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In this paper, we compare the energy efficiencies (EEs) of direct transmission (DT), one-way relay transmission (OWRT) and two-way relay transmission (TWRT) in a system where two sourcie nodes transmit to each other and may be assisted by an amplify-and-forward relay node. We first find the maximum EEs of DT, OWRT and TWRT by jointly optimizing the transmission time and the transmit powers at each node. Then we compare the maximum EEs of the three strategies, and analyze the impact of circuit powers and bidirectional data amounts. Analytical and simulation results show that relaying is not always more energy efficient than DT. The EE of TWRT is higher than those of DT and OWRT when the bidirectional data amounts are equal. Otherwise, the advantage of TWRT diminishes, while either DT or OWRT may provide higher EE.