Mühlherr's twist conjecture for finite-rank Coxeter systems

Let $(W,S)$ be a Coxeter system of finite rank, and let $S'$ be another set of Coxeter generators of $W$. Define

$$S^W=\{wsw^{-1}:s\in S\text{ and }w\in W\}.$$

The set $S$ is sharp-angled with respect to $S'$ if, for each pair $s,t\in S$ such that $2<m(s,t)<\infty$, there is a $w\in W$ such that $w\{s,t\}w^{-1}\subseteq S'$. The Coxeter systems $(W,S)$ and $(W,S')$ are twist equivalent if there is a finite sequence of elementary twists transforming $S$ into $S'$.

Twist conjecture. If $S'\subseteq S^W$ and $S$ is sharp-angled with respect to $S'$, then $(W,S)$ is twist equivalent to $(W,S')$.

This conjecture concerns the isomorphism problem for finite-rank Coxeter systems and predicts that the stated inclusion and sharp-angledness conditions are sufficient for the two generating sets to be related by elementary twists. It is attributed to Mühlherr; the supplied source gives no resolution, so its status remains open.