A note on leftmost innermost term reduction

Küchlin presents an indeterministic abstract term-reduction algorithm that allows one to select arbitrarily which node to reduce next---an algorithm that (by using explicit labeling of nodes) is optimal in the sense that it does not attempt to reduce nodes again that have already been fully reduced by it. He then analyzes two standard reduction algorithms (leftmost innermost and leftmost outermost reduction) that employ implicit labeling of nodes to preclude attempts to reduce anew already fully reduced nodes. In the case of leftmost innermost reduction, the implicit labeling designates all terms to the left of or below the term currently being reduced as being already fully reduced. His algorithm for leftmost innermost reduction is as follows: