Long transient
{{ABBB,BBBBA}{1,4,7,14,19,19,22,13,16,9,11,7,7,6,4,5,2,4,1,3,1,2,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}}
In[]:=
Length/@MultiwayGrowthList[{"A""BBB","BBBB""A"},{"ABAAA"},200,2000]
Out[]=
In[]:=
Position[%439,0]
Out[]=
In[]:=
MultiwaySystem[{"A""BBB","BBBB""A"},{"ABAAA"},30,"StatesGraphStructure"]
Out[]=
In[]:=
MultiwaySystem[{"A""BBB","BBBB""A"},{"AAAA"},30,"StatesGraphStructure"]
Out[]=
In[]:=
FirstPosition[#,0]&/@Table[Length/@MultiwayGrowthList[{"A""BBB","BBBB""A"},{StringRepeat["A",n]},200,2000],{n,10}]
Out[]=
{{3},{10},{17},{24},{31},{38},{45},{52},Missing[NotFound],Missing[NotFound]}
In[]:=
Flatten[%]
Out[]=
{3,10,17,24,31,38,45,52,Missing[NotFound],Missing[NotFound]}
In[]:=
Differences[%]
Out[]=
{7,7,7,7,7,7,7,-52+Missing[NotFound],0}
In[]:=
Total/@%
Out[]=
{2,13,44,132,381,1086,3082,8733,Total[None],Total[None]}
FindSequenceFunction[{2,13,44,132,381,1086,3082,8733,n]
Out[]=
In[]:=
Ratios@{2,13,44,132,381,1086,3082,8733}
Out[]=

13
2
,
44
13
,3,
127
44
,
362
127
,
1541
543
,
8733
3082

In[]:=
%//N
Out[]=
{6.5,3.38462,3.,2.88636,2.85039,2.83794,2.83355}
​
​
In[]:=
TotalCausalInvariantQ[{"A""BBB","BBBB""A"},3]
Out[]=
True
In[]:=
Length/@MultiwayGrowthList[{"AA""ABBAB","BAB""A"},{"ABAAA"},200,2000]
Out[]=
In[]:=
ListLinePlot[%]
Out[]=
In[]:=
Length/@MultiwayGrowthList[{"A""B","A""BBBB","AB""BBA"},{"ABAAA"},200,2000]
Out[]=
In[]:=
ListLinePlot[%209,PlotRangeAll]
Out[]=
In[]:=
Length/@MultiwayGrowthList[{"A""BBBBBB","AB""BBA"},{"ABAAA"},200,2000]
Out[]=
In[]:=
MultiwaySystem[{"A""BBBBBB","AB""BBA"},{"ABAAA"},20,"StatesGraphStructure"]
Out[]=
Generates this many unique strings:
In[]:=
Total[%212]
Out[]=
4979
​
In[]:=
Length/@MultiwayGrowthList[{"AB""BA","BAA""AABB"},{"ABAAA"},60,4000]
Out[]=
{1,2,2,3,7,10,11,15,21,25,28,35,43,49,59,68,81,91,103,123,139,155,173,198,227,247,274,307,343,380,411,457,504,549,601,654,716,775,838,916,987,1065,1144,1237,1338,1426,1528,1642,1760,1883,1998,2139,2282,2426,2580,2738,2913,3085,3264,3468,3662}
​
In[]:=
Length/@MultiwayGrowthList[{"AB""A","ABA""BAABBB"},{"ABAAA"},60,4000]
Out[]=
{1,2,1,1,2,3,4,6,10,15,20,24,28,36,45,55,66,77,86,93,104,117,132,151,170,185,195,207,224,245,271,296,316,333,350,369,392,423,456,483,506,528,550,576,612,651,683,711,740,769,799,837,879,917,952,987,1021,1056,1100,1146,1187}