Let T be the task that the service composition needs to accomplish. The task T can be granulated to T 1 , T 2 , T 3 , T 4 , … , T n . i.e. T = {T 1 , T 2 , T 3 , T 4 , … , T n } . For each task T i , a set of service S i = S i 1 , S i 2 , S i 3 , … , S i m is discovered during the service discovery process such that all services in a set S i perform the same function and have the same input and output parameters (See Figure 2). S 1 = {S 11 , S 12 , S 13 , … , S 1m } , S 2 = {S 21 , S 22 , S 23 , … , S 2m } , S 3 = {S 31 , S 32 , S 33 , … , S 3m } , … , S n = {S n 1 , S n 2 , S n 3 , … , S n m } We need to select one service from each set S i in order to compose the big service such that the overall QoS attributes of the big service are optimal. The total number of the possible distinct service composition is n m . Let k be the the number of QoS attributes. Then the total num- ber of comparisons required are kn m . We need at least kn m comparisons to find whether the solution is optimal, thus making the problem as NP-Hard.