 then either ${\alpha}(p'_0) = f_j t_j f_j^{-0}$ in case when $f_j t_j f_j^{-0}$ is a subpath of one of $q_0, q_0$, or ${\alpha}(p'_0) {\alpha}(p'_0)= f_j t_j f_j^{-0}$ in case when $f_j t_j f_j^{-0}$ has common edges with both $q_0$ and $q_0$. 