MAYBE
Time: 0.008512
TRS:
 {             app(app(app(if(), true()), x), y) -> x,
              app(app(app(if(), false()), x), y) -> y,
  app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(if(), app(f, x)), app(app(cons(), x), app(app(filter(), f), xs))), app(app(filter(), f), xs)),
                    app(app(filter(), f), nil()) -> nil()}
 DP:
  DP:
   {app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
    app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(if(), app(f, x)), app(app(cons(), x), app(app(filter(), f), xs))), app(app(filter(), f), xs)),
    app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(if(), app(f, x)), app(app(cons(), x), app(app(filter(), f), xs))),
    app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter(), f), xs),
    app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(cons(), x), app(app(filter(), f), xs)),
    app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(if(), app(f, x))}
  TRS:
  {             app(app(app(if(), true()), x), y) -> x,
               app(app(app(if(), false()), x), y) -> y,
   app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(if(), app(f, x)), app(app(cons(), x), app(app(filter(), f), xs))), app(app(filter(), f), xs)),
                     app(app(filter(), f), nil()) -> nil()}
  UR:
   {             app(app(app(if(), true()), x), y) -> x,
                app(app(app(if(), false()), x), y) -> y,
    app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(if(), app(f, x)), app(app(cons(), x), app(app(filter(), f), xs))), app(app(filter(), f), xs)),
                      app(app(filter(), f), nil()) -> nil(),
                                           a(z, w) -> z,
                                           a(z, w) -> w}
   EDG:
    {(app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(if(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(if(), app(f, x)), app(app(cons(), x), app(app(filter(), f), xs))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(if(), app(f, x)), app(app(cons(), x), app(app(filter(), f), xs))), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(if(), app(f, x)), app(app(cons(), x), app(app(filter(), f), xs))), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(if(), app(f, x)), app(app(cons(), x), app(app(filter(), f), xs))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(if(), app(f, x)))}
    STATUS:
     arrows: 0.666667
     SCCS (1):
      Scc:
       {app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
        app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter(), f), xs)}
      
      SCC (2):
       Strict:
        {app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
         app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter(), f), xs)}
       Weak:
       {             app(app(app(if(), true()), x), y) -> x,
                    app(app(app(if(), false()), x), y) -> y,
        app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(if(), app(f, x)), app(app(cons(), x), app(app(filter(), f), xs))), app(app(filter(), f), xs)),
                          app(app(filter(), f), nil()) -> nil()}
       Open