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