YES

We show the termination of the TRS R:

  f(x,y) -> x
  g(a()) -> h(a(),b(),a())
  i(x) -> f(x,x)
  h(x,x,y) -> g(x)

-- SCC decomposition.

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

p1: g#(a()) -> h#(a(),b(),a())
p2: i#(x) -> f#(x,x)
p3: h#(x,x,y) -> g#(x)

and R consists of:

r1: f(x,y) -> x
r2: g(a()) -> h(a(),b(),a())
r3: i(x) -> f(x,x)
r4: h(x,x,y) -> g(x)

The estimated dependency graph contains the following SCCs:

  (no SCCs)