YES

TRS:

  minus(x,0()) -> x
  minus(s(x),s(y)) -> minus(x,y)
  f(0()) -> s(0())
  f(s(x)) -> minus(s(x),g(f(x)))
  g(0()) -> 0()
  g(s(x)) -> minus(s(x),f(g(x)))

max/plus interpretations on N:

  minus_A(x1,x2) = max{24, x1, 24}
  minus#_A(x1,x2) = max{22, 23, 10}
  0_A = 1
  0#_A = 0
  s_A(x1) = max{19, 13 + x1}
  s#_A(x1) = max{9, 21 + x1}
  f_A(x1) = max{19, 10 + x1}
  f#_A(x1) = max{24, 7 + x1}
  g_A(x1) = max{17, 5 + x1}
  g#_A(x1) = max{25, x1}

precedence:

  f > g > minus = 0 = s