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 ELPO with interpretations on natural numbers

  f_A(x1,x2) = x1 + x2 + 1
  i_A(x1) = x1
  e_A = 1
  f#_A(x1,x2) = x1
  e#_A = 0

and precedence:

i > f > e
)