Ranking function synthesis is a key aspect to the success of
modern termination provers for imperative programs. While it is
well-known how to generate linear ranking functions for relations over
(mathematical) integers or rationals, efficient synthesis of ranking
functions for machine-level integers (bit-vectors) is an open
problem. This is particularly relevant for the verification of
low-level code. We propose several novel algorithms to generate
ranking functions for relations over machine integers: a complete
method based on a reduction to Presburger arithmetic, and a
template-matching approach for predefined classes of ranking functions
based on reduction to SAT- and QBF-solving.
The utility of our algorithms is demonstrated on examples drawn from
Windows device drivers.