YES

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

(COMMENT
Termination is shown by KBO with weight

  w0 = 1
  w(f) = 0
  w(i) = 0
  w(e) = 1

and precedence:

  i > f > e
)