# Kolmogorov complexity of \$ y \$ given \$ x = yz \$ with \$ K (x) geq ell (x) – O (1) \$

I am trying to solve Exercise 2.2.2 of "An Introduction to the Kolmogorov Complexity and Its Applications" (Li & Vitányi, Vol 3). The exercise is the following (paraphrased):

Let $$x$$ satisfied $$K (x) geq n – O (1)$$, or $$n = ell (x)$$ is the length of $$x$$ in a binary encoding. CA watch $$K (y) geq frac {n} {2} – O (1)$$ for $$x = yz$$ with $$ell (y) = ell (z)$$.

I have tried but I have failed to apply the method of incompressibility, exploiting the fact that there are many $$x$$ in a way. More direct approaches to trying to find intelligent recursive functions of $$y$$ and $$z$$ also did not work.