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We report on the First International Competition on Computational Models of Argumentation (ICCMA'15) which took place in the first half of 2015 and focused on reasoning tasks in abstract argumentation frameworks. Performance of submitted solvers was evaluated on four computational problems wrt. four different semantics relating to the verification of the acceptance status of arguments, and computing jointly acceptable sets of arguments. In this paper, we describe the technical setup of the competition, and give an overview on the submitted solvers. Moreover, we report on the results and discuss our findings. [ABSTRACT FROM AUTHOR]