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Difference constraints have been used for termination analysis in theliterature, where they denote relational inequalities of the form x' <= y + c,and describe that the value of x in the current state is at most the value of yin the previous state plus some integer constant c. In this paper, we arguethat the complexity of imperative programs typically arises from counterincrements and resets, which can be modeled naturally by differenceconstraints. We present the first practical algorithm for the analysis ofdifference constraint programs and describe how C programs can be abstracted todifference constraint programs. Our approach contributes to the field ofautomated complexity and (resource) bound analysis by enabling automatedamortized complexity analysis for a new class of programs and providing aconceptually simple program model that relates invariant- and bound analysis.We demonstrate the effectiveness of our approach through a thoroughexperimental comparison on real world C code: our tool Loopus computes thecomplexity for considerably more functions in less time than related tools fromthe literature.

Difference Constraints: An adequate Abstraction for Complexity Analysis of Imperative Programs