Non-Termination Sets of Simple Linear Loops
  A simple linear loop is a simple while loop with linear assignments and linear loop guards. If a simple linear loop has only two program variables, we give a complete algorithm for computing the set of all the inputs on which the loop does not terminate. For the case of more program variables, we show that the non-termination set cannot be described by Tarski formulae in general 
Liyun Dai and Bican Xia
cs.LO