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Are there any known reversible pairing functions f: $f: \mathbb N \times \mathbb N \to \mathbb N$ that can be computed in constant time (FAC⁰)?

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Are there any pairing functions computable in constant time (AC⁰)

Are there any known reversible pairing functions f: ℕ ⨉ ℕ → ℕ that can be computed in constant time (FAC⁰)?