Sustainability has captured the attention of the classical management of business processes. Organizations have become increasingly aware of the need to achieve information technology (IT)-enabled business processes that are successful in their economy and ecological and social impact. In this context, Green BPM concerns business processes' modeling, deployment, optimization, and management with dedicated consideration for environmental consequences. Automated process discovery is a crucial process mining task to help organizations to get knowledge of the process they carry out in their daily operation, providing the basis for insights and evidence-based improvement decisions. Several process discovery algorithms have been developed and evaluated by the classical measures on resulting models, such as fitness, precision, f-score, soundness, complexity (size, structuredness, and control-flow complexity), generalization, and the execution time of the algorithm. Within the context of automated process discovery, sustainability adds a new indicator: energy efficiency. This paper extends a well-known benchmark for evaluating automated process discovery methods, measuring the energy efficiency of selected discovery methods with the same publicly available dataset. The expected contribution is to raise more awareness among the developers of process discovery methods about the energy impact of their solutions beyond the more traditional well-known measures.