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{6, 1 + x1}
  f#_A(x1) = max{3, 5}
  0_A = 6
  0#_A = 5
  1_A = 7
  1#_A = 4
  s_A(x1) = max{1, -1}
  s#_A(x1) = max{0, 1}
  g_A(x1) = max{6, 3}
  g#_A(x1) = max{2, 2}
  +_A(x1,x2) = max{6, 0, 5 + x2}
  +#_A(x1,x2) = max{2, 2, 2}

precedence:

  f > 0 = g > 1 = s > +