why it said the "The left recursion has been removed at the cost of an extra non-terminal symbol(E1) and a little extra complexity"? When I read the book "A Practical approach to compiler construction" the chapter 4 "approaches to syntax analysis" and the section 4.2.3.3 Left Recursion, it says:


  "The left recursion has been removed at the cost of an extra non-terminal symbol"


I have no idea why say that, since $A_1$ still contain recursion?
That grammar has recursion but not left recursion.  Check the definition of left recursion (e.g., https://en.wikipedia.org/wiki/Left_recursion, or consult your favorite textbook on formal languages).