Let $A={001,0011,11,101}$ and $B={01,111,111,010}$. Similarly, let $C={00,001,1000}$ and $D={0,11,011}$. Which of the following pairs have a post-correspondence solution?

For pair $(A,B)$:

Take sequence of indices:

$3,4,1$

From $A$ side:

$A_3A_4A_1=11\ 101\ 001=11101001$

From $B$ side:

$B_3B_4B_1=111\ 010\ 01=11101001$

Both strings are equal.

So, pair $(A,B)$ has a PCP solution.

For pair $(C,D)$:

Starting must be with first pair because only it gives matching prefix:

$C_1=00,\ D_1=0$

After this, extra $0$ remains on upper side. Repeating first pair keeps increasing extra zeros, and other pairs do not match the required prefix properly.

So, pair $(C,D)$ has no PCP solution.