MAYBE
MAYBE
TRS:
 {
                     active(2nd(X)) -> 2nd(active(X)),
  active(2nd(cons1(X, cons(Y, Z)))) -> mark(Y),
           active(2nd(cons(X, X1))) -> mark(2nd(cons1(X, X1))),
              active(cons1(X1, X2)) -> cons1(X1, active(X2)),
              active(cons1(X1, X2)) -> cons1(active(X1), X2),
               active(cons(X1, X2)) -> cons(active(X1), X2),
                    active(from(X)) -> mark(cons(X, from(s(X)))),
                    active(from(X)) -> from(active(X)),
                       active(s(X)) -> s(active(X)),
                       2nd(mark(X)) -> mark(2nd(X)),
                         2nd(ok(X)) -> ok(2nd(X)),
                cons1(X1, mark(X2)) -> mark(cons1(X1, X2)),
                cons1(mark(X1), X2) -> mark(cons1(X1, X2)),
              cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2)),
                 cons(mark(X1), X2) -> mark(cons(X1, X2)),
               cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
                      from(mark(X)) -> mark(from(X)),
                        from(ok(X)) -> ok(from(X)),
                         s(mark(X)) -> mark(s(X)),
                           s(ok(X)) -> ok(s(X)),
                     proper(2nd(X)) -> 2nd(proper(X)),
              proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2)),
               proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
                    proper(from(X)) -> from(proper(X)),
                       proper(s(X)) -> s(proper(X)),
                       top(mark(X)) -> top(proper(X)),
                         top(ok(X)) -> top(active(X))
 }
 DUP: We consider a duplicating system.
  Trs:
   {
                       active(2nd(X)) -> 2nd(active(X)),
    active(2nd(cons1(X, cons(Y, Z)))) -> mark(Y),
             active(2nd(cons(X, X1))) -> mark(2nd(cons1(X, X1))),
                active(cons1(X1, X2)) -> cons1(X1, active(X2)),
                active(cons1(X1, X2)) -> cons1(active(X1), X2),
                 active(cons(X1, X2)) -> cons(active(X1), X2),
                      active(from(X)) -> mark(cons(X, from(s(X)))),
                      active(from(X)) -> from(active(X)),
                         active(s(X)) -> s(active(X)),
                         2nd(mark(X)) -> mark(2nd(X)),
                           2nd(ok(X)) -> ok(2nd(X)),
                  cons1(X1, mark(X2)) -> mark(cons1(X1, X2)),
                  cons1(mark(X1), X2) -> mark(cons1(X1, X2)),
                cons1(ok(X1), ok(X2)) -> ok(cons1(X1, X2)),
                   cons(mark(X1), X2) -> mark(cons(X1, X2)),
                 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
                        from(mark(X)) -> mark(from(X)),
                          from(ok(X)) -> ok(from(X)),
                           s(mark(X)) -> mark(s(X)),
                             s(ok(X)) -> ok(s(X)),
                       proper(2nd(X)) -> 2nd(proper(X)),
                proper(cons1(X1, X2)) -> cons1(proper(X1), proper(X2)),
                 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
                      proper(from(X)) -> from(proper(X)),
                         proper(s(X)) -> s(proper(X)),
                         top(mark(X)) -> top(proper(X)),
                           top(ok(X)) -> top(active(X))
   }
  Fail