Here, a TM M$4$ is solving what is called the element distinctness problem. It is given a list of strings over $\{0,1\}$ separated by #s and its job is to accept if all the strings are different. The language is E $=\{$#x$1$#x$2$# $$ #xl$|$ each xi in $\{0,1\}$ and xi $=$ xj for each i $=$ j$\}.$ Machine M$4$ works by comparing x$1$ with x$2$ through xl$,$ then by comparing x$2$ with x$3$ through xl$,$ and so on$.$ An informal description of the TM M$4$ deciding this language follows. M$4=$On input w: $1.$ Place a mark on top of the leftmost tape symbol. If that symbol was a blank, accept. If that symbol was a #$,$ continue with the next stage. Otherwise, reject. $2.$ Scan right to the next # and place a second mark on top of it$.$ If no # is encountered before a blank symbol, only x$1$ was present, so accept. $3.$ By zig$-$zagging, compare the two strings to the right of the marked #s$.$ If they are equal, reject. $4.$ Move the rightmost of the two marks to the next # symbol to the right. If no # symbol is encountered before a blank symbol, move the leftmost mark to the next # to its right and the rightmost mark to the # after that. This time, if no # is available for the rightmost mark, all the strings have been compared, so accept. $5.$ Go to stage $3.$