First-order finite satisfiability vs tree automata in safety verification

In this paper we deal with verification of safety properties of term-rewriting systems. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which further resolved by a generic finite model finding procedure. A finite countermodel produced during successful verification provides with a concise description of the system invariant sufficient to demonstrate a specific safety property. We show the relative completeness of this approach with respect to the tree automata completion technique. On a set of examples taken from the literature we demonstrate the efficiency of finite model finding approach as well as its explanatory power.