YES

   2: a() -> a'()
   3: f(a'(),x1) -> f(x1,x1)
   4: f(x1,a'()) -> f(x1,x1)
   5: f(a'(),a'()) -> b()
   6: b() -> f(a'(),a'())

@Development Closedness
--- R
   2: a() -> a'()
   3: f(a'(),x1) -> f(x1,x1)
   4: f(x1,a'()) -> f(x1,x1)
   5: f(a'(),a'()) -> b()
   6: b() -> f(a'(),a'())

--- S
   2: a() -> a'()
   3: f(a'(),x1) -> f(x1,x1)
   4: f(x1,a'()) -> f(x1,x1)
   5: f(a'(),a'()) -> b()
   6: b() -> f(a'(),a'())


NOTE: input TRS is reduced

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

reduced to
   2: a() -> a'()
   3: f(a'(),x1) -> f(x1,x1)
   4: f(x1,a'()) -> f(x1,x1)
   5: f(a'(),a'()) -> b()
   6: b() -> f(a'(),a'())