Gabow's exchange-distance conjecture for disjoint matroid bases

Let $M$ be a matroid of rank $r$, and let $X_1$ and $X_2$ be disjoint bases. The exchange distance of two basis sequences is the minimum number of symmetric exchanges needed to transform one sequence into the other. Gabow's conjecture. The exchange distance of $(X_1,X_2)$ and $(X_2,X_1)$ is $r$. This problem was formulated by Gabow and later stated as a conjecture by Wiedemann and by Cordovil and Moreira. It is known for several classes of matroids, but remains open in general.