Size-Change Termination, Monotonicity Constraints and Ranking Functions

TL;DR

This paper extends size-change termination theory to general monotonicity constraints, providing decision procedures and efficient ranking function construction methods for program termination proofs.

Contribution

It adapts and extends size-change graph theory to the broader class of monotonicity constraints, improving decision procedures and ranking function synthesis.

Findings

Decision procedures for termination in the general case

Construction of global ranking functions in singly-exponential time

Enhanced theoretical framework for monotonicity constraints

Abstract

Size-Change Termination (SCT) is a method of proving 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>y' and x>=y' are allowed, we have size-change graphs. Both theory and practice are now more evolved in this restricted framework then in the general framework of monotonicity constraints. This paper shows that it is possible to extend and adapt some theory from the domain of size-change graphs to the general case, thus complementing previous work on monotonicity constraints. In particular, we present precise decision procedures for termination; and 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.