This paper presents the first step of a wider research effort to apply tree automata completion to the static analysis of functional programs. Tree Automata Completion is a family of techniques for com-puting or approximating the set of terms reachable by a rewriting rela-tion. The completion algorithm we focus on is parameterized by a set E of equations controlling the precision of the approximation and influenc-ing its termination. For completion to be used as a static analysis, the first step is to guarantee its termination. In this work, we thus give a sufficient condition on E and T (F) for completion algorithm to always terminate. In the particular setting of functional programs, this condi-tion can be relaxed into a condition on E and T (C) (terms built on the set of constructors) that is closer to what is done in the field of static analysis, where abstractions are performed on data.