MAYBE
Trs:
 {     f(true(), x, y, z) -> del(.(y, z)),
      f(false(), x, y, z) -> .(x, del(.(y, z))),
       del(.(x, .(y, z))) -> f(=(x, y), x, y, z),
          =(nil(), nil()) -> true(),
        =(nil(), .(y, z)) -> false(),
        =(.(x, y), nil()) -> false(),
  =(.(x, y), .(u(), v())) -> and(=(x, u()), =(y, v()))}
 Comment:
  We consider a duplicating trs.
  FAIL:
   Open