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 computing or approximating the set of terms reachable by a rewriting relation. The completion algorithm we focus on is parameterized by a set $E$ of equations controlling the precision of the approximation and influencing 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 $\TF$ for completion algorithm to always terminate. In the particular setting of functional programs, this condition can be relaxed into a condition on $E$ and $\TC$ (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.