MAYBE
Time: 0.294074
TRS:
 { app(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h),
  app(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)),
   app(app(app(app(app(if_reach_2(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> true(),
  app(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(or(), app(app(app(app(reach(), x), y), i), h)), app(app(app(app(reach(), v), y), app(app(union(), i), h)), empty())),
                                           app(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h),
                                                                  app(app(app(app(reach(), x), y), empty()), h) -> false(),
                                                                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(eq(), app(s(), x)), app(s(), y)) -> app(app(eq(), x), y),
                                                                               app(app(eq(), app(s(), x)), 0()) -> false(),
                                                                               app(app(eq(), 0()), app(s(), x)) -> false(),
                                                                                       app(app(eq(), 0()), 0()) -> true(),
                                                                                      app(app(or(), true()), y) -> true(),
                                                                                     app(app(or(), false()), y) -> y,
                                                           app(app(union(), app(app(app(edge(), x), y), i)), h) -> app(app(app(edge(), x), y), app(app(union(), i), h)),
                                                                                  app(app(union(), empty()), h) -> h,
                                                                    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(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h),
     app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)),
     app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(if_reach_2(), app(app(eq(), y), v)), x), y),
     app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), y), v),
     app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(if_reach_2(), app(app(eq(), y), v)), x),
     app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(eq(), y),
     app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(if_reach_2(), app(app(eq(), y), v)),
    app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)),
    app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(edge(), u), v), h),
    app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(reach(), x), y), i),
    app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(reach(), x), y),
    app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(reach(), x),
    app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h),
    app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()),
    app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(reach(), x), y), i),
    app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(reach(), v), y), app(app(union(), i), h)),
    app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(or(), app(app(app(app(reach(), x), y), i), h)), app(app(app(app(reach(), v), y), app(app(union(), i), h)), empty())),
    app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(union(), i), h),
    app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(reach(), x), y),
    app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(reach(), v), y),
    app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(or(), app(app(app(app(reach(), x), y), i), h)),
    app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(union(), i),
    app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(reach(), x),
    app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(reach(), v),
                                                 app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h),
                                                 app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)),
                                                 app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(if_reach_1(), app(app(eq(), x), u)), x), y),
                                                 app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), x), u),
                                                 app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(if_reach_1(), app(app(eq(), x), u)), x),
                                                 app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(eq(), x),
                                                 app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(if_reach_1(), app(app(eq(), x), u)),
                                                                      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(eq(), app(s(), x)), app(s(), y)) -> app#(app(eq(), x), y),
                                                                             app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(eq(), x),
                                                                 app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(app(edge(), x), y), app(app(union(), i), h)),
                                                                 app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(union(), i), h),
                                                                 app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(union(), i),
                                                                          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(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h),
   app(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)),
    app(app(app(app(app(if_reach_2(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> true(),
   app(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(or(), app(app(app(app(reach(), x), y), i), h)), app(app(app(app(reach(), v), y), app(app(union(), i), h)), empty())),
                                            app(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h),
                                                                   app(app(app(app(reach(), x), y), empty()), h) -> false(),
                                                                 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(eq(), app(s(), x)), app(s(), y)) -> app(app(eq(), x), y),
                                                                                app(app(eq(), app(s(), x)), 0()) -> false(),
                                                                                app(app(eq(), 0()), app(s(), x)) -> false(),
                                                                                        app(app(eq(), 0()), 0()) -> true(),
                                                                                       app(app(or(), true()), y) -> true(),
                                                                                      app(app(or(), false()), y) -> y,
                                                            app(app(union(), app(app(app(edge(), x), y), i)), h) -> app(app(app(edge(), x), y), app(app(union(), i), h)),
                                                                                   app(app(union(), empty()), h) -> h,
                                                                     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(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h),
    app(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)),
     app(app(app(app(app(if_reach_2(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> true(),
    app(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(or(), app(app(app(app(reach(), x), y), i), h)), app(app(app(app(reach(), v), y), app(app(union(), i), h)), empty())),
                                             app(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h),
                                                                    app(app(app(app(reach(), x), y), empty()), h) -> false(),
                                                                  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(eq(), app(s(), x)), app(s(), y)) -> app(app(eq(), x), y),
                                                                                 app(app(eq(), app(s(), x)), 0()) -> false(),
                                                                                 app(app(eq(), 0()), app(s(), x)) -> false(),
                                                                                         app(app(eq(), 0()), 0()) -> true(),
                                                                                        app(app(or(), true()), y) -> true(),
                                                                                       app(app(or(), false()), y) -> y,
                                                             app(app(union(), app(app(app(edge(), x), y), i)), h) -> app(app(app(edge(), x), y), app(app(union(), i), h)),
                                                                                    app(app(union(), empty()), h) -> h,
                                                                      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(z, w) -> z,
                                                                                                          a(z, w) -> w}
   EDG:
    {
     (app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(app(eq(), x), y), app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(eq(), x))
     (app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(app(eq(), x), y), app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(app(eq(), x), y))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), x), u), app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(eq(), x))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), x), u), app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(app(eq(), x), y))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(reach(), v))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(reach(), x))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(union(), i))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(or(), app(app(app(app(reach(), x), y), i), h)))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(reach(), v), y))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(reach(), x), y))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(union(), i), h))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(or(), app(app(app(app(reach(), x), y), i), h)), app(app(app(app(reach(), v), y), app(app(union(), i), h)), empty())))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(reach(), v), y), app(app(union(), i), h)))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(reach(), x), y), i))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(if_reach_1(), app(app(eq(), x), u)))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(eq(), x))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(if_reach_1(), app(app(eq(), x), u)), x))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), x), u))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(if_reach_1(), app(app(eq(), x), u)), x), y))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(reach(), x))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(reach(), x), y))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(reach(), x), y), i))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(edge(), u), v), h))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(if_reach_2(), app(app(eq(), y), v)))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(eq(), y))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(if_reach_2(), app(app(eq(), y), v)), x))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), y), v))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(if_reach_2(), app(app(eq(), y), v)), x), y))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)))
     (app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(if_reach_1(), app(app(eq(), x), u)))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(eq(), x))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(if_reach_1(), app(app(eq(), x), u)), x))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), x), u))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(if_reach_1(), app(app(eq(), x), u)), x), y))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h))
     (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(union(), app(app(app(edge(), x), y), i)), h) -> app#(union(), i))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(union(), i), h))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(app(edge(), x), y), app(app(union(), i), h)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(eq(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(app(eq(), 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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(if_reach_1(), app(app(eq(), x), u)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(eq(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(if_reach_1(), app(app(eq(), x), u)), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), x), u))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(if_reach_1(), app(app(eq(), x), u)), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(reach(), v))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(reach(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(union(), i))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(or(), app(app(app(app(reach(), x), y), i), h)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(reach(), v), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(reach(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(union(), i), h))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(or(), app(app(app(app(reach(), x), y), i), h)), app(app(app(app(reach(), v), y), app(app(union(), i), h)), empty())))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(reach(), v), y), app(app(union(), i), h)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(reach(), x), y), i))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(reach(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(reach(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(reach(), x), y), i))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(edge(), u), v), h))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(if_reach_2(), app(app(eq(), y), v)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(eq(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(if_reach_2(), app(app(eq(), y), v)), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), y), v))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(if_reach_2(), app(app(eq(), y), v)), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h))
     (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(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), y), v), app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(app(eq(), x), y))
     (app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), y), v), app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(eq(), 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(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(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(if_reach_2(), app(app(eq(), y), v)), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), y), v))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(if_reach_2(), app(app(eq(), y), v)), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(eq(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(if_reach_2(), app(app(eq(), y), v)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(edge(), u), v), h))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(reach(), x), y), i))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(reach(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(reach(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(reach(), x), y), i))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(reach(), v), y), app(app(union(), i), h)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(or(), app(app(app(app(reach(), x), y), i), h)), app(app(app(app(reach(), v), y), app(app(union(), i), h)), empty())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(union(), i), h))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(reach(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(reach(), v), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(or(), app(app(app(app(reach(), x), y), i), h)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(union(), i))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(reach(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(reach(), v))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(if_reach_1(), app(app(eq(), x), u)), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), x), u))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(if_reach_1(), app(app(eq(), x), u)), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(eq(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(if_reach_1(), app(app(eq(), x), u)))
     (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(eq(), app(s(), x)), app(s(), y)) -> app#(app(eq(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(eq(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(app(edge(), x), y), app(app(union(), i), h)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(union(), i), h))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(union(), i))
     (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(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(union(), i), h), app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(app(edge(), x), y), app(app(union(), i), h)))
     (app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(union(), i), h), app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(union(), i), h))
     (app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(union(), i), h), app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(union(), i))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(union(), i), h), app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(app(edge(), x), y), app(app(union(), i), h)))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(union(), i), h), app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(union(), i), h))
     (app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(union(), i), h), app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(union(), i))
     (app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h))
     (app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)))
     (app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(if_reach_1(), app(app(eq(), x), u)), x), y))
     (app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(eq(), x), u))
     (app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(if_reach_1(), app(app(eq(), x), u)), x))
     (app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(eq(), x))
     (app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)), app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(if_reach_1(), app(app(eq(), x), u)))
    }
    STATUS:
     arrows: 0.931180
     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#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h),
        app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)),
        app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h),
        app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()),
                                                     app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h)}
      Scc:
       {app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(union(), i), h)}
      Scc:
       {app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(app(eq(), 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(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h),
        app(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)),
         app(app(app(app(app(if_reach_2(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> true(),
        app(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(or(), app(app(app(app(reach(), x), y), i), h)), app(app(app(app(reach(), v), y), app(app(union(), i), h)), empty())),
                                                 app(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h),
                                                                        app(app(app(app(reach(), x), y), empty()), h) -> false(),
                                                                      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(eq(), app(s(), x)), app(s(), y)) -> app(app(eq(), x), y),
                                                                                     app(app(eq(), app(s(), x)), 0()) -> false(),
                                                                                     app(app(eq(), 0()), app(s(), x)) -> false(),
                                                                                             app(app(eq(), 0()), 0()) -> true(),
                                                                                            app(app(or(), true()), y) -> true(),
                                                                                           app(app(or(), false()), y) -> y,
                                                                 app(app(union(), app(app(app(edge(), x), y), i)), h) -> app(app(app(edge(), x), y), app(app(union(), i), h)),
                                                                                        app(app(union(), empty()), h) -> h,
                                                                          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()}
       Open
      
      
      
      
      
      
      SCC (5):
       Strict:
        { app#(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h),
         app#(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)),
         app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), x), y), i), h),
         app#(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(reach(), v), y), app(app(union(), i), h)), empty()),
                                                      app#(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app#(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h)}
       Weak:
       { app(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h),
        app(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)),
         app(app(app(app(app(if_reach_2(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> true(),
        app(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(or(), app(app(app(app(reach(), x), y), i), h)), app(app(app(app(reach(), v), y), app(app(union(), i), h)), empty())),
                                                 app(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h),
                                                                        app(app(app(app(reach(), x), y), empty()), h) -> false(),
                                                                      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(eq(), app(s(), x)), app(s(), y)) -> app(app(eq(), x), y),
                                                                                     app(app(eq(), app(s(), x)), 0()) -> false(),
                                                                                     app(app(eq(), 0()), app(s(), x)) -> false(),
                                                                                             app(app(eq(), 0()), 0()) -> true(),
                                                                                            app(app(or(), true()), y) -> true(),
                                                                                           app(app(or(), false()), y) -> y,
                                                                 app(app(union(), app(app(app(edge(), x), y), i)), h) -> app(app(app(edge(), x), y), app(app(union(), i), h)),
                                                                                        app(app(union(), empty()), h) -> h,
                                                                          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()}
       Open
      
      
      
      
      
      
      
      
      SCC (1):
       Strict:
        {app#(app(union(), app(app(app(edge(), x), y), i)), h) -> app#(app(union(), i), h)}
       Weak:
       { app(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h),
        app(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)),
         app(app(app(app(app(if_reach_2(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> true(),
        app(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(or(), app(app(app(app(reach(), x), y), i), h)), app(app(app(app(reach(), v), y), app(app(union(), i), h)), empty())),
                                                 app(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h),
                                                                        app(app(app(app(reach(), x), y), empty()), h) -> false(),
                                                                      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(eq(), app(s(), x)), app(s(), y)) -> app(app(eq(), x), y),
                                                                                     app(app(eq(), app(s(), x)), 0()) -> false(),
                                                                                     app(app(eq(), 0()), app(s(), x)) -> false(),
                                                                                             app(app(eq(), 0()), 0()) -> true(),
                                                                                            app(app(or(), true()), y) -> true(),
                                                                                           app(app(or(), false()), y) -> y,
                                                                 app(app(union(), app(app(app(edge(), x), y), i)), h) -> app(app(app(edge(), x), y), app(app(union(), i), h)),
                                                                                        app(app(union(), empty()), h) -> h,
                                                                          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()}
       Open
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      SCC (1):
       Strict:
        {app#(app(eq(), app(s(), x)), app(s(), y)) -> app#(app(eq(), x), y)}
       Weak:
       { app(app(app(app(app(if_reach_1(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_2(), app(app(eq(), y), v)), x), y), app(app(app(edge(), u), v), i)), h),
        app(app(app(app(app(if_reach_1(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(reach(), x), y), i), app(app(app(edge(), u), v), h)),
         app(app(app(app(app(if_reach_2(), true()), x), y), app(app(app(edge(), u), v), i)), h) -> true(),
        app(app(app(app(app(if_reach_2(), false()), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(or(), app(app(app(app(reach(), x), y), i), h)), app(app(app(app(reach(), v), y), app(app(union(), i), h)), empty())),
                                                 app(app(app(app(reach(), x), y), app(app(app(edge(), u), v), i)), h) -> app(app(app(app(app(if_reach_1(), app(app(eq(), x), u)), x), y), app(app(app(edge(), u), v), i)), h),
                                                                        app(app(app(app(reach(), x), y), empty()), h) -> false(),
                                                                      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(eq(), app(s(), x)), app(s(), y)) -> app(app(eq(), x), y),
                                                                                     app(app(eq(), app(s(), x)), 0()) -> false(),
                                                                                     app(app(eq(), 0()), app(s(), x)) -> false(),
                                                                                             app(app(eq(), 0()), 0()) -> true(),
                                                                                            app(app(or(), true()), y) -> true(),
                                                                                           app(app(or(), false()), y) -> y,
                                                                 app(app(union(), app(app(app(edge(), x), y), i)), h) -> app(app(app(edge(), x), y), app(app(union(), i), h)),
                                                                                        app(app(union(), empty()), h) -> h,
                                                                          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()}
       Open