theory – Algorithm for Root System of Coxeter Group Generated by Permutations

Suppose we are given a group $G$ in terms of generators $t_1, …, t_n$ which are order 2 in $S_m$ (however we don’t assume anything other than that these elements generate $G$ and have order 2). Since $G$ is finite and generated by transpositions, it must have a root system. What is the best known algorithm for finding the root system?