YES

3 decompositions
 #1 -----------
   3: a() -> a'()

 #2 -----------
   4: h(x1,a'(),x2) -> h(x1,x2,x2)

 #3 -----------
   5: g() -> f()
   6: f() -> g()

@Jouannaud and Kirchner's criterion
--- R
   3: a() -> a'()

--- S
   3: a() -> a'()


@Development Closedness
--- R
   4: h(x1,a'(),x2) -> h(x1,x2,x2)

--- S
   4: h(x1,a'(),x2) -> h(x1,x2,x2)


@Development Closedness
--- R
   5: g() -> f()
   6: f() -> g()

--- S
   5: g() -> f()
   6: f() -> g()


NOTE: input TRS is reduced

original is
   1: h(f(),a(),a()) -> h(g(),a(),a())
   2: h(g(),a(),a()) -> h(f(),a(),a())
   3: a() -> a'()
   4: h(x1,a'(),x2) -> h(x1,x2,x2)
   5: g() -> f()
   6: f() -> g()

reduced to
   3: a() -> a'()
   4: h(x1,a'(),x2) -> h(x1,x2,x2)
   5: g() -> f()
   6: f() -> g()