WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 61 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 675 ms] (8) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(0(2(1(x1))))))) -> 0(0(2(1(0(2(1(x1))))))) 2(3(0(4(3(3(2(x1))))))) -> 2(0(3(3(4(3(2(x1))))))) 1(1(4(1(2(3(3(5(x1)))))))) -> 1(1(4(1(3(2(3(5(x1)))))))) 1(2(2(5(5(1(3(4(x1)))))))) -> 1(3(2(2(5(1(5(4(x1)))))))) 2(3(1(2(3(1(0(1(x1)))))))) -> 2(3(2(1(3(1(0(1(x1)))))))) 5(4(1(2(1(0(5(1(x1)))))))) -> 5(4(1(1(2(0(5(1(x1)))))))) 1(1(2(0(2(1(3(1(0(x1))))))))) -> 1(1(2(0(2(3(1(1(0(x1))))))))) 2(1(4(3(2(3(1(5(1(x1))))))))) -> 2(1(4(2(3(3(1(5(1(x1))))))))) 5(1(2(1(4(1(2(4(0(x1))))))))) -> 5(1(2(1(4(4(2(1(0(x1))))))))) 0(4(3(5(2(5(0(4(3(0(x1)))))))))) -> 0(5(1(1(5(1(0(2(1(1(x1)))))))))) 5(3(5(4(4(5(4(3(1(0(x1)))))))))) -> 3(3(1(1(0(0(2(2(1(5(x1)))))))))) 0(0(2(3(2(0(2(2(2(4(5(x1))))))))))) -> 0(4(4(2(5(5(4(5(2(1(x1)))))))))) 0(2(5(3(2(5(2(5(4(4(4(x1))))))))))) -> 1(3(5(0(3(1(5(4(2(5(x1)))))))))) 0(4(0(4(3(0(5(4(5(3(4(x1))))))))))) -> 5(1(5(5(4(1(1(4(0(5(x1)))))))))) 0(5(3(0(0(1(2(1(5(3(1(x1))))))))))) -> 5(5(4(5(0(2(1(0(5(1(x1)))))))))) 1(0(3(3(0(3(2(2(3(4(1(x1))))))))))) -> 1(4(5(2(0(1(0(4(0(1(x1)))))))))) 1(4(3(5(3(0(1(4(3(2(4(x1))))))))))) -> 3(3(2(5(5(2(0(0(4(2(x1)))))))))) 1(5(0(5(3(0(5(2(5(5(3(x1))))))))))) -> 4(2(5(1(2(1(2(0(1(3(x1)))))))))) 2(0(1(0(0(4(0(3(0(1(0(x1))))))))))) -> 2(0(5(0(5(2(0(2(0(0(x1)))))))))) 2(3(4(5(4(5(4(0(5(0(0(x1))))))))))) -> 2(0(5(3(1(4(0(3(2(4(x1)))))))))) 2(4(1(0(3(4(3(1(5(1(2(x1))))))))))) -> 2(4(5(1(4(3(4(3(4(1(x1)))))))))) 2(4(1(2(1(3(0(1(4(1(4(x1))))))))))) -> 5(5(2(2(2(1(4(1(5(4(x1)))))))))) 2(4(3(3(3(4(4(0(3(0(5(x1))))))))))) -> 1(0(5(3(5(2(4(4(0(0(x1)))))))))) 2(5(1(3(5(5(2(4(2(3(4(x1))))))))))) -> 1(1(1(3(1(5(4(2(4(4(x1)))))))))) 2(5(2(2(3(2(1(2(2(5(5(x1))))))))))) -> 1(4(2(5(0(0(3(3(0(3(x1)))))))))) 2(5(2(3(4(0(0(5(2(4(5(x1))))))))))) -> 3(0(3(1(5(3(4(5(1(5(x1)))))))))) 3(2(1(5(3(3(4(4(4(1(0(x1))))))))))) -> 3(4(5(0(5(0(0(5(1(3(x1)))))))))) 3(3(2(5(0(1(1(4(4(2(5(x1))))))))))) -> 2(3(4(0(2(2(0(0(0(1(x1)))))))))) 3(4(3(0(3(1(1(4(3(2(4(x1))))))))))) -> 0(2(5(0(2(0(3(2(0(3(x1)))))))))) 3(4(5(2(3(3(4(0(2(0(0(x1))))))))))) -> 3(4(1(1(2(0(0(5(1(1(x1)))))))))) 3(5(5(4(5(2(2(4(4(1(5(x1))))))))))) -> 0(1(5(0(5(3(2(0(4(0(x1)))))))))) 4(0(1(3(5(0(2(0(4(3(2(x1))))))))))) -> 0(2(2(3(0(0(4(0(1(0(x1)))))))))) 4(0(5(1(5(5(5(2(4(5(4(x1))))))))))) -> 2(3(1(4(3(0(5(2(2(3(x1)))))))))) 4(2(0(2(3(1(0(0(3(0(0(x1))))))))))) -> 3(3(3(0(3(2(5(5(5(4(x1)))))))))) 4(2(3(0(1(3(4(2(2(3(2(x1))))))))))) -> 2(2(4(4(4(3(0(0(5(5(x1)))))))))) 4(3(1(5(1(5(3(1(4(0(1(x1))))))))))) -> 4(3(1(5(1(5(3(4(1(0(1(x1))))))))))) 4(5(3(4(4(2(0(0(0(4(0(x1))))))))))) -> 4(5(5(0(0(3(1(5(3(1(x1)))))))))) 5(0(2(1(0(1(0(1(5(0(4(x1))))))))))) -> 5(0(2(1(0(0(1(1(5(0(4(x1))))))))))) 1(2(0(5(1(0(4(2(1(1(4(2(x1)))))))))))) -> 1(2(0(5(0(1(4(2(1(1(4(2(x1)))))))))))) 1(3(1(5(3(2(1(5(4(1(0(2(x1)))))))))))) -> 3(2(2(2(0(1(3(0(5(0(x1)))))))))) 3(1(1(2(2(5(3(2(4(0(1(0(x1)))))))))))) -> 3(4(0(5(1(2(5(1(5(2(x1)))))))))) 4(1(4(0(1(1(0(3(5(5(1(5(x1)))))))))))) -> 4(2(0(2(3(0(5(4(4(2(x1)))))))))) 5(0(2(1(1(0(4(5(3(0(1(0(x1)))))))))))) -> 5(0(2(1(1(0(5(4(0(3(1(0(x1)))))))))))) 3(3(3(1(1(1(5(5(1(2(3(3(4(x1))))))))))))) -> 3(3(3(1(1(1(5(5(1(3(2(3(4(x1))))))))))))) 5(4(3(0(5(0(3(0(1(4(0(5(3(x1))))))))))))) -> 5(4(3(0(5(3(0(0(1(4(0(5(3(x1))))))))))))) 1(4(5(2(4(3(1(1(2(5(1(4(0(4(x1)))))))))))))) -> 1(4(2(5(4(3(1(1(2(5(1(4(0(4(x1)))))))))))))) 3(4(0(0(3(4(4(1(0(3(4(4(2(4(x1)))))))))))))) -> 3(4(0(0(3(4(1(4(0(3(4(4(2(4(x1)))))))))))))) 3(0(4(5(2(4(3(5(2(2(2(3(5(2(4(x1))))))))))))))) -> 2(4(0(3(5(4(3(2(5(2(5(2(3(2(4(x1))))))))))))))) 3(5(1(5(0(2(3(2(2(5(3(0(4(1(2(1(x1)))))))))))))))) -> 3(5(1(5(0(2(3(2(3(2(5(0(4(1(2(1(x1)))))))))))))))) 1(1(0(2(0(2(4(4(3(5(0(1(3(3(3(3(5(x1))))))))))))))))) -> 1(1(0(2(0(2(4(3(4(5(0(1(3(3(3(3(5(x1))))))))))))))))) 2(0(3(4(3(0(5(1(3(0(0(5(4(4(3(4(1(x1))))))))))))))))) -> 2(0(3(4(0(3(5(1(3(0(0(5(4(4(3(4(1(x1))))))))))))))))) 5(1(2(2(0(0(5(5(3(2(2(5(3(0(4(5(1(x1))))))))))))))))) -> 5(1(2(2(0(5(0(5(3(2(5(2(3(0(4(5(1(x1))))))))))))))))) 4(0(0(2(0(3(4(0(4(1(4(3(4(5(2(1(1(4(x1)))))))))))))))))) -> 4(0(0(2(0(3(4(0(1(4(4(3(4(5(2(1(1(4(x1)))))))))))))))))) 0(4(5(3(4(0(0(1(3(3(0(2(1(5(3(2(3(5(1(x1))))))))))))))))))) -> 0(4(5(3(4(0(0(1(3(3(0(2(5(1(3(2(3(5(1(x1))))))))))))))))))) 5(0(5(4(5(1(0(4(2(4(4(3(0(0(4(1(2(3(1(x1))))))))))))))))))) -> 5(0(5(4(5(1(0(4(2(4(3(4(0(0(4(1(2(3(1(x1))))))))))))))))))) 4(2(5(5(1(4(5(1(1(5(5(4(1(1(1(1(0(0(1(3(1(x1))))))))))))))))))))) -> 5(5(4(5(2(1(5(4(1(5(1(1(1(1(1(4(0(0(3(1(1(x1))))))))))))))))))))) 0(4(5(0(1(1(1(0(5(5(2(1(2(1(3(1(3(4(2(5(0(1(x1)))))))))))))))))))))) -> 5(0(4(0(1(1(1(5(0(5(2(1(2(1(1(3(3(4(2(5(0(1(x1)))))))))))))))))))))) 2(0(1(1(4(4(4(4(0(4(0(1(5(5(0(2(0(0(0(5(5(4(x1)))))))))))))))))))))) -> 2(0(1(1(4(4(4(4(0(4(0(1(5(0(5(2(0(0(0(5(5(4(x1)))))))))))))))))))))) 3(5(4(1(1(0(5(3(2(4(4(2(4(0(4(4(1(2(0(4(4(4(x1)))))))))))))))))))))) -> 3(5(4(1(1(0(5(3(2(4(4(2(0(4(4(4(1(2(0(4(4(4(x1)))))))))))))))))))))) 1(0(0(4(5(4(4(4(4(5(0(3(5(4(0(4(2(4(4(3(3(4(4(x1))))))))))))))))))))))) -> 1(0(0(4(5(4(4(4(4(5(0(3(4(5(0(4(2(4(4(3(3(4(4(x1))))))))))))))))))))))) 1(1(3(4(4(0(5(0(4(5(5(4(0(4(0(0(1(1(5(3(3(4(1(x1))))))))))))))))))))))) -> 1(1(3(4(4(0(5(0(4(5(4(5(0(4(0(0(1(1(5(3(3(4(1(x1))))))))))))))))))))))) 2(5(4(2(2(3(2(5(5(2(0(4(2(4(2(0(1(5(1(2(4(2(3(x1))))))))))))))))))))))) -> 2(5(4(2(2(3(2(5(5(2(0(4(2(4(2(0(1(5(1(4(2(2(3(x1))))))))))))))))))))))) 1(2(1(2(1(2(1(1(3(1(3(1(5(1(4(3(3(3(0(0(5(4(3(0(x1)))))))))))))))))))))))) -> 1(2(1(2(2(1(3(4(1(1(5(1(0(3(1(3(3(3(1(4(0(0(3(5(x1)))))))))))))))))))))))) 0(2(3(3(0(2(3(3(4(5(3(5(5(2(5(1(0(2(2(3(1(5(1(5(1(x1))))))))))))))))))))))))) -> 0(2(3(3(0(2(3(3(4(5(3(5(5(2(5(1(0(2(2(3(5(1(1(5(1(x1))))))))))))))))))))))))) 0(4(2(3(4(4(3(3(4(5(5(3(4(1(5(1(4(2(1(2(0(5(5(0(2(x1))))))))))))))))))))))))) -> 0(4(2(3(4(4(3(3(4(5(5(3(4(1(5(1(4(2(1(0(2(5(5(0(2(x1))))))))))))))))))))))))) 3(1(3(0(0(4(0(2(1(2(5(0(2(4(5(3(1(0(1(0(1(5(4(3(0(x1))))))))))))))))))))))))) -> 3(1(3(0(0(4(0(2(1(2(5(0(2(4(5(3(1(0(0(1(1(5(4(3(0(x1))))))))))))))))))))))))) 3(2(3(5(2(2(2(5(5(1(3(4(3(5(2(5(2(4(4(5(1(2(4(3(5(x1))))))))))))))))))))))))) -> 3(2(3(5(2(2(2(5(5(1(3(3(4(5(2(5(2(4(4(5(1(2(4(3(5(x1))))))))))))))))))))))))) 2(0(0(1(2(1(2(4(2(3(5(4(5(3(3(4(0(4(2(4(2(2(3(5(3(4(x1)))))))))))))))))))))))))) -> 2(0(0(1(2(1(4(2(2(3(5(4(5(3(3(4(0(4(2(4(2(2(3(5(3(4(x1)))))))))))))))))))))))))) 2(5(2(2(1(1(3(4(3(4(5(4(2(1(4(1(3(5(0(2(2(4(5(1(5(5(x1)))))))))))))))))))))))))) -> 2(5(2(2(1(1(3(4(3(4(5(4(2(1(4(1(3(5(0(2(2(5(4(1(5(5(x1)))))))))))))))))))))))))) 1(4(0(1(1(4(0(2(3(0(3(0(1(3(5(3(0(5(2(4(0(1(4(4(1(1(5(x1))))))))))))))))))))))))))) -> 1(4(0(1(1(4(0(2(3(0(3(0(1(3(5(3(0(5(2(4(1(0(4(4(1(1(5(x1))))))))))))))))))))))))))) 5(1(1(2(2(5(5(1(4(3(5(0(1(4(2(4(3(1(5(1(1(1(5(1(1(2(0(x1))))))))))))))))))))))))))) -> 1(5(2(1(5(2(5(3(4(1(5(4(1(0(2(1(4(3(1(5(1(5(1(1(1(0(2(x1))))))))))))))))))))))))))) 0(2(4(5(2(2(4(3(3(5(2(3(0(0(2(1(3(0(3(1(1(3(2(4(1(2(0(1(x1)))))))))))))))))))))))))))) -> 0(2(4(5(2(2(4(3(5(3(2(3(0(0(2(1(3(0(3(1(1(3(2(4(1(2(0(1(x1)))))))))))))))))))))))))))) 2(3(5(1(2(1(0(0(3(4(0(2(4(1(5(1(5(1(2(2(2(5(0(2(5(0(1(1(x1)))))))))))))))))))))))))))) -> 2(3(5(1(1(2(0(0(3(4(0(2(4(1(5(1(5(1(2(2(2(5(0(2(5(0(1(1(x1)))))))))))))))))))))))))))) 5(4(4(5(5(1(1(3(4(3(0(0(4(3(0(4(1(2(0(5(5(0(5(5(5(5(0(2(x1)))))))))))))))))))))))))))) -> 5(4(4(5(5(1(1(3(3(4(0(0(4(3(0(4(1(2(0(5(5(0(5(5(5(5(0(2(x1)))))))))))))))))))))))))))) 4(1(5(1(3(5(0(5(5(3(4(5(3(4(1(2(4(4(3(2(2(3(2(0(0(5(3(0(3(x1))))))))))))))))))))))))))))) -> 4(1(5(3(1(5(0(5(5(3(4(5(3(4(1(2(4(4(3(2(2(3(2(0(0(5(3(0(3(x1))))))))))))))))))))))))))))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encArg(cons_1(x_1)) -> 1(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)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(0(2(1(x1))))))) -> 0(0(2(1(0(2(1(x1))))))) 2(3(0(4(3(3(2(x1))))))) -> 2(0(3(3(4(3(2(x1))))))) 1(1(4(1(2(3(3(5(x1)))))))) -> 1(1(4(1(3(2(3(5(x1)))))))) 1(2(2(5(5(1(3(4(x1)))))))) -> 1(3(2(2(5(1(5(4(x1)))))))) 2(3(1(2(3(1(0(1(x1)))))))) -> 2(3(2(1(3(1(0(1(x1)))))))) 5(4(1(2(1(0(5(1(x1)))))))) -> 5(4(1(1(2(0(5(1(x1)))))))) 1(1(2(0(2(1(3(1(0(x1))))))))) -> 1(1(2(0(2(3(1(1(0(x1))))))))) 2(1(4(3(2(3(1(5(1(x1))))))))) -> 2(1(4(2(3(3(1(5(1(x1))))))))) 5(1(2(1(4(1(2(4(0(x1))))))))) -> 5(1(2(1(4(4(2(1(0(x1))))))))) 0(4(3(5(2(5(0(4(3(0(x1)))))))))) -> 0(5(1(1(5(1(0(2(1(1(x1)))))))))) 5(3(5(4(4(5(4(3(1(0(x1)))))))))) -> 3(3(1(1(0(0(2(2(1(5(x1)))))))))) 0(0(2(3(2(0(2(2(2(4(5(x1))))))))))) -> 0(4(4(2(5(5(4(5(2(1(x1)))))))))) 0(2(5(3(2(5(2(5(4(4(4(x1))))))))))) -> 1(3(5(0(3(1(5(4(2(5(x1)))))))))) 0(4(0(4(3(0(5(4(5(3(4(x1))))))))))) -> 5(1(5(5(4(1(1(4(0(5(x1)))))))))) 0(5(3(0(0(1(2(1(5(3(1(x1))))))))))) -> 5(5(4(5(0(2(1(0(5(1(x1)))))))))) 1(0(3(3(0(3(2(2(3(4(1(x1))))))))))) -> 1(4(5(2(0(1(0(4(0(1(x1)))))))))) 1(4(3(5(3(0(1(4(3(2(4(x1))))))))))) -> 3(3(2(5(5(2(0(0(4(2(x1)))))))))) 1(5(0(5(3(0(5(2(5(5(3(x1))))))))))) -> 4(2(5(1(2(1(2(0(1(3(x1)))))))))) 2(0(1(0(0(4(0(3(0(1(0(x1))))))))))) -> 2(0(5(0(5(2(0(2(0(0(x1)))))))))) 2(3(4(5(4(5(4(0(5(0(0(x1))))))))))) -> 2(0(5(3(1(4(0(3(2(4(x1)))))))))) 2(4(1(0(3(4(3(1(5(1(2(x1))))))))))) -> 2(4(5(1(4(3(4(3(4(1(x1)))))))))) 2(4(1(2(1(3(0(1(4(1(4(x1))))))))))) -> 5(5(2(2(2(1(4(1(5(4(x1)))))))))) 2(4(3(3(3(4(4(0(3(0(5(x1))))))))))) -> 1(0(5(3(5(2(4(4(0(0(x1)))))))))) 2(5(1(3(5(5(2(4(2(3(4(x1))))))))))) -> 1(1(1(3(1(5(4(2(4(4(x1)))))))))) 2(5(2(2(3(2(1(2(2(5(5(x1))))))))))) -> 1(4(2(5(0(0(3(3(0(3(x1)))))))))) 2(5(2(3(4(0(0(5(2(4(5(x1))))))))))) -> 3(0(3(1(5(3(4(5(1(5(x1)))))))))) 3(2(1(5(3(3(4(4(4(1(0(x1))))))))))) -> 3(4(5(0(5(0(0(5(1(3(x1)))))))))) 3(3(2(5(0(1(1(4(4(2(5(x1))))))))))) -> 2(3(4(0(2(2(0(0(0(1(x1)))))))))) 3(4(3(0(3(1(1(4(3(2(4(x1))))))))))) -> 0(2(5(0(2(0(3(2(0(3(x1)))))))))) 3(4(5(2(3(3(4(0(2(0(0(x1))))))))))) -> 3(4(1(1(2(0(0(5(1(1(x1)))))))))) 3(5(5(4(5(2(2(4(4(1(5(x1))))))))))) -> 0(1(5(0(5(3(2(0(4(0(x1)))))))))) 4(0(1(3(5(0(2(0(4(3(2(x1))))))))))) -> 0(2(2(3(0(0(4(0(1(0(x1)))))))))) 4(0(5(1(5(5(5(2(4(5(4(x1))))))))))) -> 2(3(1(4(3(0(5(2(2(3(x1)))))))))) 4(2(0(2(3(1(0(0(3(0(0(x1))))))))))) -> 3(3(3(0(3(2(5(5(5(4(x1)))))))))) 4(2(3(0(1(3(4(2(2(3(2(x1))))))))))) -> 2(2(4(4(4(3(0(0(5(5(x1)))))))))) 4(3(1(5(1(5(3(1(4(0(1(x1))))))))))) -> 4(3(1(5(1(5(3(4(1(0(1(x1))))))))))) 4(5(3(4(4(2(0(0(0(4(0(x1))))))))))) -> 4(5(5(0(0(3(1(5(3(1(x1)))))))))) 5(0(2(1(0(1(0(1(5(0(4(x1))))))))))) -> 5(0(2(1(0(0(1(1(5(0(4(x1))))))))))) 1(2(0(5(1(0(4(2(1(1(4(2(x1)))))))))))) -> 1(2(0(5(0(1(4(2(1(1(4(2(x1)))))))))))) 1(3(1(5(3(2(1(5(4(1(0(2(x1)))))))))))) -> 3(2(2(2(0(1(3(0(5(0(x1)))))))))) 3(1(1(2(2(5(3(2(4(0(1(0(x1)))))))))))) -> 3(4(0(5(1(2(5(1(5(2(x1)))))))))) 4(1(4(0(1(1(0(3(5(5(1(5(x1)))))))))))) -> 4(2(0(2(3(0(5(4(4(2(x1)))))))))) 5(0(2(1(1(0(4(5(3(0(1(0(x1)))))))))))) -> 5(0(2(1(1(0(5(4(0(3(1(0(x1)))))))))))) 3(3(3(1(1(1(5(5(1(2(3(3(4(x1))))))))))))) -> 3(3(3(1(1(1(5(5(1(3(2(3(4(x1))))))))))))) 5(4(3(0(5(0(3(0(1(4(0(5(3(x1))))))))))))) -> 5(4(3(0(5(3(0(0(1(4(0(5(3(x1))))))))))))) 1(4(5(2(4(3(1(1(2(5(1(4(0(4(x1)))))))))))))) -> 1(4(2(5(4(3(1(1(2(5(1(4(0(4(x1)))))))))))))) 3(4(0(0(3(4(4(1(0(3(4(4(2(4(x1)))))))))))))) -> 3(4(0(0(3(4(1(4(0(3(4(4(2(4(x1)))))))))))))) 3(0(4(5(2(4(3(5(2(2(2(3(5(2(4(x1))))))))))))))) -> 2(4(0(3(5(4(3(2(5(2(5(2(3(2(4(x1))))))))))))))) 3(5(1(5(0(2(3(2(2(5(3(0(4(1(2(1(x1)))))))))))))))) -> 3(5(1(5(0(2(3(2(3(2(5(0(4(1(2(1(x1)))))))))))))))) 1(1(0(2(0(2(4(4(3(5(0(1(3(3(3(3(5(x1))))))))))))))))) -> 1(1(0(2(0(2(4(3(4(5(0(1(3(3(3(3(5(x1))))))))))))))))) 2(0(3(4(3(0(5(1(3(0(0(5(4(4(3(4(1(x1))))))))))))))))) -> 2(0(3(4(0(3(5(1(3(0(0(5(4(4(3(4(1(x1))))))))))))))))) 5(1(2(2(0(0(5(5(3(2(2(5(3(0(4(5(1(x1))))))))))))))))) -> 5(1(2(2(0(5(0(5(3(2(5(2(3(0(4(5(1(x1))))))))))))))))) 4(0(0(2(0(3(4(0(4(1(4(3(4(5(2(1(1(4(x1)))))))))))))))))) -> 4(0(0(2(0(3(4(0(1(4(4(3(4(5(2(1(1(4(x1)))))))))))))))))) 0(4(5(3(4(0(0(1(3(3(0(2(1(5(3(2(3(5(1(x1))))))))))))))))))) -> 0(4(5(3(4(0(0(1(3(3(0(2(5(1(3(2(3(5(1(x1))))))))))))))))))) 5(0(5(4(5(1(0(4(2(4(4(3(0(0(4(1(2(3(1(x1))))))))))))))))))) -> 5(0(5(4(5(1(0(4(2(4(3(4(0(0(4(1(2(3(1(x1))))))))))))))))))) 4(2(5(5(1(4(5(1(1(5(5(4(1(1(1(1(0(0(1(3(1(x1))))))))))))))))))))) -> 5(5(4(5(2(1(5(4(1(5(1(1(1(1(1(4(0(0(3(1(1(x1))))))))))))))))))))) 0(4(5(0(1(1(1(0(5(5(2(1(2(1(3(1(3(4(2(5(0(1(x1)))))))))))))))))))))) -> 5(0(4(0(1(1(1(5(0(5(2(1(2(1(1(3(3(4(2(5(0(1(x1)))))))))))))))))))))) 2(0(1(1(4(4(4(4(0(4(0(1(5(5(0(2(0(0(0(5(5(4(x1)))))))))))))))))))))) -> 2(0(1(1(4(4(4(4(0(4(0(1(5(0(5(2(0(0(0(5(5(4(x1)))))))))))))))))))))) 3(5(4(1(1(0(5(3(2(4(4(2(4(0(4(4(1(2(0(4(4(4(x1)))))))))))))))))))))) -> 3(5(4(1(1(0(5(3(2(4(4(2(0(4(4(4(1(2(0(4(4(4(x1)))))))))))))))))))))) 1(0(0(4(5(4(4(4(4(5(0(3(5(4(0(4(2(4(4(3(3(4(4(x1))))))))))))))))))))))) -> 1(0(0(4(5(4(4(4(4(5(0(3(4(5(0(4(2(4(4(3(3(4(4(x1))))))))))))))))))))))) 1(1(3(4(4(0(5(0(4(5(5(4(0(4(0(0(1(1(5(3(3(4(1(x1))))))))))))))))))))))) -> 1(1(3(4(4(0(5(0(4(5(4(5(0(4(0(0(1(1(5(3(3(4(1(x1))))))))))))))))))))))) 2(5(4(2(2(3(2(5(5(2(0(4(2(4(2(0(1(5(1(2(4(2(3(x1))))))))))))))))))))))) -> 2(5(4(2(2(3(2(5(5(2(0(4(2(4(2(0(1(5(1(4(2(2(3(x1))))))))))))))))))))))) 1(2(1(2(1(2(1(1(3(1(3(1(5(1(4(3(3(3(0(0(5(4(3(0(x1)))))))))))))))))))))))) -> 1(2(1(2(2(1(3(4(1(1(5(1(0(3(1(3(3(3(1(4(0(0(3(5(x1)))))))))))))))))))))))) 0(2(3(3(0(2(3(3(4(5(3(5(5(2(5(1(0(2(2(3(1(5(1(5(1(x1))))))))))))))))))))))))) -> 0(2(3(3(0(2(3(3(4(5(3(5(5(2(5(1(0(2(2(3(5(1(1(5(1(x1))))))))))))))))))))))))) 0(4(2(3(4(4(3(3(4(5(5(3(4(1(5(1(4(2(1(2(0(5(5(0(2(x1))))))))))))))))))))))))) -> 0(4(2(3(4(4(3(3(4(5(5(3(4(1(5(1(4(2(1(0(2(5(5(0(2(x1))))))))))))))))))))))))) 3(1(3(0(0(4(0(2(1(2(5(0(2(4(5(3(1(0(1(0(1(5(4(3(0(x1))))))))))))))))))))))))) -> 3(1(3(0(0(4(0(2(1(2(5(0(2(4(5(3(1(0(0(1(1(5(4(3(0(x1))))))))))))))))))))))))) 3(2(3(5(2(2(2(5(5(1(3(4(3(5(2(5(2(4(4(5(1(2(4(3(5(x1))))))))))))))))))))))))) -> 3(2(3(5(2(2(2(5(5(1(3(3(4(5(2(5(2(4(4(5(1(2(4(3(5(x1))))))))))))))))))))))))) 2(0(0(1(2(1(2(4(2(3(5(4(5(3(3(4(0(4(2(4(2(2(3(5(3(4(x1)))))))))))))))))))))))))) -> 2(0(0(1(2(1(4(2(2(3(5(4(5(3(3(4(0(4(2(4(2(2(3(5(3(4(x1)))))))))))))))))))))))))) 2(5(2(2(1(1(3(4(3(4(5(4(2(1(4(1(3(5(0(2(2(4(5(1(5(5(x1)))))))))))))))))))))))))) -> 2(5(2(2(1(1(3(4(3(4(5(4(2(1(4(1(3(5(0(2(2(5(4(1(5(5(x1)))))))))))))))))))))))))) 1(4(0(1(1(4(0(2(3(0(3(0(1(3(5(3(0(5(2(4(0(1(4(4(1(1(5(x1))))))))))))))))))))))))))) -> 1(4(0(1(1(4(0(2(3(0(3(0(1(3(5(3(0(5(2(4(1(0(4(4(1(1(5(x1))))))))))))))))))))))))))) 5(1(1(2(2(5(5(1(4(3(5(0(1(4(2(4(3(1(5(1(1(1(5(1(1(2(0(x1))))))))))))))))))))))))))) -> 1(5(2(1(5(2(5(3(4(1(5(4(1(0(2(1(4(3(1(5(1(5(1(1(1(0(2(x1))))))))))))))))))))))))))) 0(2(4(5(2(2(4(3(3(5(2(3(0(0(2(1(3(0(3(1(1(3(2(4(1(2(0(1(x1)))))))))))))))))))))))))))) -> 0(2(4(5(2(2(4(3(5(3(2(3(0(0(2(1(3(0(3(1(1(3(2(4(1(2(0(1(x1)))))))))))))))))))))))))))) 2(3(5(1(2(1(0(0(3(4(0(2(4(1(5(1(5(1(2(2(2(5(0(2(5(0(1(1(x1)))))))))))))))))))))))))))) -> 2(3(5(1(1(2(0(0(3(4(0(2(4(1(5(1(5(1(2(2(2(5(0(2(5(0(1(1(x1)))))))))))))))))))))))))))) 5(4(4(5(5(1(1(3(4(3(0(0(4(3(0(4(1(2(0(5(5(0(5(5(5(5(0(2(x1)))))))))))))))))))))))))))) -> 5(4(4(5(5(1(1(3(3(4(0(0(4(3(0(4(1(2(0(5(5(0(5(5(5(5(0(2(x1)))))))))))))))))))))))))))) 4(1(5(1(3(5(0(5(5(3(4(5(3(4(1(2(4(4(3(2(2(3(2(0(0(5(3(0(3(x1))))))))))))))))))))))))))))) -> 4(1(5(3(1(5(0(5(5(3(4(5(3(4(1(2(4(4(3(2(2(3(2(0(0(5(3(0(3(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_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)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(0(2(1(x1))))))) -> 0(0(2(1(0(2(1(x1))))))) 2(3(0(4(3(3(2(x1))))))) -> 2(0(3(3(4(3(2(x1))))))) 1(1(4(1(2(3(3(5(x1)))))))) -> 1(1(4(1(3(2(3(5(x1)))))))) 1(2(2(5(5(1(3(4(x1)))))))) -> 1(3(2(2(5(1(5(4(x1)))))))) 2(3(1(2(3(1(0(1(x1)))))))) -> 2(3(2(1(3(1(0(1(x1)))))))) 5(4(1(2(1(0(5(1(x1)))))))) -> 5(4(1(1(2(0(5(1(x1)))))))) 1(1(2(0(2(1(3(1(0(x1))))))))) -> 1(1(2(0(2(3(1(1(0(x1))))))))) 2(1(4(3(2(3(1(5(1(x1))))))))) -> 2(1(4(2(3(3(1(5(1(x1))))))))) 5(1(2(1(4(1(2(4(0(x1))))))))) -> 5(1(2(1(4(4(2(1(0(x1))))))))) 0(4(3(5(2(5(0(4(3(0(x1)))))))))) -> 0(5(1(1(5(1(0(2(1(1(x1)))))))))) 5(3(5(4(4(5(4(3(1(0(x1)))))))))) -> 3(3(1(1(0(0(2(2(1(5(x1)))))))))) 0(0(2(3(2(0(2(2(2(4(5(x1))))))))))) -> 0(4(4(2(5(5(4(5(2(1(x1)))))))))) 0(2(5(3(2(5(2(5(4(4(4(x1))))))))))) -> 1(3(5(0(3(1(5(4(2(5(x1)))))))))) 0(4(0(4(3(0(5(4(5(3(4(x1))))))))))) -> 5(1(5(5(4(1(1(4(0(5(x1)))))))))) 0(5(3(0(0(1(2(1(5(3(1(x1))))))))))) -> 5(5(4(5(0(2(1(0(5(1(x1)))))))))) 1(0(3(3(0(3(2(2(3(4(1(x1))))))))))) -> 1(4(5(2(0(1(0(4(0(1(x1)))))))))) 1(4(3(5(3(0(1(4(3(2(4(x1))))))))))) -> 3(3(2(5(5(2(0(0(4(2(x1)))))))))) 1(5(0(5(3(0(5(2(5(5(3(x1))))))))))) -> 4(2(5(1(2(1(2(0(1(3(x1)))))))))) 2(0(1(0(0(4(0(3(0(1(0(x1))))))))))) -> 2(0(5(0(5(2(0(2(0(0(x1)))))))))) 2(3(4(5(4(5(4(0(5(0(0(x1))))))))))) -> 2(0(5(3(1(4(0(3(2(4(x1)))))))))) 2(4(1(0(3(4(3(1(5(1(2(x1))))))))))) -> 2(4(5(1(4(3(4(3(4(1(x1)))))))))) 2(4(1(2(1(3(0(1(4(1(4(x1))))))))))) -> 5(5(2(2(2(1(4(1(5(4(x1)))))))))) 2(4(3(3(3(4(4(0(3(0(5(x1))))))))))) -> 1(0(5(3(5(2(4(4(0(0(x1)))))))))) 2(5(1(3(5(5(2(4(2(3(4(x1))))))))))) -> 1(1(1(3(1(5(4(2(4(4(x1)))))))))) 2(5(2(2(3(2(1(2(2(5(5(x1))))))))))) -> 1(4(2(5(0(0(3(3(0(3(x1)))))))))) 2(5(2(3(4(0(0(5(2(4(5(x1))))))))))) -> 3(0(3(1(5(3(4(5(1(5(x1)))))))))) 3(2(1(5(3(3(4(4(4(1(0(x1))))))))))) -> 3(4(5(0(5(0(0(5(1(3(x1)))))))))) 3(3(2(5(0(1(1(4(4(2(5(x1))))))))))) -> 2(3(4(0(2(2(0(0(0(1(x1)))))))))) 3(4(3(0(3(1(1(4(3(2(4(x1))))))))))) -> 0(2(5(0(2(0(3(2(0(3(x1)))))))))) 3(4(5(2(3(3(4(0(2(0(0(x1))))))))))) -> 3(4(1(1(2(0(0(5(1(1(x1)))))))))) 3(5(5(4(5(2(2(4(4(1(5(x1))))))))))) -> 0(1(5(0(5(3(2(0(4(0(x1)))))))))) 4(0(1(3(5(0(2(0(4(3(2(x1))))))))))) -> 0(2(2(3(0(0(4(0(1(0(x1)))))))))) 4(0(5(1(5(5(5(2(4(5(4(x1))))))))))) -> 2(3(1(4(3(0(5(2(2(3(x1)))))))))) 4(2(0(2(3(1(0(0(3(0(0(x1))))))))))) -> 3(3(3(0(3(2(5(5(5(4(x1)))))))))) 4(2(3(0(1(3(4(2(2(3(2(x1))))))))))) -> 2(2(4(4(4(3(0(0(5(5(x1)))))))))) 4(3(1(5(1(5(3(1(4(0(1(x1))))))))))) -> 4(3(1(5(1(5(3(4(1(0(1(x1))))))))))) 4(5(3(4(4(2(0(0(0(4(0(x1))))))))))) -> 4(5(5(0(0(3(1(5(3(1(x1)))))))))) 5(0(2(1(0(1(0(1(5(0(4(x1))))))))))) -> 5(0(2(1(0(0(1(1(5(0(4(x1))))))))))) 1(2(0(5(1(0(4(2(1(1(4(2(x1)))))))))))) -> 1(2(0(5(0(1(4(2(1(1(4(2(x1)))))))))))) 1(3(1(5(3(2(1(5(4(1(0(2(x1)))))))))))) -> 3(2(2(2(0(1(3(0(5(0(x1)))))))))) 3(1(1(2(2(5(3(2(4(0(1(0(x1)))))))))))) -> 3(4(0(5(1(2(5(1(5(2(x1)))))))))) 4(1(4(0(1(1(0(3(5(5(1(5(x1)))))))))))) -> 4(2(0(2(3(0(5(4(4(2(x1)))))))))) 5(0(2(1(1(0(4(5(3(0(1(0(x1)))))))))))) -> 5(0(2(1(1(0(5(4(0(3(1(0(x1)))))))))))) 3(3(3(1(1(1(5(5(1(2(3(3(4(x1))))))))))))) -> 3(3(3(1(1(1(5(5(1(3(2(3(4(x1))))))))))))) 5(4(3(0(5(0(3(0(1(4(0(5(3(x1))))))))))))) -> 5(4(3(0(5(3(0(0(1(4(0(5(3(x1))))))))))))) 1(4(5(2(4(3(1(1(2(5(1(4(0(4(x1)))))))))))))) -> 1(4(2(5(4(3(1(1(2(5(1(4(0(4(x1)))))))))))))) 3(4(0(0(3(4(4(1(0(3(4(4(2(4(x1)))))))))))))) -> 3(4(0(0(3(4(1(4(0(3(4(4(2(4(x1)))))))))))))) 3(0(4(5(2(4(3(5(2(2(2(3(5(2(4(x1))))))))))))))) -> 2(4(0(3(5(4(3(2(5(2(5(2(3(2(4(x1))))))))))))))) 3(5(1(5(0(2(3(2(2(5(3(0(4(1(2(1(x1)))))))))))))))) -> 3(5(1(5(0(2(3(2(3(2(5(0(4(1(2(1(x1)))))))))))))))) 1(1(0(2(0(2(4(4(3(5(0(1(3(3(3(3(5(x1))))))))))))))))) -> 1(1(0(2(0(2(4(3(4(5(0(1(3(3(3(3(5(x1))))))))))))))))) 2(0(3(4(3(0(5(1(3(0(0(5(4(4(3(4(1(x1))))))))))))))))) -> 2(0(3(4(0(3(5(1(3(0(0(5(4(4(3(4(1(x1))))))))))))))))) 5(1(2(2(0(0(5(5(3(2(2(5(3(0(4(5(1(x1))))))))))))))))) -> 5(1(2(2(0(5(0(5(3(2(5(2(3(0(4(5(1(x1))))))))))))))))) 4(0(0(2(0(3(4(0(4(1(4(3(4(5(2(1(1(4(x1)))))))))))))))))) -> 4(0(0(2(0(3(4(0(1(4(4(3(4(5(2(1(1(4(x1)))))))))))))))))) 0(4(5(3(4(0(0(1(3(3(0(2(1(5(3(2(3(5(1(x1))))))))))))))))))) -> 0(4(5(3(4(0(0(1(3(3(0(2(5(1(3(2(3(5(1(x1))))))))))))))))))) 5(0(5(4(5(1(0(4(2(4(4(3(0(0(4(1(2(3(1(x1))))))))))))))))))) -> 5(0(5(4(5(1(0(4(2(4(3(4(0(0(4(1(2(3(1(x1))))))))))))))))))) 4(2(5(5(1(4(5(1(1(5(5(4(1(1(1(1(0(0(1(3(1(x1))))))))))))))))))))) -> 5(5(4(5(2(1(5(4(1(5(1(1(1(1(1(4(0(0(3(1(1(x1))))))))))))))))))))) 0(4(5(0(1(1(1(0(5(5(2(1(2(1(3(1(3(4(2(5(0(1(x1)))))))))))))))))))))) -> 5(0(4(0(1(1(1(5(0(5(2(1(2(1(1(3(3(4(2(5(0(1(x1)))))))))))))))))))))) 2(0(1(1(4(4(4(4(0(4(0(1(5(5(0(2(0(0(0(5(5(4(x1)))))))))))))))))))))) -> 2(0(1(1(4(4(4(4(0(4(0(1(5(0(5(2(0(0(0(5(5(4(x1)))))))))))))))))))))) 3(5(4(1(1(0(5(3(2(4(4(2(4(0(4(4(1(2(0(4(4(4(x1)))))))))))))))))))))) -> 3(5(4(1(1(0(5(3(2(4(4(2(0(4(4(4(1(2(0(4(4(4(x1)))))))))))))))))))))) 1(0(0(4(5(4(4(4(4(5(0(3(5(4(0(4(2(4(4(3(3(4(4(x1))))))))))))))))))))))) -> 1(0(0(4(5(4(4(4(4(5(0(3(4(5(0(4(2(4(4(3(3(4(4(x1))))))))))))))))))))))) 1(1(3(4(4(0(5(0(4(5(5(4(0(4(0(0(1(1(5(3(3(4(1(x1))))))))))))))))))))))) -> 1(1(3(4(4(0(5(0(4(5(4(5(0(4(0(0(1(1(5(3(3(4(1(x1))))))))))))))))))))))) 2(5(4(2(2(3(2(5(5(2(0(4(2(4(2(0(1(5(1(2(4(2(3(x1))))))))))))))))))))))) -> 2(5(4(2(2(3(2(5(5(2(0(4(2(4(2(0(1(5(1(4(2(2(3(x1))))))))))))))))))))))) 1(2(1(2(1(2(1(1(3(1(3(1(5(1(4(3(3(3(0(0(5(4(3(0(x1)))))))))))))))))))))))) -> 1(2(1(2(2(1(3(4(1(1(5(1(0(3(1(3(3(3(1(4(0(0(3(5(x1)))))))))))))))))))))))) 0(2(3(3(0(2(3(3(4(5(3(5(5(2(5(1(0(2(2(3(1(5(1(5(1(x1))))))))))))))))))))))))) -> 0(2(3(3(0(2(3(3(4(5(3(5(5(2(5(1(0(2(2(3(5(1(1(5(1(x1))))))))))))))))))))))))) 0(4(2(3(4(4(3(3(4(5(5(3(4(1(5(1(4(2(1(2(0(5(5(0(2(x1))))))))))))))))))))))))) -> 0(4(2(3(4(4(3(3(4(5(5(3(4(1(5(1(4(2(1(0(2(5(5(0(2(x1))))))))))))))))))))))))) 3(1(3(0(0(4(0(2(1(2(5(0(2(4(5(3(1(0(1(0(1(5(4(3(0(x1))))))))))))))))))))))))) -> 3(1(3(0(0(4(0(2(1(2(5(0(2(4(5(3(1(0(0(1(1(5(4(3(0(x1))))))))))))))))))))))))) 3(2(3(5(2(2(2(5(5(1(3(4(3(5(2(5(2(4(4(5(1(2(4(3(5(x1))))))))))))))))))))))))) -> 3(2(3(5(2(2(2(5(5(1(3(3(4(5(2(5(2(4(4(5(1(2(4(3(5(x1))))))))))))))))))))))))) 2(0(0(1(2(1(2(4(2(3(5(4(5(3(3(4(0(4(2(4(2(2(3(5(3(4(x1)))))))))))))))))))))))))) -> 2(0(0(1(2(1(4(2(2(3(5(4(5(3(3(4(0(4(2(4(2(2(3(5(3(4(x1)))))))))))))))))))))))))) 2(5(2(2(1(1(3(4(3(4(5(4(2(1(4(1(3(5(0(2(2(4(5(1(5(5(x1)))))))))))))))))))))))))) -> 2(5(2(2(1(1(3(4(3(4(5(4(2(1(4(1(3(5(0(2(2(5(4(1(5(5(x1)))))))))))))))))))))))))) 1(4(0(1(1(4(0(2(3(0(3(0(1(3(5(3(0(5(2(4(0(1(4(4(1(1(5(x1))))))))))))))))))))))))))) -> 1(4(0(1(1(4(0(2(3(0(3(0(1(3(5(3(0(5(2(4(1(0(4(4(1(1(5(x1))))))))))))))))))))))))))) 5(1(1(2(2(5(5(1(4(3(5(0(1(4(2(4(3(1(5(1(1(1(5(1(1(2(0(x1))))))))))))))))))))))))))) -> 1(5(2(1(5(2(5(3(4(1(5(4(1(0(2(1(4(3(1(5(1(5(1(1(1(0(2(x1))))))))))))))))))))))))))) 0(2(4(5(2(2(4(3(3(5(2(3(0(0(2(1(3(0(3(1(1(3(2(4(1(2(0(1(x1)))))))))))))))))))))))))))) -> 0(2(4(5(2(2(4(3(5(3(2(3(0(0(2(1(3(0(3(1(1(3(2(4(1(2(0(1(x1)))))))))))))))))))))))))))) 2(3(5(1(2(1(0(0(3(4(0(2(4(1(5(1(5(1(2(2(2(5(0(2(5(0(1(1(x1)))))))))))))))))))))))))))) -> 2(3(5(1(1(2(0(0(3(4(0(2(4(1(5(1(5(1(2(2(2(5(0(2(5(0(1(1(x1)))))))))))))))))))))))))))) 5(4(4(5(5(1(1(3(4(3(0(0(4(3(0(4(1(2(0(5(5(0(5(5(5(5(0(2(x1)))))))))))))))))))))))))))) -> 5(4(4(5(5(1(1(3(3(4(0(0(4(3(0(4(1(2(0(5(5(0(5(5(5(5(0(2(x1)))))))))))))))))))))))))))) 4(1(5(1(3(5(0(5(5(3(4(5(3(4(1(2(4(4(3(2(2(3(2(0(0(5(3(0(3(x1))))))))))))))))))))))))))))) -> 4(1(5(3(1(5(0(5(5(3(4(5(3(4(1(2(4(4(3(2(2(3(2(0(0(5(3(0(3(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_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)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(0(1(2(0(2(1(x1))))))) -> 0(0(2(1(0(2(1(x1))))))) 2(3(0(4(3(3(2(x1))))))) -> 2(0(3(3(4(3(2(x1))))))) 1(1(4(1(2(3(3(5(x1)))))))) -> 1(1(4(1(3(2(3(5(x1)))))))) 1(2(2(5(5(1(3(4(x1)))))))) -> 1(3(2(2(5(1(5(4(x1)))))))) 2(3(1(2(3(1(0(1(x1)))))))) -> 2(3(2(1(3(1(0(1(x1)))))))) 5(4(1(2(1(0(5(1(x1)))))))) -> 5(4(1(1(2(0(5(1(x1)))))))) 1(1(2(0(2(1(3(1(0(x1))))))))) -> 1(1(2(0(2(3(1(1(0(x1))))))))) 2(1(4(3(2(3(1(5(1(x1))))))))) -> 2(1(4(2(3(3(1(5(1(x1))))))))) 5(1(2(1(4(1(2(4(0(x1))))))))) -> 5(1(2(1(4(4(2(1(0(x1))))))))) 0(4(3(5(2(5(0(4(3(0(x1)))))))))) -> 0(5(1(1(5(1(0(2(1(1(x1)))))))))) 5(3(5(4(4(5(4(3(1(0(x1)))))))))) -> 3(3(1(1(0(0(2(2(1(5(x1)))))))))) 0(0(2(3(2(0(2(2(2(4(5(x1))))))))))) -> 0(4(4(2(5(5(4(5(2(1(x1)))))))))) 0(2(5(3(2(5(2(5(4(4(4(x1))))))))))) -> 1(3(5(0(3(1(5(4(2(5(x1)))))))))) 0(4(0(4(3(0(5(4(5(3(4(x1))))))))))) -> 5(1(5(5(4(1(1(4(0(5(x1)))))))))) 0(5(3(0(0(1(2(1(5(3(1(x1))))))))))) -> 5(5(4(5(0(2(1(0(5(1(x1)))))))))) 1(0(3(3(0(3(2(2(3(4(1(x1))))))))))) -> 1(4(5(2(0(1(0(4(0(1(x1)))))))))) 1(4(3(5(3(0(1(4(3(2(4(x1))))))))))) -> 3(3(2(5(5(2(0(0(4(2(x1)))))))))) 1(5(0(5(3(0(5(2(5(5(3(x1))))))))))) -> 4(2(5(1(2(1(2(0(1(3(x1)))))))))) 2(0(1(0(0(4(0(3(0(1(0(x1))))))))))) -> 2(0(5(0(5(2(0(2(0(0(x1)))))))))) 2(3(4(5(4(5(4(0(5(0(0(x1))))))))))) -> 2(0(5(3(1(4(0(3(2(4(x1)))))))))) 2(4(1(0(3(4(3(1(5(1(2(x1))))))))))) -> 2(4(5(1(4(3(4(3(4(1(x1)))))))))) 2(4(1(2(1(3(0(1(4(1(4(x1))))))))))) -> 5(5(2(2(2(1(4(1(5(4(x1)))))))))) 2(4(3(3(3(4(4(0(3(0(5(x1))))))))))) -> 1(0(5(3(5(2(4(4(0(0(x1)))))))))) 2(5(1(3(5(5(2(4(2(3(4(x1))))))))))) -> 1(1(1(3(1(5(4(2(4(4(x1)))))))))) 2(5(2(2(3(2(1(2(2(5(5(x1))))))))))) -> 1(4(2(5(0(0(3(3(0(3(x1)))))))))) 2(5(2(3(4(0(0(5(2(4(5(x1))))))))))) -> 3(0(3(1(5(3(4(5(1(5(x1)))))))))) 3(2(1(5(3(3(4(4(4(1(0(x1))))))))))) -> 3(4(5(0(5(0(0(5(1(3(x1)))))))))) 3(3(2(5(0(1(1(4(4(2(5(x1))))))))))) -> 2(3(4(0(2(2(0(0(0(1(x1)))))))))) 3(4(3(0(3(1(1(4(3(2(4(x1))))))))))) -> 0(2(5(0(2(0(3(2(0(3(x1)))))))))) 3(4(5(2(3(3(4(0(2(0(0(x1))))))))))) -> 3(4(1(1(2(0(0(5(1(1(x1)))))))))) 3(5(5(4(5(2(2(4(4(1(5(x1))))))))))) -> 0(1(5(0(5(3(2(0(4(0(x1)))))))))) 4(0(1(3(5(0(2(0(4(3(2(x1))))))))))) -> 0(2(2(3(0(0(4(0(1(0(x1)))))))))) 4(0(5(1(5(5(5(2(4(5(4(x1))))))))))) -> 2(3(1(4(3(0(5(2(2(3(x1)))))))))) 4(2(0(2(3(1(0(0(3(0(0(x1))))))))))) -> 3(3(3(0(3(2(5(5(5(4(x1)))))))))) 4(2(3(0(1(3(4(2(2(3(2(x1))))))))))) -> 2(2(4(4(4(3(0(0(5(5(x1)))))))))) 4(3(1(5(1(5(3(1(4(0(1(x1))))))))))) -> 4(3(1(5(1(5(3(4(1(0(1(x1))))))))))) 4(5(3(4(4(2(0(0(0(4(0(x1))))))))))) -> 4(5(5(0(0(3(1(5(3(1(x1)))))))))) 5(0(2(1(0(1(0(1(5(0(4(x1))))))))))) -> 5(0(2(1(0(0(1(1(5(0(4(x1))))))))))) 1(2(0(5(1(0(4(2(1(1(4(2(x1)))))))))))) -> 1(2(0(5(0(1(4(2(1(1(4(2(x1)))))))))))) 1(3(1(5(3(2(1(5(4(1(0(2(x1)))))))))))) -> 3(2(2(2(0(1(3(0(5(0(x1)))))))))) 3(1(1(2(2(5(3(2(4(0(1(0(x1)))))))))))) -> 3(4(0(5(1(2(5(1(5(2(x1)))))))))) 4(1(4(0(1(1(0(3(5(5(1(5(x1)))))))))))) -> 4(2(0(2(3(0(5(4(4(2(x1)))))))))) 5(0(2(1(1(0(4(5(3(0(1(0(x1)))))))))))) -> 5(0(2(1(1(0(5(4(0(3(1(0(x1)))))))))))) 3(3(3(1(1(1(5(5(1(2(3(3(4(x1))))))))))))) -> 3(3(3(1(1(1(5(5(1(3(2(3(4(x1))))))))))))) 5(4(3(0(5(0(3(0(1(4(0(5(3(x1))))))))))))) -> 5(4(3(0(5(3(0(0(1(4(0(5(3(x1))))))))))))) 1(4(5(2(4(3(1(1(2(5(1(4(0(4(x1)))))))))))))) -> 1(4(2(5(4(3(1(1(2(5(1(4(0(4(x1)))))))))))))) 3(4(0(0(3(4(4(1(0(3(4(4(2(4(x1)))))))))))))) -> 3(4(0(0(3(4(1(4(0(3(4(4(2(4(x1)))))))))))))) 3(0(4(5(2(4(3(5(2(2(2(3(5(2(4(x1))))))))))))))) -> 2(4(0(3(5(4(3(2(5(2(5(2(3(2(4(x1))))))))))))))) 3(5(1(5(0(2(3(2(2(5(3(0(4(1(2(1(x1)))))))))))))))) -> 3(5(1(5(0(2(3(2(3(2(5(0(4(1(2(1(x1)))))))))))))))) 1(1(0(2(0(2(4(4(3(5(0(1(3(3(3(3(5(x1))))))))))))))))) -> 1(1(0(2(0(2(4(3(4(5(0(1(3(3(3(3(5(x1))))))))))))))))) 2(0(3(4(3(0(5(1(3(0(0(5(4(4(3(4(1(x1))))))))))))))))) -> 2(0(3(4(0(3(5(1(3(0(0(5(4(4(3(4(1(x1))))))))))))))))) 5(1(2(2(0(0(5(5(3(2(2(5(3(0(4(5(1(x1))))))))))))))))) -> 5(1(2(2(0(5(0(5(3(2(5(2(3(0(4(5(1(x1))))))))))))))))) 4(0(0(2(0(3(4(0(4(1(4(3(4(5(2(1(1(4(x1)))))))))))))))))) -> 4(0(0(2(0(3(4(0(1(4(4(3(4(5(2(1(1(4(x1)))))))))))))))))) 0(4(5(3(4(0(0(1(3(3(0(2(1(5(3(2(3(5(1(x1))))))))))))))))))) -> 0(4(5(3(4(0(0(1(3(3(0(2(5(1(3(2(3(5(1(x1))))))))))))))))))) 5(0(5(4(5(1(0(4(2(4(4(3(0(0(4(1(2(3(1(x1))))))))))))))))))) -> 5(0(5(4(5(1(0(4(2(4(3(4(0(0(4(1(2(3(1(x1))))))))))))))))))) 4(2(5(5(1(4(5(1(1(5(5(4(1(1(1(1(0(0(1(3(1(x1))))))))))))))))))))) -> 5(5(4(5(2(1(5(4(1(5(1(1(1(1(1(4(0(0(3(1(1(x1))))))))))))))))))))) 0(4(5(0(1(1(1(0(5(5(2(1(2(1(3(1(3(4(2(5(0(1(x1)))))))))))))))))))))) -> 5(0(4(0(1(1(1(5(0(5(2(1(2(1(1(3(3(4(2(5(0(1(x1)))))))))))))))))))))) 2(0(1(1(4(4(4(4(0(4(0(1(5(5(0(2(0(0(0(5(5(4(x1)))))))))))))))))))))) -> 2(0(1(1(4(4(4(4(0(4(0(1(5(0(5(2(0(0(0(5(5(4(x1)))))))))))))))))))))) 3(5(4(1(1(0(5(3(2(4(4(2(4(0(4(4(1(2(0(4(4(4(x1)))))))))))))))))))))) -> 3(5(4(1(1(0(5(3(2(4(4(2(0(4(4(4(1(2(0(4(4(4(x1)))))))))))))))))))))) 1(0(0(4(5(4(4(4(4(5(0(3(5(4(0(4(2(4(4(3(3(4(4(x1))))))))))))))))))))))) -> 1(0(0(4(5(4(4(4(4(5(0(3(4(5(0(4(2(4(4(3(3(4(4(x1))))))))))))))))))))))) 1(1(3(4(4(0(5(0(4(5(5(4(0(4(0(0(1(1(5(3(3(4(1(x1))))))))))))))))))))))) -> 1(1(3(4(4(0(5(0(4(5(4(5(0(4(0(0(1(1(5(3(3(4(1(x1))))))))))))))))))))))) 2(5(4(2(2(3(2(5(5(2(0(4(2(4(2(0(1(5(1(2(4(2(3(x1))))))))))))))))))))))) -> 2(5(4(2(2(3(2(5(5(2(0(4(2(4(2(0(1(5(1(4(2(2(3(x1))))))))))))))))))))))) 1(2(1(2(1(2(1(1(3(1(3(1(5(1(4(3(3(3(0(0(5(4(3(0(x1)))))))))))))))))))))))) -> 1(2(1(2(2(1(3(4(1(1(5(1(0(3(1(3(3(3(1(4(0(0(3(5(x1)))))))))))))))))))))))) 0(2(3(3(0(2(3(3(4(5(3(5(5(2(5(1(0(2(2(3(1(5(1(5(1(x1))))))))))))))))))))))))) -> 0(2(3(3(0(2(3(3(4(5(3(5(5(2(5(1(0(2(2(3(5(1(1(5(1(x1))))))))))))))))))))))))) 0(4(2(3(4(4(3(3(4(5(5(3(4(1(5(1(4(2(1(2(0(5(5(0(2(x1))))))))))))))))))))))))) -> 0(4(2(3(4(4(3(3(4(5(5(3(4(1(5(1(4(2(1(0(2(5(5(0(2(x1))))))))))))))))))))))))) 3(1(3(0(0(4(0(2(1(2(5(0(2(4(5(3(1(0(1(0(1(5(4(3(0(x1))))))))))))))))))))))))) -> 3(1(3(0(0(4(0(2(1(2(5(0(2(4(5(3(1(0(0(1(1(5(4(3(0(x1))))))))))))))))))))))))) 3(2(3(5(2(2(2(5(5(1(3(4(3(5(2(5(2(4(4(5(1(2(4(3(5(x1))))))))))))))))))))))))) -> 3(2(3(5(2(2(2(5(5(1(3(3(4(5(2(5(2(4(4(5(1(2(4(3(5(x1))))))))))))))))))))))))) 2(0(0(1(2(1(2(4(2(3(5(4(5(3(3(4(0(4(2(4(2(2(3(5(3(4(x1)))))))))))))))))))))))))) -> 2(0(0(1(2(1(4(2(2(3(5(4(5(3(3(4(0(4(2(4(2(2(3(5(3(4(x1)))))))))))))))))))))))))) 2(5(2(2(1(1(3(4(3(4(5(4(2(1(4(1(3(5(0(2(2(4(5(1(5(5(x1)))))))))))))))))))))))))) -> 2(5(2(2(1(1(3(4(3(4(5(4(2(1(4(1(3(5(0(2(2(5(4(1(5(5(x1)))))))))))))))))))))))))) 1(4(0(1(1(4(0(2(3(0(3(0(1(3(5(3(0(5(2(4(0(1(4(4(1(1(5(x1))))))))))))))))))))))))))) -> 1(4(0(1(1(4(0(2(3(0(3(0(1(3(5(3(0(5(2(4(1(0(4(4(1(1(5(x1))))))))))))))))))))))))))) 5(1(1(2(2(5(5(1(4(3(5(0(1(4(2(4(3(1(5(1(1(1(5(1(1(2(0(x1))))))))))))))))))))))))))) -> 1(5(2(1(5(2(5(3(4(1(5(4(1(0(2(1(4(3(1(5(1(5(1(1(1(0(2(x1))))))))))))))))))))))))))) 0(2(4(5(2(2(4(3(3(5(2(3(0(0(2(1(3(0(3(1(1(3(2(4(1(2(0(1(x1)))))))))))))))))))))))))))) -> 0(2(4(5(2(2(4(3(5(3(2(3(0(0(2(1(3(0(3(1(1(3(2(4(1(2(0(1(x1)))))))))))))))))))))))))))) 2(3(5(1(2(1(0(0(3(4(0(2(4(1(5(1(5(1(2(2(2(5(0(2(5(0(1(1(x1)))))))))))))))))))))))))))) -> 2(3(5(1(1(2(0(0(3(4(0(2(4(1(5(1(5(1(2(2(2(5(0(2(5(0(1(1(x1)))))))))))))))))))))))))))) 5(4(4(5(5(1(1(3(4(3(0(0(4(3(0(4(1(2(0(5(5(0(5(5(5(5(0(2(x1)))))))))))))))))))))))))))) -> 5(4(4(5(5(1(1(3(3(4(0(0(4(3(0(4(1(2(0(5(5(0(5(5(5(5(0(2(x1)))))))))))))))))))))))))))) 4(1(5(1(3(5(0(5(5(3(4(5(3(4(1(2(4(4(3(2(2(3(2(0(0(5(3(0(3(x1))))))))))))))))))))))))))))) -> 4(1(5(3(1(5(0(5(5(3(4(5(3(4(1(2(4(4(3(2(2(3(2(0(0(5(3(0(3(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_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)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) encode_3(x_1) -> 3(encArg(x_1)) encode_4(x_1) -> 4(encArg(x_1)) encode_5(x_1) -> 5(encArg(x_1)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (7) CpxTrsMatchBoundsProof (FINISHED) A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 2. The certificate found is represented by the following graph. "[73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 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878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1000, 1001, 1002, 1003, 1004, 1005, 1006, 1007, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1027, 1028, 1029, 1030, 1031, 1032, 1033, 1034, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1044, 1045, 1046, 1047, 1048, 1049, 1050, 1051, 1052, 1053, 1054, 1055, 1056, 1057, 1058, 1059, 1060, 1061, 1062, 1063, 1064, 1065, 1066, 1067, 1068, 1069, 1070, 1071, 1072, 1073, 1074, 1075, 1076, 1077, 1078, 1079, 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 1100, 1101, 1102, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 1110] {(73,74,[0_1|0, 2_1|0, 1_1|0, 5_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]), (73,75,[0_1|1, 2_1|1, 1_1|1, 5_1|1, 3_1|1, 4_1|1]), (73,76,[0_1|2]), (73,82,[0_1|2]), (73,91,[0_1|2]), (73,100,[5_1|2]), (73,109,[0_1|2]), (73,127,[5_1|2]), (73,148,[0_1|2]), (73,172,[1_1|2]), (73,181,[0_1|2]), (73,205,[0_1|2]), (73,232,[5_1|2]), (73,241,[2_1|2]), (73,247,[2_1|2]), (73,254,[2_1|2]), (73,263,[2_1|2]), (73,290,[2_1|2]), (73,298,[2_1|2]), (73,307,[2_1|2]), (73,328,[2_1|2]), (73,344,[2_1|2]), (73,369,[2_1|2]), (73,378,[5_1|2]), (73,387,[1_1|2]), (73,396,[1_1|2]), (73,405,[1_1|2]), (73,414,[2_1|2]), (73,439,[3_1|2]), (73,448,[2_1|2]), (73,470,[1_1|2]), 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(922,923,[4_1|2]), (923,924,[4_1|2]), (924,925,[2_1|2]), (925,926,[0_1|2]), (926,927,[4_1|2]), (927,928,[4_1|2]), (928,929,[4_1|2]), (929,930,[1_1|2]), (930,931,[2_1|2]), (931,932,[0_1|2]), (932,933,[4_1|2]), (933,934,[4_1|2]), (934,75,[4_1|2]), (934,643,[4_1|2]), (934,1000,[4_1|2]), (934,1055,[4_1|2]), (934,1065,[4_1|2]), (934,1074,[4_1|2]), (934,1083,[4_1|2]), (934,982,[0_1|2]), (934,991,[2_1|2]), (934,1017,[3_1|2]), (934,1026,[2_1|2]), (934,1035,[5_1|2]), (935,936,[4_1|2]), (936,937,[0_1|2]), (937,938,[5_1|2]), (938,939,[1_1|2]), (939,940,[2_1|2]), (940,941,[5_1|2]), (941,942,[1_1|2]), (942,943,[5_1|2]), (943,75,[2_1|2]), (943,76,[2_1|2]), (943,82,[2_1|2]), (943,91,[2_1|2]), (943,109,[2_1|2]), (943,148,[2_1|2]), (943,181,[2_1|2]), (943,205,[2_1|2]), (943,859,[2_1|2]), (943,890,[2_1|2]), (943,982,[2_1|2]), (943,388,[2_1|2]), (943,574,[2_1|2]), (943,241,[2_1|2]), (943,247,[2_1|2]), (943,254,[2_1|2]), (943,263,[2_1|2]), (943,290,[2_1|2]), (943,298,[2_1|2]), (943,307,[2_1|2]), (943,328,[2_1|2]), (943,344,[2_1|2]), (943,369,[2_1|2]), (943,378,[5_1|2]), (943,387,[1_1|2]), (943,396,[1_1|2]), (943,405,[1_1|2]), (943,414,[2_1|2]), (943,439,[3_1|2]), (943,448,[2_1|2]), (944,945,[1_1|2]), (945,946,[3_1|2]), (946,947,[0_1|2]), (947,948,[0_1|2]), (948,949,[4_1|2]), (949,950,[0_1|2]), (950,951,[2_1|2]), (951,952,[1_1|2]), (952,953,[2_1|2]), (953,954,[5_1|2]), (954,955,[0_1|2]), (955,956,[2_1|2]), (956,957,[4_1|2]), (957,958,[5_1|2]), (958,959,[3_1|2]), (959,960,[1_1|2]), (960,961,[0_1|2]), (961,962,[0_1|2]), (962,963,[1_1|2]), (963,964,[1_1|2]), (964,965,[5_1|2]), (964,668,[5_1|2]), (965,966,[4_1|2]), (966,967,[3_1|2]), (966,968,[2_1|2]), (967,75,[0_1|2]), (967,76,[0_1|2]), (967,82,[0_1|2]), (967,91,[0_1|2]), (967,109,[0_1|2]), (967,148,[0_1|2]), (967,181,[0_1|2]), (967,205,[0_1|2]), (967,859,[0_1|2]), (967,890,[0_1|2]), (967,982,[0_1|2]), (967,440,[0_1|2]), (967,671,[0_1|2]), (967,100,[5_1|2]), (967,127,[5_1|2]), (967,172,[1_1|2]), (967,232,[5_1|2]), (968,969,[4_1|2]), (969,970,[0_1|2]), (970,971,[3_1|2]), (971,972,[5_1|2]), (972,973,[4_1|2]), (973,974,[3_1|2]), (974,975,[2_1|2]), (975,976,[5_1|2]), (976,977,[2_1|2]), (977,978,[5_1|2]), (978,979,[2_1|2]), (979,980,[3_1|2]), (980,981,[2_1|2]), (980,369,[2_1|2]), (980,378,[5_1|2]), (980,387,[1_1|2]), (981,75,[4_1|2]), (981,643,[4_1|2]), (981,1000,[4_1|2]), (981,1055,[4_1|2]), (981,1065,[4_1|2]), (981,1074,[4_1|2]), (981,1083,[4_1|2]), (981,370,[4_1|2]), (981,969,[4_1|2]), (981,982,[0_1|2]), (981,991,[2_1|2]), (981,1017,[3_1|2]), (981,1026,[2_1|2]), (981,1035,[5_1|2]), (982,983,[2_1|2]), (983,984,[2_1|2]), (984,985,[3_1|2]), (985,986,[0_1|2]), (986,987,[0_1|2]), (987,988,[4_1|2]), (988,989,[0_1|2]), (989,990,[1_1|2]), (989,564,[1_1|2]), (989,573,[1_1|2]), (990,75,[0_1|2]), (990,241,[0_1|2]), (990,247,[0_1|2]), (990,254,[0_1|2]), (990,263,[0_1|2]), (990,290,[0_1|2]), (990,298,[0_1|2]), (990,307,[0_1|2]), (990,328,[0_1|2]), (990,344,[0_1|2]), (990,369,[0_1|2]), (990,414,[0_1|2]), (990,448,[0_1|2]), (990,838,[0_1|2]), (990,968,[0_1|2]), (990,991,[0_1|2]), (990,1026,[0_1|2]), (990,653,[0_1|2]), (990,815,[0_1|2]), (990,76,[0_1|2]), (990,82,[0_1|2]), (990,91,[0_1|2]), (990,100,[5_1|2]), (990,109,[0_1|2]), (990,127,[5_1|2]), (990,148,[0_1|2]), (990,172,[1_1|2]), (990,181,[0_1|2]), (990,205,[0_1|2]), (990,232,[5_1|2]), (991,992,[3_1|2]), (992,993,[1_1|2]), (993,994,[4_1|2]), (994,995,[3_1|2]), (995,996,[0_1|2]), (996,997,[5_1|2]), (997,998,[2_1|2]), (998,999,[2_1|2]), (998,241,[2_1|2]), (998,247,[2_1|2]), (998,254,[2_1|2]), (998,263,[2_1|2]), (999,75,[3_1|2]), (999,643,[3_1|2]), (999,1000,[3_1|2]), (999,1055,[3_1|2]), (999,1065,[3_1|2]), (999,1074,[3_1|2]), (999,1083,[3_1|2]), (999,662,[3_1|2]), (999,669,[3_1|2]), (999,681,[3_1|2]), (999,805,[3_1|2]), (999,814,[3_1|2]), (999,838,[2_1|2]), (999,847,[3_1|2]), (999,859,[0_1|2]), (999,868,[3_1|2]), (999,877,[3_1|2]), (999,890,[0_1|2]), (999,899,[3_1|2]), (999,914,[3_1|2]), (999,935,[3_1|2]), (999,944,[3_1|2]), (999,968,[2_1|2]), (1000,1001,[0_1|2]), (1001,1002,[0_1|2]), (1002,1003,[2_1|2]), (1003,1004,[0_1|2]), (1004,1005,[3_1|2]), (1005,1006,[4_1|2]), (1006,1007,[0_1|2]), (1007,1008,[1_1|2]), (1008,1009,[4_1|2]), (1009,1010,[4_1|2]), (1010,1011,[3_1|2]), (1011,1012,[4_1|2]), (1012,1013,[5_1|2]), (1013,1014,[2_1|2]), (1014,1015,[1_1|2]), (1014,470,[1_1|2]), (1015,1016,[1_1|2]), (1015,595,[3_1|2]), (1015,604,[1_1|2]), (1015,617,[1_1|2]), (1016,75,[4_1|2]), (1016,643,[4_1|2]), (1016,1000,[4_1|2]), (1016,1055,[4_1|2]), (1016,1065,[4_1|2]), (1016,1074,[4_1|2]), (1016,1083,[4_1|2]), (1016,406,[4_1|2]), (1016,565,[4_1|2]), (1016,605,[4_1|2]), (1016,618,[4_1|2]), (1016,472,[4_1|2]), (1016,982,[0_1|2]), (1016,991,[2_1|2]), (1016,1017,[3_1|2]), (1016,1026,[2_1|2]), (1016,1035,[5_1|2]), (1017,1018,[3_1|2]), (1018,1019,[3_1|2]), (1019,1020,[0_1|2]), (1020,1021,[3_1|2]), (1021,1022,[2_1|2]), (1022,1023,[5_1|2]), (1023,1024,[5_1|2]), (1024,1025,[5_1|2]), (1024,661,[5_1|2]), (1024,668,[5_1|2]), (1024,680,[5_1|2]), (1025,75,[4_1|2]), (1025,76,[4_1|2]), (1025,82,[4_1|2]), (1025,91,[4_1|2]), (1025,109,[4_1|2]), (1025,148,[4_1|2]), (1025,181,[4_1|2]), (1025,205,[4_1|2]), (1025,859,[4_1|2]), (1025,890,[4_1|2]), (1025,982,[4_1|2, 0_1|2]), (1025,77,[4_1|2]), (1025,991,[2_1|2]), (1025,1000,[4_1|2]), (1025,1017,[3_1|2]), (1025,1026,[2_1|2]), (1025,1035,[5_1|2]), (1025,1055,[4_1|2]), (1025,1065,[4_1|2]), (1025,1074,[4_1|2]), (1025,1083,[4_1|2]), (1026,1027,[2_1|2]), (1027,1028,[4_1|2]), (1028,1029,[4_1|2]), (1029,1030,[4_1|2]), (1030,1031,[3_1|2]), (1031,1032,[0_1|2]), (1032,1033,[0_1|2]), (1033,1034,[5_1|2]), (1034,75,[5_1|2]), (1034,241,[5_1|2]), (1034,247,[5_1|2]), (1034,254,[5_1|2]), (1034,263,[5_1|2]), (1034,290,[5_1|2]), (1034,298,[5_1|2]), (1034,307,[5_1|2]), (1034,328,[5_1|2]), (1034,344,[5_1|2]), (1034,369,[5_1|2]), (1034,414,[5_1|2]), (1034,448,[5_1|2]), (1034,838,[5_1|2]), (1034,968,[5_1|2]), (1034,991,[5_1|2]), (1034,1026,[5_1|2]), (1034,653,[5_1|2]), (1034,815,[5_1|2]), (1034,249,[5_1|2]), (1034,661,[5_1|2]), (1034,668,[5_1|2]), (1034,680,[5_1|2]), (1034,707,[5_1|2]), (1034,715,[5_1|2]), (1034,731,[1_1|2]), (1034,757,[3_1|2]), (1034,766,[5_1|2]), (1034,776,[5_1|2]), (1034,787,[5_1|2]), (1035,1036,[5_1|2]), (1036,1037,[4_1|2]), (1037,1038,[5_1|2]), (1038,1039,[2_1|2]), (1039,1040,[1_1|2]), (1040,1041,[5_1|2]), (1041,1042,[4_1|2]), (1042,1043,[1_1|2]), (1043,1044,[5_1|2]), (1044,1045,[1_1|2]), (1045,1046,[1_1|2]), (1046,1047,[1_1|2]), (1047,1048,[1_1|2]), (1048,1049,[1_1|2]), (1049,1050,[4_1|2]), (1050,1051,[0_1|2]), (1051,1052,[0_1|2]), (1052,1053,[3_1|2]), (1052,935,[3_1|2]), (1053,1054,[1_1|2]), (1053,470,[1_1|2]), (1053,477,[1_1|2]), (1053,485,[1_1|2]), (1053,501,[1_1|2]), (1054,75,[1_1|2]), (1054,172,[1_1|2]), (1054,387,[1_1|2]), (1054,396,[1_1|2]), (1054,405,[1_1|2]), (1054,470,[1_1|2]), (1054,477,[1_1|2]), (1054,485,[1_1|2]), (1054,501,[1_1|2]), (1054,523,[1_1|2]), (1054,530,[1_1|2]), (1054,541,[1_1|2]), (1054,564,[1_1|2]), (1054,573,[1_1|2]), (1054,604,[1_1|2]), (1054,617,[1_1|2]), (1054,731,[1_1|2]), (1054,945,[1_1|2]), (1054,595,[3_1|2]), (1054,643,[4_1|2]), (1054,652,[3_1|2]), (1055,1056,[3_1|2]), (1056,1057,[1_1|2]), (1057,1058,[5_1|2]), (1058,1059,[1_1|2]), (1059,1060,[5_1|2]), (1060,1061,[3_1|2]), (1061,1062,[4_1|2]), (1062,1063,[1_1|2]), (1063,1064,[0_1|2]), (1064,75,[1_1|2]), (1064,172,[1_1|2]), (1064,387,[1_1|2]), (1064,396,[1_1|2]), (1064,405,[1_1|2]), (1064,470,[1_1|2]), (1064,477,[1_1|2]), (1064,485,[1_1|2]), (1064,501,[1_1|2]), (1064,523,[1_1|2]), (1064,530,[1_1|2]), (1064,541,[1_1|2]), (1064,564,[1_1|2]), (1064,573,[1_1|2]), (1064,604,[1_1|2]), (1064,617,[1_1|2]), (1064,731,[1_1|2]), (1064,891,[1_1|2]), (1064,620,[1_1|2]), (1064,595,[3_1|2]), (1064,643,[4_1|2]), (1064,652,[3_1|2]), (1065,1066,[5_1|2]), (1066,1067,[5_1|2]), (1067,1068,[0_1|2]), (1068,1069,[0_1|2]), (1069,1070,[3_1|2]), (1070,1071,[1_1|2]), (1071,1072,[5_1|2]), (1072,1073,[3_1|2]), (1072,935,[3_1|2]), (1072,944,[3_1|2]), (1073,75,[1_1|2]), (1073,76,[1_1|2]), (1073,82,[1_1|2]), (1073,91,[1_1|2]), (1073,109,[1_1|2]), (1073,148,[1_1|2]), (1073,181,[1_1|2]), (1073,205,[1_1|2]), (1073,859,[1_1|2]), (1073,890,[1_1|2]), (1073,982,[1_1|2]), (1073,1001,[1_1|2]), (1073,470,[1_1|2]), (1073,477,[1_1|2]), (1073,485,[1_1|2]), (1073,501,[1_1|2]), (1073,523,[1_1|2]), (1073,530,[1_1|2]), (1073,541,[1_1|2]), (1073,564,[1_1|2]), (1073,573,[1_1|2]), (1073,595,[3_1|2]), (1073,604,[1_1|2]), (1073,617,[1_1|2]), (1073,643,[4_1|2]), (1073,652,[3_1|2]), (1074,1075,[2_1|2]), (1075,1076,[0_1|2]), (1076,1077,[2_1|2]), (1077,1078,[3_1|2]), (1078,1079,[0_1|2]), (1079,1080,[5_1|2]), (1080,1081,[4_1|2]), (1081,1082,[4_1|2]), (1081,1017,[3_1|2]), (1081,1026,[2_1|2]), (1081,1035,[5_1|2]), (1082,75,[2_1|2]), (1082,100,[2_1|2]), (1082,127,[2_1|2]), (1082,232,[2_1|2]), (1082,378,[2_1|2, 5_1|2]), (1082,661,[2_1|2]), (1082,668,[2_1|2]), (1082,680,[2_1|2]), (1082,707,[2_1|2]), (1082,715,[2_1|2]), (1082,766,[2_1|2]), (1082,776,[2_1|2]), (1082,787,[2_1|2]), (1082,1035,[2_1|2]), (1082,732,[2_1|2]), (1082,102,[2_1|2]), (1082,241,[2_1|2]), (1082,247,[2_1|2]), (1082,254,[2_1|2]), (1082,263,[2_1|2]), (1082,290,[2_1|2]), (1082,298,[2_1|2]), (1082,307,[2_1|2]), (1082,328,[2_1|2]), (1082,344,[2_1|2]), (1082,369,[2_1|2]), (1082,387,[1_1|2]), (1082,396,[1_1|2]), (1082,405,[1_1|2]), (1082,414,[2_1|2]), (1082,439,[3_1|2]), (1082,448,[2_1|2]), (1083,1084,[1_1|2]), (1084,1085,[5_1|2]), (1085,1086,[3_1|2]), (1086,1087,[1_1|2]), (1087,1088,[5_1|2]), (1088,1089,[0_1|2]), (1089,1090,[5_1|2]), (1090,1091,[5_1|2]), (1091,1092,[3_1|2]), (1092,1093,[4_1|2]), (1093,1094,[5_1|2]), (1094,1095,[3_1|2]), (1095,1096,[4_1|2]), (1096,1097,[1_1|2]), (1097,1098,[2_1|2]), (1098,1099,[4_1|2]), (1099,1100,[4_1|2]), (1100,1101,[3_1|2]), (1101,1102,[2_1|2]), (1102,1103,[2_1|2]), (1103,1104,[3_1|2]), (1104,1105,[2_1|2]), (1105,1106,[0_1|2]), (1106,1107,[0_1|2]), (1107,1108,[5_1|2]), (1108,1109,[3_1|2]), (1109,1110,[0_1|2]), (1110,75,[3_1|2]), (1110,439,[3_1|2]), (1110,595,[3_1|2]), (1110,652,[3_1|2]), (1110,757,[3_1|2]), (1110,805,[3_1|2]), (1110,814,[3_1|2]), (1110,847,[3_1|2]), (1110,868,[3_1|2]), (1110,877,[3_1|2]), (1110,899,[3_1|2]), (1110,914,[3_1|2]), (1110,935,[3_1|2]), (1110,944,[3_1|2]), (1110,1017,[3_1|2]), (1110,441,[3_1|2]), (1110,838,[2_1|2]), (1110,859,[0_1|2]), (1110,890,[0_1|2]), (1110,968,[2_1|2])}" ---------------------------------------- (8) BOUNDS(1, n^1)