Case 1

In[]:=
GraphPlot[Rule@@@WolframModel[{{0,1},{0,2},{0,3}}{{1,2},{2,3},{3,1},{3,4},{4,4}},Table[0,3,2],20,"FinalState"]]
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In[]:=
GraphPlot[Rule@@@WolframModel[{{0,1},{0,2},{0,3}}{{1,2},{2,3},{3,1},{3,4},{4,4}},Table[0,3,2],30,"FinalState"]]
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In[]:=
RulePlot[WolframModel[{{0,1},{0,2},{0,3}}{{1,2},{2,3},{3,1},{3,4},{4,4}}]]
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Case 2 [ Identical up to orientation of rule == evolution order ]

In[]:=
GraphPlot[Rule@@@WolframModel[{{0,1},{0,2},{0,3}}{{1,2},{2,3},{2,4},{3,1},{4,4}},Table[0,3,2],20,"FinalState"]]
Out[]=
In[]:=
GraphPlot[Rule@@@WolframModel[{{0,1},{0,2},{0,3}}{{1,2},{2,3},{2,4},{3,1},{4,4}},Table[0,3,2],30,"FinalState"]]
Out[]=