Equational approximations for tree automata completion

In this paper we deal with the verification of safety properties of infinite-state systems modeled by term-rewriting systems. An over-approximation of the set of reachable terms of a term-rewriting system R is obtained by automatically constructing a finite tree automaton. The construction is parameterized by a set E of equations on terms, and we also show that the approximating automata recognize at most the set of R/E-reachable terms. Finally, we present some experiments carried out with the implementation of our algorithm. In particular, we show how some approximations from the literature can be defined using equational approximations