YES

(VAR x0 x1 x y z)
(RULES
  multiply(x0,multiply(inverse(x0),x1)) -> x1
  inverse(multiply(x1,x0)) -> multiply(inverse(x0),inverse(x1))
  inverse(identity()) -> identity()
  inverse(inverse(x0)) -> x0
  c() -> inverse(b())
  multiply(x0,identity()) -> x0
  multiply(x0,inverse(x0)) -> identity()
  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 EKBO with interpretations on natural numbers

  multiply_A(x1,x2) = x1 + x2 + 146731
  identity_A = 146731
  inverse_A(x1) = x1
  c_A = 2
  b_A = 1
  identity#_A = 0
  c#_A = 0
  b#_A = 0

weights

  w0 = 3
  w(multiply) = 0
  w(identity) = 5
  w(inverse) = 0
  w(c) = 11
  w(b) = 7

and precedence:

inverse > b > c > multiply > identity
)