YES

We show the termination of the relative TRS R/S:

  R:
  f(x) -> x

  S:
  a() -> g(a())

-- SCC decomposition.

Consider the non-minimal dependency pair problem (P, R), where P consists of

  (no rules)

and R consists of:

r1: f(x) -> x
r2: a() -> g(a())

The estimated dependency graph contains the following SCCs:

  (no SCCs)