  Loop acceleration can be used to prove safety, reachability, runtime bounds,
and (non-)termination of programs. To this end, a variety of acceleration
techniques has been proposed. However, so far all of them have been monolithic,
i.e., a single loop could not be accelerated using a combination of several
different acceleration techniques. In contrast, we present a calculus that
allows for combining acceleration techniques in a modular way and we show how
to integrate many existing acceleration techniques into our calculus. Moreover,
we propose two novel acceleration techniques that can be incorporated into our
calculus seamlessly. Some of these acceleration techniques apply only to
non-terminating loops. Thus, combining them with our novel calculus results in
a new, modular approach for proving non-termination. An empirical evaluation
demonstrates the applicability of our approach, both for loop acceleration and
for proving non-termination.

Logic in Computer Science;Programming Languages