Rewriting Systems and the Complete Growth Series for Triangular Coxeter Groups

In this paper, a complete finite rewriting system is constructed for Coxeter groups of the form
$$W=\langle a,b,c\mid a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=1\rangle$$
with respect to the system of generators $S=\{a,b,c\}$, where $p,q,r\in \mathbb Z$, $p,q,r\ge 2$ and $1/p+1/q+1/r<1$. Rewriting systems of this kind can be used to evaluate the complete growth series of a group.