We consider the system 457.

  Alphabet:

    abs : [o -> o] --> o 
    app : [o * o] --> o 
    or : [o * o] --> o 
    tt : [] --> o 

  Rules:

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

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.