YES

TRS:

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

linear polynomial interpretations on N:

  :_A(x1,x2) = 1
  :#_A(x1,x2) = 0
  C_A = 1
  C#_A = 0

precedence:

  : = C