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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 63 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 227 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))) -> 0(2(0(2(2(3(0(2(3(1(x1)))))))))) 0(4(2(1(5(x1))))) -> 3(0(4(5(3(3(2(3(3(3(x1)))))))))) 1(1(4(1(0(x1))))) -> 3(5(3(3(2(0(2(3(3(3(x1)))))))))) 0(0(5(2(2(1(x1)))))) -> 1(3(5(3(1(2(0(2(2(3(x1)))))))))) 0(4(1(4(0(0(x1)))))) -> 3(3(2(3(0(4(5(0(3(0(x1)))))))))) 0(4(3(4(2(1(x1)))))) -> 0(5(3(3(3(0(0(2(0(2(x1)))))))))) 1(1(2(0(5(4(x1)))))) -> 1(3(2(0(2(3(1(5(1(4(x1)))))))))) 1(1(3(1(4(2(x1)))))) -> 0(2(0(2(2(2(3(0(5(2(x1)))))))))) 1(3(4(0(4(1(x1)))))) -> 1(3(3(0(2(5(4(5(3(0(x1)))))))))) 1(4(0(4(1(4(x1)))))) -> 5(2(5(0(5(5(4(5(0(2(x1)))))))))) 1(4(1(5(4(3(x1)))))) -> 3(2(4(2(5(5(4(3(3(2(x1)))))))))) 1(4(2(3(4(4(x1)))))) -> 3(0(3(3(2(5(3(2(1(2(x1)))))))))) 1(4(3(1(5(1(x1)))))) -> 3(3(2(4(3(3(0(2(0(2(x1)))))))))) 1(5(4(0(5(3(x1)))))) -> 3(1(3(2(0(3(3(1(3(2(x1)))))))))) 1(5(5(0(1(0(x1)))))) -> 1(3(2(3(5(5(4(0(2(5(x1)))))))))) 5(1(1(5(5(4(x1)))))) -> 5(1(3(3(3(0(2(0(3(2(x1)))))))))) 0(0(0(0(5(5(1(x1))))))) -> 0(0(2(2(3(3(2(2(5(0(x1)))))))))) 0(0(1(5(1(2(1(x1))))))) -> 1(0(2(2(0(4(5(0(2(1(x1)))))))))) 0(0(3(4(0(5(4(x1))))))) -> 0(2(2(1(0(2(1(4(3(2(x1)))))))))) 0(0(5(2(2(0(5(x1))))))) -> 0(2(3(3(4(2(4(0(2(1(x1)))))))))) 0(1(1(1(0(0(5(x1))))))) -> 0(2(2(0(2(5(2(5(5(3(x1)))))))))) 0(4(1(1(0(0(5(x1))))))) -> 1(3(2(3(4(3(0(2(5(3(x1)))))))))) 0(4(3(4(0(1(0(x1))))))) -> 3(2(4(0(5(0(1(5(2(0(x1)))))))))) 0(5(1(1(4(2(3(x1))))))) -> 0(2(4(2(4(4(1(5(3(2(x1)))))))))) 0(5(1(4(4(0(4(x1))))))) -> 0(5(1(2(5(3(3(2(0(4(x1)))))))))) 1(0(0(3(4(3(5(x1))))))) -> 3(2(4(3(3(1(3(2(1(1(x1)))))))))) 1(0(1(0(0(4(2(x1))))))) -> 1(3(2(3(2(1(2(5(0(5(x1)))))))))) 1(0(3(4(1(1(5(x1))))))) -> 1(0(3(5(2(4(3(1(3(2(x1)))))))))) 1(0(4(1(1(4(1(x1))))))) -> 0(0(5(0(2(4(2(0(2(3(x1)))))))))) 1(1(0(3(0(1(5(x1))))))) -> 0(2(0(2(0(2(0(4(5(1(x1)))))))))) 1(1(1(3(1(1(4(x1))))))) -> 3(1(2(3(3(0(2(0(5(2(x1)))))))))) 1(1(1(4(0(5(0(x1))))))) -> 3(5(5(2(2(4(0(2(0(0(x1)))))))))) 1(1(1(5(4(0(5(x1))))))) -> 3(4(3(5(3(3(2(5(3(3(x1)))))))))) 1(1(4(0(5(1(4(x1))))))) -> 4(2(2(3(0(3(2(5(0(2(x1)))))))))) 1(1(4(2(0(4(3(x1))))))) -> 3(1(3(4(4(3(0(2(3(3(x1)))))))))) 1(3(4(0(5(1(5(x1))))))) -> 1(3(3(5(0(2(0(3(3(1(x1)))))))))) 1(3(5(0(0(0(0(x1))))))) -> 3(3(3(3(5(5(3(2(0(1(x1)))))))))) 1(4(0(0(0(1(5(x1))))))) -> 3(3(0(4(4(0(3(1(1(3(x1)))))))))) 1(4(0(0(5(4(4(x1))))))) -> 2(2(4(0(4(2(5(3(3(2(x1)))))))))) 1(4(1(1(1(1(1(x1))))))) -> 4(1(0(2(2(1(2(5(1(3(x1)))))))))) 1(4(2(1(1(1(1(x1))))))) -> 1(5(2(4(0(2(4(5(0(1(x1)))))))))) 1(4(2(1(3(4(3(x1))))))) -> 3(1(3(2(3(3(5(2(5(1(x1)))))))))) 1(4(3(0(0(4(1(x1))))))) -> 5(5(2(4(2(5(2(2(4(3(x1)))))))))) 2(0(0(1(1(1(1(x1))))))) -> 2(1(5(4(5(5(0(2(2(1(x1)))))))))) 2(0(4(0(0(0(0(x1))))))) -> 2(5(2(2(2(5(4(2(0(0(x1)))))))))) 2(1(1(3(5(1(4(x1))))))) -> 2(1(1(3(2(2(3(5(0(2(x1)))))))))) 2(1(4(0(1(4(5(x1))))))) -> 2(4(5(3(3(2(3(3(3(5(x1)))))))))) 3(0(0(1(1(4(3(x1))))))) -> 0(5(3(1(3(2(0(2(4(3(x1)))))))))) 3(0(0(5(4(4(4(x1))))))) -> 3(3(1(3(2(3(0(3(3(1(x1)))))))))) 3(0(4(1(4(0(0(x1))))))) -> 0(4(0(2(2(2(0(5(5(0(x1)))))))))) 3(4(3(4(3(4(0(x1))))))) -> 3(5(5(1(0(2(4(3(2(0(x1)))))))))) 3(5(1(4(0(1(4(x1))))))) -> 0(3(2(5(0(2(2(2(0(2(x1)))))))))) 4(0(1(1(0(5(1(x1))))))) -> 4(3(2(5(2(1(1(3(3(2(x1)))))))))) 4(1(1(2(0(4(1(x1))))))) -> 4(0(2(4(0(0(2(0(2(3(x1)))))))))) 4(1(5(0(1(0(1(x1))))))) -> 4(3(0(3(5(5(2(4(0(2(x1)))))))))) 5(1(2(3(4(4(5(x1))))))) -> 5(4(0(2(0(2(1(2(4(5(x1)))))))))) 5(3(1(4(4(1(1(x1))))))) -> 5(0(2(5(2(5(0(2(4(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(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)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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 (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))) -> 0(2(0(2(2(3(0(2(3(1(x1)))))))))) 0(4(2(1(5(x1))))) -> 3(0(4(5(3(3(2(3(3(3(x1)))))))))) 1(1(4(1(0(x1))))) -> 3(5(3(3(2(0(2(3(3(3(x1)))))))))) 0(0(5(2(2(1(x1)))))) -> 1(3(5(3(1(2(0(2(2(3(x1)))))))))) 0(4(1(4(0(0(x1)))))) -> 3(3(2(3(0(4(5(0(3(0(x1)))))))))) 0(4(3(4(2(1(x1)))))) -> 0(5(3(3(3(0(0(2(0(2(x1)))))))))) 1(1(2(0(5(4(x1)))))) -> 1(3(2(0(2(3(1(5(1(4(x1)))))))))) 1(1(3(1(4(2(x1)))))) -> 0(2(0(2(2(2(3(0(5(2(x1)))))))))) 1(3(4(0(4(1(x1)))))) -> 1(3(3(0(2(5(4(5(3(0(x1)))))))))) 1(4(0(4(1(4(x1)))))) -> 5(2(5(0(5(5(4(5(0(2(x1)))))))))) 1(4(1(5(4(3(x1)))))) -> 3(2(4(2(5(5(4(3(3(2(x1)))))))))) 1(4(2(3(4(4(x1)))))) -> 3(0(3(3(2(5(3(2(1(2(x1)))))))))) 1(4(3(1(5(1(x1)))))) -> 3(3(2(4(3(3(0(2(0(2(x1)))))))))) 1(5(4(0(5(3(x1)))))) -> 3(1(3(2(0(3(3(1(3(2(x1)))))))))) 1(5(5(0(1(0(x1)))))) -> 1(3(2(3(5(5(4(0(2(5(x1)))))))))) 5(1(1(5(5(4(x1)))))) -> 5(1(3(3(3(0(2(0(3(2(x1)))))))))) 0(0(0(0(5(5(1(x1))))))) -> 0(0(2(2(3(3(2(2(5(0(x1)))))))))) 0(0(1(5(1(2(1(x1))))))) -> 1(0(2(2(0(4(5(0(2(1(x1)))))))))) 0(0(3(4(0(5(4(x1))))))) -> 0(2(2(1(0(2(1(4(3(2(x1)))))))))) 0(0(5(2(2(0(5(x1))))))) -> 0(2(3(3(4(2(4(0(2(1(x1)))))))))) 0(1(1(1(0(0(5(x1))))))) -> 0(2(2(0(2(5(2(5(5(3(x1)))))))))) 0(4(1(1(0(0(5(x1))))))) -> 1(3(2(3(4(3(0(2(5(3(x1)))))))))) 0(4(3(4(0(1(0(x1))))))) -> 3(2(4(0(5(0(1(5(2(0(x1)))))))))) 0(5(1(1(4(2(3(x1))))))) -> 0(2(4(2(4(4(1(5(3(2(x1)))))))))) 0(5(1(4(4(0(4(x1))))))) -> 0(5(1(2(5(3(3(2(0(4(x1)))))))))) 1(0(0(3(4(3(5(x1))))))) -> 3(2(4(3(3(1(3(2(1(1(x1)))))))))) 1(0(1(0(0(4(2(x1))))))) -> 1(3(2(3(2(1(2(5(0(5(x1)))))))))) 1(0(3(4(1(1(5(x1))))))) -> 1(0(3(5(2(4(3(1(3(2(x1)))))))))) 1(0(4(1(1(4(1(x1))))))) -> 0(0(5(0(2(4(2(0(2(3(x1)))))))))) 1(1(0(3(0(1(5(x1))))))) -> 0(2(0(2(0(2(0(4(5(1(x1)))))))))) 1(1(1(3(1(1(4(x1))))))) -> 3(1(2(3(3(0(2(0(5(2(x1)))))))))) 1(1(1(4(0(5(0(x1))))))) -> 3(5(5(2(2(4(0(2(0(0(x1)))))))))) 1(1(1(5(4(0(5(x1))))))) -> 3(4(3(5(3(3(2(5(3(3(x1)))))))))) 1(1(4(0(5(1(4(x1))))))) -> 4(2(2(3(0(3(2(5(0(2(x1)))))))))) 1(1(4(2(0(4(3(x1))))))) -> 3(1(3(4(4(3(0(2(3(3(x1)))))))))) 1(3(4(0(5(1(5(x1))))))) -> 1(3(3(5(0(2(0(3(3(1(x1)))))))))) 1(3(5(0(0(0(0(x1))))))) -> 3(3(3(3(5(5(3(2(0(1(x1)))))))))) 1(4(0(0(0(1(5(x1))))))) -> 3(3(0(4(4(0(3(1(1(3(x1)))))))))) 1(4(0(0(5(4(4(x1))))))) -> 2(2(4(0(4(2(5(3(3(2(x1)))))))))) 1(4(1(1(1(1(1(x1))))))) -> 4(1(0(2(2(1(2(5(1(3(x1)))))))))) 1(4(2(1(1(1(1(x1))))))) -> 1(5(2(4(0(2(4(5(0(1(x1)))))))))) 1(4(2(1(3(4(3(x1))))))) -> 3(1(3(2(3(3(5(2(5(1(x1)))))))))) 1(4(3(0(0(4(1(x1))))))) -> 5(5(2(4(2(5(2(2(4(3(x1)))))))))) 2(0(0(1(1(1(1(x1))))))) -> 2(1(5(4(5(5(0(2(2(1(x1)))))))))) 2(0(4(0(0(0(0(x1))))))) -> 2(5(2(2(2(5(4(2(0(0(x1)))))))))) 2(1(1(3(5(1(4(x1))))))) -> 2(1(1(3(2(2(3(5(0(2(x1)))))))))) 2(1(4(0(1(4(5(x1))))))) -> 2(4(5(3(3(2(3(3(3(5(x1)))))))))) 3(0(0(1(1(4(3(x1))))))) -> 0(5(3(1(3(2(0(2(4(3(x1)))))))))) 3(0(0(5(4(4(4(x1))))))) -> 3(3(1(3(2(3(0(3(3(1(x1)))))))))) 3(0(4(1(4(0(0(x1))))))) -> 0(4(0(2(2(2(0(5(5(0(x1)))))))))) 3(4(3(4(3(4(0(x1))))))) -> 3(5(5(1(0(2(4(3(2(0(x1)))))))))) 3(5(1(4(0(1(4(x1))))))) -> 0(3(2(5(0(2(2(2(0(2(x1)))))))))) 4(0(1(1(0(5(1(x1))))))) -> 4(3(2(5(2(1(1(3(3(2(x1)))))))))) 4(1(1(2(0(4(1(x1))))))) -> 4(0(2(4(0(0(2(0(2(3(x1)))))))))) 4(1(5(0(1(0(1(x1))))))) -> 4(3(0(3(5(5(2(4(0(2(x1)))))))))) 5(1(2(3(4(4(5(x1))))))) -> 5(4(0(2(0(2(1(2(4(5(x1)))))))))) 5(3(1(4(4(1(1(x1))))))) -> 5(0(2(5(2(5(0(2(4(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_5(x_1)) -> 5(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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: 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))) -> 0(2(0(2(2(3(0(2(3(1(x1)))))))))) 0(4(2(1(5(x1))))) -> 3(0(4(5(3(3(2(3(3(3(x1)))))))))) 1(1(4(1(0(x1))))) -> 3(5(3(3(2(0(2(3(3(3(x1)))))))))) 0(0(5(2(2(1(x1)))))) -> 1(3(5(3(1(2(0(2(2(3(x1)))))))))) 0(4(1(4(0(0(x1)))))) -> 3(3(2(3(0(4(5(0(3(0(x1)))))))))) 0(4(3(4(2(1(x1)))))) -> 0(5(3(3(3(0(0(2(0(2(x1)))))))))) 1(1(2(0(5(4(x1)))))) -> 1(3(2(0(2(3(1(5(1(4(x1)))))))))) 1(1(3(1(4(2(x1)))))) -> 0(2(0(2(2(2(3(0(5(2(x1)))))))))) 1(3(4(0(4(1(x1)))))) -> 1(3(3(0(2(5(4(5(3(0(x1)))))))))) 1(4(0(4(1(4(x1)))))) -> 5(2(5(0(5(5(4(5(0(2(x1)))))))))) 1(4(1(5(4(3(x1)))))) -> 3(2(4(2(5(5(4(3(3(2(x1)))))))))) 1(4(2(3(4(4(x1)))))) -> 3(0(3(3(2(5(3(2(1(2(x1)))))))))) 1(4(3(1(5(1(x1)))))) -> 3(3(2(4(3(3(0(2(0(2(x1)))))))))) 1(5(4(0(5(3(x1)))))) -> 3(1(3(2(0(3(3(1(3(2(x1)))))))))) 1(5(5(0(1(0(x1)))))) -> 1(3(2(3(5(5(4(0(2(5(x1)))))))))) 5(1(1(5(5(4(x1)))))) -> 5(1(3(3(3(0(2(0(3(2(x1)))))))))) 0(0(0(0(5(5(1(x1))))))) -> 0(0(2(2(3(3(2(2(5(0(x1)))))))))) 0(0(1(5(1(2(1(x1))))))) -> 1(0(2(2(0(4(5(0(2(1(x1)))))))))) 0(0(3(4(0(5(4(x1))))))) -> 0(2(2(1(0(2(1(4(3(2(x1)))))))))) 0(0(5(2(2(0(5(x1))))))) -> 0(2(3(3(4(2(4(0(2(1(x1)))))))))) 0(1(1(1(0(0(5(x1))))))) -> 0(2(2(0(2(5(2(5(5(3(x1)))))))))) 0(4(1(1(0(0(5(x1))))))) -> 1(3(2(3(4(3(0(2(5(3(x1)))))))))) 0(4(3(4(0(1(0(x1))))))) -> 3(2(4(0(5(0(1(5(2(0(x1)))))))))) 0(5(1(1(4(2(3(x1))))))) -> 0(2(4(2(4(4(1(5(3(2(x1)))))))))) 0(5(1(4(4(0(4(x1))))))) -> 0(5(1(2(5(3(3(2(0(4(x1)))))))))) 1(0(0(3(4(3(5(x1))))))) -> 3(2(4(3(3(1(3(2(1(1(x1)))))))))) 1(0(1(0(0(4(2(x1))))))) -> 1(3(2(3(2(1(2(5(0(5(x1)))))))))) 1(0(3(4(1(1(5(x1))))))) -> 1(0(3(5(2(4(3(1(3(2(x1)))))))))) 1(0(4(1(1(4(1(x1))))))) -> 0(0(5(0(2(4(2(0(2(3(x1)))))))))) 1(1(0(3(0(1(5(x1))))))) -> 0(2(0(2(0(2(0(4(5(1(x1)))))))))) 1(1(1(3(1(1(4(x1))))))) -> 3(1(2(3(3(0(2(0(5(2(x1)))))))))) 1(1(1(4(0(5(0(x1))))))) -> 3(5(5(2(2(4(0(2(0(0(x1)))))))))) 1(1(1(5(4(0(5(x1))))))) -> 3(4(3(5(3(3(2(5(3(3(x1)))))))))) 1(1(4(0(5(1(4(x1))))))) -> 4(2(2(3(0(3(2(5(0(2(x1)))))))))) 1(1(4(2(0(4(3(x1))))))) -> 3(1(3(4(4(3(0(2(3(3(x1)))))))))) 1(3(4(0(5(1(5(x1))))))) -> 1(3(3(5(0(2(0(3(3(1(x1)))))))))) 1(3(5(0(0(0(0(x1))))))) -> 3(3(3(3(5(5(3(2(0(1(x1)))))))))) 1(4(0(0(0(1(5(x1))))))) -> 3(3(0(4(4(0(3(1(1(3(x1)))))))))) 1(4(0(0(5(4(4(x1))))))) -> 2(2(4(0(4(2(5(3(3(2(x1)))))))))) 1(4(1(1(1(1(1(x1))))))) -> 4(1(0(2(2(1(2(5(1(3(x1)))))))))) 1(4(2(1(1(1(1(x1))))))) -> 1(5(2(4(0(2(4(5(0(1(x1)))))))))) 1(4(2(1(3(4(3(x1))))))) -> 3(1(3(2(3(3(5(2(5(1(x1)))))))))) 1(4(3(0(0(4(1(x1))))))) -> 5(5(2(4(2(5(2(2(4(3(x1)))))))))) 2(0(0(1(1(1(1(x1))))))) -> 2(1(5(4(5(5(0(2(2(1(x1)))))))))) 2(0(4(0(0(0(0(x1))))))) -> 2(5(2(2(2(5(4(2(0(0(x1)))))))))) 2(1(1(3(5(1(4(x1))))))) -> 2(1(1(3(2(2(3(5(0(2(x1)))))))))) 2(1(4(0(1(4(5(x1))))))) -> 2(4(5(3(3(2(3(3(3(5(x1)))))))))) 3(0(0(1(1(4(3(x1))))))) -> 0(5(3(1(3(2(0(2(4(3(x1)))))))))) 3(0(0(5(4(4(4(x1))))))) -> 3(3(1(3(2(3(0(3(3(1(x1)))))))))) 3(0(4(1(4(0(0(x1))))))) -> 0(4(0(2(2(2(0(5(5(0(x1)))))))))) 3(4(3(4(3(4(0(x1))))))) -> 3(5(5(1(0(2(4(3(2(0(x1)))))))))) 3(5(1(4(0(1(4(x1))))))) -> 0(3(2(5(0(2(2(2(0(2(x1)))))))))) 4(0(1(1(0(5(1(x1))))))) -> 4(3(2(5(2(1(1(3(3(2(x1)))))))))) 4(1(1(2(0(4(1(x1))))))) -> 4(0(2(4(0(0(2(0(2(3(x1)))))))))) 4(1(5(0(1(0(1(x1))))))) -> 4(3(0(3(5(5(2(4(0(2(x1)))))))))) 5(1(2(3(4(4(5(x1))))))) -> 5(4(0(2(0(2(1(2(4(5(x1)))))))))) 5(3(1(4(4(1(1(x1))))))) -> 5(0(2(5(2(5(0(2(4(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_5(x_1)) -> 5(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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: 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))) -> 0(2(0(2(2(3(0(2(3(1(x1)))))))))) 0(4(2(1(5(x1))))) -> 3(0(4(5(3(3(2(3(3(3(x1)))))))))) 1(1(4(1(0(x1))))) -> 3(5(3(3(2(0(2(3(3(3(x1)))))))))) 0(0(5(2(2(1(x1)))))) -> 1(3(5(3(1(2(0(2(2(3(x1)))))))))) 0(4(1(4(0(0(x1)))))) -> 3(3(2(3(0(4(5(0(3(0(x1)))))))))) 0(4(3(4(2(1(x1)))))) -> 0(5(3(3(3(0(0(2(0(2(x1)))))))))) 1(1(2(0(5(4(x1)))))) -> 1(3(2(0(2(3(1(5(1(4(x1)))))))))) 1(1(3(1(4(2(x1)))))) -> 0(2(0(2(2(2(3(0(5(2(x1)))))))))) 1(3(4(0(4(1(x1)))))) -> 1(3(3(0(2(5(4(5(3(0(x1)))))))))) 1(4(0(4(1(4(x1)))))) -> 5(2(5(0(5(5(4(5(0(2(x1)))))))))) 1(4(1(5(4(3(x1)))))) -> 3(2(4(2(5(5(4(3(3(2(x1)))))))))) 1(4(2(3(4(4(x1)))))) -> 3(0(3(3(2(5(3(2(1(2(x1)))))))))) 1(4(3(1(5(1(x1)))))) -> 3(3(2(4(3(3(0(2(0(2(x1)))))))))) 1(5(4(0(5(3(x1)))))) -> 3(1(3(2(0(3(3(1(3(2(x1)))))))))) 1(5(5(0(1(0(x1)))))) -> 1(3(2(3(5(5(4(0(2(5(x1)))))))))) 5(1(1(5(5(4(x1)))))) -> 5(1(3(3(3(0(2(0(3(2(x1)))))))))) 0(0(0(0(5(5(1(x1))))))) -> 0(0(2(2(3(3(2(2(5(0(x1)))))))))) 0(0(1(5(1(2(1(x1))))))) -> 1(0(2(2(0(4(5(0(2(1(x1)))))))))) 0(0(3(4(0(5(4(x1))))))) -> 0(2(2(1(0(2(1(4(3(2(x1)))))))))) 0(0(5(2(2(0(5(x1))))))) -> 0(2(3(3(4(2(4(0(2(1(x1)))))))))) 0(1(1(1(0(0(5(x1))))))) -> 0(2(2(0(2(5(2(5(5(3(x1)))))))))) 0(4(1(1(0(0(5(x1))))))) -> 1(3(2(3(4(3(0(2(5(3(x1)))))))))) 0(4(3(4(0(1(0(x1))))))) -> 3(2(4(0(5(0(1(5(2(0(x1)))))))))) 0(5(1(1(4(2(3(x1))))))) -> 0(2(4(2(4(4(1(5(3(2(x1)))))))))) 0(5(1(4(4(0(4(x1))))))) -> 0(5(1(2(5(3(3(2(0(4(x1)))))))))) 1(0(0(3(4(3(5(x1))))))) -> 3(2(4(3(3(1(3(2(1(1(x1)))))))))) 1(0(1(0(0(4(2(x1))))))) -> 1(3(2(3(2(1(2(5(0(5(x1)))))))))) 1(0(3(4(1(1(5(x1))))))) -> 1(0(3(5(2(4(3(1(3(2(x1)))))))))) 1(0(4(1(1(4(1(x1))))))) -> 0(0(5(0(2(4(2(0(2(3(x1)))))))))) 1(1(0(3(0(1(5(x1))))))) -> 0(2(0(2(0(2(0(4(5(1(x1)))))))))) 1(1(1(3(1(1(4(x1))))))) -> 3(1(2(3(3(0(2(0(5(2(x1)))))))))) 1(1(1(4(0(5(0(x1))))))) -> 3(5(5(2(2(4(0(2(0(0(x1)))))))))) 1(1(1(5(4(0(5(x1))))))) -> 3(4(3(5(3(3(2(5(3(3(x1)))))))))) 1(1(4(0(5(1(4(x1))))))) -> 4(2(2(3(0(3(2(5(0(2(x1)))))))))) 1(1(4(2(0(4(3(x1))))))) -> 3(1(3(4(4(3(0(2(3(3(x1)))))))))) 1(3(4(0(5(1(5(x1))))))) -> 1(3(3(5(0(2(0(3(3(1(x1)))))))))) 1(3(5(0(0(0(0(x1))))))) -> 3(3(3(3(5(5(3(2(0(1(x1)))))))))) 1(4(0(0(0(1(5(x1))))))) -> 3(3(0(4(4(0(3(1(1(3(x1)))))))))) 1(4(0(0(5(4(4(x1))))))) -> 2(2(4(0(4(2(5(3(3(2(x1)))))))))) 1(4(1(1(1(1(1(x1))))))) -> 4(1(0(2(2(1(2(5(1(3(x1)))))))))) 1(4(2(1(1(1(1(x1))))))) -> 1(5(2(4(0(2(4(5(0(1(x1)))))))))) 1(4(2(1(3(4(3(x1))))))) -> 3(1(3(2(3(3(5(2(5(1(x1)))))))))) 1(4(3(0(0(4(1(x1))))))) -> 5(5(2(4(2(5(2(2(4(3(x1)))))))))) 2(0(0(1(1(1(1(x1))))))) -> 2(1(5(4(5(5(0(2(2(1(x1)))))))))) 2(0(4(0(0(0(0(x1))))))) -> 2(5(2(2(2(5(4(2(0(0(x1)))))))))) 2(1(1(3(5(1(4(x1))))))) -> 2(1(1(3(2(2(3(5(0(2(x1)))))))))) 2(1(4(0(1(4(5(x1))))))) -> 2(4(5(3(3(2(3(3(3(5(x1)))))))))) 3(0(0(1(1(4(3(x1))))))) -> 0(5(3(1(3(2(0(2(4(3(x1)))))))))) 3(0(0(5(4(4(4(x1))))))) -> 3(3(1(3(2(3(0(3(3(1(x1)))))))))) 3(0(4(1(4(0(0(x1))))))) -> 0(4(0(2(2(2(0(5(5(0(x1)))))))))) 3(4(3(4(3(4(0(x1))))))) -> 3(5(5(1(0(2(4(3(2(0(x1)))))))))) 3(5(1(4(0(1(4(x1))))))) -> 0(3(2(5(0(2(2(2(0(2(x1)))))))))) 4(0(1(1(0(5(1(x1))))))) -> 4(3(2(5(2(1(1(3(3(2(x1)))))))))) 4(1(1(2(0(4(1(x1))))))) -> 4(0(2(4(0(0(2(0(2(3(x1)))))))))) 4(1(5(0(1(0(1(x1))))))) -> 4(3(0(3(5(5(2(4(0(2(x1)))))))))) 5(1(2(3(4(4(5(x1))))))) -> 5(4(0(2(0(2(1(2(4(5(x1)))))))))) 5(3(1(4(4(1(1(x1))))))) -> 5(0(2(5(2(5(0(2(4(1(x1)))))))))) 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)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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: 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. "[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, 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, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628] {(86,87,[0_1|0, 1_1|0, 5_1|0, 2_1|0, 3_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]), (86,88,[0_1|1, 1_1|1, 5_1|1, 2_1|1, 3_1|1, 4_1|1]), (86,89,[0_1|2]), (86,98,[0_1|2]), (86,107,[3_1|2]), (86,116,[3_1|2]), (86,125,[1_1|2]), (86,134,[0_1|2]), (86,143,[3_1|2]), (86,152,[1_1|2]), (86,161,[0_1|2]), (86,170,[0_1|2]), (86,179,[1_1|2]), (86,188,[0_1|2]), (86,197,[0_1|2]), (86,206,[0_1|2]), (86,215,[3_1|2]), (86,224,[4_1|2]), (86,233,[3_1|2]), (86,242,[1_1|2]), (86,251,[0_1|2]), (86,260,[0_1|2]), (86,269,[3_1|2]), (86,278,[3_1|2]), (86,287,[3_1|2]), (86,296,[1_1|2]), (86,305,[1_1|2]), (86,314,[3_1|2]), (86,323,[5_1|2]), (86,332,[3_1|2]), (86,341,[2_1|2]), (86,350,[3_1|2]), (86,359,[4_1|2]), (86,368,[3_1|2]), (86,377,[1_1|2]), (86,386,[3_1|2]), (86,395,[3_1|2]), (86,404,[5_1|2]), (86,413,[3_1|2]), (86,422,[1_1|2]), (86,431,[3_1|2]), (86,440,[1_1|2]), (86,449,[1_1|2]), (86,458,[0_1|2]), (86,467,[5_1|2]), (86,476,[5_1|2]), (86,485,[5_1|2]), (86,494,[2_1|2]), (86,503,[2_1|2]), (86,512,[2_1|2]), (86,521,[2_1|2]), (86,530,[0_1|2]), (86,539,[3_1|2]), (86,548,[0_1|2]), (86,557,[3_1|2]), (86,566,[0_1|2]), (86,575,[4_1|2]), (86,584,[4_1|2]), (86,593,[4_1|2]), (87,87,[cons_0_1|0, cons_1_1|0, cons_5_1|0, cons_2_1|0, cons_3_1|0, cons_4_1|0]), (88,87,[encArg_1|1]), (88,88,[0_1|1, 1_1|1, 5_1|1, 2_1|1, 3_1|1, 4_1|1]), (88,89,[0_1|2]), (88,98,[0_1|2]), (88,107,[3_1|2]), (88,116,[3_1|2]), (88,125,[1_1|2]), (88,134,[0_1|2]), (88,143,[3_1|2]), (88,152,[1_1|2]), (88,161,[0_1|2]), (88,170,[0_1|2]), (88,179,[1_1|2]), (88,188,[0_1|2]), (88,197,[0_1|2]), (88,206,[0_1|2]), (88,215,[3_1|2]), (88,224,[4_1|2]), (88,233,[3_1|2]), (88,242,[1_1|2]), (88,251,[0_1|2]), (88,260,[0_1|2]), (88,269,[3_1|2]), (88,278,[3_1|2]), (88,287,[3_1|2]), (88,296,[1_1|2]), (88,305,[1_1|2]), (88,314,[3_1|2]), (88,323,[5_1|2]), (88,332,[3_1|2]), (88,341,[2_1|2]), (88,350,[3_1|2]), (88,359,[4_1|2]), (88,368,[3_1|2]), (88,377,[1_1|2]), (88,386,[3_1|2]), (88,395,[3_1|2]), (88,404,[5_1|2]), (88,413,[3_1|2]), (88,422,[1_1|2]), (88,431,[3_1|2]), (88,440,[1_1|2]), (88,449,[1_1|2]), (88,458,[0_1|2]), (88,467,[5_1|2]), (88,476,[5_1|2]), (88,485,[5_1|2]), (88,494,[2_1|2]), (88,503,[2_1|2]), (88,512,[2_1|2]), (88,521,[2_1|2]), (88,530,[0_1|2]), 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(105,485,[5_1|2]), (106,88,[3_1|2]), (106,323,[3_1|2]), (106,404,[3_1|2]), (106,467,[3_1|2]), (106,476,[3_1|2]), (106,485,[3_1|2]), (106,135,[3_1|2]), (106,207,[3_1|2]), (106,531,[3_1|2]), (106,460,[3_1|2]), (106,530,[0_1|2]), (106,539,[3_1|2]), (106,548,[0_1|2]), (106,557,[3_1|2]), (106,566,[0_1|2]), (107,108,[0_1|2]), (108,109,[4_1|2]), (109,110,[5_1|2]), (110,111,[3_1|2]), (111,112,[3_1|2]), (112,113,[2_1|2]), (113,114,[3_1|2]), (114,115,[3_1|2]), (115,88,[3_1|2]), (115,323,[3_1|2]), (115,404,[3_1|2]), (115,467,[3_1|2]), (115,476,[3_1|2]), (115,485,[3_1|2]), (115,378,[3_1|2]), (115,496,[3_1|2]), (115,530,[0_1|2]), (115,539,[3_1|2]), (115,548,[0_1|2]), (115,557,[3_1|2]), (115,566,[0_1|2]), (116,117,[3_1|2]), (117,118,[2_1|2]), (118,119,[3_1|2]), (119,120,[0_1|2]), (120,121,[4_1|2]), (121,122,[5_1|2]), (122,123,[0_1|2]), (123,124,[3_1|2]), (123,530,[0_1|2]), (123,539,[3_1|2]), (123,548,[0_1|2]), (124,88,[0_1|2]), (124,89,[0_1|2]), (124,98,[0_1|2]), (124,134,[0_1|2]), (124,161,[0_1|2]), (124,170,[0_1|2]), (124,188,[0_1|2]), (124,197,[0_1|2]), (124,206,[0_1|2]), (124,251,[0_1|2]), (124,260,[0_1|2]), (124,458,[0_1|2]), (124,530,[0_1|2]), (124,548,[0_1|2]), (124,566,[0_1|2]), (124,171,[0_1|2]), (124,459,[0_1|2]), (124,107,[3_1|2]), (124,116,[3_1|2]), (124,125,[1_1|2]), (124,143,[3_1|2]), (124,152,[1_1|2]), (124,179,[1_1|2]), (125,126,[3_1|2]), (126,127,[2_1|2]), (127,128,[3_1|2]), (128,129,[4_1|2]), (129,130,[3_1|2]), (130,131,[0_1|2]), (131,132,[2_1|2]), (132,133,[5_1|2]), (132,485,[5_1|2]), (133,88,[3_1|2]), (133,323,[3_1|2]), (133,404,[3_1|2]), (133,467,[3_1|2]), (133,476,[3_1|2]), (133,485,[3_1|2]), (133,135,[3_1|2]), (133,207,[3_1|2]), (133,531,[3_1|2]), (133,460,[3_1|2]), (133,530,[0_1|2]), (133,539,[3_1|2]), (133,548,[0_1|2]), (133,557,[3_1|2]), (133,566,[0_1|2]), (134,135,[5_1|2]), (135,136,[3_1|2]), (136,137,[3_1|2]), (137,138,[3_1|2]), (138,139,[0_1|2]), (139,140,[0_1|2]), (140,141,[2_1|2]), (141,142,[0_1|2]), (142,88,[2_1|2]), (142,125,[2_1|2]), (142,152,[2_1|2]), (142,179,[2_1|2]), (142,242,[2_1|2]), (142,296,[2_1|2]), (142,305,[2_1|2]), (142,377,[2_1|2]), (142,422,[2_1|2]), (142,440,[2_1|2]), (142,449,[2_1|2]), (142,495,[2_1|2]), (142,513,[2_1|2]), (142,494,[2_1|2]), (142,503,[2_1|2]), (142,512,[2_1|2]), (142,521,[2_1|2]), (143,144,[2_1|2]), (144,145,[4_1|2]), (145,146,[0_1|2]), (146,147,[5_1|2]), (147,148,[0_1|2]), (148,149,[1_1|2]), (149,150,[5_1|2]), (150,151,[2_1|2]), (150,494,[2_1|2]), (150,503,[2_1|2]), (151,88,[0_1|2]), (151,89,[0_1|2]), (151,98,[0_1|2]), (151,134,[0_1|2]), (151,161,[0_1|2]), (151,170,[0_1|2]), (151,188,[0_1|2]), (151,197,[0_1|2]), (151,206,[0_1|2]), (151,251,[0_1|2]), (151,260,[0_1|2]), (151,458,[0_1|2]), (151,530,[0_1|2]), (151,548,[0_1|2]), (151,566,[0_1|2]), (151,180,[0_1|2]), (151,450,[0_1|2]), (151,107,[3_1|2]), (151,116,[3_1|2]), (151,125,[1_1|2]), (151,143,[3_1|2]), (151,152,[1_1|2]), (151,179,[1_1|2]), (152,153,[3_1|2]), (153,154,[5_1|2]), (154,155,[3_1|2]), (155,156,[1_1|2]), (156,157,[2_1|2]), (157,158,[0_1|2]), (158,159,[2_1|2]), (159,160,[2_1|2]), (160,88,[3_1|2]), (160,125,[3_1|2]), (160,152,[3_1|2]), (160,179,[3_1|2]), (160,242,[3_1|2]), (160,296,[3_1|2]), (160,305,[3_1|2]), (160,377,[3_1|2]), (160,422,[3_1|2]), (160,440,[3_1|2]), (160,449,[3_1|2]), (160,495,[3_1|2]), (160,513,[3_1|2]), (160,530,[0_1|2]), (160,539,[3_1|2]), (160,548,[0_1|2]), (160,557,[3_1|2]), (160,566,[0_1|2]), (161,162,[2_1|2]), (162,163,[3_1|2]), (163,164,[3_1|2]), (164,165,[4_1|2]), (165,166,[2_1|2]), (166,167,[4_1|2]), (167,168,[0_1|2]), (168,169,[2_1|2]), (168,512,[2_1|2]), (168,521,[2_1|2]), (169,88,[1_1|2]), (169,323,[1_1|2, 5_1|2]), (169,404,[1_1|2, 5_1|2]), (169,467,[1_1|2]), (169,476,[1_1|2]), (169,485,[1_1|2]), (169,135,[1_1|2]), (169,207,[1_1|2]), (169,531,[1_1|2]), (169,215,[3_1|2]), (169,224,[4_1|2]), (169,233,[3_1|2]), (169,242,[1_1|2]), (169,251,[0_1|2]), (169,260,[0_1|2]), (169,269,[3_1|2]), (169,278,[3_1|2]), (169,287,[3_1|2]), (169,296,[1_1|2]), (169,305,[1_1|2]), (169,314,[3_1|2]), (169,332,[3_1|2]), (169,341,[2_1|2]), (169,350,[3_1|2]), (169,359,[4_1|2]), (169,368,[3_1|2]), (169,377,[1_1|2]), (169,386,[3_1|2]), (169,395,[3_1|2]), (169,413,[3_1|2]), (169,422,[1_1|2]), (169,431,[3_1|2]), (169,440,[1_1|2]), (169,449,[1_1|2]), (169,458,[0_1|2]), (170,171,[0_1|2]), (171,172,[2_1|2]), (172,173,[2_1|2]), (173,174,[3_1|2]), (174,175,[3_1|2]), (175,176,[2_1|2]), (176,177,[2_1|2]), (177,178,[5_1|2]), (178,88,[0_1|2]), (178,125,[0_1|2, 1_1|2]), (178,152,[0_1|2, 1_1|2]), (178,179,[0_1|2, 1_1|2]), (178,242,[0_1|2]), (178,296,[0_1|2]), (178,305,[0_1|2]), (178,377,[0_1|2]), (178,422,[0_1|2]), (178,440,[0_1|2]), (178,449,[0_1|2]), (178,468,[0_1|2]), (178,89,[0_1|2]), (178,98,[0_1|2]), (178,107,[3_1|2]), (178,116,[3_1|2]), (178,134,[0_1|2]), (178,143,[3_1|2]), (178,161,[0_1|2]), (178,170,[0_1|2]), (178,188,[0_1|2]), (178,197,[0_1|2]), (178,206,[0_1|2]), (179,180,[0_1|2]), (180,181,[2_1|2]), (181,182,[2_1|2]), (182,183,[0_1|2]), (183,184,[4_1|2]), (184,185,[5_1|2]), (185,186,[0_1|2]), (186,187,[2_1|2]), (186,512,[2_1|2]), (186,521,[2_1|2]), (187,88,[1_1|2]), (187,125,[1_1|2]), (187,152,[1_1|2]), (187,179,[1_1|2]), (187,242,[1_1|2]), (187,296,[1_1|2]), (187,305,[1_1|2]), (187,377,[1_1|2]), (187,422,[1_1|2]), (187,440,[1_1|2]), (187,449,[1_1|2]), (187,495,[1_1|2]), (187,513,[1_1|2]), (187,215,[3_1|2]), (187,224,[4_1|2]), (187,233,[3_1|2]), (187,251,[0_1|2]), (187,260,[0_1|2]), (187,269,[3_1|2]), (187,278,[3_1|2]), (187,287,[3_1|2]), (187,314,[3_1|2]), (187,323,[5_1|2]), (187,332,[3_1|2]), (187,341,[2_1|2]), (187,350,[3_1|2]), (187,359,[4_1|2]), (187,368,[3_1|2]), (187,386,[3_1|2]), (187,395,[3_1|2]), (187,404,[5_1|2]), (187,413,[3_1|2]), (187,431,[3_1|2]), (187,458,[0_1|2]), (188,189,[2_1|2]), (189,190,[2_1|2]), (190,191,[1_1|2]), (191,192,[0_1|2]), (192,193,[2_1|2]), (193,194,[1_1|2]), (194,195,[4_1|2]), (195,196,[3_1|2]), (196,88,[2_1|2]), (196,224,[2_1|2]), (196,359,[2_1|2]), (196,575,[2_1|2]), 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(493,242,[1_1|2]), (493,296,[1_1|2]), (493,305,[1_1|2]), (493,377,[1_1|2]), (493,422,[1_1|2]), (493,440,[1_1|2]), (493,449,[1_1|2]), (493,215,[3_1|2]), (493,224,[4_1|2]), (493,233,[3_1|2]), (493,251,[0_1|2]), (493,260,[0_1|2]), (493,269,[3_1|2]), (493,278,[3_1|2]), (493,287,[3_1|2]), (493,314,[3_1|2]), (493,323,[5_1|2]), (493,332,[3_1|2]), (493,341,[2_1|2]), (493,350,[3_1|2]), (493,359,[4_1|2]), (493,368,[3_1|2]), (493,386,[3_1|2]), (493,395,[3_1|2]), (493,404,[5_1|2]), (493,413,[3_1|2]), (493,431,[3_1|2]), (493,458,[0_1|2]), (494,495,[1_1|2]), (495,496,[5_1|2]), (496,497,[4_1|2]), (497,498,[5_1|2]), (498,499,[5_1|2]), (499,500,[0_1|2]), (500,501,[2_1|2]), (501,502,[2_1|2]), (501,512,[2_1|2]), (501,521,[2_1|2]), (502,88,[1_1|2]), (502,125,[1_1|2]), (502,152,[1_1|2]), (502,179,[1_1|2]), (502,242,[1_1|2]), (502,296,[1_1|2]), (502,305,[1_1|2]), (502,377,[1_1|2]), (502,422,[1_1|2]), (502,440,[1_1|2]), (502,449,[1_1|2]), (502,215,[3_1|2]), (502,224,[4_1|2]), (502,233,[3_1|2]), (502,251,[0_1|2]), (502,260,[0_1|2]), (502,269,[3_1|2]), (502,278,[3_1|2]), (502,287,[3_1|2]), (502,314,[3_1|2]), (502,323,[5_1|2]), (502,332,[3_1|2]), (502,341,[2_1|2]), (502,350,[3_1|2]), (502,359,[4_1|2]), (502,368,[3_1|2]), (502,386,[3_1|2]), (502,395,[3_1|2]), (502,404,[5_1|2]), (502,413,[3_1|2]), (502,431,[3_1|2]), (502,458,[0_1|2]), (503,504,[5_1|2]), (504,505,[2_1|2]), (505,506,[2_1|2]), (506,507,[2_1|2]), (507,508,[5_1|2]), (508,509,[4_1|2]), (509,510,[2_1|2]), (509,494,[2_1|2]), (510,511,[0_1|2]), (510,152,[1_1|2]), (510,161,[0_1|2]), (510,170,[0_1|2]), (510,179,[1_1|2]), (510,188,[0_1|2]), (511,88,[0_1|2]), (511,89,[0_1|2]), (511,98,[0_1|2]), (511,134,[0_1|2]), (511,161,[0_1|2]), (511,170,[0_1|2]), (511,188,[0_1|2]), (511,197,[0_1|2]), (511,206,[0_1|2]), (511,251,[0_1|2]), (511,260,[0_1|2]), (511,458,[0_1|2]), (511,530,[0_1|2]), (511,548,[0_1|2]), (511,566,[0_1|2]), (511,171,[0_1|2]), (511,459,[0_1|2]), (511,107,[3_1|2]), (511,116,[3_1|2]), (511,125,[1_1|2]), (511,143,[3_1|2]), (511,152,[1_1|2]), (511,179,[1_1|2]), (512,513,[1_1|2]), (513,514,[1_1|2]), (514,515,[3_1|2]), (515,516,[2_1|2]), (516,517,[2_1|2]), (517,518,[3_1|2]), (518,519,[5_1|2]), (519,520,[0_1|2]), (520,88,[2_1|2]), (520,224,[2_1|2]), (520,359,[2_1|2]), (520,575,[2_1|2]), (520,584,[2_1|2]), (520,593,[2_1|2]), (520,494,[2_1|2]), (520,503,[2_1|2]), (520,512,[2_1|2]), (520,521,[2_1|2]), (521,522,[4_1|2]), (522,523,[5_1|2]), (523,524,[3_1|2]), (524,525,[3_1|2]), (525,526,[2_1|2]), (526,527,[3_1|2]), (527,528,[3_1|2]), (528,529,[3_1|2]), (528,566,[0_1|2]), (529,88,[5_1|2]), (529,323,[5_1|2]), (529,404,[5_1|2]), (529,467,[5_1|2]), (529,476,[5_1|2]), (529,485,[5_1|2]), (530,531,[5_1|2]), (531,532,[3_1|2]), (532,533,[1_1|2]), (533,534,[3_1|2]), (534,535,[2_1|2]), (535,536,[0_1|2]), (536,537,[2_1|2]), (537,538,[4_1|2]), (538,88,[3_1|2]), (538,107,[3_1|2]), (538,116,[3_1|2]), (538,143,[3_1|2]), (538,215,[3_1|2]), (538,233,[3_1|2]), (538,269,[3_1|2]), (538,278,[3_1|2]), (538,287,[3_1|2]), (538,314,[3_1|2]), (538,332,[3_1|2]), (538,350,[3_1|2]), (538,368,[3_1|2]), (538,386,[3_1|2]), (538,395,[3_1|2]), (538,413,[3_1|2]), (538,431,[3_1|2]), (538,539,[3_1|2]), (538,557,[3_1|2]), (538,576,[3_1|2]), (538,594,[3_1|2]), (538,530,[0_1|2]), (538,548,[0_1|2]), (538,566,[0_1|2]), (539,540,[3_1|2]), (540,541,[1_1|2]), (541,542,[3_1|2]), (542,543,[2_1|2]), (543,544,[3_1|2]), (544,545,[0_1|2]), (545,546,[3_1|2]), (546,547,[3_1|2]), (547,88,[1_1|2]), (547,224,[1_1|2, 4_1|2]), (547,359,[1_1|2, 4_1|2]), (547,575,[1_1|2]), (547,584,[1_1|2]), (547,593,[1_1|2]), (547,215,[3_1|2]), (547,233,[3_1|2]), (547,242,[1_1|2]), (547,251,[0_1|2]), (547,260,[0_1|2]), (547,269,[3_1|2]), (547,278,[3_1|2]), (547,287,[3_1|2]), (547,296,[1_1|2]), (547,305,[1_1|2]), (547,314,[3_1|2]), (547,323,[5_1|2]), (547,332,[3_1|2]), (547,341,[2_1|2]), (547,350,[3_1|2]), (547,368,[3_1|2]), (547,377,[1_1|2]), (547,386,[3_1|2]), (547,395,[3_1|2]), (547,404,[5_1|2]), (547,413,[3_1|2]), (547,422,[1_1|2]), (547,431,[3_1|2]), (547,440,[1_1|2]), (547,449,[1_1|2]), (547,458,[0_1|2]), (548,549,[4_1|2]), (549,550,[0_1|2]), (550,551,[2_1|2]), (551,552,[2_1|2]), (552,553,[2_1|2]), (553,554,[0_1|2]), (554,555,[5_1|2]), (555,556,[5_1|2]), (556,88,[0_1|2]), (556,89,[0_1|2]), (556,98,[0_1|2]), (556,134,[0_1|2]), (556,161,[0_1|2]), (556,170,[0_1|2]), (556,188,[0_1|2]), (556,197,[0_1|2]), (556,206,[0_1|2]), (556,251,[0_1|2]), (556,260,[0_1|2]), (556,458,[0_1|2]), (556,530,[0_1|2]), (556,548,[0_1|2]), (556,566,[0_1|2]), (556,171,[0_1|2]), (556,459,[0_1|2]), (556,107,[3_1|2]), (556,116,[3_1|2]), (556,125,[1_1|2]), (556,143,[3_1|2]), (556,152,[1_1|2]), (556,179,[1_1|2]), (557,558,[5_1|2]), (558,559,[5_1|2]), (559,560,[1_1|2]), (560,561,[0_1|2]), (561,562,[2_1|2]), (562,563,[4_1|2]), (563,564,[3_1|2]), (564,565,[2_1|2]), (564,494,[2_1|2]), (564,503,[2_1|2]), (565,88,[0_1|2]), (565,89,[0_1|2]), (565,98,[0_1|2]), (565,134,[0_1|2]), (565,161,[0_1|2]), (565,170,[0_1|2]), (565,188,[0_1|2]), (565,197,[0_1|2]), (565,206,[0_1|2]), (565,251,[0_1|2]), (565,260,[0_1|2]), (565,458,[0_1|2]), (565,530,[0_1|2]), (565,548,[0_1|2]), (565,566,[0_1|2]), (565,585,[0_1|2]), (565,107,[3_1|2]), (565,116,[3_1|2]), (565,125,[1_1|2]), (565,143,[3_1|2]), (565,152,[1_1|2]), (565,179,[1_1|2]), (566,567,[3_1|2]), (567,568,[2_1|2]), (568,569,[5_1|2]), (569,570,[0_1|2]), (570,571,[2_1|2]), (571,572,[2_1|2]), (572,573,[2_1|2]), (573,574,[0_1|2]), (574,88,[2_1|2]), (574,224,[2_1|2]), (574,359,[2_1|2]), (574,575,[2_1|2]), (574,584,[2_1|2]), (574,593,[2_1|2]), (574,494,[2_1|2]), (574,503,[2_1|2]), (574,512,[2_1|2]), (574,521,[2_1|2]), (575,576,[3_1|2]), (576,577,[2_1|2]), (577,578,[5_1|2]), (578,579,[2_1|2]), (579,580,[1_1|2]), (580,581,[1_1|2]), (581,582,[3_1|2]), (582,583,[3_1|2]), (583,88,[2_1|2]), (583,125,[2_1|2]), (583,152,[2_1|2]), (583,179,[2_1|2]), (583,242,[2_1|2]), (583,296,[2_1|2]), (583,305,[2_1|2]), (583,377,[2_1|2]), (583,422,[2_1|2]), (583,440,[2_1|2]), (583,449,[2_1|2]), (583,468,[2_1|2]), (583,208,[2_1|2]), (583,494,[2_1|2]), (583,503,[2_1|2]), (583,512,[2_1|2]), (583,521,[2_1|2]), (584,585,[0_1|2]), (585,586,[2_1|2]), (586,587,[4_1|2]), (587,588,[0_1|2]), (588,589,[0_1|2]), (589,590,[2_1|2]), (590,591,[0_1|2]), (591,592,[2_1|2]), (592,88,[3_1|2]), (592,125,[3_1|2]), (592,152,[3_1|2]), (592,179,[3_1|2]), (592,242,[3_1|2]), (592,296,[3_1|2]), (592,305,[3_1|2]), (592,377,[3_1|2]), (592,422,[3_1|2]), (592,440,[3_1|2]), (592,449,[3_1|2]), (592,360,[3_1|2]), (592,530,[0_1|2]), (592,539,[3_1|2]), (592,548,[0_1|2]), (592,557,[3_1|2]), (592,566,[0_1|2]), (593,594,[3_1|2]), (594,595,[0_1|2]), (595,596,[3_1|2]), (596,597,[5_1|2]), (597,598,[5_1|2]), (598,599,[2_1|2]), (599,600,[4_1|2]), (600,601,[0_1|2]), (601,88,[2_1|2]), (601,125,[2_1|2]), (601,152,[2_1|2]), (601,179,[2_1|2]), (601,242,[2_1|2]), (601,296,[2_1|2]), (601,305,[2_1|2]), (601,377,[2_1|2]), (601,422,[2_1|2]), (601,440,[2_1|2]), (601,449,[2_1|2]), (601,494,[2_1|2]), (601,503,[2_1|2]), (601,512,[2_1|2]), (601,521,[2_1|2]), (602,603,[0_1|3]), (603,604,[4_1|3]), (604,605,[5_1|3]), (605,606,[3_1|3]), (606,607,[3_1|3]), (607,608,[2_1|3]), (608,609,[3_1|3]), (609,610,[3_1|3]), (610,496,[3_1|3]), (611,612,[2_1|3]), (612,613,[0_1|3]), (613,614,[2_1|3]), (614,615,[2_1|3]), (615,616,[3_1|3]), (616,617,[0_1|3]), (617,618,[2_1|3]), (618,619,[3_1|3]), (619,125,[1_1|3]), (619,152,[1_1|3]), (619,179,[1_1|3]), (619,242,[1_1|3]), (619,296,[1_1|3]), (619,305,[1_1|3]), (619,377,[1_1|3]), (619,422,[1_1|3]), (619,440,[1_1|3]), (619,449,[1_1|3]), (620,621,[5_1|3]), (621,622,[3_1|3]), (622,623,[3_1|3]), (623,624,[2_1|3]), (624,625,[0_1|3]), (625,626,[2_1|3]), (626,627,[3_1|3]), (627,628,[3_1|3]), (628,361,[3_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)