initialize the current plan to the empty plan
:= I
while   (  ) = 0 do perform breadth first search for a state  ' with   (  ')
( )
if no such state can be found then output "Fail", stop endif add the actions on the path to ' at the end of the current plan
!!

endwhile S

$$S\qquad S^{\prime}$$
$${\boldsymbol{S}}$$
$$S^{\prime}$$
$\mathfrak{S}$. 
5.2 Completeness Definition 7 (Dead End) Let  O, I, G  be a planning task.  A state S is called a iff it is reachable and no sequence of actions achieves the goal from it, i.e., iff 3 P
Result I, P  and ¬¬ P¹  G ⊆ Result S, P¹
S
N
Proposition 4  Let P     O, I, G   be a planning task.  If P is dead-end free, then enforced hill-climbing will find a solution.

Proof:
Result I, P
P
S
N
h S
s

$$\mathbb{N}$$

S'