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, g)
• the element at index g of stack tree = node (g_val, g_left, g_right)

then result of rotating tree twice = result of storing (node (root_val, g, right)) at index ri of stack (result of storing (node (g_val, left, g_right)) at index g of stack (result of storing (node (l_val, l_left, g_left)) at index left of stack tree))