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(h(), z), app(e(), x)) -> app(app(h(), app(c(), z)), app(app(d(), z), x)),
                                app(app(d(), z), app(app(g(), x), y)) -> app(app(g(), app(e(), x)), app(app(d(), z), y)),
                            app(app(d(), z), app(app(g(), 0()), 0())) -> app(e(), 0()),
  app(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))),
                              app(app(g(), app(e(), x)), app(e(), y)) -> app(e(), app(app(g(), x), 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()}
 DP:
  Strict:
   {                    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(h(), z), app(e(), x)) -> app#(app(h(), app(c(), z)), app(app(d(), z), x)),
                                          app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x),
                                          app#(app(h(), z), app(e(), x)) -> app#(h(), app(c(), z)),
                                          app#(app(h(), z), app(e(), x)) -> app#(c(), z),
                                          app#(app(h(), z), app(e(), x)) -> app#(d(), z),
                                  app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y),
                                  app#(app(d(), z), app(app(g(), x), y)) -> app#(app(g(), app(e(), x)), app(app(d(), z), y)),
                                  app#(app(d(), z), app(app(g(), x), y)) -> app#(e(), x),
                                  app#(app(d(), z), app(app(g(), x), y)) -> app#(g(), app(e(), x)),
                              app#(app(d(), z), app(app(g(), 0()), 0())) -> app#(e(), 0()),
    app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)),
    app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)),
    app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))),
    app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(d(), z),
    app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))),
                                app#(app(g(), app(e(), x)), app(e(), y)) -> app#(app(g(), x), y),
                                app#(app(g(), app(e(), x)), app(e(), y)) -> app#(e(), app(app(g(), x), y)),
                                app#(app(g(), app(e(), x)), app(e(), y)) -> app#(g(), 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#(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))}
  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(h(), z), app(e(), x)) -> app(app(h(), app(c(), z)), app(app(d(), z), x)),
                                 app(app(d(), z), app(app(g(), x), y)) -> app(app(g(), app(e(), x)), app(app(d(), z), y)),
                             app(app(d(), z), app(app(g(), 0()), 0())) -> app(e(), 0()),
   app(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))),
                               app(app(g(), app(e(), x)), app(e(), y)) -> app(e(), app(app(g(), x), 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()}
  EDG:
   {
    (app#(app(g(), app(e(), x)), app(e(), y)) -> app#(app(g(), x), y), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(g(), x))
    (app#(app(g(), app(e(), x)), app(e(), y)) -> app#(app(g(), x), y), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(e(), app(app(g(), x), y)))
    (app#(app(g(), app(e(), x)), app(e(), y)) -> app#(app(g(), x), y), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(app(g(), x), y))
    (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(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#(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(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#(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#(cons(), 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#(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#(f, x))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(g(), x))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(e(), app(app(g(), x), y)))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(app(g(), x), y))
    (app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))))
    (app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(d(), z))
    (app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))))
    (app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)))
    (app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)))
    (app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x), app#(app(d(), z), app(app(g(), 0()), 0())) -> app#(e(), 0()))
    (app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x), app#(app(d(), z), app(app(g(), x), y)) -> app#(g(), app(e(), x)))
    (app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x), app#(app(d(), z), app(app(g(), x), y)) -> app#(e(), x))
    (app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(g(), app(e(), x)), app(app(d(), z), y)))
    (app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y))
    (app#(app(h(), z), app(e(), x)) -> app#(app(h(), app(c(), z)), app(app(d(), z), x)), app#(app(h(), z), app(e(), x)) -> app#(d(), z))
    (app#(app(h(), z), app(e(), x)) -> app#(app(h(), app(c(), z)), app(app(d(), z), x)), app#(app(h(), z), app(e(), x)) -> app#(c(), z))
    (app#(app(h(), z), app(e(), x)) -> app#(app(h(), app(c(), z)), app(app(d(), z), x)), app#(app(h(), z), app(e(), x)) -> app#(h(), app(c(), z)))
    (app#(app(h(), z), app(e(), x)) -> app#(app(h(), app(c(), z)), app(app(d(), z), x)), app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x))
    (app#(app(h(), z), app(e(), x)) -> app#(app(h(), app(c(), z)), app(app(d(), z), x)), app#(app(h(), z), app(e(), x)) -> app#(app(h(), app(c(), z)), app(app(d(), z), x)))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(g(), app(e(), x)), app(app(d(), z), y)), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(g(), x))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(g(), app(e(), x)), app(app(d(), z), y)), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(e(), app(app(g(), x), y)))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(g(), app(e(), x)), app(app(d(), z), y)), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(app(g(), x), y))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(d(), z))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)), app#(app(d(), z), app(app(g(), 0()), 0())) -> app#(e(), 0()))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)), app#(app(d(), z), app(app(g(), x), y)) -> app#(g(), app(e(), x)))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)), app#(app(d(), z), app(app(g(), x), y)) -> app#(e(), x))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(g(), app(e(), x)), app(app(d(), z), y)))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y))
    (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#(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#(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(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#(f, x))
    (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(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#(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#(f, x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(g(), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(e(), app(app(g(), x), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(app(g(), x), y))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(d(), z))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), z), app(app(g(), 0()), 0())) -> app#(e(), 0()))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), z), app(app(g(), x), y)) -> app#(g(), app(e(), x)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), z), app(app(g(), x), y)) -> app#(e(), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(g(), app(e(), x)), app(app(d(), z), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(h(), z), app(e(), x)) -> app#(d(), z))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(h(), z), app(e(), x)) -> app#(c(), z))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(h(), z), app(e(), x)) -> app#(h(), app(c(), z)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(h(), z), app(e(), x)) -> app#(app(h(), app(c(), z)), app(app(d(), z), x)))
    (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(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(), true()), f), x), xs) -> app#(filter(), f))
    (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#(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(cons(), x), 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(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#(cons(), x))
    (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(), 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(), false()), f), x), xs) -> app#(filter(), f))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(h(), z), app(e(), x)) -> app#(app(h(), app(c(), z)), app(app(d(), z), x)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(h(), z), app(e(), x)) -> app#(app(d(), z), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(h(), z), app(e(), x)) -> app#(h(), app(c(), z)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(h(), z), app(e(), x)) -> app#(c(), z))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(h(), z), app(e(), x)) -> app#(d(), z))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(g(), app(e(), x)), app(app(d(), z), y)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), z), app(app(g(), x), y)) -> app#(e(), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), z), app(app(g(), x), y)) -> app#(g(), app(e(), x)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), z), app(app(g(), 0()), 0())) -> app#(e(), 0()))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(d(), z))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(app(g(), x), y))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(e(), app(app(g(), x), y)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(g(), app(e(), x)), app(e(), y)) -> app#(g(), 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#(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#(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#(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#(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#(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(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#(filter2(), app(f, x)))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(g(), app(e(), x)), app(app(d(), z), y)))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), z), app(app(g(), x), y)) -> app#(e(), x))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), z), app(app(g(), x), y)) -> app#(g(), app(e(), x)))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), z), app(app(g(), 0()), 0())) -> app#(e(), 0()))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(d(), z))
    (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(g(), app(app(d(), app(c(), z)), app(app(g(), 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#(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#(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(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#(filter2(), app(f, x)))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(g(), app(e(), x)), app(app(d(), z), y)))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y), app#(app(d(), z), app(app(g(), x), y)) -> app#(e(), x))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y), app#(app(d(), z), app(app(g(), x), y)) -> app#(g(), app(e(), x)))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y), app#(app(d(), z), app(app(g(), 0()), 0())) -> app#(e(), 0()))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(d(), z))
    (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))))
   }
   SCCS:
    Scc:
     {app#(app(g(), app(e(), x)), app(e(), y)) -> app#(app(g(), x), y)}
    Scc:
     {                              app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y),
      app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)),
      app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y))}
    Scc:
     {app#(app(h(), z), app(e(), x)) -> app#(app(h(), app(c(), z)), app(app(d(), z), x))}
    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)}
    SCC:
     Strict:
      {app#(app(g(), app(e(), x)), app(e(), y)) -> app#(app(g(), 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(h(), z), app(e(), x)) -> app(app(h(), app(c(), z)), app(app(d(), z), x)),
                                    app(app(d(), z), app(app(g(), x), y)) -> app(app(g(), app(e(), x)), app(app(d(), z), y)),
                                app(app(d(), z), app(app(g(), 0()), 0())) -> app(e(), 0()),
      app(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))),
                                  app(app(g(), app(e(), x)), app(e(), y)) -> app(e(), app(app(g(), x), 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()}
     SPSC:
      Simple Projection:
       pi(app#) = 1
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {                              app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y),
       app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), z), app(app(g(), x), y)),
       app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), 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(h(), z), app(e(), x)) -> app(app(h(), app(c(), z)), app(app(d(), z), x)),
                                    app(app(d(), z), app(app(g(), x), y)) -> app(app(g(), app(e(), x)), app(app(d(), z), y)),
                                app(app(d(), z), app(app(g(), 0()), 0())) -> app(e(), 0()),
      app(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))),
                                  app(app(g(), app(e(), x)), app(e(), y)) -> app(e(), app(app(g(), x), 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()}
     SPSC:
      Simple Projection:
       pi(app#) = 1
      Strict:
       {                              app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y),
        app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y))}
      EDG:
       {(app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)))
        (app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y))
        (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y))
        (app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)))}
       SCCS:
        Scc:
         {                              app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y),
          app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y))}
        SCC:
         Strict:
          {                              app#(app(d(), z), app(app(g(), x), y)) -> app#(app(d(), z), y),
           app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), 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(h(), z), app(e(), x)) -> app(app(h(), app(c(), z)), app(app(d(), z), x)),
                                        app(app(d(), z), app(app(g(), x), y)) -> app(app(g(), app(e(), x)), app(app(d(), z), y)),
                                    app(app(d(), z), app(app(g(), 0()), 0())) -> app(e(), 0()),
          app(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))),
                                      app(app(g(), app(e(), x)), app(e(), y)) -> app(e(), app(app(g(), x), 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()}
         SPSC:
          Simple Projection:
           pi(app#) = 1
          Strict:
           {app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y))}
          EDG:
           {(app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)), app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y)))}
           SCCS:
            Scc:
             {app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), x), y))}
            SCC:
             Strict:
              {app#(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app#(app(d(), app(c(), z)), app(app(g(), 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(h(), z), app(e(), x)) -> app(app(h(), app(c(), z)), app(app(d(), z), x)),
                                            app(app(d(), z), app(app(g(), x), y)) -> app(app(g(), app(e(), x)), app(app(d(), z), y)),
                                        app(app(d(), z), app(app(g(), 0()), 0())) -> app(e(), 0()),
              app(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))),
                                          app(app(g(), app(e(), x)), app(e(), y)) -> app(e(), app(app(g(), x), 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()}
             SPSC:
              Simple Projection:
               pi(app#) = 1
              Strict:
               {}
              Qed
    SCC:
     Strict:
      {app#(app(h(), z), app(e(), x)) -> app#(app(h(), app(c(), z)), app(app(d(), z), 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(h(), z), app(e(), x)) -> app(app(h(), app(c(), z)), app(app(d(), z), x)),
                                    app(app(d(), z), app(app(g(), x), y)) -> app(app(g(), app(e(), x)), app(app(d(), z), y)),
                                app(app(d(), z), app(app(g(), 0()), 0())) -> app(e(), 0()),
      app(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))),
                                  app(app(g(), app(e(), x)), app(e(), y)) -> app(e(), app(app(g(), x), 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
    SCC:
     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)}
     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(h(), z), app(e(), x)) -> app(app(h(), app(c(), z)), app(app(d(), z), x)),
                                    app(app(d(), z), app(app(g(), x), y)) -> app(app(g(), app(e(), x)), app(app(d(), z), y)),
                                app(app(d(), z), app(app(g(), 0()), 0())) -> app(e(), 0()),
      app(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))),
                                  app(app(g(), app(e(), x)), app(e(), y)) -> app(e(), app(app(g(), x), 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()}
     SPSC:
      Simple Projection:
       pi(app#) = 1
      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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)}
      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#(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(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(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#(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(), 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#(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(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))}
       SCCS:
        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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)}
        SCC:
         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(filter(), f), app(app(cons(), x), xs)) -> app#(f, 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(h(), z), app(e(), x)) -> app(app(h(), app(c(), z)), app(app(d(), z), x)),
                                        app(app(d(), z), app(app(g(), x), y)) -> app(app(g(), app(e(), x)), app(app(d(), z), y)),
                                    app(app(d(), z), app(app(g(), 0()), 0())) -> app(e(), 0()),
          app(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))),
                                      app(app(g(), app(e(), x)), app(e(), y)) -> app(e(), app(app(g(), x), 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()}
         SPSC:
          Simple Projection:
           pi(app#) = 1
          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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)}
          EDG:
           {(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(), 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#(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(), 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#(f, x))}
           SCCS:
            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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)}
            SCC:
             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(filter(), f), app(app(cons(), x), xs)) -> app#(f, 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(h(), z), app(e(), x)) -> app(app(h(), app(c(), z)), app(app(d(), z), x)),
                                            app(app(d(), z), app(app(g(), x), y)) -> app(app(g(), app(e(), x)), app(app(d(), z), y)),
                                        app(app(d(), z), app(app(g(), 0()), 0())) -> app(e(), 0()),
              app(app(d(), app(c(), z)), app(app(g(), app(app(g(), x), y)), 0())) -> app(app(g(), app(app(d(), app(c(), z)), app(app(g(), x), y))), app(app(d(), z), app(app(g(), x), y))),
                                          app(app(g(), app(e(), x)), app(e(), y)) -> app(e(), app(app(g(), x), 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()}
             SPSC:
              Simple Projection:
               pi(app#) = 1
              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)}
              EDG:
               {}
               SCCS:
                
                Qed