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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 146 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 79 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))) -> 1(3(0(2(x1)))) 0(1(2(x1))) -> 3(1(2(0(x1)))) 0(1(2(x1))) -> 2(0(4(1(3(x1))))) 0(1(2(x1))) -> 3(0(2(1(3(x1))))) 0(1(2(x1))) -> 3(3(0(2(1(x1))))) 0(1(2(x1))) -> 1(3(3(0(2(3(x1)))))) 0(1(2(x1))) -> 2(0(4(3(1(3(x1)))))) 0(1(2(x1))) -> 3(0(1(3(1(2(x1)))))) 0(1(2(x1))) -> 3(0(5(3(1(2(x1)))))) 0(5(2(x1))) -> 1(5(0(2(x1)))) 0(5(2(x1))) -> 3(5(0(2(x1)))) 0(5(2(x1))) -> 3(0(5(1(2(x1))))) 0(5(2(x1))) -> 3(5(3(0(2(x1))))) 0(5(2(x1))) -> 1(5(5(3(0(2(x1)))))) 0(5(2(x1))) -> 5(0(4(3(1(2(x1)))))) 1(5(2(x1))) -> 5(3(1(2(x1)))) 1(5(2(x1))) -> 1(5(3(1(2(x1))))) 0(0(5(4(x1)))) -> 5(3(0(4(0(0(x1)))))) 0(1(0(1(x1)))) -> 1(1(3(0(3(0(x1)))))) 0(1(1(2(x1)))) -> 2(1(1(3(0(2(x1)))))) 0(1(2(5(x1)))) -> 3(0(5(1(2(x1))))) 0(1(2(5(x1)))) -> 3(5(3(1(2(0(x1)))))) 0(1(3(2(x1)))) -> 3(0(2(1(3(5(x1)))))) 0(1(4(2(x1)))) -> 3(0(0(4(1(2(x1)))))) 0(1(4(2(x1)))) -> 4(0(1(3(1(2(x1)))))) 0(5(2(4(x1)))) -> 5(5(3(0(2(4(x1)))))) 0(5(2(5(x1)))) -> 0(2(3(5(5(x1))))) 0(5(3(2(x1)))) -> 3(0(2(1(5(x1))))) 0(5(3(2(x1)))) -> 5(3(1(4(0(2(x1)))))) 1(0(3(4(x1)))) -> 1(0(4(1(3(x1))))) 1(5(3(2(x1)))) -> 3(1(3(5(2(x1))))) 5(0(1(2(x1)))) -> 1(5(0(4(1(2(x1)))))) 5(1(0(2(x1)))) -> 3(1(5(0(2(x1))))) 5(1(1(2(x1)))) -> 1(3(5(2(1(3(x1)))))) 5(1(5(2(x1)))) -> 1(3(5(5(2(x1))))) 0(0(1(3(2(x1))))) -> 0(3(1(2(0(3(x1)))))) 0(0(5(3(2(x1))))) -> 0(3(0(3(2(5(x1)))))) 0(1(0(3(4(x1))))) -> 4(0(1(3(0(3(x1)))))) 0(1(0(5(4(x1))))) -> 3(0(4(0(1(5(x1)))))) 0(1(2(4(4(x1))))) -> 0(4(1(2(1(4(x1)))))) 0(1(5(3(2(x1))))) -> 1(2(3(0(4(5(x1)))))) 0(5(4(2(4(x1))))) -> 4(5(3(0(4(2(x1)))))) 0(5(4(4(2(x1))))) -> 0(4(4(3(5(2(x1)))))) 1(0(1(3(4(x1))))) -> 4(1(1(3(0(3(x1)))))) 1(0(3(4(5(x1))))) -> 2(1(3(0(4(5(x1)))))) 1(1(3(4(2(x1))))) -> 2(5(1(3(1(4(x1)))))) 1(5(3(2(2(x1))))) -> 2(3(5(3(1(2(x1)))))) 5(0(5(2(4(x1))))) -> 5(1(5(0(4(2(x1)))))) 5(1(0(5(2(x1))))) -> 1(5(0(2(3(5(x1)))))) 5(1(1(2(1(x1))))) -> 3(1(2(5(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(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(1(2(x1))) -> 1(3(0(2(x1)))) 0(1(2(x1))) -> 3(1(2(0(x1)))) 0(1(2(x1))) -> 2(0(4(1(3(x1))))) 0(1(2(x1))) -> 3(0(2(1(3(x1))))) 0(1(2(x1))) -> 3(3(0(2(1(x1))))) 0(1(2(x1))) -> 1(3(3(0(2(3(x1)))))) 0(1(2(x1))) -> 2(0(4(3(1(3(x1)))))) 0(1(2(x1))) -> 3(0(1(3(1(2(x1)))))) 0(1(2(x1))) -> 3(0(5(3(1(2(x1)))))) 0(5(2(x1))) -> 1(5(0(2(x1)))) 0(5(2(x1))) -> 3(5(0(2(x1)))) 0(5(2(x1))) -> 3(0(5(1(2(x1))))) 0(5(2(x1))) -> 3(5(3(0(2(x1))))) 0(5(2(x1))) -> 1(5(5(3(0(2(x1)))))) 0(5(2(x1))) -> 5(0(4(3(1(2(x1)))))) 1(5(2(x1))) -> 5(3(1(2(x1)))) 1(5(2(x1))) -> 1(5(3(1(2(x1))))) 0(0(5(4(x1)))) -> 5(3(0(4(0(0(x1)))))) 0(1(0(1(x1)))) -> 1(1(3(0(3(0(x1)))))) 0(1(1(2(x1)))) -> 2(1(1(3(0(2(x1)))))) 0(1(2(5(x1)))) -> 3(0(5(1(2(x1))))) 0(1(2(5(x1)))) -> 3(5(3(1(2(0(x1)))))) 0(1(3(2(x1)))) -> 3(0(2(1(3(5(x1)))))) 0(1(4(2(x1)))) -> 3(0(0(4(1(2(x1)))))) 0(1(4(2(x1)))) -> 4(0(1(3(1(2(x1)))))) 0(5(2(4(x1)))) -> 5(5(3(0(2(4(x1)))))) 0(5(2(5(x1)))) -> 0(2(3(5(5(x1))))) 0(5(3(2(x1)))) -> 3(0(2(1(5(x1))))) 0(5(3(2(x1)))) -> 5(3(1(4(0(2(x1)))))) 1(0(3(4(x1)))) -> 1(0(4(1(3(x1))))) 1(5(3(2(x1)))) -> 3(1(3(5(2(x1))))) 5(0(1(2(x1)))) -> 1(5(0(4(1(2(x1)))))) 5(1(0(2(x1)))) -> 3(1(5(0(2(x1))))) 5(1(1(2(x1)))) -> 1(3(5(2(1(3(x1)))))) 5(1(5(2(x1)))) -> 1(3(5(5(2(x1))))) 0(0(1(3(2(x1))))) -> 0(3(1(2(0(3(x1)))))) 0(0(5(3(2(x1))))) -> 0(3(0(3(2(5(x1)))))) 0(1(0(3(4(x1))))) -> 4(0(1(3(0(3(x1)))))) 0(1(0(5(4(x1))))) -> 3(0(4(0(1(5(x1)))))) 0(1(2(4(4(x1))))) -> 0(4(1(2(1(4(x1)))))) 0(1(5(3(2(x1))))) -> 1(2(3(0(4(5(x1)))))) 0(5(4(2(4(x1))))) -> 4(5(3(0(4(2(x1)))))) 0(5(4(4(2(x1))))) -> 0(4(4(3(5(2(x1)))))) 1(0(1(3(4(x1))))) -> 4(1(1(3(0(3(x1)))))) 1(0(3(4(5(x1))))) -> 2(1(3(0(4(5(x1)))))) 1(1(3(4(2(x1))))) -> 2(5(1(3(1(4(x1)))))) 1(5(3(2(2(x1))))) -> 2(3(5(3(1(2(x1)))))) 5(0(5(2(4(x1))))) -> 5(1(5(0(4(2(x1)))))) 5(1(0(5(2(x1))))) -> 1(5(0(2(3(5(x1)))))) 5(1(1(2(1(x1))))) -> 3(1(2(5(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(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(1(2(x1))) -> 1(3(0(2(x1)))) 0(1(2(x1))) -> 3(1(2(0(x1)))) 0(1(2(x1))) -> 2(0(4(1(3(x1))))) 0(1(2(x1))) -> 3(0(2(1(3(x1))))) 0(1(2(x1))) -> 3(3(0(2(1(x1))))) 0(1(2(x1))) -> 1(3(3(0(2(3(x1)))))) 0(1(2(x1))) -> 2(0(4(3(1(3(x1)))))) 0(1(2(x1))) -> 3(0(1(3(1(2(x1)))))) 0(1(2(x1))) -> 3(0(5(3(1(2(x1)))))) 0(5(2(x1))) -> 1(5(0(2(x1)))) 0(5(2(x1))) -> 3(5(0(2(x1)))) 0(5(2(x1))) -> 3(0(5(1(2(x1))))) 0(5(2(x1))) -> 3(5(3(0(2(x1))))) 0(5(2(x1))) -> 1(5(5(3(0(2(x1)))))) 0(5(2(x1))) -> 5(0(4(3(1(2(x1)))))) 1(5(2(x1))) -> 5(3(1(2(x1)))) 1(5(2(x1))) -> 1(5(3(1(2(x1))))) 0(0(5(4(x1)))) -> 5(3(0(4(0(0(x1)))))) 0(1(0(1(x1)))) -> 1(1(3(0(3(0(x1)))))) 0(1(1(2(x1)))) -> 2(1(1(3(0(2(x1)))))) 0(1(2(5(x1)))) -> 3(0(5(1(2(x1))))) 0(1(2(5(x1)))) -> 3(5(3(1(2(0(x1)))))) 0(1(3(2(x1)))) -> 3(0(2(1(3(5(x1)))))) 0(1(4(2(x1)))) -> 3(0(0(4(1(2(x1)))))) 0(1(4(2(x1)))) -> 4(0(1(3(1(2(x1)))))) 0(5(2(4(x1)))) -> 5(5(3(0(2(4(x1)))))) 0(5(2(5(x1)))) -> 0(2(3(5(5(x1))))) 0(5(3(2(x1)))) -> 3(0(2(1(5(x1))))) 0(5(3(2(x1)))) -> 5(3(1(4(0(2(x1)))))) 1(0(3(4(x1)))) -> 1(0(4(1(3(x1))))) 1(5(3(2(x1)))) -> 3(1(3(5(2(x1))))) 5(0(1(2(x1)))) -> 1(5(0(4(1(2(x1)))))) 5(1(0(2(x1)))) -> 3(1(5(0(2(x1))))) 5(1(1(2(x1)))) -> 1(3(5(2(1(3(x1)))))) 5(1(5(2(x1)))) -> 1(3(5(5(2(x1))))) 0(0(1(3(2(x1))))) -> 0(3(1(2(0(3(x1)))))) 0(0(5(3(2(x1))))) -> 0(3(0(3(2(5(x1)))))) 0(1(0(3(4(x1))))) -> 4(0(1(3(0(3(x1)))))) 0(1(0(5(4(x1))))) -> 3(0(4(0(1(5(x1)))))) 0(1(2(4(4(x1))))) -> 0(4(1(2(1(4(x1)))))) 0(1(5(3(2(x1))))) -> 1(2(3(0(4(5(x1)))))) 0(5(4(2(4(x1))))) -> 4(5(3(0(4(2(x1)))))) 0(5(4(4(2(x1))))) -> 0(4(4(3(5(2(x1)))))) 1(0(1(3(4(x1))))) -> 4(1(1(3(0(3(x1)))))) 1(0(3(4(5(x1))))) -> 2(1(3(0(4(5(x1)))))) 1(1(3(4(2(x1))))) -> 2(5(1(3(1(4(x1)))))) 1(5(3(2(2(x1))))) -> 2(3(5(3(1(2(x1)))))) 5(0(5(2(4(x1))))) -> 5(1(5(0(4(2(x1)))))) 5(1(0(5(2(x1))))) -> 1(5(0(2(3(5(x1)))))) 5(1(1(2(1(x1))))) -> 3(1(2(5(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(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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(1(2(x1))) -> 1(3(0(2(x1)))) 0(1(2(x1))) -> 3(1(2(0(x1)))) 0(1(2(x1))) -> 2(0(4(1(3(x1))))) 0(1(2(x1))) -> 3(0(2(1(3(x1))))) 0(1(2(x1))) -> 3(3(0(2(1(x1))))) 0(1(2(x1))) -> 1(3(3(0(2(3(x1)))))) 0(1(2(x1))) -> 2(0(4(3(1(3(x1)))))) 0(1(2(x1))) -> 3(0(1(3(1(2(x1)))))) 0(1(2(x1))) -> 3(0(5(3(1(2(x1)))))) 0(5(2(x1))) -> 1(5(0(2(x1)))) 0(5(2(x1))) -> 3(5(0(2(x1)))) 0(5(2(x1))) -> 3(0(5(1(2(x1))))) 0(5(2(x1))) -> 3(5(3(0(2(x1))))) 0(5(2(x1))) -> 1(5(5(3(0(2(x1)))))) 0(5(2(x1))) -> 5(0(4(3(1(2(x1)))))) 1(5(2(x1))) -> 5(3(1(2(x1)))) 1(5(2(x1))) -> 1(5(3(1(2(x1))))) 0(0(5(4(x1)))) -> 5(3(0(4(0(0(x1)))))) 0(1(0(1(x1)))) -> 1(1(3(0(3(0(x1)))))) 0(1(1(2(x1)))) -> 2(1(1(3(0(2(x1)))))) 0(1(2(5(x1)))) -> 3(0(5(1(2(x1))))) 0(1(2(5(x1)))) -> 3(5(3(1(2(0(x1)))))) 0(1(3(2(x1)))) -> 3(0(2(1(3(5(x1)))))) 0(1(4(2(x1)))) -> 3(0(0(4(1(2(x1)))))) 0(1(4(2(x1)))) -> 4(0(1(3(1(2(x1)))))) 0(5(2(4(x1)))) -> 5(5(3(0(2(4(x1)))))) 0(5(2(5(x1)))) -> 0(2(3(5(5(x1))))) 0(5(3(2(x1)))) -> 3(0(2(1(5(x1))))) 0(5(3(2(x1)))) -> 5(3(1(4(0(2(x1)))))) 1(0(3(4(x1)))) -> 1(0(4(1(3(x1))))) 1(5(3(2(x1)))) -> 3(1(3(5(2(x1))))) 5(0(1(2(x1)))) -> 1(5(0(4(1(2(x1)))))) 5(1(0(2(x1)))) -> 3(1(5(0(2(x1))))) 5(1(1(2(x1)))) -> 1(3(5(2(1(3(x1)))))) 5(1(5(2(x1)))) -> 1(3(5(5(2(x1))))) 0(0(1(3(2(x1))))) -> 0(3(1(2(0(3(x1)))))) 0(0(5(3(2(x1))))) -> 0(3(0(3(2(5(x1)))))) 0(1(0(3(4(x1))))) -> 4(0(1(3(0(3(x1)))))) 0(1(0(5(4(x1))))) -> 3(0(4(0(1(5(x1)))))) 0(1(2(4(4(x1))))) -> 0(4(1(2(1(4(x1)))))) 0(1(5(3(2(x1))))) -> 1(2(3(0(4(5(x1)))))) 0(5(4(2(4(x1))))) -> 4(5(3(0(4(2(x1)))))) 0(5(4(4(2(x1))))) -> 0(4(4(3(5(2(x1)))))) 1(0(1(3(4(x1))))) -> 4(1(1(3(0(3(x1)))))) 1(0(3(4(5(x1))))) -> 2(1(3(0(4(5(x1)))))) 1(1(3(4(2(x1))))) -> 2(5(1(3(1(4(x1)))))) 1(5(3(2(2(x1))))) -> 2(3(5(3(1(2(x1)))))) 5(0(5(2(4(x1))))) -> 5(1(5(0(4(2(x1)))))) 5(1(0(5(2(x1))))) -> 1(5(0(2(3(5(x1)))))) 5(1(1(2(1(x1))))) -> 3(1(2(5(1(1(x1)))))) encArg(2(x_1)) -> 2(encArg(x_1)) encArg(3(x_1)) -> 3(encArg(x_1)) encArg(4(x_1)) -> 4(encArg(x_1)) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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 3. The certificate found is represented by the following graph. "[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, 359, 360, 361, 362] {(78,79,[0_1|0, 1_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]), (78,80,[2_1|1, 3_1|1, 4_1|1, 0_1|1, 1_1|1, 5_1|1]), (78,81,[1_1|2]), (78,84,[3_1|2]), (78,87,[2_1|2]), (78,91,[3_1|2]), (78,95,[3_1|2]), (78,99,[1_1|2]), (78,104,[2_1|2]), (78,109,[3_1|2]), (78,114,[3_1|2]), (78,119,[3_1|2]), (78,123,[3_1|2]), (78,128,[0_1|2]), (78,133,[1_1|2]), (78,138,[4_1|2]), (78,143,[3_1|2]), (78,148,[2_1|2]), (78,153,[3_1|2]), (78,158,[3_1|2]), (78,163,[4_1|2]), (78,168,[1_1|2]), (78,173,[1_1|2]), (78,176,[3_1|2]), (78,179,[3_1|2]), 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(225,202,[3_1|2]), (225,206,[5_1|2]), (225,216,[0_1|2]), (225,304,[3_1|2]), (225,221,[5_1|2]), (225,226,[0_1|2]), (225,231,[0_1|2]), (225,308,[1_1|3]), (225,311,[3_1|3]), (225,314,[2_1|3]), (225,318,[3_1|3]), (225,322,[3_1|3]), (225,326,[1_1|3]), (225,331,[2_1|3]), (225,336,[3_1|3]), (225,341,[3_1|3]), (226,227,[3_1|2]), (227,228,[0_1|2]), (228,229,[3_1|2]), (229,230,[2_1|2]), (230,80,[5_1|2]), (230,87,[5_1|2]), (230,104,[5_1|2]), (230,148,[5_1|2]), (230,247,[5_1|2]), (230,256,[5_1|2]), (230,266,[5_1|2]), (230,271,[1_1|2]), (230,276,[5_1|2]), (230,281,[3_1|2]), (230,285,[1_1|2]), (230,290,[1_1|2]), (230,295,[3_1|2]), (230,300,[1_1|2]), (231,232,[3_1|2]), (232,233,[1_1|2]), (233,234,[2_1|2]), (234,235,[0_1|2]), (235,80,[3_1|2]), (235,87,[3_1|2]), (235,104,[3_1|2]), (235,148,[3_1|2]), (235,247,[3_1|2]), (235,256,[3_1|2]), (235,266,[3_1|2]), (236,237,[3_1|2]), (237,238,[1_1|2]), (238,80,[2_1|2]), (238,87,[2_1|2]), (238,104,[2_1|2]), (238,148,[2_1|2]), (238,247,[2_1|2]), (238,256,[2_1|2]), (238,266,[2_1|2]), (239,240,[5_1|2]), (240,241,[3_1|2]), (241,242,[1_1|2]), (242,80,[2_1|2]), (242,87,[2_1|2]), (242,104,[2_1|2]), (242,148,[2_1|2]), (242,247,[2_1|2]), (242,256,[2_1|2]), (242,266,[2_1|2]), (243,244,[1_1|2]), (244,245,[3_1|2]), (245,246,[5_1|2]), (246,80,[2_1|2]), (246,87,[2_1|2]), (246,104,[2_1|2]), (246,148,[2_1|2]), (246,247,[2_1|2]), (246,256,[2_1|2]), (246,266,[2_1|2]), (247,248,[3_1|2]), (248,249,[5_1|2]), (249,250,[3_1|2]), (250,251,[1_1|2]), (251,80,[2_1|2]), (251,87,[2_1|2]), (251,104,[2_1|2]), (251,148,[2_1|2]), (251,247,[2_1|2]), (251,256,[2_1|2]), (251,266,[2_1|2]), (252,253,[0_1|2]), (253,254,[4_1|2]), (254,255,[1_1|2]), (255,80,[3_1|2]), (255,138,[3_1|2]), (255,163,[3_1|2]), (255,211,[3_1|2]), (255,261,[3_1|2]), (256,257,[1_1|2]), (257,258,[3_1|2]), (258,259,[0_1|2]), (259,260,[4_1|2]), (260,80,[5_1|2]), (260,188,[5_1|2]), (260,193,[5_1|2]), (260,206,[5_1|2]), (260,221,[5_1|2]), (260,236,[5_1|2]), (260,276,[5_1|2]), (260,212,[5_1|2]), (260,271,[1_1|2]), (260,281,[3_1|2]), (260,285,[1_1|2]), (260,290,[1_1|2]), (260,295,[3_1|2]), (260,300,[1_1|2]), (261,262,[1_1|2]), (262,263,[1_1|2]), (263,264,[3_1|2]), (264,265,[0_1|2]), (265,80,[3_1|2]), (265,138,[3_1|2]), (265,163,[3_1|2]), (265,211,[3_1|2]), (265,261,[3_1|2]), (266,267,[5_1|2]), (267,268,[1_1|2]), (268,269,[3_1|2]), (269,270,[1_1|2]), (270,80,[4_1|2]), (270,87,[4_1|2]), (270,104,[4_1|2]), (270,148,[4_1|2]), (270,247,[4_1|2]), (270,256,[4_1|2]), (270,266,[4_1|2]), (271,272,[5_1|2]), (272,273,[0_1|2]), (273,274,[4_1|2]), (274,275,[1_1|2]), (275,80,[2_1|2]), (275,87,[2_1|2]), (275,104,[2_1|2]), (275,148,[2_1|2]), (275,247,[2_1|2]), (275,256,[2_1|2]), (275,266,[2_1|2]), (275,169,[2_1|2]), (276,277,[1_1|2]), (277,278,[5_1|2]), (278,279,[0_1|2]), (279,280,[4_1|2]), (280,80,[2_1|2]), (280,138,[2_1|2]), (280,163,[2_1|2]), (280,211,[2_1|2]), (280,261,[2_1|2]), (281,282,[1_1|2]), (282,283,[5_1|2]), (283,284,[0_1|2]), (284,80,[2_1|2]), (284,87,[2_1|2]), (284,104,[2_1|2]), (284,148,[2_1|2]), (284,247,[2_1|2]), (284,256,[2_1|2]), (284,266,[2_1|2]), (284,199,[2_1|2]), (285,286,[5_1|2]), (286,287,[0_1|2]), (287,288,[2_1|2]), (288,289,[3_1|2]), (289,80,[5_1|2]), (289,87,[5_1|2]), (289,104,[5_1|2]), (289,148,[5_1|2]), (289,247,[5_1|2]), (289,256,[5_1|2]), (289,266,[5_1|2]), (289,271,[1_1|2]), (289,276,[5_1|2]), (289,281,[3_1|2]), (289,285,[1_1|2]), (289,290,[1_1|2]), (289,295,[3_1|2]), (289,300,[1_1|2]), (290,291,[3_1|2]), (291,292,[5_1|2]), (292,293,[2_1|2]), (293,294,[1_1|2]), (294,80,[3_1|2]), (294,87,[3_1|2]), (294,104,[3_1|2]), (294,148,[3_1|2]), (294,247,[3_1|2]), (294,256,[3_1|2]), (294,266,[3_1|2]), (294,169,[3_1|2]), (295,296,[1_1|2]), (296,297,[2_1|2]), (297,298,[5_1|2]), (297,290,[1_1|2]), (297,295,[3_1|2]), (297,353,[1_1|3]), (297,358,[3_1|3]), (298,299,[1_1|2]), (298,266,[2_1|2]), (299,80,[1_1|2]), (299,81,[1_1|2]), (299,99,[1_1|2]), (299,133,[1_1|2]), (299,168,[1_1|2]), (299,173,[1_1|2]), (299,183,[1_1|2]), (299,239,[1_1|2]), (299,252,[1_1|2]), (299,271,[1_1|2]), (299,285,[1_1|2]), (299,290,[1_1|2]), (299,300,[1_1|2]), (299,149,[1_1|2]), (299,257,[1_1|2]), (299,236,[5_1|2]), (299,243,[3_1|2]), (299,247,[2_1|2]), (299,256,[2_1|2]), (299,261,[4_1|2]), (299,266,[2_1|2]), (300,301,[3_1|2]), (301,302,[5_1|2]), (302,303,[5_1|2]), (303,80,[2_1|2]), (303,87,[2_1|2]), (303,104,[2_1|2]), (303,148,[2_1|2]), (303,247,[2_1|2]), (303,256,[2_1|2]), (303,266,[2_1|2]), (304,305,[0_1|2]), (305,306,[5_1|2]), (306,307,[1_1|2]), (307,87,[2_1|2]), (307,104,[2_1|2]), (307,148,[2_1|2]), (307,247,[2_1|2]), (307,256,[2_1|2]), (307,266,[2_1|2]), (308,309,[3_1|3]), (309,310,[0_1|3]), (310,169,[2_1|3]), (311,312,[1_1|3]), (312,313,[2_1|3]), (313,169,[0_1|3]), (314,315,[0_1|3]), (315,316,[4_1|3]), (316,317,[1_1|3]), (317,169,[3_1|3]), (318,319,[0_1|3]), (319,320,[2_1|3]), (320,321,[1_1|3]), (321,169,[3_1|3]), (322,323,[3_1|3]), (323,324,[0_1|3]), (324,325,[2_1|3]), (325,169,[1_1|3]), (326,327,[3_1|3]), (327,328,[3_1|3]), (328,329,[0_1|3]), (329,330,[2_1|3]), (330,169,[3_1|3]), (331,332,[0_1|3]), (332,333,[4_1|3]), (333,334,[3_1|3]), (334,335,[1_1|3]), (335,169,[3_1|3]), (336,337,[0_1|3]), (337,338,[1_1|3]), (338,339,[3_1|3]), (339,340,[1_1|3]), (340,169,[2_1|3]), (341,342,[0_1|3]), (342,343,[5_1|3]), (343,344,[3_1|3]), (344,345,[1_1|3]), (345,169,[2_1|3]), (346,347,[3_1|3]), (347,348,[1_1|3]), (348,87,[2_1|3]), (348,104,[2_1|3]), (348,148,[2_1|3]), (348,247,[2_1|3]), (348,256,[2_1|3]), (348,266,[2_1|3]), (349,350,[5_1|3]), (350,351,[3_1|3]), (351,352,[1_1|3]), (352,87,[2_1|3]), (352,104,[2_1|3]), (352,148,[2_1|3]), (352,247,[2_1|3]), (352,256,[2_1|3]), (352,266,[2_1|3]), (353,354,[3_1|3]), (354,355,[5_1|3]), (355,356,[2_1|3]), (356,357,[1_1|3]), (357,87,[3_1|3]), (357,104,[3_1|3]), (357,148,[3_1|3]), (357,247,[3_1|3]), (357,256,[3_1|3]), (357,266,[3_1|3]), (357,169,[3_1|3]), (358,359,[1_1|3]), (359,360,[2_1|3]), (360,361,[5_1|3]), (361,362,[1_1|3]), (362,149,[1_1|3]), (362,257,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)