MAYBE
Time: 0.011516
TRS:
 {                app(app(and(), true()), true()) -> true(),
                 app(app(and(), true()), false()) -> false(),
                 app(app(and(), false()), true()) -> false(),
                app(app(and(), false()), false()) -> false(),
                   app(app(or(), true()), true()) -> true(),
                  app(app(or(), true()), false()) -> true(),
                  app(app(or(), false()), true()) -> true(),
                 app(app(or(), false()), false()) -> false(),
   app(app(forall(), p), app(app(cons(), x), xs)) -> app(app(and(), app(p, x)), app(app(forall(), p), xs)),
                     app(app(forall(), p), nil()) -> true(),
  app(app(forsome(), p), app(app(cons(), x), xs)) -> app(app(or(), app(p, x)), app(app(forsome(), p), xs)),
                    app(app(forsome(), p), nil()) -> false()}
 DP:
  DP:
   { app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x),
     app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(and(), app(p, x)), app(app(forall(), p), xs)),
     app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs),
     app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(and(), app(p, x)),
    app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x),
    app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(or(), app(p, x)), app(app(forsome(), p), xs)),
    app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs),
    app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(or(), app(p, x))}
  TRS:
  {                app(app(and(), true()), true()) -> true(),
                  app(app(and(), true()), false()) -> false(),
                  app(app(and(), false()), true()) -> false(),
                 app(app(and(), false()), false()) -> false(),
                    app(app(or(), true()), true()) -> true(),
                   app(app(or(), true()), false()) -> true(),
                   app(app(or(), false()), true()) -> true(),
                  app(app(or(), false()), false()) -> false(),
    app(app(forall(), p), app(app(cons(), x), xs)) -> app(app(and(), app(p, x)), app(app(forall(), p), xs)),
                      app(app(forall(), p), nil()) -> true(),
   app(app(forsome(), p), app(app(cons(), x), xs)) -> app(app(or(), app(p, x)), app(app(forsome(), p), xs)),
                     app(app(forsome(), p), nil()) -> false()}
  UR:
   {                app(app(and(), true()), true()) -> true(),
                   app(app(and(), true()), false()) -> false(),
                   app(app(and(), false()), true()) -> false(),
                  app(app(and(), false()), false()) -> false(),
                     app(app(or(), true()), true()) -> true(),
                    app(app(or(), true()), false()) -> true(),
                    app(app(or(), false()), true()) -> true(),
                   app(app(or(), false()), false()) -> false(),
     app(app(forall(), p), app(app(cons(), x), xs)) -> app(app(and(), app(p, x)), app(app(forall(), p), xs)),
                       app(app(forall(), p), nil()) -> true(),
    app(app(forsome(), p), app(app(cons(), x), xs)) -> app(app(or(), app(p, x)), app(app(forsome(), p), xs)),
                      app(app(forsome(), p), nil()) -> false(),
                                            a(y, z) -> y,
                                            a(y, z) -> z}
   EDG:
    {(app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(or(), app(p, x)))
     (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs))
     (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(or(), app(p, x)), app(app(forsome(), p), xs)))
     (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x))
     (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(and(), app(p, x)))
     (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs))
     (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(and(), app(p, x)), app(app(forall(), p), xs)))
     (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x))
     (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(or(), app(p, x)))
     (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs))
     (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(or(), app(p, x)), app(app(forsome(), p), xs)))
     (app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x))
     (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x))
     (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(and(), app(p, x)), app(app(forall(), p), xs)))
     (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs))
     (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(and(), app(p, x)))
     (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x))
     (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(and(), app(p, x)), app(app(forall(), p), xs)))
     (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs))
     (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(and(), app(p, x)))
     (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x))
     (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(or(), app(p, x)), app(app(forsome(), p), xs)))
     (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs))
     (app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x), app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(or(), app(p, x)))}
    STATUS:
     arrows: 0.625000
     SCCS (1):
      Scc:
       { app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x),
         app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs),
        app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x),
        app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs)}
      
      SCC (4):
       Strict:
        { app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(p, x),
          app#(app(forall(), p), app(app(cons(), x), xs)) -> app#(app(forall(), p), xs),
         app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(p, x),
         app#(app(forsome(), p), app(app(cons(), x), xs)) -> app#(app(forsome(), p), xs)}
       Weak:
       {                app(app(and(), true()), true()) -> true(),
                       app(app(and(), true()), false()) -> false(),
                       app(app(and(), false()), true()) -> false(),
                      app(app(and(), false()), false()) -> false(),
                         app(app(or(), true()), true()) -> true(),
                        app(app(or(), true()), false()) -> true(),
                        app(app(or(), false()), true()) -> true(),
                       app(app(or(), false()), false()) -> false(),
         app(app(forall(), p), app(app(cons(), x), xs)) -> app(app(and(), app(p, x)), app(app(forall(), p), xs)),
                           app(app(forall(), p), nil()) -> true(),
        app(app(forsome(), p), app(app(cons(), x), xs)) -> app(app(or(), app(p, x)), app(app(forsome(), p), xs)),
                          app(app(forsome(), p), nil()) -> false()}
       Open