YES

TRS:

  norm(nil()) -> 0()
  norm(g(x,y)) -> s(norm(x))
  f(x,nil()) -> g(nil(),x)
  f(x,g(y,z)) -> g(f(x,y),z)
  rem(nil(),y) -> nil()
  rem(g(x,y),0()) -> g(x,y)
  rem(g(x,y),s(z)) -> rem(x,z)

max/plus interpretations on N:

  norm_A(x1) = max{0, x1}
  norm#_A(x1) = max{0, x1}
  nil_A = 0
  nil#_A = 0
  0_A = 0
  0#_A = 0
  g_A(x1,x2) = max{0, x1, x2}
  g#_A(x1,x2) = max{0, x1, x2}
  s_A(x1) = max{0, x1}
  s#_A(x1) = max{0, x1}
  f_A(x1,x2) = max{0, x1, x2}
  f#_A(x1,x2) = max{0, x1, x2}
  rem_A(x1,x2) = max{0, x1, x2}
  rem#_A(x1,x2) = max{0, x1, x2}

precedence:

  nil > 0 = f > g > s = rem > norm