YES

(VAR x0 x1 x y z)
(RULES
  f(a(),f(a(),f(a(),x0))) -> f(b(),f(a(),f(a(),f(b(),x0))))
  f(a(),f(a(),a())) -> f(b(),f(a(),f(a(),b())))
  i(f(x1,x0)) -> f(i(x0),i(x1))
  f(i(x0),x0) -> f(b(),b())
  i(a()) -> f(b(),f(a(),b()))
  f(i(x0),f(x0,x1)) -> x1
  i(i(x0)) -> x0
  i(b()) -> b()
  f(a(),f(b(),f(a(),x0))) -> f(b(),x0)
  f(b(),f(b(),x0)) -> x0
  f(a(),f(b(),a())) -> b()
  f(x1,f(i(x1),x0)) -> x0
  f(x,f(b(),b())) -> x
  e() -> f(b(),b())
  f(x,i(x)) -> f(b(),b())
  f(f(x,y),z) -> f(x,f(y,z))
)

(COMMENT
Termination is shown by LPO with precedence:

  i > a > e > b > f
)