Automatic uncomputation aims to provide programming-language-level support to facilitate the correct and safe use of ancilla qubits in quantum computing, but efforts have only been made for clean ancillas, leaving dirty ancillas unexplored. We present a unified formalization of the uncomputation of both clean and dirty ancillas. For the first time, we prove that checking the existence of uncomputation is coNP-hard. We introduce two complementary synthesis-oriented existence checking methods: a syntax-directed static reasoning system and a rewrite-based normalization procedure (\RwUnx), together forming a top-down pipeline. We implement \RwUnx in Qiskit. Compared with the state-of-the-art \Reqompx, \RwUnx handles practical benchmarks with complex dependencies where \Reqompx does not, and achieves higher success rates in random-circuit experiments.

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