Algorithm A2: Correct two consecutive insertion symbols

Input:  $n,a,\mathit{y},0{\mathit{x}}_j^{n+2}$. Output:  $\mathit{c}=(c_1,c_2,\dots ,c_n)\in C(n,4)$.  1:Calculate $\Delta$ and $h_1+h_2$ as in Table 3.  2:Set $j=1$.  3:if  $\Delta \ge 2\parallel \mathit{r}\prime \prime \parallel$  then  4:   while $j\le n+1$ do  5:     if mod$(\Delta ,2)=1$ then  6:        if $2k_{0{\mathit{x}}_j^{n+2}}(j-1)+2(n-j)+5=\Delta$ then  7:          $x_j={\overline{x}}_{j-1}$; $x_{j+1}=x_{j-1}$  8:          $\mathit{c}=$ins2_correct2$(j,n,a,\mathit{y},h_1+h_2)$  9:        else  10:          $j\leftarrow j+1$  11:        end if  12:     else  13:        if $2k_{0{\mathit{x}}_j^{n+2}}(j-1)+2(n-j)+4=\Delta$ then  14:          $x_j={\overline{x}}_{j-1}$; $x_{j+1}={\overline{x}}_{j-1}$  15:          $\mathit{c}=$ins2_correct2$(j,n,a,\mathit{y},h_1+h_2)$  16:        else  17:          $j\leftarrow j+1$  18:        end if  19:     end if  20:   end while  21:else  22:   while $j\le n+1$ do  23:     if mod$(\Delta ,2)=1$ then  24:        if $2k_{0{\mathit{x}}_j^{n+2}}(j-1)+1=\Delta$ then  25:          $x_j=x_{j-1}$; $x_{j+1}={\overline{x}}_{j-1}$  26:          $\mathit{c}=$ins2_correct2$(j,n,a,\mathit{y},h_1+h_2)$  27:        else  28:          $j\leftarrow j+1$  29:        end if  30:     else  31:        if $2k_{0{\mathit{x}}_j^{n+2}}(j-1)=\Delta$ then  32:          $x_j=x_{j-1}$; $x_{j+1}=x_{j-1}$  33:          $\mathit{c}=$ins2_correct2$(j,n,a,\mathit{y},h_1+h_2)$  34:        else  35:          $j\leftarrow j+1$  36:        end if  37:     end if  38:   end while  39:end if