Property $R_{\mathrm{\infty }}$ for some spherical and affine Artin-Tits groups

Let $n\ge 2$. In this note we give a short uniform proof of property $R_{\mathrm{\infty }}$ for the Artin-Tits groups of spherical types $A_n$, $B_n$, $D_4$, $I_2(m)$ ($m\ge 3$), their pure subgroups, and for the Artin-Tits groups of affine types ${\tilde{A}}_{n-1}$ and ${\tilde{C}}_n$. In particular, we provide an alternative proof of a recent result of Dekimpe, Gon\c{c}alves and Ocampo, who established property $R_{\mathrm{\infty }}$ for pure Artin braid groups.