MAYBE
MAYBE
TRS:
 {
                   cons(mark(X1), X2) -> mark(cons(X1, X2)),
                 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
                 active(cons(X1, X2)) -> cons(active(X1), X2),
                      active(zeros()) -> mark(cons(0(), zeros())),
                  active(U12(X1, X2)) -> U12(active(X1), X2),
                 active(U12(tt(), L)) -> mark(s(length(L))),
                  active(U11(X1, X2)) -> U11(active(X1), X2),
                 active(U11(tt(), L)) -> mark(U12(tt(), L)),
                         active(s(X)) -> s(active(X)),
                    active(length(X)) -> length(active(X)),
           active(length(cons(N, L))) -> mark(U11(tt(), L)),
                active(length(nil())) -> mark(0()),
          active(U22(X1, X2, X3, X4)) -> U22(active(X1), X2, X3, X4),
          active(U22(tt(), IL, M, N)) -> mark(U23(tt(), IL, M, N)),
          active(U21(X1, X2, X3, X4)) -> U21(active(X1), X2, X3, X4),
          active(U21(tt(), IL, M, N)) -> mark(U22(tt(), IL, M, N)),
          active(U23(X1, X2, X3, X4)) -> U23(active(X1), X2, X3, X4),
          active(U23(tt(), IL, M, N)) -> mark(cons(N, take(M, IL))),
                 active(take(X1, X2)) -> take(X1, active(X2)),
                 active(take(X1, X2)) -> take(active(X1), X2),
                active(take(0(), IL)) -> mark(nil()),
      active(take(s(M), cons(N, IL))) -> mark(U21(tt(), IL, M, N)),
                    U12(mark(X1), X2) -> mark(U12(X1, X2)),
                  U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)),
                    U11(mark(X1), X2) -> mark(U11(X1, X2)),
                  U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)),
                           s(mark(X)) -> mark(s(X)),
                             s(ok(X)) -> ok(s(X)),
                      length(mark(X)) -> mark(length(X)),
                        length(ok(X)) -> ok(length(X)),
            U22(mark(X1), X2, X3, X4) -> mark(U22(X1, X2, X3, X4)),
  U22(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U22(X1, X2, X3, X4)),
            U21(mark(X1), X2, X3, X4) -> mark(U21(X1, X2, X3, X4)),
  U21(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U21(X1, X2, X3, X4)),
            U23(mark(X1), X2, X3, X4) -> mark(U23(X1, X2, X3, X4)),
  U23(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U23(X1, X2, X3, X4)),
                   take(X1, mark(X2)) -> mark(take(X1, X2)),
                   take(mark(X1), X2) -> mark(take(X1, X2)),
                 take(ok(X1), ok(X2)) -> ok(take(X1, X2)),
                 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
                          proper(0()) -> ok(0()),
                      proper(zeros()) -> ok(zeros()),
                  proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)),
                         proper(tt()) -> ok(tt()),
                  proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)),
                         proper(s(X)) -> s(proper(X)),
                    proper(length(X)) -> length(proper(X)),
          proper(U22(X1, X2, X3, X4)) ->
  U22(proper(X1), proper(X2), proper(X3), proper(X4)),
          proper(U21(X1, X2, X3, X4)) ->
  U21(proper(X1), proper(X2), proper(X3), proper(X4)),
          proper(U23(X1, X2, X3, X4)) ->
  U23(proper(X1), proper(X2), proper(X3), proper(X4)),
                 proper(take(X1, X2)) -> take(proper(X1), proper(X2)),
                        proper(nil()) -> ok(nil()),
                         top(mark(X)) -> top(proper(X)),
                           top(ok(X)) -> top(active(X))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
                     cons(mark(X1), X2) -> mark(cons(X1, X2)),
                   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)),
                   active(cons(X1, X2)) -> cons(active(X1), X2),
                        active(zeros()) -> mark(cons(0(), zeros())),
                    active(U12(X1, X2)) -> U12(active(X1), X2),
                   active(U12(tt(), L)) -> mark(s(length(L))),
                    active(U11(X1, X2)) -> U11(active(X1), X2),
                   active(U11(tt(), L)) -> mark(U12(tt(), L)),
                           active(s(X)) -> s(active(X)),
                      active(length(X)) -> length(active(X)),
             active(length(cons(N, L))) -> mark(U11(tt(), L)),
                  active(length(nil())) -> mark(0()),
            active(U22(X1, X2, X3, X4)) -> U22(active(X1), X2, X3, X4),
            active(U22(tt(), IL, M, N)) -> mark(U23(tt(), IL, M, N)),
            active(U21(X1, X2, X3, X4)) -> U21(active(X1), X2, X3, X4),
            active(U21(tt(), IL, M, N)) -> mark(U22(tt(), IL, M, N)),
            active(U23(X1, X2, X3, X4)) -> U23(active(X1), X2, X3, X4),
            active(U23(tt(), IL, M, N)) -> mark(cons(N, take(M, IL))),
                   active(take(X1, X2)) -> take(X1, active(X2)),
                   active(take(X1, X2)) -> take(active(X1), X2),
                  active(take(0(), IL)) -> mark(nil()),
        active(take(s(M), cons(N, IL))) -> mark(U21(tt(), IL, M, N)),
                      U12(mark(X1), X2) -> mark(U12(X1, X2)),
                    U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)),
                      U11(mark(X1), X2) -> mark(U11(X1, X2)),
                    U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)),
                             s(mark(X)) -> mark(s(X)),
                               s(ok(X)) -> ok(s(X)),
                        length(mark(X)) -> mark(length(X)),
                          length(ok(X)) -> ok(length(X)),
              U22(mark(X1), X2, X3, X4) -> mark(U22(X1, X2, X3, X4)),
    U22(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U22(X1, X2, X3, X4)),
              U21(mark(X1), X2, X3, X4) -> mark(U21(X1, X2, X3, X4)),
    U21(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U21(X1, X2, X3, X4)),
              U23(mark(X1), X2, X3, X4) -> mark(U23(X1, X2, X3, X4)),
    U23(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U23(X1, X2, X3, X4)),
                     take(X1, mark(X2)) -> mark(take(X1, X2)),
                     take(mark(X1), X2) -> mark(take(X1, X2)),
                   take(ok(X1), ok(X2)) -> ok(take(X1, X2)),
                   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)),
                            proper(0()) -> ok(0()),
                        proper(zeros()) -> ok(zeros()),
                    proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)),
                           proper(tt()) -> ok(tt()),
                    proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)),
                           proper(s(X)) -> s(proper(X)),
                      proper(length(X)) -> length(proper(X)),
            proper(U22(X1, X2, X3, X4)) ->
    U22(proper(X1), proper(X2), proper(X3), proper(X4)),
            proper(U21(X1, X2, X3, X4)) ->
    U21(proper(X1), proper(X2), proper(X3), proper(X4)),
            proper(U23(X1, X2, X3, X4)) ->
    U23(proper(X1), proper(X2), proper(X3), proper(X4)),
                   proper(take(X1, X2)) -> take(proper(X1), proper(X2)),
                          proper(nil()) -> ok(nil()),
                           top(mark(X)) -> top(proper(X)),
                             top(ok(X)) -> top(active(X))
   }
  Fail