Innermost Reachability of Bottom-Up Innermost Term Rewriting Systems

Abstract

Durand and Sénizergues (2007) showed that reachability of bottom-up linear term rewriting systems is decidable. In this paper we propose the class of bottom-up innermost systems by replacing “bottom-up rewriting” with “bottom-up innermost rewriting”, and show that innermost reachability is decidable for bottom-up innermost left-linear term rewriting systems. Furthermore, we give a class of bottom-up innermost systems—the class of strongly k-bottom-up innermost systems—and show that it is decidable whether a left-linear term rewriting system belongs to the class.