Answers.Body: <p>After 10 minutes, Stockfish says:</p>
  
  <pre>
  <code>
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rb1 c5 2.dxc6+ Kc7 3.b4 Ra7 4.Rb3 Ne6 5.Rb2 Ng5 6.Rb1 Ne6 7.b5 Ng5 8.Kf2 Ra8 9.Rd1 Ne6 10.Rd2 Nc5 11.Ke2 Ne6 12.Rd1 Rg8 13.Rc1 Ng5 14.Rh1 Ra8
  </code>
  </pre>
  
  <p>...with the machine clearly not finding a plan. But what happens if we play a 'do nothing' move for Black's first move?</p>
  
  <pre>
  <code>
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rb1 f6 2.b4 Ra6 3.bxa5 Rxa5 4.Rb3 Ra8 5.Rcb4 Nf7 6.Ra3 Ra5 7.Rb5 Ka6 8.Ra1 Nd8 9.Kd3 Nf7 10.Rxa5+ Kxa5 11.Rb1 Ng5 12.Ke2 Ka6 13.Rb4 Ka7 14.Kf2 Nh7 15.Rb5 Ka6 16.Ke2 Ng5  (663.81)
  </code>
  </pre>
  
  <p>White removes the Black Rook but then it gets pretty slow. Black's superb Knight and that weak <code>f</code> pawn are keeping Black in the game.</p>
  
  <p>So what about the obvious 1.b4?</p>
  
  <pre>
  <code>
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.b4 f6 2.bxa5 Rxa5 3.Rb4 Rc5 4.Ra3 Ra5 5.Rb5 Ka6 6.Ra1 Nf7 7.c4 Nd8 8.Ra3 Nf7 9.Kd3 Ng5 10.Kd2 Nh3 11.Ra1 Ng5 12.Ke2 Nf7 13.Kf2 Nd8 14.Ke1 Nf7 15.Ra2 Ng5 16.Kf2 Nf7 17.Ra3
  </code>
  </pre>
  
  <p>No dice.  Black looks solid.</p>
  
  <p>From what I can see, Black holds.</p>
  
  <p><strong>EDIT</strong></p>
  
  <p>ALNS asked about this variation: <code>1.Rc6 Ne6! 2.g5 Nd8!?</code> so I fired Stockfish back up.</p>
  
  <p>I couldn't get past that hanging g-pawn, so the first variation is <code>1.Rc6 Ne6 2.g5</code>. Stockfish used 4800 seconds on this (80 minutes).</p>
  
  <pre>
  <code>[Title "1.Rc6 Ne6 2.g5"]
  [fen "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rc6 Ne6 2.g5 Nxg5 3.b4 Ne6 4.Rc4 Ng5 5.bxa5 Rxa5 6.Rb4 Nh7 7.Rbb1 Nf6 8.Kd3 Nxh5 9.Rh1 Nf6 10.Rxh6 Nd7 11.Rh8 Nc5+ 12.Kc4 Na6 13.Rf8 b5+ 14.Kb3 Nc5+ 15.Kb4 Rxa4+ 16.Rxa4 bxa4 17.Rh8 Kb6 18.Rh6 Kb7
  </code>
  </pre>
  
  <p>So it's kinda sharp, but again it is hard to see how any progress will be made.  The position is rated .59 White's favor - the least favorable score for White for any variation we've discussed.</p>
  
  <p>Now, on to the main variation <code>1.Rc6 Ne6 2.g5 Nd8</code></p>
  
  <pre>
  <code>[Title "1.Rc6 Ne6 2.g5 Nd8"]
  [fen "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rc6 Ne6 2.g5 Nd8 3.Rc4 hxg5 4.h6 c5 5.h7 Nc6 6.dxc6+ Kxc6 7.Rh1 Rh8 8.Kf2 Kd7 9.Rh6 Ke7 10.Kg2 f6 11.Kf2 Ke6 12.Rh1 Ke7 13.Rh2 Ke6 14.Kg2 Kf7 15.Kf1 Ke7 16.Rh6 Kf7 17.Kf2 
  </code>
  </pre>
  
  <p>That's after almost 2 hours.  White is rated +3 and seems to be able to engineer a break on the Queenside. This is enough for a win. The Knight seems misplaced on <code>d8</code>.  I'd grab the pawn on <code>g5</code> instead.</p>
  
  <p><strong>EDIT</strong> - ALNS has 2 more variations to look at</p>
  
  <pre>
  <code>[Title "5... Ne6"]
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1. Rc6 Ne6 2. g5 Nd8 3. Rc4 hxg5 4. h6 c5 5. h7 Ne6 6.dxe6 fxe6 7.Rh1 Rh8 8.Kd3 Kc7 9.b4 Kd7 10.bxa5 bxa5 11.Ke2 Kc6 12.Kd2 Kd7 13.Kd3 Ke8 14.Ke2 Kf7 15.Rd1 Rxh7 16.Rxd6 Rh2+ 17.Kf1 g4 18.fxg4 Ke7 19.Rc6 Kf6 20.R4xc5 Kg5 21.Rxe5+ Kxg4 22.Rcxe6 Kf3 23.Kg1 Rg2+ 24.Kh1 Rc2 25.Rxa5 Rxc3 26.Rf5 Rc1+ 27.Kh2
  </code>
  </pre>
  
  <p>With, after several hours of processing, a healthy score of +7.5 in White's favor. Black is dead lost. I like to add complete variations to these threads, but all these moves are suspect after moves 4 or 5. In this variation, Black captures the pawn on <code>h7</code> but in doing so allows White to run amok.  I don't care much for the Knight sacrifice; holding when down a full Rook is tough.</p>
  
  <p>edit - 8.Kd3 is a killer move. Black can get the Rook with <code>8... d5</code> but after <code>9.Re4 dxe4 10. Kxe4</code> Black's king-side pawns all drop.</p>
  
  <pre>
  <code>
  [Title "5. dxc6"]
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rc6 Ne6 2.g5 Nd8 3.Rc4 hxg5 4.h6 c5 5.dxc6 Nxc6 6.Rd1 Kc7 7.b4 Kd7 8.bxa5 Rxa5 9.h7 Ra8 10.Rb1 Kc7 11.Rh1 Rh8 12.Rh5 Kd7 13.Kd3 f6 14.Rh6 Kc7 15.Ke2 Kd7 16.Rh5 Kc7 17.Rh2 Kd7 18.Kd3 Kc7 19.Rh1 Kd7  (10405.71)
  </code>
  </pre>
  
  <p>This comes up as +2.2 for White.  I don't like this because it allows the misplaced Knight on <code>d8</code> to reposition with tempo. The simpler <code>5. h7</code> puts the pressure on Black and wins the Knight and then the game per the previous diagram.</p>
  
  <p><strong>EDIT</strong>
  This is in regards to the "White King Infiltrates" variation mentioned in the OP's post.</p>
  
  <pre>
  <code>
  [title "Infiltration"]
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.b4 c5 2.dxc6+ Kc7 3. bxa5?!+= (3.Rc1 Ne6 4.b5 Rg8 5.Rb1 Re8 6.Ra1 Ra8 7.Rd1 Rd8 8.Kf1 Ra8 9.Rd2 Nc5 10.Kf2 Ne6 11.Ke2 Rd8 12.Kf1 Ra8 13.Kf2 Nc5 14.Ke2 Ne6 15.Rb2 Rh8 16.Kf1 Rh7 17.Kf2 Nc5 18.Rd2 Rh8+/-) 3... bxa5 4. Rb1 Ra7 5.Kf2 Ne6 6. Kg2 Ng5 7.Rb5 f6 8. Rb1 Ne6?! ( 8...Nh7 9.Kf1 Ng5 10.Ke2 Ne6 11.Rb5 Ng5 12.Rb2 Ne6 13.Rd2 Ra8 14.Rd5 Ng5 15.Kf2 Nh3+ 16.Ke1 Ng1 17.Rd3 Nh3 18.Rd1 Ng5 19.Rb1 Ra7 20.Ke2+/-) 9. g5 Nxg5?! (9...fxg5 10.Kh3 Nc5 11.Kg4+/-) 10.Rb5 Ne6 11. Kh3 Nc5?? (11...Ng5+ 12.Kg4 Nh7 13.Kf5 Ng5 14.Kxf6 Nxf3 15.Rb2 Ng5 16.Kg7 f3 17.Kxh6 Ne6 18.Rb1 Nf4 19.Kg5+/-)
  </code>
  </pre>
  
  <p>The variations show a significant deviation from what Stockfish thought was best. All variations except for the last indicate a move that loses perhaps a pawn. Black's 11th move is fatal, however.  The associated variation shows White with a moderate advantage.  Black can make White work for it.</p>
  
  <p><strong>FINAL EDIT</strong></p>
  
  <p>Here's Stockfish playing itself at 15 minutes per move.</p>
  
  <pre>
  <code>
  [title "Granite is tasty"]
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rc6 Ne6 2.Kf1 f6 3.b4 Nd8 4.Rc4 Kc8 5.Kf2 Kd7 6.Rc1 Nf7 7.Ke2 Ra7 8.Rc2 
  Ra8 9.Ra2 Ra7 10.Ra1 Ra8 11.Kf1 Nd8 12.Ra2 Nf7 13.Kf2 Ra7 14.Ra1 Ra8 15.
  Ke2 Nd8 16.Kd3 Nf7 17.Ra2 Ng5 18.Ke2 Nf7 19.Ra3 Nd8 20.Kf2 Nb7 21.Ra2 Nd8 
  22.Rc2 Nf7 23.Rc1 Ng5 24.Rc6 Nf7 25.Ke2 Nd8 26.Rc4 Nf7 27.Rc2 Kc8 28.Ke1 *
  </code>
  </pre>
  
  <p>...with White clearly not finding a break-through. Black holds, thanks to that magnificent Knight... and White's Rook being bottled up.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-15T10:23:07.150Z
Answers.Text: Upvoted! I will try to find a refutation of your plans, so there will be follow up questions...
Answers.UserDisplayName: AlwaysLearningNewStuff
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-19T08:47:45.597Z
Answers.Text: In the last line, `Rc4` is out of play. Black will ignore any action on the queenside, so after `Kg7-Rxh7` we will have pawn ending, where Black has good chances due to `...g4!` push. Also, instead of `5...Nc6` I would play `5...Ne6! 6.dxe6 fxe6 7.Rh1 Rh8 9.Rh6 d5!` when Black restores the piece with good drawing chances. The question remains, whether White should play `5.dxc6+` instead of `5.h7`. What happens if Black plays `5...f6` instead of `5...c5`? Can you examine those lines? Thank you ( already upvoted! )
Answers.UserDisplayName: AlwaysLearningNewStuff
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-20T13:37:11.447Z
Answers.Text: @AlwaysLearningNewStuff - variation added. The other is processing.
Answers.UserDisplayName: Tony Ennis
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-20T14:55:02.783Z
Answers.Text: @AlwaysLearningNewStuff actually, I am getting confused on the variations. If you could list specific move sequences, that would help. For example, I am not sure if you're looking for a `5.dxc6+ f6` variation, or two different variations, one for each of those moves.
Answers.UserDisplayName: Tony Ennis
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-20T17:55:25.620Z
Answers.Text: @AlwaysLearningNewStuff updated again.  Ask me another question.
Answers.UserDisplayName: Tony Ennis
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-23T01:31:25.010Z
Answers.Text: @AlwaysLearningNewStuff one final variation. I let the machine play the position.
Answers.UserDisplayName: Tony Ennis
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-23T08:25:11.563Z
Answers.Text: I think that you are correct, White indeed can't make headway... I have investigated `c5` sacrifice at some point but Black seems to hold. Good work, I will award bounty as promised ( I need to wait another 4 hours before I can do that )! Best regards.
Answers.UserDisplayName: AlwaysLearningNewStuff
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-15T00:30:29.460Z
Answers.LastActivityDate: 2014-07-23T01:30:27.903Z
Answers.LastEditDate: 2014-07-23T01:30:27.903Z
Answers.UserDisplayName: Tony Ennis
Answers.Body: <p>You appear to have almost succeeded. If you c pawn were on c5 instead of c7, I'd say that you had succeeded.</p>
  
  <p>I would play b4 as White. (And NOT b5 afterward.) That forces open one, if not two files among the two leftmost files. White should aim for an "outside" passed pawn on the a file, which should be enough for him to win. </p>
  
  <p>Your knight is on the kingside, and being "slow moving," probably won't get to the queen side fast enough to stop White's penetration there.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-14T20:30:17.213Z
Answers.LastActivityDate: 2014-07-14T20:30:17.213Z
Answers.UserDisplayName: Tom Au
Answers.Body: <p>To aim for a draw for Black, I would play against the fact that the white rook has trapped itself out of play on c4 once the move <code>c3</code> was played. If Black can get in <code>...c5</code> then even after an en passant capture, White will never be able to force a pawn break that yields freedom for the rook. Some illustrative variations follow where <code>...c5</code> isn't stopped. Among such lines, the main line of the next PGN viewer offers the most "freedom" for the rook, <em>but even after <code>6...Kxb7</code> below the rook has no safe squares</em>, and never will so long as Black sits tight:</p>
  
  <pre><code>[Event "?"]
  [Site "?"]
  [Date "????.??.??"]
  [Round "?"]
  [White "?"]
  [Black "?"]
  [Result "*"]
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.b4 
              ( 1.Rb1 c5 2.dxc6+ Kc7 3.b4 Ra7 )
  1...c5 2.dxc6+ 
              ( 2.Rb1 Kc7 )
  2...Kc7 3.bxa5 
              ( 3.b5 f6 )
  3...bxa5 4.Rb1 Ra7 5.Rb7+ Rxb7 6.cxb7+ Kxb7 *
  </code></pre>
  
  <p>So White really needs to prevent <code>...c5</code>, and so must try <code>1.Rc6</code> in order to hope for progress. Even here, Black can go for the same plan via <code>1...Ne6</code>, aiming for <code>...Nd8</code> to force <code>Rc4</code> and get <code>...c5</code> in after all. The side variations below illustrate this idea. The main line below shows the only idea I see to force freedom for the rook; <em>it works, but at the cost of sacrificing the g-pawn to gain enough time</em>. I think Black should be able to hold the final position, but at least White has won the b4 square to get that rook back in the game. I think this is White's best chance to play for a win, as all his pieces are back to life, and there is at least the possibility of play on both wings now.</p>
  
  <pre><code>[Event "?"]
  [Site "?"]
  [Date "????.??.??"]
  [Round "?"]
  [White "?"]
  [Black "?"]
  [Result "*"]
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rc6 Ne6 2.g5 $5 
      ( 2.Rb1 Nd8 3.Rc4 f6 4.b4 Kc8 5.bxa5 bxa5 6.Rb6 Kd7 )
      ( 2.Rg1 f6 3.Rb1 Nd8 4.Rc4 c5 5.dxc6+ Kc7 6.Kd3 Ra7 7.b4 Ra8 )
      ( 2.b4 Nd8 3.Rc4 f6 )
  2...Nxg5 3.b4 Ne6 4.bxa5 Rxa5 
      ( 4...bxa5 $4 5.Rb1+ Kc8 6.dxe6 )
  5.Rc4 Ng7 *
  </code></pre>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-15T10:22:18.823Z
Answers.Text: There is a small problem I see with this sub-line in your answer: `1.Rc6 f6 2.b4 Ra7 3.bxa5 bxa5 4.Rb1+ Ka8 ( 4...Kc8 5.R1b6! +- ) 5.c4! +-` This seems very strong, can you show me how you refute this plan? Upvoted your answer ( I really like the idea of good knight vs clumsy rook ).
Answers.UserDisplayName: AlwaysLearningNewStuff
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-15T11:29:50.507Z
Answers.Text: @AlwaysLearningNewStuff, that is an idea I missed. Perhaps the problem already lies with my `2...Ra7` in that line. I will return to this post later ... off to work for now.
Answers.UserDisplayName: ETD
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-15T12:49:37.147Z
Answers.Text: @AlwaysLearningNewStuff, I considered the matter during my commute, and I think the whole rook trapping idea still works fine. But your line shows that Black can't waste time after `1.Rc6`. Instead of my original line, I think Black should respond immediately with `1...Ne6`, with the idea of following up with `2...Nd8` and then `...c5` after `Rc4`. I believe that this immediate action gives White no time to stop the idea. So as of now I still think this plan for Black holds up; I'll edit later based on your correction (and any other errors of mine that might come to light).
Answers.UserDisplayName: ETD
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-15T23:52:20.483Z
Answers.Text: @AlwaysLearningNewStuff, I have edited in light of your comments, and have found an idea for White that I think successfully stops my rook-trapping plan via a pawn sacrifice. It's the best option I see for White to make progress.
Answers.UserDisplayName: ETD
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-16T01:14:21.410Z
Answers.Text: `1.Rc6 Ne6 2.Kf1 f6 3.b4 Nd8 4.Rc4 Nf7 5.Kf2 Kc8 6.Ke2 Kb7 7.Rc1 Kc8 8.Rc2 Kd7 9.bxa5 bxa5 10.Rc6`, with no improvement to White's position.  This is a great example of a Knight being worth a Rook.
Answers.UserDisplayName: Tony Ennis
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-16T02:56:36.167Z
Answers.Text: `1.Rc6 f6 2.Rc4 Nf7 3.Rc1 Kc8 4.Rg1 Ng5 5.Rc6 Kb7 6.Rf1 Kc8 7.Rc1 Nf7 8.Rc4 Kd7 9.Ra1 Ng5 10.Rc6 Nf7 11.Rb1 Nd8 12.Rc4 Nf7 13.Kd3 Ng5 14.Rf1 Kc8 15.Rc6 +1.77`  Again, nada.
Answers.UserDisplayName: Tony Ennis
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-16T17:10:02.260Z
Answers.Text: @TonyEnnis: I am investigating pawn sacrifice with `g5!` at some point. I am changing my mind towards `...Rxa5` instead of `...bxa5`, with posting a knight to `c5`. As I have said, timely `g5!` does pose a problem at some point...
Answers.UserDisplayName: AlwaysLearningNewStuff
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-19T08:57:55.197Z
Answers.Text: After carefully studying `...c5!` idea I came to the conclusion that White needs to stop it immediately with `1.Rc6.` Here, White has dangerous idea of `g5!` at some moment when things get complicated. Can we confirm that Black holds the following line: `1.Rc6 Ne6! 2.g5 Nd8!?` ? This is the position I need help with. If White plays `3.Rc4` then Black repeats the position with `3...Ng5`, so I need help with White's other moves...
Answers.UserDisplayName: AlwaysLearningNewStuff
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-19T15:48:38.067Z
Answers.Text: @AlwaysLearningNewStuff, in the line `1.Rc6 Ne6 2.g5 Nd8`, you mention `3...Ng5` as a potential follow-up to `3.Rc4`, but that move isn't available because the knight has played to d8 already.
Answers.UserDisplayName: ETD
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-19T16:02:03.650Z
Answers.Text: * If White plays `3.Rc4` then Black repeats the position with `3...Ng5`* -> my mistake, I meant `1.Rc6 Ne6! 2.Rc4 Ng5`. I was able to find winning lines for every move Black plays, that is why I need help with the previously mentioned line...
Answers.UserDisplayName: AlwaysLearningNewStuff
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-21T10:48:45.543Z
Answers.Text: I think I have found a refutation of your plan with `...c5!?`, please see my edited post.
Answers.UserDisplayName: AlwaysLearningNewStuff
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2014-07-15T03:54:17.250Z
Answers.LastActivityDate: 2014-07-15T23:50:07.367Z
Answers.LastEditDate: 2014-07-15T23:50:07.367Z
Answers.UserDisplayName: ETD
Body: <p>I have managed to create a temporary "fortress" after losing the exchange. Analyzing the position after the game ended, I was able to find a plan for White to breakthrough. After further analysis I was able to find the defense for Black. </p>
  
  <p>My "gut feeling" tells me that White should win anyway but I need help in finding the solution. </p>
  
  <p>Below is the position:</p>
  
  <pre><code>[Title "White to move"]
  [fen "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  </code></pre>
  
  <h2>EDITED on July, 21th 2014 :</h2>
  
  <p>Since nobody ( not even engines! ) considered option of penetrating on the kingside with the King via light squares, I am submitting lines that can guide others when constructing their answers.</p>
  
  <pre><code>[Title "White to move"]
  [fen "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.b4 c5!? 2.dxc6+ Kc7 3.bxa5 bxa5 4.Rb1! Ra7 $8 5.Kf2! Ne6 6.Kg2! Ng5 ( 6...Nc5 7.Rxc5! dxc5 8.g5!+- Kxc6 ( 8...hxg5? 9.Rb7+ Rxb7 10.cxb7+- ) ( 8...Ra8 9.Rb7+ Kxc6 10.Rxf7 hxg5 11.h6 Kd6 12.h7 Ke6 13.Ra7! Rd8 14.Kh3 Kf6 15.Kg4 Kg6 16.Rxa5+- ) ( 8...f6 9.g6!?+- )  9.Rb8!+-  ) 7.Rb5! f6 ( 7...Ne6 8.g5!+- ) 8.Rb1! $22 Ne6 9.g5!! Nxg5 ( 9...fxg5 10.Rb7+! $8 Rxb7 11.cxb7 Kxb7 12.Kh3+- ) ( 9...hxg5 10.Rb7+ Rxb7 11.cxb7+ Kxb7 12.h6+- ) 10.Rb5! Ne6 11.Kh3 $22 Nc5 ( 11...Ng5+ 12.Kg4+- ) ( 11...Ng7 12.Kg4+- ) 12.Rcxc5!+- dxc5 13.Rb7+ Rxb7 14.cxb7 Kxb7 15.Kg4+-
  </code></pre>
  
  <p>Based on the above lines, I have tried to "sit in place", and came to the critical position where Black seems to hold:</p>
  
  <pre><code>[Title "White to move"]
  [fen "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.b4 f6 2.bxa5 Rxa5 $8 ( 2...bxa5? 3.Rb1+ Kc8 4.Rbb6! Kd7 5.Rb7+- ) 3.Rcb4 Nf7 4.c4 Nd8 5.Rb5! Rxb5 ( 5...Ra8 6.a5! ) 6.cxb5! $8 Nf7 7.Ra3! Ng5 8.Kd2 Kb8 ( 8...Nf7!? ) 9.Kc2 Kb7 10.Rc3! Nh7 11.Kb3 Nf8 12.Kb4 Nd7 13.a5 bxa5+ ( 13...Nc5!? 14.a6+! $8 Kb8 15.Kc4! Nd7 16.Kd3 Nc5+ $8 ( 16...Nf8 17.a7+!+- ) 17.Ke2 Ka7 $8 ( 17...Na4? 18.a7+!+- ) 18.Kf2 Kb8 $8 19.Kg2 Ka7 20.Kh3 Kb8 21.g5!+- fxg5 $8 22.Kg4 Ka7 23.Kf5 Kb8 24.Rc2!! Ka7 25.Rc1! Kb8 26.Rg1! Nb3 27.Rxg5!! Nd4+ 28.Kg4! Nxb5 29.Rg6 Ka7 ( 29...Nd4 30.Rxh6 b5 31.Rh7! b4 32.a7+! Kxa7 ( 32...Kb7 33.Rxc7+!+- ) 33.Rxc7+ Kb6 34.Rc1+- ) 30.Rxh6 Kxa6 31.Rh7 Kb7 ( 31...Nd4 32.Rxc7+- ) 32.h6 Nd4 33.Rg7+- ) 14.Kxa5
  </code></pre>
  
  <p>It seems that Black can indeed create an impregnable fortress. Sacrifice with <code>b6</code> does not work, and knight will always be able to reach <code>g5</code> in time to stop White king from penetrating via <code>g5</code> sacrifice. If White sacrifices on <code>g5</code> too early, Black will always have <code>Nf6</code> and will move around his king, maintaining blockade. Lines where White sacrifices rook on <code>g5</code> end bad since Black sacrifices the knight and has won pawn endgame.</p>
  
  <p>I will investigate few more ideas ( like <code>c5</code> sacrifice ), before I officially accepting an answer...</p>
  
  <h2>END OF EDIT</h2>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-07-15T00:59:39.933Z
Comments.Text: If you have alternate ideas on how White could proceed, let me know and I'll run them through Stockfish.
Comments.UserDisplayName: Tony Ennis
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-07-18T20:55:40.017Z
Comments.Text: @TonyEnnis: After carefully studying `...c5!` idea I came to the conclusion that White needs to stop it immediately with `1.Rc6`. Here, White has dangerous idea of `g5!` at some moment when things get complicated. Can we confirm that Black holds the following line: `1.Rc6 Ne6! 2.g5 Nd8!?` ? This is the position I need help with. If White plays `3.Rc4` then Black repeats the position with `3...Ng5`, so I need help with White's other moves...
Comments.UserDisplayName: AlwaysLearningNewStuff
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-07-19T00:04:16.450Z
Comments.Text: I'm on it.  More to come.
Comments.UserDisplayName: Tony Ennis
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-07-19T03:39:34.847Z
Comments.Text: I added 2 more variations to my post below.
Comments.UserDisplayName: Tony Ennis
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-07-21T10:50:02.267Z
Comments.Text: @TonyEnnis: Please see my edit. It seems that `...c5` fails, but that your approach of "doing nothing" works for now. I still have few ideas to explore... Thank you for helping out...
Comments.UserDisplayName: AlwaysLearningNewStuff
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-07-21T22:28:57.553Z
Comments.Text: I ran your new variation through the mill, the one where White infiltrates on the Kingside.  Stockfish notes a game-losing blunder. See my edit below.
Comments.UserDisplayName: Tony Ennis
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-07-21T22:49:12.847Z
Comments.Text: @AlwaysLearningNewStuff, in the first PGN of your latest edit, you assess the side variation with `9...fxg5 10.Rb7+ Rxb7 11.cxb7+ Kxb7 12.Kh3` as being winning for White, but that rook is still trapped, and in fact **Black** is winning *handily* there. White is helpless against the plan of `...Nf8` heading for b6 to attack the jailed rook. Any White counterplay with pawns is way too slow, and Black is crushing. (Note that the uselessness of the rook means that the white king heading for the h6 pawn is rather harmless, given the speed of a `...g4` breakthrough in response.)
Comments.UserDisplayName: ETD
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-07-21T22:52:46.477Z
Comments.Text: I've lost track of where various thoughts/assessments sit in all the back-and-forth on this thread, but thus far, I *think* I still stand by my answer below.
Comments.UserDisplayName: ETD
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-07-22T12:25:24.687Z
Comments.Text: @ETD: Wonderful idea that I Have missed! I guess that ...c5! indeed holds, so I will get back to the ...f6 idea I had in mind when White responds with Rc6. Thank you so much, I really have learned a lot from this seemingly simple position! I will contact you again either by accepting your answer/rewarding you with bounty/asking for examination of one last line. Best regards.
Comments.UserDisplayName: AlwaysLearningNewStuff
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-07-22T12:33:52.920Z
Comments.Text: @ETD: I have learned a lot from your ideas that I find appropriate to award you the bounty. Thanks again and best regards!
Comments.UserDisplayName: AlwaysLearningNewStuff
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2014-07-22T12:36:26.893Z
Comments.Text: @TonyEnnis: I have officially accepted member *ETD's* answer because of its clear strategical idea, and very important comment that refuted the analysis from my edited post. I have already upvoted your answer, and once I award the bounty to member *ETD* I will do so for your answer too. I appreciate the great effort you took to help me ,so I believe this is the least I can do. Be patient. Thanks again, best regards!
Comments.UserDisplayName: AlwaysLearningNewStuff
Tags: <analysis>
Title: Can White engineer a winning breakthrough?
ThreadText: # Can White engineer a winning breakthrough?
  
  (Asked by: username_0 on 2014-07-14)
  
  I have managed to create a temporary "fortress" after losing the exchange. Analyzing the position after the game ended, I was able to find a plan for White to breakthrough. After further analysis I was able to find the defense for Black.
  
  My "gut feeling" tells me that White should win anyway but I need help in finding the solution.
  
  Below is the position:
  
  ```
  [Title "White to move"]
  [fen "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  ```
  
  ## EDITED on July, 21th 2014 :
  
  Since nobody ( not even engines! ) considered option of penetrating on the kingside with the King via light squares, I am submitting lines that can guide others when constructing their answers.
  
  ```
  [Title "White to move"]
  [fen "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.b4 c5!? 2.dxc6+ Kc7 3.bxa5 bxa5 4.Rb1! Ra7 $8 5.Kf2! Ne6 6.Kg2! Ng5 ( 6...Nc5 7.Rxc5! dxc5 8.g5!+- Kxc6 ( 8...hxg5? 9.Rb7+ Rxb7 10.cxb7+- ) ( 8...Ra8 9.Rb7+ Kxc6 10.Rxf7 hxg5 11.h6 Kd6 12.h7 Ke6 13.Ra7! Rd8 14.Kh3 Kf6 15.Kg4 Kg6 16.Rxa5+- ) ( 8...f6 9.g6!?+- )  9.Rb8!+-  ) 7.Rb5! f6 ( 7...Ne6 8.g5!+- ) 8.Rb1! $22 Ne6 9.g5!! Nxg5 ( 9...fxg5 10.Rb7+! $8 Rxb7 11.cxb7 Kxb7 12.Kh3+- ) ( 9...hxg5 10.Rb7+ Rxb7 11.cxb7+ Kxb7 12.h6+- ) 10.Rb5! Ne6 11.Kh3 $22 Nc5 ( 11...Ng5+ 12.Kg4+- ) ( 11...Ng7 12.Kg4+- ) 12.Rcxc5!+- dxc5 13.Rb7+ Rxb7 14.cxb7 Kxb7 15.Kg4+-
  
  ```
  
  Based on the above lines, I have tried to "sit in place", and came to the critical position where Black seems to hold:
  
  ```
  [Title "White to move"]
  [fen "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.b4 f6 2.bxa5 Rxa5 $8 ( 2...bxa5? 3.Rb1+ Kc8 4.Rbb6! Kd7 5.Rb7+- ) 3.Rcb4 Nf7 4.c4 Nd8 5.Rb5! Rxb5 ( 5...Ra8 6.a5! ) 6.cxb5! $8 Nf7 7.Ra3! Ng5 8.Kd2 Kb8 ( 8...Nf7!? ) 9.Kc2 Kb7 10.Rc3! Nh7 11.Kb3 Nf8 12.Kb4 Nd7 13.a5 bxa5+ ( 13...Nc5!? 14.a6+! $8 Kb8 15.Kc4! Nd7 16.Kd3 Nc5+ $8 ( 16...Nf8 17.a7+!+- ) 17.Ke2 Ka7 $8 ( 17...Na4? 18.a7+!+- ) 18.Kf2 Kb8 $8 19.Kg2 Ka7 20.Kh3 Kb8 21.g5!+- fxg5 $8 22.Kg4 Ka7 23.Kf5 Kb8 24.Rc2!! Ka7 25.Rc1! Kb8 26.Rg1! Nb3 27.Rxg5!! Nd4+ 28.Kg4! Nxb5 29.Rg6 Ka7 ( 29...Nd4 30.Rxh6 b5 31.Rh7! b4 32.a7+! Kxa7 ( 32...Kb7 33.Rxc7+!+- ) 33.Rxc7+ Kb6 34.Rc1+- ) 30.Rxh6 Kxa6 31.Rh7 Kb7 ( 31...Nd4 32.Rxc7+- ) 32.h6 Nd4 33.Rg7+- ) 14.Kxa5
  
  ```
  
  It seems that Black can indeed create an impregnable fortress. Sacrifice with `b6` does not work, and knight will always be able to reach `g5` in time to stop White king from penetrating via `g5` sacrifice. If White sacrifices on `g5` too early, Black will always have `Nf6` and will move around his king, maintaining blockade. Lines where White sacrifices rook on `g5` end bad since Black sacrifices the knight and has won pawn endgame.
  
  I will investigate few more ideas ( like `c5` sacrifice ), before I officially accepting an answer...
  
  ## END OF EDIT
  
  **Tags:** analysis
  
  > **Comments:**
  > **username_1**: If you have alternate ideas on how White could proceed, let me know and I'll run them through Stockfish.  
  > **username_0**: @username_1: After carefully studying `...c5!` idea I came to the conclusion that White needs to stop it immediately with `1.Rc6`. Here, White has dangerous idea of `g5!` at some moment when things get complicated. Can we confirm that Black holds the following line: `1.Rc6 Ne6! 2.g5 Nd8!?` ? This is the position I need help with. If White plays `3.Rc4` then Black repeats the position with `3...Ng5`, so I need help with White's other moves...  
  > **username_1**: I'm on it.  More to come.  
  > **username_1**: I added 2 more variations to my post below.  
  > **username_0**: @username_1: Please see my edit. It seems that `...c5` fails, but that your approach of "doing nothing" works for now. I still have few ideas to explore... Thank you for helping out...  
  > **username_1**: I ran your new variation through the mill, the one where White infiltrates on the Kingside.  Stockfish notes a game-losing blunder. See my edit below.  
  > **username_2**: @username_0, in the first PGN of your latest edit, you assess the side variation with `9...fxg5 10.Rb7+ Rxb7 11.cxb7+ Kxb7 12.Kh3` as being winning for White, but that rook is still trapped, and in fact **Black** is winning *handily* there. White is helpless against the plan of `...Nf8` heading for b6 to attack the jailed rook. Any White counterplay with pawns is way too slow, and Black is crushing. (Note that the uselessness of the rook means that the white king heading for the h6 pawn is rather harmless, given the speed of a `...g4` breakthrough in response.)  
  > **username_2**: I've lost track of where various thoughts/assessments sit in all the back-and-forth on this thread, but thus far, I *think* I still stand by my answer below.  
  > **username_0**: @username_2: Wonderful idea that I Have missed! I guess that ...c5! indeed holds, so I will get back to the ...f6 idea I had in mind when White responds with Rc6. Thank you so much, I really have learned a lot from this seemingly simple position! I will contact you again either by accepting your answer/rewarding you with bounty/asking for examination of one last line. Best regards.  
  > **username_0**: @username_2: I have learned a lot from your ideas that I find appropriate to award you the bounty. Thanks again and best regards!  
  > **username_0**: @username_1: I have officially accepted member *ETD's* answer because of its clear strategical idea, and very important comment that refuted the analysis from my edited post. I have already upvoted your answer, and once I award the bounty to member *ETD* I will do so for your answer too. I appreciate the great effort you took to help me ,so I believe this is the least I can do. Be patient. Thanks again, best regards!  
  
  ---
  
  ## 3 answers
  
  ### Answer by username_2 on 2014-07-15. Score: 4 | Accepted answer
  
  To aim for a draw for Black, I would play against the fact that the white rook has trapped itself out of play on c4 once the move `c3` was played. If Black can get in `...c5` then even after an en passant capture, White will never be able to force a pawn break that yields freedom for the rook. Some illustrative variations follow where `...c5` isn't stopped. Among such lines, the main line of the next PGN viewer offers the most "freedom" for the rook, *but even after `6...Kxb7` below the rook has no safe squares*, and never will so long as Black sits tight:
  
  ```
  [Event "?"]
  [Site "?"]
  [Date "????.??.??"]
  [Round "?"]
  [White "?"]
  [Black "?"]
  [Result "*"]
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.b4 
              ( 1.Rb1 c5 2.dxc6+ Kc7 3.b4 Ra7 )
  1...c5 2.dxc6+ 
              ( 2.Rb1 Kc7 )
  2...Kc7 3.bxa5 
              ( 3.b5 f6 )
  3...bxa5 4.Rb1 Ra7 5.Rb7+ Rxb7 6.cxb7+ Kxb7 *
  
  ```
  
  So White really needs to prevent `...c5`, and so must try `1.Rc6` in order to hope for progress. Even here, Black can go for the same plan via `1...Ne6`, aiming for `...Nd8` to force `Rc4` and get `...c5` in after all. The side variations below illustrate this idea. The main line below shows the only idea I see to force freedom for the rook; *it works, but at the cost of sacrificing the g-pawn to gain enough time*. I think Black should be able to hold the final position, but at least White has won the b4 square to get that rook back in the game. I think this is White's best chance to play for a win, as all his pieces are back to life, and there is at least the possibility of play on both wings now.
  
  ```
  [Event "?"]
  [Site "?"]
  [Date "????.??.??"]
  [Round "?"]
  [White "?"]
  [Black "?"]
  [Result "*"]
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rc6 Ne6 2.g5 $5 
      ( 2.Rb1 Nd8 3.Rc4 f6 4.b4 Kc8 5.bxa5 bxa5 6.Rb6 Kd7 )
      ( 2.Rg1 f6 3.Rb1 Nd8 4.Rc4 c5 5.dxc6+ Kc7 6.Kd3 Ra7 7.b4 Ra8 )
      ( 2.b4 Nd8 3.Rc4 f6 )
  2...Nxg5 3.b4 Ne6 4.bxa5 Rxa5 
      ( 4...bxa5 $4 5.Rb1+ Kc8 6.dxe6 )
  5.Rc4 Ng7 *
  
  ```
  
  > **Comments:**
  > **username_0**: There is a small problem I see with this sub-line in your answer: `1.Rc6 f6 2.b4 Ra7 3.bxa5 bxa5 4.Rb1+ Ka8 ( 4...Kc8 5.R1b6! +- ) 5.c4! +-` This seems very strong, can you show me how you refute this plan? Upvoted your answer ( I really like the idea of good knight vs clumsy rook ).  
  > **username_2**: @username_0, that is an idea I missed. Perhaps the problem already lies with my `2...Ra7` in that line. I will return to this post later ... off to work for now.  
  > **username_2**: @username_0, I considered the matter during my commute, and I think the whole rook trapping idea still works fine. But your line shows that Black can't waste time after `1.Rc6`. Instead of my original line, I think Black should respond immediately with `1...Ne6`, with the idea of following up with `2...Nd8` and then `...c5` after `Rc4`. I believe that this immediate action gives White no time to stop the idea. So as of now I still think this plan for Black holds up; I'll edit later based on your correction (and any other errors of mine that might come to light).  
  > **username_2**: @username_0, I have edited in light of your comments, and have found an idea for White that I think successfully stops my rook-trapping plan via a pawn sacrifice. It's the best option I see for White to make progress.  
  > **username_1**: `1.Rc6 Ne6 2.Kf1 f6 3.b4 Nd8 4.Rc4 Nf7 5.Kf2 Kc8 6.Ke2 Kb7 7.Rc1 Kc8 8.Rc2 Kd7 9.bxa5 bxa5 10.Rc6`, with no improvement to White's position.  This is a great example of a Knight being worth a Rook.  
  > **username_1**: `1.Rc6 f6 2.Rc4 Nf7 3.Rc1 Kc8 4.Rg1 Ng5 5.Rc6 Kb7 6.Rf1 Kc8 7.Rc1 Nf7 8.Rc4 Kd7 9.Ra1 Ng5 10.Rc6 Nf7 11.Rb1 Nd8 12.Rc4 Nf7 13.Kd3 Ng5 14.Rf1 Kc8 15.Rc6 +1.77`  Again, nada.  
  > **username_0**: @username_1: I am investigating pawn sacrifice with `g5!` at some point. I am changing my mind towards `...Rxa5` instead of `...bxa5`, with posting a knight to `c5`. As I have said, timely `g5!` does pose a problem at some point...  
  > **username_0**: After carefully studying `...c5!` idea I came to the conclusion that White needs to stop it immediately with `1.Rc6.` Here, White has dangerous idea of `g5!` at some moment when things get complicated. Can we confirm that Black holds the following line: `1.Rc6 Ne6! 2.g5 Nd8!?` ? This is the position I need help with. If White plays `3.Rc4` then Black repeats the position with `3...Ng5`, so I need help with White's other moves...  
  > **username_2**: @username_0, in the line `1.Rc6 Ne6 2.g5 Nd8`, you mention `3...Ng5` as a potential follow-up to `3.Rc4`, but that move isn't available because the knight has played to d8 already.  
  > **username_0**: * If White plays `3.Rc4` then Black repeats the position with `3...Ng5`* -> my mistake, I meant `1.Rc6 Ne6! 2.Rc4 Ng5`. I was able to find winning lines for every move Black plays, that is why I need help with the previously mentioned line...  
  > **username_0**: I think I have found a refutation of your plan with `...c5!?`, please see my edited post.  
  
  ---
  
  ### Answer by username_1 on 2014-07-15. Score: 4
  
  After 10 minutes, Stockfish says:
  
  ```
  
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rb1 c5 2.dxc6+ Kc7 3.b4 Ra7 4.Rb3 Ne6 5.Rb2 Ng5 6.Rb1 Ne6 7.b5 Ng5 8.Kf2 Ra8 9.Rd1 Ne6 10.Rd2 Nc5 11.Ke2 Ne6 12.Rd1 Rg8 13.Rc1 Ng5 14.Rh1 Ra8
  
  ```
  
  ...with the machine clearly not finding a plan. But what happens if we play a 'do nothing' move for Black's first move?
  
  ```
  
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rb1 f6 2.b4 Ra6 3.bxa5 Rxa5 4.Rb3 Ra8 5.Rcb4 Nf7 6.Ra3 Ra5 7.Rb5 Ka6 8.Ra1 Nd8 9.Kd3 Nf7 10.Rxa5+ Kxa5 11.Rb1 Ng5 12.Ke2 Ka6 13.Rb4 Ka7 14.Kf2 Nh7 15.Rb5 Ka6 16.Ke2 Ng5  (663.81)
  
  ```
  
  White removes the Black Rook but then it gets pretty slow. Black's superb Knight and that weak `f` pawn are keeping Black in the game.
  
  So what about the obvious 1.b4?
  
  ```
  
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.b4 f6 2.bxa5 Rxa5 3.Rb4 Rc5 4.Ra3 Ra5 5.Rb5 Ka6 6.Ra1 Nf7 7.c4 Nd8 8.Ra3 Nf7 9.Kd3 Ng5 10.Kd2 Nh3 11.Ra1 Ng5 12.Ke2 Nf7 13.Kf2 Nd8 14.Ke1 Nf7 15.Ra2 Ng5 16.Kf2 Nf7 17.Ra3
  
  ```
  
  No dice. Black looks solid.
  
  From what I can see, Black holds.
  
  **EDIT**
  
  ALNS asked about this variation: `1.Rc6 Ne6! 2.g5 Nd8!?` so I fired Stockfish back up.
  
  I couldn't get past that hanging g-pawn, so the first variation is `1.Rc6 Ne6 2.g5`. Stockfish used 4800 seconds on this (80 minutes).
  
  ```
  
  [Title "1.Rc6 Ne6 2.g5"]
  [fen "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rc6 Ne6 2.g5 Nxg5 3.b4 Ne6 4.Rc4 Ng5 5.bxa5 Rxa5 6.Rb4 Nh7 7.Rbb1 Nf6 8.Kd3 Nxh5 9.Rh1 Nf6 10.Rxh6 Nd7 11.Rh8 Nc5+ 12.Kc4 Na6 13.Rf8 b5+ 14.Kb3 Nc5+ 15.Kb4 Rxa4+ 16.Rxa4 bxa4 17.Rh8 Kb6 18.Rh6 Kb7
  
  ```
  
  So it's kinda sharp, but again it is hard to see how any progress will be made. The position is rated .59 White's favor - the least favorable score for White for any variation we've discussed.
  
  Now, on to the main variation `1.Rc6 Ne6 2.g5 Nd8`
  
  ```
  
  [Title "1.Rc6 Ne6 2.g5 Nd8"]
  [fen "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rc6 Ne6 2.g5 Nd8 3.Rc4 hxg5 4.h6 c5 5.h7 Nc6 6.dxc6+ Kxc6 7.Rh1 Rh8 8.Kf2 Kd7 9.Rh6 Ke7 10.Kg2 f6 11.Kf2 Ke6 12.Rh1 Ke7 13.Rh2 Ke6 14.Kg2 Kf7 15.Kf1 Ke7 16.Rh6 Kf7 17.Kf2 
  
  ```
  
  That's after almost 2 hours. White is rated +3 and seems to be able to engineer a break on the Queenside. This is enough for a win. The Knight seems misplaced on `d8`. I'd grab the pawn on `g5` instead.
  
  **EDIT** - ALNS has 2 more variations to look at
  
  ```
  
  [Title "5... Ne6"]
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1. Rc6 Ne6 2. g5 Nd8 3. Rc4 hxg5 4. h6 c5 5. h7 Ne6 6.dxe6 fxe6 7.Rh1 Rh8 8.Kd3 Kc7 9.b4 Kd7 10.bxa5 bxa5 11.Ke2 Kc6 12.Kd2 Kd7 13.Kd3 Ke8 14.Ke2 Kf7 15.Rd1 Rxh7 16.Rxd6 Rh2+ 17.Kf1 g4 18.fxg4 Ke7 19.Rc6 Kf6 20.R4xc5 Kg5 21.Rxe5+ Kxg4 22.Rcxe6 Kf3 23.Kg1 Rg2+ 24.Kh1 Rc2 25.Rxa5 Rxc3 26.Rf5 Rc1+ 27.Kh2
  
  ```
  
  With, after several hours of processing, a healthy score of +7.5 in White's favor. Black is dead lost. I like to add complete variations to these threads, but all these moves are suspect after moves 4 or 5. In this variation, Black captures the pawn on `h7` but in doing so allows White to run amok. I don't care much for the Knight sacrifice; holding when down a full Rook is tough.
  
  edit - 8.Kd3 is a killer move. Black can get the Rook with `8... d5` but after `9.Re4 dxe4 10. Kxe4` Black's king-side pawns all drop.
  
  ```
  
  [Title "5. dxc6"]
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rc6 Ne6 2.g5 Nd8 3.Rc4 hxg5 4.h6 c5 5.dxc6 Nxc6 6.Rd1 Kc7 7.b4 Kd7 8.bxa5 Rxa5 9.h7 Ra8 10.Rb1 Kc7 11.Rh1 Rh8 12.Rh5 Kd7 13.Kd3 f6 14.Rh6 Kc7 15.Ke2 Kd7 16.Rh5 Kc7 17.Rh2 Kd7 18.Kd3 Kc7 19.Rh1 Kd7  (10405.71)
  
  ```
  
  This comes up as +2.2 for White. I don't like this because it allows the misplaced Knight on `d8` to reposition with tempo. The simpler `5. h7` puts the pressure on Black and wins the Knight and then the game per the previous diagram.
  
  **EDIT**
  This is in regards to the "White King Infiltrates" variation mentioned in the OP's post.
  
  ```
  
  [title "Infiltration"]
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.b4 c5 2.dxc6+ Kc7 3. bxa5?!+= (3.Rc1 Ne6 4.b5 Rg8 5.Rb1 Re8 6.Ra1 Ra8 7.Rd1 Rd8 8.Kf1 Ra8 9.Rd2 Nc5 10.Kf2 Ne6 11.Ke2 Rd8 12.Kf1 Ra8 13.Kf2 Nc5 14.Ke2 Ne6 15.Rb2 Rh8 16.Kf1 Rh7 17.Kf2 Nc5 18.Rd2 Rh8+/-) 3... bxa5 4. Rb1 Ra7 5.Kf2 Ne6 6. Kg2 Ng5 7.Rb5 f6 8. Rb1 Ne6?! ( 8...Nh7 9.Kf1 Ng5 10.Ke2 Ne6 11.Rb5 Ng5 12.Rb2 Ne6 13.Rd2 Ra8 14.Rd5 Ng5 15.Kf2 Nh3+ 16.Ke1 Ng1 17.Rd3 Nh3 18.Rd1 Ng5 19.Rb1 Ra7 20.Ke2+/-) 9. g5 Nxg5?! (9...fxg5 10.Kh3 Nc5 11.Kg4+/-) 10.Rb5 Ne6 11. Kh3 Nc5?? (11...Ng5+ 12.Kg4 Nh7 13.Kf5 Ng5 14.Kxf6 Nxf3 15.Rb2 Ng5 16.Kg7 f3 17.Kxh6 Ne6 18.Rb1 Nf4 19.Kg5+/-)
  
  ```
  
  The variations show a significant deviation from what Stockfish thought was best. All variations except for the last indicate a move that loses perhaps a pawn. Black's 11th move is fatal, however. The associated variation shows White with a moderate advantage. Black can make White work for it.
  
  **FINAL EDIT**
  
  Here's Stockfish playing itself at 15 minutes per move.
  
  ```
  
  [title "Granite is tasty"]
  [FEN "r7/1kp2p2/1p1p3p/p2Pp1nP/P1R1PpP1/1PP2P2/4K3/R7 w - - 0 1"]
  
  1.Rc6 Ne6 2.Kf1 f6 3.b4 Nd8 4.Rc4 Kc8 5.Kf2 Kd7 6.Rc1 Nf7 7.Ke2 Ra7 8.Rc2 
  Ra8 9.Ra2 Ra7 10.Ra1 Ra8 11.Kf1 Nd8 12.Ra2 Nf7 13.Kf2 Ra7 14.Ra1 Ra8 15.
  Ke2 Nd8 16.Kd3 Nf7 17.Ra2 Ng5 18.Ke2 Nf7 19.Ra3 Nd8 20.Kf2 Nb7 21.Ra2 Nd8 
  22.Rc2 Nf7 23.Rc1 Ng5 24.Rc6 Nf7 25.Ke2 Nd8 26.Rc4 Nf7 27.Rc2 Kc8 28.Ke1 *
  
  ```
  
  ...with White clearly not finding a break-through. Black holds, thanks to that magnificent Knight... and White's Rook being bottled up.
  
  > **Comments:**
  > **username_0**: Upvoted! I will try to find a refutation of your plans, so there will be follow up questions...  
  > **username_0**: In the last line, `Rc4` is out of play. Black will ignore any action on the queenside, so after `Kg7-Rxh7` we will have pawn ending, where Black has good chances due to `...g4!` push. Also, instead of `5...Nc6` I would play `5...Ne6! 6.dxe6 fxe6 7.Rh1 Rh8 9.Rh6 d5!` when Black restores the piece with good drawing chances. The question remains, whether White should play `5.dxc6+` instead of `5.h7`. What happens if Black plays `5...f6` instead of `5...c5`? Can you examine those lines? Thank you ( already upvoted! )  
  > **username_1**: @username_0 - variation added. The other is processing.  
  > **username_1**: @username_0 actually, I am getting confused on the variations. If you could list specific move sequences, that would help. For example, I am not sure if you're looking for a `5.dxc6+ f6` variation, or two different variations, one for each of those moves.  
  > **username_1**: @username_0 updated again.  Ask me another question.  
  > **username_1**: @username_0 one final variation. I let the machine play the position.  
  > **username_0**: I think that you are correct, White indeed can't make headway... I have investigated `c5` sacrifice at some point but Black seems to hold. Good work, I will award bounty as promised ( I need to wait another 4 hours before I can do that )! Best regards.  
  
  ---
  
  ### Answer by username_3 on 2014-07-14. Score: 1
  
  You appear to have almost succeeded. If you c pawn were on c5 instead of c7, I'd say that you had succeeded.
  
  I would play b4 as White. (And NOT b5 afterward.) That forces open one, if not two files among the two leftmost files. White should aim for an "outside" passed pawn on the a file, which should be enough for him to win.
  
  Your knight is on the kingside, and being "slow moving," probably won't get to the queen side fast enough to stop White's penetration there.
  
  
  ---
  
  