allrules12=EnumerateWolframModelRules[{{1,2}}{{2,2}}];
Select[allrules12,!ConnectedHypergraphQ[WolframModel[#,{{0,0}},4,"FinalState"]]&]
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InteractiveListSelectorSW[ParallelMapMonitored[{ConnectedHypergraphQ[WolframModel[#,{{0,0}},4,"FinalState"]],WolframModel[#,{{0,0}},4,"CausalGraph"],MultiwaySystem[WolframModel[#],{{0,0}},4,"StatesGraphStructure"]}#&,EnumerateWolframModelRules[{{1,2}}{{2,2}}]]]
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Out[]=
{{{1,1}}{{1,1},{1,1}},{{1,2}}{{1,1},{2,3}}}
XYifyRule[{{1,1}}{{1,1},{1,1}}]
In[]:=
{{x,x}}{{x,x},{x,x}}
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WolframModel[{{1,1}}{{1,1},{1,1}},Automatic,5,"StatesPlotsList"]
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WolframModel[{{1,2}}{{1,1},{1,3}},Automatic,5,"StatesPlotsList"]
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WolframModel[{{1,2}}{{1,2},{2,3}},Automatic,5,"StatesPlotsList"]
In[]:=
Out[]=
{{{1,1}}{{1,1},{1,1}},{{1,2}}{{1,1},{2,3}},{{1,2}}{{1,1},{1,3}},{{1,2}}{{1,2},{2,3}}}