It is helpful to think of the search process as building up a search tree that is superimposed SEARCH NODE over the state space.
The root of the search tree is a search node corresponding to the initial state.
The leaf nodes of the tree correspond to states that do not have successors in the tree, either because they have not been expanded yet, or because they were expanded, but generated the empty set.
At each step, the search algorithm chooses one leaf node to expand