From the feedback received I updated the main line (from pos 39). I post an update of this endgame. Now it is more clear that f7 is a weak point, and it is tricky for black to try to stop the two menaces: f7 and play on the c file ... It is not clear whether to try to take e5 pawn or play on the queenside without stopping rook menaces.
Edit 1: From your suggestions I tried to improve the game ... but somehow I think that white can improve the game ... I arrive at this position that seems nice for black (with idea of b3 and promote ...)
[Title "Side to move: Black"] [StartFlipped "0"] [fen "8/5p2/4p2p/3pP1pP/1p1n4/k7/P2R1KP1/8 b - - 5 45"]
Here I post the update the rest of analysis :
[Event "Android 2.3.5"] [Site "GT-I9001"] [Date "2015.04.20"] [Round "-"] [White "Stockfish 4"] [Black "Mandor"] [Result "*"] [Startply "75"] [fen ""] 1.e4 e6 2.d4 d5 3.Nc3 Nf6 4.e5 Nfd7 5.Nce2 c5 6.c3 Nc6 7.f4 Qb6 8.Nf3 cxd4 9.cxd4 Be7 10.Nc3 O-O 11.Be2 a6 12.O-O Qa7 13.Be3 b5 14.Qc2 Nb6 15.b3 b4 16.Nb5 Qd7 17.Nd6 Bxd6 18.exd6 Qxd6 19.Ne5 Ne7 20.Bd3 g6 21.Rac1 a5 22.Qc5 Qxc5 23.dxc5 Nd7 24.c6 Nxe5 25.fxe5 Ba6 26.Bxa6 Rxa6 27.Bc5 Nxc6 28.Bxf8 Kxf8 29.Rfe1 Ke7 30.Rc2 Kd7 31.Rf2 Nd8 32.Kf1 Rc6 33.Ke2 Rc2+ 34.Kf1 Rxf2+ 35.Kxf2 Nc6 36.h3 Kc7 37.h4 Kb6 38.Kf3 h6 39.Kg4 Kb5 40.Kg3 a4 41.bxa4+ Kxa4 42.h5 g5 43.Re2 Ka3 44.Kf2 Nd4 45.Rd2 b3 46.axb3 Nc6 47.Ke3 Kb4 48. Rc2 Kb5 49.Rc1 Nxe5 50.Rc7 Kb6 51.Re7 Kc6 52.b4 Kd6 53.Rb7 Ng4+ 54.Kd4 e5+ 55.Kc3 d4+ 56.Kc4 Ne3+ 57.Kd3 Nxg2 *
All suggestions are welcome! Thanks!
Edit 2: From this position : 8/5p1p/1kn1p1p1/p2pP3/1p5P/1P3K2/P5P1/4R3 b - - 2 38
Summarizing until now from the core position. Is it possible to win with black? How? :) 1) Plan put Knight on f6 seems to fail due to: 38. Kf3 (for example) .. Nd4+ 39. Kf4 Nb5 40. Rf1! (and ok Knight, you can occupy f6 and I will let rook take f7 for example with Ke3 )
2) Plan to change e5 pawn for f7 pawn I did not manage to have anything. Usually the white rook could counter attack on the back rank, and somehow the king and rook will take the kingside pawns.
3) Plan to put king on b5 for me seems the most promising... but I did not manage to make it work : 38. Kf3 (to be coherent) h6 39. Kg4 (yes seems strange) Kb5 40. Kf4 a4 (with initial idea but ..) 41. bxa4+ Kxa4 42. Rc1! .. and what to do? Kb5 ?¿ And how to progress ? :( (I though something like 42. Rc1 42. g5 43. hxg5 hxg5 44. Kxg5 Nxe5 45. Kf6 ...