YES

TRS:

  :(:(x,y),z) -> :(x,:(y,z))
  :(+(x,y),z) -> +(:(x,z),:(y,z))
  :(z,+(x,f(y))) -> :(g(z,y),+(x,a()))

linear polynomial interpretations on N:

  :_A(x1,x2) = 0
  :#_A(x1,x2) = x2 + 1
  +_A(x1,x2) = x2
  +#_A(x1,x2) = 0
  f_A(x1) = x1 + 2
  f#_A(x1) = 5
  g_A(x1,x2) = x2 + 1
  g#_A(x1,x2) = 0
  a_A = 1
  a#_A = 4

precedence:

  f > a > : > + = g