```// ************************************************************************** //
//                                                                            //
//    eses                   eses                                             //
//   eses                     eses                                            //
//  eses    eseses  esesese    eses   Embedded Systems Group                  //
//  ese    ese  ese ese         ese                                           //
//  ese    eseseses eseseses    ese   Department of Computer Science          //
//  eses   eses          ese   eses                                           //
//   eses   eseses  eseseses  eses    University of Kaiserslautern            //
//    eses                   eses                                             //
//                                                                            //
// ************************************************************************** //
// The following module implements an algorithm to compute the transitive hull//
// of a binary relation or a graph. It is based on an algorithm for boolean   //
// matrix multiplication that requires O(1) time using O(N^3) processors.     //
// This algorithm is used for iterative squaring of the given matrix so that  //
// in total O(log(N)) time with O(N^3) processors is required.                //
// Note that t is a memorized variable, so that it is sufficient to only set  //
// potentially new elements t[i][j] while those that are already true remain  //
// so automatically. Finally note that it is an CRCW algorithm since several  //
// writes to the same t[i][j] with the same value true are possible.          //
// ************************************************************************** //

[7][7]bool t;

function log2Ceil(nat n) : nat {
nat h,l;
h = 1;
l = 0;
while(h<n) {
h = h*2;
l = l+1;
}

return l;
}

function TransHull_OlogN(nat n, [][]bool a):nat{
nat i,j,k,h;
//copy matrix a to t
for(i=0..n-1){
for(j=0..n-1){
t[i][j]=a[i][j];
}
}
//iterative squaring
for(h=0..log2Ceil(n)-1){
for(i=0..n-1){
for(j=0..n-1){
for(k=0..n-1){
if(t[i][k] & t[k][j]){
t[i][j]=true;
}
}
}
}
}

return 1;
}

nat x,n,i,j;
[7][7]bool a;
bool test_passed;
a[0][1] = true;
a[1][2] = true;
a[2][1] = true;
a[2][4] = true;
a[2][7] = true;
a[3][2] = true;
a[3][4] = true;
a[4][5] = true;
a[5][4] = true;
a[5][6] = true;
a[5][8] = true;
a[6][5] = true;
a[7][7] = true;
n = 9;
x = TransHull_OlogN(n,a);

for(i=0..n-1){
for(j=0..n-1){
if(!((t[i][j] <->
(i==0 & (j==1 | j==2 | j==4 | j==5 | j==6 | j==7 | j==8) |
i==1 & (j==1 | j==2 | j==4 | j==5 | j==6 | j==7 | j==8) |
i==2 & (j==1 | j==2 | j==4 | j==5 | j==6 | j==7 | j==8) |
i==3 & (j==1 | j==2 | j==4 | j==5 | j==6 | j==7 | j==8) |
i==4 & (              j==4 | j==5 | j==6 |        j==8) |
i==5 & (              j==4 | j==5 | j==6 |        j==8) |
i==6 & (              j==4 | j==5 | j==6 |        j==8) |
i==7 &  j==7)
)))
{
test_passed = false;
}

}

}
}
```