def METHOD_NAME(self, path):
    r"""If the path basename is unique among the resent experiments, this
    is used. Otherwise, the full path is used.
    Parameters
    ----------
    path
        The path to shorten unambiguously.
    Returns
    -------
    The unambiguously shortened path.
    """
    basename = os.path.basename(path)
    basenames = \
        [os.path.basename(_path)
         for _path in self.main_window.recent_files]
    return path if basenames.count(basename) > 1 else basename