We consider the system 458.

  Alphabet:

    abs : [o -> o] --> o 
    app : [o * o] --> o 
    bot : [] --> o 

  Rules:

    app(abs(/\x.X(x)), Y) => X(Y) 
    abs(/\x.app(X, x)) => X 
    app(bot, X) => bot 
    abs(/\x.bot) => bot 

This system is non-terminating, as demonstrated by the following reduction:

  app(abs(/\x.app(x, x)), abs(/\y.app(y, y))) 
    => (/\x.app(x, x)) abs(/\y.app(y, y)) 
    =>_beta app(abs(/\x.app(x, x)), abs(/\y.app(y, y))) 

That is, a term reduces to itself.