2 problems

Let $G$ be a group, and let $B(\Gamma)$ be a right-angled Baumslag–Solitar–Artin group whose underlying undirected graph is a star graph. Suppose that $G$ is virtually $B(\Gamma)$,…

Deficiency-one decidability conjecture. If $|A|-|R|=1$, then the Diophantine problem in $G$ is decidable.