 An obvious example of a complete c.e. set is \(\HP\). For since \(\HP = \{\langle i,n \rangle : \exists s T_1(i,n,s)\}\) and \(T_1(x,y,z)\) is a computable relation, it follows from  Proposition 3.2  that \(\HP\) is c.e. And on the other hand, if \(A = W_i\), then \(n \in A\) if and only if \(\langle i,n \rangle \in \HP\) thus showing that \(W_i \leq_m \HP\).