Rational rewriting

So far, the works in this area have tried to define suitable properties of non-terminating relations in order to guarantee that the intended infinite term can be reached as the limit of w-converging derivations. The main advantage of these approaches is the generality of the framework with respect to the set of infinite definable terms: no a priori assumption is made on the set of definable infinite data structure. Restrictions instead apply on the kind of infinite derivations they can deal with (top erminating/strongly convergent) and on the term rewriting system, in order to guarantee the reachability of the infinite terms within w-steps. To this respect the restrictions are quite heavy since only left-linear (orthogonal) term rewriting systems can be managed. In this paper we propose a different approach based on the following consideration: in the above mentioned papers the need for considering non-terminating relations is a side effect of the definitional mechanism for infinite terms. That is the only way to deal with infinite terms is by giving the rules for constructing them.