YES

TRS:

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

max/plus interpretations on N:

  a_A = 4
  a#_A = 4
  g_A(x1) = max{2, 2 + x1}
  g#_A(x1) = max{2, 2 + x1}
  c_A = 0
  c#_A = 0
  b_A = 5
  b#_A = 5
  f_A(x1,x2) = max{3, 3 + x1, 3 + x2}
  f#_A(x1,x2) = max{3, 3 + x1, 3 + x2}

precedence:

  b > g > c = f > a