Twisted conjugacy classes in nilpotent groups

Let $N$ be a finitely generated nilpotent group. Algorithm is constructed such, that for every automorphism $\varphi \in Aut(N)$ defines the Reidemeister number $R(\varphi )\mathrm{.}$ It is proved that any free nilpotent group of rank $r=2$ or $r=3$ and class $c\ge 4r,$ or rank $r\ge 4$ and class $c\ge 2r,$ belongs to the class $R_{\mathrm{\infty }}\mathrm{.}$