LoAT (Lower bounds Analysis Tool): Lower runtime bounds for integer programs. 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.

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