YES

(VAR x z)
(RULES
  f(x,a()) -> x
  f(a(),z) -> a()
  b() -> a()
  g(x) -> x
  c() -> a()
)

(COMMENT
Termination is shown by EKBO with interpretations on natural numbers

  c_A = 0
  a_A = 0
  g_A(x1) = x1
  f_A(x1,x2) = 0
  b_A = 1
  c#_A = 0
  a#_A = 0
  f#_A(x1,x2) = x1 + x2
  b#_A = 0

weights

  w0 = 1
  w(c) = 2
  w(a) = 1
  w(g) = 1
  w(f) = 0
  w(b) = 2

and precedence:

g > f > b > a > c
)