YES

(VAR x1 x0 x y z)
(RULES
  i2(f(x1,x0)) -> f(i2(x0),i2(x1))
  i1(f(x1,x0)) -> f(i2(x0),i1(x1))
  f(i1(x0),x1) -> f(i2(x0),x1)
  i2(i2(i2(x0))) -> i2(x0)
  i3(x0) -> f(i2(x0),a3())
  i1(i2(i2(x0))) -> i1(x0)
  f(i2(x1),f(x1,x0)) -> x0
  f(i2(i2(x0)),x1) -> f(x0,x1)
  i1(i1(x0)) -> i1(i2(x0))
  f(x0,i1(a3())) -> i1(i2(x0))
  i2(i1(x0)) -> i2(i2(x0))
  f(x0,a2()) -> i2(i2(x0))
  f(x,i1(x)) -> i1(a3())
  f(x1,f(i2(x1),x0)) -> x0
  i1(a2()) -> i1(a3())
  a1() -> i1(a3())
  i2(a2()) -> a2()
  i2(a3()) -> a2()
  f(x,i2(x)) -> a2()
  f(a3(),y) -> y
  f(a2(),y) -> y
  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 + 2
  a1_A = 10
  a2_A = 0
  a3_A = 0
  i1_A(x1) = x1 + 1
  i2_A(x1) = x1
  i3_A(x1) = x1 + 5
  a1#_A = 0
  a2#_A = 0
  a3#_A = 0
  i1#_A(x1) = x1

weights

  w0 = 1
  w(f) = 2
  w(a1) = 3
  w(a2) = 1
  w(a3) = 1
  w(i1) = 1
  w(i2) = 0
  w(i3) = 5

and precedence:

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