Prolog: lowest common ancestor (LCA)

lca.pl

ancestor(A, B) :- parent(A, B).
ancestor(A, B) :- parent(X, B), ancestor(A, X).
lca(A, B, X) :- ancestor(X, A), ancestor(X, B).

Try with this tree:

parent(a, b).
parent(a, c).
parent(b, d).
parent(b, e).
parent(c, f).
parent(c, g).
parent(d, h).
parent(d, i).
parent(d, j).
parent(e, k).
parent(f, l).
parent(f, m).
parent(g, n).
parent(g, o).
parent(g, p).
parent(g, q).
parent(k, r).
parent(k, s).
parent(m, t).
parent(m, u).
parent(m, v).
parent(o, w).
parent(p, x).
parent(x, y).
parent(x, z).

This won't give you the lowest common ancestor, but the complete list of common ancestors.