YES

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

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

  multiply_A(x1,x2) = x1 + x2 + 1
  identity_A = 1
  inverse_A(x1) = x1
  c_A = 1
  b_A = 4
  multiply#_A(x1,x2) = x2
  identity#_A = 0
  c#_A = 0
  b#_A = 0

weights

  w0 = 2
  w(multiply) = 0
  w(identity) = 3
  w(inverse) = 0
  w(c) = 3
  w(b) = 4

and precedence:

inverse > identity > multiply > c > b
)