YES

Problem:
 :(:(:(:(C(),x),y),z),u) -> :(:(x,z),:(:(:(x,y),z),u))

Proof:
 DP Processor:
  DPs:
   :#(:(:(:(C(),x),y),z),u) -> :#(x,y)
   :#(:(:(:(C(),x),y),z),u) -> :#(:(x,y),z)
   :#(:(:(:(C(),x),y),z),u) -> :#(:(:(x,y),z),u)
   :#(:(:(:(C(),x),y),z),u) -> :#(x,z)
   :#(:(:(:(C(),x),y),z),u) -> :#(:(x,z),:(:(:(x,y),z),u))
  TRS:
   :(:(:(:(C(),x),y),z),u) -> :(:(x,z),:(:(:(x,y),z),u))
  Arctic Interpretation Processor:
   dimension: 1
   interpretation:
    [:#](x0, x1) = x0 + 0,
    
    [:](x0, x1) = 1x0 + x1 + 3,
    
    [C] = 0
   orientation:
    :#(:(:(:(C(),x),y),z),u) = 2x + 1y + z + 5 >= x + 0 = :#(x,y)
    
    :#(:(:(:(C(),x),y),z),u) = 2x + 1y + z + 5 >= 1x + y + 3 = :#(:(x,y),z)
    
    :#(:(:(:(C(),x),y),z),u) = 2x + 1y + z + 5 >= 2x + 1y + z + 4 = :#(:(:(x,y),z),u)
    
    :#(:(:(:(C(),x),y),z),u) = 2x + 1y + z + 5 >= x + 0 = :#(x,z)
    
    :#(:(:(:(C(),x),y),z),u) = 2x + 1y + z + 5 >= 1x + z + 3 = :#(:(x,z),:(:(:(x,y),z),u))
    
    :(:(:(:(C(),x),y),z),u) = u + 3x + 2y + 1z + 6 >= u + 3x + 2y + 1z + 5 = :(:(x,z),:(:(:(x,y),z),u))
   problem:
    DPs:
     :#(:(:(:(C(),x),y),z),u) -> :#(:(:(x,y),z),u)
     :#(:(:(:(C(),x),y),z),u) -> :#(:(x,z),:(:(:(x,y),z),u))
    TRS:
     :(:(:(:(C(),x),y),z),u) -> :(:(x,z),:(:(:(x,y),z),u))
   LPO Processor:
    argument filtering:
     pi(C) = []
     pi(:) = [0,1]
     pi(:#) = 0
    precedence:
     :# ~ : ~ C
    problem:
     DPs:
      
     TRS:
      :(:(:(:(C(),x),y),z),u) -> :(:(x,z),:(:(:(x,y),z),u))
    Qed