Non-cooperative game theory deals with games with complete rules. Most solution concepts in non-cooperative game theory are defined on the normal form. It is ex ante not clear whether a strategic situation is noncooperative and thus can be analyzed as a normal form game. The means to verify the completeness of the rules is to write the game in extensive form. However, many extensive form games have the same semi-reduced normal form. This paper characterizes the class of finite extensive form games with perfect recall and the same semi-reduced normal form by replicating the work of Elmes and Reny (1994) in a theoretical framework developed by Alos-Ferrer and Ritzberger. The necessary and sufficient conditions are three transformations of the extensive form. These are embedded in the space of extensive form games and an order relation is established.