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 KBO with weight

  w0 = 1
  w(c) = 1
  w(a) = 2
  w(g) = 1
  w(f) = 0
  w(b) = 3

and precedence:

  f > g > a > b > c
)