context free – Multi step left recursion removal

I’m given a grammar:

R -> RUR | RR | R* | (R) | a | b

And the alphabet set is:

{a,b}

Now if I’m to remove the left recursion, is this solution correct:

R -> R* | (R) | a | b R' R''
R' -> e | URR'
R'' -> e | RR''

Theroy:
If A->Aa|b then:

A -> bA'
A' -> e|aA'

So R -> RUR | RR | R* | (R) | a | b becomes:

R -> RR | R* | (R) | a | b R'
R' -> e | URR'

Then R -> RR | R* | (R) | a | b R' becomes:

R -> R* | (R) | a | b R' R''
R'' -> e | RR''

Here e is epsilon and U is union.