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WOLFRAM NOTEBOOK
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e22=EnumerateHypergraphs[{{2,2}}]
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{{{1,1},{1,1}},{{1,1},{1,2}},{{1,1},{2,1}},{{1,2},{1,2}},{{1,2},{2,1}},{{1,2},{1,3}},{{1,2},{2,3}},{{1,2},{3,2}}}
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Outer[HypergraphUnifications,e22,e22,1]
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HypergraphUnifications[#,#]&/@e22
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WolframModelPlot[#,EdgeStyleReplacePart[Table[Automatic,Length[#]],Join[Thread[Intersection[Values[#2],Values[#3]]Purple],Thread[Values[#2]Red],Thread[Values[#3]Blue]]]]&@@@HypergraphUnifications[{{1,2},{2,3}},{{1,2},{2,3}}]
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HypergraphUnificationPlot[h1_,h2_]:=WolframModelPlot[#,EdgeStyleReplacePart[Table[Automatic,Length[#]],Join[Thread[Intersection[Values[#2],Values[#3]]Purple],Thread[Values[#2]Red],Thread[Values[#3]Blue]]]]&@@@HypergraphUnifications[h1,h2]
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HypergraphUnificationPlot[h1_]:=WolframModelPlot[#,EdgeStyleReplacePart[Table[Automatic,Length[#]],Join[Thread[Intersection[Values[#2],Values[#3]]Purple],Thread[Values[#2]Red],Thread[Values[#3]Blue]]]]&@@@h1
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HypergraphUnificationPlot[#,#]&[{{1,2},{2,1}}]
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Function[h,Select[HypergraphUnifications[h,h],Length[First[#]]Length[h]&]]/@e22
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Transpose[{WolframModelPlot/@e22,HypergraphUnificationPlot/@%292}]
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Combined rules
It is the Wolfram model multiway system
“Cumulative rule” is an unification of branches in multiway system