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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).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), 144 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 296 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(x1)))) -> 3(3(0(x1))) 0(3(1(3(x1)))) -> 2(4(3(x1))) 5(1(0(0(x1)))) -> 5(3(3(x1))) 0(3(2(4(5(x1))))) -> 2(5(1(5(x1)))) 3(0(0(0(4(x1))))) -> 5(5(1(4(x1)))) 5(4(2(4(3(x1))))) -> 0(5(3(1(3(x1))))) 5(3(0(0(2(0(x1)))))) -> 5(3(2(4(3(x1))))) 4(3(5(0(3(0(5(3(x1)))))))) -> 4(1(0(3(3(0(5(0(x1)))))))) 0(0(3(3(3(4(3(3(1(x1))))))))) -> 5(5(2(4(0(0(1(0(3(x1))))))))) 1(0(2(1(5(1(1(5(4(x1))))))))) -> 1(0(0(0(1(4(3(5(4(x1))))))))) 3(3(1(5(4(0(4(0(4(x1))))))))) -> 4(0(1(3(4(3(4(4(x1)))))))) 1(3(3(2(4(1(2(2(2(1(x1)))))))))) -> 1(4(3(5(3(3(1(2(1(1(x1)))))))))) 4(1(4(5(2(4(0(1(5(4(x1)))))))))) -> 4(0(3(4(3(5(2(2(4(x1))))))))) 5(4(1(4(3(2(2(2(1(2(x1)))))))))) -> 0(5(2(0(1(5(3(2(0(2(x1)))))))))) 1(2(1(2(5(2(4(3(3(4(5(x1))))))))))) -> 1(4(3(4(0(4(2(5(5(5(x1)))))))))) 3(2(0(2(2(3(3(5(4(1(5(x1))))))))))) -> 2(1(2(0(2(3(4(4(5(4(0(x1))))))))))) 4(5(4(0(1(5(5(4(5(2(4(x1))))))))))) -> 3(1(2(1(0(4(5(2(0(2(4(x1))))))))))) 0(1(4(1(0(0(3(4(1(5(3(1(x1)))))))))))) -> 0(4(4(1(2(3(0(0(0(1(3(1(x1)))))))))))) 1(3(4(5(1(0(0(4(5(5(3(1(x1)))))))))))) -> 1(1(2(0(2(1(2(3(0(4(3(1(x1)))))))))))) 5(1(2(3(2(2(4(2(1(5(4(0(x1)))))))))))) -> 5(5(4(0(5(2(2(5(5(2(5(x1))))))))))) 0(3(0(4(4(4(1(1(4(5(4(3(3(x1))))))))))))) -> 0(2(3(2(3(3(4(1(1(4(2(3(x1)))))))))))) 4(1(1(0(1(3(4(5(2(3(5(5(1(x1))))))))))))) -> 4(1(1(0(3(4(5(2(4(3(3(0(1(x1))))))))))))) 5(2(5(4(4(3(4(1(0(1(0(1(2(x1))))))))))))) -> 5(4(2(0(1(3(2(4(5(4(3(4(x1)))))))))))) 3(3(3(1(3(0(5(2(5(4(4(3(2(1(1(x1))))))))))))))) -> 3(4(5(5(1(2(5(2(2(1(4(1(0(1(1(x1))))))))))))))) 3(5(0(2(1(2(2(3(5(3(1(3(1(1(4(x1))))))))))))))) -> 4(3(1(0(2(5(3(3(2(4(1(5(5(4(x1)))))))))))))) 5(3(4(5(1(2(5(0(0(0(5(4(1(4(4(x1))))))))))))))) -> 5(4(5(5(5(1(3(3(4(1(5(5(1(4(x1)))))))))))))) 1(5(2(4(4(3(4(2(3(3(1(1(4(2(5(2(x1)))))))))))))))) -> 1(5(1(3(0(0(0(2(4(4(5(0(4(0(5(2(5(x1))))))))))))))))) 3(1(2(3(5(2(0(0(4(4(3(3(3(1(4(0(4(x1))))))))))))))))) -> 1(2(3(0(1(0(2(1(0(2(3(5(3(4(1(0(4(x1))))))))))))))))) 2(2(0(3(4(0(1(4(2(0(3(0(2(2(4(2(4(4(x1)))))))))))))))))) -> 5(5(3(0(2(1(2(1(4(4(5(5(1(1(0(3(1(4(x1)))))))))))))))))) 0(2(3(0(4(0(1(0(1(4(5(3(5(2(4(1(0(3(3(x1))))))))))))))))))) -> 0(3(0(5(3(5(4(3(1(4(0(3(4(5(3(1(1(1(x1)))))))))))))))))) 0(4(1(2(3(5(3(1(4(0(1(0(5(5(4(0(3(3(0(x1))))))))))))))))))) -> 1(5(5(2(5(0(4(4(4(4(5(3(3(4(2(3(4(x1))))))))))))))))) 3(0(4(3(0(2(3(4(4(1(2(3(0(0(2(0(4(1(1(x1))))))))))))))))))) -> 3(0(3(0(5(0(0(0(3(3(2(1(1(2(3(0(1(1(1(0(x1)))))))))))))))))))) 3(2(3(1(4(4(1(2(5(1(5(0(4(5(1(0(1(0(2(x1))))))))))))))))))) -> 0(5(5(4(5(0(1(1(3(5(1(5(2(0(4(0(2(0(2(x1))))))))))))))))))) 5(0(0(3(0(4(0(3(5(3(1(3(1(4(1(2(0(1(3(x1))))))))))))))))))) -> 2(2(0(3(4(5(1(3(2(0(4(4(0(5(4(0(2(3(x1)))))))))))))))))) 1(0(4(1(0(4(0(1(3(1(1(0(2(5(4(1(0(3(3(2(x1)))))))))))))))))))) -> 1(5(5(0(3(5(0(5(4(3(4(3(5(1(3(5(4(1(x1)))))))))))))))))) 2(0(5(5(5(0(3(5(0(0(4(2(1(5(5(0(2(4(1(1(x1)))))))))))))))))))) -> 2(0(0(5(1(1(4(2(5(5(3(2(5(1(4(3(4(5(2(x1))))))))))))))))))) 3(1(1(3(4(3(1(5(5(4(1(1(3(5(0(1(2(3(0(0(x1)))))))))))))))))))) -> 1(1(1(3(3(4(1(4(5(1(4(0(5(1(2(2(1(4(3(2(x1)))))))))))))))))))) 0(0(1(3(4(3(1(1(3(3(2(0(4(4(3(0(0(5(5(2(0(x1))))))))))))))))))))) -> 2(4(5(5(2(1(5(2(4(2(1(0(2(4(4(3(5(2(4(3(x1)))))))))))))))))))) 0(5(1(4(0(5(1(3(4(3(3(1(1(4(5(1(4(1(4(0(0(x1))))))))))))))))))))) -> 5(4(1(2(5(2(0(0(2(2(2(0(3(0(4(4(0(0(5(3(x1)))))))))))))))))))) 4(2(3(1(3(1(1(5(3(4(2(0(5(5(3(3(2(0(5(4(1(x1))))))))))))))))))))) -> 4(3(0(4(5(3(2(4(3(0(0(5(1(5(5(4(5(3(0(0(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_5(x_1)) -> 5(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(x1)))) -> 3(3(0(x1))) 0(3(1(3(x1)))) -> 2(4(3(x1))) 5(1(0(0(x1)))) -> 5(3(3(x1))) 0(3(2(4(5(x1))))) -> 2(5(1(5(x1)))) 3(0(0(0(4(x1))))) -> 5(5(1(4(x1)))) 5(4(2(4(3(x1))))) -> 0(5(3(1(3(x1))))) 5(3(0(0(2(0(x1)))))) -> 5(3(2(4(3(x1))))) 4(3(5(0(3(0(5(3(x1)))))))) -> 4(1(0(3(3(0(5(0(x1)))))))) 0(0(3(3(3(4(3(3(1(x1))))))))) -> 5(5(2(4(0(0(1(0(3(x1))))))))) 1(0(2(1(5(1(1(5(4(x1))))))))) -> 1(0(0(0(1(4(3(5(4(x1))))))))) 3(3(1(5(4(0(4(0(4(x1))))))))) -> 4(0(1(3(4(3(4(4(x1)))))))) 1(3(3(2(4(1(2(2(2(1(x1)))))))))) -> 1(4(3(5(3(3(1(2(1(1(x1)))))))))) 4(1(4(5(2(4(0(1(5(4(x1)))))))))) -> 4(0(3(4(3(5(2(2(4(x1))))))))) 5(4(1(4(3(2(2(2(1(2(x1)))))))))) -> 0(5(2(0(1(5(3(2(0(2(x1)))))))))) 1(2(1(2(5(2(4(3(3(4(5(x1))))))))))) -> 1(4(3(4(0(4(2(5(5(5(x1)))))))))) 3(2(0(2(2(3(3(5(4(1(5(x1))))))))))) -> 2(1(2(0(2(3(4(4(5(4(0(x1))))))))))) 4(5(4(0(1(5(5(4(5(2(4(x1))))))))))) -> 3(1(2(1(0(4(5(2(0(2(4(x1))))))))))) 0(1(4(1(0(0(3(4(1(5(3(1(x1)))))))))))) -> 0(4(4(1(2(3(0(0(0(1(3(1(x1)))))))))))) 1(3(4(5(1(0(0(4(5(5(3(1(x1)))))))))))) -> 1(1(2(0(2(1(2(3(0(4(3(1(x1)))))))))))) 5(1(2(3(2(2(4(2(1(5(4(0(x1)))))))))))) -> 5(5(4(0(5(2(2(5(5(2(5(x1))))))))))) 0(3(0(4(4(4(1(1(4(5(4(3(3(x1))))))))))))) -> 0(2(3(2(3(3(4(1(1(4(2(3(x1)))))))))))) 4(1(1(0(1(3(4(5(2(3(5(5(1(x1))))))))))))) -> 4(1(1(0(3(4(5(2(4(3(3(0(1(x1))))))))))))) 5(2(5(4(4(3(4(1(0(1(0(1(2(x1))))))))))))) -> 5(4(2(0(1(3(2(4(5(4(3(4(x1)))))))))))) 3(3(3(1(3(0(5(2(5(4(4(3(2(1(1(x1))))))))))))))) -> 3(4(5(5(1(2(5(2(2(1(4(1(0(1(1(x1))))))))))))))) 3(5(0(2(1(2(2(3(5(3(1(3(1(1(4(x1))))))))))))))) -> 4(3(1(0(2(5(3(3(2(4(1(5(5(4(x1)))))))))))))) 5(3(4(5(1(2(5(0(0(0(5(4(1(4(4(x1))))))))))))))) -> 5(4(5(5(5(1(3(3(4(1(5(5(1(4(x1)))))))))))))) 1(5(2(4(4(3(4(2(3(3(1(1(4(2(5(2(x1)))))))))))))))) -> 1(5(1(3(0(0(0(2(4(4(5(0(4(0(5(2(5(x1))))))))))))))))) 3(1(2(3(5(2(0(0(4(4(3(3(3(1(4(0(4(x1))))))))))))))))) -> 1(2(3(0(1(0(2(1(0(2(3(5(3(4(1(0(4(x1))))))))))))))))) 2(2(0(3(4(0(1(4(2(0(3(0(2(2(4(2(4(4(x1)))))))))))))))))) -> 5(5(3(0(2(1(2(1(4(4(5(5(1(1(0(3(1(4(x1)))))))))))))))))) 0(2(3(0(4(0(1(0(1(4(5(3(5(2(4(1(0(3(3(x1))))))))))))))))))) -> 0(3(0(5(3(5(4(3(1(4(0(3(4(5(3(1(1(1(x1)))))))))))))))))) 0(4(1(2(3(5(3(1(4(0(1(0(5(5(4(0(3(3(0(x1))))))))))))))))))) -> 1(5(5(2(5(0(4(4(4(4(5(3(3(4(2(3(4(x1))))))))))))))))) 3(0(4(3(0(2(3(4(4(1(2(3(0(0(2(0(4(1(1(x1))))))))))))))))))) -> 3(0(3(0(5(0(0(0(3(3(2(1(1(2(3(0(1(1(1(0(x1)))))))))))))))))))) 3(2(3(1(4(4(1(2(5(1(5(0(4(5(1(0(1(0(2(x1))))))))))))))))))) -> 0(5(5(4(5(0(1(1(3(5(1(5(2(0(4(0(2(0(2(x1))))))))))))))))))) 5(0(0(3(0(4(0(3(5(3(1(3(1(4(1(2(0(1(3(x1))))))))))))))))))) -> 2(2(0(3(4(5(1(3(2(0(4(4(0(5(4(0(2(3(x1)))))))))))))))))) 1(0(4(1(0(4(0(1(3(1(1(0(2(5(4(1(0(3(3(2(x1)))))))))))))))))))) -> 1(5(5(0(3(5(0(5(4(3(4(3(5(1(3(5(4(1(x1)))))))))))))))))) 2(0(5(5(5(0(3(5(0(0(4(2(1(5(5(0(2(4(1(1(x1)))))))))))))))))))) -> 2(0(0(5(1(1(4(2(5(5(3(2(5(1(4(3(4(5(2(x1))))))))))))))))))) 3(1(1(3(4(3(1(5(5(4(1(1(3(5(0(1(2(3(0(0(x1)))))))))))))))))))) -> 1(1(1(3(3(4(1(4(5(1(4(0(5(1(2(2(1(4(3(2(x1)))))))))))))))))))) 0(0(1(3(4(3(1(1(3(3(2(0(4(4(3(0(0(5(5(2(0(x1))))))))))))))))))))) -> 2(4(5(5(2(1(5(2(4(2(1(0(2(4(4(3(5(2(4(3(x1)))))))))))))))))))) 0(5(1(4(0(5(1(3(4(3(3(1(1(4(5(1(4(1(4(0(0(x1))))))))))))))))))))) -> 5(4(1(2(5(2(0(0(2(2(2(0(3(0(4(4(0(0(5(3(x1)))))))))))))))))))) 4(2(3(1(3(1(1(5(3(4(2(0(5(5(3(3(2(0(5(4(1(x1))))))))))))))))))))) -> 4(3(0(4(5(3(2(4(3(0(0(5(1(5(5(4(5(3(0(0(4(x1))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(x1)))) -> 3(3(0(x1))) 0(3(1(3(x1)))) -> 2(4(3(x1))) 5(1(0(0(x1)))) -> 5(3(3(x1))) 0(3(2(4(5(x1))))) -> 2(5(1(5(x1)))) 3(0(0(0(4(x1))))) -> 5(5(1(4(x1)))) 5(4(2(4(3(x1))))) -> 0(5(3(1(3(x1))))) 5(3(0(0(2(0(x1)))))) -> 5(3(2(4(3(x1))))) 4(3(5(0(3(0(5(3(x1)))))))) -> 4(1(0(3(3(0(5(0(x1)))))))) 0(0(3(3(3(4(3(3(1(x1))))))))) -> 5(5(2(4(0(0(1(0(3(x1))))))))) 1(0(2(1(5(1(1(5(4(x1))))))))) -> 1(0(0(0(1(4(3(5(4(x1))))))))) 3(3(1(5(4(0(4(0(4(x1))))))))) -> 4(0(1(3(4(3(4(4(x1)))))))) 1(3(3(2(4(1(2(2(2(1(x1)))))))))) -> 1(4(3(5(3(3(1(2(1(1(x1)))))))))) 4(1(4(5(2(4(0(1(5(4(x1)))))))))) -> 4(0(3(4(3(5(2(2(4(x1))))))))) 5(4(1(4(3(2(2(2(1(2(x1)))))))))) -> 0(5(2(0(1(5(3(2(0(2(x1)))))))))) 1(2(1(2(5(2(4(3(3(4(5(x1))))))))))) -> 1(4(3(4(0(4(2(5(5(5(x1)))))))))) 3(2(0(2(2(3(3(5(4(1(5(x1))))))))))) -> 2(1(2(0(2(3(4(4(5(4(0(x1))))))))))) 4(5(4(0(1(5(5(4(5(2(4(x1))))))))))) -> 3(1(2(1(0(4(5(2(0(2(4(x1))))))))))) 0(1(4(1(0(0(3(4(1(5(3(1(x1)))))))))))) -> 0(4(4(1(2(3(0(0(0(1(3(1(x1)))))))))))) 1(3(4(5(1(0(0(4(5(5(3(1(x1)))))))))))) -> 1(1(2(0(2(1(2(3(0(4(3(1(x1)))))))))))) 5(1(2(3(2(2(4(2(1(5(4(0(x1)))))))))))) -> 5(5(4(0(5(2(2(5(5(2(5(x1))))))))))) 0(3(0(4(4(4(1(1(4(5(4(3(3(x1))))))))))))) -> 0(2(3(2(3(3(4(1(1(4(2(3(x1)))))))))))) 4(1(1(0(1(3(4(5(2(3(5(5(1(x1))))))))))))) -> 4(1(1(0(3(4(5(2(4(3(3(0(1(x1))))))))))))) 5(2(5(4(4(3(4(1(0(1(0(1(2(x1))))))))))))) -> 5(4(2(0(1(3(2(4(5(4(3(4(x1)))))))))))) 3(3(3(1(3(0(5(2(5(4(4(3(2(1(1(x1))))))))))))))) -> 3(4(5(5(1(2(5(2(2(1(4(1(0(1(1(x1))))))))))))))) 3(5(0(2(1(2(2(3(5(3(1(3(1(1(4(x1))))))))))))))) -> 4(3(1(0(2(5(3(3(2(4(1(5(5(4(x1)))))))))))))) 5(3(4(5(1(2(5(0(0(0(5(4(1(4(4(x1))))))))))))))) -> 5(4(5(5(5(1(3(3(4(1(5(5(1(4(x1)))))))))))))) 1(5(2(4(4(3(4(2(3(3(1(1(4(2(5(2(x1)))))))))))))))) -> 1(5(1(3(0(0(0(2(4(4(5(0(4(0(5(2(5(x1))))))))))))))))) 3(1(2(3(5(2(0(0(4(4(3(3(3(1(4(0(4(x1))))))))))))))))) -> 1(2(3(0(1(0(2(1(0(2(3(5(3(4(1(0(4(x1))))))))))))))))) 2(2(0(3(4(0(1(4(2(0(3(0(2(2(4(2(4(4(x1)))))))))))))))))) -> 5(5(3(0(2(1(2(1(4(4(5(5(1(1(0(3(1(4(x1)))))))))))))))))) 0(2(3(0(4(0(1(0(1(4(5(3(5(2(4(1(0(3(3(x1))))))))))))))))))) -> 0(3(0(5(3(5(4(3(1(4(0(3(4(5(3(1(1(1(x1)))))))))))))))))) 0(4(1(2(3(5(3(1(4(0(1(0(5(5(4(0(3(3(0(x1))))))))))))))))))) -> 1(5(5(2(5(0(4(4(4(4(5(3(3(4(2(3(4(x1))))))))))))))))) 3(0(4(3(0(2(3(4(4(1(2(3(0(0(2(0(4(1(1(x1))))))))))))))))))) -> 3(0(3(0(5(0(0(0(3(3(2(1(1(2(3(0(1(1(1(0(x1)))))))))))))))))))) 3(2(3(1(4(4(1(2(5(1(5(0(4(5(1(0(1(0(2(x1))))))))))))))))))) -> 0(5(5(4(5(0(1(1(3(5(1(5(2(0(4(0(2(0(2(x1))))))))))))))))))) 5(0(0(3(0(4(0(3(5(3(1(3(1(4(1(2(0(1(3(x1))))))))))))))))))) -> 2(2(0(3(4(5(1(3(2(0(4(4(0(5(4(0(2(3(x1)))))))))))))))))) 1(0(4(1(0(4(0(1(3(1(1(0(2(5(4(1(0(3(3(2(x1)))))))))))))))))))) -> 1(5(5(0(3(5(0(5(4(3(4(3(5(1(3(5(4(1(x1)))))))))))))))))) 2(0(5(5(5(0(3(5(0(0(4(2(1(5(5(0(2(4(1(1(x1)))))))))))))))))))) -> 2(0(0(5(1(1(4(2(5(5(3(2(5(1(4(3(4(5(2(x1))))))))))))))))))) 3(1(1(3(4(3(1(5(5(4(1(1(3(5(0(1(2(3(0(0(x1)))))))))))))))))))) -> 1(1(1(3(3(4(1(4(5(1(4(0(5(1(2(2(1(4(3(2(x1)))))))))))))))))))) 0(0(1(3(4(3(1(1(3(3(2(0(4(4(3(0(0(5(5(2(0(x1))))))))))))))))))))) -> 2(4(5(5(2(1(5(2(4(2(1(0(2(4(4(3(5(2(4(3(x1)))))))))))))))))))) 0(5(1(4(0(5(1(3(4(3(3(1(1(4(5(1(4(1(4(0(0(x1))))))))))))))))))))) -> 5(4(1(2(5(2(0(0(2(2(2(0(3(0(4(4(0(0(5(3(x1)))))))))))))))))))) 4(2(3(1(3(1(1(5(3(4(2(0(5(5(3(3(2(0(5(4(1(x1))))))))))))))))))))) -> 4(3(0(4(5(3(2(4(3(0(0(5(1(5(5(4(5(3(0(0(4(x1))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: FULL ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(x1)))) -> 3(3(0(x1))) 0(3(1(3(x1)))) -> 2(4(3(x1))) 5(1(0(0(x1)))) -> 5(3(3(x1))) 0(3(2(4(5(x1))))) -> 2(5(1(5(x1)))) 3(0(0(0(4(x1))))) -> 5(5(1(4(x1)))) 5(4(2(4(3(x1))))) -> 0(5(3(1(3(x1))))) 5(3(0(0(2(0(x1)))))) -> 5(3(2(4(3(x1))))) 4(3(5(0(3(0(5(3(x1)))))))) -> 4(1(0(3(3(0(5(0(x1)))))))) 0(0(3(3(3(4(3(3(1(x1))))))))) -> 5(5(2(4(0(0(1(0(3(x1))))))))) 1(0(2(1(5(1(1(5(4(x1))))))))) -> 1(0(0(0(1(4(3(5(4(x1))))))))) 3(3(1(5(4(0(4(0(4(x1))))))))) -> 4(0(1(3(4(3(4(4(x1)))))))) 1(3(3(2(4(1(2(2(2(1(x1)))))))))) -> 1(4(3(5(3(3(1(2(1(1(x1)))))))))) 4(1(4(5(2(4(0(1(5(4(x1)))))))))) -> 4(0(3(4(3(5(2(2(4(x1))))))))) 5(4(1(4(3(2(2(2(1(2(x1)))))))))) -> 0(5(2(0(1(5(3(2(0(2(x1)))))))))) 1(2(1(2(5(2(4(3(3(4(5(x1))))))))))) -> 1(4(3(4(0(4(2(5(5(5(x1)))))))))) 3(2(0(2(2(3(3(5(4(1(5(x1))))))))))) -> 2(1(2(0(2(3(4(4(5(4(0(x1))))))))))) 4(5(4(0(1(5(5(4(5(2(4(x1))))))))))) -> 3(1(2(1(0(4(5(2(0(2(4(x1))))))))))) 0(1(4(1(0(0(3(4(1(5(3(1(x1)))))))))))) -> 0(4(4(1(2(3(0(0(0(1(3(1(x1)))))))))))) 1(3(4(5(1(0(0(4(5(5(3(1(x1)))))))))))) -> 1(1(2(0(2(1(2(3(0(4(3(1(x1)))))))))))) 5(1(2(3(2(2(4(2(1(5(4(0(x1)))))))))))) -> 5(5(4(0(5(2(2(5(5(2(5(x1))))))))))) 0(3(0(4(4(4(1(1(4(5(4(3(3(x1))))))))))))) -> 0(2(3(2(3(3(4(1(1(4(2(3(x1)))))))))))) 4(1(1(0(1(3(4(5(2(3(5(5(1(x1))))))))))))) -> 4(1(1(0(3(4(5(2(4(3(3(0(1(x1))))))))))))) 5(2(5(4(4(3(4(1(0(1(0(1(2(x1))))))))))))) -> 5(4(2(0(1(3(2(4(5(4(3(4(x1)))))))))))) 3(3(3(1(3(0(5(2(5(4(4(3(2(1(1(x1))))))))))))))) -> 3(4(5(5(1(2(5(2(2(1(4(1(0(1(1(x1))))))))))))))) 3(5(0(2(1(2(2(3(5(3(1(3(1(1(4(x1))))))))))))))) -> 4(3(1(0(2(5(3(3(2(4(1(5(5(4(x1)))))))))))))) 5(3(4(5(1(2(5(0(0(0(5(4(1(4(4(x1))))))))))))))) -> 5(4(5(5(5(1(3(3(4(1(5(5(1(4(x1)))))))))))))) 1(5(2(4(4(3(4(2(3(3(1(1(4(2(5(2(x1)))))))))))))))) -> 1(5(1(3(0(0(0(2(4(4(5(0(4(0(5(2(5(x1))))))))))))))))) 3(1(2(3(5(2(0(0(4(4(3(3(3(1(4(0(4(x1))))))))))))))))) -> 1(2(3(0(1(0(2(1(0(2(3(5(3(4(1(0(4(x1))))))))))))))))) 2(2(0(3(4(0(1(4(2(0(3(0(2(2(4(2(4(4(x1)))))))))))))))))) -> 5(5(3(0(2(1(2(1(4(4(5(5(1(1(0(3(1(4(x1)))))))))))))))))) 0(2(3(0(4(0(1(0(1(4(5(3(5(2(4(1(0(3(3(x1))))))))))))))))))) -> 0(3(0(5(3(5(4(3(1(4(0(3(4(5(3(1(1(1(x1)))))))))))))))))) 0(4(1(2(3(5(3(1(4(0(1(0(5(5(4(0(3(3(0(x1))))))))))))))))))) -> 1(5(5(2(5(0(4(4(4(4(5(3(3(4(2(3(4(x1))))))))))))))))) 3(0(4(3(0(2(3(4(4(1(2(3(0(0(2(0(4(1(1(x1))))))))))))))))))) -> 3(0(3(0(5(0(0(0(3(3(2(1(1(2(3(0(1(1(1(0(x1)))))))))))))))))))) 3(2(3(1(4(4(1(2(5(1(5(0(4(5(1(0(1(0(2(x1))))))))))))))))))) -> 0(5(5(4(5(0(1(1(3(5(1(5(2(0(4(0(2(0(2(x1))))))))))))))))))) 5(0(0(3(0(4(0(3(5(3(1(3(1(4(1(2(0(1(3(x1))))))))))))))))))) -> 2(2(0(3(4(5(1(3(2(0(4(4(0(5(4(0(2(3(x1)))))))))))))))))) 1(0(4(1(0(4(0(1(3(1(1(0(2(5(4(1(0(3(3(2(x1)))))))))))))))))))) -> 1(5(5(0(3(5(0(5(4(3(4(3(5(1(3(5(4(1(x1)))))))))))))))))) 2(0(5(5(5(0(3(5(0(0(4(2(1(5(5(0(2(4(1(1(x1)))))))))))))))))))) -> 2(0(0(5(1(1(4(2(5(5(3(2(5(1(4(3(4(5(2(x1))))))))))))))))))) 3(1(1(3(4(3(1(5(5(4(1(1(3(5(0(1(2(3(0(0(x1)))))))))))))))))))) -> 1(1(1(3(3(4(1(4(5(1(4(0(5(1(2(2(1(4(3(2(x1)))))))))))))))))))) 0(0(1(3(4(3(1(1(3(3(2(0(4(4(3(0(0(5(5(2(0(x1))))))))))))))))))))) -> 2(4(5(5(2(1(5(2(4(2(1(0(2(4(4(3(5(2(4(3(x1)))))))))))))))))))) 0(5(1(4(0(5(1(3(4(3(3(1(1(4(5(1(4(1(4(0(0(x1))))))))))))))))))))) -> 5(4(1(2(5(2(0(0(2(2(2(0(3(0(4(4(0(0(5(3(x1)))))))))))))))))))) 4(2(3(1(3(1(1(5(3(4(2(0(5(5(3(3(2(0(5(4(1(x1))))))))))))))))))))) -> 4(3(0(4(5(3(2(4(3(0(0(5(1(5(5(4(5(3(0(0(4(x1))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_5(x_1)) -> 5(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(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] {(151,152,[0_1|0, 5_1|0, 3_1|0, 4_1|0, 1_1|0, 2_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, 5_1|1, 3_1|1, 4_1|1, 1_1|1, 2_1|1]), (151,154,[3_1|2]), (151,156,[2_1|2]), (151,175,[5_1|2]), (151,183,[2_1|2]), (151,185,[2_1|2]), (151,188,[0_1|2]), (151,199,[0_1|2]), (151,210,[0_1|2]), (151,227,[1_1|2]), (151,243,[5_1|2]), (151,262,[5_1|2]), (151,264,[5_1|2]), (151,274,[0_1|2]), (151,278,[0_1|2]), (151,287,[5_1|2]), (151,291,[5_1|2]), (151,304,[5_1|2]), (151,315,[2_1|2]), (151,332,[5_1|2]), (151,335,[3_1|2]), (151,354,[4_1|2]), (151,361,[3_1|2]), (151,375,[2_1|2]), (151,385,[0_1|2]), (151,403,[4_1|2]), (151,416,[1_1|2]), (151,432,[1_1|2]), (151,451,[4_1|2]), (151,458,[4_1|2]), (151,466,[4_1|2]), (151,478,[3_1|2]), (151,488,[4_1|2]), (151,508,[1_1|2]), (151,516,[1_1|2]), (151,533,[1_1|2]), (151,542,[1_1|2]), (151,553,[1_1|2]), (151,562,[1_1|2]), (151,578,[5_1|2]), (151,595,[2_1|2]), (152,152,[cons_0_1|0, cons_5_1|0, cons_3_1|0, cons_4_1|0, cons_1_1|0, cons_2_1|0]), (153,152,[encArg_1|1]), (153,153,[0_1|1, 5_1|1, 3_1|1, 4_1|1, 1_1|1, 2_1|1]), (153,154,[3_1|2]), (153,156,[2_1|2]), (153,175,[5_1|2]), (153,183,[2_1|2]), (153,185,[2_1|2]), (153,188,[0_1|2]), (153,199,[0_1|2]), (153,210,[0_1|2]), (153,227,[1_1|2]), (153,243,[5_1|2]), (153,262,[5_1|2]), (153,264,[5_1|2]), (153,274,[0_1|2]), (153,278,[0_1|2]), (153,287,[5_1|2]), (153,291,[5_1|2]), (153,304,[5_1|2]), (153,315,[2_1|2]), (153,332,[5_1|2]), (153,335,[3_1|2]), (153,354,[4_1|2]), (153,361,[3_1|2]), (153,375,[2_1|2]), (153,385,[0_1|2]), (153,403,[4_1|2]), 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(415,153,[4_1|2]), (415,354,[4_1|2]), (415,403,[4_1|2]), (415,451,[4_1|2]), (415,458,[4_1|2]), (415,466,[4_1|2]), (415,488,[4_1|2]), (415,534,[4_1|2]), (415,554,[4_1|2]), (415,478,[3_1|2]), (416,417,[2_1|2]), (417,418,[3_1|2]), (418,419,[0_1|2]), (419,420,[1_1|2]), (420,421,[0_1|2]), (421,422,[2_1|2]), (422,423,[1_1|2]), (423,424,[0_1|2]), (424,425,[2_1|2]), (425,426,[3_1|2]), (426,427,[5_1|2]), (427,428,[3_1|2]), (428,429,[4_1|2]), (429,430,[1_1|2]), (429,516,[1_1|2]), (430,431,[0_1|2]), (430,227,[1_1|2]), (431,153,[4_1|2]), (431,354,[4_1|2]), (431,403,[4_1|2]), (431,451,[4_1|2]), (431,458,[4_1|2]), (431,466,[4_1|2]), (431,488,[4_1|2]), (431,200,[4_1|2]), (431,478,[3_1|2]), (432,433,[1_1|2]), (433,434,[1_1|2]), (434,435,[3_1|2]), (435,436,[3_1|2]), (436,437,[4_1|2]), (437,438,[1_1|2]), (438,439,[4_1|2]), (439,440,[5_1|2]), (440,441,[1_1|2]), (441,442,[4_1|2]), (442,443,[0_1|2]), (443,444,[5_1|2]), (444,445,[1_1|2]), (445,446,[2_1|2]), (446,447,[2_1|2]), (447,448,[1_1|2]), (448,449,[4_1|2]), (449,450,[3_1|2]), (449,375,[2_1|2]), (449,385,[0_1|2]), (450,153,[2_1|2]), (450,188,[2_1|2]), (450,199,[2_1|2]), (450,210,[2_1|2]), (450,274,[2_1|2]), (450,278,[2_1|2]), (450,385,[2_1|2]), (450,578,[5_1|2]), (450,595,[2_1|2]), (451,452,[1_1|2]), (452,453,[0_1|2]), (453,454,[3_1|2]), (454,455,[3_1|2]), (455,456,[0_1|2]), (456,457,[5_1|2]), (456,315,[2_1|2]), (457,153,[0_1|2]), (457,154,[0_1|2, 3_1|2]), (457,335,[0_1|2]), (457,361,[0_1|2]), (457,478,[0_1|2]), (457,263,[0_1|2]), (457,288,[0_1|2]), (457,276,[0_1|2]), (457,214,[0_1|2]), (457,156,[2_1|2]), (457,175,[5_1|2]), (457,183,[2_1|2]), (457,185,[2_1|2]), (457,188,[0_1|2]), (457,199,[0_1|2]), (457,210,[0_1|2]), (457,227,[1_1|2]), (457,243,[5_1|2]), (457,613,[2_1|3]), (458,459,[0_1|2]), (459,460,[3_1|2]), (460,461,[4_1|2]), (461,462,[3_1|2]), (462,463,[5_1|2]), (463,464,[2_1|2]), (464,465,[2_1|2]), (465,153,[4_1|2]), (465,354,[4_1|2]), (465,403,[4_1|2]), (465,451,[4_1|2]), (465,458,[4_1|2]), (465,466,[4_1|2]), (465,488,[4_1|2]), (465,244,[4_1|2]), (465,292,[4_1|2]), (465,305,[4_1|2]), (465,478,[3_1|2]), (466,467,[1_1|2]), (467,468,[1_1|2]), (468,469,[0_1|2]), (469,470,[3_1|2]), (470,471,[4_1|2]), (471,472,[5_1|2]), (472,473,[2_1|2]), (473,474,[4_1|2]), (474,475,[3_1|2]), (475,476,[3_1|2]), (476,477,[0_1|2]), (476,199,[0_1|2]), (477,153,[1_1|2]), (477,227,[1_1|2]), (477,416,[1_1|2]), (477,432,[1_1|2]), (477,508,[1_1|2]), (477,516,[1_1|2]), (477,533,[1_1|2]), (477,542,[1_1|2]), (477,553,[1_1|2]), (477,562,[1_1|2]), (477,334,[1_1|2]), (478,479,[1_1|2]), (479,480,[2_1|2]), (480,481,[1_1|2]), (481,482,[0_1|2]), (482,483,[4_1|2]), (483,484,[5_1|2]), (484,485,[2_1|2]), (485,486,[0_1|2]), (486,487,[2_1|2]), (487,153,[4_1|2]), (487,354,[4_1|2]), (487,403,[4_1|2]), (487,451,[4_1|2]), (487,458,[4_1|2]), (487,466,[4_1|2]), (487,488,[4_1|2]), (487,157,[4_1|2]), (487,184,[4_1|2]), (487,478,[3_1|2]), (488,489,[3_1|2]), (489,490,[0_1|2]), (490,491,[4_1|2]), (491,492,[5_1|2]), (492,493,[3_1|2]), (493,494,[2_1|2]), (494,495,[4_1|2]), (495,496,[3_1|2]), (496,497,[0_1|2]), (497,498,[0_1|2]), (498,499,[5_1|2]), (499,500,[1_1|2]), (500,501,[5_1|2]), (501,502,[5_1|2]), (502,503,[4_1|2]), (503,504,[5_1|2]), (504,505,[3_1|2]), (505,506,[0_1|2]), (506,507,[0_1|2]), (506,227,[1_1|2]), (507,153,[4_1|2]), (507,227,[4_1|2]), (507,416,[4_1|2]), (507,432,[4_1|2]), (507,508,[4_1|2]), (507,516,[4_1|2]), (507,533,[4_1|2]), (507,542,[4_1|2]), (507,553,[4_1|2]), (507,562,[4_1|2]), (507,452,[4_1|2]), (507,467,[4_1|2]), (507,245,[4_1|2]), (507,451,[4_1|2]), (507,458,[4_1|2]), (507,466,[4_1|2]), (507,478,[3_1|2]), (507,488,[4_1|2]), (508,509,[0_1|2]), (509,510,[0_1|2]), (510,511,[0_1|2]), (511,512,[1_1|2]), (512,513,[4_1|2]), (513,514,[3_1|2]), (514,515,[5_1|2]), (514,274,[0_1|2]), (514,278,[0_1|2]), (514,618,[0_1|3]), (515,153,[4_1|2]), (515,354,[4_1|2]), (515,403,[4_1|2]), (515,451,[4_1|2]), (515,458,[4_1|2]), (515,466,[4_1|2]), (515,488,[4_1|2]), (515,244,[4_1|2]), (515,292,[4_1|2]), (515,305,[4_1|2]), (515,478,[3_1|2]), (516,517,[5_1|2]), (517,518,[5_1|2]), (518,519,[0_1|2]), (519,520,[3_1|2]), (520,521,[5_1|2]), (521,522,[0_1|2]), (522,523,[5_1|2]), (523,524,[4_1|2]), (524,525,[3_1|2]), (525,526,[4_1|2]), (526,527,[3_1|2]), (527,528,[5_1|2]), (528,529,[1_1|2]), (529,530,[3_1|2]), (530,531,[5_1|2]), (530,278,[0_1|2]), (531,532,[4_1|2]), (531,458,[4_1|2]), (531,466,[4_1|2]), (532,153,[1_1|2]), (532,156,[1_1|2]), (532,183,[1_1|2]), (532,185,[1_1|2]), (532,315,[1_1|2]), (532,375,[1_1|2]), (532,595,[1_1|2]), (532,508,[1_1|2]), (532,516,[1_1|2]), (532,533,[1_1|2]), (532,542,[1_1|2]), (532,553,[1_1|2]), (532,562,[1_1|2]), (533,534,[4_1|2]), (534,535,[3_1|2]), (535,536,[5_1|2]), (536,537,[3_1|2]), (537,538,[3_1|2]), (538,539,[1_1|2]), (539,540,[2_1|2]), (540,541,[1_1|2]), (541,153,[1_1|2]), (541,227,[1_1|2]), (541,416,[1_1|2]), (541,432,[1_1|2]), (541,508,[1_1|2]), (541,516,[1_1|2]), (541,533,[1_1|2]), (541,542,[1_1|2]), (541,553,[1_1|2]), (541,562,[1_1|2]), (541,376,[1_1|2]), (542,543,[1_1|2]), (543,544,[2_1|2]), (544,545,[0_1|2]), (545,546,[2_1|2]), (546,547,[1_1|2]), (547,548,[2_1|2]), (548,549,[3_1|2]), (549,550,[0_1|2]), (550,551,[4_1|2]), (551,552,[3_1|2]), (551,416,[1_1|2]), (551,432,[1_1|2]), (552,153,[1_1|2]), (552,227,[1_1|2]), (552,416,[1_1|2]), (552,432,[1_1|2]), (552,508,[1_1|2]), (552,516,[1_1|2]), (552,533,[1_1|2]), (552,542,[1_1|2]), (552,553,[1_1|2]), (552,562,[1_1|2]), (552,479,[1_1|2]), (553,554,[4_1|2]), (554,555,[3_1|2]), (555,556,[4_1|2]), (556,557,[0_1|2]), (557,558,[4_1|2]), (558,559,[2_1|2]), (559,560,[5_1|2]), (560,561,[5_1|2]), (561,153,[5_1|2]), (561,175,[5_1|2]), (561,243,[5_1|2]), (561,262,[5_1|2]), (561,264,[5_1|2]), (561,287,[5_1|2]), (561,291,[5_1|2]), (561,304,[5_1|2]), (561,332,[5_1|2]), (561,578,[5_1|2]), (561,363,[5_1|2]), (561,274,[0_1|2]), (561,278,[0_1|2]), (561,315,[2_1|2]), (561,616,[5_1|3]), (562,563,[5_1|2]), (563,564,[1_1|2]), (564,565,[3_1|2]), (565,566,[0_1|2]), (566,567,[0_1|2]), (567,568,[0_1|2]), (568,569,[2_1|2]), (569,570,[4_1|2]), (570,571,[4_1|2]), (571,572,[5_1|2]), (572,573,[0_1|2]), (573,574,[4_1|2]), (574,575,[0_1|2]), (575,576,[5_1|2]), (575,304,[5_1|2]), (576,577,[2_1|2]), (577,153,[5_1|2]), (577,156,[5_1|2]), (577,183,[5_1|2]), (577,185,[5_1|2]), (577,315,[5_1|2, 2_1|2]), (577,375,[5_1|2]), (577,595,[5_1|2]), (577,262,[5_1|2]), (577,264,[5_1|2]), (577,274,[0_1|2]), (577,278,[0_1|2]), (577,287,[5_1|2]), (577,291,[5_1|2]), (577,304,[5_1|2]), (577,616,[5_1|3]), (578,579,[5_1|2]), (579,580,[3_1|2]), (580,581,[0_1|2]), (581,582,[2_1|2]), (582,583,[1_1|2]), (583,584,[2_1|2]), (584,585,[1_1|2]), (585,586,[4_1|2]), (586,587,[4_1|2]), (587,588,[5_1|2]), (588,589,[5_1|2]), (589,590,[1_1|2]), (590,591,[1_1|2]), (591,592,[0_1|2]), (591,624,[2_1|3]), (592,593,[3_1|2]), (593,594,[1_1|2]), (594,153,[4_1|2]), (594,354,[4_1|2]), (594,403,[4_1|2]), (594,451,[4_1|2]), (594,458,[4_1|2]), (594,466,[4_1|2]), (594,488,[4_1|2]), (594,478,[3_1|2]), (595,596,[0_1|2]), (596,597,[0_1|2]), (597,598,[5_1|2]), (598,599,[1_1|2]), (599,600,[1_1|2]), (600,601,[4_1|2]), (601,602,[2_1|2]), (602,603,[5_1|2]), (603,604,[5_1|2]), (604,605,[3_1|2]), (605,606,[2_1|2]), (606,607,[5_1|2]), (607,608,[1_1|2]), (608,609,[4_1|2]), (609,610,[3_1|2]), (610,611,[4_1|2]), (611,612,[5_1|2]), (611,304,[5_1|2]), (612,153,[2_1|2]), (612,227,[2_1|2]), (612,416,[2_1|2]), (612,432,[2_1|2]), (612,508,[2_1|2]), (612,516,[2_1|2]), (612,533,[2_1|2]), (612,542,[2_1|2]), (612,553,[2_1|2]), (612,562,[2_1|2]), (612,433,[2_1|2]), (612,543,[2_1|2]), (612,468,[2_1|2]), (612,578,[5_1|2]), (612,595,[2_1|2]), (613,614,[5_1|3]), (614,615,[1_1|3]), (615,158,[5_1|3]), (615,332,[5_1|3]), (616,617,[3_1|3]), (617,510,[3_1|3]), (618,619,[5_1|3]), (619,620,[3_1|3]), (620,621,[1_1|3]), (620,533,[1_1|2]), (620,542,[1_1|2]), (621,153,[3_1|3]), (621,154,[3_1|3]), (621,335,[3_1|3, 3_1|2]), (621,361,[3_1|3, 3_1|2]), (621,478,[3_1|3]), (621,332,[5_1|2]), (621,354,[4_1|2]), (621,375,[2_1|2]), (621,385,[0_1|2]), (621,403,[4_1|2]), (621,416,[1_1|2]), (621,432,[1_1|2]), (622,623,[3_1|3]), (622,335,[3_1|2]), (623,183,[0_1|3]), (623,185,[0_1|3]), (623,613,[0_1|3]), (624,625,[4_1|3]), (625,478,[3_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)