YES

(VAR x0 x)
(RULES
  a(a(a(b(x0)))) -> a(b(a(a(x0))))
  a(b(a(a(b(x))))) -> a(x)
)

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

  a_A(x1) = 0
  b_A(x1) = 1

weights

  w0 = 1
  w(a) = 1
  w(b) = 1

and precedence:

a > b
)