Does for any program it exists a program that is complexitively independant?

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So we fix a system turing complet, as the system is fixed it makes sens to speak of complexity with a coefficient like 3t, or 10t² on this system. Let L be all the linear complexity decision problems. Let x be in L of complexity t->at we note a=N(x).

question: let A in L does it exists B in L such that N((A,B)) = N(A)+N(B) (big bonus point if A -> B is calculable)

I think sometimes about complexity, and it leads to the conclusion this is a key question.