In 2014, Heizmann et al. proposed a novel framework for program termination analysis. The analysis starts with a termination proof of a sample path. The path is generalized to a Buchi automaton (BA) whose language (by construction) represents a set of terminating paths. All these paths can be safely removed from the program. The removal of paths is done using automata difference, implemented via BA complementation and intersection. The analysis constructs in this way a set of BAs that jointly "cover" the behavior of the program, thus proving its termination. An implementation of the approach in Ultimate Automizer won the 1st place in the Termination category of SV-COMP 2017.

In this paper, we exploit advanced automata-based algorithms and propose several non-trivial improvements of the framework. To alleviate the complementation computation for BAs—one of the most expensive operations in the framework—, we propose a multi-stage generalization construction. We start with generalizations producing subclasses of BAs (such as deterministic BAs) for which efficient complementation algorithms are known, and proceed to more general classes only if necessary. Particularly, we focus on the quite expressive subclass of semideterministic BAs and provide an improved complementation algorithm for this class. Our experimental evaluation shows that the proposed approach significantly improves the power of termination checking within the Ultimate Automizer framework.