MathDB

The alphabet of the tribe AAB consists of the only letters

A

and

B

. However, if you insert or delete the combination

AAA

BBB

for any words, the meaning of the word will not change. In addition, if

AB

is replaced with

BBAA

, or vice versa, the meaning of the word doesn't change. The same holds for

BA

and

AABB

. Is it true that

AB

and

BA

have the same meaning?

Problem Statement