FMI V1

halting.tex

\begin{lstlisting}[mathescape=true]
$\Pi'$($\Pi$, I) = {
  // from ex. 1: $\Pi$ may not halt $\Rightarrow$ (c)
  var result = call $\Pi$(I);
  
  // == is an operator, not a function call
  return (result == I + I);
}
\end{lstlisting}

N-SORTED-ELEMENTS.js

/**
 * N-SORTED-ELEMENTS
 * INSTANCE: A non-empty list L = (e1 , . . . , en ) of non-negative integers.
 * QUESTION: Does the list L contain a sub-list of k consecutive sorted numbers
 *           in ascending order (from left to right)?
 */

include("ringo/term");
include("ringo/shell");

var size     = parseInt(readln("Enter size of list: "), 10);
var k        = parseInt(readln("Enter k: "), 10);
var numRange = parseInt(readln("Enter numRange: "), 10);

var list = [];

for (var i = 0; i < size; i++) {
   list.push(Math.floor(Math.random() * numRange));
}

writeln("k: " + k);
writeln("List: " + list);

// The FMI relevant code starts here
var N_SORTED_ELEMENTS = function(list, k) {
   var ascCounter = 0;
   for (var i = 0; i < size - 1; i++) {
   
      writeln("Comparing: list[" + i + "] :: list[" + (i + 1) + "] --> " + list[i] + " :: " + list[i + 1]);
   
      if (list[i + 1] - list[i] === 1) {
         ascCounter ++;
         
         writeln("  << ASC >> ascCounter++ to " + ascCounter);
         
         // Check if the number of consecutive is fulfilled
         // Positive Instance!
         if (ascCounter >= (k - 1)) {
            return true;
         }
         
      } else {
         ascCounter = 0;
      }
   }

   // Negative Instance
   return false;
};

writeln((N_SORTED_ELEMENTS(list, k) ? "YES" : "NO"));