Transforming context-sensitive rewrite systems

Abstract

We present two new transformation techniques for proving termination of context-sensitive rewriting. Our first method is simple, sound, and more powerful than previously suggested transformations. However, it is not complete, i.e., there are terminating context-sensitive rewrite systems that are transformed into non-terminating term rewrite systems. The second method that we present in this paper is both sound and complete. This latter result can be interpreted as stating that from a termination perspective there is no reason to study context-sensitive rewriting.