1. LiteRed example 1.nb — One-loop off-shell massless vertex.
   Dashed lines denote massless propagators
   1. l2
   2. (p-l)2
   3. (q+l)2
2. 
3. LiteRed example 2.nb— Two-loop onshell mass operator. Dashed lines — massless propagators, solid lines — massive propagators.
   Constraint: p2=1.
   1. (p - l)2-1
   2. (p - l - r)2-1
   3. (p - r)2-1
   4. l2
   5. r2
4. 
5. LiteRed example 3.nb— Two-loop on-shell vertex. Dashed lines — massless propagators.
   Constraint: p2=q2=0.
   1. (l - r)2 — numerator
   2. l2
   3. r2
   4. (p - l)2
   5. (q - r)2
   6. (p - l + r)2
   7. (q - r + l)2
6. 
7. LiteRed example 4.nb— Three-loop on-shell massive propagator.
   Constraint: p2=1
   1. (l-k)2 — numerator
   2. (p-l)2-1
   3. (p-l-r)2-1
   4. (p-l-r-k)2-1
   5. (p-r-k)2-1
   6. (p-k)2-1
   7. l2
   8. r2
   9. k2
8. 
9. LiteRed example 5.nb— Three-loop on-shell vertex. Constraint: p2=q2=0.
   1. r2 — numerator
   2. 2 p˙l — numerator
   3. 2 q˙k — numerator
   4. (r+p)2
   5. (r-q)2
   6. k2
   7. (k-r)2
   8. l2
   9. (l+r)2
   10. (k+p)2
   11. (l+r-k)2
   12. (l+q)2
10. 
11. LiteRed example 6.nb — Two-loop cross-box.
    Constraints: p12=p22=1, k12=k22=0
    1. (p2 - l)2 — numerator
    2. (p1 - r)2 — numerator
    3. l2
    4. r2
    5. (k1-l)2
    6. (k2-r)2
    7. (k1-l+r)2
    8. (k2-r+l)2
    9. (k1-l+r-p1)2
12. 
13. LiteRed example 7.nb— Four-loop massive tadpole.
    
    1. (k4-k1)2 — numerator
    2. k12+1
    3. k22+1
    4. k32+1
    5. k42+1
    6. (k1-k2+k4)2+1
    7. (k1-k3+k4)2+1
    8. (k1-k2)2
    9. (k2-k3)2
    10. (k3-k4)2
14. 
15. LiteRed example 8.nb— mapping between bases.
    Some sectors of bases v1, v2, and v3 are equivalent.
    Since version 1.5, LiteRed can find those mappings and optionally skip rules construction in mapped sectors (ExtMappedSectors->True option of SolvejSector, set by default).
16.