YES

We show the termination of the TRS R:

  f(f(x,a()),a()) -> f(f(f(x,a()),f(a(),a())),a())

-- SCC decomposition.

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

p1: f#(f(x,a()),a()) -> f#(f(f(x,a()),f(a(),a())),a())
p2: f#(f(x,a()),a()) -> f#(f(x,a()),f(a(),a()))
p3: f#(f(x,a()),a()) -> f#(a(),a())

and R consists of:

r1: f(f(x,a()),a()) -> f(f(f(x,a()),f(a(),a())),a())

The estimated dependency graph contains the following SCCs:

  (no SCCs)