Abstract. Recursive path ordering (RPO) is a well-known reduction ordering introduced by Dershowitz [6], that is useful for proving termination of term rewriting systems (TRSs). Jouannaud and Rubio generalized this ordering to the higher-order case thus creating the higher-order recursive path ordering (HORPO) [8]. They proved that this ordering can be used for proving termination of higher-order TRSs which essentially comes down to proving well-foundedness of the union of HORPO and βreduction relation of simply typed lambda calculus (λ →), [1]. This result entails well-foundedness of RPO and termination of λ →. This paper describes author’s undertaking of providing a complete, axiomfree, fully constructive formalization of those results in the theorem prover Coq. Formalization is complete and hence it contains all the dependant results for λ → , multisets and multiset extension of the relation. Also decidability of HORPO has been proven and due to constructive nature of this proof a certified algorithm to verify whether two terms can be oriented with HORPO can be extracted from this proof. 1