user5784: What is the maximum DTC and the maximum DTZ in the endgame KRPKRP (rook+pawn
 against rook+pawn) ?

user-1: According to longest checkmates in chess, the longest DTM (depth-to-mate) for KRP vs KRP is 112 moves, starting from this position with white to move:
[FEN "8/7P/1K5R/8/1r1k4/8/4p3/8 w - - 0 1"]

The analysis ignores the 50 move rule.
Additionally, according to the Syzygy tablebases., the maximum KRP-KRP DTZ is 122 ply.
[Title "DTZ 122 Ply"]
[FEN "8/8/8/1P3p2/8/8/2R2r2/k1K5 b - - 0 1"]


5784: <p>What is the maximum DTC and the maximum DTZ in the endgame KRPKRP (rook+pawn
 against rook+pawn) ?</p>
 -1: <p>According to <a href="http://kirill-kryukov.com/chess/longest-checkmates/#3+3" rel="nofollow noreferrer">longest checkmates in chess</a>, the longest DTM (depth-to-<em>mate</em>) for KRP vs KRP is <strong>112 moves</strong>, starting from this position with white to move:</p>
<pre><code>[FEN &quot;8/7P/1K5R/8/1r1k4/8/4p3/8 w - - 0 1&quot;]
</code></pre>
<p>The analysis ignores the 50 move rule.</p>
<p>Additionally, according to the <a href="https://syzygy-tables.info/?fen=8/8/8/1P3p2/8/8/2R2r2/k1K5_b_-_-_0_1" rel="nofollow noreferrer">Syzygy tablebases.</a>, the maximum KRP-KRP DTZ is 122 ply.</p>
<pre><code>[Title &quot;DTZ 122 Ply&quot;]
[FEN &quot;8/8/8/1P3p2/8/8/2R2r2/k1K5 b - - 0 1&quot;]
</code></pre>
