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tree-equal  tree-1 tree-2 &key test test-not ⇒  generalized-boolean
tree-1—a tree.
tree-2—a tree.
test—a designator for a function of two arguments that returns a generalized boolean.
test-not—a designator for a function of two arguments that returns a generalized boolean.
generalized-boolean—a generalized boolean.
tree-equal tests whether two trees are of the same shape and have the same leaves. tree-equal returns true if tree-1 and tree-2 are both atoms and satisfy the test, or if they are both conses and the car of tree-1 is tree-equal to the car of tree-2 and the cdr of tree-1 is tree-equal to the cdr of tree-2. Otherwise, tree-equal returns false.
tree-equal recursively compares conses but not any other objects that have components.
The first argument to the :test or :test-not function is tree-1 or a car or cdr of tree-1; the second argument is tree-2 or a car or cdr of tree-2.
 (setq tree1 '(1 (1 2))
       tree2 '(1 (1 2))) ⇒  (1 (1 2))
 (tree-equal tree1 tree2) ⇒  true
 (eql tree1 tree2) ⇒  false
 (setq tree1 '('a ('b 'c))
       tree2 '('a ('b 'c))) ⇒  ('a ('b 'c)) 
⇒  ((QUOTE A) ((QUOTE B) (QUOTE C)))
 (tree-equal tree1 tree2 :test 'eq) ⇒  true
The consequences are undefined if both tree-1 and tree-2 are circular.
equal ,
Traversal Rules and Side Effects
The :test-not parameter is deprecated.