{{3,2}}{{5,2}},4

In[]:=
Select[Union[Table[RandomWolframModelRule[{{3,2}}{{5,2}},4],50]],NewVerticesQ]
Out[]=
In[]:=
ParallelMapMonitored[SafeHyperModelTestButton[#,10,4]&,%]
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In[]:=
WolframModel[{{1,1},{2,1},{3,3}}{{2,1},{2,2},{3,3},{4,1},{4,2}},Table[0,3,2],20]
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In[]:=
Graph[Rule@@@%["FinalState"]]
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In[]:=
Graph[Rule@@@WolframModel[{{1,1},{2,1},{3,3}}{{2,1},{2,2},{3,3},{4,1},{4,2}},Table[0,3,2],40,"FinalState"]]
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Another rule

In[]:=
RulePlot[WolframModel[{{1,2},{1,2},{3,1}}{{1,1},{1,4},{2,1},{2,4},{4,3}}]]
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In[]:=
RulePlot[WolframModel[{{1,2},{1,2},{3,1}}{{1,1},{1,4},{2,1},{2,4},{4,3}}],VertexLabelsAutomatic]
Out[]=
In[]:=
WolframModel[{{1,2},{1,2},{3,1}}{{1,1},{1,4},{2,1},{2,4},{4,3}},Table[0,3,2],20]
Out[]=
In[]:=
Graph[Rule@@@%["FinalState"]]
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New explorer

Another rule

NOTE: this is an LHS disconnected rule.....
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