MAYBE
Time: 0.036950
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(*(), app(s(), x)), y) -> app(app(+(), app(app(*(), x), y)), y),
                             app(app(*(), 0()), y) -> 0(),
                     app(app(+(), x), app(s(), y)) -> app(s(), app(app(+(), x), y)),
                             app(app(+(), x), 0()) -> x,
       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(),
                             app(p(), app(s(), x)) -> x,
                          app(fact(), app(s(), x)) -> app(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))),
                                  app(fact(), 0()) -> app(s(), 0())}
 DP:
  DP:
   { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f),
                       app#(app(*(), app(s(), x)), y) -> app#(app(*(), x), y),
                       app#(app(*(), app(s(), x)), y) -> app#(app(+(), app(app(*(), x), y)), y),
                       app#(app(*(), app(s(), x)), y) -> app#(*(), x),
                       app#(app(*(), app(s(), x)), y) -> app#(+(), app(app(*(), x), y)),
                       app#(app(+(), x), app(s(), y)) -> app#(app(+(), x), y),
                       app#(app(+(), x), app(s(), y)) -> app#(s(), app(app(+(), x), y)),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), 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(app(app(filter2(), app(f, x)), f), x), xs),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)),
                            app#(fact(), app(s(), x)) -> app#(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))),
                            app#(fact(), app(s(), x)) -> app#(p(), app(s(), x)),
                            app#(fact(), app(s(), x)) -> app#(fact(), app(p(), app(s(), x))),
                            app#(fact(), app(s(), x)) -> app#(*(), app(s(), x)),
                                    app#(fact(), 0()) -> app#(s(), 0())}
  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(*(), app(s(), x)), y) -> app(app(+(), app(app(*(), x), y)), y),
                              app(app(*(), 0()), y) -> 0(),
                      app(app(+(), x), app(s(), y)) -> app(s(), app(app(+(), x), y)),
                              app(app(+(), x), 0()) -> x,
        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(),
                              app(p(), app(s(), x)) -> x,
                           app(fact(), app(s(), x)) -> app(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))),
                                   app(fact(), 0()) -> app(s(), 0())}
  UR:
   { 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(*(), app(s(), x)), y) -> app(app(+(), app(app(*(), x), y)), y),
                               app(app(*(), 0()), y) -> 0(),
                       app(app(+(), x), app(s(), y)) -> app(s(), app(app(+(), x), y)),
                               app(app(+(), x), 0()) -> x,
         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(),
                               app(p(), app(s(), x)) -> x,
                            app(fact(), app(s(), x)) -> app(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))),
                                    app(fact(), 0()) -> app(s(), 0()),
                                             a(z, w) -> z,
                                             a(z, w) -> w}
   EDG:
    {
     (app#(app(*(), app(s(), x)), y) -> app#(app(*(), x), y), app#(app(*(), app(s(), x)), y) -> app#(+(), app(app(*(), x), y)))
     (app#(app(*(), app(s(), x)), y) -> app#(app(*(), x), y), app#(app(*(), app(s(), x)), y) -> app#(*(), x))
     (app#(app(*(), app(s(), x)), y) -> app#(app(*(), x), y), app#(app(*(), app(s(), x)), y) -> app#(app(+(), app(app(*(), x), y)), y))
     (app#(app(*(), app(s(), x)), y) -> app#(app(*(), x), y), app#(app(*(), app(s(), x)), y) -> app#(app(*(), x), y))
     (app#(app(+(), x), app(s(), y)) -> app#(app(+(), x), y), app#(app(+(), x), app(s(), y)) -> app#(s(), app(app(+(), x), y)))
     (app#(app(+(), x), app(s(), y)) -> app#(app(+(), x), y), app#(app(+(), x), app(s(), y)) -> app#(app(+(), x), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), false()), f), 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(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(fact(), 0()) -> app#(s(), 0()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(fact(), app(s(), x)) -> app#(*(), app(s(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(fact(), app(s(), x)) -> app#(fact(), app(p(), app(s(), x))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(fact(), app(s(), x)) -> app#(p(), app(s(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(fact(), app(s(), x)) -> app#(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), 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(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), 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(app(app(filter2(), app(f, x)), f), x), 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#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(+(), x), app(s(), y)) -> app#(s(), app(app(+(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(+(), x), app(s(), y)) -> app#(app(+(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(*(), app(s(), x)), y) -> app#(+(), app(app(*(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(*(), app(s(), x)), y) -> app#(*(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(*(), app(s(), x)), y) -> app#(app(+(), app(app(*(), x), y)), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(*(), app(s(), x)), y) -> app#(app(*(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(fact(), app(s(), x)) -> app#(fact(), app(p(), app(s(), x))), app#(fact(), 0()) -> app#(s(), 0()))
     (app#(fact(), app(s(), x)) -> app#(fact(), app(p(), app(s(), x))), app#(fact(), app(s(), x)) -> app#(*(), app(s(), x)))
     (app#(fact(), app(s(), x)) -> app#(fact(), app(p(), app(s(), x))), app#(fact(), app(s(), x)) -> app#(fact(), app(p(), app(s(), x))))
     (app#(fact(), app(s(), x)) -> app#(fact(), app(p(), app(s(), x))), app#(fact(), app(s(), x)) -> app#(p(), app(s(), x)))
     (app#(fact(), app(s(), x)) -> app#(fact(), app(p(), app(s(), x))), app#(fact(), app(s(), x)) -> app#(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))))
     (app#(fact(), app(s(), x)) -> app#(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))), app#(app(*(), app(s(), x)), y) -> app#(app(*(), x), y))
     (app#(fact(), app(s(), x)) -> app#(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))), app#(app(*(), app(s(), x)), y) -> app#(app(+(), app(app(*(), x), y)), y))
     (app#(fact(), app(s(), x)) -> app#(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))), app#(app(*(), app(s(), x)), y) -> app#(*(), x))
     (app#(fact(), app(s(), x)) -> app#(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))), app#(app(*(), app(s(), x)), y) -> app#(+(), app(app(*(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(*(), app(s(), x)), y) -> app#(app(*(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(*(), app(s(), x)), y) -> app#(app(+(), app(app(*(), x), y)), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(*(), app(s(), x)), y) -> app#(*(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(*(), app(s(), x)), y) -> app#(+(), app(app(*(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(+(), x), app(s(), y)) -> app#(app(+(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(+(), x), app(s(), y)) -> app#(s(), app(app(+(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(fact(), app(s(), x)) -> app#(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(fact(), app(s(), x)) -> app#(p(), app(s(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(fact(), app(s(), x)) -> app#(fact(), app(p(), app(s(), x))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(fact(), app(s(), x)) -> app#(*(), app(s(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(fact(), 0()) -> app#(s(), 0()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(*(), app(s(), x)), y) -> app#(app(+(), app(app(*(), x), y)), y), app#(app(+(), x), app(s(), y)) -> app#(app(+(), x), y))
     (app#(app(*(), app(s(), x)), y) -> app#(app(+(), app(app(*(), x), y)), y), app#(app(+(), x), app(s(), y)) -> app#(s(), app(app(+(), x), y)))
    }
    STATUS:
     arrows: 0.868343
     SCCS (4):
      Scc:
       { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
        app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), 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(app(filter2(), app(f, x)), f), x), xs)}
      Scc:
       {app#(fact(), app(s(), x)) -> app#(fact(), app(p(), app(s(), x)))}
      Scc:
       {app#(app(*(), app(s(), x)), y) -> app#(app(*(), x), y)}
      Scc:
       {app#(app(+(), x), app(s(), y)) -> app#(app(+(), x), y)}
      
      SCC (6):
       Strict:
        { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
         app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
              app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
              app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), 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(app(filter2(), app(f, x)), f), x), xs)}
       Weak:
       { 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(*(), app(s(), x)), y) -> app(app(+(), app(app(*(), x), y)), y),
                                   app(app(*(), 0()), y) -> 0(),
                           app(app(+(), x), app(s(), y)) -> app(s(), app(app(+(), x), y)),
                                   app(app(+(), x), 0()) -> x,
             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(),
                                   app(p(), app(s(), x)) -> x,
                                app(fact(), app(s(), x)) -> app(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))),
                                        app(fact(), 0()) -> app(s(), 0())}
       Open
      SCC (1):
       Strict:
        {app#(fact(), app(s(), x)) -> app#(fact(), app(p(), app(s(), x)))}
       Weak:
       { 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(*(), app(s(), x)), y) -> app(app(+(), app(app(*(), x), y)), y),
                                   app(app(*(), 0()), y) -> 0(),
                           app(app(+(), x), app(s(), y)) -> app(s(), app(app(+(), x), y)),
                                   app(app(+(), x), 0()) -> x,
             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(),
                                   app(p(), app(s(), x)) -> x,
                                app(fact(), app(s(), x)) -> app(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))),
                                        app(fact(), 0()) -> app(s(), 0())}
       Open
      
      
      
      
      
      
      
      
      
      
      
      
      SCC (1):
       Strict:
        {app#(app(*(), app(s(), x)), y) -> app#(app(*(), x), y)}
       Weak:
       { 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(*(), app(s(), x)), y) -> app(app(+(), app(app(*(), x), y)), y),
                                   app(app(*(), 0()), y) -> 0(),
                           app(app(+(), x), app(s(), y)) -> app(s(), app(app(+(), x), y)),
                                   app(app(+(), x), 0()) -> x,
             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(),
                                   app(p(), app(s(), x)) -> x,
                                app(fact(), app(s(), x)) -> app(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))),
                                        app(fact(), 0()) -> app(s(), 0())}
       Open
      
      
      
      SCC (1):
       Strict:
        {app#(app(+(), x), app(s(), y)) -> app#(app(+(), x), y)}
       Weak:
       { 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(*(), app(s(), x)), y) -> app(app(+(), app(app(*(), x), y)), y),
                                   app(app(*(), 0()), y) -> 0(),
                           app(app(+(), x), app(s(), y)) -> app(s(), app(app(+(), x), y)),
                                   app(app(+(), x), 0()) -> x,
             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(),
                                   app(p(), app(s(), x)) -> x,
                                app(fact(), app(s(), x)) -> app(app(*(), app(s(), x)), app(fact(), app(p(), app(s(), x)))),
                                        app(fact(), 0()) -> app(s(), 0())}
       Open