YES

We show the termination of the TRS R:

  g(b()) -> f(b())
  f(a()) -> g(a())
  b() -> a()

-- SCC decomposition.

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

p1: g#(b()) -> f#(b())
p2: f#(a()) -> g#(a())

and R consists of:

r1: g(b()) -> f(b())
r2: f(a()) -> g(a())
r3: b() -> a()

The estimated dependency graph contains the following SCCs:

  (no SCCs)