Then the following moves are introduced in M.

            for .finally introduce,

          

That is, the DPDA M enters the state p after replacing X with (after starting at state q, on input a and with X on the top of the stack). But ---- it now takes a sequence of moves ( number of moves to be precise) for the same.

Lemma 2 If L is a DCFL , then L=L(M) for some such that if ,then is either or of the form XY for some

Proof : Let for some DPDA.