Using invariant relations in the termination analysis of while loops

Abstract

Proving program termination plays an important role in ensuring reliability of software systems. Many researchers have lent much attention to this open long-standing problem, most of them were interested in proving that iterative programs terminate under a given input. In this paper, we present a method to solve a more interesting and challenging problem, namely, the generation of the termination condition of while loops i.e. condition over initial states under which a loop terminates normally. To this effect, we use a concept introduced by Mili et al., viz. invariant relation.