YES
TRS:
 {   msort(nil()) -> nil(),
   msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y)))),
    min(x, nil()) -> x,
  min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z)),
    del(x, nil()) -> nil(),
  del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z)))}
 DP:
  Strict:
   { msort#(.(x, y)) -> msort#(del(min(x, y), .(x, y))),
     msort#(.(x, y)) -> min#(x, y),
     msort#(.(x, y)) -> del#(min(x, y), .(x, y)),
    min#(x, .(y, z)) -> min#(x, z),
    min#(x, .(y, z)) -> min#(y, z),
    del#(x, .(y, z)) -> del#(x, z)}
  Weak:
  {   msort(nil()) -> nil(),
    msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y)))),
     min(x, nil()) -> x,
   min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z)),
     del(x, nil()) -> nil(),
   del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z)))}
  EDG:
   {(min#(x, .(y, z)) -> min#(x, z), min#(x, .(y, z)) -> min#(y, z))
    (min#(x, .(y, z)) -> min#(x, z), min#(x, .(y, z)) -> min#(x, z))
    (del#(x, .(y, z)) -> del#(x, z), del#(x, .(y, z)) -> del#(x, z))
    (msort#(.(x, y)) -> msort#(del(min(x, y), .(x, y))), msort#(.(x, y)) -> del#(min(x, y), .(x, y)))
    (msort#(.(x, y)) -> msort#(del(min(x, y), .(x, y))), msort#(.(x, y)) -> min#(x, y))
    (msort#(.(x, y)) -> msort#(del(min(x, y), .(x, y))), msort#(.(x, y)) -> msort#(del(min(x, y), .(x, y))))
    (msort#(.(x, y)) -> min#(x, y), min#(x, .(y, z)) -> min#(x, z))
    (msort#(.(x, y)) -> min#(x, y), min#(x, .(y, z)) -> min#(y, z))
    (min#(x, .(y, z)) -> min#(y, z), min#(x, .(y, z)) -> min#(x, z))
    (min#(x, .(y, z)) -> min#(y, z), min#(x, .(y, z)) -> min#(y, z))
    (msort#(.(x, y)) -> del#(min(x, y), .(x, y)), del#(x, .(y, z)) -> del#(x, z))}
   SCCS:
    Scc:
     {del#(x, .(y, z)) -> del#(x, z)}
    Scc:
     {min#(x, .(y, z)) -> min#(x, z),
      min#(x, .(y, z)) -> min#(y, z)}
    Scc:
     {msort#(.(x, y)) -> msort#(del(min(x, y), .(x, y)))}
    SCC:
     Strict:
      {del#(x, .(y, z)) -> del#(x, z)}
     Weak:
     {   msort(nil()) -> nil(),
       msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y)))),
        min(x, nil()) -> x,
      min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z)),
        del(x, nil()) -> nil(),
      del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z)))}
     SPSC:
      Simple Projection:
       pi(del#) = 1
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {min#(x, .(y, z)) -> min#(x, z),
       min#(x, .(y, z)) -> min#(y, z)}
     Weak:
     {   msort(nil()) -> nil(),
       msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y)))),
        min(x, nil()) -> x,
      min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z)),
        del(x, nil()) -> nil(),
      del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z)))}
     SPSC:
      Simple Projection:
       pi(min#) = 1
      Strict:
       {min#(x, .(y, z)) -> min#(y, z)}
      EDG:
       {(min#(x, .(y, z)) -> min#(y, z), min#(x, .(y, z)) -> min#(y, z))}
       SCCS:
        Scc:
         {min#(x, .(y, z)) -> min#(y, z)}
        SCC:
         Strict:
          {min#(x, .(y, z)) -> min#(y, z)}
         Weak:
         {   msort(nil()) -> nil(),
           msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y)))),
            min(x, nil()) -> x,
          min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z)),
            del(x, nil()) -> nil(),
          del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z)))}
         SPSC:
          Simple Projection:
           pi(min#) = 1
          Strict:
           {}
          Qed
    SCC:
     Strict:
      {msort#(.(x, y)) -> msort#(del(min(x, y), .(x, y)))}
     Weak:
     {   msort(nil()) -> nil(),
       msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y)))),
        min(x, nil()) -> x,
      min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z)),
        del(x, nil()) -> nil(),
      del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z)))}
     POLY:
      Argument Filtering:
       pi(=) = [], pi(<=) = [], pi(if) = [], pi(del) = [], pi(min) = [], pi(.) = [], pi(msort#) = 0, pi(msort) = [], pi(nil) = []
      Usable Rules:
       {}
      Interpretation:
       [del] = 0,
       [.] = 1
      Strict:
       {}
      Weak:
       {   msort(nil()) -> nil(),
         msort(.(x, y)) -> .(min(x, y), msort(del(min(x, y), .(x, y)))),
          min(x, nil()) -> x,
        min(x, .(y, z)) -> if(<=(x, y), min(x, z), min(y, z)),
          del(x, nil()) -> nil(),
        del(x, .(y, z)) -> if(=(x, y), z, .(y, del(x, z)))}
      Qed