Show that there are more than 2ⁿ improper binary trees with n internal nodes such that no pair are isomorphic (see Exercise C-8.33).

Exercise C-8.33

Two ordered trees T′ and T′′ are said to be isomorphic if one of the following holds:

• Both T′ and T′′ are empty.

• Both T′ and T′′ consist of a single node

• The roots of T′ and T′′ have the same number k ≥ 1 of subtrees, and the i^th such subtree of T′ is isomorphic to the i^th such subtree of T′′ for i = 1, . . . ,k.

Design an algorithm that tests whether two given ordered trees are isomorphic. What is the running time of your algorithm?