WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 124 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 54 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) 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)))) -> 1(4(3(x1))) 1(2(0(4(2(x1))))) -> 3(4(5(4(x1)))) 3(3(0(3(2(x1))))) -> 3(2(4(1(x1)))) 5(2(1(0(4(x1))))) -> 5(5(4(5(x1)))) 0(1(4(5(0(5(x1)))))) -> 3(0(4(0(3(5(x1)))))) 0(2(5(2(1(5(x1)))))) -> 5(2(1(5(4(x1))))) 0(3(5(1(5(5(x1)))))) -> 0(5(1(5(4(x1))))) 2(2(5(1(4(5(4(3(x1)))))))) -> 2(2(3(3(0(1(0(3(x1)))))))) 0(0(0(2(4(1(2(2(4(x1))))))))) -> 0(0(0(4(3(3(4(4(x1)))))))) 2(4(4(3(4(2(0(3(2(x1))))))))) -> 3(4(3(4(1(3(3(1(x1)))))))) 0(1(4(3(2(3(2(3(5(3(x1)))))))))) -> 1(4(3(0(3(4(2(5(3(x1))))))))) 0(2(1(5(0(4(3(1(4(2(2(x1))))))))))) -> 0(0(4(0(5(1(0(5(4(4(2(x1))))))))))) 4(4(3(3(0(2(4(2(4(4(1(5(x1)))))))))))) -> 4(4(0(4(3(1(5(5(5(2(5(x1))))))))))) 5(3(0(0(5(5(2(0(2(2(3(3(x1)))))))))))) -> 5(5(4(1(5(2(0(5(2(4(3(x1))))))))))) 0(2(0(2(5(5(1(5(0(2(5(2(2(x1))))))))))))) -> 5(4(3(1(4(0(1(0(1(5(2(x1))))))))))) 0(3(1(4(4(2(0(5(4(0(1(0(4(x1))))))))))))) -> 0(0(4(4(1(0(4(0(0(2(2(4(4(x1))))))))))))) 1(2(4(1(1(0(2(5(3(4(0(1(4(0(3(x1))))))))))))))) -> 1(1(0(4(5(0(3(2(0(5(2(0(0(3(3(x1))))))))))))))) 2(3(5(2(4(4(5(1(4(4(4(1(3(2(3(x1))))))))))))))) -> 2(3(3(1(1(1(5(3(3(5(1(3(5(2(3(x1))))))))))))))) 5(4(2(5(2(5(3(2(3(3(1(5(0(0(5(x1))))))))))))))) -> 5(2(3(5(4(1(3(1(4(4(4(4(1(3(5(x1))))))))))))))) 0(0(2(4(1(2(2(1(3(2(0(4(5(5(4(2(x1)))))))))))))))) -> 0(5(1(1(0(2(3(5(4(3(0(2(5(2(3(5(1(x1))))))))))))))))) 0(1(1(5(3(0(1(4(2(2(4(0(1(0(2(3(4(x1))))))))))))))))) -> 0(4(2(2(0(1(5(4(4(0(2(2(2(5(5(4(x1)))))))))))))))) 0(2(3(2(5(2(4(3(2(4(3(0(2(4(5(1(3(x1))))))))))))))))) -> 3(4(3(5(2(5(3(1(5(0(1(0(5(5(2(3(x1)))))))))))))))) 4(5(4(5(4(2(1(4(5(0(2(0(4(3(0(0(1(0(0(2(x1)))))))))))))))))))) -> 4(4(2(2(5(2(0(0(0(5(3(4(1(2(2(1(1(5(0(0(x1)))))))))))))))))))) 3(0(1(0(5(2(4(4(4(5(2(4(1(1(4(5(4(0(3(2(1(x1))))))))))))))))))))) -> 3(4(2(0(4(5(2(2(2(3(3(3(5(0(5(5(3(2(1(1(4(x1))))))))))))))))))))) 3(3(2(1(0(0(3(1(2(0(2(1(2(3(5(4(0(2(2(1(1(x1))))))))))))))))))))) -> 3(4(5(2(4(3(4(3(5(3(4(5(4(2(5(5(1(0(1(x1))))))))))))))))))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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_3(x_1)) -> 3(encArg(x_1)) encArg(cons_5(x_1)) -> 5(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 (innermost) 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)))) -> 1(4(3(x1))) 1(2(0(4(2(x1))))) -> 3(4(5(4(x1)))) 3(3(0(3(2(x1))))) -> 3(2(4(1(x1)))) 5(2(1(0(4(x1))))) -> 5(5(4(5(x1)))) 0(1(4(5(0(5(x1)))))) -> 3(0(4(0(3(5(x1)))))) 0(2(5(2(1(5(x1)))))) -> 5(2(1(5(4(x1))))) 0(3(5(1(5(5(x1)))))) -> 0(5(1(5(4(x1))))) 2(2(5(1(4(5(4(3(x1)))))))) -> 2(2(3(3(0(1(0(3(x1)))))))) 0(0(0(2(4(1(2(2(4(x1))))))))) -> 0(0(0(4(3(3(4(4(x1)))))))) 2(4(4(3(4(2(0(3(2(x1))))))))) -> 3(4(3(4(1(3(3(1(x1)))))))) 0(1(4(3(2(3(2(3(5(3(x1)))))))))) -> 1(4(3(0(3(4(2(5(3(x1))))))))) 0(2(1(5(0(4(3(1(4(2(2(x1))))))))))) -> 0(0(4(0(5(1(0(5(4(4(2(x1))))))))))) 4(4(3(3(0(2(4(2(4(4(1(5(x1)))))))))))) -> 4(4(0(4(3(1(5(5(5(2(5(x1))))))))))) 5(3(0(0(5(5(2(0(2(2(3(3(x1)))))))))))) -> 5(5(4(1(5(2(0(5(2(4(3(x1))))))))))) 0(2(0(2(5(5(1(5(0(2(5(2(2(x1))))))))))))) -> 5(4(3(1(4(0(1(0(1(5(2(x1))))))))))) 0(3(1(4(4(2(0(5(4(0(1(0(4(x1))))))))))))) -> 0(0(4(4(1(0(4(0(0(2(2(4(4(x1))))))))))))) 1(2(4(1(1(0(2(5(3(4(0(1(4(0(3(x1))))))))))))))) -> 1(1(0(4(5(0(3(2(0(5(2(0(0(3(3(x1))))))))))))))) 2(3(5(2(4(4(5(1(4(4(4(1(3(2(3(x1))))))))))))))) -> 2(3(3(1(1(1(5(3(3(5(1(3(5(2(3(x1))))))))))))))) 5(4(2(5(2(5(3(2(3(3(1(5(0(0(5(x1))))))))))))))) -> 5(2(3(5(4(1(3(1(4(4(4(4(1(3(5(x1))))))))))))))) 0(0(2(4(1(2(2(1(3(2(0(4(5(5(4(2(x1)))))))))))))))) -> 0(5(1(1(0(2(3(5(4(3(0(2(5(2(3(5(1(x1))))))))))))))))) 0(1(1(5(3(0(1(4(2(2(4(0(1(0(2(3(4(x1))))))))))))))))) -> 0(4(2(2(0(1(5(4(4(0(2(2(2(5(5(4(x1)))))))))))))))) 0(2(3(2(5(2(4(3(2(4(3(0(2(4(5(1(3(x1))))))))))))))))) -> 3(4(3(5(2(5(3(1(5(0(1(0(5(5(2(3(x1)))))))))))))))) 4(5(4(5(4(2(1(4(5(0(2(0(4(3(0(0(1(0(0(2(x1)))))))))))))))))))) -> 4(4(2(2(5(2(0(0(0(5(3(4(1(2(2(1(1(5(0(0(x1)))))))))))))))))))) 3(0(1(0(5(2(4(4(4(5(2(4(1(1(4(5(4(0(3(2(1(x1))))))))))))))))))))) -> 3(4(2(0(4(5(2(2(2(3(3(3(5(0(5(5(3(2(1(1(4(x1))))))))))))))))))))) 3(3(2(1(0(0(3(1(2(0(2(1(2(3(5(4(0(2(2(1(1(x1))))))))))))))))))))) -> 3(4(5(2(4(3(4(3(5(3(4(5(4(2(5(5(1(0(1(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_3(x_1)) -> 3(encArg(x_1)) encArg(cons_5(x_1)) -> 5(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: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) 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)))) -> 1(4(3(x1))) 1(2(0(4(2(x1))))) -> 3(4(5(4(x1)))) 3(3(0(3(2(x1))))) -> 3(2(4(1(x1)))) 5(2(1(0(4(x1))))) -> 5(5(4(5(x1)))) 0(1(4(5(0(5(x1)))))) -> 3(0(4(0(3(5(x1)))))) 0(2(5(2(1(5(x1)))))) -> 5(2(1(5(4(x1))))) 0(3(5(1(5(5(x1)))))) -> 0(5(1(5(4(x1))))) 2(2(5(1(4(5(4(3(x1)))))))) -> 2(2(3(3(0(1(0(3(x1)))))))) 0(0(0(2(4(1(2(2(4(x1))))))))) -> 0(0(0(4(3(3(4(4(x1)))))))) 2(4(4(3(4(2(0(3(2(x1))))))))) -> 3(4(3(4(1(3(3(1(x1)))))))) 0(1(4(3(2(3(2(3(5(3(x1)))))))))) -> 1(4(3(0(3(4(2(5(3(x1))))))))) 0(2(1(5(0(4(3(1(4(2(2(x1))))))))))) -> 0(0(4(0(5(1(0(5(4(4(2(x1))))))))))) 4(4(3(3(0(2(4(2(4(4(1(5(x1)))))))))))) -> 4(4(0(4(3(1(5(5(5(2(5(x1))))))))))) 5(3(0(0(5(5(2(0(2(2(3(3(x1)))))))))))) -> 5(5(4(1(5(2(0(5(2(4(3(x1))))))))))) 0(2(0(2(5(5(1(5(0(2(5(2(2(x1))))))))))))) -> 5(4(3(1(4(0(1(0(1(5(2(x1))))))))))) 0(3(1(4(4(2(0(5(4(0(1(0(4(x1))))))))))))) -> 0(0(4(4(1(0(4(0(0(2(2(4(4(x1))))))))))))) 1(2(4(1(1(0(2(5(3(4(0(1(4(0(3(x1))))))))))))))) -> 1(1(0(4(5(0(3(2(0(5(2(0(0(3(3(x1))))))))))))))) 2(3(5(2(4(4(5(1(4(4(4(1(3(2(3(x1))))))))))))))) -> 2(3(3(1(1(1(5(3(3(5(1(3(5(2(3(x1))))))))))))))) 5(4(2(5(2(5(3(2(3(3(1(5(0(0(5(x1))))))))))))))) -> 5(2(3(5(4(1(3(1(4(4(4(4(1(3(5(x1))))))))))))))) 0(0(2(4(1(2(2(1(3(2(0(4(5(5(4(2(x1)))))))))))))))) -> 0(5(1(1(0(2(3(5(4(3(0(2(5(2(3(5(1(x1))))))))))))))))) 0(1(1(5(3(0(1(4(2(2(4(0(1(0(2(3(4(x1))))))))))))))))) -> 0(4(2(2(0(1(5(4(4(0(2(2(2(5(5(4(x1)))))))))))))))) 0(2(3(2(5(2(4(3(2(4(3(0(2(4(5(1(3(x1))))))))))))))))) -> 3(4(3(5(2(5(3(1(5(0(1(0(5(5(2(3(x1)))))))))))))))) 4(5(4(5(4(2(1(4(5(0(2(0(4(3(0(0(1(0(0(2(x1)))))))))))))))))))) -> 4(4(2(2(5(2(0(0(0(5(3(4(1(2(2(1(1(5(0(0(x1)))))))))))))))))))) 3(0(1(0(5(2(4(4(4(5(2(4(1(1(4(5(4(0(3(2(1(x1))))))))))))))))))))) -> 3(4(2(0(4(5(2(2(2(3(3(3(5(0(5(5(3(2(1(1(4(x1))))))))))))))))))))) 3(3(2(1(0(0(3(1(2(0(2(1(2(3(5(4(0(2(2(1(1(x1))))))))))))))))))))) -> 3(4(5(2(4(3(4(3(5(3(4(5(4(2(5(5(1(0(1(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_3(x_1)) -> 3(encArg(x_1)) encArg(cons_5(x_1)) -> 5(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: INNERMOST ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) 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)))) -> 1(4(3(x1))) 1(2(0(4(2(x1))))) -> 3(4(5(4(x1)))) 3(3(0(3(2(x1))))) -> 3(2(4(1(x1)))) 5(2(1(0(4(x1))))) -> 5(5(4(5(x1)))) 0(1(4(5(0(5(x1)))))) -> 3(0(4(0(3(5(x1)))))) 0(2(5(2(1(5(x1)))))) -> 5(2(1(5(4(x1))))) 0(3(5(1(5(5(x1)))))) -> 0(5(1(5(4(x1))))) 2(2(5(1(4(5(4(3(x1)))))))) -> 2(2(3(3(0(1(0(3(x1)))))))) 0(0(0(2(4(1(2(2(4(x1))))))))) -> 0(0(0(4(3(3(4(4(x1)))))))) 2(4(4(3(4(2(0(3(2(x1))))))))) -> 3(4(3(4(1(3(3(1(x1)))))))) 0(1(4(3(2(3(2(3(5(3(x1)))))))))) -> 1(4(3(0(3(4(2(5(3(x1))))))))) 0(2(1(5(0(4(3(1(4(2(2(x1))))))))))) -> 0(0(4(0(5(1(0(5(4(4(2(x1))))))))))) 4(4(3(3(0(2(4(2(4(4(1(5(x1)))))))))))) -> 4(4(0(4(3(1(5(5(5(2(5(x1))))))))))) 5(3(0(0(5(5(2(0(2(2(3(3(x1)))))))))))) -> 5(5(4(1(5(2(0(5(2(4(3(x1))))))))))) 0(2(0(2(5(5(1(5(0(2(5(2(2(x1))))))))))))) -> 5(4(3(1(4(0(1(0(1(5(2(x1))))))))))) 0(3(1(4(4(2(0(5(4(0(1(0(4(x1))))))))))))) -> 0(0(4(4(1(0(4(0(0(2(2(4(4(x1))))))))))))) 1(2(4(1(1(0(2(5(3(4(0(1(4(0(3(x1))))))))))))))) -> 1(1(0(4(5(0(3(2(0(5(2(0(0(3(3(x1))))))))))))))) 2(3(5(2(4(4(5(1(4(4(4(1(3(2(3(x1))))))))))))))) -> 2(3(3(1(1(1(5(3(3(5(1(3(5(2(3(x1))))))))))))))) 5(4(2(5(2(5(3(2(3(3(1(5(0(0(5(x1))))))))))))))) -> 5(2(3(5(4(1(3(1(4(4(4(4(1(3(5(x1))))))))))))))) 0(0(2(4(1(2(2(1(3(2(0(4(5(5(4(2(x1)))))))))))))))) -> 0(5(1(1(0(2(3(5(4(3(0(2(5(2(3(5(1(x1))))))))))))))))) 0(1(1(5(3(0(1(4(2(2(4(0(1(0(2(3(4(x1))))))))))))))))) -> 0(4(2(2(0(1(5(4(4(0(2(2(2(5(5(4(x1)))))))))))))))) 0(2(3(2(5(2(4(3(2(4(3(0(2(4(5(1(3(x1))))))))))))))))) -> 3(4(3(5(2(5(3(1(5(0(1(0(5(5(2(3(x1)))))))))))))))) 4(5(4(5(4(2(1(4(5(0(2(0(4(3(0(0(1(0(0(2(x1)))))))))))))))))))) -> 4(4(2(2(5(2(0(0(0(5(3(4(1(2(2(1(1(5(0(0(x1)))))))))))))))))))) 3(0(1(0(5(2(4(4(4(5(2(4(1(1(4(5(4(0(3(2(1(x1))))))))))))))))))))) -> 3(4(2(0(4(5(2(2(2(3(3(3(5(0(5(5(3(2(1(1(4(x1))))))))))))))))))))) 3(3(2(1(0(0(3(1(2(0(2(1(2(3(5(4(0(2(2(1(1(x1))))))))))))))))))))) -> 3(4(5(2(4(3(4(3(5(3(4(5(4(2(5(5(1(0(1(x1))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_5(x_1)) -> 5(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: INNERMOST ---------------------------------------- (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. "[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, 359, 360, 361, 362, 363, 364, 365] {(111,112,[0_1|0, 1_1|0, 3_1|0, 5_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]), (111,113,[0_1|1, 1_1|1, 3_1|1, 5_1|1, 2_1|1, 4_1|1]), (111,114,[1_1|2]), (111,116,[3_1|2]), (111,121,[1_1|2]), (111,129,[0_1|2]), (111,144,[5_1|2]), (111,148,[0_1|2]), (111,158,[5_1|2]), (111,168,[3_1|2]), (111,183,[0_1|2]), (111,187,[0_1|2]), (111,199,[0_1|2]), (111,206,[0_1|2]), (111,222,[3_1|2]), (111,225,[1_1|2]), (111,239,[3_1|2]), (111,242,[3_1|2]), (111,260,[3_1|2]), (111,280,[5_1|2]), (111,283,[5_1|2]), (111,293,[5_1|2]), (111,307,[2_1|2]), (111,314,[3_1|2]), (111,321,[2_1|2]), (111,335,[4_1|2]), (111,345,[4_1|2]), (112,112,[cons_0_1|0, cons_1_1|0, cons_3_1|0, cons_5_1|0, cons_2_1|0, cons_4_1|0]), (113,112,[encArg_1|1]), (113,113,[0_1|1, 1_1|1, 3_1|1, 5_1|1, 2_1|1, 4_1|1]), (113,114,[1_1|2]), (113,116,[3_1|2]), (113,121,[1_1|2]), (113,129,[0_1|2]), (113,144,[5_1|2]), (113,148,[0_1|2]), (113,158,[5_1|2]), (113,168,[3_1|2]), (113,183,[0_1|2]), (113,187,[0_1|2]), (113,199,[0_1|2]), (113,206,[0_1|2]), (113,222,[3_1|2]), (113,225,[1_1|2]), (113,239,[3_1|2]), (113,242,[3_1|2]), (113,260,[3_1|2]), (113,280,[5_1|2]), (113,283,[5_1|2]), (113,293,[5_1|2]), (113,307,[2_1|2]), (113,314,[3_1|2]), (113,321,[2_1|2]), (113,335,[4_1|2]), (113,345,[4_1|2]), (114,115,[4_1|2]), (115,113,[3_1|2]), (115,116,[3_1|2]), (115,168,[3_1|2]), (115,222,[3_1|2]), (115,239,[3_1|2]), (115,242,[3_1|2]), (115,260,[3_1|2]), (115,314,[3_1|2]), (115,322,[3_1|2]), (116,117,[0_1|2]), (117,118,[4_1|2]), (118,119,[0_1|2]), (118,183,[0_1|2]), (119,120,[3_1|2]), (120,113,[5_1|2]), (120,144,[5_1|2]), (120,158,[5_1|2]), (120,280,[5_1|2]), (120,283,[5_1|2]), (120,293,[5_1|2]), (120,184,[5_1|2]), (120,207,[5_1|2]), (121,122,[4_1|2]), (122,123,[3_1|2]), (123,124,[0_1|2]), (124,125,[3_1|2]), (125,126,[4_1|2]), (126,127,[2_1|2]), (127,128,[5_1|2]), (127,283,[5_1|2]), (128,113,[3_1|2]), (128,116,[3_1|2]), (128,168,[3_1|2]), (128,222,[3_1|2]), (128,239,[3_1|2]), (128,242,[3_1|2]), (128,260,[3_1|2]), (128,314,[3_1|2]), (129,130,[4_1|2]), (130,131,[2_1|2]), (131,132,[2_1|2]), (132,133,[0_1|2]), (133,134,[1_1|2]), (134,135,[5_1|2]), (135,136,[4_1|2]), (136,137,[4_1|2]), (137,138,[0_1|2]), (138,139,[2_1|2]), (139,140,[2_1|2]), (140,141,[2_1|2]), (141,142,[5_1|2]), (142,143,[5_1|2]), (142,293,[5_1|2]), (143,113,[4_1|2]), (143,335,[4_1|2]), (143,345,[4_1|2]), (143,169,[4_1|2]), (143,223,[4_1|2]), (143,243,[4_1|2]), (143,261,[4_1|2]), (143,315,[4_1|2]), (144,145,[2_1|2]), (145,146,[1_1|2]), (146,147,[5_1|2]), (146,293,[5_1|2]), (147,113,[4_1|2]), (147,144,[4_1|2]), (147,158,[4_1|2]), (147,280,[4_1|2]), (147,283,[4_1|2]), (147,293,[4_1|2]), (147,147,[4_1|2]), (147,335,[4_1|2]), (147,345,[4_1|2]), (148,149,[0_1|2]), (149,150,[4_1|2]), (150,151,[0_1|2]), (151,152,[5_1|2]), (152,153,[1_1|2]), (153,154,[0_1|2]), (154,155,[5_1|2]), (155,156,[4_1|2]), (156,157,[4_1|2]), (157,113,[2_1|2]), (157,307,[2_1|2]), (157,321,[2_1|2]), (157,308,[2_1|2]), (157,314,[3_1|2]), (158,159,[4_1|2]), (159,160,[3_1|2]), (160,161,[1_1|2]), (161,162,[4_1|2]), (162,163,[0_1|2]), (163,164,[1_1|2]), (164,165,[0_1|2]), (165,166,[1_1|2]), (166,167,[5_1|2]), (166,280,[5_1|2]), (167,113,[2_1|2]), (167,307,[2_1|2]), (167,321,[2_1|2]), (167,308,[2_1|2]), (167,314,[3_1|2]), (168,169,[4_1|2]), (169,170,[3_1|2]), (170,171,[5_1|2]), (171,172,[2_1|2]), (172,173,[5_1|2]), (173,174,[3_1|2]), (174,175,[1_1|2]), (175,176,[5_1|2]), (176,177,[0_1|2]), (177,178,[1_1|2]), (178,179,[0_1|2]), (179,180,[5_1|2]), (180,181,[5_1|2]), (181,182,[2_1|2]), (181,321,[2_1|2]), (182,113,[3_1|2]), (182,116,[3_1|2]), (182,168,[3_1|2]), (182,222,[3_1|2]), (182,239,[3_1|2]), (182,242,[3_1|2]), (182,260,[3_1|2]), (182,314,[3_1|2]), (183,184,[5_1|2]), (184,185,[1_1|2]), (185,186,[5_1|2]), (185,293,[5_1|2]), (186,113,[4_1|2]), (186,144,[4_1|2]), (186,158,[4_1|2]), (186,280,[4_1|2]), (186,283,[4_1|2]), (186,293,[4_1|2]), (186,281,[4_1|2]), (186,284,[4_1|2]), (186,335,[4_1|2]), (186,345,[4_1|2]), (187,188,[0_1|2]), (188,189,[4_1|2]), (189,190,[4_1|2]), (190,191,[1_1|2]), (191,192,[0_1|2]), (192,193,[4_1|2]), (193,194,[0_1|2]), (194,195,[0_1|2]), (195,196,[2_1|2]), (196,197,[2_1|2]), (196,314,[3_1|2]), (197,198,[4_1|2]), (197,335,[4_1|2]), (198,113,[4_1|2]), (198,335,[4_1|2]), (198,345,[4_1|2]), (198,130,[4_1|2]), (199,200,[0_1|2]), (200,201,[0_1|2]), (201,202,[4_1|2]), (202,203,[3_1|2]), (203,204,[3_1|2]), (204,205,[4_1|2]), (204,335,[4_1|2]), (205,113,[4_1|2]), (205,335,[4_1|2]), (205,345,[4_1|2]), (206,207,[5_1|2]), (207,208,[1_1|2]), (208,209,[1_1|2]), (209,210,[0_1|2]), (210,211,[2_1|2]), (211,212,[3_1|2]), (212,213,[5_1|2]), (213,214,[4_1|2]), (214,215,[3_1|2]), (215,216,[0_1|2]), (216,217,[2_1|2]), (217,218,[5_1|2]), (218,219,[2_1|2]), (219,220,[3_1|2]), (220,221,[5_1|2]), (221,113,[1_1|2]), (221,307,[1_1|2]), (221,321,[1_1|2]), (221,222,[3_1|2]), (221,225,[1_1|2]), (222,223,[4_1|2]), (222,345,[4_1|2]), (223,224,[5_1|2]), (223,293,[5_1|2]), (224,113,[4_1|2]), (224,307,[4_1|2]), (224,321,[4_1|2]), (224,131,[4_1|2]), (224,335,[4_1|2]), (224,345,[4_1|2]), (225,226,[1_1|2]), (226,227,[0_1|2]), (227,228,[4_1|2]), (228,229,[5_1|2]), (229,230,[0_1|2]), (230,231,[3_1|2]), (231,232,[2_1|2]), (232,233,[0_1|2]), (233,234,[5_1|2]), (234,235,[2_1|2]), (235,236,[0_1|2]), (236,237,[0_1|2]), (237,238,[3_1|2]), (237,239,[3_1|2]), (237,242,[3_1|2]), (238,113,[3_1|2]), (238,116,[3_1|2]), (238,168,[3_1|2]), (238,222,[3_1|2]), (238,239,[3_1|2]), (238,242,[3_1|2]), (238,260,[3_1|2]), (238,314,[3_1|2]), (239,240,[2_1|2]), (240,241,[4_1|2]), (241,113,[1_1|2]), (241,307,[1_1|2]), (241,321,[1_1|2]), (241,240,[1_1|2]), (241,222,[3_1|2]), (241,225,[1_1|2]), (242,243,[4_1|2]), (243,244,[5_1|2]), (244,245,[2_1|2]), (245,246,[4_1|2]), (246,247,[3_1|2]), (247,248,[4_1|2]), (248,249,[3_1|2]), (249,250,[5_1|2]), (250,251,[3_1|2]), (251,252,[4_1|2]), (252,253,[5_1|2]), (253,254,[4_1|2]), (254,255,[2_1|2]), (255,256,[5_1|2]), (256,257,[5_1|2]), (257,258,[1_1|2]), (258,259,[0_1|2]), (258,114,[1_1|2]), (258,116,[3_1|2]), (258,121,[1_1|2]), (258,129,[0_1|2]), (258,364,[1_1|3]), (259,113,[1_1|2]), (259,114,[1_1|2]), (259,121,[1_1|2]), (259,225,[1_1|2]), (259,226,[1_1|2]), (259,222,[3_1|2]), (260,261,[4_1|2]), (261,262,[2_1|2]), (262,263,[0_1|2]), (263,264,[4_1|2]), (264,265,[5_1|2]), (265,266,[2_1|2]), (266,267,[2_1|2]), (267,268,[2_1|2]), (268,269,[3_1|2]), (269,270,[3_1|2]), (270,271,[3_1|2]), (271,272,[5_1|2]), (272,273,[0_1|2]), (273,274,[5_1|2]), (274,275,[5_1|2]), (275,276,[3_1|2]), (276,277,[2_1|2]), (277,278,[1_1|2]), (278,279,[1_1|2]), (279,113,[4_1|2]), (279,114,[4_1|2]), (279,121,[4_1|2]), (279,225,[4_1|2]), (279,335,[4_1|2]), (279,345,[4_1|2]), (280,281,[5_1|2]), (281,282,[4_1|2]), (281,345,[4_1|2]), (282,113,[5_1|2]), (282,335,[5_1|2]), (282,345,[5_1|2]), (282,130,[5_1|2]), (282,280,[5_1|2]), (282,283,[5_1|2]), (282,293,[5_1|2]), (283,284,[5_1|2]), (284,285,[4_1|2]), (285,286,[1_1|2]), (286,287,[5_1|2]), (287,288,[2_1|2]), (288,289,[0_1|2]), (289,290,[5_1|2]), (290,291,[2_1|2]), (291,292,[4_1|2]), (292,113,[3_1|2]), (292,116,[3_1|2]), (292,168,[3_1|2]), (292,222,[3_1|2]), (292,239,[3_1|2]), (292,242,[3_1|2]), (292,260,[3_1|2]), (292,314,[3_1|2]), (292,323,[3_1|2]), (292,310,[3_1|2]), (293,294,[2_1|2]), (294,295,[3_1|2]), (295,296,[5_1|2]), (296,297,[4_1|2]), (297,298,[1_1|2]), (298,299,[3_1|2]), (299,300,[1_1|2]), (300,301,[4_1|2]), (301,302,[4_1|2]), (302,303,[4_1|2]), (303,304,[4_1|2]), (304,305,[1_1|2]), (305,306,[3_1|2]), (306,113,[5_1|2]), (306,144,[5_1|2]), (306,158,[5_1|2]), (306,280,[5_1|2]), (306,283,[5_1|2]), (306,293,[5_1|2]), (306,184,[5_1|2]), (306,207,[5_1|2]), (307,308,[2_1|2]), (308,309,[3_1|2]), (309,310,[3_1|2]), (310,311,[0_1|2]), (311,312,[1_1|2]), (312,313,[0_1|2]), (312,183,[0_1|2]), (312,187,[0_1|2]), (313,113,[3_1|2]), (313,116,[3_1|2]), (313,168,[3_1|2]), (313,222,[3_1|2]), (313,239,[3_1|2]), (313,242,[3_1|2]), (313,260,[3_1|2]), (313,314,[3_1|2]), (313,160,[3_1|2]), (314,315,[4_1|2]), (315,316,[3_1|2]), (316,317,[4_1|2]), (317,318,[1_1|2]), (318,319,[3_1|2]), (319,320,[3_1|2]), (320,113,[1_1|2]), (320,307,[1_1|2]), (320,321,[1_1|2]), (320,240,[1_1|2]), (320,222,[3_1|2]), (320,225,[1_1|2]), (321,322,[3_1|2]), (322,323,[3_1|2]), (323,324,[1_1|2]), (324,325,[1_1|2]), (325,326,[1_1|2]), (326,327,[5_1|2]), (327,328,[3_1|2]), (328,329,[3_1|2]), (329,330,[5_1|2]), (330,331,[1_1|2]), (331,332,[3_1|2]), (332,333,[5_1|2]), (333,334,[2_1|2]), (333,321,[2_1|2]), (334,113,[3_1|2]), (334,116,[3_1|2]), (334,168,[3_1|2]), (334,222,[3_1|2]), (334,239,[3_1|2]), (334,242,[3_1|2]), (334,260,[3_1|2]), (334,314,[3_1|2]), (334,322,[3_1|2]), (335,336,[4_1|2]), (336,337,[0_1|2]), (337,338,[4_1|2]), (338,339,[3_1|2]), (339,340,[1_1|2]), (340,341,[5_1|2]), (341,342,[5_1|2]), (342,343,[5_1|2]), (343,344,[2_1|2]), (344,113,[5_1|2]), (344,144,[5_1|2]), (344,158,[5_1|2]), (344,280,[5_1|2]), (344,283,[5_1|2]), (344,293,[5_1|2]), (345,346,[4_1|2]), (346,347,[2_1|2]), (347,348,[2_1|2]), (348,349,[5_1|2]), (349,350,[2_1|2]), (350,351,[0_1|2]), (351,352,[0_1|2]), (352,353,[0_1|2]), (353,354,[5_1|2]), (354,355,[3_1|2]), (355,356,[4_1|2]), (356,357,[1_1|2]), (357,358,[2_1|2]), (358,359,[2_1|2]), (359,360,[1_1|2]), (360,361,[1_1|2]), (361,362,[5_1|2]), (362,363,[0_1|2]), (362,199,[0_1|2]), (362,206,[0_1|2]), (362,121,[1_1|2]), (363,113,[0_1|2]), (363,307,[0_1|2]), (363,321,[0_1|2]), (363,114,[1_1|2]), (363,116,[3_1|2]), (363,121,[1_1|2]), (363,129,[0_1|2]), (363,144,[5_1|2]), (363,148,[0_1|2]), (363,158,[5_1|2]), (363,168,[3_1|2]), (363,183,[0_1|2]), (363,187,[0_1|2]), (363,199,[0_1|2]), (363,206,[0_1|2]), (364,365,[4_1|3]), (365,322,[3_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)