; 2; 1; Universit`a di Pisa, Dipartimento di Informatica; 2
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; Corso Italia 40, I-56214 Pisa, Italy; TUB, Fachbereich 13 Informatik, Franklinstrae 28/29, D-10587 Berlin, Germany
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. Rational terms (possibly infinite terms with finitely many subterms) can be represented in a finite way via -terms, that is, terms over a signature extended with self-instantiation operators. For example, f ! = f(f(f(: : :))) can be represented as x :f(x) (or also as x :f(f(x)), f(x :f(x)), . . . ). Now, if we reduce a -term t to s via a rewriting rule using standard notions of the theory of Term Rewriting Systems, how are the rational terms corresponding to t and to s related? We answer to this question in a satisfactory way, resorting to the definition of infinite parallel rewriting proposed in . We also provide a simple, algebraic description of -term rewriting through a variation of Meseguer's Rewriting Logic formalism. 1 Introduction Rational terms are possibly infinite terms with a finite set of subterms. They show up in a natural way in Theoretical Computer Science whenever some finite cyclic structures are of concern (for example data flow diagrams, cyclic te...