Let $\mathfrak{g}$ be a semisimple Lie algebra of rank l and let $\Delta^+$ be its set of positive roots. Denote by $s_1,...,s_l$ the simple generators of its Weyl group and let $w_0$ be the longest element of the Weyl group.

We have a bijective correspondence between convex orderings on $\Delta^+$ and reduced decompositions of $w_0.$

My question is: given a reduced decomposition $w_0=s_{i_i}\dots s_{i_n},$ with corresponding convex order $\alpha_{i_1}< \dots < \alpha_{i_n}$ on $\Delta^+$ what is the reduced decomposition that corresponds to the opposite convex order $\alpha_{i_n}< \dots < \alpha_{i_1}$?

Thank you so much in advance