ellers.txt

set_equal(x,y):
    x.next == y && x == y.prev


set_remove(x):
    x.prev.next = x.next
    x.next.prev = x.prev
    x.next = x
    x.prev = x


join(x,y):

  xp<-x   y->yn

x.next.prev = y.prev
y.prev.next = x.next
x.next = y
y.prev = x



because of non-crossing property:
x.next > y => y.last < x.next

if x.next > y:

       xp<-x----------->xn
            \
             y---->yn

       xp<-x          ->xn
            \        /
             y---->yn

y.last(=y.prev).next = x.next
x.next.prev = y.last
x.next = y
y.prev = x


if y.prev < x:

       xp<----x
               \
  yp<-----------y--->yn

       xp<----x
      /        \
  yp<-          y--->yn

x.first(=x.next).prev = y.prev
y.prev.next = x.first
x.next = y
y.prev = x