  We describe an algorithm for proving termination of programs abstracted to
systems of monotonicity constraints in the integer domain. Monotonicity
constraints are a non-trivial extension of the well-known size-change
termination method. While deciding termination for systems of monotonicity
constraints is PSPACE complete, we focus on a well-defined and significant
subset, which we call MCNP, designed to be amenable to a SAT-based solution.
Our technique is based on the search for a special type of ranking function
defined in terms of bounded differences between multisets of integer values. We
describe the application of our approach as the back-end for the termination
analysis of Java Bytecode (JBC). At the front-end, systems of monotonicity
constraints are obtained by abstracting information, using two different
termination analyzers: AProVE and COSTA. Preliminary results reveal that our
approach provides a good trade-off between precision and cost of analysis.
