MAYBE
Time: 0.037020
TRS:
 {                  app(app(map(), f), nil()) -> nil(),
  app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                    app(app(minus(), x), 0()) -> x,
  app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))),
    app(app(div(), app(s(), x)), app(s(), y)) -> app(s(), app(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y))),
            app(app(div(), 0()), app(s(), y)) -> 0(),
                        app(p(), app(s(), x)) -> x,
                                 app(id(), x) -> x,
                                 app(id(), x) -> app(s(), app(s(), app(s(), x))),
                       app(id(), app(p(), x)) -> app(id(), app(s(), app(id(), x)))}
 DP:
  DP:
   {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(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))),
    app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), app(p(), app(s(), x))),
    app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(p(), app(s(), x)),
    app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(p(), app(s(), y)),
      app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), app(id(), y)),
      app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y)),
      app#(app(div(), app(s(), x)), app(s(), y)) -> app#(minus(), x),
      app#(app(div(), app(s(), x)), app(s(), y)) -> app#(s(), app(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y))),
      app#(app(div(), app(s(), x)), app(s(), y)) -> app#(div(), app(app(minus(), x), app(id(), y))),
      app#(app(div(), app(s(), x)), app(s(), y)) -> app#(id(), y),
                                   app#(id(), x) -> app#(s(), x),
                                   app#(id(), x) -> app#(s(), app(s(), x)),
                                   app#(id(), x) -> app#(s(), app(s(), app(s(), x))),
                         app#(id(), app(p(), x)) -> app#(s(), app(id(), x)),
                         app#(id(), app(p(), x)) -> app#(id(), x),
                         app#(id(), app(p(), x)) -> app#(id(), app(s(), app(id(), x)))}
  TRS:
  {                  app(app(map(), f), nil()) -> nil(),
   app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                     app(app(minus(), x), 0()) -> x,
   app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))),
     app(app(div(), app(s(), x)), app(s(), y)) -> app(s(), app(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y))),
             app(app(div(), 0()), app(s(), y)) -> 0(),
                         app(p(), app(s(), x)) -> x,
                                  app(id(), x) -> x,
                                  app(id(), x) -> app(s(), app(s(), app(s(), x))),
                        app(id(), app(p(), x)) -> app(id(), app(s(), app(id(), x)))}
  UR:
   {                  app(app(map(), f), nil()) -> nil(),
    app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                      app(app(minus(), x), 0()) -> x,
    app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))),
      app(app(div(), app(s(), x)), app(s(), y)) -> app(s(), app(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y))),
              app(app(div(), 0()), app(s(), y)) -> 0(),
                          app(p(), app(s(), x)) -> x,
                                   app(id(), x) -> x,
                                   app(id(), x) -> app(s(), app(s(), app(s(), x))),
                         app(id(), app(p(), x)) -> app(id(), app(s(), app(id(), x))),
                                        a(z, w) -> z,
                                        a(z, w) -> w}
   EDG:
    {(app#(id(), app(p(), x)) -> app#(id(), app(s(), app(id(), x))), app#(id(), x) -> app#(s(), app(s(), app(s(), x))))
     (app#(id(), app(p(), x)) -> app#(id(), app(s(), app(id(), x))), app#(id(), x) -> app#(s(), app(s(), x)))
     (app#(id(), app(p(), x)) -> app#(id(), app(s(), app(id(), x))), app#(id(), x) -> app#(s(), x))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(id(), y), app#(id(), app(p(), x)) -> app#(id(), app(s(), app(id(), x))))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(id(), y), app#(id(), app(p(), x)) -> app#(id(), x))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(id(), y), app#(id(), app(p(), x)) -> app#(s(), app(id(), x)))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(id(), y), app#(id(), x) -> app#(s(), app(s(), app(s(), x))))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(id(), y), app#(id(), x) -> app#(s(), app(s(), x)))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(id(), y), app#(id(), x) -> app#(s(), x))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), app(id(), y)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(p(), app(s(), y)))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), app(id(), y)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(p(), app(s(), x)))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), app(id(), y)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), app(p(), app(s(), x))))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), app(id(), y)), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(id(), app(p(), x)) -> app#(id(), app(s(), app(id(), x))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(id(), app(p(), x)) -> app#(id(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(id(), app(p(), x)) -> app#(s(), app(id(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(id(), x) -> app#(s(), app(s(), app(s(), x))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(id(), x) -> app#(s(), app(s(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(id(), x) -> app#(s(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(div(), app(s(), x)), app(s(), y)) -> app#(id(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(div(), app(s(), x)), app(s(), y)) -> app#(div(), app(app(minus(), x), app(id(), y))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(div(), app(s(), x)), app(s(), y)) -> app#(s(), app(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(div(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), app(id(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(p(), app(s(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(p(), app(s(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), app(p(), app(s(), x))))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))))
     (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(div(), app(s(), x)), app(s(), y)) -> app#(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y)), app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(minus(), x), app(id(), y)))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y)), app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y)))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y)), app#(app(div(), app(s(), x)), app(s(), y)) -> app#(minus(), x))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y)), app#(app(div(), app(s(), x)), app(s(), y)) -> app#(s(), app(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y))))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y)), app#(app(div(), app(s(), x)), app(s(), y)) -> app#(div(), app(app(minus(), x), app(id(), y))))
     (app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y)), app#(app(div(), app(s(), x)), app(s(), y)) -> app#(id(), y))
     (app#(id(), app(p(), x)) -> app#(id(), x), app#(id(), x) -> app#(s(), x))
     (app#(id(), app(p(), x)) -> app#(id(), x), app#(id(), x) -> app#(s(), app(s(), x)))
     (app#(id(), app(p(), x)) -> app#(id(), x), app#(id(), x) -> app#(s(), app(s(), app(s(), x))))
     (app#(id(), app(p(), x)) -> app#(id(), x), app#(id(), app(p(), x)) -> app#(s(), app(id(), x)))
     (app#(id(), app(p(), x)) -> app#(id(), x), app#(id(), app(p(), x)) -> app#(id(), x))
     (app#(id(), app(p(), x)) -> app#(id(), x), app#(id(), app(p(), x)) -> app#(id(), app(s(), app(id(), 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(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(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#(cons(), app(f, x)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(minus(), app(p(), app(s(), x))))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(p(), app(s(), x)))
     (app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))), app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(p(), app(s(), y)))}
    STATUS:
     arrows: 0.867500
     SCCS (4):
      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(div(), app(s(), x)), app(s(), y)) -> app#(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y))}
      Scc:
       {app#(id(), app(p(), x)) -> app#(id(), x)}
      Scc:
       {app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y)))}
      
      SCC (2):
       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(map(), f), nil()) -> nil(),
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                          app(app(minus(), x), 0()) -> x,
        app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))),
          app(app(div(), app(s(), x)), app(s(), y)) -> app(s(), app(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y))),
                  app(app(div(), 0()), app(s(), y)) -> 0(),
                              app(p(), app(s(), x)) -> x,
                                       app(id(), x) -> x,
                                       app(id(), x) -> app(s(), app(s(), app(s(), x))),
                             app(id(), app(p(), x)) -> app(id(), app(s(), app(id(), x)))}
       Open
      SCC (1):
       Strict:
        {app#(app(div(), app(s(), x)), app(s(), y)) -> app#(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y))}
       Weak:
       {                  app(app(map(), f), nil()) -> nil(),
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                          app(app(minus(), x), 0()) -> x,
        app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))),
          app(app(div(), app(s(), x)), app(s(), y)) -> app(s(), app(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y))),
                  app(app(div(), 0()), app(s(), y)) -> 0(),
                              app(p(), app(s(), x)) -> x,
                                       app(id(), x) -> x,
                                       app(id(), x) -> app(s(), app(s(), app(s(), x))),
                             app(id(), app(p(), x)) -> app(id(), app(s(), app(id(), x)))}
       Open
      
      SCC (1):
       Strict:
        {app#(id(), app(p(), x)) -> app#(id(), x)}
       Weak:
       {                  app(app(map(), f), nil()) -> nil(),
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                          app(app(minus(), x), 0()) -> x,
        app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))),
          app(app(div(), app(s(), x)), app(s(), y)) -> app(s(), app(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y))),
                  app(app(div(), 0()), app(s(), y)) -> 0(),
                              app(p(), app(s(), x)) -> x,
                                       app(id(), x) -> x,
                                       app(id(), x) -> app(s(), app(s(), app(s(), x))),
                             app(id(), app(p(), x)) -> app(id(), app(s(), app(id(), x)))}
       Open
      
      
      
      
      
      
      
      
      
      
      
      SCC (1):
       Strict:
        {app#(app(minus(), app(s(), x)), app(s(), y)) -> app#(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y)))}
       Weak:
       {                  app(app(map(), f), nil()) -> nil(),
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                          app(app(minus(), x), 0()) -> x,
        app(app(minus(), app(s(), x)), app(s(), y)) -> app(app(minus(), app(p(), app(s(), x))), app(p(), app(s(), y))),
          app(app(div(), app(s(), x)), app(s(), y)) -> app(s(), app(app(div(), app(app(minus(), x), app(id(), y))), app(s(), y))),
                  app(app(div(), 0()), app(s(), y)) -> 0(),
                              app(p(), app(s(), x)) -> x,
                                       app(id(), x) -> x,
                                       app(id(), x) -> app(s(), app(s(), app(s(), x))),
                             app(id(), app(p(), x)) -> app(id(), app(s(), app(id(), x)))}
       Open