Prove that function G is not a pseudo-random generator I'm trying to do the following assignment:


  Let $G:\{0,1\}^n \rightarrow \{0,1\}^{n+1}$ and $G':\{0,1\}^n \rightarrow \{0,1\}^{n+2}$ be two pseudorandom generators. Prove
  that the function $G'':\{0,1\}^n \xrightarrow{}\{0,1\}^{2n+3}$ defined
  by $$G''(s_1, \dots, s_n) = (G(s_1,\dots,s_n),G'(G(s_1,\dots,s_n)))$$
  is not a pseudorandom generator.


I know that despite $G$ and $G'$ are pseudorandom functions, the way in which they
are combined makes the new function vulnerable. Letting $G''(s_1,\dots, s_n) = (y_1, \dots, y_{2n+3})$ is possible to create $(y_{n+2}, \dots, y_{2n+3})$ from $(y_1, \dots, y_{n+1})$. I think it's possible to crete a distinguisher that exploits this fact, but I don't know how to prove it.

Any help about how to move on?
You can construct a discriminator which applies G' on the first half of the output in question and compares it to the second half. If they match claim it came from G'' otherwise call it random. 

This discriminator has no false negatives and a false positive rate of $2^{-n-2}$. 

The ability to build an efficient discriminator with non negligible success probability proves G'' is not pseudo random.