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As tax authorities around the world increase their use of AI-based techniques, taxpayers are increasingly at a loss about whether and how the ensuing decisions follow the procedures required by law and respect their substantive rights. The use of XAI has been proposed as a response to this issue, but it is still an open question whether current XAI techniques are enough to meet existing legal requirements. The paper approaches this question in the context of a case study: a prototype tax fraud detector trained on an anonymized dataset of real-world cases handled by the Buenos Aires (Argentina) tax authority. The decisions produced by this detector are explained through the use of various classification methods, and the outputs of these explanation models are evaluated on their explanatory power and on their compliance with the legal obligation that tax authorities provide the rationale behind their decision-making. 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