[32] Show that there is a constant c such that for every d we have that if K(x) > l(x) + K(l(x)) − (d −

c) then C(x) > l(x) − 2d.

Comments. This shows that if we can compress the K-complexity of some x less than d−c below l(x)+K(l(x)), then we can compress the Ccomplexity less than 2d below l(x). Here l(x) +K(l(x)) = K+(x)−O(1)

in Example 3.2.2 on page 213, and l(x) = C+(x)−O(1) of Exercise 3.3.1 on page 218. Source: [A. Nies, Computability and Randomness, Oxford Univ. Press, 2009].