Problem 3: Combining two TM programs into one

Now append together the programs of the two machines M_ab and M₁₂₃₄, to obtain a new Turing Machine M_ab1234 over the alphavet {a, b}, which first replaces all a's by 1/3 and all b's by 2/4 and then determines if the resulting string is in L_abcd

Note: If you created M_ab and M₁₂₃₄ correctly, then the only thing you have to do here is to make the accept state of M_ab be the same the (former) initial state of M₁₂₃₄

Example: if input is abbbab, it will first be transformed to 122434, and then it will be REJECTED.

In your comments for M _ab1234, indicate what language this machine accepts, making the description of this language as simple as possible. Hint: this language is simple to describe.