The Free On-line Dictionary of Computing (30 December 2018):

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)