Résumé
We study the notion of boundedness in the contextof positive existential rules, that is, whether thereexists an upper bound to the depth of the chase pro-cedure, that is independent from the initial instance.By focussing our attention on the oblivious and thesemi-oblivious chase variants, we give a character-ization of boundedness in terms of FO-rewritabilityand chase termination. We show that it is decidableto recognize if a set of rules is bounded for several classes and outline the complexity of the problem.