Transformation for Refining Unraveled Conditional Term Rewriting Systems

Unravelings, transformations from conditional term rewriting systems (CTRSs, for short) into unconditional term rewriting systems, are valuable for analyzing properties of CTRSs. In order to completely simulate rewrite sequences of CTRSs, the restriction by a particular context-sensitive and membership condition that is determined by extra function symbols introduced due to the unravelings, must be imposed on the rewrite relations of the unraveled CTRSs. In this paper, in order to weaken the context-sensitive and membership condition, we propose a transformation applied to the unraveled CTRSs, that reduces the number of the extra symbols. In the transformation, updating the context-sensitive condition properly, we remove the extra symbols that satisfy a certain condition. If the transformation succeeds in removing all of the extra symbols, we obtain the TRSs that are computationally equivalent with the original CTRSs.