YES

(VAR x y z)
(RULES
  add(multiply(x,inverse(y)),multiply(x,add(x,inverse(y)))) -> x
  add(multiply(x,inverse(y)),multiply(y,add(x,inverse(y)))) -> x
  add(multiply(x,inverse(x)),multiply(y,one())) -> y
  add(x,inverse(x)) -> one()
  add(multiply(y,x),multiply(z,x)) -> multiply(x,add(y,z))
)

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

  multiply_A(x1,x2) = x1 + x2 + 24867
  add_A(x1,x2) = x1 + x2 + 16304
  inverse_A(x1) = x1 + 1
  one_A = 0
  multiply#_A(x1,x2) = x1 + x2
  add#_A(x1,x2) = x1 + x2
  one#_A = 0

weights

  w0 = 1
  w(multiply) = 0
  w(add) = 0
  w(inverse) = 1
  w(one) = 1

and precedence:

inverse > add > multiply > one
)