MAYBE
TRS:
 {            app(app(app(curry(), g), x), y) -> app(app(g, x), y),
             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(),
                                        inc() -> app(map(), app(app(curry(), plus()), app(s(), 0())))}
 DP:
  Strict:
   {            app#(app(app(curry(), g), x), y) -> app#(g, x),
                app#(app(app(curry(), g), x), y) -> app#(app(g, 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)),
                                          inc#() -> app#(app(curry(), plus()), app(s(), 0())),
                                          inc#() -> app#(s(), 0()),
                                          inc#() -> app#(map(), app(app(curry(), plus()), app(s(), 0()))),
                                          inc#() -> app#(curry(), plus())}
  Weak:
  {            app(app(app(curry(), g), x), y) -> app(app(g, x), y),
              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(),
                                         inc() -> app(map(), app(app(curry(), plus()), app(s(), 0())))}
  EDG:
   {(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(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(app(curry(), g), x), y) -> app#(g, x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(curry(), g), x), y) -> app#(app(g, 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#(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#(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#(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(app(curry(), g), x), y) -> app#(g, x), app#(app(app(curry(), g), x), y) -> app#(g, x))
    (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y))
    (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
    (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
    (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
    (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(app(curry(), g), x), y) -> app#(g, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
    (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(app(curry(), g), x), y) -> app#(g, x))
    (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(app(curry(), g), x), y) -> app#(app(g, x), y))
    (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
    (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
    (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
    (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
    (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(app(curry(), g), x), y) -> app#(app(g, x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))}
   SCCS:
    Scc:
     {app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)}
    Scc:
     {            app#(app(app(curry(), g), x), y) -> app#(g, x),
                  app#(app(app(curry(), g), x), y) -> app#(app(g, 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)}
    SCC:
     Strict:
      {app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)}
     Weak:
     {            app(app(app(curry(), g), x), y) -> app(app(g, x), y),
                 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(),
                                            inc() -> app(map(), app(app(curry(), plus()), app(s(), 0())))}
     Fail
    SCC:
     Strict:
      {            app#(app(app(curry(), g), x), y) -> app#(g, x),
                   app#(app(app(curry(), g), x), y) -> app#(app(g, 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)}
     Weak:
     {            app(app(app(curry(), g), x), y) -> app(app(g, x), y),
                 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(),
                                            inc() -> app(map(), app(app(curry(), plus()), app(s(), 0())))}
     Fail