Proof : Consider an arbitrary instance of PCP and construct the CFG's and from the ordered pairs of strings.

We construct a new grammar G from and as follows.

          where

         

is same as that of and .

        

This constructions gives a reduction of PCP to the -------- of whether a CFG is ambiguous, thus leading to the undecidability of the given problem. That is, we will now show that the PCP has a solution if and only if G is ambiguous. (where G is constructed from an arbitrary instance of PCP).