Infinite Normal Forms for Non-Linear Term Rewritting Systems

Nonterminating rewrite relations have recently been studied in order to set a framework within which infinite terms can be seen as limits of infinite converging derivations. Results about the existence of infinite normal forms have been given only for orthogonal term rewriting systems, namely left-linear and nonoverlapping systems. In this paper we show that some of those results can be extended to a particular class of nonorthogonal term rewriting systems. We deal with systems in which the nonterminating rules are unfolding rules that model the operational semantics of a recursive operator. The left-linearity requirement is replaced by a retraction property of the supporting term algebra, that allows the definition of a rewrite relation modulo a congruence relation induced on the set of terms by the unfolding rules