YES

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

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

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

and precedence:

g > f > b > a > c
)