Size-change termination, monotonicity constraints and ranking functions

Abstract

Size-change termination involves deducing program termination based on the impossibility of infinite descent. To this end we may use a program abstraction in which transitions are described by monotonicity constraints over (abstract) variables. When only constraints of the form x >′ and x≥y′are allowed, we have size-change graphs, for which both theory and practice are now more evolved then for general monotonicity constraints. This work shows that it is possible to transfer some theory from the domain of size-change graphs to the general case, complementing and extending previous work on monotonicity constraints. Significantly, we provide a procedure to construct explicit global ranking functions from monotonicity constraints in singly-exponential time, which is better than what has been published so far even for size-change graphs. We also consider the integer domain, where general monotonicity constraints are essential because the domain is not well-founded. © 2009 Springer Berlin Heidelberg.