I am reading the paper "Virtual knot groups by Se-Goo Kim". In the proof of Lemma 2, the author first considered a group presentation $\langle t_1, \ldots, t_n~|~r_1, \ldots, r_m \rangle $, where $m=n$ or $m=n-1$. After this author has written "If $m=n-1$, by doubling the relator $r_m$, we may assume $m=n$."
I am not sure what he meant by "doubling the relator $r_m$". I have attached the screenshot.
Can someone clear this doubt? It would be helpful for me. Thank you.
It means considering $$\Pi'=\langle t_1,\dots, t_n\mid r_1, \dots, r_n, r_{m+1}\rangle,$$ where $r_{m+1}=r_m$. Then $\operatorname{def}(\Pi')=n-(m+1)$, and since $m=n-1$ by hypothesis, $\operatorname{def}(\Pi')=n-n=0$.
As @DerekHolt points out, though, it's not clear what to do if $n=1, m=0$, since then there's no relator to double, although perhaps one might accept $r_1:=t_1$; that is, introduce the relation $t_1=1$.