YES

(VAR x0 x x1 y z)
(RULES
  R(x0) -> x0
  t(x) -> x
  r(x0) -> x0
  s(x0) -> x0
  S(x0) -> x0
  T(x0) -> x0
  i(f(x1,x0)) -> f(i(x0),i(x1))
  i(i(x0)) -> x0
  f(x1,f(i(x1),x0)) -> x0
  f(i(x1),f(x1,x0)) -> x0
  i(e()) -> e()
  f(x,e()) -> x
  f(e(),x) -> x
  f(i(x),x) -> e()
  f(x,i(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
  w(T) = 42
  w(r) = 2
  w(t) = 1
  w(R) = 24
  w(s) = 4
  w(S) = 3

and precedence:

  i > T > R > t > S > s > r > f > e
)