Consider the following position with white to move.
The black king is far from the action, the white pawn is far advanced, and the white king is is near the pawn. Black simply cannot hope to win – the best outcome for black is a draw. Clearly, black can draw if he can exchange his rook for the pawn. Thus, black’s objective is to capture the pawn.
Regarding white, the worst possible outcome is a draw. But given the advanced pawn and the position of his king, there is a possibility that white could win. White will apply rule 2.2 to guide his play. White cannot lose the pawn in exchange for the rook. And he needs to make forward progress.
White has five possible moves. Four of those moves draw. For example, 1. Kb7? Rc5 2. c7 Rxd7+ 3. Kxd7 draw. The only move that does not lose the pawn is 1. c7.
Here we have to make a new rule, although in this case it’s a difficult rule to write down without making it hundreds of lines due to how many caveats there are! But here is my attempt:
3. If no other rule takes precedence, and you believe you have a won position, and you believe you must queen a pawn to win, then make a move that leads to the shortest sequence of moves that forces the queening of the pawn and does not change the outcome of the position. Conversely, if no other rule takes precedence, and you believe you have a lost position, and you believe your opponent must queen a pawn to win, then make a move that requires the longest sequence of forced moves to queen the pawn.
Based on that rule, the most optimal move for black is 1. … Rd6+ since this is the only move that prevents the immediate queening of the pawn.
Now white has five moves. However, four of those moves allow black to either win the pawn and the game, or the exchange of the rook and pawn. For example, 2. Kb7? Rd7 3. Kb8 Rxc7 4. Kxc7. Also consider 2. Kc5? Rd1 followed by 3. … Rc1 regardless of what move white plays.
Correct is 2. Kb5. Now black cannot prevent the queening of the pawn. So he makes things as difficult for white as possible with 2. … Rd7 3. c8Q Rb8+ 4. Ka4 Ra2+ 5. Kb3 Rb2+ 6. Kc3 and white has mate in ten. Note that throughout this entire sequence of moves that white is applying Principle of Forward Progress.