  The disjunctive restricted chase is a sound and complete procedure for
solving boolean conjunctive query entailment over knowledge bases of
disjunctive existential rules. Alas, this procedure does not always terminate
and checking if it does is undecidable. However, we can use acyclicity notions
(sufficient conditions that imply termination) to effectively apply the chase
in many real-world cases. To know if these conditions are as general as
possible, we can use cyclicity notions (sufficient conditions that imply
non-termination). In this paper, we discuss some issues with previously
existing cyclicity notions, propose some novel notions for non-termination by
dismantling the original idea, and empirically verify the generality of the new
criteria.
