It is possible to make use of algebraic properties like operator commutativity and associativity to reduce the register requirements of the tree. For example, consider the tree shown in Figure 11.10.
The label of the tree in Figure 11.10 is two, but since + is a commutative operator, we can interchange the left and the right subtrees, as shown in Figure 11.11. This brings the register requirement of the tree down to one.
Similarly, associativity can be used to reduce the register requirement. Consider the tree shown in Figure 11.12.