isn't the assumption that every node would make $2$ comparisons false? Since lets consider the case where the root compares its value with its children and it makes a swap. Then the swapped value has to be compared with its children, wne then that might propoagte till the leaf. So in this case, doesn't it require more than $2$ swaps per node? $(10)$

$\{$:$[$ simile $to],[7\frac{?}{?}$& $8.7$ swaps with $2],[\frac{?}{?}$& $8$ swops with $4])$

Now $9$ compores with

$0$ & $2$ and swaps with

O$,$ Then $9$ drops deun.

Now $9$ will have to

compores with $1$ & $6$

and would have to

swap with $1?$ So

it would require more

then $2$ comporisons

per node?