Cordovil–Moreira cyclic ordering conjecture for two matroid bases

Let $M$ be a finite loopless matroid of rank $r$, and let $B=\{b_1,\dots,b_r\}$ and $B'=\{b'_1,\dots,b'_r\}$ be two bases of $M$. A cyclic ordering is an ordering considered cyclically, so that every block of $r$ consecutive elements is required to be a base. Cordovil–Moreira's conjecture. There are permutations $(b_{\pi(1)},\ldots,b_{\pi(r)})$ of the elements of $B$ and $(b'_{\pi'(1)},\ldots,b'_{\pi'(r)})$ of the elements of $B'$ such that the combined sequence $(b_{\pi(1)},\ldots,b_{\pi(r)},b'_{\pi'(1)},\ldots,b'_{\pi'(r)})$ is a cyclic ordering in which every $r$ cyclically consecutive elements form a base. This conjecture is known for graphical matroids, but remains open for general matroids.