Eventual Linear Ranking Functions
Roberto Bagnara, Fred Mesnard · 2013
Program termination is a hot research topic in program anal-ysis. The last few years have witnessed the development of termination analyzers for programming languages such as C and Java with remarkable precision and performance. These systems are largely based on techniques and tools coming from the field of declarative constraint programming. In this paper, we first recall an algorithm based on Farkas ’ Lemma for discovering linear ranking functions proving termination of a certain class of loops. Then we propose an extension of this method for showing the existence of eventual linear ranking functions, i.e., linear functions that become rank-ing functions after a finite unrolling of the loop. We show correctness and completeness of this algorithm. Keywords termination analysis, ranking function, eventual linear rank-ing function. 1.