I believe this is correct!

I wrote some code in Mathematica to generate the tree:

Diagram M:Code:treedepth = 9; F[n_] := F[n] = n - M[F[n - 1]]; M[n_] := M[n] = n - F[M[n - 1]]; F[0] = 1; M[0] = 0; TreePlot[Reverse[Table[i -> F[i], {i, 4, Fibonacci[treedepth + 3]}]], Bottom, VertexLabeling -> True] TreePlot[Reverse[Table[i -> M[i], {i, 3, Fibonacci[treedepth + 3] - 1}]], Bottom, VertexLabeling -> True]

Diagram F: