We consider existential rules (also called Tuple-Generating Dependencies or Datalog+/- rules). These rules are particularly well-suited to the topical ontological query answering problem, which consists of querying data while taking terminological knowledge into account. Since this problem is not decidable in general, various conditions ensuring decidability have been proposed in the literature. In this paper, we focus on conditions that restrict the way rules may interact to ensure that the forward chaining mechanism is finite. After a review of existing proposals, we propose a generalization of the notion of rule dependency, namely k-dependency, that allows to enlarge halting cases. It can also be used to compile the rule base, which leads to improve query answering algorithms.