YES

(VAR x1 x0 x2 x y z)
(RULES
  i(f(x1,x0)) -> f(i(x0),i(x1))
  i(h(x0)) -> h(i(x0))
  f(i(x0),f(x0,x1)) -> x1
  h(e()) -> e()
  f(i(x0),x0) -> e()
  i(i(x0)) -> x0
  i(e()) -> e()
  f(e(),x0) -> x0
  f(h(x0),f(h(x1),x2)) -> f(h(f(x0,x1)),x2)
  f(x1,f(i(x1),x0)) -> x0
  f(h(x),h(y)) -> h(f(x,y))
  f(x,e()) -> x
  f(x,i(x)) -> e()
  f(f(x,y),z) -> f(x,f(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 = 0
  h_A(x1) = x1
  f#_A(x1,x2) = x1
  e#_A = 0

weights

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

and precedence:

i > h > f > e
)