if the following are true:

• find root index in tree = ri
• the element at index ri of stack tree = node (root_val, left, right)
• the element at index left of stack tree = node (l_val, l_left, l_right)
• new_val < root_val
• new_val > l_val

then result of inserting new_val to tree tree = result of rotating (result of rotating (output of the bst_insert function where input tree is tree, value is new_val and index is ri) twice) clockwise