from
The Free On-line Dictionary of Computing (8 July 2008)
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)