YES
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)))}
 DP:
  Strict:
   {      qsort#(.(x, y)) -> qsort#(lowers(x, y)),
          qsort#(.(x, y)) -> qsort#(greaters(x, y)),
          qsort#(.(x, y)) -> lowers#(x, y),
          qsort#(.(x, y)) -> greaters#(x, y),
      lowers#(x, .(y, z)) -> lowers#(x, z),
    greaters#(x, .(y, z)) -> greaters#(x, z)}
  Weak:
  {        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)))}
  EDG:
   {(greaters#(x, .(y, z)) -> greaters#(x, z), greaters#(x, .(y, z)) -> greaters#(x, z))
    (qsort#(.(x, y)) -> greaters#(x, y), greaters#(x, .(y, z)) -> greaters#(x, z))
    (qsort#(.(x, y)) -> lowers#(x, y), lowers#(x, .(y, z)) -> lowers#(x, z))
    (lowers#(x, .(y, z)) -> lowers#(x, z), lowers#(x, .(y, z)) -> lowers#(x, z))}
   SCCS:
    Scc:
     {greaters#(x, .(y, z)) -> greaters#(x, z)}
    Scc:
     {lowers#(x, .(y, z)) -> lowers#(x, z)}
    SCC:
     Strict:
      {greaters#(x, .(y, z)) -> greaters#(x, z)}
     Weak:
     {        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)))}
     SPSC:
      Simple Projection:
       pi(greaters#) = 1
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {lowers#(x, .(y, z)) -> lowers#(x, z)}
     Weak:
     {        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)))}
     SPSC:
      Simple Projection:
       pi(lowers#) = 1
      Strict:
       {}
      Qed