Cyclone: A Heterogeneous Tool for Verifying Infinite Descent

The Infinite Descent property underpins key verification techniques, such as size-change program termination and cyclic proofs. Deciding whether the Infinite Descent property holds of a given program or cyclic deduction is PSPACE-complete, with several exponential time algorithms in the literature. In this paper, we consider algorithms with better time complexity but which are (necessarily) incomplete. Concretely, we formulate and evaluate a number of alternative algorithms for semi-deciding Infinite Descent. Our aim is to improve average runtime performance by utilising more efficient algorithms for specific subclasses of input. We present Cyclone, a tool integrating these algorithms with an existing (complete) decision procedure. We evaluate Cyclone on a large suite of examples harvested from the Cyclist theorem prover, finding that the incomplete algorithms achieve extremely high coverage and afford substantial runtime improvement in practice. We thus believe that the Cyclone tool will foster broader adoption of techniques based on Infinite Descent and expand their practical applications.