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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 96 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 270 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(2(3(x1))))) -> 0(4(1(4(3(x1))))) 2(1(4(3(1(x1))))) -> 4(1(5(3(x1)))) 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 0(1(1(3(2(3(1(3(2(x1))))))))) -> 0(0(5(3(3(1(1(0(x1)))))))) 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 0(1(1(1(2(2(4(1(1(1(x1)))))))))) -> 2(1(2(4(0(2(2(5(0(x1))))))))) 2(2(2(1(4(1(1(3(0(2(x1)))))))))) -> 0(2(0(4(2(3(5(4(0(x1))))))))) 2(2(4(2(1(2(3(2(1(4(x1)))))))))) -> 3(3(3(0(4(5(0(2(4(x1))))))))) 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 3(2(1(1(4(2(4(5(2(5(3(3(x1)))))))))))) -> 5(1(3(1(2(4(1(2(2(1(0(x1))))))))))) 5(1(3(3(0(3(5(2(1(4(1(5(x1)))))))))))) -> 3(5(5(5(5(0(1(5(4(2(5(x1))))))))))) 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 1(2(5(2(4(4(0(3(4(0(3(3(2(x1))))))))))))) -> 1(2(4(2(5(3(5(2(1(3(2(0(x1)))))))))))) 5(5(0(2(4(4(2(4(2(2(0(3(4(x1))))))))))))) -> 5(3(5(2(0(0(4(4(5(5(5(2(x1)))))))))))) 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 2(2(4(0(2(2(4(3(5(0(2(3(3(5(3(x1))))))))))))))) -> 2(1(5(1(3(5(5(5(5(0(0(2(5(x1))))))))))))) 5(0(2(2(0(2(4(3(2(2(4(5(0(2(3(x1))))))))))))))) -> 5(4(1(1(5(4(5(0(2(3(0(3(3(3(x1)))))))))))))) 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 3(3(3(4(0(3(1(4(4(4(4(1(3(3(1(4(x1)))))))))))))))) -> 5(5(2(4(0(0(3(0(4(5(0(2(2(2(x1)))))))))))))) 3(3(3(5(3(1(1(2(2(3(4(2(0(2(1(1(x1)))))))))))))))) -> 5(5(1(4(1(4(1(2(5(2(0(5(2(3(1(x1))))))))))))))) 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 0(2(0(4(4(4(3(4(0(3(5(1(5(5(3(1(4(3(x1)))))))))))))))))) -> 5(2(2(1(1(2(4(2(3(5(0(0(3(1(1(4(0(x1))))))))))))))))) 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 3(0(4(4(4(1(1(2(5(2(1(1(4(3(4(4(4(2(x1)))))))))))))))))) -> 3(3(4(5(3(3(5(4(3(3(5(2(3(3(5(3(x1)))))))))))))))) 0(0(4(1(2(3(5(0(4(0(5(2(4(3(2(3(1(5(1(x1))))))))))))))))))) -> 4(5(3(2(0(2(3(4(5(5(1(1(5(1(5(5(1(4(x1)))))))))))))))))) 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(2(3(x1))))) -> 0(4(1(4(3(x1))))) 2(1(4(3(1(x1))))) -> 4(1(5(3(x1)))) 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 0(1(1(3(2(3(1(3(2(x1))))))))) -> 0(0(5(3(3(1(1(0(x1)))))))) 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 0(1(1(1(2(2(4(1(1(1(x1)))))))))) -> 2(1(2(4(0(2(2(5(0(x1))))))))) 2(2(2(1(4(1(1(3(0(2(x1)))))))))) -> 0(2(0(4(2(3(5(4(0(x1))))))))) 2(2(4(2(1(2(3(2(1(4(x1)))))))))) -> 3(3(3(0(4(5(0(2(4(x1))))))))) 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 3(2(1(1(4(2(4(5(2(5(3(3(x1)))))))))))) -> 5(1(3(1(2(4(1(2(2(1(0(x1))))))))))) 5(1(3(3(0(3(5(2(1(4(1(5(x1)))))))))))) -> 3(5(5(5(5(0(1(5(4(2(5(x1))))))))))) 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 1(2(5(2(4(4(0(3(4(0(3(3(2(x1))))))))))))) -> 1(2(4(2(5(3(5(2(1(3(2(0(x1)))))))))))) 5(5(0(2(4(4(2(4(2(2(0(3(4(x1))))))))))))) -> 5(3(5(2(0(0(4(4(5(5(5(2(x1)))))))))))) 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 2(2(4(0(2(2(4(3(5(0(2(3(3(5(3(x1))))))))))))))) -> 2(1(5(1(3(5(5(5(5(0(0(2(5(x1))))))))))))) 5(0(2(2(0(2(4(3(2(2(4(5(0(2(3(x1))))))))))))))) -> 5(4(1(1(5(4(5(0(2(3(0(3(3(3(x1)))))))))))))) 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 3(3(3(4(0(3(1(4(4(4(4(1(3(3(1(4(x1)))))))))))))))) -> 5(5(2(4(0(0(3(0(4(5(0(2(2(2(x1)))))))))))))) 3(3(3(5(3(1(1(2(2(3(4(2(0(2(1(1(x1)))))))))))))))) -> 5(5(1(4(1(4(1(2(5(2(0(5(2(3(1(x1))))))))))))))) 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 0(2(0(4(4(4(3(4(0(3(5(1(5(5(3(1(4(3(x1)))))))))))))))))) -> 5(2(2(1(1(2(4(2(3(5(0(0(3(1(1(4(0(x1))))))))))))))))) 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 3(0(4(4(4(1(1(2(5(2(1(1(4(3(4(4(4(2(x1)))))))))))))))))) -> 3(3(4(5(3(3(5(4(3(3(5(2(3(3(5(3(x1)))))))))))))))) 0(0(4(1(2(3(5(0(4(0(5(2(4(3(2(3(1(5(1(x1))))))))))))))))))) -> 4(5(3(2(0(2(3(4(5(5(1(1(5(1(5(5(1(4(x1)))))))))))))))))) 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(2(3(x1))))) -> 0(4(1(4(3(x1))))) 2(1(4(3(1(x1))))) -> 4(1(5(3(x1)))) 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 0(1(1(3(2(3(1(3(2(x1))))))))) -> 0(0(5(3(3(1(1(0(x1)))))))) 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 0(1(1(1(2(2(4(1(1(1(x1)))))))))) -> 2(1(2(4(0(2(2(5(0(x1))))))))) 2(2(2(1(4(1(1(3(0(2(x1)))))))))) -> 0(2(0(4(2(3(5(4(0(x1))))))))) 2(2(4(2(1(2(3(2(1(4(x1)))))))))) -> 3(3(3(0(4(5(0(2(4(x1))))))))) 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 3(2(1(1(4(2(4(5(2(5(3(3(x1)))))))))))) -> 5(1(3(1(2(4(1(2(2(1(0(x1))))))))))) 5(1(3(3(0(3(5(2(1(4(1(5(x1)))))))))))) -> 3(5(5(5(5(0(1(5(4(2(5(x1))))))))))) 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 1(2(5(2(4(4(0(3(4(0(3(3(2(x1))))))))))))) -> 1(2(4(2(5(3(5(2(1(3(2(0(x1)))))))))))) 5(5(0(2(4(4(2(4(2(2(0(3(4(x1))))))))))))) -> 5(3(5(2(0(0(4(4(5(5(5(2(x1)))))))))))) 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 2(2(4(0(2(2(4(3(5(0(2(3(3(5(3(x1))))))))))))))) -> 2(1(5(1(3(5(5(5(5(0(0(2(5(x1))))))))))))) 5(0(2(2(0(2(4(3(2(2(4(5(0(2(3(x1))))))))))))))) -> 5(4(1(1(5(4(5(0(2(3(0(3(3(3(x1)))))))))))))) 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 3(3(3(4(0(3(1(4(4(4(4(1(3(3(1(4(x1)))))))))))))))) -> 5(5(2(4(0(0(3(0(4(5(0(2(2(2(x1)))))))))))))) 3(3(3(5(3(1(1(2(2(3(4(2(0(2(1(1(x1)))))))))))))))) -> 5(5(1(4(1(4(1(2(5(2(0(5(2(3(1(x1))))))))))))))) 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 0(2(0(4(4(4(3(4(0(3(5(1(5(5(3(1(4(3(x1)))))))))))))))))) -> 5(2(2(1(1(2(4(2(3(5(0(0(3(1(1(4(0(x1))))))))))))))))) 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 3(0(4(4(4(1(1(2(5(2(1(1(4(3(4(4(4(2(x1)))))))))))))))))) -> 3(3(4(5(3(3(5(4(3(3(5(2(3(3(5(3(x1)))))))))))))))) 0(0(4(1(2(3(5(0(4(0(5(2(4(3(2(3(1(5(1(x1))))))))))))))))))) -> 4(5(3(2(0(2(3(4(5(5(1(1(5(1(5(5(1(4(x1)))))))))))))))))) 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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(2(3(x1))))) -> 0(4(1(4(3(x1))))) 2(1(4(3(1(x1))))) -> 4(1(5(3(x1)))) 1(2(3(5(3(0(x1)))))) -> 1(1(4(3(5(1(x1)))))) 2(1(3(5(0(0(x1)))))) -> 4(4(2(4(5(0(x1)))))) 4(3(5(1(5(1(x1)))))) -> 4(0(2(4(5(4(x1)))))) 0(0(1(2(2(0(4(2(x1)))))))) -> 2(4(0(0(4(4(3(0(x1)))))))) 0(1(1(3(2(3(1(3(2(x1))))))))) -> 0(0(5(3(3(1(1(0(x1)))))))) 1(2(5(5(5(2(5(3(5(x1))))))))) -> 4(5(3(2(5(1(3(2(5(x1))))))))) 4(1(5(1(2(4(1(4(1(x1))))))))) -> 4(2(3(1(3(0(1(3(1(x1))))))))) 0(1(1(1(2(2(4(1(1(1(x1)))))))))) -> 2(1(2(4(0(2(2(5(0(x1))))))))) 2(2(2(1(4(1(1(3(0(2(x1)))))))))) -> 0(2(0(4(2(3(5(4(0(x1))))))))) 2(2(4(2(1(2(3(2(1(4(x1)))))))))) -> 3(3(3(0(4(5(0(2(4(x1))))))))) 1(3(1(5(0(4(2(2(0(5(5(x1))))))))))) -> 4(4(1(2(2(5(2(2(2(0(5(x1))))))))))) 2(0(1(3(1(2(5(4(3(4(4(x1))))))))))) -> 2(1(2(4(4(2(3(4(2(4(4(x1))))))))))) 4(1(0(5(3(4(3(5(4(1(1(x1))))))))))) -> 4(4(4(3(3(2(0(2(4(5(3(x1))))))))))) 3(2(1(1(4(2(4(5(2(5(3(3(x1)))))))))))) -> 5(1(3(1(2(4(1(2(2(1(0(x1))))))))))) 5(1(3(3(0(3(5(2(1(4(1(5(x1)))))))))))) -> 3(5(5(5(5(0(1(5(4(2(5(x1))))))))))) 5(3(3(5(3(4(0(5(0(2(4(0(x1)))))))))))) -> 5(5(3(2(5(4(4(2(1(1(1(3(x1)))))))))))) 0(1(3(1(5(2(2(4(4(5(5(2(4(x1))))))))))))) -> 0(3(4(0(0(4(0(2(1(3(4(3(4(x1))))))))))))) 1(2(5(2(4(4(0(3(4(0(3(3(2(x1))))))))))))) -> 1(2(4(2(5(3(5(2(1(3(2(0(x1)))))))))))) 5(5(0(2(4(4(2(4(2(2(0(3(4(x1))))))))))))) -> 5(3(5(2(0(0(4(4(5(5(5(2(x1)))))))))))) 1(3(5(3(2(3(4(1(5(1(4(1(0(3(x1)))))))))))))) -> 1(1(1(0(0(2(0(3(4(2(1(3(0(3(x1)))))))))))))) 2(2(4(0(2(2(4(3(5(0(2(3(3(5(3(x1))))))))))))))) -> 2(1(5(1(3(5(5(5(5(0(0(2(5(x1))))))))))))) 5(0(2(2(0(2(4(3(2(2(4(5(0(2(3(x1))))))))))))))) -> 5(4(1(1(5(4(5(0(2(3(0(3(3(3(x1)))))))))))))) 0(1(4(2(0(5(1(5(2(4(0(0(3(4(4(2(x1)))))))))))))))) -> 4(1(5(4(1(0(2(0(3(4(4(1(1(3(4(2(x1)))))))))))))))) 2(2(5(1(3(4(5(3(1(4(1(2(3(4(2(2(x1)))))))))))))))) -> 2(5(2(0(4(2(4(4(2(3(4(0(0(4(3(2(x1)))))))))))))))) 3(3(3(4(0(3(1(4(4(4(4(1(3(3(1(4(x1)))))))))))))))) -> 5(5(2(4(0(0(3(0(4(5(0(2(2(2(x1)))))))))))))) 3(3(3(5(3(1(1(2(2(3(4(2(0(2(1(1(x1)))))))))))))))) -> 5(5(1(4(1(4(1(2(5(2(0(5(2(3(1(x1))))))))))))))) 4(3(0(3(2(4(5(0(2(5(0(0(4(2(3(1(x1)))))))))))))))) -> 4(4(4(2(3(3(4(5(0(5(2(2(1(2(0(3(x1)))))))))))))))) 1(3(0(4(0(4(2(3(0(2(3(5(0(5(3(5(3(x1))))))))))))))))) -> 1(0(3(0(1(4(5(1(5(3(5(2(3(2(0(1(3(x1))))))))))))))))) 3(5(1(3(0(0(3(3(3(3(1(0(3(0(5(2(0(x1))))))))))))))))) -> 3(5(3(4(3(5(0(5(1(2(0(4(1(5(3(2(0(x1))))))))))))))))) 5(4(5(3(0(3(3(3(1(2(0(0(2(3(3(2(0(x1))))))))))))))))) -> 5(2(0(1(4(2(4(1(2(0(0(4(2(3(1(2(2(x1))))))))))))))))) 0(2(0(4(4(4(3(4(0(3(5(1(5(5(3(1(4(3(x1)))))))))))))))))) -> 5(2(2(1(1(2(4(2(3(5(0(0(3(1(1(4(0(x1))))))))))))))))) 0(4(4(1(2(0(2(2(0(3(3(5(2(2(3(2(3(1(x1)))))))))))))))))) -> 4(4(0(4(0(0(0(1(3(0(3(3(4(4(4(0(2(4(x1)))))))))))))))))) 3(0(4(4(4(1(1(2(5(2(1(1(4(3(4(4(4(2(x1)))))))))))))))))) -> 3(3(4(5(3(3(5(4(3(3(5(2(3(3(5(3(x1)))))))))))))))) 0(0(4(1(2(3(5(0(4(0(5(2(4(3(2(3(1(5(1(x1))))))))))))))))))) -> 4(5(3(2(0(2(3(4(5(5(1(1(5(1(5(5(1(4(x1)))))))))))))))))) 0(4(2(5(2(1(0(1(0(1(3(3(5(1(1(2(5(0(2(x1))))))))))))))))))) -> 2(4(1(3(3(5(0(2(0(3(3(5(3(0(1(4(5(0(2(x1))))))))))))))))))) 1(0(0(4(4(4(1(3(2(4(5(1(2(5(3(2(3(2(2(5(2(x1))))))))))))))))))))) -> 1(4(5(1(3(5(4(2(4(4(4(5(0(2(2(1(1(1(1(3(4(x1))))))))))))))))))))) 3(4(4(4(2(1(5(3(1(4(1(5(3(5(3(3(0(2(1(3(1(x1))))))))))))))))))))) -> 3(4(3(0(3(3(4(4(3(4(0(1(4(0(1(5(1(5(4(2(3(x1))))))))))))))))))))) 5(2(1(2(2(4(5(2(2(3(3(3(1(0(3(4(1(0(0(3(2(x1))))))))))))))))))))) -> 5(2(3(2(4(0(2(2(3(1(4(3(2(1(2(1(2(5(5(2(4(x1))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(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. "[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, 629, 630] {(151,152,[0_1|0, 2_1|0, 1_1|0, 4_1|0, 3_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]), (151,153,[0_1|1, 2_1|1, 1_1|1, 4_1|1, 3_1|1, 5_1|1]), (151,154,[0_1|2]), (151,158,[0_1|2]), (151,165,[2_1|2]), (151,173,[0_1|2]), (151,185,[4_1|2]), (151,200,[2_1|2]), (151,207,[4_1|2]), (151,224,[5_1|2]), (151,240,[4_1|2]), (151,257,[2_1|2]), (151,275,[4_1|2]), (151,278,[4_1|2]), (151,283,[0_1|2]), (151,291,[3_1|2]), (151,299,[2_1|2]), (151,311,[2_1|2]), (151,326,[2_1|2]), (151,336,[1_1|2]), (151,341,[4_1|2]), (151,349,[1_1|2]), (151,360,[4_1|2]), (151,370,[1_1|2]), (151,383,[1_1|2]), (151,399,[1_1|2]), (151,419,[4_1|2]), (151,424,[4_1|2]), (151,439,[4_1|2]), (151,447,[4_1|2]), (151,457,[5_1|2]), (151,467,[5_1|2]), (151,480,[5_1|2]), (151,494,[3_1|2]), (151,510,[3_1|2]), (151,525,[3_1|2]), (151,545,[3_1|2]), (151,555,[5_1|2]), (151,566,[5_1|2]), (151,577,[5_1|2]), (151,590,[5_1|2]), (151,606,[5_1|2]), (152,152,[cons_0_1|0, cons_2_1|0, cons_1_1|0, cons_4_1|0, cons_3_1|0, cons_5_1|0]), (153,152,[encArg_1|1]), (153,153,[0_1|1, 2_1|1, 1_1|1, 4_1|1, 3_1|1, 5_1|1]), (153,154,[0_1|2]), (153,158,[0_1|2]), (153,165,[2_1|2]), (153,173,[0_1|2]), (153,185,[4_1|2]), (153,200,[2_1|2]), (153,207,[4_1|2]), (153,224,[5_1|2]), (153,240,[4_1|2]), (153,257,[2_1|2]), (153,275,[4_1|2]), (153,278,[4_1|2]), (153,283,[0_1|2]), (153,291,[3_1|2]), (153,299,[2_1|2]), (153,311,[2_1|2]), (153,326,[2_1|2]), (153,336,[1_1|2]), (153,341,[4_1|2]), (153,349,[1_1|2]), (153,360,[4_1|2]), (153,370,[1_1|2]), (153,383,[1_1|2]), (153,399,[1_1|2]), 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(429,430,[4_1|2]), (430,431,[5_1|2]), (431,432,[0_1|2]), (432,433,[5_1|2]), (433,434,[2_1|2]), (434,435,[2_1|2]), (435,436,[1_1|2]), (436,437,[2_1|2]), (437,438,[0_1|2]), (438,153,[3_1|2]), (438,336,[3_1|2]), (438,349,[3_1|2]), (438,370,[3_1|2]), (438,383,[3_1|2]), (438,399,[3_1|2]), (438,442,[3_1|2]), (438,457,[5_1|2]), (438,467,[5_1|2]), (438,480,[5_1|2]), (438,494,[3_1|2]), (438,510,[3_1|2]), (438,525,[3_1|2]), (439,440,[2_1|2]), (440,441,[3_1|2]), (441,442,[1_1|2]), (442,443,[3_1|2]), (443,444,[0_1|2]), (443,173,[0_1|2]), (444,445,[1_1|2]), (444,360,[4_1|2]), (445,446,[3_1|2]), (446,153,[1_1|2]), (446,336,[1_1|2]), (446,349,[1_1|2]), (446,370,[1_1|2]), (446,383,[1_1|2]), (446,399,[1_1|2]), (446,186,[1_1|2]), (446,276,[1_1|2]), (446,341,[4_1|2]), (446,360,[4_1|2]), (447,448,[4_1|2]), (448,449,[4_1|2]), (449,450,[3_1|2]), (450,451,[3_1|2]), (451,452,[2_1|2]), (452,453,[0_1|2]), (453,454,[2_1|2]), (454,455,[4_1|2]), (455,456,[5_1|2]), (455,555,[5_1|2]), (456,153,[3_1|2]), (456,336,[3_1|2]), (456,349,[3_1|2]), (456,370,[3_1|2]), (456,383,[3_1|2]), (456,399,[3_1|2]), (456,337,[3_1|2]), (456,371,[3_1|2]), (456,580,[3_1|2]), (456,457,[5_1|2]), (456,467,[5_1|2]), (456,480,[5_1|2]), (456,494,[3_1|2]), (456,510,[3_1|2]), (456,525,[3_1|2]), (457,458,[1_1|2]), (458,459,[3_1|2]), (459,460,[1_1|2]), (460,461,[2_1|2]), (461,462,[4_1|2]), (462,463,[1_1|2]), (463,464,[2_1|2]), (464,465,[2_1|2]), (465,466,[1_1|2]), (465,399,[1_1|2]), (466,153,[0_1|2]), (466,291,[0_1|2]), (466,494,[0_1|2]), (466,510,[0_1|2]), (466,525,[0_1|2]), (466,545,[0_1|2]), (466,292,[0_1|2]), (466,511,[0_1|2]), (466,154,[0_1|2]), (466,158,[0_1|2]), (466,165,[2_1|2]), (466,173,[0_1|2]), (466,185,[4_1|2]), (466,200,[2_1|2]), (466,207,[4_1|2]), (466,224,[5_1|2]), (466,240,[4_1|2]), (466,257,[2_1|2]), (467,468,[5_1|2]), (468,469,[2_1|2]), (469,470,[4_1|2]), (470,471,[0_1|2]), (471,472,[0_1|2]), (472,473,[3_1|2]), (473,474,[0_1|2]), (474,475,[4_1|2]), (475,476,[5_1|2]), (476,477,[0_1|2]), (477,478,[2_1|2]), (477,283,[0_1|2]), (478,479,[2_1|2]), (478,283,[0_1|2]), (478,291,[3_1|2]), (478,299,[2_1|2]), (478,311,[2_1|2]), (479,153,[2_1|2]), (479,185,[2_1|2]), (479,207,[2_1|2]), (479,240,[2_1|2]), (479,275,[2_1|2, 4_1|2]), (479,278,[2_1|2, 4_1|2]), (479,341,[2_1|2]), (479,360,[2_1|2]), (479,419,[2_1|2]), (479,424,[2_1|2]), (479,439,[2_1|2]), (479,447,[2_1|2]), (479,400,[2_1|2]), (479,283,[0_1|2]), (479,291,[3_1|2]), (479,299,[2_1|2]), (479,311,[2_1|2]), (479,326,[2_1|2]), (480,481,[5_1|2]), (481,482,[1_1|2]), (482,483,[4_1|2]), (483,484,[1_1|2]), (484,485,[4_1|2]), (485,486,[1_1|2]), (486,487,[2_1|2]), (487,488,[5_1|2]), (488,489,[2_1|2]), (489,490,[0_1|2]), (490,491,[5_1|2]), (491,492,[2_1|2]), (492,493,[3_1|2]), (493,153,[1_1|2]), (493,336,[1_1|2]), (493,349,[1_1|2]), (493,370,[1_1|2]), (493,383,[1_1|2]), (493,399,[1_1|2]), (493,337,[1_1|2]), (493,371,[1_1|2]), (493,341,[4_1|2]), (493,360,[4_1|2]), (494,495,[5_1|2]), (495,496,[3_1|2]), (496,497,[4_1|2]), (497,498,[3_1|2]), (498,499,[5_1|2]), (499,500,[0_1|2]), (500,501,[5_1|2]), (501,502,[1_1|2]), (502,503,[2_1|2]), (503,504,[0_1|2]), (504,505,[4_1|2]), (505,506,[1_1|2]), (506,507,[5_1|2]), (507,508,[3_1|2]), (508,509,[2_1|2]), (508,326,[2_1|2]), (509,153,[0_1|2]), (509,154,[0_1|2]), (509,158,[0_1|2]), (509,173,[0_1|2]), (509,283,[0_1|2]), (509,592,[0_1|2]), (509,165,[2_1|2]), (509,185,[4_1|2]), (509,200,[2_1|2]), (509,207,[4_1|2]), (509,224,[5_1|2]), (509,240,[4_1|2]), (509,257,[2_1|2]), (510,511,[3_1|2]), (511,512,[4_1|2]), (512,513,[5_1|2]), (513,514,[3_1|2]), (514,515,[3_1|2]), (515,516,[5_1|2]), (516,517,[4_1|2]), (517,518,[3_1|2]), (518,519,[3_1|2]), (519,520,[5_1|2]), (520,521,[2_1|2]), (521,522,[3_1|2]), (522,523,[3_1|2]), (523,524,[5_1|2]), (523,555,[5_1|2]), (524,153,[3_1|2]), (524,165,[3_1|2]), (524,200,[3_1|2]), (524,257,[3_1|2]), (524,299,[3_1|2]), (524,311,[3_1|2]), (524,326,[3_1|2]), (524,440,[3_1|2]), (524,280,[3_1|2]), (524,427,[3_1|2]), (524,457,[5_1|2]), (524,467,[5_1|2]), (524,480,[5_1|2]), (524,494,[3_1|2]), (524,510,[3_1|2]), (524,525,[3_1|2]), (525,526,[4_1|2]), (526,527,[3_1|2]), (527,528,[0_1|2]), (528,529,[3_1|2]), (529,530,[3_1|2]), (530,531,[4_1|2]), (531,532,[4_1|2]), (532,533,[3_1|2]), (533,534,[4_1|2]), (534,535,[0_1|2]), (535,536,[1_1|2]), (536,537,[4_1|2]), (537,538,[0_1|2]), (538,539,[1_1|2]), (539,540,[5_1|2]), (540,541,[1_1|2]), (541,542,[5_1|2]), (542,543,[4_1|2]), (543,544,[2_1|2]), (544,153,[3_1|2]), (544,336,[3_1|2]), (544,349,[3_1|2]), (544,370,[3_1|2]), (544,383,[3_1|2]), (544,399,[3_1|2]), (544,457,[5_1|2]), (544,467,[5_1|2]), (544,480,[5_1|2]), (544,494,[3_1|2]), (544,510,[3_1|2]), (544,525,[3_1|2]), (545,546,[5_1|2]), (546,547,[5_1|2]), (547,548,[5_1|2]), (548,549,[5_1|2]), (549,550,[0_1|2]), (550,551,[1_1|2]), (551,552,[5_1|2]), (552,553,[4_1|2]), (553,554,[2_1|2]), (554,153,[5_1|2]), (554,224,[5_1|2]), (554,457,[5_1|2]), (554,467,[5_1|2]), (554,480,[5_1|2]), (554,555,[5_1|2]), (554,566,[5_1|2]), (554,577,[5_1|2]), (554,590,[5_1|2]), (554,606,[5_1|2]), (554,187,[5_1|2]), (554,277,[5_1|2]), (554,545,[3_1|2]), (555,556,[5_1|2]), (556,557,[3_1|2]), (557,558,[2_1|2]), (558,559,[5_1|2]), (559,560,[4_1|2]), (560,561,[4_1|2]), (561,562,[2_1|2]), (562,563,[1_1|2]), (563,564,[1_1|2]), (564,565,[1_1|2]), (564,360,[4_1|2]), (564,370,[1_1|2]), (564,383,[1_1|2]), (565,153,[3_1|2]), (565,154,[3_1|2]), (565,158,[3_1|2]), (565,173,[3_1|2]), (565,283,[3_1|2]), (565,420,[3_1|2]), (565,202,[3_1|2]), (565,457,[5_1|2]), (565,467,[5_1|2]), (565,480,[5_1|2]), (565,494,[3_1|2]), (565,510,[3_1|2]), (565,525,[3_1|2]), (566,567,[3_1|2]), (567,568,[5_1|2]), (568,569,[2_1|2]), (569,570,[0_1|2]), (570,571,[0_1|2]), (571,572,[4_1|2]), (572,573,[4_1|2]), (573,574,[5_1|2]), (574,575,[5_1|2]), (575,576,[5_1|2]), (575,606,[5_1|2]), (576,153,[2_1|2]), (576,185,[2_1|2]), (576,207,[2_1|2]), (576,240,[2_1|2]), (576,275,[2_1|2, 4_1|2]), (576,278,[2_1|2, 4_1|2]), (576,341,[2_1|2]), (576,360,[2_1|2]), (576,419,[2_1|2]), (576,424,[2_1|2]), (576,439,[2_1|2]), (576,447,[2_1|2]), (576,526,[2_1|2]), (576,175,[2_1|2]), (576,283,[0_1|2]), (576,291,[3_1|2]), (576,299,[2_1|2]), (576,311,[2_1|2]), (576,326,[2_1|2]), (577,578,[4_1|2]), (578,579,[1_1|2]), (579,580,[1_1|2]), (580,581,[5_1|2]), (581,582,[4_1|2]), (582,583,[5_1|2]), (583,584,[0_1|2]), (584,585,[2_1|2]), (585,586,[3_1|2]), (586,587,[0_1|2]), (587,588,[3_1|2]), (587,467,[5_1|2]), (587,480,[5_1|2]), (588,589,[3_1|2]), (588,467,[5_1|2]), (588,480,[5_1|2]), (589,153,[3_1|2]), (589,291,[3_1|2]), (589,494,[3_1|2]), (589,510,[3_1|2]), (589,525,[3_1|2]), (589,545,[3_1|2]), (589,457,[5_1|2]), (589,467,[5_1|2]), (589,480,[5_1|2]), (590,591,[2_1|2]), (591,592,[0_1|2]), (592,593,[1_1|2]), (593,594,[4_1|2]), (594,595,[2_1|2]), (595,596,[4_1|2]), (596,597,[1_1|2]), (597,598,[2_1|2]), (598,599,[0_1|2]), (599,600,[0_1|2]), (600,601,[4_1|2]), (601,602,[2_1|2]), (602,603,[3_1|2]), (603,604,[1_1|2]), (604,605,[2_1|2]), (604,283,[0_1|2]), (604,291,[3_1|2]), (604,299,[2_1|2]), (604,311,[2_1|2]), (605,153,[2_1|2]), (605,154,[2_1|2]), (605,158,[2_1|2]), (605,173,[2_1|2]), (605,283,[2_1|2, 0_1|2]), (605,275,[4_1|2]), (605,278,[4_1|2]), (605,291,[3_1|2]), (605,299,[2_1|2]), (605,311,[2_1|2]), (605,326,[2_1|2]), (606,607,[2_1|2]), (607,608,[3_1|2]), (608,609,[2_1|2]), (609,610,[4_1|2]), (610,611,[0_1|2]), (611,612,[2_1|2]), (612,613,[2_1|2]), (613,614,[3_1|2]), (614,615,[1_1|2]), (615,616,[4_1|2]), (616,617,[3_1|2]), (617,618,[2_1|2]), (618,619,[1_1|2]), (619,620,[2_1|2]), (620,621,[1_1|2]), (621,622,[2_1|2]), (622,623,[5_1|2]), (623,624,[5_1|2]), (624,625,[2_1|2]), (625,153,[4_1|2]), (625,165,[4_1|2]), (625,200,[4_1|2]), (625,257,[4_1|2]), (625,299,[4_1|2]), (625,311,[4_1|2]), (625,326,[4_1|2]), (625,419,[4_1|2]), (625,424,[4_1|2]), (625,439,[4_1|2]), (625,447,[4_1|2]), (626,627,[0_1|3]), (627,628,[2_1|3]), (628,629,[4_1|3]), (629,630,[5_1|3]), (630,458,[4_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)