YES

(VAR x0 x1 x2 x y z)
(RULES
  f(e(),f(i(x0),x1)) -> f(i(x0),x1)
  i(f(x1,x0)) -> f(i(x0),i(x1))
  f(e(),i(x0)) -> i(x0)
  f(x0,f(x2,f(i(x2),x1))) -> f(x0,x1)
  f(x0,f(x1,i(x1))) -> x0
  i(i(x0)) -> f(e(),x0)
  f(i(x1),f(x1,x0)) -> f(e(),x0)
  f(x0,f(e(),x1)) -> f(x0,x1)
  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 ELPO with interpretations on natural numbers

  f_A(x1,x2) = x1 + x2
  i_A(x1) = x1
  e_A = 0
  f#_A(x1,x2) = 0
  i#_A(x1) = 0
  e#_A = 0

and precedence:

i > f > e
)