YES

We show the termination of the TRS R:

  f(f(X)) -> f(a(b(f(X))))
  f(a(g(X))) -> b(X)
  b(X) -> a(X)

-- SCC decomposition.

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

p1: f#(f(X)) -> f#(a(b(f(X))))
p2: f#(f(X)) -> b#(f(X))
p3: f#(a(g(X))) -> b#(X)

and R consists of:

r1: f(f(X)) -> f(a(b(f(X))))
r2: f(a(g(X))) -> b(X)
r3: b(X) -> a(X)

The estimated dependency graph contains the following SCCs:

  (no SCCs)