Apply the backflow algorithm to the digraph below

T$1(8)$

T$2(5)$

T$3(10)$

T$4(6)$

T$5(12)$

T$6(9)$

T$7(2)$

T$8(4)$

T$9(11)$

T$10(7)$

End

$[$Graphs generated by this script: setBorder$(60,30,60,30)$;initPicture$(0,4,1,4)$; fontsize$=14$;fontstyle$=$'none';marker$=$"arrow";line$([0,4],[1\mathrm{.}5,4])$;line$([0,3],[1\mathrm{.}5,4])$;line$([0,3],[1,3])$;line$([0,2],[1,2])$;line$([0,1],[4,2\mathrm{.}5])$;line$([1\mathrm{.}5,4],[3,4])$;line$([1\mathrm{.}5,4],[3,3])$;line$([1,3],[2,3])$;line$([1,2],[2,3])$;line$([2,3],[3,3])$;line$([3,4],[4,2\mathrm{.}5])$;line$([3,3],[4,2\mathrm{.}5])$;fontbackground$=$'white';fontfill$=$'blue';text$([0,4],\text{'}$T$1(8)\text{'},$'aboveleft'$)$;dot$([0,4])$;fontfill$=$'blue';text$([0,3],\text{'}$T$2(5)\text{'},$'aboveleft'$)$;dot$([0,3])$;fontfill$=$'blue';text$([0,2],\text{'}$T$3(10)\text{'},$'belowleft'$)$;dot$([0,2])$;fontfill$=$'blue';text$([0,1],\text{'}$T$4(6)\text{'},$'belowleft'$)$;dot$([0,1])$;fontfill$=$'blue';text$([1\mathrm{.}5,4],\text{'}$T$5(12)\text{'},$'aboveleft'$)$;dot$([1\mathrm{.}5,4])$;fontfill$=$'blue';text$([1,3],\text{'}$T$6(9)\text{'},$'aboveleft'$)$;dot$([1,3])$;fontfill$=$'blue';text$([1,2],\text{'}$T$7(2)\text{'},$'belowleft'$)$;dot$([1,2])$;fontfill$=$'blue';text$([2,3],\text{'}$T$8(4)\text{'},$'aboveleft'$)$;dot$([2,3])$;fontfill$=$'blue';text$([3,4],\text{'}$T$9(11)\text{'},$'aboveright'$)$;dot$([3,4])$;fontfill$=$'blue';text$([3,3],\text{'}$T$10(7)\text{'},$'aboveright'$)$;dot$([3,3])$;fontfill$=$'blue';text$([4,2\mathrm{.}5],$'End','belowright'$)$;dot$([4,2\mathrm{.}5])$;$]$