YES

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

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

  f_A(x1,x2) = x1 + x2
  i_A(x1) = x1
  e_A = 1
  a_A = 0
  b_A = 1
  f#_A(x1,x2) = x1
  i#_A(x1) = x1
  e#_A = 0
  a#_A = 0
  b#_A = 0

and precedence:

e > b > i > f > a
)