It is great to have two different mode. Though the approximate result is not as good as the exact one. But it is way faster and uses way less resource. We can switch between different mode at different case.
With either too high or too low constrain, the runtime grows exponentially. If the constrain is too low, it must iterate through all answers to find one correct result. If it is too high, then it may waste too much time fill the first processor.
One important factor of the runtime is the max number of cut to check. If we set max = 10 with size = 30, we get the time of 0.914. However, it is impossible to get the max size before running, I believe this time would be a great representation of the runtime of clingo.
AMPL is the fastest implementation in part 1 and 3, much faster than the others. clingo is the clearest and the easiest way to write it but it is not that fastest one. Each language has its own pros and cons so it is hard to create a single language with all the pros but no cons.
