YES

TRS:

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

max/plus interpretations on N:

  f_A(x1) = max{1, 5 + x1}
  f#_A(x1) = max{3, 3 + x1}
  a_A(x1) = max{3, -10 + x1}
  a#_A(x1) = max{3, 2}
  b_A(x1) = max{9, 2 + x1}
  b#_A(x1) = max{1, 3}
  g_A(x1) = max{1, 14 + x1}
  g#_A(x1) = max{0, 0}

precedence:

  f > b > a = g