MAYBE
Time: 0.026653
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), app(s(), y)) -> app(pred(), app(app(minus(), x), y)),
                         app(app(minus(), x), 0()) -> 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(), 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(pred(), app(s(), x)) -> x}
 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(minus(), x), app(s(), y)) -> app#(app(minus(), x), y),
                   app#(app(minus(), x), app(s(), y)) -> app#(pred(), app(app(minus(), x), y)),
          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#(s(), 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#(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))}
  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), app(s(), y)) -> app(pred(), app(app(minus(), x), y)),
                          app(app(minus(), x), 0()) -> 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(), 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(pred(), app(s(), x)) -> x}
  UR:
   { 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), app(s(), y)) -> app(pred(), app(app(minus(), x), y)),
                           app(app(minus(), x), 0()) -> 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(), 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(pred(), app(s(), x)) -> x,
                                             a(z, w) -> z,
                                             a(z, w) -> w}
   EDG:
    {
     (app#(app(minus(), x), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), x), app(s(), y)) -> app#(pred(), app(app(minus(), x), y)))
     (app#(app(minus(), x), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), x), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(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(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(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#(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#(app(minus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(minus(), x), app(s(), y)) -> app#(pred(), app(app(minus(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(minus(), x), app(s(), y)) -> app#(app(minus(), 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(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(), x), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(minus(), x), app(s(), y)) -> app#(pred(), 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(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#(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#(minus(), x))
     (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#(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(quot(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), x), app(s(), y)) -> app#(app(minus(), x), y))
     (app#(app(quot(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), y), app#(app(minus(), x), app(s(), y)) -> app#(pred(), 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#(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#(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#(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#(quot(), app(app(minus(), x), y)))
    }
    STATUS:
     arrows: 0.849174
     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(quot(), app(s(), x)), app(s(), y)) -> app#(app(quot(), app(app(minus(), x), y)), app(s(), y))}
      Scc:
       {app#(app(minus(), x), app(s(), y)) -> app#(app(minus(), 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(minus(), x), app(s(), y)) -> app(pred(), app(app(minus(), x), y)),
                               app(app(minus(), x), 0()) -> 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(), 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(pred(), app(s(), x)) -> x}
       Open
      
      
      
      
      
      
      
      
      SCC (1):
       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), app(s(), y)) -> app(pred(), app(app(minus(), x), y)),
                               app(app(minus(), x), 0()) -> 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(), 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(pred(), app(s(), x)) -> x}
       Open
      
      
      
      
      SCC (1):
       Strict:
        {app#(app(minus(), 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), app(s(), y)) -> app(pred(), app(app(minus(), x), y)),
                               app(app(minus(), x), 0()) -> 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(), 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(pred(), app(s(), x)) -> x}
       Open