MAYBE
Time: 0.171074
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(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                                app(app(plus(), x), 0()) -> x,
  app(app(times(), x), app(app(plus(), y), app(s(), z))) -> app(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))),
                       app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x),
                               app(app(times(), x), 0()) -> 0(),
             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()}
 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(plus(), x), app(s(), y)) -> app#(app(plus(), x), y),
                          app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)),
    app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), y), app(app(times(), app(s(), z)), 0())),
    app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))),
    app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))),
    app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(s(), z)),
    app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), app(s(), z)), 0()),
    app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))),
    app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(times(), app(s(), z)),
                         app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x),
                         app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y),
                         app#(app(times(), x), app(s(), y)) -> app#(plus(), app(app(times(), 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))}
  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(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                                 app(app(plus(), x), 0()) -> x,
   app(app(times(), x), app(app(plus(), y), app(s(), z))) -> app(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))),
                        app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x),
                                app(app(times(), x), 0()) -> 0(),
              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()}
  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(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                                  app(app(plus(), x), 0()) -> x,
    app(app(times(), x), app(app(plus(), y), app(s(), z))) -> app(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))),
                         app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x),
                                 app(app(times(), x), 0()) -> 0(),
               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(),
                                                   a(w, v) -> w,
                                                   a(w, v) -> v}
   EDG:
    {
     (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(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(s(), y)) -> app#(plus(), app(app(times(), x), y)))
     (app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y))
     (app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x))
     (app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(times(), app(s(), z)))
     (app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))))
     (app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), app(s(), z)), 0()))
     (app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(s(), z)))
     (app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))))
     (app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))))
     (app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), y), app(app(times(), app(s(), z)), 0())))
     (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(times(), x), app(s(), y)) -> app#(plus(), app(app(times(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(times(), app(s(), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), app(s(), z)), 0()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(s(), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), y), app(app(times(), app(s(), z)), 0())))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), 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#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(s(), z)), app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(s(), z)), app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(s(), z)), app#(app(times(), x), app(s(), y)) -> app#(plus(), app(app(times(), x), y)))
     (app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), y), app(app(times(), app(s(), z)), 0())))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(s(), z)))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), app(s(), z)), 0()))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(times(), app(s(), z)))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))), app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))), app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))), app#(app(times(), x), app(s(), y)) -> app#(plus(), app(app(times(), x), y)))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), y), app(app(times(), app(s(), z)), 0())), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), y), app(app(times(), app(s(), z)), 0())), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), 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(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), y), app(app(times(), app(s(), z)), 0())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(s(), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), app(s(), z)), 0()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(times(), app(s(), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(s(), y)) -> app#(plus(), app(app(times(), 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(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (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)))
    }
    STATUS:
     arrows: 0.855967
     SCCS (3):
      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#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))),
        app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(s(), z)),
                             app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y)}
      Scc:
       {app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), 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(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                                      app(app(plus(), x), 0()) -> x,
        app(app(times(), x), app(app(plus(), y), app(s(), z))) -> app(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))),
                             app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x),
                                     app(app(times(), x), 0()) -> 0(),
                   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()}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [app](x0, x1) = x0 + x1,
         
         [plus] = 0,
         
         [times] = 1,
         
         [s] = 0,
         
         [0] = 0,
         
         [nil] = 0,
         
         [map] = 0,
         
         [cons] = 1,
         
         [filter] = 0,
         
         [filter2] = 1,
         
         [true] = 1,
         
         [false] = 1,
         
         [app#](x0, x1) = x0
        Strict:
         app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)
         1 + 1x + 0f + 1xs >= 0 + 0x + 0f + 1xs
         app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)
         1 + 1x + 0f + 1xs >= 0 + 1x + 0f
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)
         1 + 1x + 0f + 1xs >= 0 + 0f + 1xs
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)
         1 + 1x + 0f + 1xs >= 0 + 1x + 0f
         app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs)
         0 + 0x + 0f + 1xs >= 0 + 0f + 1xs
         app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs)
         0 + 0x + 0f + 1xs >= 0 + 0f + 1xs
        Weak:
         app(app(filter(), f), nil()) -> nil()
         0 + 1f >= 0
         app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs)
         1 + 1x + 1f + 1xs >= 1 + 2x + 2f + 1xs
         app(app(map(), f), nil()) -> nil()
         0 + 1f >= 0
         app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs))
         1 + 1x + 1f + 1xs >= 1 + 1x + 2f + 1xs
         app(app(times(), x), 0()) -> 0()
         1 + 1x >= 0
         app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x)
         1 + 1x + 1y >= 1 + 2x + 1y
         app(app(times(), x), app(app(plus(), y), app(s(), z))) -> app(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z)))
         1 + 1x + 1y + 1z >= 3 + 2x + 1y + 2z
         app(app(plus(), x), 0()) -> x
         0 + 1x >= 1x
         app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y))
         0 + 1x + 1y >= 0 + 1x + 1y
         app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs)
         2 + 1x + 1f + 1xs >= 0 + 1f + 1xs
         app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs))
         2 + 1x + 1f + 1xs >= 1 + 1x + 1f + 1xs
       SCCS (0):
        
        
        
     
     
     SCC (3):
      Strict:
       {app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0()))),
        app#(app(times(), x), app(app(plus(), y), app(s(), z))) -> app#(app(times(), x), app(s(), z)),
                             app#(app(times(), x), app(s(), y)) -> app#(app(times(), 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(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                                     app(app(plus(), x), 0()) -> x,
       app(app(times(), x), app(app(plus(), y), app(s(), z))) -> app(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))),
                            app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x),
                                    app(app(times(), x), 0()) -> 0(),
                  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
     
     
     
     
     
     
     
     SCC (1):
      Strict:
       {app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), 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(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                                     app(app(plus(), x), 0()) -> x,
       app(app(times(), x), app(app(plus(), y), app(s(), z))) -> app(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z))),
                            app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x),
                                    app(app(times(), x), 0()) -> 0(),
                  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()}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [app](x0, x1) = x0 + x1,
        
        [plus] = 0,
        
        [times] = 1,
        
        [s] = 1,
        
        [0] = 0,
        
        [nil] = 0,
        
        [map] = 0,
        
        [cons] = 0,
        
        [filter] = 0,
        
        [filter2] = 0,
        
        [true] = 0,
        
        [false] = 0,
        
        [app#](x0, x1) = x0 + 1
       Strict:
        app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y)
        2 + 0x + 1y >= 1 + 0x + 1y
       Weak:
        app(app(filter(), f), nil()) -> nil()
        0 + 1f >= 0
        app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs)
        0 + 1x + 1f + 1xs >= 0 + 2x + 2f + 1xs
        app(app(map(), f), nil()) -> nil()
        0 + 1f >= 0
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs))
        0 + 1x + 1f + 1xs >= 0 + 1x + 2f + 1xs
        app(app(times(), x), 0()) -> 0()
        1 + 1x >= 0
        app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x)
        2 + 1x + 1y >= 1 + 2x + 1y
        app(app(times(), x), app(app(plus(), y), app(s(), z))) -> app(app(plus(), app(app(times(), x), app(app(plus(), y), app(app(times(), app(s(), z)), 0())))), app(app(times(), x), app(s(), z)))
        2 + 1x + 1y + 1z >= 5 + 2x + 1y + 2z
        app(app(plus(), x), 0()) -> x
        0 + 1x >= 1x
        app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y))
        1 + 1x + 1y >= 1 + 1x + 1y
        app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs)
        0 + 1x + 1f + 1xs >= 0 + 1f + 1xs
        app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs))
        0 + 1x + 1f + 1xs >= 0 + 1x + 1f + 1xs
      Qed