<Dl> <Dd> h (x) ≤ d (x, y) + h (y) (\ displaystyle h (x) \ leq d (x, y) + h (y)) </Dd> </Dl> <Dd> h (x) ≤ d (x, y) + h (y) (\ displaystyle h (x) \ leq d (x, y) + h (y)) </Dd> <P> This ensures that for any path X from the initial node to x: </P> <Dl> <Dd> L (X) + h (x) ≤ L (X) + d (x, y) + h (y) = L (Y) + h (y) (\ displaystyle L (X) + h (x) \ leq L (X) + d (x, y) + h (y) = L (Y) + h (y)) </Dd> </Dl>

Which is better aa* or ao* algorithm