@causative: You are completely wrong. Let C be an interpreter for L written in M. Let P be an M-program that on input (Q,x) runs Q via C on x. Then for every string x we have K[L](x) = |(Q,x)| for some L-program Q and also K[M](x) ≤ |(P,(Q,x))| ≤ |P|+O(log(|P|))+|(Q,x)| (using the obvious pair-coding). —
user21820 1 min ago