The following technical report is available from http://aib.informatik.rwth-aachen.de:
Lower Runtime Bounds for Integer Programs Florian Frohn, Matthias Naaf, Jera Hensel, Marc Brockschmidt, and Jürgen Giesl AIB 2016-03
We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs. To this end, we construct symbolic representations of program executions using a framework for iterative, under-approximating program simplification. The core of this simplification is a method for (under-approximating) program acceleration based on recurrence solving and a variation of ranking functions. Afterwards, we deduce asymptotic lower bounds from the resulting simplified programs. We implemented our technique in our tool LoAT and show that it infers non-trivial lower bounds for a large number of examples.