Source : Free On-Line Dictionary of Computing

termination analysis
     
        A program analysis which attempts to determine whether
        evaluation of a given expression will definitely terminate.
     
        Evaluation of a constant is bound to terminate, as is
        evaluation of a non-{recursive} function applied to arguments
        which are either not evaluated or which can themselves be
        proved to terminate.  A recursive function can be shown to
        terminate if it can be shown that the arguments of the
        recursive calls are bound to reach some value at which the
        recursion will cease.
     
        Termination analysis can never guarantee to give the correct
        answer because this would be equivalent to solving the
        {halting problem} so the answer it gives is either "definitely
        terminates" or "don't know".
     
        (1994-10-20)