. Deterministic conditional rewrite systems are interesting because they permit extra variables on the right-hand sides of the rules. If such a system is quasi-reductive, then it is terminating and has a computable rewrite relation. It will be shown that every deterministic CTRS R can be transformed into an unconditional TRS U(R) such that termination of U(R) implies quasi-reductivity of R. The main theorem states that quasi-reductivity of R implies innermost termination of U(R). These results have interesting applications in two different areas: modularity in term rewriting and termination proofs of well-moded logic programs. 1 Introduction Conditional term rewriting systems (CTRSs) are the basis of functional logic programming; see [Han94] for an overview of this field. In CTRSs variables on the right-hand side of a rewrite rule which do not occur on the left-hand side are often forbidden. This is because it is in general not clear how to instantiate them. On the other hand, a rest..