  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.
