González-Meneses–Wiest polynomial bound for cyclic sliding periods

Let $B_n$ be the braid group on $n$ strands, let $x\in B_n$ have canonical length $r$, and let $\mathfrak{s}$ denote the cyclic sliding operation. Let $t$ be the minimal positive integer such that

$$\mathfrak{s}^k(x)=\mathfrak{s}^t(x)$$

for some integer $k$ with $0\leqslant k<t$. González-Meneses–Wiest conjecture. The integer $t$ is bounded by a polynomial in $r$ and $n$. The conjecture would give polynomial complexity, in both braid length and braid index, for the reducibility algorithm based on iterated cyclic sliding. The source presents no resolution of the conjecture.