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)))

linear polynomial interpretations on N:

  minus_A(x1,x2) = x1
  minus#_A(x1,x2) = x1
  0_A = 6
  0#_A = 8
  s_A(x1) = x1 + 4
  s#_A(x1) = 8
  f_A(x1) = x1 + 5
  f#_A(x1) = x1 + 3
  g_A(x1) = x1 + 1
  g#_A(x1) = x1 + 1

precedence:

  s > g > f > minus = 0