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Gundogan is very good for tiki taka after about six years with Pep Guardiola at Manchester City. Even Pep upgraded initial tiki taka from Barcelona to Bayern Munich then Manchester City, the core idea of tiki taka was digested by Gundogan. He will not have difficulty in Barcelona especially we saw Xavi did not change the initial tiki taka too much in one season and a half with Barcelona.
I agree, both teams have the same style of play where both focus on ball possession with short and accurate passes.
Of course this will make it easier for Ilkay Gundogan to adapt to the game, but it might be hampered if he doesn't get good support from other players. But I'm sure Ilkay Gundogan won't have too many difficulties during his adaptation at Barcelona, that's because of his professionalism and high experience as a top player.
They did not want to sign a too long contract with an old player like Gundogan but it is what the player wanted. Without agreement, they had to separated and Gundogan also want to challenge himself at a new league, La Liga.
Whether Manchester City has plans to keep Ilkay Gundogan or not before his contract expires last season, Ilkay Gundogan also has a desire to play in La Liga with Barcelona.