YES

(VAR x0 x1 x2 a)
(RULES
  multiply(multiply(x0,x1),x2) -> multiply(x0,multiply(x1,x2))
  inverse(multiply(x1,x0)) -> multiply(inverse(x0),inverse(x1))
  double_divide(x0,x1) -> multiply(inverse(x0),inverse(x1))
  multiply(x0,inverse(x0)) -> identity()
  multiply(inverse(a),a) -> identity()
  multiply(x1,multiply(inverse(x1),x0)) -> x0
  multiply(inverse(x1),multiply(x1,x0)) -> x0
  multiply(identity(),x0) -> x0
  multiply(x0,identity()) -> x0
  inverse(identity()) -> identity()
  inverse(inverse(x0)) -> x0
)

(COMMENT
Termination is shown by LPO with precedence:

  double_divide > inverse > multiply > identity
)