'Compare `word1` and `word2` for equality in the group
using the group\'s rewriting system. If the system is
confluent, the returned answer is necessarily correct.
(If it isn\'t, `False` could be returned in some cases
where in fact `word1 == word2`)'

def equals(self, word1, word2):

    if (self.reduce((word1 * (word2 ** (-1)))) == self.identity):
        return True
    elif self._rewriting_system.is_confluent:
        return False
    return None
