YES

TRS:

  f(0()) -> 1()
  f(s(x)) -> g(f(x))
  g(x) -> +(x,s(x))
  f(s(x)) -> +(f(x),s(f(x)))

linear polynomial interpretations on N:

  f_A(x1) = x1 + 1
  f#_A(x1) = x1 + 3
  0_A = 1
  0#_A = 1
  1_A = 0
  1#_A = 0
  s_A(x1) = x1 + 1
  s#_A(x1) = 1
  g_A(x1) = 0
  g#_A(x1) = x1 + 2
  +_A(x1,x2) = 0
  +#_A(x1,x2) = x2

precedence:

  + > f > 1 = g > 0 = s