DisplayBigraph[g=GradedBigraph[{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{1,0}},{{1,1}}]]

DisplayBigraph/@(p=FindGraphPartners[g])

p2=Flatten[BigraphWithDuals/@p,1];

p3=Cases[Flatten[Outer[List,BigraphWithDuals[g],p2],1],{a_,b_}/;FullOcneanuTest[a,b]];

p3=FusionAtlas`PairOdometer`Private`ChooseIsomorphismRepresentatives[p3]

DisplayBigraph/@%

SetDebugMode[True]

{fr}=FindFusionRules@@p3[[1]];

Union[DeleteCases[Flatten[fr[[-1,All,2]]],_Integer]]

FindDimensionFunctions[EvenPart[fr/._Z$15803->1]]

FindDimensionFunctions[EvenPart[fr/._Z$15803->0]]

{fr}=FindFusionRules@@Reverse[p3[[1]]];

FindDimensionFunctions[EvenPart[fr]]

FullSimplify[%]

{fr}=FindFusionRules@@p3[[2]];

FindDimensionFunctions[EvenPart[fr/._Z$16429->1]]

FindDimensionFunctions[EvenPart[fr/._Z$16429->0]]

{fr}=FindFusionRules@@Reverse[p3[[2]]];

FindDimensionFunctions[EvenPart[fr]]

FullSimplify[%]