/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 43 ms] (4) CpxRelTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 442 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(0(2(2(3(x1)))))) -> 0(2(2(1(0(3(x1)))))) 0(4(4(1(0(4(x1)))))) -> 0(4(4(4(0(1(x1)))))) 0(4(0(0(4(2(3(5(1(x1))))))))) -> 5(0(3(2(4(0(0(1(4(x1))))))))) 1(2(3(1(0(1(4(2(0(x1))))))))) -> 4(0(3(2(1(1(2(1(0(x1))))))))) 1(3(4(0(4(1(1(2(3(5(4(4(x1)))))))))))) -> 2(4(4(0(1(3(5(1(4(3(4(1(x1)))))))))))) 4(1(1(3(3(0(1(5(0(4(4(2(2(3(3(5(4(3(x1)))))))))))))))))) -> 4(0(4(2(4(3(1(3(4(3(5(1(2(0(3(5(1(3(x1)))))))))))))))))) 1(0(4(3(1(2(1(2(0(4(3(3(2(1(5(2(3(2(1(x1))))))))))))))))))) -> 1(4(2(1(1(4(1(0(3(0(5(3(1(3(2(2(3(2(2(x1))))))))))))))))))) 1(1(1(3(0(4(5(0(3(0(1(1(3(0(4(5(3(3(0(x1))))))))))))))))))) -> 4(5(0(3(3(4(1(0(0(1(1(1(3(1(0(3(5(3(0(x1))))))))))))))))))) 1(3(2(3(0(5(0(4(1(1(2(4(4(3(3(5(4(0(5(x1))))))))))))))))))) -> 4(2(1(2(5(3(4(1(1(3(0(0(3(3(4(0(5(4(5(x1))))))))))))))))))) 3(0(2(2(0(1(1(5(0(1(1(1(0(2(0(4(5(0(1(x1))))))))))))))))))) -> 5(1(2(1(4(0(0(3(0(1(0(0(1(0(1(2(5(1(2(x1))))))))))))))))))) 0(2(1(5(4(1(5(4(0(1(2(0(2(1(2(1(1(1(3(5(2(5(x1)))))))))))))))))))))) -> 2(1(1(3(5(4(2(5(0(5(2(1(1(1(2(1(4(0(2(0(5(1(x1)))))))))))))))))))))) 2(2(5(3(3(3(0(4(1(3(5(4(5(1(3(4(1(0(3(5(4(0(x1)))))))))))))))))))))) -> 0(1(5(3(4(1(3(5(3(3(1(3(4(5(3(4(4(0(2(2(5(0(x1)))))))))))))))))))))) 2(5(5(1(4(3(3(2(1(1(1(5(0(4(4(3(5(1(4(1(4(5(2(x1))))))))))))))))))))))) -> 3(4(5(1(4(4(5(2(1(5(5(5(0(1(2(1(1(1(3(4(3(4(2(x1))))))))))))))))))))))) 3(4(0(2(2(3(2(4(2(3(5(3(5(0(1(3(5(5(2(4(4(2(3(3(x1)))))))))))))))))))))))) -> 5(5(3(2(2(2(0(5(4(3(3(3(2(0(2(4(2(1(5(3(4(3(4(3(x1)))))))))))))))))))))))) 5(5(2(0(2(1(5(5(2(1(4(4(5(2(4(4(1(1(1(3(2(5(5(5(x1)))))))))))))))))))))))) -> 5(4(5(0(5(4(2(1(2(4(1(1(2(1(2(4(5(3(1(5(2(5(5(5(x1)))))))))))))))))))))))) 1(5(2(4(1(3(3(5(3(0(4(2(5(1(5(2(0(1(0(3(0(5(5(1(4(x1))))))))))))))))))))))))) -> 1(5(2(3(1(5(4(5(5(2(3(4(2(3(5(4(1(1(3(0(0(1(0(5(0(x1))))))))))))))))))))))))) 3(1(5(1(0(4(4(1(1(2(2(0(2(3(3(2(2(3(3(5(4(1(2(5(1(x1))))))))))))))))))))))))) -> 1(3(0(3(5(5(2(1(2(3(2(5(2(3(1(0(2(1(3(1(4(1(2(4(4(x1))))))))))))))))))))))))) 0(0(1(4(0(0(4(2(1(5(5(3(0(3(4(0(1(4(3(1(5(5(2(0(0(2(3(x1))))))))))))))))))))))))))) -> 0(0(5(4(1(2(4(2(1(5(4(2(0(5(0(0(0(3(4(1(3(5(3(0(1(0(3(x1))))))))))))))))))))))))))) 1(1(5(4(4(5(0(4(5(1(1(0(3(2(1(3(0(2(1(5(3(2(0(4(5(0(2(x1))))))))))))))))))))))))))) -> 2(3(4(0(1(5(0(5(1(1(2(0(3(4(1(3(0(4(1(5(2(5(0(4(2(5(1(x1))))))))))))))))))))))))))) 1(5(2(4(3(0(1(4(3(5(0(5(0(1(3(2(0(1(4(3(3(2(1(0(1(5(5(x1))))))))))))))))))))))))))) -> 1(5(1(4(1(0(0(3(5(5(0(0(3(0(1(1(4(5(3(2(3(1(2(4(2(5(3(x1))))))))))))))))))))))))))) 0(1(2(5(3(3(1(0(4(1(4(2(0(1(0(4(4(1(0(5(3(2(1(2(5(2(5(1(x1)))))))))))))))))))))))))))) -> 0(1(1(5(3(5(4(0(2(3(0(0(0(4(5(1(4(1(2(1(5(2(1(4(3(2(2(1(x1)))))))))))))))))))))))))))) 0(4(1(4(2(2(4(0(0(3(5(3(0(0(5(0(4(5(5(5(3(2(1(1(0(2(3(1(x1)))))))))))))))))))))))))))) -> 0(1(2(4(1(1(3(0(5(2(3(0(3(0(5(0(4(5(2(4(5(4(1(5(0(2(0(3(x1)))))))))))))))))))))))))))) 2(0(3(1(0(4(3(1(5(2(2(4(1(1(3(0(2(4(2(5(2(2(2(4(1(5(5(1(2(x1))))))))))))))))))))))))))))) -> 2(0(0(2(2(1(5(2(3(1(3(3(1(4(5(2(1(4(2(5(2(2(2(0(5(4(4(1(1(x1))))))))))))))))))))))))))))) 0(5(0(2(3(0(4(0(0(4(3(3(5(0(4(5(4(1(4(0(2(5(5(5(3(1(5(2(2(3(3(x1))))))))))))))))))))))))))))))) -> 2(3(5(3(5(0(4(0(0(0(3(3(4(0(4(1(4(5(3(4(2(5(5(5(5(2(0(0(2(1(3(x1))))))))))))))))))))))))))))))) 1(2(3(5(3(5(0(3(3(3(1(3(1(0(3(3(5(2(0(3(4(4(0(0(4(0(4(0(0(2(2(x1))))))))))))))))))))))))))))))) -> 1(3(3(5(0(5(5(3(4(1(2(3(3(0(0(4(2(1(0(0(0(3(2(3(4(0(3(0(4(3(2(x1))))))))))))))))))))))))))))))) 3(2(4(2(2(3(1(4(1(2(0(1(0(5(2(1(3(0(1(1(2(0(4(0(1(0(3(4(2(1(4(x1))))))))))))))))))))))))))))))) -> 0(2(1(2(1(4(1(3(1(2(4(5(0(0(2(1(1(4(1(3(4(0(1(0(2(3(3(2(0(2(4(x1))))))))))))))))))))))))))))))) 4(0(4(0(4(2(1(5(1(2(3(1(0(0(3(3(4(3(5(4(2(1(5(5(3(4(0(1(3(5(2(x1))))))))))))))))))))))))))))))) -> 4(0(4(3(1(2(3(4(2(5(3(2(0(5(1(3(4(1(0(3(5(1(2(4(1(3(0(4(0(5(5(x1))))))))))))))))))))))))))))))) 2(2(4(3(5(5(4(1(3(0(4(5(5(2(2(3(3(5(2(1(0(3(1(1(0(3(3(3(0(0(1(0(3(x1))))))))))))))))))))))))))))))))) -> 2(4(1(5(1(5(0(4(0(0(0(2(3(2(3(3(2(5(1(5(1(3(3(2(5(3(3(4(3(1(0(0(3(x1))))))))))))))))))))))))))))))))) 2(4(4(0(2(1(3(5(0(0(1(4(4(2(1(1(2(0(0(5(2(2(3(2(5(5(1(0(1(1(3(4(4(5(x1)))))))))))))))))))))))))))))))))) -> 2(4(3(0(5(0(1(1(1(0(2(1(1(2(2(2(4(0(0(4(5(2(4(3(5(5(0(4(1(1(3(4(2(5(x1)))))))))))))))))))))))))))))))))) 5(4(3(5(2(3(5(1(2(2(3(1(3(2(3(2(4(1(0(1(4(5(4(1(4(4(0(1(0(2(5(2(2(0(x1)))))))))))))))))))))))))))))))))) -> 5(4(1(5(2(2(5(3(4(0(5(0(4(2(3(0(0(3(4(5(2(1(4(2(3(4(1(1(2(1(1(2(2(3(x1)))))))))))))))))))))))))))))))))) 0(3(0(4(5(5(5(1(3(0(4(4(3(4(5(2(5(0(0(1(5(0(5(5(0(4(5(1(1(0(4(3(4(5(2(x1))))))))))))))))))))))))))))))))))) -> 0(3(0(0(1(5(5(1(3(4(4(1(4(0(4(5(5(4(2(2(5(5(5(5(0(0(0(1(3(4(5(3(4(5(0(x1))))))))))))))))))))))))))))))))))) 4(2(1(2(2(1(5(1(5(3(0(5(3(5(0(4(4(3(1(2(1(2(0(2(4(4(3(1(1(4(4(5(5(1(2(x1))))))))))))))))))))))))))))))))))) -> 4(1(5(2(2(0(5(3(0(2(2(2(1(5(3(4(1(2(1(5(3(1(0(3(4(4(4(1(1(4(4(5(5(2(1(x1))))))))))))))))))))))))))))))))))) 5(4(4(1(1(3(5(2(2(2(5(3(3(3(0(4(5(3(2(3(0(5(5(1(2(2(0(1(1(3(1(5(0(0(2(x1))))))))))))))))))))))))))))))))))) -> 3(4(5(1(0(2(3(2(3(2(0(3(5(3(1(4(5(2(2(2(0(1(5(5(2(1(1(4(5(3(5(0(0(1(3(x1))))))))))))))))))))))))))))))))))) 0(0(3(0(0(0(3(4(1(4(0(5(2(1(5(2(4(1(1(1(5(2(2(5(3(4(0(0(4(3(1(3(5(4(1(1(x1)))))))))))))))))))))))))))))))))))) -> 0(0(1(4(0(5(0(1(4(4(0(0(2(1(5(3(1(0(1(0(5(2(2(5(3(4(3(1(4(3(3(4(5(1(2(1(x1)))))))))))))))))))))))))))))))))))) 2(1(1(4(3(2(2(4(1(5(3(3(3(3(2(4(4(3(0(1(4(3(2(0(0(2(1(5(2(2(3(0(1(5(1(2(x1)))))))))))))))))))))))))))))))))))) -> 0(3(1(2(3(4(0(2(2(3(1(3(1(3(5(4(4(3(2(1(4(3(4(2(0(1(1(5(2(2(3(0(5(2(1(2(x1)))))))))))))))))))))))))))))))))))) 4(5(4(4(4(0(4(4(5(5(2(0(2(5(0(3(1(4(3(4(3(0(1(4(4(1(0(4(5(4(3(3(1(1(0(5(x1)))))))))))))))))))))))))))))))))))) -> 4(4(4(5(3(1(1(2(5(5(3(4(4(5(1(3(3(4(4(0(0(0(5(0(1(1(0(4(5(2(0(3(4(4(4(4(x1)))))))))))))))))))))))))))))))))))) 0(0(5(5(1(0(1(4(5(2(0(5(2(5(2(1(0(5(1(1(4(5(0(2(1(0(3(4(1(2(5(0(1(4(4(5(3(5(x1)))))))))))))))))))))))))))))))))))))) -> 0(3(4(5(1(0(0(5(1(0(0(5(4(5(0(1(2(5(5(4(4(1(0(2(1(3(2(2(1(0(5(1(5(1(4(5(2(5(x1)))))))))))))))))))))))))))))))))))))) 0(1(3(0(3(1(0(3(0(4(3(0(3(2(1(3(5(0(5(3(0(1(0(1(1(4(3(0(5(1(4(3(3(3(0(0(0(5(3(4(x1)))))))))))))))))))))))))))))))))))))))) -> 0(3(1(0(5(4(0(3(0(4(5(0(5(1(3(3(0(0(3(0(3(1(3(2(1(1(5(4(3(1(1(0(3(3(0(0(3(4(3(0(x1)))))))))))))))))))))))))))))))))))))))) 4(3(3(0(0(0(3(2(4(3(0(0(4(4(2(4(4(2(1(2(5(5(0(0(4(2(5(5(1(0(4(4(5(0(2(3(3(2(4(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) -> 4(2(2(4(0(0(3(2(5(3(4(5(4(0(0(4(0(2(1(0(5(5(2(4(3(3(5(4(1(0(4(4(0(0(4(3(3(2(2(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) 0(1(0(4(0(1(1(1(1(1(0(3(4(3(3(1(4(0(2(0(1(1(0(4(4(3(3(5(0(1(1(0(3(0(4(0(0(4(0(3(1(3(5(3(5(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(3(1(0(1(3(1(0(1(5(3(4(0(3(1(4(0(2(3(1(4(0(5(4(0(3(0(1(1(1(0(0(0(4(0(0(4(1(5(1(1(4(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) 0(2(2(3(1(3(4(0(5(3(3(2(0(2(1(5(0(2(0(3(2(1(4(5(0(4(4(0(2(3(0(1(2(1(2(1(1(5(3(2(3(0(3(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(5(0(3(4(2(5(0(3(2(1(2(1(3(0(1(0(3(4(0(4(4(0(2(2(0(2(3(3(3(2(1(3(1(1(5(2(1(3(5(0(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) 2(2(0(4(5(5(3(5(1(2(3(5(2(5(5(3(3(2(1(1(1(3(1(3(5(3(4(1(5(2(1(1(4(1(1(2(2(3(2(4(2(2(5(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(5(1(3(2(1(3(1(3(2(5(5(3(5(5(1(2(1(3(5(3(1(2(4(0(3(5(4(2(4(1(1(2(2(3(3(2(2(4(5(5(3(x1))))))))))))))))))))))))))))))))))))))))))))) 2(5(0(5(0(1(5(1(3(4(4(3(1(3(3(3(0(5(3(3(0(4(3(3(3(2(4(4(2(2(5(2(4(3(3(5(1(2(1(0(4(1(5(2(3(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(0(5(0(2(5(1(3(3(2(3(1(4(3(2(0(5(3(3(4(4(3(2(3(2(4(1(0(4(5(2(4(3(0(5(1(1(2(3(4(1(5(3(3(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))) 4(5(4(2(3(3(2(4(1(0(3(4(4(3(1(4(0(0(1(4(4(4(5(2(0(4(2(2(2(2(0(4(3(4(3(0(3(2(5(3(3(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(3(2(5(4(2(3(1(4(4(4(4(3(2(4(4(0(1(4(4(2(0(0(3(4(3(2(0(2(0(1(3(4(3(0(3(5(2(3(2(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) 0(3(1(4(5(1(2(2(4(5(1(3(5(3(2(3(0(4(5(2(1(4(4(5(3(1(0(1(1(2(5(3(4(5(5(0(2(3(0(4(1(0(3(3(0(2(4(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(1(4(5(1(5(2(2(5(2(3(4(4(4(3(0(5(4(2(2(3(4(0(5(1(0(0(1(2(1(3(5(5(2(0(5(3(1(4(1(0(3(3(4(1(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(4(4(2(5(4(5(2(1(4(4(2(0(2(3(5(0(3(3(5(0(3(5(0(4(0(0(5(5(2(5(0(4(0(3(2(2(1(5(3(2(4(3(1(5(4(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(2(1(2(0(4(5(5(5(4(4(5(0(0(3(4(0(2(3(4(3(3(1(2(4(5(4(5(2(5(2(0(5(0(3(0(0(1(5(3(2(1(2(1(5(4(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 2(3(1(5(1(2(3(3(3(5(2(1(5(5(3(4(0(5(2(2(2(3(2(3(3(3(3(1(3(2(2(0(2(1(4(1(4(4(3(2(4(4(0(4(2(4(3(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 1(3(2(3(3(2(3(4(2(4(2(0(1(5(3(4(0(5(2(2(1(3(2(1(5(3(3(3(3(2(2(0(2(2(4(4(3(1(5(3(0(4(5(4(2(3(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) 4(5(5(4(4(4(3(3(2(0(1(4(5(3(1(1(5(4(3(0(2(4(2(5(4(2(0(3(4(1(4(2(5(1(5(4(0(4(0(0(2(2(2(0(3(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(5(4(4(5(3(1(2(1(3(4(5(3(3(1(2(4(3(1(4(2(5(4(4(4(0(4(0(0(4(2(0(1(5(2(2(2(0(0(5(2(2(0(3(5(4(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(3(5(2(5(4(0(1(4(5(5(2(1(2(5(4(1(3(1(3(5(3(4(2(5(0(1(3(5(3(3(0(2(2(2(2(5(1(4(5(3(1(4(0(2(1(5(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(3(5(2(5(4(0(5(5(5(4(2(1(3(3(0(1(1(2(3(5(1(4(2(1(5(1(4(0(2(3(0(3(2(2(3(5(1(1(5(3(1(1(4(2(4(5(1(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) 4(0(3(4(1(4(0(4(5(3(0(2(3(4(2(0(5(2(4(1(5(3(0(4(2(5(3(5(1(0(1(1(0(3(5(3(3(4(5(0(4(4(3(3(2(1(1(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(0(4(5(1(0(4(5(3(0(2(3(4(2(0(5(2(4(1(0(3(0(1(1(5(0(3(1(1(4(3(5(2(5(2(5(4(4(3(5(4(3(3(3(4(0(3(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(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(0(2(2(3(x1)))))) -> 0(2(2(1(0(3(x1)))))) 0(4(4(1(0(4(x1)))))) -> 0(4(4(4(0(1(x1)))))) 0(4(0(0(4(2(3(5(1(x1))))))))) -> 5(0(3(2(4(0(0(1(4(x1))))))))) 1(2(3(1(0(1(4(2(0(x1))))))))) -> 4(0(3(2(1(1(2(1(0(x1))))))))) 1(3(4(0(4(1(1(2(3(5(4(4(x1)))))))))))) -> 2(4(4(0(1(3(5(1(4(3(4(1(x1)))))))))))) 4(1(1(3(3(0(1(5(0(4(4(2(2(3(3(5(4(3(x1)))))))))))))))))) -> 4(0(4(2(4(3(1(3(4(3(5(1(2(0(3(5(1(3(x1)))))))))))))))))) 1(0(4(3(1(2(1(2(0(4(3(3(2(1(5(2(3(2(1(x1))))))))))))))))))) -> 1(4(2(1(1(4(1(0(3(0(5(3(1(3(2(2(3(2(2(x1))))))))))))))))))) 1(1(1(3(0(4(5(0(3(0(1(1(3(0(4(5(3(3(0(x1))))))))))))))))))) -> 4(5(0(3(3(4(1(0(0(1(1(1(3(1(0(3(5(3(0(x1))))))))))))))))))) 1(3(2(3(0(5(0(4(1(1(2(4(4(3(3(5(4(0(5(x1))))))))))))))))))) -> 4(2(1(2(5(3(4(1(1(3(0(0(3(3(4(0(5(4(5(x1))))))))))))))))))) 3(0(2(2(0(1(1(5(0(1(1(1(0(2(0(4(5(0(1(x1))))))))))))))))))) -> 5(1(2(1(4(0(0(3(0(1(0(0(1(0(1(2(5(1(2(x1))))))))))))))))))) 0(2(1(5(4(1(5(4(0(1(2(0(2(1(2(1(1(1(3(5(2(5(x1)))))))))))))))))))))) -> 2(1(1(3(5(4(2(5(0(5(2(1(1(1(2(1(4(0(2(0(5(1(x1)))))))))))))))))))))) 2(2(5(3(3(3(0(4(1(3(5(4(5(1(3(4(1(0(3(5(4(0(x1)))))))))))))))))))))) -> 0(1(5(3(4(1(3(5(3(3(1(3(4(5(3(4(4(0(2(2(5(0(x1)))))))))))))))))))))) 2(5(5(1(4(3(3(2(1(1(1(5(0(4(4(3(5(1(4(1(4(5(2(x1))))))))))))))))))))))) -> 3(4(5(1(4(4(5(2(1(5(5(5(0(1(2(1(1(1(3(4(3(4(2(x1))))))))))))))))))))))) 3(4(0(2(2(3(2(4(2(3(5(3(5(0(1(3(5(5(2(4(4(2(3(3(x1)))))))))))))))))))))))) -> 5(5(3(2(2(2(0(5(4(3(3(3(2(0(2(4(2(1(5(3(4(3(4(3(x1)))))))))))))))))))))))) 5(5(2(0(2(1(5(5(2(1(4(4(5(2(4(4(1(1(1(3(2(5(5(5(x1)))))))))))))))))))))))) -> 5(4(5(0(5(4(2(1(2(4(1(1(2(1(2(4(5(3(1(5(2(5(5(5(x1)))))))))))))))))))))))) 1(5(2(4(1(3(3(5(3(0(4(2(5(1(5(2(0(1(0(3(0(5(5(1(4(x1))))))))))))))))))))))))) -> 1(5(2(3(1(5(4(5(5(2(3(4(2(3(5(4(1(1(3(0(0(1(0(5(0(x1))))))))))))))))))))))))) 3(1(5(1(0(4(4(1(1(2(2(0(2(3(3(2(2(3(3(5(4(1(2(5(1(x1))))))))))))))))))))))))) -> 1(3(0(3(5(5(2(1(2(3(2(5(2(3(1(0(2(1(3(1(4(1(2(4(4(x1))))))))))))))))))))))))) 0(0(1(4(0(0(4(2(1(5(5(3(0(3(4(0(1(4(3(1(5(5(2(0(0(2(3(x1))))))))))))))))))))))))))) -> 0(0(5(4(1(2(4(2(1(5(4(2(0(5(0(0(0(3(4(1(3(5(3(0(1(0(3(x1))))))))))))))))))))))))))) 1(1(5(4(4(5(0(4(5(1(1(0(3(2(1(3(0(2(1(5(3(2(0(4(5(0(2(x1))))))))))))))))))))))))))) -> 2(3(4(0(1(5(0(5(1(1(2(0(3(4(1(3(0(4(1(5(2(5(0(4(2(5(1(x1))))))))))))))))))))))))))) 1(5(2(4(3(0(1(4(3(5(0(5(0(1(3(2(0(1(4(3(3(2(1(0(1(5(5(x1))))))))))))))))))))))))))) -> 1(5(1(4(1(0(0(3(5(5(0(0(3(0(1(1(4(5(3(2(3(1(2(4(2(5(3(x1))))))))))))))))))))))))))) 0(1(2(5(3(3(1(0(4(1(4(2(0(1(0(4(4(1(0(5(3(2(1(2(5(2(5(1(x1)))))))))))))))))))))))))))) -> 0(1(1(5(3(5(4(0(2(3(0(0(0(4(5(1(4(1(2(1(5(2(1(4(3(2(2(1(x1)))))))))))))))))))))))))))) 0(4(1(4(2(2(4(0(0(3(5(3(0(0(5(0(4(5(5(5(3(2(1(1(0(2(3(1(x1)))))))))))))))))))))))))))) -> 0(1(2(4(1(1(3(0(5(2(3(0(3(0(5(0(4(5(2(4(5(4(1(5(0(2(0(3(x1)))))))))))))))))))))))))))) 2(0(3(1(0(4(3(1(5(2(2(4(1(1(3(0(2(4(2(5(2(2(2(4(1(5(5(1(2(x1))))))))))))))))))))))))))))) -> 2(0(0(2(2(1(5(2(3(1(3(3(1(4(5(2(1(4(2(5(2(2(2(0(5(4(4(1(1(x1))))))))))))))))))))))))))))) 0(5(0(2(3(0(4(0(0(4(3(3(5(0(4(5(4(1(4(0(2(5(5(5(3(1(5(2(2(3(3(x1))))))))))))))))))))))))))))))) -> 2(3(5(3(5(0(4(0(0(0(3(3(4(0(4(1(4(5(3(4(2(5(5(5(5(2(0(0(2(1(3(x1))))))))))))))))))))))))))))))) 1(2(3(5(3(5(0(3(3(3(1(3(1(0(3(3(5(2(0(3(4(4(0(0(4(0(4(0(0(2(2(x1))))))))))))))))))))))))))))))) -> 1(3(3(5(0(5(5(3(4(1(2(3(3(0(0(4(2(1(0(0(0(3(2(3(4(0(3(0(4(3(2(x1))))))))))))))))))))))))))))))) 3(2(4(2(2(3(1(4(1(2(0(1(0(5(2(1(3(0(1(1(2(0(4(0(1(0(3(4(2(1(4(x1))))))))))))))))))))))))))))))) -> 0(2(1(2(1(4(1(3(1(2(4(5(0(0(2(1(1(4(1(3(4(0(1(0(2(3(3(2(0(2(4(x1))))))))))))))))))))))))))))))) 4(0(4(0(4(2(1(5(1(2(3(1(0(0(3(3(4(3(5(4(2(1(5(5(3(4(0(1(3(5(2(x1))))))))))))))))))))))))))))))) -> 4(0(4(3(1(2(3(4(2(5(3(2(0(5(1(3(4(1(0(3(5(1(2(4(1(3(0(4(0(5(5(x1))))))))))))))))))))))))))))))) 2(2(4(3(5(5(4(1(3(0(4(5(5(2(2(3(3(5(2(1(0(3(1(1(0(3(3(3(0(0(1(0(3(x1))))))))))))))))))))))))))))))))) -> 2(4(1(5(1(5(0(4(0(0(0(2(3(2(3(3(2(5(1(5(1(3(3(2(5(3(3(4(3(1(0(0(3(x1))))))))))))))))))))))))))))))))) 2(4(4(0(2(1(3(5(0(0(1(4(4(2(1(1(2(0(0(5(2(2(3(2(5(5(1(0(1(1(3(4(4(5(x1)))))))))))))))))))))))))))))))))) -> 2(4(3(0(5(0(1(1(1(0(2(1(1(2(2(2(4(0(0(4(5(2(4(3(5(5(0(4(1(1(3(4(2(5(x1)))))))))))))))))))))))))))))))))) 5(4(3(5(2(3(5(1(2(2(3(1(3(2(3(2(4(1(0(1(4(5(4(1(4(4(0(1(0(2(5(2(2(0(x1)))))))))))))))))))))))))))))))))) -> 5(4(1(5(2(2(5(3(4(0(5(0(4(2(3(0(0(3(4(5(2(1(4(2(3(4(1(1(2(1(1(2(2(3(x1)))))))))))))))))))))))))))))))))) 0(3(0(4(5(5(5(1(3(0(4(4(3(4(5(2(5(0(0(1(5(0(5(5(0(4(5(1(1(0(4(3(4(5(2(x1))))))))))))))))))))))))))))))))))) -> 0(3(0(0(1(5(5(1(3(4(4(1(4(0(4(5(5(4(2(2(5(5(5(5(0(0(0(1(3(4(5(3(4(5(0(x1))))))))))))))))))))))))))))))))))) 4(2(1(2(2(1(5(1(5(3(0(5(3(5(0(4(4(3(1(2(1(2(0(2(4(4(3(1(1(4(4(5(5(1(2(x1))))))))))))))))))))))))))))))))))) -> 4(1(5(2(2(0(5(3(0(2(2(2(1(5(3(4(1(2(1(5(3(1(0(3(4(4(4(1(1(4(4(5(5(2(1(x1))))))))))))))))))))))))))))))))))) 5(4(4(1(1(3(5(2(2(2(5(3(3(3(0(4(5(3(2(3(0(5(5(1(2(2(0(1(1(3(1(5(0(0(2(x1))))))))))))))))))))))))))))))))))) -> 3(4(5(1(0(2(3(2(3(2(0(3(5(3(1(4(5(2(2(2(0(1(5(5(2(1(1(4(5(3(5(0(0(1(3(x1))))))))))))))))))))))))))))))))))) 0(0(3(0(0(0(3(4(1(4(0(5(2(1(5(2(4(1(1(1(5(2(2(5(3(4(0(0(4(3(1(3(5(4(1(1(x1)))))))))))))))))))))))))))))))))))) -> 0(0(1(4(0(5(0(1(4(4(0(0(2(1(5(3(1(0(1(0(5(2(2(5(3(4(3(1(4(3(3(4(5(1(2(1(x1)))))))))))))))))))))))))))))))))))) 2(1(1(4(3(2(2(4(1(5(3(3(3(3(2(4(4(3(0(1(4(3(2(0(0(2(1(5(2(2(3(0(1(5(1(2(x1)))))))))))))))))))))))))))))))))))) -> 0(3(1(2(3(4(0(2(2(3(1(3(1(3(5(4(4(3(2(1(4(3(4(2(0(1(1(5(2(2(3(0(5(2(1(2(x1)))))))))))))))))))))))))))))))))))) 4(5(4(4(4(0(4(4(5(5(2(0(2(5(0(3(1(4(3(4(3(0(1(4(4(1(0(4(5(4(3(3(1(1(0(5(x1)))))))))))))))))))))))))))))))))))) -> 4(4(4(5(3(1(1(2(5(5(3(4(4(5(1(3(3(4(4(0(0(0(5(0(1(1(0(4(5(2(0(3(4(4(4(4(x1)))))))))))))))))))))))))))))))))))) 0(0(5(5(1(0(1(4(5(2(0(5(2(5(2(1(0(5(1(1(4(5(0(2(1(0(3(4(1(2(5(0(1(4(4(5(3(5(x1)))))))))))))))))))))))))))))))))))))) -> 0(3(4(5(1(0(0(5(1(0(0(5(4(5(0(1(2(5(5(4(4(1(0(2(1(3(2(2(1(0(5(1(5(1(4(5(2(5(x1)))))))))))))))))))))))))))))))))))))) 0(1(3(0(3(1(0(3(0(4(3(0(3(2(1(3(5(0(5(3(0(1(0(1(1(4(3(0(5(1(4(3(3(3(0(0(0(5(3(4(x1)))))))))))))))))))))))))))))))))))))))) -> 0(3(1(0(5(4(0(3(0(4(5(0(5(1(3(3(0(0(3(0(3(1(3(2(1(1(5(4(3(1(1(0(3(3(0(0(3(4(3(0(x1)))))))))))))))))))))))))))))))))))))))) 4(3(3(0(0(0(3(2(4(3(0(0(4(4(2(4(4(2(1(2(5(5(0(0(4(2(5(5(1(0(4(4(5(0(2(3(3(2(4(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) -> 4(2(2(4(0(0(3(2(5(3(4(5(4(0(0(4(0(2(1(0(5(5(2(4(3(3(5(4(1(0(4(4(0(0(4(3(3(2(2(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) 0(1(0(4(0(1(1(1(1(1(0(3(4(3(3(1(4(0(2(0(1(1(0(4(4(3(3(5(0(1(1(0(3(0(4(0(0(4(0(3(1(3(5(3(5(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(3(1(0(1(3(1(0(1(5(3(4(0(3(1(4(0(2(3(1(4(0(5(4(0(3(0(1(1(1(0(0(0(4(0(0(4(1(5(1(1(4(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) 0(2(2(3(1(3(4(0(5(3(3(2(0(2(1(5(0(2(0(3(2(1(4(5(0(4(4(0(2(3(0(1(2(1(2(1(1(5(3(2(3(0(3(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(5(0(3(4(2(5(0(3(2(1(2(1(3(0(1(0(3(4(0(4(4(0(2(2(0(2(3(3(3(2(1(3(1(1(5(2(1(3(5(0(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) 2(2(0(4(5(5(3(5(1(2(3(5(2(5(5(3(3(2(1(1(1(3(1(3(5(3(4(1(5(2(1(1(4(1(1(2(2(3(2(4(2(2(5(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(5(1(3(2(1(3(1(3(2(5(5(3(5(5(1(2(1(3(5(3(1(2(4(0(3(5(4(2(4(1(1(2(2(3(3(2(2(4(5(5(3(x1))))))))))))))))))))))))))))))))))))))))))))) 2(5(0(5(0(1(5(1(3(4(4(3(1(3(3(3(0(5(3(3(0(4(3(3(3(2(4(4(2(2(5(2(4(3(3(5(1(2(1(0(4(1(5(2(3(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(0(5(0(2(5(1(3(3(2(3(1(4(3(2(0(5(3(3(4(4(3(2(3(2(4(1(0(4(5(2(4(3(0(5(1(1(2(3(4(1(5(3(3(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))) 4(5(4(2(3(3(2(4(1(0(3(4(4(3(1(4(0(0(1(4(4(4(5(2(0(4(2(2(2(2(0(4(3(4(3(0(3(2(5(3(3(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(3(2(5(4(2(3(1(4(4(4(4(3(2(4(4(0(1(4(4(2(0(0(3(4(3(2(0(2(0(1(3(4(3(0(3(5(2(3(2(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) 0(3(1(4(5(1(2(2(4(5(1(3(5(3(2(3(0(4(5(2(1(4(4(5(3(1(0(1(1(2(5(3(4(5(5(0(2(3(0(4(1(0(3(3(0(2(4(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(1(4(5(1(5(2(2(5(2(3(4(4(4(3(0(5(4(2(2(3(4(0(5(1(0(0(1(2(1(3(5(5(2(0(5(3(1(4(1(0(3(3(4(1(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(4(4(2(5(4(5(2(1(4(4(2(0(2(3(5(0(3(3(5(0(3(5(0(4(0(0(5(5(2(5(0(4(0(3(2(2(1(5(3(2(4(3(1(5(4(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(2(1(2(0(4(5(5(5(4(4(5(0(0(3(4(0(2(3(4(3(3(1(2(4(5(4(5(2(5(2(0(5(0(3(0(0(1(5(3(2(1(2(1(5(4(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 2(3(1(5(1(2(3(3(3(5(2(1(5(5(3(4(0(5(2(2(2(3(2(3(3(3(3(1(3(2(2(0(2(1(4(1(4(4(3(2(4(4(0(4(2(4(3(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 1(3(2(3(3(2(3(4(2(4(2(0(1(5(3(4(0(5(2(2(1(3(2(1(5(3(3(3(3(2(2(0(2(2(4(4(3(1(5(3(0(4(5(4(2(3(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) 4(5(5(4(4(4(3(3(2(0(1(4(5(3(1(1(5(4(3(0(2(4(2(5(4(2(0(3(4(1(4(2(5(1(5(4(0(4(0(0(2(2(2(0(3(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(5(4(4(5(3(1(2(1(3(4(5(3(3(1(2(4(3(1(4(2(5(4(4(4(0(4(0(0(4(2(0(1(5(2(2(2(0(0(5(2(2(0(3(5(4(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(3(5(2(5(4(0(1(4(5(5(2(1(2(5(4(1(3(1(3(5(3(4(2(5(0(1(3(5(3(3(0(2(2(2(2(5(1(4(5(3(1(4(0(2(1(5(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(3(5(2(5(4(0(5(5(5(4(2(1(3(3(0(1(1(2(3(5(1(4(2(1(5(1(4(0(2(3(0(3(2(2(3(5(1(1(5(3(1(1(4(2(4(5(1(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) 4(0(3(4(1(4(0(4(5(3(0(2(3(4(2(0(5(2(4(1(5(3(0(4(2(5(3(5(1(0(1(1(0(3(5(3(3(4(5(0(4(4(3(3(2(1(1(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(0(4(5(1(0(4(5(3(0(2(3(4(2(0(5(2(4(1(0(3(0(1(1(5(0(3(1(1(4(3(5(2(5(2(5(4(4(3(5(4(3(3(3(4(0(3(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(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(0(2(2(3(x1)))))) -> 0(2(2(1(0(3(x1)))))) 0(4(4(1(0(4(x1)))))) -> 0(4(4(4(0(1(x1)))))) 0(4(0(0(4(2(3(5(1(x1))))))))) -> 5(0(3(2(4(0(0(1(4(x1))))))))) 1(2(3(1(0(1(4(2(0(x1))))))))) -> 4(0(3(2(1(1(2(1(0(x1))))))))) 1(3(4(0(4(1(1(2(3(5(4(4(x1)))))))))))) -> 2(4(4(0(1(3(5(1(4(3(4(1(x1)))))))))))) 4(1(1(3(3(0(1(5(0(4(4(2(2(3(3(5(4(3(x1)))))))))))))))))) -> 4(0(4(2(4(3(1(3(4(3(5(1(2(0(3(5(1(3(x1)))))))))))))))))) 1(0(4(3(1(2(1(2(0(4(3(3(2(1(5(2(3(2(1(x1))))))))))))))))))) -> 1(4(2(1(1(4(1(0(3(0(5(3(1(3(2(2(3(2(2(x1))))))))))))))))))) 1(1(1(3(0(4(5(0(3(0(1(1(3(0(4(5(3(3(0(x1))))))))))))))))))) -> 4(5(0(3(3(4(1(0(0(1(1(1(3(1(0(3(5(3(0(x1))))))))))))))))))) 1(3(2(3(0(5(0(4(1(1(2(4(4(3(3(5(4(0(5(x1))))))))))))))))))) -> 4(2(1(2(5(3(4(1(1(3(0(0(3(3(4(0(5(4(5(x1))))))))))))))))))) 3(0(2(2(0(1(1(5(0(1(1(1(0(2(0(4(5(0(1(x1))))))))))))))))))) -> 5(1(2(1(4(0(0(3(0(1(0(0(1(0(1(2(5(1(2(x1))))))))))))))))))) 0(2(1(5(4(1(5(4(0(1(2(0(2(1(2(1(1(1(3(5(2(5(x1)))))))))))))))))))))) -> 2(1(1(3(5(4(2(5(0(5(2(1(1(1(2(1(4(0(2(0(5(1(x1)))))))))))))))))))))) 2(2(5(3(3(3(0(4(1(3(5(4(5(1(3(4(1(0(3(5(4(0(x1)))))))))))))))))))))) -> 0(1(5(3(4(1(3(5(3(3(1(3(4(5(3(4(4(0(2(2(5(0(x1)))))))))))))))))))))) 2(5(5(1(4(3(3(2(1(1(1(5(0(4(4(3(5(1(4(1(4(5(2(x1))))))))))))))))))))))) -> 3(4(5(1(4(4(5(2(1(5(5(5(0(1(2(1(1(1(3(4(3(4(2(x1))))))))))))))))))))))) 3(4(0(2(2(3(2(4(2(3(5(3(5(0(1(3(5(5(2(4(4(2(3(3(x1)))))))))))))))))))))))) -> 5(5(3(2(2(2(0(5(4(3(3(3(2(0(2(4(2(1(5(3(4(3(4(3(x1)))))))))))))))))))))))) 5(5(2(0(2(1(5(5(2(1(4(4(5(2(4(4(1(1(1(3(2(5(5(5(x1)))))))))))))))))))))))) -> 5(4(5(0(5(4(2(1(2(4(1(1(2(1(2(4(5(3(1(5(2(5(5(5(x1)))))))))))))))))))))))) 1(5(2(4(1(3(3(5(3(0(4(2(5(1(5(2(0(1(0(3(0(5(5(1(4(x1))))))))))))))))))))))))) -> 1(5(2(3(1(5(4(5(5(2(3(4(2(3(5(4(1(1(3(0(0(1(0(5(0(x1))))))))))))))))))))))))) 3(1(5(1(0(4(4(1(1(2(2(0(2(3(3(2(2(3(3(5(4(1(2(5(1(x1))))))))))))))))))))))))) -> 1(3(0(3(5(5(2(1(2(3(2(5(2(3(1(0(2(1(3(1(4(1(2(4(4(x1))))))))))))))))))))))))) 0(0(1(4(0(0(4(2(1(5(5(3(0(3(4(0(1(4(3(1(5(5(2(0(0(2(3(x1))))))))))))))))))))))))))) -> 0(0(5(4(1(2(4(2(1(5(4(2(0(5(0(0(0(3(4(1(3(5(3(0(1(0(3(x1))))))))))))))))))))))))))) 1(1(5(4(4(5(0(4(5(1(1(0(3(2(1(3(0(2(1(5(3(2(0(4(5(0(2(x1))))))))))))))))))))))))))) -> 2(3(4(0(1(5(0(5(1(1(2(0(3(4(1(3(0(4(1(5(2(5(0(4(2(5(1(x1))))))))))))))))))))))))))) 1(5(2(4(3(0(1(4(3(5(0(5(0(1(3(2(0(1(4(3(3(2(1(0(1(5(5(x1))))))))))))))))))))))))))) -> 1(5(1(4(1(0(0(3(5(5(0(0(3(0(1(1(4(5(3(2(3(1(2(4(2(5(3(x1))))))))))))))))))))))))))) 0(1(2(5(3(3(1(0(4(1(4(2(0(1(0(4(4(1(0(5(3(2(1(2(5(2(5(1(x1)))))))))))))))))))))))))))) -> 0(1(1(5(3(5(4(0(2(3(0(0(0(4(5(1(4(1(2(1(5(2(1(4(3(2(2(1(x1)))))))))))))))))))))))))))) 0(4(1(4(2(2(4(0(0(3(5(3(0(0(5(0(4(5(5(5(3(2(1(1(0(2(3(1(x1)))))))))))))))))))))))))))) -> 0(1(2(4(1(1(3(0(5(2(3(0(3(0(5(0(4(5(2(4(5(4(1(5(0(2(0(3(x1)))))))))))))))))))))))))))) 2(0(3(1(0(4(3(1(5(2(2(4(1(1(3(0(2(4(2(5(2(2(2(4(1(5(5(1(2(x1))))))))))))))))))))))))))))) -> 2(0(0(2(2(1(5(2(3(1(3(3(1(4(5(2(1(4(2(5(2(2(2(0(5(4(4(1(1(x1))))))))))))))))))))))))))))) 0(5(0(2(3(0(4(0(0(4(3(3(5(0(4(5(4(1(4(0(2(5(5(5(3(1(5(2(2(3(3(x1))))))))))))))))))))))))))))))) -> 2(3(5(3(5(0(4(0(0(0(3(3(4(0(4(1(4(5(3(4(2(5(5(5(5(2(0(0(2(1(3(x1))))))))))))))))))))))))))))))) 1(2(3(5(3(5(0(3(3(3(1(3(1(0(3(3(5(2(0(3(4(4(0(0(4(0(4(0(0(2(2(x1))))))))))))))))))))))))))))))) -> 1(3(3(5(0(5(5(3(4(1(2(3(3(0(0(4(2(1(0(0(0(3(2(3(4(0(3(0(4(3(2(x1))))))))))))))))))))))))))))))) 3(2(4(2(2(3(1(4(1(2(0(1(0(5(2(1(3(0(1(1(2(0(4(0(1(0(3(4(2(1(4(x1))))))))))))))))))))))))))))))) -> 0(2(1(2(1(4(1(3(1(2(4(5(0(0(2(1(1(4(1(3(4(0(1(0(2(3(3(2(0(2(4(x1))))))))))))))))))))))))))))))) 4(0(4(0(4(2(1(5(1(2(3(1(0(0(3(3(4(3(5(4(2(1(5(5(3(4(0(1(3(5(2(x1))))))))))))))))))))))))))))))) -> 4(0(4(3(1(2(3(4(2(5(3(2(0(5(1(3(4(1(0(3(5(1(2(4(1(3(0(4(0(5(5(x1))))))))))))))))))))))))))))))) 2(2(4(3(5(5(4(1(3(0(4(5(5(2(2(3(3(5(2(1(0(3(1(1(0(3(3(3(0(0(1(0(3(x1))))))))))))))))))))))))))))))))) -> 2(4(1(5(1(5(0(4(0(0(0(2(3(2(3(3(2(5(1(5(1(3(3(2(5(3(3(4(3(1(0(0(3(x1))))))))))))))))))))))))))))))))) 2(4(4(0(2(1(3(5(0(0(1(4(4(2(1(1(2(0(0(5(2(2(3(2(5(5(1(0(1(1(3(4(4(5(x1)))))))))))))))))))))))))))))))))) -> 2(4(3(0(5(0(1(1(1(0(2(1(1(2(2(2(4(0(0(4(5(2(4(3(5(5(0(4(1(1(3(4(2(5(x1)))))))))))))))))))))))))))))))))) 5(4(3(5(2(3(5(1(2(2(3(1(3(2(3(2(4(1(0(1(4(5(4(1(4(4(0(1(0(2(5(2(2(0(x1)))))))))))))))))))))))))))))))))) -> 5(4(1(5(2(2(5(3(4(0(5(0(4(2(3(0(0(3(4(5(2(1(4(2(3(4(1(1(2(1(1(2(2(3(x1)))))))))))))))))))))))))))))))))) 0(3(0(4(5(5(5(1(3(0(4(4(3(4(5(2(5(0(0(1(5(0(5(5(0(4(5(1(1(0(4(3(4(5(2(x1))))))))))))))))))))))))))))))))))) -> 0(3(0(0(1(5(5(1(3(4(4(1(4(0(4(5(5(4(2(2(5(5(5(5(0(0(0(1(3(4(5(3(4(5(0(x1))))))))))))))))))))))))))))))))))) 4(2(1(2(2(1(5(1(5(3(0(5(3(5(0(4(4(3(1(2(1(2(0(2(4(4(3(1(1(4(4(5(5(1(2(x1))))))))))))))))))))))))))))))))))) -> 4(1(5(2(2(0(5(3(0(2(2(2(1(5(3(4(1(2(1(5(3(1(0(3(4(4(4(1(1(4(4(5(5(2(1(x1))))))))))))))))))))))))))))))))))) 5(4(4(1(1(3(5(2(2(2(5(3(3(3(0(4(5(3(2(3(0(5(5(1(2(2(0(1(1(3(1(5(0(0(2(x1))))))))))))))))))))))))))))))))))) -> 3(4(5(1(0(2(3(2(3(2(0(3(5(3(1(4(5(2(2(2(0(1(5(5(2(1(1(4(5(3(5(0(0(1(3(x1))))))))))))))))))))))))))))))))))) 0(0(3(0(0(0(3(4(1(4(0(5(2(1(5(2(4(1(1(1(5(2(2(5(3(4(0(0(4(3(1(3(5(4(1(1(x1)))))))))))))))))))))))))))))))))))) -> 0(0(1(4(0(5(0(1(4(4(0(0(2(1(5(3(1(0(1(0(5(2(2(5(3(4(3(1(4(3(3(4(5(1(2(1(x1)))))))))))))))))))))))))))))))))))) 2(1(1(4(3(2(2(4(1(5(3(3(3(3(2(4(4(3(0(1(4(3(2(0(0(2(1(5(2(2(3(0(1(5(1(2(x1)))))))))))))))))))))))))))))))))))) -> 0(3(1(2(3(4(0(2(2(3(1(3(1(3(5(4(4(3(2(1(4(3(4(2(0(1(1(5(2(2(3(0(5(2(1(2(x1)))))))))))))))))))))))))))))))))))) 4(5(4(4(4(0(4(4(5(5(2(0(2(5(0(3(1(4(3(4(3(0(1(4(4(1(0(4(5(4(3(3(1(1(0(5(x1)))))))))))))))))))))))))))))))))))) -> 4(4(4(5(3(1(1(2(5(5(3(4(4(5(1(3(3(4(4(0(0(0(5(0(1(1(0(4(5(2(0(3(4(4(4(4(x1)))))))))))))))))))))))))))))))))))) 0(0(5(5(1(0(1(4(5(2(0(5(2(5(2(1(0(5(1(1(4(5(0(2(1(0(3(4(1(2(5(0(1(4(4(5(3(5(x1)))))))))))))))))))))))))))))))))))))) -> 0(3(4(5(1(0(0(5(1(0(0(5(4(5(0(1(2(5(5(4(4(1(0(2(1(3(2(2(1(0(5(1(5(1(4(5(2(5(x1)))))))))))))))))))))))))))))))))))))) 0(1(3(0(3(1(0(3(0(4(3(0(3(2(1(3(5(0(5(3(0(1(0(1(1(4(3(0(5(1(4(3(3(3(0(0(0(5(3(4(x1)))))))))))))))))))))))))))))))))))))))) -> 0(3(1(0(5(4(0(3(0(4(5(0(5(1(3(3(0(0(3(0(3(1(3(2(1(1(5(4(3(1(1(0(3(3(0(0(3(4(3(0(x1)))))))))))))))))))))))))))))))))))))))) 4(3(3(0(0(0(3(2(4(3(0(0(4(4(2(4(4(2(1(2(5(5(0(0(4(2(5(5(1(0(4(4(5(0(2(3(3(2(4(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) -> 4(2(2(4(0(0(3(2(5(3(4(5(4(0(0(4(0(2(1(0(5(5(2(4(3(3(5(4(1(0(4(4(0(0(4(3(3(2(2(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) 0(1(0(4(0(1(1(1(1(1(0(3(4(3(3(1(4(0(2(0(1(1(0(4(4(3(3(5(0(1(1(0(3(0(4(0(0(4(0(3(1(3(5(3(5(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(3(1(0(1(3(1(0(1(5(3(4(0(3(1(4(0(2(3(1(4(0(5(4(0(3(0(1(1(1(0(0(0(4(0(0(4(1(5(1(1(4(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) 0(2(2(3(1(3(4(0(5(3(3(2(0(2(1(5(0(2(0(3(2(1(4(5(0(4(4(0(2(3(0(1(2(1(2(1(1(5(3(2(3(0(3(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(5(0(3(4(2(5(0(3(2(1(2(1(3(0(1(0(3(4(0(4(4(0(2(2(0(2(3(3(3(2(1(3(1(1(5(2(1(3(5(0(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) 2(2(0(4(5(5(3(5(1(2(3(5(2(5(5(3(3(2(1(1(1(3(1(3(5(3(4(1(5(2(1(1(4(1(1(2(2(3(2(4(2(2(5(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(5(1(3(2(1(3(1(3(2(5(5(3(5(5(1(2(1(3(5(3(1(2(4(0(3(5(4(2(4(1(1(2(2(3(3(2(2(4(5(5(3(x1))))))))))))))))))))))))))))))))))))))))))))) 2(5(0(5(0(1(5(1(3(4(4(3(1(3(3(3(0(5(3(3(0(4(3(3(3(2(4(4(2(2(5(2(4(3(3(5(1(2(1(0(4(1(5(2(3(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(0(5(0(2(5(1(3(3(2(3(1(4(3(2(0(5(3(3(4(4(3(2(3(2(4(1(0(4(5(2(4(3(0(5(1(1(2(3(4(1(5(3(3(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))) 4(5(4(2(3(3(2(4(1(0(3(4(4(3(1(4(0(0(1(4(4(4(5(2(0(4(2(2(2(2(0(4(3(4(3(0(3(2(5(3(3(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(3(2(5(4(2(3(1(4(4(4(4(3(2(4(4(0(1(4(4(2(0(0(3(4(3(2(0(2(0(1(3(4(3(0(3(5(2(3(2(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) 0(3(1(4(5(1(2(2(4(5(1(3(5(3(2(3(0(4(5(2(1(4(4(5(3(1(0(1(1(2(5(3(4(5(5(0(2(3(0(4(1(0(3(3(0(2(4(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(1(4(5(1(5(2(2(5(2(3(4(4(4(3(0(5(4(2(2(3(4(0(5(1(0(0(1(2(1(3(5(5(2(0(5(3(1(4(1(0(3(3(4(1(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(4(4(2(5(4(5(2(1(4(4(2(0(2(3(5(0(3(3(5(0(3(5(0(4(0(0(5(5(2(5(0(4(0(3(2(2(1(5(3(2(4(3(1(5(4(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(2(1(2(0(4(5(5(5(4(4(5(0(0(3(4(0(2(3(4(3(3(1(2(4(5(4(5(2(5(2(0(5(0(3(0(0(1(5(3(2(1(2(1(5(4(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 2(3(1(5(1(2(3(3(3(5(2(1(5(5(3(4(0(5(2(2(2(3(2(3(3(3(3(1(3(2(2(0(2(1(4(1(4(4(3(2(4(4(0(4(2(4(3(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 1(3(2(3(3(2(3(4(2(4(2(0(1(5(3(4(0(5(2(2(1(3(2(1(5(3(3(3(3(2(2(0(2(2(4(4(3(1(5(3(0(4(5(4(2(3(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) 4(5(5(4(4(4(3(3(2(0(1(4(5(3(1(1(5(4(3(0(2(4(2(5(4(2(0(3(4(1(4(2(5(1(5(4(0(4(0(0(2(2(2(0(3(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(5(4(4(5(3(1(2(1(3(4(5(3(3(1(2(4(3(1(4(2(5(4(4(4(0(4(0(0(4(2(0(1(5(2(2(2(0(0(5(2(2(0(3(5(4(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(3(5(2(5(4(0(1(4(5(5(2(1(2(5(4(1(3(1(3(5(3(4(2(5(0(1(3(5(3(3(0(2(2(2(2(5(1(4(5(3(1(4(0(2(1(5(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(3(5(2(5(4(0(5(5(5(4(2(1(3(3(0(1(1(2(3(5(1(4(2(1(5(1(4(0(2(3(0(3(2(2(3(5(1(1(5(3(1(1(4(2(4(5(1(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) 4(0(3(4(1(4(0(4(5(3(0(2(3(4(2(0(5(2(4(1(5(3(0(4(2(5(3(5(1(0(1(1(0(3(5(3(3(4(5(0(4(4(3(3(2(1(1(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(0(4(5(1(0(4(5(3(0(2(3(4(2(0(5(2(4(1(0(3(0(1(1(5(0(3(1(1(4(3(5(2(5(2(5(4(4(3(5(4(3(3(3(4(0(3(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_4(x_1)) -> 4(encArg(x_1)) encArg(cons_3(x_1)) -> 3(encArg(x_1)) encArg(cons_2(x_1)) -> 2(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(0(2(2(3(x1)))))) -> 0(2(2(1(0(3(x1)))))) 0(4(4(1(0(4(x1)))))) -> 0(4(4(4(0(1(x1)))))) 0(4(0(0(4(2(3(5(1(x1))))))))) -> 5(0(3(2(4(0(0(1(4(x1))))))))) 1(2(3(1(0(1(4(2(0(x1))))))))) -> 4(0(3(2(1(1(2(1(0(x1))))))))) 1(3(4(0(4(1(1(2(3(5(4(4(x1)))))))))))) -> 2(4(4(0(1(3(5(1(4(3(4(1(x1)))))))))))) 4(1(1(3(3(0(1(5(0(4(4(2(2(3(3(5(4(3(x1)))))))))))))))))) -> 4(0(4(2(4(3(1(3(4(3(5(1(2(0(3(5(1(3(x1)))))))))))))))))) 1(0(4(3(1(2(1(2(0(4(3(3(2(1(5(2(3(2(1(x1))))))))))))))))))) -> 1(4(2(1(1(4(1(0(3(0(5(3(1(3(2(2(3(2(2(x1))))))))))))))))))) 1(1(1(3(0(4(5(0(3(0(1(1(3(0(4(5(3(3(0(x1))))))))))))))))))) -> 4(5(0(3(3(4(1(0(0(1(1(1(3(1(0(3(5(3(0(x1))))))))))))))))))) 1(3(2(3(0(5(0(4(1(1(2(4(4(3(3(5(4(0(5(x1))))))))))))))))))) -> 4(2(1(2(5(3(4(1(1(3(0(0(3(3(4(0(5(4(5(x1))))))))))))))))))) 3(0(2(2(0(1(1(5(0(1(1(1(0(2(0(4(5(0(1(x1))))))))))))))))))) -> 5(1(2(1(4(0(0(3(0(1(0(0(1(0(1(2(5(1(2(x1))))))))))))))))))) 0(2(1(5(4(1(5(4(0(1(2(0(2(1(2(1(1(1(3(5(2(5(x1)))))))))))))))))))))) -> 2(1(1(3(5(4(2(5(0(5(2(1(1(1(2(1(4(0(2(0(5(1(x1)))))))))))))))))))))) 2(2(5(3(3(3(0(4(1(3(5(4(5(1(3(4(1(0(3(5(4(0(x1)))))))))))))))))))))) -> 0(1(5(3(4(1(3(5(3(3(1(3(4(5(3(4(4(0(2(2(5(0(x1)))))))))))))))))))))) 2(5(5(1(4(3(3(2(1(1(1(5(0(4(4(3(5(1(4(1(4(5(2(x1))))))))))))))))))))))) -> 3(4(5(1(4(4(5(2(1(5(5(5(0(1(2(1(1(1(3(4(3(4(2(x1))))))))))))))))))))))) 3(4(0(2(2(3(2(4(2(3(5(3(5(0(1(3(5(5(2(4(4(2(3(3(x1)))))))))))))))))))))))) -> 5(5(3(2(2(2(0(5(4(3(3(3(2(0(2(4(2(1(5(3(4(3(4(3(x1)))))))))))))))))))))))) 5(5(2(0(2(1(5(5(2(1(4(4(5(2(4(4(1(1(1(3(2(5(5(5(x1)))))))))))))))))))))))) -> 5(4(5(0(5(4(2(1(2(4(1(1(2(1(2(4(5(3(1(5(2(5(5(5(x1)))))))))))))))))))))))) 1(5(2(4(1(3(3(5(3(0(4(2(5(1(5(2(0(1(0(3(0(5(5(1(4(x1))))))))))))))))))))))))) -> 1(5(2(3(1(5(4(5(5(2(3(4(2(3(5(4(1(1(3(0(0(1(0(5(0(x1))))))))))))))))))))))))) 3(1(5(1(0(4(4(1(1(2(2(0(2(3(3(2(2(3(3(5(4(1(2(5(1(x1))))))))))))))))))))))))) -> 1(3(0(3(5(5(2(1(2(3(2(5(2(3(1(0(2(1(3(1(4(1(2(4(4(x1))))))))))))))))))))))))) 0(0(1(4(0(0(4(2(1(5(5(3(0(3(4(0(1(4(3(1(5(5(2(0(0(2(3(x1))))))))))))))))))))))))))) -> 0(0(5(4(1(2(4(2(1(5(4(2(0(5(0(0(0(3(4(1(3(5(3(0(1(0(3(x1))))))))))))))))))))))))))) 1(1(5(4(4(5(0(4(5(1(1(0(3(2(1(3(0(2(1(5(3(2(0(4(5(0(2(x1))))))))))))))))))))))))))) -> 2(3(4(0(1(5(0(5(1(1(2(0(3(4(1(3(0(4(1(5(2(5(0(4(2(5(1(x1))))))))))))))))))))))))))) 1(5(2(4(3(0(1(4(3(5(0(5(0(1(3(2(0(1(4(3(3(2(1(0(1(5(5(x1))))))))))))))))))))))))))) -> 1(5(1(4(1(0(0(3(5(5(0(0(3(0(1(1(4(5(3(2(3(1(2(4(2(5(3(x1))))))))))))))))))))))))))) 0(1(2(5(3(3(1(0(4(1(4(2(0(1(0(4(4(1(0(5(3(2(1(2(5(2(5(1(x1)))))))))))))))))))))))))))) -> 0(1(1(5(3(5(4(0(2(3(0(0(0(4(5(1(4(1(2(1(5(2(1(4(3(2(2(1(x1)))))))))))))))))))))))))))) 0(4(1(4(2(2(4(0(0(3(5(3(0(0(5(0(4(5(5(5(3(2(1(1(0(2(3(1(x1)))))))))))))))))))))))))))) -> 0(1(2(4(1(1(3(0(5(2(3(0(3(0(5(0(4(5(2(4(5(4(1(5(0(2(0(3(x1)))))))))))))))))))))))))))) 2(0(3(1(0(4(3(1(5(2(2(4(1(1(3(0(2(4(2(5(2(2(2(4(1(5(5(1(2(x1))))))))))))))))))))))))))))) -> 2(0(0(2(2(1(5(2(3(1(3(3(1(4(5(2(1(4(2(5(2(2(2(0(5(4(4(1(1(x1))))))))))))))))))))))))))))) 0(5(0(2(3(0(4(0(0(4(3(3(5(0(4(5(4(1(4(0(2(5(5(5(3(1(5(2(2(3(3(x1))))))))))))))))))))))))))))))) -> 2(3(5(3(5(0(4(0(0(0(3(3(4(0(4(1(4(5(3(4(2(5(5(5(5(2(0(0(2(1(3(x1))))))))))))))))))))))))))))))) 1(2(3(5(3(5(0(3(3(3(1(3(1(0(3(3(5(2(0(3(4(4(0(0(4(0(4(0(0(2(2(x1))))))))))))))))))))))))))))))) -> 1(3(3(5(0(5(5(3(4(1(2(3(3(0(0(4(2(1(0(0(0(3(2(3(4(0(3(0(4(3(2(x1))))))))))))))))))))))))))))))) 3(2(4(2(2(3(1(4(1(2(0(1(0(5(2(1(3(0(1(1(2(0(4(0(1(0(3(4(2(1(4(x1))))))))))))))))))))))))))))))) -> 0(2(1(2(1(4(1(3(1(2(4(5(0(0(2(1(1(4(1(3(4(0(1(0(2(3(3(2(0(2(4(x1))))))))))))))))))))))))))))))) 4(0(4(0(4(2(1(5(1(2(3(1(0(0(3(3(4(3(5(4(2(1(5(5(3(4(0(1(3(5(2(x1))))))))))))))))))))))))))))))) -> 4(0(4(3(1(2(3(4(2(5(3(2(0(5(1(3(4(1(0(3(5(1(2(4(1(3(0(4(0(5(5(x1))))))))))))))))))))))))))))))) 2(2(4(3(5(5(4(1(3(0(4(5(5(2(2(3(3(5(2(1(0(3(1(1(0(3(3(3(0(0(1(0(3(x1))))))))))))))))))))))))))))))))) -> 2(4(1(5(1(5(0(4(0(0(0(2(3(2(3(3(2(5(1(5(1(3(3(2(5(3(3(4(3(1(0(0(3(x1))))))))))))))))))))))))))))))))) 2(4(4(0(2(1(3(5(0(0(1(4(4(2(1(1(2(0(0(5(2(2(3(2(5(5(1(0(1(1(3(4(4(5(x1)))))))))))))))))))))))))))))))))) -> 2(4(3(0(5(0(1(1(1(0(2(1(1(2(2(2(4(0(0(4(5(2(4(3(5(5(0(4(1(1(3(4(2(5(x1)))))))))))))))))))))))))))))))))) 5(4(3(5(2(3(5(1(2(2(3(1(3(2(3(2(4(1(0(1(4(5(4(1(4(4(0(1(0(2(5(2(2(0(x1)))))))))))))))))))))))))))))))))) -> 5(4(1(5(2(2(5(3(4(0(5(0(4(2(3(0(0(3(4(5(2(1(4(2(3(4(1(1(2(1(1(2(2(3(x1)))))))))))))))))))))))))))))))))) 0(3(0(4(5(5(5(1(3(0(4(4(3(4(5(2(5(0(0(1(5(0(5(5(0(4(5(1(1(0(4(3(4(5(2(x1))))))))))))))))))))))))))))))))))) -> 0(3(0(0(1(5(5(1(3(4(4(1(4(0(4(5(5(4(2(2(5(5(5(5(0(0(0(1(3(4(5(3(4(5(0(x1))))))))))))))))))))))))))))))))))) 4(2(1(2(2(1(5(1(5(3(0(5(3(5(0(4(4(3(1(2(1(2(0(2(4(4(3(1(1(4(4(5(5(1(2(x1))))))))))))))))))))))))))))))))))) -> 4(1(5(2(2(0(5(3(0(2(2(2(1(5(3(4(1(2(1(5(3(1(0(3(4(4(4(1(1(4(4(5(5(2(1(x1))))))))))))))))))))))))))))))))))) 5(4(4(1(1(3(5(2(2(2(5(3(3(3(0(4(5(3(2(3(0(5(5(1(2(2(0(1(1(3(1(5(0(0(2(x1))))))))))))))))))))))))))))))))))) -> 3(4(5(1(0(2(3(2(3(2(0(3(5(3(1(4(5(2(2(2(0(1(5(5(2(1(1(4(5(3(5(0(0(1(3(x1))))))))))))))))))))))))))))))))))) 0(0(3(0(0(0(3(4(1(4(0(5(2(1(5(2(4(1(1(1(5(2(2(5(3(4(0(0(4(3(1(3(5(4(1(1(x1)))))))))))))))))))))))))))))))))))) -> 0(0(1(4(0(5(0(1(4(4(0(0(2(1(5(3(1(0(1(0(5(2(2(5(3(4(3(1(4(3(3(4(5(1(2(1(x1)))))))))))))))))))))))))))))))))))) 2(1(1(4(3(2(2(4(1(5(3(3(3(3(2(4(4(3(0(1(4(3(2(0(0(2(1(5(2(2(3(0(1(5(1(2(x1)))))))))))))))))))))))))))))))))))) -> 0(3(1(2(3(4(0(2(2(3(1(3(1(3(5(4(4(3(2(1(4(3(4(2(0(1(1(5(2(2(3(0(5(2(1(2(x1)))))))))))))))))))))))))))))))))))) 4(5(4(4(4(0(4(4(5(5(2(0(2(5(0(3(1(4(3(4(3(0(1(4(4(1(0(4(5(4(3(3(1(1(0(5(x1)))))))))))))))))))))))))))))))))))) -> 4(4(4(5(3(1(1(2(5(5(3(4(4(5(1(3(3(4(4(0(0(0(5(0(1(1(0(4(5(2(0(3(4(4(4(4(x1)))))))))))))))))))))))))))))))))))) 0(0(5(5(1(0(1(4(5(2(0(5(2(5(2(1(0(5(1(1(4(5(0(2(1(0(3(4(1(2(5(0(1(4(4(5(3(5(x1)))))))))))))))))))))))))))))))))))))) -> 0(3(4(5(1(0(0(5(1(0(0(5(4(5(0(1(2(5(5(4(4(1(0(2(1(3(2(2(1(0(5(1(5(1(4(5(2(5(x1)))))))))))))))))))))))))))))))))))))) 0(1(3(0(3(1(0(3(0(4(3(0(3(2(1(3(5(0(5(3(0(1(0(1(1(4(3(0(5(1(4(3(3(3(0(0(0(5(3(4(x1)))))))))))))))))))))))))))))))))))))))) -> 0(3(1(0(5(4(0(3(0(4(5(0(5(1(3(3(0(0(3(0(3(1(3(2(1(1(5(4(3(1(1(0(3(3(0(0(3(4(3(0(x1)))))))))))))))))))))))))))))))))))))))) 4(3(3(0(0(0(3(2(4(3(0(0(4(4(2(4(4(2(1(2(5(5(0(0(4(2(5(5(1(0(4(4(5(0(2(3(3(2(4(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) -> 4(2(2(4(0(0(3(2(5(3(4(5(4(0(0(4(0(2(1(0(5(5(2(4(3(3(5(4(1(0(4(4(0(0(4(3(3(2(2(4(0(4(x1)))))))))))))))))))))))))))))))))))))))))) 0(1(0(4(0(1(1(1(1(1(0(3(4(3(3(1(4(0(2(0(1(1(0(4(4(3(3(5(0(1(1(0(3(0(4(0(0(4(0(3(1(3(5(3(5(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(3(1(0(1(3(1(0(1(5(3(4(0(3(1(4(0(2(3(1(4(0(5(4(0(3(0(1(1(1(0(0(0(4(0(0(4(1(5(1(1(4(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) 0(2(2(3(1(3(4(0(5(3(3(2(0(2(1(5(0(2(0(3(2(1(4(5(0(4(4(0(2(3(0(1(2(1(2(1(1(5(3(2(3(0(3(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(5(0(3(4(2(5(0(3(2(1(2(1(3(0(1(0(3(4(0(4(4(0(2(2(0(2(3(3(3(2(1(3(1(1(5(2(1(3(5(0(5(2(x1))))))))))))))))))))))))))))))))))))))))))))) 2(2(0(4(5(5(3(5(1(2(3(5(2(5(5(3(3(2(1(1(1(3(1(3(5(3(4(1(5(2(1(1(4(1(1(2(2(3(2(4(2(2(5(3(3(x1))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(5(1(3(2(1(3(1(3(2(5(5(3(5(5(1(2(1(3(5(3(1(2(4(0(3(5(4(2(4(1(1(2(2(3(3(2(2(4(5(5(3(x1))))))))))))))))))))))))))))))))))))))))))))) 2(5(0(5(0(1(5(1(3(4(4(3(1(3(3(3(0(5(3(3(0(4(3(3(3(2(4(4(2(2(5(2(4(3(3(5(1(2(1(0(4(1(5(2(3(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(0(5(0(2(5(1(3(3(2(3(1(4(3(2(0(5(3(3(4(4(3(2(3(2(4(1(0(4(5(2(4(3(0(5(1(1(2(3(4(1(5(3(3(5(3(x1))))))))))))))))))))))))))))))))))))))))))))))) 4(5(4(2(3(3(2(4(1(0(3(4(4(3(1(4(0(0(1(4(4(4(5(2(0(4(2(2(2(2(0(4(3(4(3(0(3(2(5(3(3(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 4(5(3(2(5(4(2(3(1(4(4(4(4(3(2(4(4(0(1(4(4(2(0(0(3(4(3(2(0(2(0(1(3(4(3(0(3(5(2(3(2(0(5(3(0(4(1(x1))))))))))))))))))))))))))))))))))))))))))))))) 0(3(1(4(5(1(2(2(4(5(1(3(5(3(2(3(0(4(5(2(1(4(4(5(3(1(0(1(1(2(5(3(4(5(5(0(2(3(0(4(1(0(3(3(0(2(4(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(3(1(4(5(1(5(2(2(5(2(3(4(4(4(3(0(5(4(2(2(3(4(0(5(1(0(0(1(2(1(3(5(5(2(0(5(3(1(4(1(0(3(3(4(1(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(4(4(2(5(4(5(2(1(4(4(2(0(2(3(5(0(3(3(5(0(3(5(0(4(0(0(5(5(2(5(0(4(0(3(2(2(1(5(3(2(4(3(1(5(4(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(2(1(2(0(4(5(5(5(4(4(5(0(0(3(4(0(2(3(4(3(3(1(2(4(5(4(5(2(5(2(0(5(0(3(0(0(1(5(3(2(1(2(1(5(4(3(4(x1)))))))))))))))))))))))))))))))))))))))))))))))) 2(3(1(5(1(2(3(3(3(5(2(1(5(5(3(4(0(5(2(2(2(3(2(3(3(3(3(1(3(2(2(0(2(1(4(1(4(4(3(2(4(4(0(4(2(4(3(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 1(3(2(3(3(2(3(4(2(4(2(0(1(5(3(4(0(5(2(2(1(3(2(1(5(3(3(3(3(2(2(0(2(2(4(4(3(1(5(3(0(4(5(4(2(3(4(1(x1)))))))))))))))))))))))))))))))))))))))))))))))) 4(5(5(4(4(4(3(3(2(0(1(4(5(3(1(1(5(4(3(0(2(4(2(5(4(2(0(3(4(1(4(2(5(1(5(4(0(4(0(0(2(2(2(0(3(0(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 4(0(5(4(4(5(3(1(2(1(3(4(5(3(3(1(2(4(3(1(4(2(5(4(4(4(0(4(0(0(4(2(0(1(5(2(2(2(0(0(5(2(2(0(3(5(4(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 1(3(5(2(5(4(0(1(4(5(5(2(1(2(5(4(1(3(1(3(5(3(4(2(5(0(1(3(5(3(3(0(2(2(2(2(5(1(4(5(3(1(4(0(2(1(5(1(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(3(5(2(5(4(0(5(5(5(4(2(1(3(3(0(1(1(2(3(5(1(4(2(1(5(1(4(0(2(3(0(3(2(2(3(5(1(1(5(3(1(1(4(2(4(5(1(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) 4(0(3(4(1(4(0(4(5(3(0(2(3(4(2(0(5(2(4(1(5(3(0(4(2(5(3(5(1(0(1(1(0(3(5(3(3(4(5(0(4(4(3(3(2(1(1(5(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 4(1(0(4(5(1(0(4(5(3(0(2(3(4(2(0(5(2(4(1(0(3(0(1(1(5(0(3(1(1(4(3(5(2(5(2(5(4(4(3(5(4(3(3(3(4(0(3(5(x1))))))))))))))))))))))))))))))))))))))))))))))))) encArg(cons_0(x_1)) -> 0(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_2(x_1)) -> 2(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. "[83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 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, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 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, 1111, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1120, 1121, 1122, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1130, 1131, 1132, 1133, 1134, 1135, 1136, 1137, 1138, 1139, 1140, 1141, 1142, 1143, 1144, 1145, 1146, 1147, 1148, 1149, 1150, 1151, 1152, 1153, 1154, 1155, 1156, 1157, 1158, 1159, 1160, 1161, 1162, 1163, 1164, 1165, 1166, 1167, 1168, 1169, 1170, 1171, 1172, 1173, 1174, 1175, 1176, 1177, 1178, 1179, 1180, 1181, 1182, 1183, 1184, 1185, 1186, 1187, 1188, 1189, 1190, 1191, 1192, 1193, 1194, 1195, 1196, 1197, 1198, 1199, 1200, 1201, 1202, 1203, 1204, 1205, 1206, 1207, 1208, 1209, 1210, 1211, 1212, 1213, 1214, 1215, 1216, 1217, 1218, 1219, 1220, 1221, 1222, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1230, 1231, 1232, 1233, 1234, 1235, 1236, 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1403, 1404, 1405, 1406, 1407, 1408, 1409, 1410, 1411, 1412, 1413, 1414, 1415, 1416, 1417, 1418, 1419, 1420, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 1430, 1431, 1432, 1433, 1434, 1435, 1436, 1437, 1438, 1439, 1440, 1441, 1442, 1443, 1444, 1445, 1446, 1447, 1448, 1449, 1450, 1451, 1452, 1453, 1454, 1455, 1456, 1457, 1458, 1459, 1460, 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469, 1470, 1471, 1472, 1473, 1474, 1475, 1476, 1477, 1478, 1479, 1480, 1481, 1482, 1483, 1484, 1485, 1486, 1487, 1488, 1489, 1490, 1491, 1492, 1493, 1494, 1495, 1496, 1497, 1498, 1499, 1500, 1501, 1502, 1503, 1504, 1505, 1506, 1507, 1508, 1509, 1510, 1511, 1512, 1513, 1514, 1515, 1516, 1517, 1518, 1519, 1520, 1521, 1522, 1523, 1524, 1525, 1526, 1527, 1528, 1529, 1530, 1531, 1532, 1533, 1534, 1535, 1536, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 1550, 1551, 1552, 1553, 1554, 1555, 1556, 1557, 1558, 1559, 1560, 1561, 1562, 1563, 1564, 1565, 1566, 1567, 1568, 1569, 1570, 1571, 1572, 1573, 1574, 1575, 1576, 1577, 1578, 1579, 1580, 1581, 1582, 1583, 1584] {(83,84,[0_1|0, 1_1|0, 4_1|0, 3_1|0, 2_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]), (83,85,[0_1|1, 1_1|1, 4_1|1, 3_1|1, 2_1|1, 5_1|1]), (83,86,[0_1|2]), (83,91,[0_1|2]), (83,135,[0_1|2]), (83,162,[0_1|2]), (83,201,[0_1|2]), (83,206,[5_1|2]), (83,214,[0_1|2]), (83,241,[2_1|2]), (83,262,[0_1|2]), (83,306,[0_1|2]), (83,332,[0_1|2]), (83,367,[0_1|2]), (83,404,[2_1|2]), (83,434,[0_1|2]), (83,468,[0_1|2]), (83,515,[4_1|2]), (83,523,[1_1|2]), (83,553,[2_1|2]), (83,564,[4_1|2]), (83,582,[2_1|2]), (83,630,[1_1|2]), (83,648,[4_1|2]), (83,666,[2_1|2]), (83,692,[1_1|2]), (83,716,[1_1|2]), (83,742,[4_1|2]), (83,789,[4_1|2]), (83,806,[4_1|2]), (83,836,[4_1|2]), (83,884,[4_1|2]), (83,918,[4_1|2]), (83,953,[4_1|2]), (83,999,[4_1|2]), (83,1046,[4_1|2]), (83,1087,[5_1|2]), (83,1105,[5_1|2]), (83,1128,[1_1|2]), (83,1152,[0_1|2]), (83,1182,[0_1|2]), (83,1203,[2_1|2]), (83,1235,[2_1|2]), (83,1279,[3_1|2]), (83,1301,[2_1|2]), (83,1347,[2_1|2]), (83,1375,[2_1|2]), (83,1408,[0_1|2]), (83,1443,[1_1|2]), (83,1490,[5_1|2]), (83,1513,[5_1|2]), (83,1546,[3_1|2]), (84,84,[cons_0_1|0, cons_1_1|0, cons_4_1|0, cons_3_1|0, cons_2_1|0, cons_5_1|0]), (85,84,[encArg_1|1]), (85,85,[0_1|1, 1_1|1, 4_1|1, 3_1|1, 2_1|1, 5_1|1]), (85,86,[0_1|2]), (85,91,[0_1|2]), (85,135,[0_1|2]), (85,162,[0_1|2]), (85,201,[0_1|2]), (85,206,[5_1|2]), (85,214,[0_1|2]), (85,241,[2_1|2]), (85,262,[0_1|2]), (85,306,[0_1|2]), (85,332,[0_1|2]), (85,367,[0_1|2]), (85,404,[2_1|2]), (85,434,[0_1|2]), (85,468,[0_1|2]), (85,515,[4_1|2]), (85,523,[1_1|2]), (85,553,[2_1|2]), (85,564,[4_1|2]), (85,582,[2_1|2]), (85,630,[1_1|2]), (85,648,[4_1|2]), (85,666,[2_1|2]), (85,692,[1_1|2]), (85,716,[1_1|2]), (85,742,[4_1|2]), (85,789,[4_1|2]), (85,806,[4_1|2]), (85,836,[4_1|2]), (85,884,[4_1|2]), (85,918,[4_1|2]), (85,953,[4_1|2]), (85,999,[4_1|2]), (85,1046,[4_1|2]), (85,1087,[5_1|2]), (85,1105,[5_1|2]), (85,1128,[1_1|2]), (85,1152,[0_1|2]), (85,1182,[0_1|2]), (85,1203,[2_1|2]), (85,1235,[2_1|2]), (85,1279,[3_1|2]), (85,1301,[2_1|2]), (85,1347,[2_1|2]), (85,1375,[2_1|2]), (85,1408,[0_1|2]), (85,1443,[1_1|2]), (85,1490,[5_1|2]), (85,1513,[5_1|2]), (85,1546,[3_1|2]), (86,87,[2_1|2]), (87,88,[2_1|2]), (88,89,[1_1|2]), (89,90,[0_1|2]), (89,434,[0_1|2]), (89,468,[0_1|2]), (90,85,[3_1|2]), (90,1279,[3_1|2]), (90,1546,[3_1|2]), (90,405,[3_1|2]), (90,583,[3_1|2]), (90,667,[3_1|2]), (90,1087,[5_1|2]), (90,1105,[5_1|2]), (90,1128,[1_1|2]), (90,1152,[0_1|2]), (91,92,[3_1|2]), (92,93,[3_1|2]), (93,94,[1_1|2]), (94,95,[0_1|2]), (95,96,[1_1|2]), (96,97,[3_1|2]), (97,98,[1_1|2]), (98,99,[0_1|2]), (99,100,[1_1|2]), (100,101,[5_1|2]), (101,102,[3_1|2]), (102,103,[4_1|2]), (103,104,[0_1|2]), (104,105,[3_1|2]), (105,106,[1_1|2]), (106,107,[4_1|2]), (107,108,[0_1|2]), (108,109,[2_1|2]), (109,110,[3_1|2]), (110,111,[1_1|2]), (111,112,[4_1|2]), (112,113,[0_1|2]), (113,114,[5_1|2]), (114,115,[4_1|2]), (115,116,[0_1|2]), (116,117,[3_1|2]), (117,118,[0_1|2]), (118,119,[1_1|2]), (119,120,[1_1|2]), (120,121,[1_1|2]), (121,122,[0_1|2]), (122,123,[0_1|2]), (123,124,[0_1|2]), (124,125,[4_1|2]), (125,126,[0_1|2]), (126,127,[0_1|2]), (127,128,[4_1|2]), (128,129,[1_1|2]), (129,130,[5_1|2]), (130,131,[1_1|2]), (131,132,[1_1|2]), (132,133,[4_1|2]), (132,1046,[4_1|2]), (133,134,[3_1|2]), (134,85,[3_1|2]), (134,206,[3_1|2]), (134,1087,[3_1|2, 5_1|2]), (134,1105,[3_1|2, 5_1|2]), (134,1490,[3_1|2]), (134,1513,[3_1|2]), (134,1128,[1_1|2]), (134,1152,[0_1|2]), (135,136,[1_1|2]), (136,137,[1_1|2]), (137,138,[5_1|2]), (138,139,[3_1|2]), (139,140,[5_1|2]), (140,141,[4_1|2]), (141,142,[0_1|2]), (142,143,[2_1|2]), (143,144,[3_1|2]), (144,145,[0_1|2]), (145,146,[0_1|2]), (146,147,[0_1|2]), (147,148,[4_1|2]), (148,149,[5_1|2]), (149,150,[1_1|2]), (150,151,[4_1|2]), (151,152,[1_1|2]), (152,153,[2_1|2]), (153,154,[1_1|2]), (154,155,[5_1|2]), (155,156,[2_1|2]), 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(1300,582,[2_1|2]), (1300,666,[2_1|2]), (1300,1203,[2_1|2]), (1300,1235,[2_1|2]), (1300,1301,[2_1|2]), (1300,1347,[2_1|2]), (1300,1375,[2_1|2]), (1300,1182,[0_1|2]), (1300,1279,[3_1|2]), (1300,1408,[0_1|2]), (1300,1443,[1_1|2]), (1301,1302,[2_1|2]), (1302,1303,[0_1|2]), (1303,1304,[5_1|2]), (1304,1305,[0_1|2]), (1305,1306,[2_1|2]), (1306,1307,[5_1|2]), (1307,1308,[1_1|2]), (1308,1309,[3_1|2]), (1309,1310,[3_1|2]), (1310,1311,[2_1|2]), (1311,1312,[3_1|2]), (1312,1313,[1_1|2]), (1313,1314,[4_1|2]), (1314,1315,[3_1|2]), (1315,1316,[2_1|2]), (1316,1317,[0_1|2]), (1317,1318,[5_1|2]), (1318,1319,[3_1|2]), (1319,1320,[3_1|2]), (1320,1321,[4_1|2]), (1321,1322,[4_1|2]), (1322,1323,[3_1|2]), (1323,1324,[2_1|2]), (1324,1325,[3_1|2]), (1325,1326,[2_1|2]), (1326,1327,[4_1|2]), (1327,1328,[1_1|2]), (1328,1329,[0_1|2]), (1329,1330,[4_1|2]), (1330,1331,[5_1|2]), (1331,1332,[2_1|2]), (1332,1333,[4_1|2]), (1333,1334,[3_1|2]), (1334,1335,[0_1|2]), (1335,1336,[5_1|2]), (1336,1337,[1_1|2]), (1337,1338,[1_1|2]), (1338,1339,[2_1|2]), (1339,1340,[3_1|2]), (1340,1341,[4_1|2]), (1341,1342,[1_1|2]), (1342,1343,[5_1|2]), (1343,1344,[3_1|2]), (1344,1345,[3_1|2]), (1345,1346,[5_1|2]), (1346,85,[3_1|2]), (1346,241,[3_1|2]), (1346,404,[3_1|2]), (1346,553,[3_1|2]), (1346,582,[3_1|2]), (1346,666,[3_1|2]), (1346,1203,[3_1|2]), (1346,1235,[3_1|2]), (1346,1301,[3_1|2]), (1346,1347,[3_1|2]), (1346,1375,[3_1|2]), (1346,1236,[3_1|2]), (1346,1302,[3_1|2]), (1346,1087,[5_1|2]), (1346,1105,[5_1|2]), (1346,1128,[1_1|2]), (1346,1152,[0_1|2]), (1347,1348,[0_1|2]), (1348,1349,[0_1|2]), (1349,1350,[2_1|2]), (1350,1351,[2_1|2]), (1351,1352,[1_1|2]), (1352,1353,[5_1|2]), (1353,1354,[2_1|2]), (1354,1355,[3_1|2]), (1355,1356,[1_1|2]), (1356,1357,[3_1|2]), (1357,1358,[3_1|2]), (1358,1359,[1_1|2]), (1359,1360,[4_1|2]), (1360,1361,[5_1|2]), (1361,1362,[2_1|2]), (1362,1363,[1_1|2]), (1363,1364,[4_1|2]), (1364,1365,[2_1|2]), (1365,1366,[5_1|2]), (1366,1367,[2_1|2]), (1367,1368,[2_1|2]), (1368,1369,[2_1|2]), (1369,1370,[0_1|2]), (1370,1371,[5_1|2]), (1370,1546,[3_1|2]), (1371,1372,[4_1|2]), (1372,1373,[4_1|2]), (1372,789,[4_1|2]), (1373,1374,[1_1|2]), (1373,648,[4_1|2]), (1373,666,[2_1|2]), (1374,85,[1_1|2]), (1374,241,[1_1|2]), (1374,404,[1_1|2]), (1374,553,[1_1|2, 2_1|2]), (1374,582,[1_1|2, 2_1|2]), (1374,666,[1_1|2, 2_1|2]), (1374,1203,[1_1|2]), (1374,1235,[1_1|2]), (1374,1301,[1_1|2]), (1374,1347,[1_1|2]), (1374,1375,[1_1|2]), (1374,1089,[1_1|2]), (1374,515,[4_1|2]), (1374,523,[1_1|2]), (1374,564,[4_1|2]), (1374,630,[1_1|2]), (1374,648,[4_1|2]), (1374,692,[1_1|2]), (1374,716,[1_1|2]), (1374,742,[4_1|2]), (1375,1376,[4_1|2]), (1376,1377,[3_1|2]), (1377,1378,[0_1|2]), (1378,1379,[5_1|2]), (1379,1380,[0_1|2]), (1380,1381,[1_1|2]), (1381,1382,[1_1|2]), (1382,1383,[1_1|2]), (1383,1384,[0_1|2]), (1384,1385,[2_1|2]), (1385,1386,[1_1|2]), (1386,1387,[1_1|2]), (1387,1388,[2_1|2]), (1388,1389,[2_1|2]), (1389,1390,[2_1|2]), (1390,1391,[4_1|2]), (1391,1392,[0_1|2]), (1392,1393,[0_1|2]), (1393,1394,[4_1|2]), (1394,1395,[5_1|2]), (1395,1396,[2_1|2]), (1396,1397,[4_1|2]), (1397,1398,[3_1|2]), (1398,1399,[5_1|2]), (1399,1400,[5_1|2]), (1400,1401,[0_1|2]), (1401,1402,[4_1|2]), (1402,1403,[1_1|2]), (1403,1404,[1_1|2]), (1404,1405,[3_1|2]), (1405,1406,[4_1|2]), (1406,1407,[2_1|2]), (1406,1279,[3_1|2]), (1406,1301,[2_1|2]), (1407,85,[5_1|2]), (1407,206,[5_1|2]), (1407,1087,[5_1|2]), (1407,1105,[5_1|2]), (1407,1490,[5_1|2]), (1407,1513,[5_1|2]), (1407,649,[5_1|2]), (1407,954,[5_1|2]), (1407,1546,[3_1|2]), (1408,1409,[3_1|2]), (1409,1410,[1_1|2]), (1410,1411,[2_1|2]), (1411,1412,[3_1|2]), (1412,1413,[4_1|2]), (1413,1414,[0_1|2]), (1414,1415,[2_1|2]), (1415,1416,[2_1|2]), (1416,1417,[3_1|2]), (1417,1418,[1_1|2]), (1418,1419,[3_1|2]), (1419,1420,[1_1|2]), (1420,1421,[3_1|2]), (1421,1422,[5_1|2]), (1422,1423,[4_1|2]), (1423,1424,[4_1|2]), (1424,1425,[3_1|2]), (1425,1426,[2_1|2]), (1426,1427,[1_1|2]), (1427,1428,[4_1|2]), (1428,1429,[3_1|2]), (1429,1430,[4_1|2]), (1430,1431,[2_1|2]), (1431,1432,[0_1|2]), (1432,1433,[1_1|2]), (1433,1434,[1_1|2]), (1434,1435,[5_1|2]), (1435,1436,[2_1|2]), (1436,1437,[2_1|2]), (1437,1438,[3_1|2]), (1438,1439,[0_1|2]), (1439,1440,[5_1|2]), (1440,1441,[2_1|2]), (1441,1442,[1_1|2]), (1441,515,[4_1|2]), (1441,523,[1_1|2]), (1442,85,[2_1|2]), (1442,241,[2_1|2]), (1442,404,[2_1|2]), (1442,553,[2_1|2]), (1442,582,[2_1|2]), (1442,666,[2_1|2]), (1442,1203,[2_1|2]), (1442,1235,[2_1|2]), (1442,1301,[2_1|2]), (1442,1347,[2_1|2]), (1442,1375,[2_1|2]), (1442,1089,[2_1|2]), (1442,1182,[0_1|2]), (1442,1279,[3_1|2]), (1442,1408,[0_1|2]), (1442,1443,[1_1|2]), (1443,1444,[3_1|2]), (1444,1445,[2_1|2]), (1445,1446,[3_1|2]), (1446,1447,[3_1|2]), (1447,1448,[2_1|2]), (1448,1449,[3_1|2]), (1449,1450,[4_1|2]), (1450,1451,[2_1|2]), (1451,1452,[4_1|2]), (1452,1453,[2_1|2]), (1453,1454,[0_1|2]), (1454,1455,[1_1|2]), (1455,1456,[5_1|2]), (1456,1457,[3_1|2]), (1457,1458,[4_1|2]), (1458,1459,[0_1|2]), (1459,1460,[5_1|2]), (1460,1461,[2_1|2]), (1461,1462,[2_1|2]), (1462,1463,[1_1|2]), (1463,1464,[3_1|2]), (1464,1465,[2_1|2]), (1465,1466,[1_1|2]), (1466,1467,[5_1|2]), (1467,1468,[3_1|2]), (1468,1469,[3_1|2]), (1469,1470,[3_1|2]), (1470,1471,[3_1|2]), (1471,1472,[2_1|2]), (1472,1473,[2_1|2]), (1473,1474,[0_1|2]), (1474,1475,[2_1|2]), (1475,1476,[2_1|2]), (1476,1477,[4_1|2]), (1477,1478,[4_1|2]), (1478,1479,[3_1|2]), (1479,1480,[1_1|2]), (1480,1481,[5_1|2]), (1481,1482,[3_1|2]), (1482,1483,[0_1|2]), (1483,1484,[4_1|2]), (1484,1485,[5_1|2]), (1485,1486,[4_1|2]), (1486,1487,[2_1|2]), (1487,1488,[3_1|2]), (1488,1489,[4_1|2]), (1488,789,[4_1|2]), (1489,85,[1_1|2]), (1489,86,[1_1|2]), (1489,91,[1_1|2]), (1489,135,[1_1|2]), (1489,162,[1_1|2]), (1489,201,[1_1|2]), (1489,214,[1_1|2]), (1489,262,[1_1|2]), (1489,306,[1_1|2]), (1489,332,[1_1|2]), (1489,367,[1_1|2]), (1489,434,[1_1|2]), (1489,468,[1_1|2]), (1489,1152,[1_1|2]), (1489,1182,[1_1|2]), (1489,1408,[1_1|2]), (1489,1378,[1_1|2]), (1489,515,[4_1|2]), (1489,523,[1_1|2]), (1489,553,[2_1|2]), (1489,564,[4_1|2]), (1489,582,[2_1|2]), (1489,630,[1_1|2]), (1489,648,[4_1|2]), (1489,666,[2_1|2]), (1489,692,[1_1|2]), (1489,716,[1_1|2]), (1489,742,[4_1|2]), (1490,1491,[4_1|2]), (1491,1492,[5_1|2]), (1492,1493,[0_1|2]), (1493,1494,[5_1|2]), (1494,1495,[4_1|2]), (1495,1496,[2_1|2]), (1496,1497,[1_1|2]), (1497,1498,[2_1|2]), (1498,1499,[4_1|2]), (1499,1500,[1_1|2]), (1500,1501,[1_1|2]), (1501,1502,[2_1|2]), (1502,1503,[1_1|2]), (1503,1504,[2_1|2]), (1504,1505,[4_1|2]), (1505,1506,[5_1|2]), (1506,1507,[3_1|2]), (1507,1508,[1_1|2]), (1508,1509,[5_1|2]), (1509,1510,[2_1|2]), (1510,1511,[5_1|2]), (1511,1512,[5_1|2]), (1511,1490,[5_1|2]), (1512,85,[5_1|2]), (1512,206,[5_1|2]), (1512,1087,[5_1|2]), (1512,1105,[5_1|2]), (1512,1490,[5_1|2]), (1512,1513,[5_1|2]), (1512,1106,[5_1|2]), (1512,1546,[3_1|2]), (1513,1514,[4_1|2]), (1514,1515,[1_1|2]), (1515,1516,[5_1|2]), (1516,1517,[2_1|2]), (1517,1518,[2_1|2]), (1518,1519,[5_1|2]), (1519,1520,[3_1|2]), (1520,1521,[4_1|2]), (1521,1522,[0_1|2]), (1522,1523,[5_1|2]), (1523,1524,[0_1|2]), (1524,1525,[4_1|2]), (1525,1526,[2_1|2]), (1526,1527,[3_1|2]), (1527,1528,[0_1|2]), (1528,1529,[0_1|2]), (1529,1530,[3_1|2]), (1530,1531,[4_1|2]), (1531,1532,[5_1|2]), (1532,1533,[2_1|2]), (1533,1534,[1_1|2]), (1534,1535,[4_1|2]), (1535,1536,[2_1|2]), (1536,1537,[3_1|2]), (1537,1538,[4_1|2]), (1538,1539,[1_1|2]), (1539,1540,[1_1|2]), (1540,1541,[2_1|2]), (1541,1542,[1_1|2]), (1542,1543,[1_1|2]), (1543,1544,[2_1|2]), (1544,1545,[2_1|2]), (1544,1443,[1_1|2]), (1545,85,[3_1|2]), (1545,86,[3_1|2]), (1545,91,[3_1|2]), (1545,135,[3_1|2]), (1545,162,[3_1|2]), (1545,201,[3_1|2]), (1545,214,[3_1|2]), (1545,262,[3_1|2]), (1545,306,[3_1|2]), (1545,332,[3_1|2]), (1545,367,[3_1|2]), (1545,434,[3_1|2]), (1545,468,[3_1|2]), (1545,1152,[3_1|2, 0_1|2]), (1545,1182,[3_1|2]), (1545,1408,[3_1|2]), (1545,1348,[3_1|2]), (1545,1303,[3_1|2]), (1545,1087,[5_1|2]), (1545,1105,[5_1|2]), (1545,1128,[1_1|2]), (1546,1547,[4_1|2]), (1547,1548,[5_1|2]), (1548,1549,[1_1|2]), (1549,1550,[0_1|2]), (1550,1551,[2_1|2]), (1551,1552,[3_1|2]), (1552,1553,[2_1|2]), (1553,1554,[3_1|2]), (1554,1555,[2_1|2]), (1555,1556,[0_1|2]), (1556,1557,[3_1|2]), (1557,1558,[5_1|2]), (1558,1559,[3_1|2]), (1559,1560,[1_1|2]), (1560,1561,[4_1|2]), (1561,1562,[5_1|2]), (1562,1563,[2_1|2]), (1563,1564,[2_1|2]), (1564,1565,[2_1|2]), (1565,1566,[0_1|2]), (1566,1567,[1_1|2]), (1567,1568,[5_1|2]), (1568,1569,[5_1|2]), (1569,1570,[2_1|2]), (1570,1571,[1_1|2]), (1571,1572,[1_1|2]), (1572,1573,[4_1|2]), (1573,1574,[5_1|2]), (1574,1575,[3_1|2]), (1575,1576,[5_1|2]), (1576,1577,[0_1|2]), (1577,1578,[0_1|2]), (1577,162,[0_1|2]), (1578,1579,[1_1|2]), (1578,553,[2_1|2]), (1578,564,[4_1|2]), (1578,582,[2_1|2]), (1579,85,[3_1|2]), (1579,241,[3_1|2]), (1579,404,[3_1|2]), (1579,553,[3_1|2]), (1579,582,[3_1|2]), (1579,666,[3_1|2]), (1579,1203,[3_1|2]), (1579,1235,[3_1|2]), (1579,1301,[3_1|2]), (1579,1347,[3_1|2]), (1579,1375,[3_1|2]), (1579,87,[3_1|2]), (1579,263,[3_1|2]), (1579,1153,[3_1|2]), (1579,1087,[5_1|2]), (1579,1105,[5_1|2]), (1579,1128,[1_1|2]), (1579,1152,[0_1|2]), (1580,1581,[4_1|3]), (1581,1582,[4_1|3]), (1582,1583,[4_1|3]), (1583,1584,[0_1|3]), (1584,839,[1_1|3])}" ---------------------------------------- (8) BOUNDS(1, n^1)