  Let $(R,m)$ be a Cohen-Macaulay local ring of positive dimension $d$ and
infinite residue field. Let $I$ be an m-primary ideal and $J$ a minimal
reduction of $I$. In this paper, we show that $\widetilde{r_J(I)}\leq r_J(I)$.
This answer to a question that made by M.E. Rossi and I. Swanson in [\ref{Rs},
Question 4.6].
