Formalizing Monotone Algebras for Certification of Termination and Complexity Proofs?

Abstract. Monotone algebras are frequently used to generate reduction orders in automated termination and complexity proofs. To be able to certify these proofs, we formalized several kinds of interpretations in the proof assistant Isabelle/HOL. We report on our integration of matrix interpretations, arctic interpretations, and nonlinear polynomial inter-pretations over various domains, including the reals.