User blog comment:GoogologyLoverG64/Bracket Notation/@comment-27513631-20160206232328/@comment-25337554-20160207032637

The example gives us more rules. [2,2,2] must be (2(2,2)2)=(1(1(2,2)1,1(2,2)1)1), so 1 can be ignored. Furthermore, since  (1(1(2,2)1,1(2,2)1)1)= (((2,2),(2,2)))=((4,4))=(256), another rule (,which should come between the first and second rule) is (a)=a.

Therefore, we can consider (1(2,3)1)=((2,3))=(8)=8, even though we don't know what "[2,2,2]=((2,2))" means.