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MultiwaySystem[{"A""B","B""A"},"AAA",2,"BranchialGraph"]
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MultiwaySystem[{"A""AB","B""A"},"AA",3,"BranchialGraph"]
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This is a squashed version of critical pair ancestry....
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MultiwaySystem[{"BA""AB"},"BBBAAA",3,"BranchialGraph"]
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MultiwaySystem[{"BA""AB"},"BBBAAA",3,"BranchialGraph"]
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MultiwaySystem[{"A""AB","B""A"},"AA",4,"BranchialGraph"]
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VertexList[%]
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{AAAA,AAABB,AABAB,AABBA,ABAAB,ABABA,ABBAA,AABBBB,ABABBB,ABBABB,ABBBAB,ABBBBA}
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DistanceMatrix[%395,DistanceFunctionEditDistance]
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GraphDistanceMatrix
//Normal
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MatrixPlot/@{%399,%397}
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MultiwaySystem[{"A""B"},"AAAAA",2,"BranchialGraph"]
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MultiwaySystem[{"A""B"},"AAAAA",1,"BranchialGraph"]
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MatrixPlot[GraphDistanceMatrix[%]]
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DistanceMatrix[VertexList[MultiwaySystem[{"A""B"},"AAAAA",2,"BranchialGraph"]],DistanceFunctionEditDistance]
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MatrixPlot[%]
Ultrametric spaces???
Edges could be labeled with predecessors