MAYBE
Time: 0.172302
TRS:
 {                app(app(app(app(f(), 0()), y), 0()), u) -> true(),
          app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
          app(app(app(app(f(), app(s(), x)), 0()), z), u) -> app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
  app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
        app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
       app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
                        app(app(app(if(), true()), x), y) -> x,
                       app(app(app(if(), false()), x), y) -> y,
                                app(app(minus(), 0()), y) -> 0(),
                      app(app(minus(), app(s(), x)), 0()) -> app(s(), x),
              app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                                   app(app(le(), 0()), y) -> true(),
                         app(app(le(), app(s(), x)), 0()) -> false(),
                 app(app(le(), app(s(), x)), app(s(), y)) -> app(app(le(), x), y),
            app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                              app(app(map(), fun), nil()) -> nil(),
         app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                           app(app(filter(), fun), nil()) -> nil(),
                                     app(perfectp(), 0()) -> false(),
                             app(perfectp(), app(s(), x)) -> app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x))}
 DP:
  DP:
   {        app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
            app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(f(), x), u), app(app(minus(), z), app(s(), x))),
            app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(minus(), z), app(s(), x)),
            app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(f(), x), u),
            app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(minus(), z),
            app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(f(), x),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), x), u), z),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(minus(), y), x),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(le(), x), y),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), x), u),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), app(s(), x)), app(app(minus(), y), x)),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(minus(), y),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(le(), x),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(if(), app(app(le(), x), y)),
    app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(f(), x),
          app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)),
          app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
          app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x),
          app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun),
         app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
         app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun),
                app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y),
                app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x),
                   app#(app(le(), app(s(), x)), app(s(), y)) -> app#(app(le(), x), y),
                   app#(app(le(), app(s(), x)), app(s(), y)) -> app#(le(), x),
              app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
              app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
              app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
              app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun),
           app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)),
                               app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)),
                               app#(perfectp(), app(s(), x)) -> app#(app(app(f(), x), app(s(), 0())), app(s(), x)),
                               app#(perfectp(), app(s(), x)) -> app#(app(f(), x), app(s(), 0())),
                               app#(perfectp(), app(s(), x)) -> app#(s(), 0()),
                               app#(perfectp(), app(s(), x)) -> app#(f(), x)}
  TRS:
  {                app(app(app(app(f(), 0()), y), 0()), u) -> true(),
           app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
           app(app(app(app(f(), app(s(), x)), 0()), z), u) -> app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
   app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
         app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
        app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
                         app(app(app(if(), true()), x), y) -> x,
                        app(app(app(if(), false()), x), y) -> y,
                                 app(app(minus(), 0()), y) -> 0(),
                       app(app(minus(), app(s(), x)), 0()) -> app(s(), x),
               app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                                    app(app(le(), 0()), y) -> true(),
                          app(app(le(), app(s(), x)), 0()) -> false(),
                  app(app(le(), app(s(), x)), app(s(), y)) -> app(app(le(), x), y),
             app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                               app(app(map(), fun), nil()) -> nil(),
          app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                            app(app(filter(), fun), nil()) -> nil(),
                                      app(perfectp(), 0()) -> false(),
                              app(perfectp(), app(s(), x)) -> app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x))}
  EDG:
   {
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(f(), x))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(if(), app(app(le(), x), y)))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(le(), x))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(minus(), y))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), app(s(), x)), app(app(minus(), y), x)))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), x), u))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(le(), x), y))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(minus(), y), x))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), x), u), z))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u))
    (app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(f(), x))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(if(), app(app(le(), x), y)))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(le(), x))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(minus(), y))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), app(s(), x)), app(app(minus(), y), x)))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), x), u))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(le(), x), y))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(minus(), y), x))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), x), u), z))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(f(), x))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(minus(), z))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(f(), x), u))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(minus(), z), app(s(), x)))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(f(), x), u), app(app(minus(), z), app(s(), x))))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(minus(), y), x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(minus(), y), x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(le(), x), y), app#(app(le(), app(s(), x)), app(s(), y)) -> app#(le(), x))
    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(le(), x), y), app#(app(le(), app(s(), x)), app(s(), y)) -> app#(app(le(), x), y))
    (app#(app(le(), app(s(), x)), app(s(), y)) -> app#(app(le(), x), y), app#(app(le(), app(s(), x)), app(s(), y)) -> app#(le(), x))
    (app#(app(le(), app(s(), x)), app(s(), y)) -> app#(app(le(), x), y), app#(app(le(), app(s(), x)), app(s(), y)) -> app#(app(le(), x), y))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(f(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(s(), 0()))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(app(f(), x), app(s(), 0())))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(app(app(f(), x), app(s(), 0())), app(s(), x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(perfectp(), app(s(), x)) -> app#(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
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    (app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(f(), x))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(f(), x), u), app(app(minus(), z), app(s(), x))))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(minus(), z), app(s(), x)))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(f(), x), u))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(minus(), z))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(f(), x))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), x), u), z))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(minus(), y), x))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(le(), x), y))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), x), u))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(f(), app(s(), x)), app(app(minus(), y), x)))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(minus(), y))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(le(), x))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(if(), app(app(le(), x), y)))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u), app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(f(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(minus(), z), app(s(), x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
    (app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(minus(), z), app(s(), x)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
   }
   STATUS:
    arrows: 0.900826
    SCCS (4):
     Scc:
      { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
       app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
            app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
            app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
         app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
         app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)}
     Scc:
      {        app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
       app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u),
       app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)}
     Scc:
      {app#(app(le(), app(s(), x)), app(s(), y)) -> app#(app(le(), x), y)}
     Scc:
      {app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y)}
     
     SCC (6):
      Strict:
       { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs),
        app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
             app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
             app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
          app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
          app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs)}
      Weak:
      {                app(app(app(app(f(), 0()), y), 0()), u) -> true(),
               app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
               app(app(app(app(f(), app(s(), x)), 0()), z), u) -> app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
       app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
             app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
            app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
                             app(app(app(if(), true()), x), y) -> x,
                            app(app(app(if(), false()), x), y) -> y,
                                     app(app(minus(), 0()), y) -> 0(),
                           app(app(minus(), app(s(), x)), 0()) -> app(s(), x),
                   app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                                        app(app(le(), 0()), y) -> true(),
                              app(app(le(), app(s(), x)), 0()) -> false(),
                      app(app(le(), app(s(), x)), app(s(), y)) -> app(app(le(), x), y),
                 app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                   app(app(map(), fun), nil()) -> nil(),
              app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                                app(app(filter(), fun), nil()) -> nil(),
                                          app(perfectp(), 0()) -> false(),
                                  app(perfectp(), app(s(), x)) -> app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x))}
      Open
     
     
     
     
     
     
     
     
     
     
     SCC (3):
      Strict:
       {        app#(app(app(app(f(), app(s(), x)), 0()), z), u) -> app#(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
        app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), x), u), z), u),
        app#(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app#(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)}
      Weak:
      {                app(app(app(app(f(), 0()), y), 0()), u) -> true(),
               app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
               app(app(app(app(f(), app(s(), x)), 0()), z), u) -> app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
       app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
             app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
            app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
                             app(app(app(if(), true()), x), y) -> x,
                            app(app(app(if(), false()), x), y) -> y,
                                     app(app(minus(), 0()), y) -> 0(),
                           app(app(minus(), app(s(), x)), 0()) -> app(s(), x),
                   app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                                        app(app(le(), 0()), y) -> true(),
                              app(app(le(), app(s(), x)), 0()) -> false(),
                      app(app(le(), app(s(), x)), app(s(), y)) -> app(app(le(), x), y),
                 app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                   app(app(map(), fun), nil()) -> nil(),
              app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                                app(app(filter(), fun), nil()) -> nil(),
                                          app(perfectp(), 0()) -> false(),
                                  app(perfectp(), app(s(), x)) -> app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x))}
      Open
     
     
     
     
     
     SCC (1):
      Strict:
       {app#(app(le(), app(s(), x)), app(s(), y)) -> app#(app(le(), x), y)}
      Weak:
      {                app(app(app(app(f(), 0()), y), 0()), u) -> true(),
               app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
               app(app(app(app(f(), app(s(), x)), 0()), z), u) -> app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
       app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
             app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
            app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
                             app(app(app(if(), true()), x), y) -> x,
                            app(app(app(if(), false()), x), y) -> y,
                                     app(app(minus(), 0()), y) -> 0(),
                           app(app(minus(), app(s(), x)), 0()) -> app(s(), x),
                   app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                                        app(app(le(), 0()), y) -> true(),
                              app(app(le(), app(s(), x)), 0()) -> false(),
                      app(app(le(), app(s(), x)), app(s(), y)) -> app(app(le(), x), y),
                 app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                   app(app(map(), fun), nil()) -> nil(),
              app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                                app(app(filter(), fun), nil()) -> nil(),
                                          app(perfectp(), 0()) -> false(),
                                  app(perfectp(), app(s(), x)) -> app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x))}
      Open
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     SCC (1):
      Strict:
       {app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y)}
      Weak:
      {                app(app(app(app(f(), 0()), y), 0()), u) -> true(),
               app(app(app(app(f(), 0()), y), app(s(), z)), u) -> false(),
               app(app(app(app(f(), app(s(), x)), 0()), z), u) -> app(app(app(app(f(), x), u), app(app(minus(), z), app(s(), x))), u),
       app(app(app(app(f(), app(s(), x)), app(s(), y)), z), u) -> app(app(app(if(), app(app(le(), x), y)), app(app(app(app(f(), app(s(), x)), app(app(minus(), y), x)), z), u)), app(app(app(app(f(), x), u), z), u)),
             app(app(app(app(filter2(), true()), fun), x), xs) -> app(app(cons(), x), app(app(filter(), fun), xs)),
            app(app(app(app(filter2(), false()), fun), x), xs) -> app(app(filter(), fun), xs),
                             app(app(app(if(), true()), x), y) -> x,
                            app(app(app(if(), false()), x), y) -> y,
                                     app(app(minus(), 0()), y) -> 0(),
                           app(app(minus(), app(s(), x)), 0()) -> app(s(), x),
                   app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                                        app(app(le(), 0()), y) -> true(),
                              app(app(le(), app(s(), x)), 0()) -> false(),
                      app(app(le(), app(s(), x)), app(s(), y)) -> app(app(le(), x), y),
                 app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                                   app(app(map(), fun), nil()) -> nil(),
              app(app(filter(), fun), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(fun, x)), fun), x), xs),
                                app(app(filter(), fun), nil()) -> nil(),
                                          app(perfectp(), 0()) -> false(),
                                  app(perfectp(), app(s(), x)) -> app(app(app(app(f(), x), app(s(), 0())), app(s(), x)), app(s(), x))}
      Open