def config_subsumes(a, b):
    """Given two configurations with the same sites, determine whether
    the first subsumes the second (all parameters in a are greater than
    or equal to those in b).
    """
    a_dict = dict(a)
    b_dict = dict(b)
    assert a_dict.keys() == b_dict.keys()

    for ident, a_param in a_dict.items():
        if a_param < b_dict[ident]:
            return False
    return True