Algorithm Complexity Analysis C#

I wrote a C# console application to read, and find the most common word in a text file. My application works for small text files but not large text files. A friend told me about algorithm complexity analysis, something I did know about in the past that I'm still learning about. Now I'm trying to figure out what's wrong with my code, why does it only work for small text files. Here's my code pasted below:

static void Main(string[] args)
        {
            String line = "";
            String word = "";
            int count = 0;
            int maxCount = 0;
            string[] string1 = new string[0];
            ArrayList words = new ArrayList();

            var path = ConfigurationSettings.AppSettings["inputFilePath"];

            if(path == null)
            {
                throw new Exception();
            }

            var watch = System.Diagnostics.Stopwatch.StartNew();

            try
            {
                //opens text file read mode
                using(StreamReader file = new StreamReader(path))
                {
                    while((line = file.ReadLine()) != null)
                    {
                        //separates and adds each word into an array
                        string1 = line.ToLower().Split(new char[] { ',', '.', ' ' }, StringSplitOptions.RemoveEmptyEntries);

                        //adds the words from the array into a list
                        foreach(String s in string1)
                        {
                            words.Add(s);
                        }
                    }

                    //looks for the most common word in the list
                    for(int i = 0; i < words.Count; i++)
                    {
                        count = 1;

                        //counts each word and stores value to count variable
                        for(int j = i + 1; j < words.Count; j++)
                        {
                            if(words[i].Equals(words[j]))
                            {
                                count++;
                            }
                        }

                        //if count > maxCount, count value stored in maxCount, and corresponding word to word variable
                        if(count > maxCount)
                        {
                            maxCount = count;
                            word = (String)words[i];
                        }
                    }

                    Console.WriteLine("The most common word is " + word + ", with " + maxCount + " occurrences.");
                    file.Close();
                }
            }
            catch(Exception e)
            {
                Console.WriteLine("There was an error opening the file: " + e.Message);
            }

            watch.Stop();
            var elapseMs = watch.ElapsedMilliseconds;

            Console.WriteLine("File processed in " + elapseMs + " milliseconds");
        }