MAYBE
MAYBE
TRS:
 {
                                                             app(
                                                                app(
                                                                   app
                                                                   (
                                                                   app
                                                                   (
                                                                   filter2(),
                                                                   true()), 
                                                                   f), 
                                                                   x
                                                                ), xs
                                                             )
  -> app(app(cons(), x), app(app(filter(), f), xs)),
                                                            app(
                                                               app(
                                                                  app
                                                                  (
                                                                  app
                                                                  (
                                                                  filter2(),
                                                                  false()), 
                                                                  f), 
                                                                  x
                                                               ), xs
                                                            )
  -> app(app(filter(), f), xs),
                                                                                   
  app(app(minus(), x), 0()) -> x,
                                                                 app(
                                                                    app
                                                                    (
                                                                    minus(),
                                                                    app
                                                                    (
                                                                    s(), x)),
                                                                    app
                                                                    (
                                                                    s(), y)
                                                                 )
  -> app(app(minus(), x), y),
                                                                  app
                                                                  (
                                                                  app
                                                                  (
                                                                  quot(),
                                                                  app(s(), x)
                                                                  ),
                                                                  app(s(), y)
                                                                  )
  -> app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                                                                          
  app(app(quot(), 0()), app(s(), y)) -> 0(),
  app(
     app(plus(), app(app(minus(), x), app(s(), 0()))),
     app(app(minus(), y), app(s(), app(s(), z)))
  ) ->
  app(
     app(plus(), app(app(minus(), y), app(s(), app(s(), z)))),
     app(app(minus(), x), app(s(), 0()))
  ),
    app(
       app(plus(), app(app(plus(), x), app(s(), 0()))),
       app(app(plus(), y), app(s(), app(s(), z)))
    )
  ->
  app(
     app(plus(), app(app(plus(), y), app(s(), app(s(), z)))),
     app(app(plus(), x), app(s(), 0()))
  ),
                                                                            
  app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                                                                                    
  app(app(plus(), 0()), y) -> y,
                                                                 app(
                                                                    app
                                                                    (
                                                                    map(), f),
                                                                    app
                                                                    (
                                                                    app
                                                                    (
                                                                    cons(), x
                                                                    ), 
                                                                    xs)
                                                                 )
  -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                                                                                   
  app(app(map(), f), nil()) -> nil(),
                                                              app(
                                                                 app(
                                                                    filter(),
                                                                    f
                                                                 ),
                                                                 app(
                                                                    app
                                                                    (
                                                                    cons(), x
                                                                    ), 
                                                                    xs
                                                                 )
                                                              )
  -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                                                                                
  app(app(filter(), f), nil()) -> nil()
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                                                               app(
                                                                  app
                                                                  (
                                                                  app
                                                                  (
                                                                  app
                                                                  (
                                                                  filter2(),
                                                                  true()), 
                                                                  f), 
                                                                  x), 
                                                                  xs
                                                               )
    -> app(app(cons(), x), app(app(filter(), f), xs)),
                                                              app(
                                                                 app(
                                                                    app
                                                                    (
                                                                    app
                                                                    (
                                                                    filter2(),
                                                                    false()),
                                                                    f), 
                                                                    x
                                                                 ), xs
                                                              )
    -> app(app(filter(), f), xs),
                                                                                     
    app(app(minus(), x), 0()) -> x,
                                                                   app
                                                                   (
                                                                   app
                                                                   (
                                                                   minus(),
                                                                   app
                                                                   (s(), x)),
                                                                   app
                                                                   (s(), y))
    -> app(app(minus(), x), y),
                                                                    app
                                                                    (
                                                                    app
                                                                    (
                                                                    quot(),
                                                                    app
                                                                    (
                                                                    s(), x)),
                                                                    app
                                                                    (
                                                                    s(), y))
    -> app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                                                                            
    app(app(quot(), 0()), app(s(), y)) -> 0(),
    app(
       app(plus(), app(app(minus(), x), app(s(), 0()))),
       app(app(minus(), y), app(s(), app(s(), z)))
    ) ->
    app(
       app(plus(), app(app(minus(), y), app(s(), app(s(), z)))),
       app(app(minus(), x), app(s(), 0()))
    ),
      app(
         app(plus(), app(app(plus(), x), app(s(), 0()))),
         app(app(plus(), y), app(s(), app(s(), z)))
      )
    ->
    app(
       app(plus(), app(app(plus(), y), app(s(), app(s(), z)))),
       app(app(plus(), x), app(s(), 0()))
    ),
                                                                              
    app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                                                                                      
    app(app(plus(), 0()), y) -> y,
                                                                   app
                                                                   (
                                                                   app
                                                                   (map(), f),
                                                                   app
                                                                   (
                                                                   app
                                                                   (cons(), x
                                                                   ), 
                                                                   xs))
    -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                                                                                     
    app(app(map(), f), nil()) -> nil(),
                                                                app(
                                                                   app
                                                                   (
                                                                   filter(),
                                                                   f),
                                                                   app
                                                                   (
                                                                   app
                                                                   (cons(), x
                                                                   ), 
                                                                   xs)
                                                                )
    -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                                                                                  
    app(app(filter(), f), nil()) -> nil()
   }
  Fail