let rec btree_nb_nodes_arities t =
match t with
|Empty->(0,0,0)
|Node(Empty, Empty)->(1,0,0)
|Node(f,Empty)
|Node(Empty,f)->let(a,b,c) = btree_nb_nodes_arities f
|Node(l,r)->let(al,bl,cl) = btree_nb_nodes_arities l
|Node(l,r)->let(ar,br,cr) = btree_nb_nodes_arities r
in (al + ar, bl + br, 1+ cl + cr)