Elimination of Unit production from context free grammar

A Unit production is like below :

		S -> B

We will apply below steps to remove Unit production:

1. Write production without Unit production
2. Check what we are missing because of Step 1

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We will understand this using one example:

		Given grammar is :

		S -> Aa/B/c
		B -> A/bb
		A -> a/bc/B
		
Solution:
		Now we will apply step 1:

		S -> Aa/c
		B -> bb
		A -> a/bc

		Now check what we are missing after applying Step 1:

		First : S -> B -> bb
		And   : S -> B -> A -> a
		And   : S -> B -> A -> bc

		So add these in the prodcution list of "S"

		S -> Aa/c/bb/a/bc
		B -> bb
		A -> a/bc

		Second : B -> A -> a
		And    : B -> A -> bc

		So add this in the prodcution list of "B"

		S -> Aa/c/bb/a/bc
		B -> bb/a/bc
		A -> a/bc

		Third: A-> B -> bb

		So add this in the prodcution list of "A"

		
		S -> Aa/c/bb/a/bc
		B -> bb/a/bc
		A -> a/bc/bb
			

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We also see one more example with 1 variation:

		S -> AC
		A -> a
		C -> B/d
		B -> D
		D -> E
		E -> b
		
Solution:
		Now apply step 1:

		S -> AC
		A -> a
		C -> b

		Now check what are we missing after applying Step 1:

		For C: C -> B -> D -> E -> b

		So add this in the production of "C"

		S -> AC
		A -> a
		C -> d/b

		For B: B -> D -> E -> b

		So add this in the production of "B"

		S -> AC
		A -> a
		C -> d/b
		B -> b

		Similarily for D and E also add:

		S -> AC
		A -> a
		C -> d/b
		B -> b
		D -> b
		E -> b

But if we see that B -> b, D -> b and E -> b
productions are useless as they can't be reached, Remove them:
		
		S -> AC
		A -> a
		C -> d/b
		
		

Next we will learn about removing useless symbols