list= {(Row[{Subscript[x, 2]}] [CirclePlus]
 1)/Subscript[x, 1], (Row[{Subscript[x,
 1], Subscript[x, 3]}] [CirclePlus]
 1)/Subscript[x, 2],
 (Row[{Subscript[x, 2]}] [CirclePlus]
 1)/Subscript[x, 3], (Row[{Subscript[y,
 2]}] [CirclePlus] 1)/Subscript[x, 1],
 (Subscript[x, 1] [CirclePlus]
 Subscript[y, 3])/Subscript[x, 2],
 (Subscript[y, 3] [CirclePlus]
 (Subscript[y, 2] + Subscript[y,
 3]))/Subscript[x, 1]}

Subscript[y,1] = list[[1]]
Subscript[y,2] = list[[2]]
Subscript[y,3] = list[[3]]
Plus[Subscript[y,1],Subscript[y,2]] = list[[4]]
Plus[Subscript[y,2],Subscript[y,3]] = list[[5]]