YES

We show the termination of the TRS R:

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

-- SCC decomposition.

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

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

and R consists of:

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

The estimated dependency graph contains the following SCCs:

  (no SCCs)