Kill null productions and eliminate unit productions S aAB

Kill null productions and eliminate unit productions.
S -> aAB
A -> ABb
B -> A
A -> _/\\_
B -> _/\\_

Solution

Problem Kill null productions and eliminate unit productions.
S -> aAB
A -> ABb
B -> A
A -> .
B -> .

Solution

Now I express the same problem into another way

S -> aAB----------------- (i)
A -> ABb\\ ----------------- (ii)
B -> A\\ ----------------------(iii)

Step 1) - put the A-> in the right side of the (i),(ii) equation

S-> aAB-à aAB/aB---------------------------------- (iv)

A->ABb -> ABb/Bb------------------------------------ (v)

Step 2)- put the B-> in the right side of the (i),(iii) equation

S->aAB/aA/a---------------------------------------------- (vi)

B-> ABb-> ABb/Ab-------------------------------------- (vii)

Step 3) put A-> and B-> in the right side of the (v), (vii) equation

A->b---------------------------------------------- (viii)

B->b----------------------------------------------- (ix)

Now we combine the eqns-(iv) & (vi)

S->ABb/aA/aB/a

We also get the Production of A & B from (v), (vii), (iix) & (ix)

A->ABb/Bb/Ab/b

B->ABb/Bb/Ab/b

Final Solution is:

S->ABb/aA/aB/a

A->ABb/Bb/Ab/b

B->ABb/Bb/Ab/b

Solution for Unite production: S-> A where A V

But we got production those have not unite production for removing

if you have any doubt please mention

Thanks