Give reductions from the hello-world problem to each of the problems below. Use the informal style of this section for describing plausible program transformations, and do not worry about the real limits such as maximum file size or memory size that real computers impose$.$
- Given a program and an input, does the program eventually halt; i.e., does the program not loop forever on the input$?$
- Given a program and an input, does the program ever produce any output$?$
- Given two programs and an input, do the programs produce the same output for the given input$?$
