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 ELPO with interpretations on natural numbers

  multiply_A(x1,x2) = x1 + x2 + 32286
  add_A(x1,x2) = x1 + x2 + 8366
  inverse_A(x1) = x1
  one_A = 0
  inverse#_A(x1) = x1
  one#_A = 0

and precedence:

add > inverse > one > multiply
)