We numerically simulate two-dimensional, decaying elastoinertial turbulence using the finitely extensible, nonlinear, elastic spring model. We vary the polymer concentration over seven decades, and observe two turbulent elastoinertial regimes. In the weakly coupled regime only the small scale structures change, while in the strongly coupled regime all structures change. This regime is dominated by elastoinertial shock waves with drag reduction properties; i.e., the energy decay rate decreases when the polymer concentration increases
