Innermost Termination of Context-Sensitive Rewriting

Context-sensitive rewriting is a restriction of term rewriting used to model evaluation strategies in functional programming and in programming languages like OBJ. For example, under certain conditions termination of an OBJ program is equivalent to innermost termination of the corresponding contextsensitive rewrite system [25]. To prove termination of context-sensitive rewriting, several methods have been proposed in the literature which transform contextsensitive rewrite systems into ordinary rewrite systems such that termination of the transformed ordinary system implies termination of the original contextsensitive system. Most of these transformations are not very satisfactory when it comes to proving innermost termination. We investigate the relationship between termination and innermost termination of context-sensitive rewriting and we examine the applicability of the different transformations for innermost termination proofs. Finally, we present a simple transformation which is both sound and complete for innermost termination.