Abstract: If P is a set of open terms, Red(P) is the set of terms that contain at least a subterm which is an instance of a term in P. The main theorem of this paper says that if L is a regular language of ground terms and P is a finite set of open terms such that L \subseteq Red(P), then there exists a finite set P* such that all the terms of P* are linear instances of terms in P and L \subseteq Red(P*). Applications of this result to ground reducibility of term rewrite systems are also discussed. This work was done while the author was visiting INRIA-Lorraine.