 Here \(l(\overline{T}_i^j)\) is the length of the code for \(T_i\) on \(U_j\) and \(l(\overline{T}_i^k)\) is the length of the code for \(T_i\) on \(U_k\). Suppose \(l(\overline{T}_i^jx) \ll l(\overline{T}_i^kx)\), i.e., the code for \(T_i\) on \(U_k\) is much less efficient that on \(U_j\). Observe that the code for \(U_j\) has constant length, i.e., \(l(\overline{U}_j^k)=c\). Since \(U_k\) is universal we can compute: 