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2: 12, 21

In[]:=
allrules=Tuples[{Rule@@@Tuples[{StringTuples["AB",1],StringTuples["AB",2]}],Rule@@@Tuples[{StringTuples["AB",2],StringTuples["AB",1]}]}]
Out[]=
In[]:=
InteractiveListSelectorSW[ParallelMapMonitored[Function[r,Labeled[MultiwaySystem[r,StringTuples["AB",6],6,"StatesGraphStructure"],TimeConstrained[Counts[CausalInvariantQ[r,#,4]&/@StringTuples["AB",4]],20]]r],allrules]]
Out[]=
In[]:=
InteractiveListSelectorSW[ParallelMapMonitored[Function[r,Labeled[MultiwaySystem[r,StringTuples["AB",2],4,"StatesGraphStructure"],TimeConstrained[Counts[CausalInvariantQ[r,#,3]&/@StringTuples["AB",2]],20]]r],allrules]]
Out[]=
In[]:=
Labeled[MultiwaySystem[#,StringTuples["AB",2],6,"StatesGraphStructure"],#]&/@{{"A""AA","AA""B"},{"A""AB","AB""B"},{"B""AB","BA""A"},{"B""AB","AA""B"}}
Out[]=
In[]:=
Labeled[MultiwaySystem[#,{"A"},8,"StatesGraphStructure"],#]&/@{{"A""AA","AA""B"},{"A""AB","AB""B"},{"A""BA","AB""B"},{"A""BA","BB""A"}}
Out[]=
In[]:=
Labeled[MultiwaySystem[#,{"AB"},20,"StatesGraphStructure"],#]&/@{{"A""AA","AA""B"},{"A""AB","AB""B"},{"A""BA","AB""B"},{"A""BA","BB""A"}}

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