In[]:=
WeaklyConnectedComponents[MultiwaySystem[{"AA""BB","BB""AA"},StringTuples["AB",6],10,"StatesGraph"]]
Out[]=
{{ABBAAA,ABBBBA,ABBABB,AAAAAA,ABAABA,AAABBA,AAAABB,AABBAA,BBAAAA,BBABBA,AABBBB,BBAABB,BBBBAA,AABAAB,BBBBBB,BAABAA,BBBAAB,BAABBB,BAAAAB,BABBAB},{AABAAA,BBBAAA,AABABB,AABBBA,BBBABB,BBBBBA,BAAAAA,AAAABA,BAAABB,BAABBA,BBAABA,BABBAA,ABBABA,BABBBB,BABAAB},{AAABBB,AAAAAB,AAABAA,ABBBBB,BBABBB,ABBAAB,AABBAB,BBAAAB,BBABAA,ABBBAA,ABAABB,BBBBAB,ABAAAA,BAABAB,ABABBA},{BBABAB,AAABAB,ABBBAB,ABAAAB,ABABBB,ABABAA},{BABABB,BABAAA,BABBBA,BAAABA,BBBABA,AABABA}}
In[]:=
Map[StringPartition[#,2]&,%,{2}]
Out[]=
In[]:=
StringTuples["AB",2]
In[]:=
Map[#/.{"AA"0,"AB"1,"BA"-1,"BB"0}&,%134,{2}]
Out[]=
In[]:=
Map[Total,%,{2}]
Out[]=
{{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},{-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1},{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1},{2,2,2,2,2,2},{-2,-2,-2,-2,-2,-2}}