Modern warfare is characterized by a complex environment of operations spanning multiple domains leveraged to achieve advantage against the adversary in both strategic competition and armed conflict. However, understanding complexity in warfare, often referred to as the art of war, is rarely framed in a structured way. This report seeks to provide an initial examination of how complex adaptive systems thinking can frame opportunities and challenges of complexity in warfare. This report is the second of a two-volume report. It provides the technical details in support of the first volume, Leveraging Complexity in Great-Power Competition and Warfare: Volume I, An Initial Exploration of How Complex Adaptive Systems Thinking Can Frame Opportunities and Challenges. Three topics are covered in this volume: a literature review of complex adaptive systems research, a complex adaptive systems lens user manual, and a Markov chain formulation of the adversary decision process. This report should be of interest to warfighting planners, wargamers, complex adaptive systems researchers, and the military science and technology community.