YES
Time: 0.001261
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:
  DP:
   {       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)}
  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)))}
  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 (2):
    Scc:
     {greaters#(x, .(y, z)) -> greaters#(x, z)}
    Scc:
     {lowers#(x, .(y, z)) -> lowers#(x, z)}
    SCC (1):
     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 (1):
     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