2,3  4,3

maxConnectedAtoms[{{2,3}}{{4,3}}]
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13
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res=ParallelMapMonitored[WolframModelTest[#,Table[{0,0,0},6]]&,Select[Table[RandomWolframModelRule[{{2,3}}{{4,3}},13],100],BiConnectedRuleQ]];
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Counts[WMFilter4/@res]
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FewEvents12,PureExponential2,DiedFast17,Disconnected2
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MakePictures[Select[res,MatchQ[WMFilter4[#],"MaybeInteresting"|"LinearRecurrenceGrowth"|"PureExponential"|"BoringDifferencesAfterTransient"|"BoringDifferences"]&&ConnectedHypergraphQ[#["FinalState"]]&]]
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{},
Clear
Copy

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​
res=ParallelMapMonitored[WolframModelTest[#,Table[{0,0,0},6]]&,Select[Table[RandomWolframModelRule[{{2,3}}{{4,3}},13],500],BiConnectedRuleQ]];
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Counts[WMFilter4/@res]
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DiedFast87,Disconnected9,FewEvents22,PureExponential2,BoringDifferences1,BoringDifferencesAfterTransient1,MaybeInteresting2
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MakePictures[Select[res,MatchQ[WMFilter4[#],"MaybeInteresting"|"LinearRecurrenceGrowth"|"PureExponential"|"BoringDifferencesAfterTransient"|"BoringDifferences"]&&ConnectedHypergraphQ[#["FinalState"]]&]]
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Complex rule

Sample:
{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,12},{9,13},{10,7},{11,14},{12,8},{13,9},{14,11}}
ParallelMapMonitored[WolframModelTest[#,Join[Table[0,2,3],Table[0,6,2]]]&,Select[Table[RandomWolframModelRule[{{2,3},{2,2}}{{4,3},{8,2}},15],50],BiConnectedRuleQ]];
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$Aborted
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Table[RandomWolframModelRule[{{2,3},{2,2}}{{4,3},{8,2}},15],10]
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$Aborted
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At this size, cannot run canonicalizer.....
RandomWolframModelRuleNC[rulesignature_Rule,s_Integer]:=Rule@@Table[Catenate[RandomInteger[{1,s},#]&/@rulesignature[[n]]],{n,1,Length[rulesignature]}]
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res=ParallelMapMonitored[WolframModelTest[#,Join[Table[0,2,3],Table[0,6,2]]]&,Select[Table[RandomWolframModelRuleNC[{{2,3},{2,2}}{{4,3},{8,2}},15],500],BiConnectedRuleQ]];
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Counts[WMFilter4/@res]
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DiedFast53,FewEvents6
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res=ParallelMapMonitored[WolframModelTest[#,Join[Table[0,2,3],Table[0,6,2]]]&,Select[Table[RandomWolframModelRuleNC[{{2,3},{2,2}}{{4,3},{8,2}},15],5000],BiConnectedRuleQ]];
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Counts[WMFilter4/@res]
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DiedFast568,FewEvents53
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res=ParallelMapMonitored[WolframModelTest[#,Join[Table[0,2,3],Table[0,6,2]]]&,Select[Table[RandomWolframModelRuleNC[{{2,3},{2,2}}{{4,3},{8,2}},15],20000],BiConnectedRuleQ]];
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Counts[WMFilter4/@res]
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DiedFast2337,FewEvents219
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MakePictures[Select[res,MatchQ[WMFilter4[#],"MaybeInteresting"|"LinearRecurrenceGrowth"|"PureExponential"|"BoringDifferencesAfterTransient"|"BoringDifferences"]&&ConnectedHypergraphQ[#["FinalState"]]&]]
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{{1,2,3},{4,5,6},{1,4},{4,1}}Join[RandomInteger[15,

Structured rule

HypergraphPlot[WolframModel[{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,12},{9,13},{10,7},{11,14},{12,8},{13,9},{14,11}},Join[Table[0,2,3],Table[0,6,2]],6,"FinalState"]]
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HypergraphPlot[WolframModel[{{1,2,3},{4,5,6},{1,3},{3,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,12},{9,13},{10,7},{11,14},{12,8},{13,9},{14,11}},Join[Table[0,2,3],Table[0,6,2]],6,"FinalState"]]
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Table[HypergraphPlot[WolframModel[{{1,2,3},{4,5,6},{1,n},{n,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,12},{9,13},{10,7},{11,14},{12,8},{13,9},{14,11}},Join[Table[0,2,3],Table[0,6,2]],6,"FinalState"]],{n,2,6}]
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HypergraphPlot[WolframModel[{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,12},{9,13},{10,7},{12,8},{13,9}},Join[Table[0,2,3],Table[0,6,2]],6,"FinalState"]]
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HypergraphPlot[WolframModel[{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,12},{9,13},{11,14}},Join[Table[0,2,3],Table[0,6,2]],6,"FinalState"]]
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HypergraphPlot[WolframModel[{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,12},{9,13},{11,14}},Join[Table[0,2,3],Table[0,12,2]],6,"FinalState"]]
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Original rules

{#1,Join[Table[0,2,3],Table[0,6,2]],#3}&@@@{{{{1,2,3},{4,5,6},{1,4},{4,1}}{{3,7,8},{6,9,10},{11,12,2},{13,14,5},{7,11},{8,10},{9,13},{10,8},{11,7},{12,14},{13,9},{14,12}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,13},{9,12},{10,7},{11,14},{12,9},{13,8},{14,11}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,13},{9,12},{10,7},{11,14},{12,9},{13,8},{14,11}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,11},{8,10},{9,13},{10,8},{11,7},{12,14},{13,9},{14,12}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{2,5},{5,2}}{{7,1,8},{9,3,10},{11,4,12},{13,6,14},{7,13},{8,10},{9,11},{10,8},{11,9},{12,14},{13,7},{14,12}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,12},{9,13},{10,7},{11,14},{12,8},{13,9},{14,11}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,11},{8,14},{9,13},{10,12},{11,7},{12,10},{13,9},{14,8}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{1,4},{4,1}}{{3,7,8},{6,9,10},{11,12,2},{13,14,5},{7,14},{8,11},{9,12},{10,13},{11,8},{12,9},{13,10},{14,7}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15}}
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MakeDirectPictures[%137,0]
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$Aborted
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MakeDirectPictures[%137,-10]
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MakeDirectPictures[%137,-7]
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MakeDirectPictures[{{{{1,2,3},{4,5,6},{1,4},{4,1}}{{3,7,8},{6,9,10},{11,12,2},{13,14,5},{7,11},{8,10},{9,13},{10,8},{11,7},{12,14},{13,9},{14,12}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,13},{9,12},{10,7},{11,14},{12,9},{13,8},{14,11}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,13},{9,12},{10,7},{11,14},{12,9},{13,8},{14,11}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,11},{8,10},{9,13},{10,8},{11,7},{12,14},{13,9},{14,12}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{2,5},{5,2}}{{7,1,8},{9,3,10},{11,4,12},{13,6,14},{7,13},{8,10},{9,11},{10,8},{11,9},{12,14},{13,7},{14,12}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,12},{9,13},{10,7},{11,14},{12,8},{13,9},{14,11}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,11},{8,14},{9,13},{10,12},{11,7},{12,10},{13,9},{14,8}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15},​​{{{1,2,3},{4,5,6},{1,4},{4,1}}{{3,7,8},{6,9,10},{11,12,2},{13,14,5},{7,14},{8,11},{9,12},{10,13},{11,8},{12,9},{13,10},{14,7}},{{1,2,3},{4,5,6},{1,4},{2,5},{3,6},{4,1},{5,2},{6,3}},15}},-9]
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RulePlot[WolframModel[{{1,2,3},{4,5,6},{1,4},{4,1}}{{2,7,8},{3,9,10},{5,11,12},{6,13,14},{7,10},{8,13},{9,12},{10,7},{11,14},{12,9},{13,8},{14,11}}]]
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