Termination Verification System for Term Rewriting Systems Using Binary Decision Diagram

Abstract

We present a method of proving the termination of term rewriting systems(computational systems specified by a set of rewrite rules)by using binary decision diagrams(BDD's) for efficient representation of provability. First, we give a recursive definition of the Boolean function that computes the provability based on a partial ordering &sc; on the set of function symbols. Then the construction of the BDD's for this function, in which a primitive expression f &sc; g consisting of two function symbols f and g is associated with the logical variable x_<fg>, is incorporated into an interactive, incremental termination verification procedure. We conduct some experiments to see how the performance of this procedure is affected by some heuristic selection of variable orderings and constraint orderings, and show that our method and heuristics are useful.