Conjecture on the complexity of the ranking algorithm

Let $m$ be the number of labels, and let Algorithm~ be the algorithm described in the paper for checking combinations of pairwise label preferences and finding $\hat{\mathbb{R}}^{M}_{\ell_R,{\mathcal{P}}}$. Complexity conjecture. Algorithm~ has to perform less than $m!^{1.8}$ computations, and its outer-complexity is in $\mathcal{O}(m!^{1.8})$. This conjecture gives an upper estimate for the time complexity of the algorithm, which is compared with both a naive implementation and the actual number of verifications in the paper. Its resolution is not established in the supplied text.