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I wanted to covert the finite automata of the question 'when no two a's and no two b's should come together' to regular expression. But I am not able to do so.

I have attached my working. Kindly see it and please tell where I am wrong. Also, I am not able to eliminate state B (and not eliminating step C) or vice-versa and draw it as a FA. Please also show the diagram if I eliminate B after eliminating C.

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