Coxeter Groups, 2-Completion, Perimeter Reduction and Subgroup   Separability
  We show that all groups in a very large class of Coxeter groups are locally quasiconvex and have uniform membership problem solvable in quadratic time. If a group in the class satisfies a further hypothesis it is subgroup separable and relevant homomorphisms are also calculable in quadratic time.   The algorithm also decides if a finitely generated subgroup has finite index. 
Paul E. Schupp