YES

TRS:

  f(a()) -> f(b())
  g(b()) -> g(a())
  f(x) -> g(x)

linear polynomial interpretations on N:

  f_A(x1) = x1
  f#_A(x1) = x1 + 1
  a_A = 4
  a#_A = 3
  b_A = 1
  b#_A = 4
  g_A(x1) = 0
  g#_A(x1) = 0

precedence:

  f > b > g > a