Alice and Bob get as an input words $x$ and $y$, which consist of $0$ and $1$. Length of $x$ is $n$ and length of $y$ is $2n$. They want to know if the word $x$ is subword of word $y$. For example, word $001$ is subword of word $1100100$. I need to prove that to know this they need to exchange not less than $\epsilon n$ bits and $\epsilon$ doesn't depend on $n$.
As I understand I need to build communication protocol $f(x, y)$, where $f(x, y) = 1$ if $x$ is substring of $y$, $f(x, y) = 0$ otherwise. Than to use method of combinatorial rectangles or method of fooling set to find its communication complexity.
Please, can you explain me how can I find communication complexity of this function? I'm totally confused than try to find out how to do it. I will be gratefull for any hint or explanation.