Consider a $($single$-$tape$)$ Turing machine M$2,$ with input alphabet $\{$a$,$ b$\}$

that has the following behaviour:

Given any input string w in $\{$a$,$ b$\},$ M$2$ halts in an accepting

state in which the contents of the tape consists of as#bt

$,$

where s is the number of as occurring in w$,$ and t is the

number of bs occurring in w$.($Note the position of the tape

head in this accepting configuration does not matter.$)$

For example, on input aba, M$2$ halts in an accepting state with tape

contents aa#b$,$ while on input babab it halts in an accepting state with

tape contents aa#bbb