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Cloning attacks threaten radio-frequency identification (RFID) applications but are hard to prevent. Existing cloning attack detection methods are enslaved to the knowledge of tag identifiers (IDs). Tag IDs, however, should be protected to enable and secure privacy-sensitive applications in anonymous RFID systems. In a first step, this paper tackles cloning attack detection in anonymous RFID systems without requiring tag IDs as a priori. To this end, we leverage unreconciled collisions to uncover cloning attacks. An unreconciled collision is probably due to responses from multiple tags with the same ID, exactly the evidence of cloning attacks. This insight inspires GREAT, our pioneer protocol for cloning attack detection in anonymous RFID systems. We evaluate the performance of GREAT through theoretical analysis and extensive simulations. The results show that GREAT can detect cloning attacks in anonymous RFID systems fairly fast with required accuracy. For example, when only six out of 50,000 tags are cloned, GREAT can detect the cloning attack in 75.5 s with a probability of at least 0.99.