def join_ops(ops1, ops2):
        """For internal use."""
        i = len(ops1) - 1
        j = 0
        while i >= 0 and j < len(ops2):
            if ops1[i] == ops2[j]:
                i -= 1
                j += 1
            else:
                break
        return ops1[:i + 1] + ops2[j:]
For internal use.