@article{KrasikovLagarias2003,
  author    = {{Ilia Krasikov and J. C. Lagarias}},
  title     = {{Bounds for the $3x+1$ problem using difference inequalities}},
  journal   = {{Acta Arithmetica}},
  year      = {{2003}},
  volume    = {{109}},
  number    = {{3}},
  pages     = {{237--258}},
  url       = {{https://eudml.org/doc/278462}},
  note      = {{MR 2004i:11020}},
}