MAYBE
MAYBE
TRS:
 {
                a(a(a(div2(), x), y), 0()) -> a(a(divides(), x), y),
  a(a(a(div2(), a(s(), x)), y), a(s(), z)) -> a(a(a(div2(), x), y), z),
        a(a(a(div2(), 0()), y), a(s(), z)) -> false(),
              a(a(a(if(), true()), x), xs) -> a(a(cons(), x), xs),
             a(a(a(if(), false()), x), xs) -> xs,
     a(a(divides(), a(s(), x)), a(s(), y)) ->
  a(a(a(div2(), x), a(s(), y)), y),
           a(a(divides(), 0()), a(s(), y)) -> true(),
    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(not(), f), x) -> a(not2(), a(f, x)),
                         a(not2(), true()) -> false(),
                        a(not2(), false()) -> true(),
           a(sieve(), a(a(cons(), x), xs)) ->
  a(a(cons(), x), a(sieve(), a(a(filter(), a(not(), a(divides(), x))), xs))),
                         a(sieve(), nil()) -> nil()
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                  a(a(a(div2(), x), y), 0()) -> a(a(divides(), x), y),
    a(a(a(div2(), a(s(), x)), y), a(s(), z)) -> a(a(a(div2(), x), y), z),
          a(a(a(div2(), 0()), y), a(s(), z)) -> false(),
                a(a(a(if(), true()), x), xs) -> a(a(cons(), x), xs),
               a(a(a(if(), false()), x), xs) -> xs,
       a(a(divides(), a(s(), x)), a(s(), y)) ->
    a(a(a(div2(), x), a(s(), y)), y),
             a(a(divides(), 0()), a(s(), y)) -> true(),
      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(not(), f), x) -> a(not2(), a(f, x)),
                           a(not2(), true()) -> false(),
                          a(not2(), false()) -> true(),
             a(sieve(), a(a(cons(), x), xs)) ->
    a(a(cons(), x), a(sieve(), a(a(filter(), a(not(), a(divides(), x))), xs))
    ),
                           a(sieve(), nil()) -> nil()
   }
  Fail