YES

Problem:
 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)))

Proof:
 DP Processor:
  DPs:
   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)
   min#(x,.(y,z)) -> min#(y,z)
   min#(x,.(y,z)) -> min#(x,z)
   del#(x,.(y,z)) -> del#(x,z)
  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)))
  Usable Rule Processor:
   DPs:
    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)
    min#(x,.(y,z)) -> min#(y,z)
    min#(x,.(y,z)) -> min#(x,z)
    del#(x,.(y,z)) -> del#(x,z)
   TRS:
    f11(x,y) -> x
    f11(x,y) -> y
    min(x,nil()) -> x
    min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
    del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
    del(x,nil()) -> nil()
   TDG Processor:
    DPs:
     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)
     min#(x,.(y,z)) -> min#(y,z)
     min#(x,.(y,z)) -> min#(x,z)
     del#(x,.(y,z)) -> del#(x,z)
    TRS:
     f11(x,y) -> x
     f11(x,y) -> y
     min(x,nil()) -> x
     min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
     del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
     del(x,nil()) -> nil()
    graph:
     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)
     min#(x,.(y,z)) -> min#(x,z) -> min#(x,.(y,z)) -> min#(x,z)
     min#(x,.(y,z)) -> min#(x,z) -> min#(x,.(y,z)) -> min#(y,z)
     del#(x,.(y,z)) -> del#(x,z) -> del#(x,.(y,z)) -> del#(x,z)
     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)
     msort#(.(x,y)) -> del#(min(x,y),.(x,y)) ->
     del#(x,.(y,z)) -> del#(x,z)
     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)) -> msort#(del(min(x,y),.(x,y))) -> msort#(.(x,y)) -> del#(min(x,y),.(x,y))
    CDG Processor:
     DPs:
      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)
      min#(x,.(y,z)) -> min#(y,z)
      min#(x,.(y,z)) -> min#(x,z)
      del#(x,.(y,z)) -> del#(x,z)
     TRS:
      f11(x,y) -> x
      f11(x,y) -> y
      min(x,nil()) -> x
      min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
      del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
      del(x,nil()) -> nil()
     graph:
      min#(x,.(y,z)) -> min#(y,z) -> 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#(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)) -> min#(x,y) -> min#(x,.(y,z)) -> min#(y,z)
      msort#(.(x,y)) -> min#(x,y) ->
      min#(x,.(y,z)) -> min#(x,z)
      msort#(.(x,y)) -> del#(min(x,y),.(x,y)) -> del#(x,.(y,z)) -> del#(x,z)
     Restore Modifier:
      DPs:
       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)
       min#(x,.(y,z)) -> min#(y,z)
       min#(x,.(y,z)) -> min#(x,z)
       del#(x,.(y,z)) -> del#(x,z)
      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)))
      SCC Processor:
       #sccs: 2
       #rules: 3
       #arcs: 8/36
       DPs:
        del#(x,.(y,z)) -> del#(x,z)
       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)))
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [del#](x0, x1) = x1,
         
         [=](x0, x1) = 0,
         
         [if](x0, x1, x2) = 0,
         
         [<=](x0, x1) = 0,
         
         [del](x0, x1) = 0,
         
         [min](x0, x1) = x0,
         
         [.](x0, x1) = x1 + 1,
         
         [msort](x0) = x0,
         
         [nil] = 0
        orientation:
         del#(x,.(y,z)) = z + 1 >= z = del#(x,z)
         
         msort(nil()) = 0 >= 0 = nil()
         
         msort(.(x,y)) = y + 1 >= 1 = .(min(x,y),msort(del(min(x,y),.(x,y))))
         
         min(x,nil()) = x >= x = x
         
         min(x,.(y,z)) = x >= 0 = if(<=(x,y),min(x,z),min(y,z))
         
         del(x,nil()) = 0 >= 0 = nil()
         
         del(x,.(y,z)) = 0 >= 0 = if(=(x,y),z,.(y,del(x,z)))
        problem:
         DPs:
          
         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)))
        Qed
       
       DPs:
        min#(x,.(y,z)) -> min#(y,z)
        min#(x,.(y,z)) -> min#(x,z)
       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)))
       Matrix Interpretation Processor:
        dimension: 1
        interpretation:
         [min#](x0, x1) = x1 + 1,
         
         [=](x0, x1) = 0,
         
         [if](x0, x1, x2) = 0,
         
         [<=](x0, x1) = 0,
         
         [del](x0, x1) = 0,
         
         [min](x0, x1) = x0,
         
         [.](x0, x1) = x0 + x1 + 1,
         
         [msort](x0) = x0 + 1,
         
         [nil] = 0
        orientation:
         min#(x,.(y,z)) = y + z + 2 >= z + 1 = min#(y,z)
         
         min#(x,.(y,z)) = y + z + 2 >= z + 1 = min#(x,z)
         
         msort(nil()) = 1 >= 0 = nil()
         
         msort(.(x,y)) = x + y + 2 >= x + 2 = .(min(x,y),msort(del(min(x,y),.(x,y))))
         
         min(x,nil()) = x >= x = x
         
         min(x,.(y,z)) = x >= 0 = if(<=(x,y),min(x,z),min(y,z))
         
         del(x,nil()) = 0 >= 0 = nil()
         
         del(x,.(y,z)) = 0 >= 0 = if(=(x,y),z,.(y,del(x,z)))
        problem:
         DPs:
          
         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)))
        Qed