An active database consists of a traditional database supplemented by a set of Event-Condition-Action (ECA) rules. One of the key questions for active database designers is that of termination of the ECA rules. The behaviour of the ECA rules may be obscure and their semantics is often not specified formally. Consequently, developing termination analysis algorithms and proving their correctness is a challenging task. In this paper we address this problem for functional active databases by adopting an abstract interpretation approach. By ``functional active databases'' we mean active databases whose transaction execution semantics have been expressed in a purely functional language. Although we demonstrate our techniques for a specific active DBMS which supports a functional database programming language interface, these techniques are directly applicable to other active DBMSs whose execution semantics have been specified using a functional or a denotational approach.