Termination Analysis of Linear Programs with Conditionals

Proving termination of program loops is necessary in many applications, especially those safety critical software. Discovering ranking function is a classical method to prove the termination, but the existence of ranking function is a sufficient condition on the termination of a loop program. In this paper, we present an algorithm to remedy the limitation of ranking function for analyzing the termination of linear programs with conditionals. We transform the linear loop programs with conditionals into the nested linear loop programs, and then check whether the inner loop terminates or not by positive eigenvalues and their corresponding eigenvectors. If one of the inner loop in the nested linear loop is nonterminating, then the linear loop is nonterminating. Otherwise, we use discovering ranking functions based on qualifier elimination to analyze the termination of the linear loop. To illustrate the main idea of the algorithm, we perform it on some examples.