MAYBE
Trs:
 {               dx(a()) -> zero(),
          dx(neg(ALPHA)) -> neg(dx(ALPHA)),
    dx(div(ALPHA, BETA)) -> minus(div(dx(ALPHA), BETA), times(ALPHA, div(dx(BETA), exp(BETA, two())))),
           dx(ln(ALPHA)) -> div(dx(ALPHA), ALPHA),
  dx(minus(ALPHA, BETA)) -> minus(dx(ALPHA), dx(BETA)),
    dx(exp(ALPHA, BETA)) -> plus(times(BETA, times(exp(ALPHA, minus(BETA, one())), dx(ALPHA))), times(exp(ALPHA, BETA), times(ln(ALPHA), dx(BETA)))),
  dx(times(ALPHA, BETA)) -> plus(times(BETA, dx(ALPHA)), times(ALPHA, dx(BETA))),
   dx(plus(ALPHA, BETA)) -> plus(dx(ALPHA), dx(BETA)),
                   dx(X) -> one()}
 Comment:
  We consider a duplicating trs.
  FAIL:
   Open