YES

We show the termination of the TRS R:

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

-- SCC decomposition.

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

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

and R consists of:

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

The estimated dependency graph contains the following SCCs:

  (no SCCs)