YES

(VAR x0 x1 x y z)
(RULES
  inverse(multiply(x0,x1)) -> multiply(inverse(x1),inverse(x0))
  multiply(x1,multiply(inverse(x1),x0)) -> x0
  multiply(x0,inverse(x0)) -> identity()
  inverse(inverse(x0)) -> x0
  inverse(identity()) -> identity()
  multiply(x0,identity()) -> x0
  multiply(inverse(x1),multiply(x1,x0)) -> x0
  multiply(multiply(x,y),z) -> multiply(x,multiply(y,z))
  multiply(inverse(x),x) -> identity()
  multiply(identity(),x) -> x
)

(COMMENT
Termination is shown by KBO with weight

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

and precedence:

  inverse > multiply > identity
)