White to move and draw. It is quite long and it requires a lot of calculation and knowledge.
I misplaced the black king. I put it on e3 instead of g3 :(
In any case, to speed things along here is what I was getting at: 1.Rf4! Kg3 2.Rf8 Re4 3.Rh8 h4 4.Rg8 Rg4 5.Rxg4! Kg4 6.Ke1/e2=. The position of the white king is critical in both the drawing lines for white, and those that lose. In the 1.Rb2+ lines, black gets a tempo to push the white king back to the c-file- this is enough to win the game in that line, and 1.Rf4 prevents black from checking from d5 to push the king back to the c-file.
Alena, 4.Ke1 is an illegal move. Is there a typo or an omitted move in your line?
It's a draw.
Now consider this line where black plays to prevent the check from g8 that force the king onto the h-file in front of the pawn: 1.Rf4! Kg3 2.Rf8 Re4 preparing to play Rg4 if needed. How does white deal with this?
The only chance to get a draw for white is to have an opportunity to check or to lock the black king on the h file. If the white rook gives a check on b2 the black king will move onto f1. Rb2+ helps white promote the h-pawn. After that the black have enough time to begin to push the h-pawn.
White can't prevent the promotion of the h-pawn.
To put it another way- at the end of your analysis, you show black playing the rook back and forth on the e-file, never making progress. Why can't black try something else to help shield the black king's escape from the h-file and the blockage of the pawn?
Alena, if you had to offer a brief description of why white can only draw with 1.Rf4, how would you do it? In other words, how is changed if white had played the other available check with the rook at move 1? What does that allow black to do to win the game? This is at the heart of the this problem and understanding of it.
It's a draw.