def sets_are_rooted_compat(one_set, other):
    """treats the 2 sets are sets of taxon IDs on the same (unstated)
    universe of taxon ids.
    Returns True clades implied by each are compatible and False otherwise
    """
    if one_set.issubset(other) or other.issubset(one_set):
        return True
    return not intersection_not_empty(one_set, other)