YES

Problem:
 qsort(nil()) -> nil()
 qsort(.(x,y)) -> ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y))))
 lowers(x,nil()) -> nil()
 lowers(x,.(y,z)) -> if(<=(y,x),.(y,lowers(x,z)),lowers(x,z))
 greaters(x,nil()) -> nil()
 greaters(x,.(y,z)) -> if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))

Proof:
 DP Processor:
  DPs:
   qsort#(.(x,y)) -> greaters#(x,y)
   qsort#(.(x,y)) -> qsort#(greaters(x,y))
   qsort#(.(x,y)) -> lowers#(x,y)
   qsort#(.(x,y)) -> qsort#(lowers(x,y))
   lowers#(x,.(y,z)) -> lowers#(x,z)
   greaters#(x,.(y,z)) -> greaters#(x,z)
  TRS:
   qsort(nil()) -> nil()
   qsort(.(x,y)) -> ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y))))
   lowers(x,nil()) -> nil()
   lowers(x,.(y,z)) -> if(<=(y,x),.(y,lowers(x,z)),lowers(x,z))
   greaters(x,nil()) -> nil()
   greaters(x,.(y,z)) -> if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))
  KBO Processor:
   argument filtering:
    pi(nil) = []
    pi(qsort) = [0]
    pi(.) = [1]
    pi(lowers) = 1
    pi(greaters) = 1
    pi(++) = []
    pi(<=) = []
    pi(if) = 2
    pi(qsort#) = 0
    pi(greaters#) = 1
    pi(lowers#) = 1
   weight function:
    w0 = 1
    w(greaters#) = w(qsort#) = w(if) = w(<=) = w(++) = w(lowers) = w(
    qsort) = w(nil) = 1
    w(lowers#) = w(greaters) = w(.) = 0
   precedence:
    if > lowers# ~ greaters# ~ qsort# ~ <= ~ ++ ~ greaters ~ lowers ~ . ~ qsort ~ nil
   problem:
    DPs:
     
    TRS:
     qsort(nil()) -> nil()
     qsort(.(x,y)) -> ++(qsort(lowers(x,y)),.(x,qsort(greaters(x,y))))
     lowers(x,nil()) -> nil()
     lowers(x,.(y,z)) -> if(<=(y,x),.(y,lowers(x,z)),lowers(x,z))
     greaters(x,nil()) -> nil()
     greaters(x,.(y,z)) -> if(<=(y,x),greaters(x,z),.(y,greaters(x,z)))
   Qed