Question: [12] Let x, y, z, and k be as before. Prove the following: (a) C(x, y) C(x)+2l(C(x)) + C(y|x) + O(1). (b) C(k(x, y))

[12] Let x, y, z, and φk be as before. Prove the following:

(a) C(x, y) ≤ C(x)+2l(C(x)) + C(y|x) + O(1).

(b) C(φk(x, y)) ≤ C(x)+2l(C(x)) + C(y|x)+2l(k) + O(1) ≤ C(x) +

2l(C(x)) + C(y)+2l(k) + O(1).

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