Here's a Python program that prompts the user to enter a string and displays the maximum consecutive increasingly ordered substring. I'll also explain the time complexity of the program.

python

def max$\_$increasing$\_$substring$($s$)$:

max$\_$substring $=""$

current$\_$substring $=""$

for i in range$($len$($s$))$:

if i $==0$ or s$[$i$]>$ s$[$i $-1]$:

current$\_$substring $+=$ s$[$i$]$

else:

if len$($current$\_$substring$)>$ len$($max$\_$substring$)$:

max$\_$substring $=$ current$\_$substring

current$\_$substring $=$ s$[$i$]$

# Check one last time at the end of the loop

if len$($current$\_$substring$)>$ len$($max$\_$substring$)$:

max$\_$substring $=$ current$\_$substring

return max$\_$substring

def main$()$:

user$\_$input $=$ input$("$Enter a string: $")$

result $=$ max$\_$increasing$\_$substring$($user$\_$input$)$

print$($f$"$Maximum consecutive increasingly ordered substring is $\{$result$\}")$

if $\_\_$name$\_\_=="\_\_$main$\_\_"$:

main$()$

Explanation:

$1.$ max$\_$increasing$\_$substring function:

$-$ It initializes $`$max$\_$substring$`$ to store the longest increasing substring found so far and $`$current$\_$substring$`$ to track the current increasing substring.

$-$ It iterates over the string, appending characters to $`$current$\_$substring$`$ if they are in increasing order compared to the previous character.

$-$ If a character is not in increasing order, it compares the length of $`$current$\_$substring$`$ with $`$max$\_$substring$`.$ If $`$current$\_$substring$`$ is longer, it updates $`$max$\_$substring$`.$

$-$ After the loop, it checks one final time to ensure the last $`$current$\_$substring$`$ is considered.

$2.$ Time Complexity:

$-$ The time complexity of this program is O$($n$),$ where n is the length of the string. The loop iterates over each character of the string exactly once, and all operations inside the loop $($comparison$,$ string concatenation$)$ are O$(1).$ Therefore, the overall time complexity is linear in relation to the input size.

Do you agree with this discussion? why or why not?