traceLower :: Machine -> (Integer, Integer) -> Integer -> (Integer, Integer)
traceLower machine (_, prev) x = (x, l')
where (bic, foundU) = beamInColumn machine x
traceLower :: Machine -> (Integer, Integer) -> Integer -> (Integer, Integer)
traceLower machine (_, prev) x = (x, l')
where (bic, foundU) = beamInColumn machine x