  We study the notion of boundedness in the context of positive existential
rules, that is, whether there exists an upper bound to the depth of the chase
procedure, that is independent from the initial instance. By focussing our
attention on the oblivious and the semi-oblivious chase variants, we give a
characterization of boundedness in terms of FO-rewritability and chase
termination. We show that it is decidable to recognize if a set of rules is
bounded for several classes and outline the complexity of the problem.
  This report contains the paper published at IJCAI 2019 and an appendix with
full proofs.
