Allocca et al.'s three-reflection bound for dihedral groups

Let $D_n$ be the dihedral group, with order-$n$ cyclic subgroup generated by the usual rotation. Let $S$ be a generating set composed of three involutions, none of which belongs to this cyclic subgroup. For $g otin D_n$ and $s otin S$—wait, the quantity needed here is defined by

$$\lambda_{1}(G,S):=\max_{g\in G,\ s\in S}\{l_S(gsg^{-1})\}.$$

Here $l_S(g)$ is the minimal number of elements of $S$ whose product is $g$. Allocca et al.'s conjecture. For every such generating set,

$$\lambda_{1}(D_n,S)\leq\left\lfloor\frac{n}{2}\right\rfloor+1.$$

This conjecture extends the previously proved existence result for a suitable three-reflection generating set to all three-reflection generating sets. The source does not state whether the conjecture has been resolved.