gr.group 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?