the cycle operation on a regular language l $,$constructs the following language: cycle $($ l $)=\{$ w $|$ w $=$xy such that yx l$\}$ consider l$4=\{01,011\}.$ then cycle $\{$l$4\}=\{01,011,10,110,101\}$ we will show that the cycle operation is a regular operation: prove that if l is regular, then cycle$($l$)$ is regular