MAYBE
Time: 0.032518
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(times(), x), 0()) -> 0(),
                 app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x),
                          app(app(plus(), x), 0()) -> x,
                  app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                          app(app(plus(), 0()), x) -> x,
                  app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
       app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                         app(app(map(), f), nil()) -> nil(),
    app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                      app(app(filter(), f), nil()) -> nil()}
 DP:
  DP:
   { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f),
                   app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y),
                   app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x),
                   app#(app(times(), x), app(s(), y)) -> app#(plus(), app(app(times(), x), y)),
                    app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y),
                    app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)),
                    app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y),
                    app#(app(plus(), app(s(), x)), y) -> app#(plus(), x),
                    app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))}
  TRS:
  { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
   app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                          app(app(times(), x), 0()) -> 0(),
                  app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x),
                           app(app(plus(), x), 0()) -> x,
                   app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                           app(app(plus(), 0()), x) -> x,
                   app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                          app(app(map(), f), nil()) -> nil(),
     app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                       app(app(filter(), f), nil()) -> nil()}
  EDG:
   {
    (app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(s(), y)) -> app#(plus(), app(app(times(), x), y)))
    (app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x))
    (app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y), app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y))
    (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
    (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
    (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
    (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
    (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
    (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(s(), y)) -> app#(plus(), app(app(times(), x), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
    (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
    (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
    (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
    (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
    (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(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(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#(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#(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(), false()), f), x), xs) -> app#(filter(), 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#(f, x))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
    (app#(app(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(times(), x), app(s(), y)) -> app#(app(times(), x), y))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), x), app(s(), y)) -> app#(plus(), app(app(times(), x), y)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), 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(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
    (app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
    (app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
    (app#(app(times(), x), app(s(), y)) -> app#(app(plus(), app(app(times(), x), y)), x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
   }
   STATUS:
    arrows: 0.841210
    SCCS (3):
     Scc:
      { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
       app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
            app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
            app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
         app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
         app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)}
     Scc:
      {app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y)}
     Scc:
      {app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y),
       app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)}
     
     SCC (6):
      Strict:
       { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
        app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)}
      Weak:
      { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
       app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                              app(app(times(), x), 0()) -> 0(),
                      app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x),
                               app(app(plus(), x), 0()) -> x,
                       app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                               app(app(plus(), 0()), x) -> x,
                       app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
            app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                              app(app(map(), f), nil()) -> nil(),
         app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                           app(app(filter(), f), nil()) -> nil()}
      Open
     
     
     
     
     
     SCC (1):
      Strict:
       {app#(app(times(), x), app(s(), y)) -> app#(app(times(), x), y)}
      Weak:
      { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
       app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                              app(app(times(), x), 0()) -> 0(),
                      app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x),
                               app(app(plus(), x), 0()) -> x,
                       app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                               app(app(plus(), 0()), x) -> x,
                       app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
            app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                              app(app(map(), f), nil()) -> nil(),
         app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                           app(app(filter(), f), nil()) -> nil()}
      Open
     
     
     
     
     
     
     SCC (2):
      Strict:
       {app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y),
        app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)}
      Weak:
      { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
       app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                              app(app(times(), x), 0()) -> 0(),
                      app(app(times(), x), app(s(), y)) -> app(app(plus(), app(app(times(), x), y)), x),
                               app(app(plus(), x), 0()) -> x,
                       app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                               app(app(plus(), 0()), x) -> x,
                       app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
            app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                              app(app(map(), f), nil()) -> nil(),
         app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                           app(app(filter(), f), nil()) -> nil()}
      Open