MAYBE
Time: 0.008101
TRS:
 {           app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                     app(app(plus(), 0()), y) -> 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(inc(), xs) -> app(app(map(), app(plus(), app(s(), 0()))), xs)}
 DP:
  DP:
   {           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#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs),
                                 app#(inc(), xs) -> app#(plus(), app(s(), 0())),
                                 app#(inc(), xs) -> app#(s(), 0()),
                                 app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0())))}
  TRS:
  {           app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                      app(app(plus(), 0()), y) -> 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(inc(), xs) -> app(app(map(), app(plus(), app(s(), 0()))), xs)}
  UR:
   {           app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                       app(app(plus(), 0()), y) -> 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(inc(), xs) -> app(app(map(), app(plus(), app(s(), 0()))), xs),
                                        a(z, w) -> z,
                                        a(z, w) -> w}
   EDG:
    {
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(inc(), xs) -> app#(s(), 0()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(inc(), xs) -> app#(plus(), app(s(), 0())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), 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(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#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(inc(), xs) -> app#(s(), 0()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(inc(), xs) -> app#(plus(), app(s(), 0())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), 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(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(cons(), app(f, x)), 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(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(cons(), app(f, x)), app(app(map(), f), xs)), 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(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(inc(), xs) -> app#(s(), 0()), app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))))
     (app#(inc(), xs) -> app#(s(), 0()), app#(inc(), xs) -> app#(s(), 0()))
     (app#(inc(), xs) -> app#(s(), 0()), app#(inc(), xs) -> app#(plus(), app(s(), 0())))
     (app#(inc(), xs) -> app#(s(), 0()), app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs))
     (app#(inc(), xs) -> app#(s(), 0()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(inc(), xs) -> app#(s(), 0()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(inc(), xs) -> app#(s(), 0()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(inc(), xs) -> app#(s(), 0()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(inc(), xs) -> app#(s(), 0()), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(inc(), xs) -> app#(s(), 0()), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(inc(), xs) -> app#(s(), 0()), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))), app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))))
     (app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))), app#(inc(), xs) -> app#(s(), 0()))
     (app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))), app#(inc(), xs) -> app#(plus(), app(s(), 0())))
     (app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))), app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs))
     (app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(inc(), xs) -> app#(s(), 0()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(inc(), xs) -> app#(plus(), app(s(), 0())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(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#(app(map(), f), xs), 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(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs), app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs))
     (app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs), app#(inc(), xs) -> app#(plus(), app(s(), 0())))
     (app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs), app#(inc(), xs) -> app#(s(), 0()))
     (app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs), app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))))
     (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(), 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#(s(), app(app(plus(), x), y)))
     (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(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> 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(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(inc(), xs) -> app#(plus(), app(s(), 0())))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(inc(), xs) -> app#(s(), 0()))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))))
     (app#(inc(), xs) -> app#(plus(), app(s(), 0())), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(inc(), xs) -> app#(plus(), app(s(), 0())), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(inc(), xs) -> app#(plus(), app(s(), 0())), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(inc(), xs) -> app#(plus(), app(s(), 0())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(inc(), xs) -> app#(plus(), app(s(), 0())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(inc(), xs) -> app#(plus(), app(s(), 0())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(inc(), xs) -> app#(plus(), app(s(), 0())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(inc(), xs) -> app#(plus(), app(s(), 0())), app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs))
     (app#(inc(), xs) -> app#(plus(), app(s(), 0())), app#(inc(), xs) -> app#(plus(), app(s(), 0())))
     (app#(inc(), xs) -> app#(plus(), app(s(), 0())), app#(inc(), xs) -> app#(s(), 0()))
     (app#(inc(), xs) -> app#(plus(), app(s(), 0())), app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), 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#(cons(), app(f, x)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), 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#(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#(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#(cons(), 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#(cons(), 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#(cons(), app(f, x)), app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(inc(), xs) -> app#(plus(), app(s(), 0())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(inc(), xs) -> app#(s(), 0()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))))
     (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#(s(), 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(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (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#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (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(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(inc(), xs) -> app#(plus(), app(s(), 0())))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(inc(), xs) -> app#(s(), 0()))
     (app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)), app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))))
     (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#(plus(), x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (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(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#(plus(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(inc(), xs) -> app#(plus(), app(s(), 0())))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(inc(), xs) -> app#(s(), 0()))
     (app#(app(plus(), app(s(), x)), y) -> app#(plus(), x), app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0()))))
    }
    STATUS:
     arrows: 0.000000
     SCCS (1):
      Scc:
       {           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#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs),
                                     app#(inc(), xs) -> app#(plus(), app(s(), 0())),
                                     app#(inc(), xs) -> app#(s(), 0()),
                                     app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0())))}
      
      SCC (11):
       Strict:
        {           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#(inc(), xs) -> app#(app(map(), app(plus(), app(s(), 0()))), xs),
                                      app#(inc(), xs) -> app#(plus(), app(s(), 0())),
                                      app#(inc(), xs) -> app#(s(), 0()),
                                      app#(inc(), xs) -> app#(map(), app(plus(), app(s(), 0())))}
       Weak:
       {           app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                           app(app(plus(), 0()), y) -> 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(inc(), xs) -> app(app(map(), app(plus(), app(s(), 0()))), xs)}
       Open