MAYBE
TRS:
 { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
  app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                         app(app(minus(), x), 0()) -> x,
       app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
        app(app(quot(), app(s(), x)), app(s(), y)) -> app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                app(app(quot(), 0()), app(s(), y)) -> 0(),
       app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                         app(app(map(), f), nil()) -> nil(),
    app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                      app(app(filter(), f), nil()) -> nil(),
                 app(log(), app(s(), app(s(), x))) -> app(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))),
                         app(log(), app(s(), 0())) -> 0()}
 DP:
  Strict:
   { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f),
         app#(app(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(quot(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y),
          app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y)),
          app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(minus(), x),
          app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
          app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(quot(), app(app(minus(), x), y)),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)),
                   app#(log(), app(s(), app(s(), x))) -> app#(app(quot(), x), app(s(), app(s(), 0()))),
                   app#(log(), app(s(), app(s(), x))) -> app#(s(), app(app(quot(), x), app(s(), app(s(), 0())))),
                   app#(log(), app(s(), app(s(), x))) -> app#(s(), app(s(), 0())),
                   app#(log(), app(s(), app(s(), x))) -> app#(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))),
                   app#(log(), app(s(), app(s(), x))) -> app#(s(), 0()),
                   app#(log(), app(s(), app(s(), x))) -> app#(quot(), x),
                   app#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))}
  Weak:
  { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
   app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                          app(app(minus(), x), 0()) -> x,
        app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
         app(app(quot(), app(s(), x)), app(s(), y)) -> app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                 app(app(quot(), 0()), app(s(), y)) -> 0(),
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                          app(app(map(), f), nil()) -> nil(),
     app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                       app(app(filter(), f), nil()) -> nil(),
                  app(log(), app(s(), app(s(), x))) -> app(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))),
                          app(log(), app(s(), 0())) -> 0()}
  EDG:
   {
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(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#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0()))))), app#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0()))))))
    (app#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0()))))), app#(log(), app(s(), app(s(), x))) -> app#(quot(), x))
    (app#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0()))))), app#(log(), app(s(), app(s(), x))) -> app#(s(), 0()))
    (app#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0()))))), app#(log(), app(s(), app(s(), x))) -> app#(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))))
    (app#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0()))))), app#(log(), app(s(), app(s(), x))) -> app#(s(), app(s(), 0())))
    (app#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0()))))), app#(log(), app(s(), app(s(), x))) -> app#(s(), app(app(quot(), x), app(s(), app(s(), 0())))))
    (app#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0()))))), app#(log(), app(s(), app(s(), x))) -> app#(app(quot(), x), app(s(), app(s(), 0()))))
    (app#(app(quot(), 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(quot(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
    (app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y)), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(quot(), app(app(minus(), x), y)))
    (app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y)), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))))
    (app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y)), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
    (app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y)), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y)))
    (app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y)), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
    (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
    (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#(log(), app(s(), app(s(), x))) -> app#(app(quot(), x), app(s(), app(s(), 0()))), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
    (app#(log(), app(s(), app(s(), x))) -> app#(app(quot(), x), app(s(), app(s(), 0()))), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y)))
    (app#(log(), app(s(), app(s(), x))) -> app#(app(quot(), x), app(s(), app(s(), 0()))), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
    (app#(log(), app(s(), app(s(), x))) -> app#(app(quot(), x), app(s(), app(s(), 0()))), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))))
    (app#(log(), app(s(), app(s(), x))) -> app#(app(quot(), x), app(s(), app(s(), 0()))), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(quot(), app(app(minus(), x), y)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(quot(), app(app(minus(), x), y)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(app(quot(), x), app(s(), app(s(), 0()))))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(s(), app(app(quot(), x), app(s(), app(s(), 0())))))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(s(), app(s(), 0())))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(s(), 0()))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(quot(), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0()))))))
    (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(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(quot(), app(app(minus(), x), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(app(quot(), x), app(s(), app(s(), 0()))))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(s(), app(app(quot(), x), app(s(), app(s(), 0())))))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(s(), app(s(), 0())))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(s(), 0()))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(quot(), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0()))))))
    (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)))
   }
   SCCS:
    Scc:
     {app#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))}
    Scc:
     {app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y))}
    Scc:
     {app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y)}
    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:
     Strict:
      {app#(log(), app(s(), app(s(), x))) -> app#(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))}
     Weak:
     { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
      app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                             app(app(minus(), x), 0()) -> x,
           app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
            app(app(quot(), app(s(), x)), app(s(), y)) -> app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                    app(app(quot(), 0()), app(s(), y)) -> 0(),
           app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                             app(app(map(), f), nil()) -> nil(),
        app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                          app(app(filter(), f), nil()) -> nil(),
                     app(log(), app(s(), app(s(), x))) -> app(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))),
                             app(log(), app(s(), 0())) -> 0()}
     Fail
    SCC:
     Strict:
      {app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y))}
     Weak:
     { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
      app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                             app(app(minus(), x), 0()) -> x,
           app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
            app(app(quot(), app(s(), x)), app(s(), y)) -> app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                    app(app(quot(), 0()), app(s(), y)) -> 0(),
           app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                             app(app(map(), f), nil()) -> nil(),
        app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                          app(app(filter(), f), nil()) -> nil(),
                     app(log(), app(s(), app(s(), x))) -> app(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))),
                             app(log(), app(s(), 0())) -> 0()}
     Fail
    SCC:
     Strict:
      {app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y)}
     Weak:
     { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
      app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                             app(app(minus(), x), 0()) -> x,
           app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
            app(app(quot(), app(s(), x)), app(s(), y)) -> app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                    app(app(quot(), 0()), app(s(), y)) -> 0(),
           app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                             app(app(map(), f), nil()) -> nil(),
        app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                          app(app(filter(), f), nil()) -> nil(),
                     app(log(), app(s(), app(s(), x))) -> app(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))),
                             app(log(), app(s(), 0())) -> 0()}
     SPSC:
      Simple Projection:
       pi(app#) = 1
      Strict:
       {}
      Qed
    SCC:
     Strict:
      { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
       app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
            app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
            app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
         app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
         app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)}
     Weak:
     { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
      app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                             app(app(minus(), x), 0()) -> x,
           app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
            app(app(quot(), app(s(), x)), app(s(), y)) -> app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                    app(app(quot(), 0()), app(s(), y)) -> 0(),
           app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                             app(app(map(), f), nil()) -> nil(),
        app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                          app(app(filter(), f), nil()) -> nil(),
                     app(log(), app(s(), app(s(), x))) -> app(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))),
                             app(log(), app(s(), 0())) -> 0()}
     SPSC:
      Simple Projection:
       pi(app#) = 1
      Strict:
       { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
        app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)}
      EDG:
       {(app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(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(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#(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(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))}
       SCCS:
        Scc:
         {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)}
        Scc:
         { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
          app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
            app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)}
        SCC:
         Strict:
          {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)}
         Weak:
         { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
          app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                                 app(app(minus(), x), 0()) -> x,
               app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                app(app(quot(), app(s(), x)), app(s(), y)) -> app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                        app(app(quot(), 0()), app(s(), y)) -> 0(),
               app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                                 app(app(map(), f), nil()) -> nil(),
            app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                              app(app(filter(), f), nil()) -> nil(),
                         app(log(), app(s(), app(s(), x))) -> app(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))),
                                 app(log(), app(s(), 0())) -> 0()}
         SPSC:
          Simple Projection:
           pi(app#) = 0
          Strict:
           {app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)}
          EDG:
           {(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))}
           SCCS:
            Scc:
             {app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)}
            SCC:
             Strict:
              {app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)}
             Weak:
             { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
              app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                                     app(app(minus(), x), 0()) -> x,
                   app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                    app(app(quot(), app(s(), x)), app(s(), y)) -> app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                            app(app(quot(), 0()), app(s(), y)) -> 0(),
                   app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                                     app(app(map(), f), nil()) -> nil(),
                app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                                  app(app(filter(), f), nil()) -> nil(),
                             app(log(), app(s(), app(s(), x))) -> app(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))),
                                     app(log(), app(s(), 0())) -> 0()}
             SPSC:
              Simple Projection:
               pi(app#) = 1
              Strict:
               {}
              Qed
        SCC:
         Strict:
          { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
           app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
             app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)}
         Weak:
         { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
          app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                                 app(app(minus(), x), 0()) -> x,
               app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), x), y),
                app(app(quot(), app(s(), x)), app(s(), y)) -> app(s(), app(app(quot(), app(app(minus(), x), y)), app(s(), y))),
                        app(app(quot(), 0()), app(s(), y)) -> 0(),
               app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                                 app(app(map(), f), nil()) -> nil(),
            app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                              app(app(filter(), f), nil()) -> nil(),
                         app(log(), app(s(), app(s(), x))) -> app(s(), app(log(), app(s(), app(app(quot(), x), app(s(), app(s(), 0())))))),
                                 app(log(), app(s(), 0())) -> 0()}
         SPSC:
          Simple Projection:
           pi(app#) = 1
          Strict:
           { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
            app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs)}
          EDG:
           {}
           SCCS:
            
            Qed