[1] These statements mask a great deal of oversimplification. For instance, if we count process steps as machine operations we are making the assumption that the number of machine operations needed to perform, say, a multiplication is independent of the size of the numbers to be multiplied, which is false if the numbers are sufficiently large. Similar remarks hold for the estimates of space. Like the design and description of a process, the analysis of a process can be carried out at various levels of abstraction.
1.2.3  Orders of Growth