11. $Z=\varnothing ;S=X_0;K=0;B=0$

12. While $S\ne \varnothing$

13. $X=Pop\left(S\right);S=S-X;$

14. if $0\in F\left(X\right)$

15. if $wid\left(X\right)<{10}^{-14}$

16. $Z=Z\cup X;$

17. else

18. computing $P_L=P_L\left(X,N_L\left(X\right)\right)$ , $P_U=P_U\left(X,N_U\left(X\right)\right)$ and $P=P_L\bigsqcup P_U$

19. $r=\left[\min \left\{\overline{P_L},\overline{P_U}\right\},\max \left\{\underset{\_}{P_L},\underset{\_}{P_U}\right\}\right]$

20. if $0\in F^{\prime }\left(X\right)$

21. if $0\in \overline{F\left(m\left(X\right)\right)}$ or $\underset{\_}{0\in F\left(X\right)}$ or $X\subset P$

22. Bisect $X=\left(X_1,X_2\right)$

23. $B=B+1;$

24. $S=S\cup X_1\cup X_2;$

25. elseif $0\notin F\left(m\left(X\right)\right)$

26. $r=\varnothing ;$

27. end

28. end

29. $X_1=P_L\cap X;$

30. $X_2=P_U\cap X;$

31. $S=S\cup X_1\cup X_2;$

32. if $r\ne \varnothing$

33. $Z=Z\cup \left\{r\cap X\right\};$

34. end

35. end

36. end

37. $K=K+1;$

38. end