Reconfigurable intelligent surfaces (RISs) have drawn considerable attention due to their ability to direct electromagnetic waves into desirable directions. Although RISs share some similarities with relays, the two have fundamental differences impacting their performance. To harness the benefits of both, we propose a downlink system wherein a relay and an RIS improve performance in terms of energy-efficiency. Using singular value decomposition (SVD), semidefinite programming (SDP), and function approximations, we propose different solutions for optimizing the beamforming matrices at the base-station (BS), the relay, and the phase shifts at the RIS to minimize the total power under quality-of-service (QoS) constraints. The problem is solved when the relay operates in half-duplex and full-duplex modes and when the reflecting elements have continuous and discrete phase shifts. Simulation results compare the performance of the system with and without the RIS or the relay, under different optimization solutions. The results show that the system with full-duplex relay and RIS outperforms the other scenarios, and the contribution of full-duplex relay is higher than that of the RIS. However, an RIS outperforms a half-duplex relay when the required QoS is high. The results also show that increasing the number of reflecting elements improves the performance better in the presence of a relay than in its absence.