YES

TRS:

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

max/plus interpretations on N:

  f_A(x1) = max{4, 2 + x1}
  f#_A(x1) = max{4, 2 + x1}
  0_A = 1
  0#_A = 1
  1_A = 0
  1#_A = 0
  s_A(x1) = max{8, 5 + x1}
  s#_A(x1) = max{8, 5 + x1}
  g_A(x1) = max{10, 5 + x1}
  g#_A(x1) = max{10, 5 + x1}
  +_A(x1,x2) = max{10, 4 + x1, x2}
  +#_A(x1,x2) = max{10, 4 + x1, x2}

precedence:

  0 > 1 > f > g > s = +