This bijection of binary trees swaps the left and right subtree of a binary tree, but ONLY if BOTH are nonempty. If either the left or right hand side tree is empty, fixes the tree.

.A...B.C...D.......C...D.A...B.

..\./...\./.........\./...\./..

...x.....x...--->....x.....x...

....\.../.............\.../....

......x.................x......

...............................

((a . b) . (c . d)) -> ((c . d) . (a . b))

or fix, if either the left or right hand side subtree is empty.