YES

TRS:

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

max/plus interpretations on N:

  :_A(x1,x2) = max{6, 3, 13}
  :#_A(x1,x2) = max{15, 7, 2 + x2}
  +_A(x1,x2) = max{7, 8, -2 + x2}
  +#_A(x1,x2) = max{0, 8, x2}
  f_A(x1) = max{16, 18 + x1}
  f#_A(x1) = max{20, 18}
  g_A(x1,x2) = max{1, 1 + x1, 1}
  g#_A(x1,x2) = max{17, 0, 6}
  a_A = 1
  a#_A = 19

precedence:

  f > a > : > + = g