Rewrite-Based Decision Procedures

The rewrite-based approach to satisfiability modulo theories consists of using generic theorem-proving strategies for first-order logic with equality. If one can prove that an inference system generates finitely many clauses from the presentation T of a theory and a finite set of ground unit clauses, then any fair strategy based on that system can be used as a T -satisfiability procedure. In this paper, we introduce a set of sufficient conditions to generalize the entire framework of rewrite-based T -satisfiability procedures to rewrite-based T -decision procedures. These conditions, collectively termed subterm-inactivity, will allow us to obtain rewrite-based T -decision procedures for several theories, namely those of equality with uninterpreted functions, arrays with or without extensionality and two of its extensions, finite sets with extensionality and recursive data structures.