MAYBE
MAYBE
TRS:
 {
             a(a(a(if(), true()), x), xs) -> a(a(cons(), x), xs),
            a(a(a(if(), false()), x), xs) -> xs,
  a(a(append(), a(a(cons(), x), xs)), ys) ->
  a(a(cons(), x), a(a(append(), xs), ys)),
                a(a(append(), nil()), ys) -> ys,
   a(a(filter(), f), a(a(cons(), x), xs)) ->
  a(a(a(if(), a(f, x)), x), a(a(filter(), f), xs)),
                 a(a(filter(), f), nil()) -> nil(),
         a(a(le(), a(s(), x)), a(s(), y)) -> a(a(le(), x), y),
               a(a(le(), a(s(), x)), 0()) -> false(),
                       a(a(le(), 0()), y) -> true(),
                        a(a(not(), f), b) -> a(not2(), a(f, b)),
                        a(not2(), true()) -> false(),
                       a(not2(), false()) -> true(),
             a(qs(), a(a(cons(), x), xs)) ->
  a(
   a(append(), a(qs(), a(a(filter(), a(le(), x)), xs))),
   a(a(cons(), x), a(qs(), a(a(filter(), a(not(), a(le(), x))), xs)))
  ),
                           a(qs(), nil()) -> nil()
 }
 DUP: We consider a duplicating system.
  Trs:
   {
               a(a(a(if(), true()), x), xs) -> a(a(cons(), x), xs),
              a(a(a(if(), false()), x), xs) -> xs,
    a(a(append(), a(a(cons(), x), xs)), ys) ->
    a(a(cons(), x), a(a(append(), xs), ys)),
                  a(a(append(), nil()), ys) -> ys,
     a(a(filter(), f), a(a(cons(), x), xs)) ->
    a(a(a(if(), a(f, x)), x), a(a(filter(), f), xs)),
                   a(a(filter(), f), nil()) -> nil(),
           a(a(le(), a(s(), x)), a(s(), y)) -> a(a(le(), x), y),
                 a(a(le(), a(s(), x)), 0()) -> false(),
                         a(a(le(), 0()), y) -> true(),
                          a(a(not(), f), b) -> a(not2(), a(f, b)),
                          a(not2(), true()) -> false(),
                         a(not2(), false()) -> true(),
               a(qs(), a(a(cons(), x), xs)) ->
    a(
     a(append(), a(qs(), a(a(filter(), a(le(), x)), xs))),
     a(a(cons(), x), a(qs(), a(a(filter(), a(not(), a(le(), x))), xs)))
    ),
                             a(qs(), nil()) -> nil()
   }
  Fail