YES

We show the termination of the TRS R:

  f(g(f(a()),h(a(),f(a())))) -> f(h(g(f(a()),a()),g(f(a()),f(a()))))

-- SCC decomposition.

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

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

and R consists of:

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

The estimated dependency graph contains the following SCCs:

  (no SCCs)