YES

(VAR x0 x1 x y z)
(RULES
  R(x0) -> x0
  t(x0) -> x0
  r(x0) -> x0
  S(x0) -> x0
  T(x0) -> x0
  s(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 EKBO with interpretations on natural numbers

  f_A(x1,x2) = x1 + x2 + 1
  i_A(x1) = x1
  e_A = 1
  T_A(x1) = x1
  r_A(x1) = x1
  t_A(x1) = x1
  R_A(x1) = x1
  s_A(x1) = x1
  S_A(x1) = x1
  e#_A = 0

weights

  w0 = 1
  w(f) = 0
  w(i) = 0
  w(e) = 1
  w(T) = 6
  w(r) = 22
  w(t) = 21
  w(R) = 56
  w(s) = 3
  w(S) = 4

and precedence:

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