The L-Depth Eventual Linear Ranking Functions for Single-Path Linear Constraint Loops

Termination of loop programs has received extensive attention in these years. In this paper, we focus on the termination of single-path linear constraint loops. For single-path linear constraint loops which have no linear ranking functions or eventual linear ranking functions, we present a complete method to detect the existence of l-depth eventual linear ranking functions. Our method extends the work of Bagnara and Mesnard. The prototype of our method has been implemented and the effectiveness of our method has been shown by experimental results.