YES

We show the termination of the TRS R:

  a(a(x)) -> a(b(a(x)))

-- SCC decomposition.

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

p1: a#(a(x)) -> a#(b(a(x)))

and R consists of:

r1: a(a(x)) -> a(b(a(x)))

The estimated dependency graph contains the following SCCs:

  (no SCCs)