Show that G is not a PRF $\DeclareMathOperator{concat}{\|}$
I'm trying to do the following assignment:


Let $F : \{0,1\}^k \times \{0,1\}^n \to \{0,1\}^n$ be a PRF. Define function family $G : \{0,1\}^k \times \{0,1\}^{n-1} \to \{0,1\}^{2n}$, for all $x \in \{0,1\}^{n-1}$, by $$G_K(x) = F_K(0 \concat x) \concat F_K(x \concat 1).$$ Show that $G$ is not a PRF.
[Remark: To do this, design an efficient PRF adversary $B$ that achieves an advantage close to 1. Remember the $B$ is an algorithm. As such it needs to specify precisely: What oracle queries does it make? What does it do with the answers it receives? How does it decide what guess to make?]



I provided an image of what I have attempted. 
The symbol $\concat$ means concatenation. Can anyone can please provide some insight on how to solve this problem.
If the adversary takes $x, y \in \{0, 1\}^n$ such that $(0 \parallel x) = (y \parallel 1)$ then

$$G_K(x) = F_K(0 \parallel x) \parallel F_K(x \parallel 1)$$
$$G_K(y) = F_K(0 \parallel y) \parallel F_K(y \parallel 1) = F_K(0 \parallel y) \parallel F_K(0 \parallel x)$$

The left half of $G_K(x)$ is equal to the right half of $G_K(y)$, which lets the adversary distinguish $G$ from a random function.