Determine a new heuristic $2($n$)$ which is dominant to the given heuristic and also consistent.

Perform A$*$ search on the hin$)$ heuristic considering A as the start node alongside G as the goal node and comment if the optimal path is returned. Push Nodes alphabetically and in case of a tie during expansion, use FIFO approach.

Comment on the consistency of F and A for hi$($n$)$