The actual decision problem statement for TSP is "Does there exist a tour of less than length L". It is easy to prove if such a tour exists: simply give me tou

The actual decision problem statement for TSP is "Does there exist a tour of less than length L". It is easy to prove if such a tour exists: simply give me tour. I can sum up the lengths and check that the sum < L. Finding such a tour is the computationally hard part in the worst of cases.