MAYBE
MAYBE
TRS:
 {
                                  app(app(app(if(), true()), xs), ys) -> xs,
                                 app(app(app(if(), false()), xs), ys) -> ys,
                                               app(app(lt(), y), 0()) ->
  false(),
                             app(app(lt(), app(s(), x)), app(s(), y)) ->
  app(app(lt(), x), y),
                                     app(app(lt(), 0()), app(s(), y)) ->
  true(),
                                                 app(app(eq(), x), x) ->
  true(),
                                     app(app(eq(), app(s(), x)), 0()) ->
  false(),
                                     app(app(eq(), 0()), app(s(), x)) ->
  false(),
                                         app(app(merge(), xs), nil()) -> xs,
  app(app(merge(), app(app(cons(), x), xs)), app(app(cons(), y), ys)) ->
  app(
     app(
        app(if(), app(app(lt(), x), y)),
        app(app(cons(), x), app(app(merge(), xs), app(app(cons(), y), ys)))
     ),
     app(
        app(
           app(if(), app(app(eq(), x), y)),
           app(app(cons(), x), app(app(merge(), xs), ys))
        ),
        app(app(cons(), y), app(app(merge(), app(app(cons(), x), xs)), ys))
     )
  ),
                                         app(app(merge(), nil()), ys) -> ys,
                          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(mult(), app(s(), x)), y) ->
  app(app(plus(), y), app(app(mult(), x), y)),
                                             app(app(mult(), 0()), x) -> 0(),
                                     app(app(plus(), app(s(), x)), y) ->
  app(s(), app(app(plus(), x), y)),
                                             app(app(plus(), 0()), x) -> 0(),
                                                            hamming() ->
  app(
     app(cons(), app(s(), 0())),
     app(app(merge(), list1()), app(app(merge(), list2()), list3()))
  ),
                                                              list1() ->
  app(app(map(), app(mult(), app(s(), app(s(), 0())))), hamming()),
                                                              list2() ->
  app(app(map(), app(mult(), app(s(), app(s(), app(s(), 0()))))), hamming()),
                                                              list3() ->
  app(
     app(
        map(),
        app(mult(), app(s(), app(s(), app(s(), app(s(), app(s(), 0()))))))
     ), hamming()
  )
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                                    app(app(app(if(), true()), xs), ys) -> xs,
                                   app(app(app(if(), false()), xs), ys) -> ys,
                                                 app(app(lt(), y), 0()) ->
    false(),
                               app(app(lt(), app(s(), x)), app(s(), y)) ->
    app(app(lt(), x), y),
                                       app(app(lt(), 0()), app(s(), y)) ->
    true(),
                                                   app(app(eq(), x), x) ->
    true(),
                                       app(app(eq(), app(s(), x)), 0()) ->
    false(),
                                       app(app(eq(), 0()), app(s(), x)) ->
    false(),
                                           app(app(merge(), xs), nil()) -> xs,
    app(app(merge(), app(app(cons(), x), xs)), app(app(cons(), y), ys)) ->
    app(
       app(
          app(if(), app(app(lt(), x), y)),
          app(app(cons(), x), app(app(merge(), xs), app(app(cons(), y), ys)))
       ),
       app(
          app(
             app(if(), app(app(eq(), x), y)),
             app(app(cons(), x), app(app(merge(), xs), ys))
          ),
          app(app(cons(), y), app(app(merge(), app(app(cons(), x), xs)), ys))
       )
    ),
                                           app(app(merge(), nil()), ys) -> ys,
                            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(mult(), app(s(), x)), y) ->
    app(app(plus(), y), app(app(mult(), x), y)),
                                               app(app(mult(), 0()), x) ->
    0(),
                                       app(app(plus(), app(s(), x)), y) ->
    app(s(), app(app(plus(), x), y)),
                                               app(app(plus(), 0()), x) ->
    0(),
                                                              hamming() ->
    app(
       app(cons(), app(s(), 0())),
       app(app(merge(), list1()), app(app(merge(), list2()), list3()))
    ),
                                                                list1() ->
    app(app(map(), app(mult(), app(s(), app(s(), 0())))), hamming()),
                                                                list2() ->
    app(app(map(), app(mult(), app(s(), app(s(), app(s(), 0()))))), hamming()
    ),
                                                                list3() ->
    app(
       app(
          map(),
          app(mult(), app(s(), app(s(), app(s(), app(s(), app(s(), 0()))))))
       ), hamming()
    )
   }
  Fail