YES

TRS:

  f(x) -> s(x)
  f(s(s(x))) -> s(f(f(x)))

linear polynomial interpretations on N:

  f_A(x1) = x1 + 1
  f#_A(x1) = x1 + 1
  s_A(x1) = x1 + 1
  s#_A(x1) = x1 + 1

precedence:

  f > s