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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 45 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 185 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(0(1(x1))) -> 2(3(1(4(0(0(x1)))))) 1(0(0(x1))) -> 0(2(3(1(0(x1))))) 1(0(1(x1))) -> 0(2(1(2(3(1(x1)))))) 1(0(1(x1))) -> 1(0(5(2(3(1(x1)))))) 1(0(1(x1))) -> 2(1(0(2(3(1(x1)))))) 4(0(0(x1))) -> 0(2(3(4(0(x1))))) 4(0(1(x1))) -> 0(2(2(1(4(x1))))) 4(0(1(x1))) -> 0(2(3(4(1(x1))))) 5(1(0(x1))) -> 5(2(3(1(0(x1))))) 5(1(0(x1))) -> 5(2(3(3(1(0(x1)))))) 5(1(1(x1))) -> 2(3(1(4(1(5(x1)))))) 5(1(1(x1))) -> 5(3(2(3(1(1(x1)))))) 0(0(3(0(x1)))) -> 4(0(0(2(3(0(x1)))))) 0(3(0(1(x1)))) -> 0(0(2(2(1(3(x1)))))) 1(0(3(1(x1)))) -> 0(1(2(3(1(3(x1)))))) 1(0(3(1(x1)))) -> 0(4(1(2(3(1(x1)))))) 1(2(5(1(x1)))) -> 5(4(2(3(1(1(x1)))))) 4(0(1(1(x1)))) -> 0(2(4(1(1(x1))))) 4(0(1(5(x1)))) -> 5(0(2(3(1(4(x1)))))) 4(0(1(5(x1)))) -> 5(4(1(3(4(0(x1)))))) 4(0(3(0(x1)))) -> 0(2(3(0(4(5(x1)))))) 4(0(3(5(x1)))) -> 0(2(3(4(1(5(x1)))))) 4(2(5(0(x1)))) -> 4(5(2(3(0(x1))))) 4(2(5(0(x1)))) -> 4(0(2(3(5(4(x1)))))) 4(3(0(0(x1)))) -> 0(2(3(4(3(0(x1)))))) 4(3(0(1(x1)))) -> 1(4(0(2(3(x1))))) 4(3(0(1(x1)))) -> 3(0(2(2(4(1(x1)))))) 5(1(1(1(x1)))) -> 2(2(1(1(5(1(x1)))))) 0(0(1(2(5(x1))))) -> 2(3(1(5(0(0(x1)))))) 0(1(3(0(0(x1))))) -> 2(3(1(0(0(0(x1)))))) 0(2(5(3(1(x1))))) -> 2(0(5(4(1(3(x1)))))) 0(2(5(5(1(x1))))) -> 0(2(1(5(4(5(x1)))))) 0(3(0(5(1(x1))))) -> 2(1(5(3(0(0(x1)))))) 0(4(3(5(1(x1))))) -> 2(4(3(1(0(5(x1)))))) 0(5(1(1(5(x1))))) -> 0(1(2(1(5(5(x1)))))) 0(5(1(3(0(x1))))) -> 2(1(3(5(0(0(x1)))))) 1(0(4(1(5(x1))))) -> 4(1(2(1(5(0(x1)))))) 1(2(4(5(1(x1))))) -> 1(4(1(5(2(3(x1)))))) 1(2(5(3(0(x1))))) -> 1(4(2(3(5(0(x1)))))) 1(3(0(4(0(x1))))) -> 0(2(3(1(4(0(x1)))))) 4(0(3(1(5(x1))))) -> 4(4(3(5(0(1(x1)))))) 4(2(5(0(0(x1))))) -> 0(5(2(0(4(4(x1)))))) 4(2(5(0(0(x1))))) -> 5(2(3(4(0(0(x1)))))) 4(2(5(3(0(x1))))) -> 4(0(2(5(2(3(x1)))))) 4(2(5(3(0(x1))))) -> 5(2(4(3(1(0(x1)))))) 4(2(5(3(1(x1))))) -> 2(3(1(5(4(2(x1)))))) 4(3(0(0(1(x1))))) -> 2(4(3(1(0(0(x1)))))) 4(3(2(5(0(x1))))) -> 0(4(2(3(4(5(x1)))))) 4(5(1(3(1(x1))))) -> 4(1(3(5(4(1(x1)))))) 5(1(4(3(1(x1))))) -> 5(3(2(4(1(1(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(0(1(x1))) -> 2(3(1(4(0(0(x1)))))) 1(0(0(x1))) -> 0(2(3(1(0(x1))))) 1(0(1(x1))) -> 0(2(1(2(3(1(x1)))))) 1(0(1(x1))) -> 1(0(5(2(3(1(x1)))))) 1(0(1(x1))) -> 2(1(0(2(3(1(x1)))))) 4(0(0(x1))) -> 0(2(3(4(0(x1))))) 4(0(1(x1))) -> 0(2(2(1(4(x1))))) 4(0(1(x1))) -> 0(2(3(4(1(x1))))) 5(1(0(x1))) -> 5(2(3(1(0(x1))))) 5(1(0(x1))) -> 5(2(3(3(1(0(x1)))))) 5(1(1(x1))) -> 2(3(1(4(1(5(x1)))))) 5(1(1(x1))) -> 5(3(2(3(1(1(x1)))))) 0(0(3(0(x1)))) -> 4(0(0(2(3(0(x1)))))) 0(3(0(1(x1)))) -> 0(0(2(2(1(3(x1)))))) 1(0(3(1(x1)))) -> 0(1(2(3(1(3(x1)))))) 1(0(3(1(x1)))) -> 0(4(1(2(3(1(x1)))))) 1(2(5(1(x1)))) -> 5(4(2(3(1(1(x1)))))) 4(0(1(1(x1)))) -> 0(2(4(1(1(x1))))) 4(0(1(5(x1)))) -> 5(0(2(3(1(4(x1)))))) 4(0(1(5(x1)))) -> 5(4(1(3(4(0(x1)))))) 4(0(3(0(x1)))) -> 0(2(3(0(4(5(x1)))))) 4(0(3(5(x1)))) -> 0(2(3(4(1(5(x1)))))) 4(2(5(0(x1)))) -> 4(5(2(3(0(x1))))) 4(2(5(0(x1)))) -> 4(0(2(3(5(4(x1)))))) 4(3(0(0(x1)))) -> 0(2(3(4(3(0(x1)))))) 4(3(0(1(x1)))) -> 1(4(0(2(3(x1))))) 4(3(0(1(x1)))) -> 3(0(2(2(4(1(x1)))))) 5(1(1(1(x1)))) -> 2(2(1(1(5(1(x1)))))) 0(0(1(2(5(x1))))) -> 2(3(1(5(0(0(x1)))))) 0(1(3(0(0(x1))))) -> 2(3(1(0(0(0(x1)))))) 0(2(5(3(1(x1))))) -> 2(0(5(4(1(3(x1)))))) 0(2(5(5(1(x1))))) -> 0(2(1(5(4(5(x1)))))) 0(3(0(5(1(x1))))) -> 2(1(5(3(0(0(x1)))))) 0(4(3(5(1(x1))))) -> 2(4(3(1(0(5(x1)))))) 0(5(1(1(5(x1))))) -> 0(1(2(1(5(5(x1)))))) 0(5(1(3(0(x1))))) -> 2(1(3(5(0(0(x1)))))) 1(0(4(1(5(x1))))) -> 4(1(2(1(5(0(x1)))))) 1(2(4(5(1(x1))))) -> 1(4(1(5(2(3(x1)))))) 1(2(5(3(0(x1))))) -> 1(4(2(3(5(0(x1)))))) 1(3(0(4(0(x1))))) -> 0(2(3(1(4(0(x1)))))) 4(0(3(1(5(x1))))) -> 4(4(3(5(0(1(x1)))))) 4(2(5(0(0(x1))))) -> 0(5(2(0(4(4(x1)))))) 4(2(5(0(0(x1))))) -> 5(2(3(4(0(0(x1)))))) 4(2(5(3(0(x1))))) -> 4(0(2(5(2(3(x1)))))) 4(2(5(3(0(x1))))) -> 5(2(4(3(1(0(x1)))))) 4(2(5(3(1(x1))))) -> 2(3(1(5(4(2(x1)))))) 4(3(0(0(1(x1))))) -> 2(4(3(1(0(0(x1)))))) 4(3(2(5(0(x1))))) -> 0(4(2(3(4(5(x1)))))) 4(5(1(3(1(x1))))) -> 4(1(3(5(4(1(x1)))))) 5(1(4(3(1(x1))))) -> 5(3(2(4(1(1(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(0(1(x1))) -> 2(3(1(4(0(0(x1)))))) 1(0(0(x1))) -> 0(2(3(1(0(x1))))) 1(0(1(x1))) -> 0(2(1(2(3(1(x1)))))) 1(0(1(x1))) -> 1(0(5(2(3(1(x1)))))) 1(0(1(x1))) -> 2(1(0(2(3(1(x1)))))) 4(0(0(x1))) -> 0(2(3(4(0(x1))))) 4(0(1(x1))) -> 0(2(2(1(4(x1))))) 4(0(1(x1))) -> 0(2(3(4(1(x1))))) 5(1(0(x1))) -> 5(2(3(1(0(x1))))) 5(1(0(x1))) -> 5(2(3(3(1(0(x1)))))) 5(1(1(x1))) -> 2(3(1(4(1(5(x1)))))) 5(1(1(x1))) -> 5(3(2(3(1(1(x1)))))) 0(0(3(0(x1)))) -> 4(0(0(2(3(0(x1)))))) 0(3(0(1(x1)))) -> 0(0(2(2(1(3(x1)))))) 1(0(3(1(x1)))) -> 0(1(2(3(1(3(x1)))))) 1(0(3(1(x1)))) -> 0(4(1(2(3(1(x1)))))) 1(2(5(1(x1)))) -> 5(4(2(3(1(1(x1)))))) 4(0(1(1(x1)))) -> 0(2(4(1(1(x1))))) 4(0(1(5(x1)))) -> 5(0(2(3(1(4(x1)))))) 4(0(1(5(x1)))) -> 5(4(1(3(4(0(x1)))))) 4(0(3(0(x1)))) -> 0(2(3(0(4(5(x1)))))) 4(0(3(5(x1)))) -> 0(2(3(4(1(5(x1)))))) 4(2(5(0(x1)))) -> 4(5(2(3(0(x1))))) 4(2(5(0(x1)))) -> 4(0(2(3(5(4(x1)))))) 4(3(0(0(x1)))) -> 0(2(3(4(3(0(x1)))))) 4(3(0(1(x1)))) -> 1(4(0(2(3(x1))))) 4(3(0(1(x1)))) -> 3(0(2(2(4(1(x1)))))) 5(1(1(1(x1)))) -> 2(2(1(1(5(1(x1)))))) 0(0(1(2(5(x1))))) -> 2(3(1(5(0(0(x1)))))) 0(1(3(0(0(x1))))) -> 2(3(1(0(0(0(x1)))))) 0(2(5(3(1(x1))))) -> 2(0(5(4(1(3(x1)))))) 0(2(5(5(1(x1))))) -> 0(2(1(5(4(5(x1)))))) 0(3(0(5(1(x1))))) -> 2(1(5(3(0(0(x1)))))) 0(4(3(5(1(x1))))) -> 2(4(3(1(0(5(x1)))))) 0(5(1(1(5(x1))))) -> 0(1(2(1(5(5(x1)))))) 0(5(1(3(0(x1))))) -> 2(1(3(5(0(0(x1)))))) 1(0(4(1(5(x1))))) -> 4(1(2(1(5(0(x1)))))) 1(2(4(5(1(x1))))) -> 1(4(1(5(2(3(x1)))))) 1(2(5(3(0(x1))))) -> 1(4(2(3(5(0(x1)))))) 1(3(0(4(0(x1))))) -> 0(2(3(1(4(0(x1)))))) 4(0(3(1(5(x1))))) -> 4(4(3(5(0(1(x1)))))) 4(2(5(0(0(x1))))) -> 0(5(2(0(4(4(x1)))))) 4(2(5(0(0(x1))))) -> 5(2(3(4(0(0(x1)))))) 4(2(5(3(0(x1))))) -> 4(0(2(5(2(3(x1)))))) 4(2(5(3(0(x1))))) -> 5(2(4(3(1(0(x1)))))) 4(2(5(3(1(x1))))) -> 2(3(1(5(4(2(x1)))))) 4(3(0(0(1(x1))))) -> 2(4(3(1(0(0(x1)))))) 4(3(2(5(0(x1))))) -> 0(4(2(3(4(5(x1)))))) 4(5(1(3(1(x1))))) -> 4(1(3(5(4(1(x1)))))) 5(1(4(3(1(x1))))) -> 5(3(2(4(1(1(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(0(1(x1))) -> 2(3(1(4(0(0(x1)))))) 1(0(0(x1))) -> 0(2(3(1(0(x1))))) 1(0(1(x1))) -> 0(2(1(2(3(1(x1)))))) 1(0(1(x1))) -> 1(0(5(2(3(1(x1)))))) 1(0(1(x1))) -> 2(1(0(2(3(1(x1)))))) 4(0(0(x1))) -> 0(2(3(4(0(x1))))) 4(0(1(x1))) -> 0(2(2(1(4(x1))))) 4(0(1(x1))) -> 0(2(3(4(1(x1))))) 5(1(0(x1))) -> 5(2(3(1(0(x1))))) 5(1(0(x1))) -> 5(2(3(3(1(0(x1)))))) 5(1(1(x1))) -> 2(3(1(4(1(5(x1)))))) 5(1(1(x1))) -> 5(3(2(3(1(1(x1)))))) 0(0(3(0(x1)))) -> 4(0(0(2(3(0(x1)))))) 0(3(0(1(x1)))) -> 0(0(2(2(1(3(x1)))))) 1(0(3(1(x1)))) -> 0(1(2(3(1(3(x1)))))) 1(0(3(1(x1)))) -> 0(4(1(2(3(1(x1)))))) 1(2(5(1(x1)))) -> 5(4(2(3(1(1(x1)))))) 4(0(1(1(x1)))) -> 0(2(4(1(1(x1))))) 4(0(1(5(x1)))) -> 5(0(2(3(1(4(x1)))))) 4(0(1(5(x1)))) -> 5(4(1(3(4(0(x1)))))) 4(0(3(0(x1)))) -> 0(2(3(0(4(5(x1)))))) 4(0(3(5(x1)))) -> 0(2(3(4(1(5(x1)))))) 4(2(5(0(x1)))) -> 4(5(2(3(0(x1))))) 4(2(5(0(x1)))) -> 4(0(2(3(5(4(x1)))))) 4(3(0(0(x1)))) -> 0(2(3(4(3(0(x1)))))) 4(3(0(1(x1)))) -> 1(4(0(2(3(x1))))) 4(3(0(1(x1)))) -> 3(0(2(2(4(1(x1)))))) 5(1(1(1(x1)))) -> 2(2(1(1(5(1(x1)))))) 0(0(1(2(5(x1))))) -> 2(3(1(5(0(0(x1)))))) 0(1(3(0(0(x1))))) -> 2(3(1(0(0(0(x1)))))) 0(2(5(3(1(x1))))) -> 2(0(5(4(1(3(x1)))))) 0(2(5(5(1(x1))))) -> 0(2(1(5(4(5(x1)))))) 0(3(0(5(1(x1))))) -> 2(1(5(3(0(0(x1)))))) 0(4(3(5(1(x1))))) -> 2(4(3(1(0(5(x1)))))) 0(5(1(1(5(x1))))) -> 0(1(2(1(5(5(x1)))))) 0(5(1(3(0(x1))))) -> 2(1(3(5(0(0(x1)))))) 1(0(4(1(5(x1))))) -> 4(1(2(1(5(0(x1)))))) 1(2(4(5(1(x1))))) -> 1(4(1(5(2(3(x1)))))) 1(2(5(3(0(x1))))) -> 1(4(2(3(5(0(x1)))))) 1(3(0(4(0(x1))))) -> 0(2(3(1(4(0(x1)))))) 4(0(3(1(5(x1))))) -> 4(4(3(5(0(1(x1)))))) 4(2(5(0(0(x1))))) -> 0(5(2(0(4(4(x1)))))) 4(2(5(0(0(x1))))) -> 5(2(3(4(0(0(x1)))))) 4(2(5(3(0(x1))))) -> 4(0(2(5(2(3(x1)))))) 4(2(5(3(0(x1))))) -> 5(2(4(3(1(0(x1)))))) 4(2(5(3(1(x1))))) -> 2(3(1(5(4(2(x1)))))) 4(3(0(0(1(x1))))) -> 2(4(3(1(0(0(x1)))))) 4(3(2(5(0(x1))))) -> 0(4(2(3(4(5(x1)))))) 4(5(1(3(1(x1))))) -> 4(1(3(5(4(1(x1)))))) 5(1(4(3(1(x1))))) -> 5(3(2(4(1(1(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 4. The certificate found is represented by the following graph. 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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, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518] {(82,83,[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]), (82,84,[2_1|1, 3_1|1, 0_1|1, 1_1|1, 4_1|1, 5_1|1]), (82,85,[2_1|2]), (82,90,[2_1|2]), (82,95,[4_1|2]), (82,100,[0_1|2]), (82,105,[2_1|2]), (82,110,[2_1|2]), (82,115,[2_1|2]), (82,120,[0_1|2]), (82,125,[2_1|2]), (82,130,[0_1|2]), (82,135,[2_1|2]), (82,140,[0_1|2]), (82,144,[0_1|2]), (82,149,[1_1|2]), (82,154,[2_1|2]), (82,159,[0_1|2]), (82,164,[0_1|2]), (82,169,[4_1|2]), (82,174,[5_1|2]), (82,179,[1_1|2]), (82,184,[1_1|2]), (82,189,[0_1|2]), (82,194,[0_1|2]), (82,198,[0_1|2]), (82,202,[0_1|2]), (82,206,[0_1|2]), (82,210,[5_1|2]), (82,215,[5_1|2]), (82,220,[0_1|2]), (82,225,[0_1|2]), (82,230,[4_1|2]), (82,235,[4_1|2]), (82,239,[4_1|2]), (82,244,[0_1|2]), (82,249,[5_1|2]), 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(459,460,[3_1|3]), (460,461,[1_1|3]), (460,140,[0_1|2]), (460,144,[0_1|2]), (460,149,[1_1|2]), (460,154,[2_1|2]), (460,159,[0_1|2]), (460,164,[0_1|2]), (460,169,[4_1|2]), (460,363,[0_1|3]), (460,367,[0_1|3]), (460,372,[1_1|3]), (460,377,[2_1|3]), (460,510,[0_1|4]), (460,514,[4_1|3]), (461,84,[0_1|3]), (461,149,[0_1|3]), (461,179,[0_1|3]), (461,184,[0_1|3]), (461,279,[0_1|3]), (461,131,[0_1|3]), (461,160,[0_1|3]), (461,100,[0_1|3, 0_1|2]), (461,120,[0_1|3, 0_1|2]), (461,130,[0_1|3, 0_1|2]), (461,140,[0_1|3]), (461,144,[0_1|3]), (461,159,[0_1|3]), (461,164,[0_1|3]), (461,189,[0_1|3]), (461,194,[0_1|3]), (461,198,[0_1|3]), (461,202,[0_1|3]), (461,206,[0_1|3]), (461,220,[0_1|3]), (461,225,[0_1|3]), (461,244,[0_1|3]), (461,269,[0_1|3]), (461,288,[0_1|3]), (461,101,[0_1|3]), (461,85,[2_1|2]), (461,90,[2_1|2]), (461,95,[4_1|2]), (461,105,[2_1|2]), (461,110,[2_1|2]), (461,115,[2_1|2]), (461,125,[2_1|2]), (461,135,[2_1|2]), (461,345,[2_1|3]), (461,327,[0_1|3]), (462,463,[2_1|3]), (463,464,[3_1|3]), (464,465,[1_1|3]), (464,382,[0_1|3]), (464,386,[0_1|3]), (464,391,[1_1|3]), (464,396,[2_1|3]), (465,100,[0_1|3]), (465,120,[0_1|3]), (465,130,[0_1|3]), (465,140,[0_1|3]), (465,144,[0_1|3]), (465,159,[0_1|3]), (465,164,[0_1|3]), (465,189,[0_1|3]), (465,194,[0_1|3]), (465,198,[0_1|3]), (465,202,[0_1|3]), (465,206,[0_1|3]), (465,220,[0_1|3]), (465,225,[0_1|3]), (465,244,[0_1|3]), (465,269,[0_1|3]), (465,288,[0_1|3]), (465,327,[0_1|3]), (465,150,[0_1|3]), (465,392,[0_1|3]), (466,467,[2_1|3]), (467,468,[3_1|3]), (468,469,[3_1|3]), (469,470,[1_1|3]), (469,382,[0_1|3]), (469,386,[0_1|3]), (469,391,[1_1|3]), (469,396,[2_1|3]), (470,100,[0_1|3]), (470,120,[0_1|3]), (470,130,[0_1|3]), (470,140,[0_1|3]), (470,144,[0_1|3]), (470,159,[0_1|3]), (470,164,[0_1|3]), (470,189,[0_1|3]), (470,194,[0_1|3]), (470,198,[0_1|3]), (470,202,[0_1|3]), (470,206,[0_1|3]), (470,220,[0_1|3]), (470,225,[0_1|3]), (470,244,[0_1|3]), (470,269,[0_1|3]), (470,288,[0_1|3]), (470,327,[0_1|3]), (470,150,[0_1|3]), (470,392,[0_1|3]), (471,472,[3_1|3]), (472,473,[1_1|3]), (473,474,[4_1|3]), (474,475,[1_1|3]), (475,149,[5_1|3]), (475,179,[5_1|3]), (475,184,[5_1|3]), (475,279,[5_1|3]), (476,477,[3_1|3]), (477,478,[2_1|3]), (478,479,[3_1|3]), (479,480,[1_1|3]), (480,149,[1_1|3]), (480,179,[1_1|3]), (480,184,[1_1|3]), (480,279,[1_1|3]), (481,482,[2_1|4]), (482,483,[3_1|4]), (483,484,[4_1|4]), (484,342,[0_1|4]), (485,486,[4_1|3]), (486,487,[0_1|3]), (487,488,[2_1|3]), (488,160,[3_1|3]), (489,490,[0_1|3]), (490,491,[2_1|3]), (491,492,[2_1|3]), (492,493,[4_1|3]), (493,160,[1_1|3]), (494,495,[2_1|4]), (495,496,[3_1|4]), (496,497,[4_1|4]), (497,327,[0_1|4]), (498,499,[2_1|4]), (499,500,[3_1|4]), (500,501,[4_1|4]), (500,401,[0_1|3]), (501,149,[0_1|4]), (501,179,[0_1|4]), (501,184,[0_1|4]), (501,279,[0_1|4]), (501,131,[0_1|4]), (501,160,[0_1|4]), (502,503,[2_1|4]), (503,504,[3_1|4]), (504,505,[4_1|4]), (505,131,[0_1|4]), (505,160,[0_1|4]), (506,507,[2_1|4]), (507,508,[3_1|4]), (508,509,[1_1|4]), (509,131,[0_1|4]), (509,160,[0_1|4]), (510,511,[2_1|4]), (511,512,[3_1|4]), (512,513,[1_1|4]), (513,327,[0_1|4]), (514,515,[1_1|3]), (515,516,[2_1|3]), (516,517,[1_1|3]), (517,518,[5_1|3]), (518,187,[0_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)