Precise cost analysis via local reasoning

The classical approach to static cost analysis is based on first transforming a given program into a set of cost relations, and then solving them into closed-form upper-bounds. The quality of the upper-bounds and the scalability of such cost analysis highly depend on the precision and efficiency of the solving phase. Several techniques for solving cost relations exist, some are efficient but not precise enough, and some are very precise but do not scale to large cost relations. In this paper we explore the gap between these techniques, seeking for ones that are both precise and efficient. In particular, we propose a novel technique that first splits the cost relation into several atomic ones, and then uses precise local reasoning for some and less precise but efficient reasoning for others. For the precise local reasoning, we propose several methods that define the cost as a solution of a universally quantified formula. Preliminary experiments demonstrate the effectiveness of our approach.