Notes on Structure-Preserving Transformations of Conditional Term Rewrite Systems

Abstract

Transforming conditional term rewrite systems (CTRSs) into unconditional systems (TRSs) is a common approach to analyze properties of CTRSs via the simpler framework of unconditional rewriting. In the past many different transformations have been introduced for this purpose. One class of transformations, so-called unravelings, have been analyzed extensively in the past. In this paper we provide an overview on another class of transformations that we call structure-preserving transformations. In these transformations the structure of the conditional rule, in particular their left-hand side is preserved in contrast to unravelings. We provide an overview of transformations of this type and define a new transformation that improves previous approaches.