YES

(VAR x1 x0 x y z)
(RULES
  i2(x1) -> f(i3(x1),a2())
  f(i3(x1),a3()) -> i3(x1)
  i3(f(x1,x0)) -> f(i3(x0),i3(x1))
  i1(x0) -> f(i3(x0),a1())
  f(i3(x0),f(x0,x1)) -> x1
  i3(i3(x0)) -> f(x0,a3())
  f(x1,f(i3(x1),x0)) -> x0
  i3(a1()) -> a3()
  i3(a2()) -> a3()
  i3(a3()) -> a3()
  f(x,i3(x)) -> a3()
  f(a3(),y) -> y
  f(a2(),y) -> y
  f(a1(),y) -> y
  f(f(x,y),z) -> f(x,f(y,z))
)

(COMMENT
Termination is shown by LPO with precedence:

  i2 > i1 > i3 > f > a1 > a2 > a3
)