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))
  LPO Processor:
   argument filtering:
    pi(C) = []
    pi(:) = [0,1]
    pi(:#) = 0
   usable rules:
    :(:(:(:(C(),x),y),z),u) -> :(:(x,z),:(:(:(x,y),z),u))
   precedence:
    :# ~ : ~ C
   problem:
    DPs:
     
    TRS:
     :(:(:(:(C(),x),y),z),u) -> :(:(x,z),:(:(:(x,y),z),u))
   Qed