MAYBE
MAYBE
TRS:
 {
                 active(dbl(X)) -> dbl(active(X)),
               active(dbl(0())) -> mark(0()),
              active(dbl(s(X))) -> mark(s(s(dbl(X)))),
                active(dbls(X)) -> dbls(active(X)),
            active(dbls(nil())) -> mark(nil()),
       active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y))),
            active(sel(X1, X2)) -> sel(X1, active(X2)),
            active(sel(X1, X2)) -> sel(active(X1), X2),
   active(sel(0(), cons(X, Y))) -> mark(X),
  active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z)),
           active(indx(X1, X2)) -> indx(active(X1), X2),
         active(indx(nil(), X)) -> mark(nil()),
    active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z))),
                active(from(X)) -> mark(cons(X, from(s(X)))),
                   dbl(mark(X)) -> mark(dbl(X)),
                     dbl(ok(X)) -> ok(dbl(X)),
                       s(ok(X)) -> ok(s(X)),
                  dbls(mark(X)) -> mark(dbls(X)),
                    dbls(ok(X)) -> ok(dbls(X)),
           cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
              sel(X1, mark(X2)) -> mark(sel(X1, X2)),
              sel(mark(X1), X2) -> mark(sel(X1, X2)),
            sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)),
             indx(mark(X1), X2) -> mark(indx(X1, X2)),
           indx(ok(X1), ok(X2)) -> ok(indx(X1, X2)),
                    from(ok(X)) -> ok(from(X)),
                    proper(0()) -> ok(0()),
                 proper(dbl(X)) -> dbl(proper(X)),
                   proper(s(X)) -> s(proper(X)),
                  proper(nil()) -> ok(nil()),
                proper(dbls(X)) -> dbls(proper(X)),
           proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
            proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)),
           proper(indx(X1, X2)) -> indx(proper(X1), proper(X2)),
                proper(from(X)) -> from(proper(X)),
                   top(mark(X)) -> top(proper(X)),
                     top(ok(X)) -> top(active(X))
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                   active(dbl(X)) -> dbl(active(X)),
                 active(dbl(0())) -> mark(0()),
                active(dbl(s(X))) -> mark(s(s(dbl(X)))),
                  active(dbls(X)) -> dbls(active(X)),
              active(dbls(nil())) -> mark(nil()),
         active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y))),
              active(sel(X1, X2)) -> sel(X1, active(X2)),
              active(sel(X1, X2)) -> sel(active(X1), X2),
     active(sel(0(), cons(X, Y))) -> mark(X),
    active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z)),
             active(indx(X1, X2)) -> indx(active(X1), X2),
           active(indx(nil(), X)) -> mark(nil()),
      active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z))),
                  active(from(X)) -> mark(cons(X, from(s(X)))),
                     dbl(mark(X)) -> mark(dbl(X)),
                       dbl(ok(X)) -> ok(dbl(X)),
                         s(ok(X)) -> ok(s(X)),
                    dbls(mark(X)) -> mark(dbls(X)),
                      dbls(ok(X)) -> ok(dbls(X)),
             cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
                sel(X1, mark(X2)) -> mark(sel(X1, X2)),
                sel(mark(X1), X2) -> mark(sel(X1, X2)),
              sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)),
               indx(mark(X1), X2) -> mark(indx(X1, X2)),
             indx(ok(X1), ok(X2)) -> ok(indx(X1, X2)),
                      from(ok(X)) -> ok(from(X)),
                      proper(0()) -> ok(0()),
                   proper(dbl(X)) -> dbl(proper(X)),
                     proper(s(X)) -> s(proper(X)),
                    proper(nil()) -> ok(nil()),
                  proper(dbls(X)) -> dbls(proper(X)),
             proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
              proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)),
             proper(indx(X1, X2)) -> indx(proper(X1), proper(X2)),
                  proper(from(X)) -> from(proper(X)),
                     top(mark(X)) -> top(proper(X)),
                       top(ok(X)) -> top(active(X))
   }
  Fail