YES

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

(COMMENT
Termination is shown by LPO with precedence:

  i > f > e
)