AC-replacement algorithm conjecture for black box groups

Let $G$ be a black box group and let $N\lhd G$. The Andrews--Curtis graph $\Delta_k(G,N)$ supports a nearest-neighbour random walk, and the AC-replacement algorithm $ACR_k(G,N)$ runs such a walk and returns a random component of the resulting tuple. AC-replacement algorithm conjecture. The algorithm $ACR_k(G,N)$ provides a good black box for $N$ for at least some $k$. This is presented as a proposed modification of the product replacement algorithm; the source gives no resolution or precise meaning of “good” beyond the stated algorithmic motivation.