Francesco Santelli has found an exception on the Bahr rule with this position:

The Bahr rule (is named after the inventor: Bahr, Walter 1905-1986) is about calculating a pawn ending where there are two blocked rook pawns and one extra outside passed pawn.

Condition 1 

The stronger side 'rook-pawn' has not crossed half of the board. (Not crossed its 4th rank),

if the rook-pawn has crossed middle of the board the stronger side will win, otherwise we have to use Bahr's rule.

Condition 2

The stronger side king stands next to its passed pawn.

Condition 3

The defender king must be standing in front of the passed pawn or in front of the attacking king.

(See examples and explanations of this rule at:

https://amateur-chess.blogspot.com/2013/03/bahrs-rule-in-king-and-pawn-endgame.html

https://likesforests.blogspot.com/2007/08/rook-pawns-outside-pawn-ii.html

https://gameknot.com/club-fm.pl?club=791&th=10233)

So back to the above position with variations given by Francesco Santelli.

(You may also try this at Nalimov's tables here: http://www.k4it.de/index.php?topic=egtb&lang=en)

The Black King, keeping an eye on the square rule of the free Pawn, does not allow the White K to cross the 2nd rank until the free Pawn is definitively pushed.

If Black has to move, white wins with the John Crum manoeuvre :