How to transform canonical decreasing ctrss into equivalent canonical trss

Abstract

We prove constructively that the class of ground-confluent and decreasing conditional term rewriting systems (CTRSs) (without extra variables) coincides with the class of orthogonal and terminating, unconditional term rewriting systems (TRSs). TRSs being included in CTRSs, this result follows from a transformation from any groundconfluent and decreasing CTRS specifying a computable function f into a TRS with the mentioned properties for f. The generated TRS is ordersorted, but we outline a similar transformation yielding an unsorted TRS.