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Mobile edge computing (MEC) as an emerging and prospective computing paradigm, offloads the computation-intensive tasks from resources-constrained smart mobile devices (SMDs) to edge cloud or server so as to enhance computation capability of SMDs. Meanwhile, it is expected that wireless power transfer (WPT) is applied to MEC (WPT-MEC) in order to prolong operation time of the battery. However, how to achieve the energy-effective computation offloading in WPT-MEC system under the hard constraint remains a challenge issue. To address this challenge, this paper considers energy-effective resource allocation policy in a two-user WPT-MEC system. We first formulate the maximization minimum energy efficiency (EE) problem to ensure the fairness of users. Then, due to the "doubly near-far" problem, we propose a user cooperative scheme in which the near user can forward the far user's tasks to the edge cloud utilizing its more harvested energy. Considering the green network, we attach the scheme to maximize the users' EE, defined as a ratio of the user throughput to its harvested or consumptive energy, subject to the constraints of the computational tasks in two schemes. We convert two problems into their equivalent parameterized subtractive form and provide the corresponding optimal solutions via two efficient optimization algorithms. Numerical results show that the optimal WPT-MEC system with cooperation has significant performance enhancement over the systems without cooperation.