MHB Designing a Non-deterministic 2-Tape Turing Machine for a Specific Language

[mathmari]

Hey!

I want to find a non-deterministic 2-tape Turing machine, that accepts the language L over $\Sigma=\{0,1\}$ in $n$ steps, with input of length $n$, $L=\{x1y \mid |y|=2|x|>0\}$.

Should the Turing machine do the following? (Wondering)
Each time that the machine reads 1 it should check if the length of the subword before 1 is equal to the half of the length of the subword after 1.
How can this be done by a non-deterministic 2-tape Turing machine? Could you give me a hint? (Wondering)

 

[mathmari]

Could we maybe do the following?

We copy the input of the first tape to the second one.
The head of the first tape starts at the beginning of the tape and the head of the second one at the end of that tape.
The head from the first tape goes one position to the right and the head from the second tape two positions to the left.
If this is correct so far, how do we know when we have to step and check if between $x$ and $y$ there is $1$ ? (Wondering)