Decidable Approximations of Sets of Descendants and Sets of Normal Forms

We present here decidable approximations of sets of descendants and sets of normal forms of Term Rewriting Systems, based on speciic tree automata techniques. In the context of rewriting logic, a Term Rewriting System is a program, and a normal form is a result of the program. Thus, approximations of sets of descendants and sets of normal forms provide tools for analysing a few properties of programs: we show how to compute a superset of results, to prove the suucient completeness property, or to nd a criterion for proving termination under a speciic strategy, the sequential reduction strategy. The main technical contribution of the paper is the construction of an approximation automaton which recognises a superset of the set of normal forms of terms in a set E, w.r.t. a Term Rewriting System R.