  Termination property of functions is an important issue in computability
theory. In this paper, we show that repeated iterations of a function can
induce an order amongst the elements of its domain set. Hasse diagram of the
poset, thus obtained, is shown to look like a forest of trees, with a possible
base set and a generator set (defined in the paper). Isomorphic forests may
arise for different functions and equivalences classes are, thus, formed. Based
on this analysis, a study of the class of deterministically terminating
functions is presented, in which the existence of a Self-Ranking Program, which
can prove its own termination, and a Universal Terminating Function, from which
every other terminating function can be derived, is conjectured.
