YES

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

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

  divide_A(x1,x2) = x1 + x2 + 2
  identity_A = 1
  multiply_A(x1,x2) = x1 + x2 + 1
  inverse_A(x1) = x1
  identity#_A = 0

weights

  w0 = 1
  w(divide) = 0
  w(identity) = 1
  w(multiply) = 0
  w(inverse) = 0

and precedence:

inverse > divide > multiply > identity
)