Finite quotient detection conjecture for the Andrews--Curtis conjecture

Let $F_2=\langle x,y\rangle$ be the free group of rank two, and let $u(x,y),v(x,y)$ be normal generators of $F_2$. For a finite factor group $G$ of $F_2$, write $\bar x,\bar y$ and $u(\bar x,\bar y),v(\bar x,\bar y)$ for the corresponding images, and let $\Delta_2(G,G)$ be the Andrews--Curtis graph of $G$. Finite quotient detection conjecture. If the normal generators $x,y$ and $u(x,y),v(x,y)$ of $F_2$ are not connected by Andrews--Curtis transformations, then there exists a finite factor group $G$ in which $(\bar x,\bar y)$ and $(u(\bar x,\bar y),v(\bar x,\bar y))$ belong to different connected components of $\Delta_2(G,G)$. This conjecture proposes a finite-quotient test for detecting counterexamples to the Andrews--Curtis conjecture; the source presents it as an open possible reduction and gives no resolution.