Certification of Complexity Proofs using CeTA

Certification of Complexity Proofs using CeTA
M. Avanzini and C. Sternagel and R. Thiemann
Proceedings of the 26th International Conference on Rewriting Techniques and Applications, volume 36 of Leibnitz International Proceedings in Informatics, pages 23–39, 2015.


Nowadays certification is widely employed by automated termination tools for term rewriting, where certifiers support most available techniques. In complexity analysis, the situation is quite different. Although tools support certification in principle, current certifiers implement only the most basic technique, namely, suitably tamed versions of reduction orders. As a consequence, only a small fraction of the proofs generated by state-of-the-art complexity tools can be certified. To improve upon this situation, we formalized a framework for the certification of modular complexity proofs and incorporated it into CeTA. We report on this extension and present the newly supported techniques (match-bounds, weak dependency pairs, dependency tuples, usable rules, and usable replacement maps), resulting in a significant increase in the number of certifiable complexity proofs. During our work we detected conflicts in theoretical results as well as bugs in existing complexity tools.


Term Rewriting, Complexity Analysis, Runtime Complexity Analysis, Certification