  In earlier work, we developed an approach for automatic complexity analysis
of integer programs, based on an alternating modular inference of upper runtime
and size bounds for program parts. In this paper, we show how recent techniques
to improve automated termination analysis of integer programs (like the
generation of multiphase-linear ranking functions and control-flow refinement)
can be integrated into our approach for the inference of runtime bounds. The
power of the resulting approach is demonstrated by an extensive experimental
evaluation with our new re-implementation of the corresponding tool KoAT.
