#!/usr/bin/env python
from ete3 import Tree

# pseudo code
# binary rooted tree comparison
def equals(tree1, tree2):

    if tree1 == tree2:
        return True
    # checking only leaf names
    if tree1.is_leaf() and tree2.is_leaf():
        if tree1.name == tree2.name:
            return True
        return False
    if tree1 is None or tree2 is None:
        return False
    if len(tree1) != len(tree2):
        return False
    elif (len(tree1.get_children()) ==  2 and len(tree2.get_children()) ==2):
        return (equals(tree1.children[0], tree2.children[0]) and
           equals(tree1.children[1], tree2.children[1])) or (equals(tree1.children[0], tree2.children[1]) and equals(tree1.children[1], tree2.children[0]))
    return False

if __name__ == '__main__':
    t1 = Tree('(a,(c,d));')
    t2 = Tree('(a, (d,c));')
    t3 = Tree('((a,b),(d,c));')
    print equals(t1, t2)
    print equals(t1, t3)
    print equals(t2, t3)