YES

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

(COMMENT
Termination is shown by EKBO with interpretations on natural numbers

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

weights

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

and precedence:

i > e > f
)