# Is it decidable whether Turing Machine never scans any tape cell more than once when started with given string

The problem:

Is it decidable that the set of pairs $$(M,w)$$ such that TM $$M$$, started with input $$w$$, never scans any tape cell more than once.

How can I easily prove above to be decidable. I found following proof confusing:

How is $$l+m$$ is upper bound on number of steps? I feel we should be doing at least $$l\times 𝑄\times \Gamma\times\{𝐿,𝑅\}+1$$ steps ($$Q$$ being number of states,$$\Gamma$$ being set of tape alphabet, $$l$$ is string length, $$L$$ and $$R$$ are head movement directions).