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