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)))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [min#](x0, x1) = 4x1 + 6,
    
    [del#](x0, x1) = 2x1 + 7,
    
    [msort#](x0) = 4x0 + 7,
    
    [=](x0, x1) = 0,
    
    [if](x0, x1, x2) = 2x0,
    
    [<=](x0, x1) = 2x0,
    
    [del](x0, x1) = 0,
    
    [min](x0, x1) = 4x0 + x1 + 6,
    
    [.](x0, x1) = 4x1 + 2,
    
    [msort](x0) = 4x0 + 2,
    
    [nil] = 0
   orientation:
    msort#(.(x,y)) = 16y + 15 >= 8y + 11 = del#(min(x,y),.(x,y))
    
    msort#(.(x,y)) = 16y + 15 >= 7 = msort#(del(min(x,y),.(x,y)))
    
    msort#(.(x,y)) = 16y + 15 >= 4y + 6 = min#(x,y)
    
    min#(x,.(y,z)) = 16z + 14 >= 4z + 6 = min#(y,z)
    
    min#(x,.(y,z)) = 16z + 14 >= 4z + 6 = min#(x,z)
    
    del#(x,.(y,z)) = 8z + 11 >= 2z + 7 = del#(x,z)
    
    msort(nil()) = 2 >= 0 = nil()
    
    msort(.(x,y)) = 16y + 10 >= 10 = .(min(x,y),msort(del(min(x,y),.(x,y))))
    
    min(x,nil()) = 4x + 6 >= x = x
    
    min(x,.(y,z)) = 4x + 4z + 8 >= 4x = 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