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I believe it would match the relaxed RCCA security, but it looks like it wouldn't be of much use because reencryption would not be secure. You could generate reencryptions of any ciphertext, but they would not be indistinguishable from each other, i.e. given $c_1$ and $c_2$ you can determine easily whether $c_2$ is a reencryption of $c_1$.

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