1. For a single statement , whose execution time does not depend on n:

   

2. For a sequence of statements: :

   

3. for i = 1 to


   

4. while (condition)


   No fixed rule: must analyze to find a bound on the number of iterations.

5. If then else

   

6. 

   e.g.

7. if then

   e.g.

8. 

Recall that is a set of functions. Rules VI, VII, and VIII are provable if we consider and to act on all pairs from the two sets. For example: .

9. Sometimes we mix and ordinary functions:

   e.g.

   In this situation, can be replaced by .

   e.g.

   

   Note that the symbol is the convention here, since the left-hand-side of the last equation is not mathematically meaningful.

10. If then (used in conditionals).