#include <iostream>
#include <utility>

using namespace std;

// Pseudokod for composition:
//
// Relation compose(Relation other)
// {
//     Relation result;
//     for (relation in this)
//     {
//         for (relation in other)
//         {
//             if (end of relation in this == start of relation in other)
//             {
//                 result.add(start of relation in this, end of relation in other);
//             }
//         }
//     }
//     return result;
// }

int main()
{
    Relation r1{};
    r1.add_relation(pair<char, char> {'a', 'b'});
    r1.add_relation(pair<char, char> {'b', 'a'});
    cout << "r1: " << r1.to_string() << endl;

    Relation r2{};
    r2.add_relation(pair<char, char> {'a', 'b'});
    r2.add_relation(pair<char, char> {'b', 'c'});
    r2.add_relation(pair<char, char> {'c', 'd'});
    r2.add_relation(pair<char, char> {'d', 'a'});
    cout << "r2: " << r2.to_string() << endl;

    Relation r3{r1.compose(r2)};
    cout << "r3: " << r3.to_string() << endl;
}