Quiz: Remember the definition of mal de mer?
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".