Consider the following algorithm for testing if a given binary tree has the binary search tree property.

$1: function TEST-BST $ (T) $ 2: $ \quad $ for $ u \in T $ do 3: $ \quad $ if $ u . l e f t \neq $ Assumes $ T $ h$ where RIGHTMOST-DESC(v) is v if v.right = null and RIGHTMOST-DESC(v.right) otherwise. Your task is to either prove the correctness of this algorithm or provide a counter example where it fails to return the correct answer.

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Consider the following algorithm for testing if a given binary tree has the binary search tree property.

$1: function TEST-BST $ (T) $ 2: $ \quad $ for $ u \in T $ do 3: $ \quad $ if $ u . l e f t \neq $ Assumes $ T $ h$ where RIGHTMOST-DESC(v) is v if v.right = null and RIGHTMOST-DESC(v.right) otherwise. Your task is to either prove the correctness of this algorithm or provide a counter example where it fails to return the correct answer.

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