Twisted conjugacy growth series conjecture

Let $G$ be a finitely presented group. For each automorphism $\psi$ of $G$, let $\mathrm{Gr}_{\psi,G}^S(n)$ denote the corresponding twisted conjugacy growth function, and let its twisted conjugacy growth series be the formal power series

$$\sum \mathrm{Gr}_{\psi,G}^S(n)x^n.$$

Twisted conjugacy growth series conjecture. The group $G$ is virtually abelian if and only if all its twisted conjugacy growth functions are rational. This is presented as a twisted analogue of the conjecture on rational conjugacy growth series; the source gives no resolution status.