Is this problem decidable?Given two representations of Turing machines $R(M_1), R(M_2)$, is the length of the computation of $M_1$ longer than the length of the computation of $M_2$ on every input?My guess is not decidable. I am not sure, however, how to justify it.I tried this: Lets enumarate all possible words from $\{0,1\}^*$ and run $M_1$ and $M_2$ simultaenously. If $M_1$ accepts/rejects and $M_2$ is still running, output NO. If $M_2$ stops and $M_1$ is still running, check next word. However, if neither $M_1$, nor $M_2$ do not halt on the word, I am stuck and cannot decide it (because I will get an instance of the halting problem for each combination of word and Turing machine).Is this reasonable or is it a wrong assumption? 
Is this problem decidable? (computation of $M_1$ longer than $M_2$ on every input)
turing machines;undecidability