1. AND Inequalities
1.1. Typical "easy"
1.1.1. open endpoint line segments
1.1.2. closed endpoint line segments
1.1.3. half open endpoints line segments
1.2. More challenging
1.2.1. DOUBLE ray in same direction (keep the short ray and its endpoint
1.2.2. DOUBLE rays in opposite direction This scenario has NO SOLUTIONS
2. OR Inequalities
2.1. Typical "easy"
2.1.1. Rays with NO overlap heading in opposite directions
2.1.2. both closed endpoints and heading away from each other and towards the infinities
2.1.3. half opened and and heading away from each other and towards the infinities
2.1.4. both open endpoints and heading away from each other and towards the infinities
2.2. More challenging
2.2.1. Double rays that head in the same direction (keep the longer ray and its endpoint)
2.2.2. Double rays that head in opposite directions and overlap This scenario is ALL REALS