In this paper we study applications of relations based on rewrite systems to regular tree languages. For instance, we want to deal with decidability problems of the form “R el(L ₁) ⊆ L ₂” where L ₁, L ₂ are regular tree languages and R el can be either IO, OI, parallel, or one step rewriting for a given rewrite system. Our method somehow standardizes previous ones because it reveals conditions R el must fulfill to preserve recognizability for the language R el(L ₁). Thanks to classes of recognizable languages wider than the regular one, we get some new results. We pursue this method to tackle the problem of computing the set of descendants of a regular tree language by a rewrite system.