FusionAtlasPaths={"~/projects/fusionatlas/package/"};
$Path=$Path~Join~FusionAtlasPaths;
<<FusionAtlas`

FSM5 = {BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1},{0,1}},{{0,1,0,0},{0,0,1,0},{0,0,0,1}},{{1,0,0},{1,0,0},{0,1,0},{0,0,1}},{{1,0,0,0},{0,0,1,0},{0,0,0,1}}],DualData[{1},{1},{1},{1,2},{1,3,2,4},{1,4,3,2}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{0,1}},{{0,1},{1,0},{0,1}},{{1,0,0},{0,1,0}},{{0,1},{1,0},{0,1}}],DualData[{1},{1},{1},{1,2},{1,2},{2,1}]]};

DisplayBigraph/@FSM5

q=N@√Root[1-((#1)^2)-4 ((#1)^3)-6 ((#1)^4)-19 ((#1)^5)-38 ((#1)^6)-67 ((#1)^7)-98 ((#1)^8)-139 ((#1)^9)-178 ((#1)^10)-218 ((#1)^11)-238 ((#1)^12)-246 ((#1)^13)-238 ((#1)^14)-218 ((#1)^15)-178 ((#1)^16)-139 ((#1)^17)-98 ((#1)^18)-67 ((#1)^19)-38 ((#1)^20)-19 ((#1)^21)-6 ((#1)^22)-4 ((#1)^23)-((#1)^24)+((#1)^26)&,2];

q+(q^(-1))

(((q+(q^(-1))))^2)

SetDebugMode[True]

FindBigraphPairExtensionsUpToDepth[2.22920][FSM5[[1]],FSM5[[2]],1]

DisplayBigraph/@Flatten[%]

vines=Cases[%,{__BigraphWithDuals},∞]

vines/.g_BigraphWithDuals:>GraphToString[g]/.{S1_String,S2_String}:>"\\left("<>"\\bigraph{"<>S1<>"}, \\bigraph{"<>S2<>"} \\right)"

Map[DisplayBigraph,vines,{2}]

KnownObstructions/@Cases[vines,_GradedBigraph,∞]

L=(2.22920^2)

Weeds[{_,_}]:={}

tikzTree[FSM5]