Consider a counter that contains k positions, ti, t2, ...tk, each of which can be 0, 1, 2 or 3. As with the binary counter, we can perform the operation INCREMENT on this counter. If we start with the counter set to 0, i.e., all its positions are set to 0, after n INCREMENT operations, the counter will hold the representation of n in base 4. For example, for k= 5 and n=8 we have: t2 t3 t4 t5 0 0 0 0 0000,000 o Jo Jo 0 0 0 0 1 0 0 1 2. 3 0 1 2 3 0 0 1 0 0 0 1 0 1 0 0 0 0 0 2 The cost of each INCREMENT operation is the number of positions that change. 5.1 Calculate the worst-case sequence complexity of performing n INCREMENT operations starting from a counter whose positions are all 0 using the aggregate method. Provide the details of the analysis. 5.2 Calculate the worst-case sequence complexity of performing n INCREMENT operations starting from a counter whose positions are all O using the accounting method. Provide the details of the analysis. Consider a counter that contains k positions, ti, t2, ...tk, each of which can be 0, 1, 2 or 3. As with the binary counter, we can perform the operation INCREMENT on this counter. If we start with the counter set to 0, i.e., all its positions are set to 0, after n INCREMENT operations, the counter will hold the representation of n in base 4. For example, for k= 5 and n=8 we have: t2 t3 t4 t5 0 0 0 0 0000,000 o Jo Jo 0 0 0 0 1 0 0 1 2. 3 0 1 2 3 0 0 1 0 0 0 1 0 1 0 0 0 0 0 2 The cost of each INCREMENT operation is the number of positions that change. 5.1 Calculate the worst-case sequence complexity of performing n INCREMENT operations starting from a counter whose positions are all 0 using the aggregate method. Provide the details of the analysis. 5.2 Calculate the worst-case sequence complexity of performing n INCREMENT operations starting from a counter whose positions are all O using the accounting method. Provide the details of the analysis