YES

TRS:

  f(f(X)) -> f(g(f(g(f(X)))))
  f(g(f(X))) -> f(g(X))

max/plus interpretations on N:

  f_A(x1) = max{13, 20 + x1}
  f#_A(x1) = max{2, 11 + x1}
  g_A(x1) = max{2, -23 + x1}
  g#_A(x1) = max{12, 0}

precedence:

  f > g