YES

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

(COMMENT
Termination is shown by LPO with precedence:

  c > inverse > multiply > identity > b > d
)