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Using a symbolic dynamics and a surrogate data approach, we show that the language exhibited by common fruit flies Drosophila ('D.') during courtship is as grammatically complex as the most complex human-spoken modern languages. This finding emerges from the study of fifty high-speed courtship videos (generally of several minutes duration) that were visually frame-by-frame dissected into 37 fundamental behavioral elements. From the symbolic dynamics of these elements, the courtship-generating language was determined with extreme confidence (significance level > 0.95). The languages categorization in terms of position in Chomsky's hierarchical language classification allows to compare Drosophila's body language not only with computer's compiler languages, but also with human-spoken languages. Drosophila's body language emerges to be at least as powerful as the languages spoken by humans.