International audienceWe present a parameterized abstract domain for proving program termination by abstract interpretation. The domain automatically synthesizes piecewise-defined ranking functions and infers sufficient conditions for program termination. The analysis uses over-approximations but we prove its soundness, meaning that all program executions respecting these sufficient conditions are indeed terminating. The abstract domain is parameterized by a numerical abstract domain for environments and a numerical abstract domain for functions. This parameterization allows to easily tune the trade-off between precision and cost of the analysis. We describe an instantiation of this generic do- main with intervals and affine functions. We define all abstract operators, including widening to ensure convergence. To illustrate the potential of the proposed framework, we have implemented a research prototype static analyzer, for a small imperative language, that yielded interesting preliminary results
