ABSTRACT. The equational reasoning tool MaedMax implements maximal ordered completion. This new approach extends the maxSMT-based method for standard completion developed by Klein and Hirokawa (2011) to ordered completion and theorem proving. MaedMax incorporates powerful ground completeness checks and supports certification of proofs by an Isabelle-based certifier. It also provides an order generation mode which can be used to synthesize term orderings for other tools. Experiments show the potential of our approach.