Status quo analysis algorithms developed within the paradigm of the graph model for conflict resolution are applied to an international river basin conflict involving the United States and Canada to assess the likeliness of various compromise resolutions. The conflict arose because the state of Montana feared that further expansion of the Sage Creek Coal Company facilities in Canada would pollute the Flathead River, which flows from British Columbia to Montana. Significant insights not generally available from a static stability analysis are obtained about potential resolutions of the conflict under study and about how decision makers' interactions may direct the conflict to distinct resolutions. Analyses also show how political considerations may affect a particular decision maker's choice, thereby influencing the evolution of the conflict.