Add long term example, update README

README.md

@@ -1,12 +1,23 @@
 # Lazy Math Instructor
 
 ## Introduction
-This is my code for the proseminar [Selected Fun Problems of the ACM Programming Contest](https://db.cs.uni-tuebingen.de/teaching/ss23/acm-programming-contest-proseminar/) at the University of Tübingen, Summer Term 2023.
+This is my code for the proseminar [Selected Fun Problems of the ACM Programming Contest](https://db.cs.uni-tuebingen.de/teaching/ss23/acm-programming-contest-proseminar/)
+at the University of Tübingen, Summer Term 2023.
 
-The problem worked on is the [Lazy Math Instructor](./Lazy-Math-Instructor.pdf): The exercise is to check arbitrary terms for equivalence.
+The problem worked on is *Lazy Math Instructor*: The exercise is to check arbitrary terms for equivalence.
 Terms may contain brackets, addition, subtraction and multiplication of integer constants and variables `a` to `z`.
 
-They are evaluated from left to right with no operator precedence.
+They are evaluated from left to right with equal operator precedence for all operations.
+
+
+## Contents
+
+This repository contains:
+- The [problem description](./Lazy-Math-Instructor.pdf)
+- My [presentation slides](./Slides.pdf)
+- My [source code](./LazyMathInstructor) (split in several `.cs` files)
+- Several input examples: [Binomial formulas](./binomial_formulas.txt), [Examples from the problem description](./problem_examples.txt) and a [long term](./long_term.txt)
+
 
 ## Usage of the program
 
@@ -21,4 +32,5 @@ Program writes to STDOUT:
   - `YES` if the `k`-th pair of terms are equivalent
   - `NO` if they aren't.
 
-Verbose mode can be enabled by passing `-v` as a command line argument, in which case the program will print each term after it was parsed, normalized and ordered deterministically.
+Verbose mode can be enabled by passing `-v` as a command line argument, in which case the program will print each addition, 
+subtraction and multiplication operation it performs, as well as each term after it was parsed, normalized and ordered deterministically.