Closed-Face Integrality and Exact Conditional Termination for Cone-Monotone Integer Equality Relations

This paper gives an exact characterization of conditional termination for a class of nondeterministic homogeneous integer equality relations over nonnegative integer coefficient vectors. The central result identifies precisely when the descending predecessor sequence reaches the weakest nontermination precondition after finitely many steps. Under pointedness of the source cone, nonzero source…