tree_depth( nil, 0).   % the depth of an empty tree is 0.
tree_depth(t(L,_,R), D) :-  % the depth of a non-empty tree is computed thus:
  tree_depth(L,L1),              % - compute the depth of the left subtree
  tree_depth(R,R1),              % - compute the depth of the right subtree
  D is 1 + max(L1,R1).            % - the overall depth is 1 more than the maximum depth in both subtrees.                               %


tree_node_diameter(t(L,_,R), D):-
    tree_depth(L,D1), tree_depth(R,D2), D is D1 + D2.

tree_diameter(T, D):-
    tree_node_diameter(T, D).

tree_diameter(t(L,_,_), D):-
   	tree_node_diameter(L,D).

tree_diameter(t(_,_,R), D):-
   	tree_node_diameter(R,D).

all_tree_diameters(T, D):-
    tree_diameter(T, D1),
    (tree_diameter(T, D2), D1 >D2), D is D1.