On the Word, Subsumption, and Complement Problem for Recurrent Term Schematizations

We investigate the word and the subsumption problem for recurrent term schematizations, which are a special type of constraints based on iteration. By means of uniication, we reduce these problems to a fragment of Presburger arithmetic. Our approach is applicable to all recurrent term schematizations having a nitary uniication algorithm. Furthermore, we study a particular form of the complement problem. Given a nite set of terms, we ask whether its complement can be nitely represented by schematizations, using only the equality predicate without negation. The answer is negative as there are ground terms too complex to be represented by schematizations with limited resources.