267,[3_1|2]), (267,268,[0_1|2]), (268,269,[1_1|2]), (269,270,[4_1|2]), (270,150,[2_1|2]), (270,240,[2_1|2]), (270,271,[2_1|2]), (270,287,[2_1|2]), (270,172,[2_1|2]), (270,219,[3_1|2]), (270,223,[5_1|2]), (270,245,[5_1|2]), (270,261,[4_1|2]), (271,272,[1_1|2]), (272,273,[3_1|2]), (273,274,[0_1|2]), (274,275,[4_1|2]), (275,276,[4_1|2]), (276,277,[1_1|2]), (277,278,[5_1|2]), (278,279,[2_1|2]), (279,280,[1_1|2]), (280,281,[0_1|2]), (281,282,[3_1|2]), (282,283,[0_1|2]), (283,284,[5_1|2]), (284,285,[0_1|2]), (285,286,[1_1|2]), (285,188,[5_1|2]), (285,192,[3_1|2]), (286,150,[5_1|2]), (286,151,[5_1|2]), (286,154,[5_1|2]), (286,159,[5_1|2]), (286,304,[5_1|2]), (287,288,[1_1|2]), (288,289,[5_1|2]), (289,290,[0_1|2]), (290,291,[0_1|2]), (291,292,[1_1|2]), (292,293,[5_1|2]), (293,294,[2_1|2]), (294,295,[2_1|2]), (295,296,[2_1|2]), (296,297,[3_1|2]), (297,298,[1_1|2]), (298,299,[0_1|2]), (299,300,[5_1|2]), (300,301,[0_1|2]), (301,302,[4_1|2]), (302,303,[3_1|2]), (302,359,[3_1|2]), (303,150,[3_1|2]), (303,240,[3_1|2]), (303,271,[3_1|2]), (303,287,[3_1|2]), (303,369,[3_1|2]), (303,359,[3_1|2]), (303,368,[3_1|2]), (303,387,[3_1|2]), (304,305,[1_1|2]), (305,306,[4_1|2]), (305,320,[4_1|2]), (306,307,[5_1|2]), (307,150,[3_1|2]), (307,192,[3_1|2]), (307,219,[3_1|2]), (307,359,[3_1|2]), (307,368,[3_1|2]), (307,387,[3_1|2]), (307,210,[3_1|2]), (308,309,[1_1|2]), (309,310,[3_1|2]), (310,311,[0_1|2]), (311,312,[5_1|2]), (312,313,[0_1|2]), (313,150,[5_1|2]), (313,171,[5_1|2]), (313,176,[5_1|2]), (313,261,[5_1|2]), (313,308,[5_1|2]), (313,314,[5_1|2]), (313,320,[5_1|2]), (313,328,[5_1|2]), (313,348,[5_1|2]), (313,177,[5_1|2]), (313,321,[5_1|2]), (313,329,[5_1|2]), (313,304,[5_1|2]), (314,315,[1_1|2]), (315,316,[2_1|2]), (316,317,[3_1|2]), (317,318,[4_1|2]), (318,319,[1_1|2]), (319,150,[4_1|2]), (319,240,[4_1|2]), (319,271,[4_1|2]), (319,287,[4_1|2]), (319,308,[4_1|2]), (319,314,[4_1|2]), (319,320,[4_1|2]), (319,328,[4_1|2]), (319,348,[4_1|2]), (320,321,[4_1|2]), (321,322,[3_1|2]), (322,323,[1_1|2]), (323,324,[3_1|2]), (324,325,[2_1|2]), (325,326,[0_1|2]), (326,327,[5_1|2]), (327,150,[2_1|2]), (327,240,[2_1|2]), (327,271,[2_1|2]), (327,287,[2_1|2]), (327,224,[2_1|2]), (327,219,[3_1|2]), (327,223,[5_1|2]), (327,245,[5_1|2]), (327,261,[4_1|2]), (328,329,[4_1|2]), (329,330,[0_1|2]), (330,331,[2_1|2]), (331,332,[1_1|2]), (332,333,[5_1|2]), (333,334,[2_1|2]), (334,335,[0_1|2]), (335,336,[4_1|2]), (336,337,[5_1|2]), (337,338,[2_1|2]), (338,339,[2_1|2]), (339,340,[3_1|2]), (340,341,[5_1|2]), (341,342,[5_1|2]), (342,343,[2_1|2]), (343,344,[2_1|2]), (344,345,[0_1|2]), (345,346,[3_1|2]), (346,347,[5_1|2]), (347,150,[4_1|2]), (347,171,[4_1|2]), (347,176,[4_1|2]), (347,261,[4_1|2]), (347,308,[4_1|2]), (347,314,[4_1|2]), (347,320,[4_1|2]), (347,328,[4_1|2]), (347,348,[4_1|2]), (348,349,[1_1|2]), (349,350,[4_1|2]), (350,351,[3_1|2]), (351,352,[4_1|2]), (352,353,[4_1|2]), (353,354,[0_1|2]), (354,355,[1_1|2]), (355,356,[3_1|2]), (356,357,[1_1|2]), (357,358,[1_1|2]), (357,188,[5_1|2]), (357,192,[3_1|2]), (358,150,[5_1|2]), (358,151,[5_1|2]), (358,154,[5_1|2]), (358,159,[5_1|2]), (358,304,[5_1|2]), (359,360,[3_1|2]), (360,361,[4_1|2]), (361,362,[1_1|2]), (362,363,[5_1|2]), (363,364,[0_1|2]), (364,365,[3_1|2]), (365,366,[0_1|2]), (366,367,[2_1|2]), (366,261,[4_1|2]), (366,271,[2_1|2]), (367,150,[4_1|2]), (367,240,[4_1|2]), (367,271,[4_1|2]), (367,287,[4_1|2]), (367,224,[4_1|2]), (367,308,[4_1|2]), (367,314,[4_1|2]), (367,320,[4_1|2]), (367,328,[4_1|2]), (367,348,[4_1|2]), (368,369,[2_1|2]), (369,370,[0_1|2]), (370,371,[1_1|2]), (371,372,[5_1|2]), (372,373,[0_1|2]), (373,374,[1_1|2]), (374,375,[5_1|2]), (375,376,[5_1|2]), (376,377,[1_1|2]), (377,378,[2_1|2]), (378,379,[3_1|2]), (379,380,[0_1|2]), (380,381,[2_1|2]), (381,382,[4_1|2]), (382,383,[2_1|2]), (383,384,[5_1|2]), (384,385,[2_1|2]), (385,386,[2_1|2]), (385,261,[4_1|2]), (385,271,[2_1|2]), (386,150,[4_1|2]), (386,171,[4_1|2]), (386,176,[4_1|2]), (386,261,[4_1|2]), (386,308,[4_1|2]), (386,314,[4_1|2]), (386,320,[4_1|2]), (386,328,[4_1|2]), (386,348,[4_1|2]), (387,388,[1_1|2]), (388,389,[3_1|2]), (389,390,[3_1|2]), (390,391,[0_1|2]), (391,392,[5_1|2]), (392,393,[4_1|2]), (393,394,[2_1|2]), (394,395,[4_1|2]), (395,396,[1_1|2]), (396,397,[2_1|2]), (397,398,[3_1|2]), (398,399,[5_1|2]), (399,400,[0_1|2]), (400,401,[3_1|2]), (401,402,[4_1|2]), (402,403,[5_1|2]), (403,404,[2_1|2]), (403,271,[2_1|2]), (404,405,[4_1|2]), (404,314,[4_1|2]), (405,150,[3_1|2]), (405,192,[3_1|2]), (405,219,[3_1|2]), (405,359,[3_1|2]), (405,368,[3_1|2]), (405,387,[3_1|2]), (405,241,[3_1|2])}" ---------------------------------------- (8) BOUNDS(1, n^1)