The following two XFST replace rules represent a cyclic feeding interaction, where the final result includes the original form because the first rule feeds into the second and the second feeds into the first. For example, the first rule would (optionally) turn bat into cat, and the second rule would (optionally) turn cat back into bat.
c (<-) b ;
b (<-) c ;
It is, of course, possible to apply the rules to a lexicon and then compare with the original lexicon, but this is very inefficient. I already have a way to detect cyclic feeding interactions of this kind involving two or more rules (by reading the source files with python), but it is not sensitive to conditional replacement, such as c (<-) b || _ x.
Is it possible to detect whether a set of rules is cyclic by using HFST, without having to apply the rules to a lexicon?