Muammar Gaddafi resigns in 2011. What happens next?

In this timeline, before the army can purge the protesters and light the bonfire which was the Libyan Civil War, members of Muammar Gaddafi's regime convince him to resign from the leadership of the Great Socialist People's Libyan Arab Jamahiriya (the official name of Gaddafi-era Libya). Gaddafi does this, but does not leave Libya. He instead goes into exile in his hometown of Sirte.

With Gaddafi peacefully removed, but his government technically still in charge, what happens next? Does the Libyan government reform itself to accommodate the protesters' demands or does Gaddafi's successor just crack down violently on the protests like Gaddafi did in our timeline?
 
Probably things would be pretty much copy of Egypt after Arab Spring. So Libya is not going to democracy and practically nothing changes.
 
Who would take over in this case? If Saif al-Islam became leader things I can imagine a much more stable, but slower transition to democracy. Saif is a moderate figure who has spoken in favour of democratising in the past, plus his worst fear before the uprising was exactly that. The public may not want to accept him though, due to who his father is, and that may cause further unrest. Gaddafi himself could be another Mubarak or Mugabe figure, peacefully overthrown but not actively targeted by the replacement government and allowed to live in peace. I can imagine him stirring trouble with the media/government from Sirte though, he never did seem like the type to retire quietly.
 
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