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)

linear polynomial interpretations on N:

  norm_A(x1) = x1
  norm#_A(x1) = x1
  nil_A = 1
  nil#_A = 1
  0_A = 0
  0#_A = 0
  g_A(x1,x2) = x1 + x2 + 1
  g#_A(x1,x2) = x1 + x2 + 1
  s_A(x1) = x1 + 1
  s#_A(x1) = x1 + 1
  f_A(x1,x2) = x1 + x2 + 1
  f#_A(x1,x2) = x1 + x2 + 1
  rem_A(x1,x2) = x1 + x2
  rem#_A(x1,x2) = x1 + x2

precedence:

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