YES

(VAR x1 x0 x y z)
(RULES
  i(f(x1,x0)) -> f(i(x0),i(x1))
  a(b(a(x0))) -> b(a(b(x0)))
  i(i(x0)) -> x0
  f(x1,f(i(x1),x0)) -> x0
  f(i(x1),f(x1,x0)) -> x0
  i(e()) -> e()
  b(b(x)) -> x
  a(a(x)) -> x
  f(e(),x) -> x
  f(x,e()) -> 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
  a_A(x1) = x1 + 2
  b_A(x1) = x1 + 1
  e#_A = 0

weights

  w0 = 1
  w(f) = 0
  w(i) = 0
  w(e) = 1
  w(a) = 2
  w(b) = 1

and precedence:

i > f > a > b > e
)