We know by Immerman–Szelepcsényi theorem that $mathsf{NL}=mathsf{coNL}$? Does it follow from this theorem that $mathsf{NL}^mathsf{NL} = mathsf{NL}$? Here, $mathsf{NL}^mathsf{NL}$ denotes the class of problems which can be solved by an $mathsf{NL}$ machine with access to an $mathsf{NL}$ oracle.
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