YES

(VAR x0 x1 x2 x y z)
(RULES
  i(f(x0,x1)) -> f(i(x1),i(x0))
  f(x0,f(i(i(x1)),x2)) -> f(x0,f(x1,x2))
  i(i(i(x0))) -> i(x0)
  f(x0,f(x2,f(i(x2),x1))) -> f(x0,x1)
  f(x0,f(x1,i(x1))) -> x0
  f(x0,i(i(x1))) -> f(x0,x1)
  f(e(),x0) -> i(i(x0))
  f(i(x1),f(x1,x0)) -> i(i(x0))
  i(e()) -> e()
  f(x,e()) -> x
  f(i(x),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
)