  We compute, using techniques originally introduced by Kohlenbach, the first
author and Nicolae, uniform rates of metastability for the proximal point
algorithm in the context of CAT(0) spaces (as first considered by Bacak),
specifically for the case where the ambient space is totally bounded. This
result is part of the program of proof mining, which aims to apply methods of
mathematical logic with the purpose of extracting quantitative information out
of ordinary mathematical proofs, which may not be necessarily constructive.
