method BadNbr$($a: array$)$ returns $($bn: int$)$

requires a $!=$ null

ensures $($a$.$Length bn $==-1)//$ If the array is too small, return $-1$

&& $($bn $>=0==>$ bn $$ a$.$Length$)//$ If a bad neighbour exists, bn is a valid index

&& $($bn $==-1==>$ forall i :: i $$ a$.$Length $==>$

$($a$[$i$]+$ a$[($i $+1)\%$ a$.$Length$]>=0))$; $//$ No bad neighbours

$\{$

$//$ Base case: if the array length is less than $2,$ no bad neighbours possible.

if a$.$Length $<mtext></mtext><mn>2</mn><mtext></mtext><mi>\{</mi>$

return $-1$; $//$ No bad neighbours in arrays with fewer than $2$ elements.

$\}$

var n :$=$ a$.$Length;

$//$ Check the wrap$-$around pair $($last and first elements$)$

if a$[$n $-1]+$ a$[0]<mtext></mtext><mn>0</mn><mtext></mtext><mi>\{</mi>$

return $0$; $//$ The right neighbour of the first element $($index $0)$ is bad

$\}$

$//$ Check for bad neighbours in consecutive pairs

var i :$=0$;

while i $$ n $-1$

invariant i n $-1$

invariant forall j :: j $$ i $==>$ a$[$j$]+$ a$[$j $+1]>=0$

$\{$

if a$[$i$]+$ a$[$i $+1]<mtext></mtext><mn>0</mn><mtext></mtext><mi>\{</mi>$

return i $+1$; $//$ The right neighbour of the current element $($index i$)$ is bad

$\}$

i :$=$ i $+1$;

$\}$

return $-1$; $//$ No bad neighbours found

$\}$

method TestBadNbr$()$

$\{$

$//$ Test case $1$: Empty array

var arr$1$ :$=$ new int$[0]$;

var res$1$ :$=$ BadNbr$($arr$1)$;

assert res$1==-1$; $//$ No bad neighbours, so return $-1$

$//$ Test case $2$: Array with one element

var arr$2$ :$=$ new int$[1]$;

arr$2[0]$ :$=5$;

var res$2$ :$=$ BadNbr$($arr$2)$;

assert res$2==-1$; $//$ No bad neighbours, so return $-1$

$//$ Test case $3$: Array with two elements where sum is negative

var arr$3$ :$=$ new int$[2]$;

arr$3[0]$ :$=1$;

arr$3[1]$ :$=-2$;

var res$3$ :$=$ BadNbr$($arr$3)$;

assert res$3==1$; $//$ Right neighbour $($index $1)$ is bad

$//$ Test case $4$: Array with three elements and a bad neighbour pair

var arr$4$ :$=$ new int$[3]$;

arr$4[0]$ :$=3$;

arr$4[1]$ :$=-4$;

arr$4[2]$ :$=1$;

var res$4$ :$=$ BadNbr$($arr$4)$;

assert res$4==1$; $//$ Right neighbour $($index $1)$ is bad

$//$ Test case $5$: Array with four elements and a wrap$-$around bad neighbour pair

var arr$5$ :$=$ new int$[4]$;

arr$5[0]$ :$=2$;

arr$5[1]$ :$=-1$;

arr$5[2]$ :$=3$;

arr$5[3]$ :$=-4$;

var res$5$ :$=$ BadNbr$($arr$5)$;

assert res$5==3$; $//$ Right neighbour $($index $3)$ is bad $($wrap$-$around pair$)$

$\}$

I changed my code to use the wrap around method but I still getting errors that the assertion will not hold

eng$2011$ dafny verify ex$1.$dfy

ex$1.$dfy$(33,11)$: Error: assertion might not hold

$|$

$33|$ assert res$1==-1$; $//$ No bad neighbours, so return $-1$

$|^^^^^^^^^^$

ex$1.$dfy$(39,11)$: Error: assertion might not hold

$|$

$39|$ assert res$2==-1$; $//$ No bad neighbours, so return $-1$

$|^^^^^^^^^^$

ex$1.$dfy$(46,11)$: Error: assertion might not hold

$|$

$46|$ assert res$3==1$; $//$ Right neighbour $($index $1)$ is bad

$|^^^^^^^^^$

ex$1.$dfy$(54,11)$: Error: assertion might not hold

$|$

$54|$ assert res$4==1$; $//$ Right neighbour $($index $1)$ is bad

$|^^^^^^^^^$

ex$1.$dfy$(63,11)$: Error: assertion might not hold

$|$

$63|$ assert res$5==3$; $//$ Right neighbour $($index $3)$ is bad $($wrap$-$around pair$)$

$|^^^^^^^^^$

Dafny program verifier finished with $1$ verified, $5$ errors