  Numerous confluence criteria for plain term rewrite systems are known. For
logically constrained rewrite system, an attractive extension of term rewriting
in which rules are equipped with logical constraints, much less is known. In
this paper we extend the strongly-closed and (almost) parallel-closed critical
pair criteria of Huet and Toyama to the logically constrained setting. We
discuss the challenges for automation and present crest, a new tool for
logically constrained rewriting in which the confluence criteria are
implemented, together with experimental data.
