type ref;
type realVar;
type classConst;
// type Field x;
// var $HeapVar : <x>[ref, Field x]x;

const unique $null : ref ;
const unique $intArrNull : [int]int ;
const unique $realArrNull : [int]realVar ;
const unique $refArrNull : [int]ref ;

const unique $arrSizeIdx : int;
var $intArrSize : [int]int;
var $realArrSize : [realVar]int;
var $refArrSize : [ref]int;

var $stringSize : [ref]int;

//built-in axioms 
axiom ($arrSizeIdx == -1);

//note: new version doesn't put helpers in the perlude anymore//Prelude finished 





// procedure is generated by joogie.
function {:inline true} $neref(x : ref, y : ref) returns (__ret : int) {
if (x != y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $realarrtoref($param00 : [int]realVar) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $modreal($param00 : realVar, $param11 : realVar) returns (__ret : realVar);



// procedure is generated by joogie.
function {:inline true} $leref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $modint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $gtref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $eqrealarray($param00 : [int]realVar, $param11 : [int]realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $addint(x : int, y : int) returns (__ret : int) {
(x + y)
}


	 //  @line: 17
// <TimesPlusUserDef: int plus(int,int)>
procedure int$TimesPlusUserDef$plus$2231($param_0 : int, $param_1 : int) returns (__ret : int) {
var $i724 : int;
var $i521 : int;
var $i623 : int;
var $i420 : int;
var i016 : int;
var i115 : int;
var $i319 : int;
var $i217 : int;
Block27:
	i016 := $param_0;
	i115 := $param_1;
	 goto Block28;
	 //  @line: 18
Block28:
	 goto Block29, Block31;
	 //  @line: 18
Block29:
	 assume ($leint((i115), (0))==1);
	 goto Block30;
	 //  @line: 18
Block31:
	 //  @line: 18
	 assume ($negInt(($leint((i115), (0))))==1);
	 //  @line: 19
	$i521 := $subint((i115), (1));
	 //  @line: 19
	 call $i623 := int$TimesPlusUserDef$plus$2231((i016), ($i521));
	 //  @line: 19
	$i724 := $addint((1), ($i623));
	 //  @line: 19
	__ret := $i724;
	 return;
	 //  @line: 20
Block30:
	 goto Block32, Block34;
	 //  @line: 20
Block32:
	 assume ($leint((i016), (0))==1);
	 goto Block33;
	 //  @line: 20
Block34:
	 //  @line: 20
	 assume ($negInt(($leint((i016), (0))))==1);
	 goto Block35;
	 //  @line: 23
Block33:
	 //  @line: 23
	__ret := 0;
	 return;
	 //  @line: 21
Block35:
	 //  @line: 21
	$i217 := $subint((i016), (1));
	 //  @line: 21
	 call $i319 := int$TimesPlusUserDef$plus$2231(($i217), (i115));
	 //  @line: 21
	$i420 := $addint((1), ($i319));
	 //  @line: 21
	__ret := $i420;
	 return;
}


// procedure is generated by joogie.
function {:inline true} $subref($param00 : ref, $param11 : ref) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $inttoreal($param00 : int) returns (__ret : realVar);



// procedure is generated by joogie.
function {:inline true} $shrint($param00 : int, $param11 : int) returns (__ret : int);



	 //  @line: 3
// <TimesPlusUserDef: void main(java.lang.String[])>
procedure void$TimesPlusUserDef$main$2229($param_0 : [int]ref)
  modifies $stringSize;
 {
var i05 : int;
var $r26 : ref;
var r02 : [int]ref;
var $r13 : ref;
var i18 : int;

 //temp local variables 
var $freshlocal0 : int;

Block17:
	r02 := $param_0;
	 assert ($geint((0), (0))==1);
	 assert ($ltint((0), ($refArrSize[r02[$arrSizeIdx]]))==1);
	 //  @line: 4
	$r13 := r02[0];
	i05 := $stringSize[$r13];
	 assert ($geint((1), (0))==1);
	 assert ($ltint((1), ($refArrSize[r02[$arrSizeIdx]]))==1);
	 //  @line: 5
	$r26 := r02[1];
	i18 := $stringSize[$r26];
	 //  @line: 6
	 call $freshlocal0 := int$TimesPlusUserDef$times$2230((i05), (i18));
	 return;
}


// procedure is generated by joogie.
function {:inline true} $negReal($param00 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $ushrint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $refarrtoref($param00 : [int]ref) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $divref($param00 : ref, $param11 : ref) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $mulref($param00 : ref, $param11 : ref) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $neint(x : int, y : int) returns (__ret : int) {
if (x != y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $ltreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $reftorefarr($param00 : ref) returns (__ret : [int]ref);



// procedure is generated by joogie.
function {:inline true} $gtint(x : int, y : int) returns (__ret : int) {
if (x > y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $reftoint($param00 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $addref($param00 : ref, $param11 : ref) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $xorreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $andref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $cmpreal(x : realVar, y : realVar) returns (__ret : int) {
if ($ltreal((x), (y)) == 1) then 1 else if ($eqreal((x), (y)) == 1) then 0 else -1
}


// <TimesPlusUserDef: void <init>()>
procedure void$TimesPlusUserDef$$la$init$ra$$2228(__this : ref)  requires ($neref((__this), ($null))==1);
 {
var r01 : ref;
Block16:
	r01 := __this;
	 assert ($neref((r01), ($null))==1);
	 //  @line: 1
	 call void$java.lang.Object$$la$init$ra$$28((r01));
	 return;
}


// procedure is generated by joogie.
function {:inline true} $addreal($param00 : realVar, $param11 : realVar) returns (__ret : realVar);



// procedure is generated by joogie.
function {:inline true} $gtreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $eqreal(x : realVar, y : realVar) returns (__ret : int) {
if (x == y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $ltint(x : int, y : int) returns (__ret : int) {
if (x < y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $newvariable($param00 : int) returns (__ret : ref);



// <java.lang.Object: void <init>()>
procedure void$java.lang.Object$$la$init$ra$$28(__this : ref);



// procedure is generated by joogie.
function {:inline true} $divint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $geint(x : int, y : int) returns (__ret : int) {
if (x >= y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $mulint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $leint(x : int, y : int) returns (__ret : int) {
if (x <= y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $shlref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $eqrefarray($param00 : [int]ref, $param11 : [int]ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $reftointarr($param00 : ref) returns (__ret : [int]int);



// procedure is generated by joogie.
function {:inline true} $ltref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $mulreal($param00 : realVar, $param11 : realVar) returns (__ret : realVar);



	 //  @line: 9
// <TimesPlusUserDef: int times(int,int)>
procedure int$TimesPlusUserDef$times$2230($param_0 : int, $param_1 : int) returns (__ret : int) {
var $i313 : int;
var i011 : int;
var $i414 : int;
var $i212 : int;
var i110 : int;
Block18:
	i011 := $param_0;
	i110 := $param_1;
	 goto Block19;
	 //  @line: 10
Block19:
	 goto Block22, Block20;
	 //  @line: 10
Block22:
	 //  @line: 10
	 assume ($negInt(($neint((i110), (0))))==1);
	 //  @line: 11
	__ret := 0;
	 return;
	 //  @line: 10
Block20:
	 assume ($neint((i110), (0))==1);
	 goto Block21;
	 //  @line: 12
Block21:
	 goto Block23, Block25;
	 //  @line: 12
Block23:
	 assume ($leint((i110), (0))==1);
	 goto Block24;
	 //  @line: 12
Block25:
	 //  @line: 12
	 assume ($negInt(($leint((i110), (0))))==1);
	 goto Block26;
	 //  @line: 14
Block24:
	 //  @line: 14
	__ret := 0;
	 return;
	 //  @line: 13
Block26:
	 //  @line: 13
	$i212 := $subint((i110), (1));
	 //  @line: 13
	 call $i313 := int$TimesPlusUserDef$times$2230((i011), ($i212));
	 //  @line: 13
	 call $i414 := int$TimesPlusUserDef$plus$2231(($i313), (i011));
	 //  @line: 13
	__ret := $i414;
	 return;
}


// procedure is generated by joogie.
function {:inline true} $shrref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $ushrreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $shrreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $divreal($param00 : realVar, $param11 : realVar) returns (__ret : realVar);



// procedure is generated by joogie.
function {:inline true} $orint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $reftorealarr($param00 : ref) returns (__ret : [int]realVar);



// procedure is generated by joogie.
function {:inline true} $cmpref(x : ref, y : ref) returns (__ret : int) {
if ($ltref((x), (y)) == 1) then 1 else if ($eqref((x), (y)) == 1) then 0 else -1
}


// procedure is generated by joogie.
function {:inline true} $realtoint($param00 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $geref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $orreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $eqint(x : int, y : int) returns (__ret : int) {
if (x == y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $ushrref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $modref($param00 : ref, $param11 : ref) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $eqintarray($param00 : [int]int, $param11 : [int]int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $negRef($param00 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $lereal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $nereal(x : realVar, y : realVar) returns (__ret : int) {
if (x != y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $instanceof($param00 : ref, $param11 : classConst) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $xorref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $orref($param00 : ref, $param11 : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $intarrtoref($param00 : [int]int) returns (__ret : ref);



// procedure is generated by joogie.
function {:inline true} $subreal($param00 : realVar, $param11 : realVar) returns (__ret : realVar);



// procedure is generated by joogie.
function {:inline true} $shlreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $negInt(x : int) returns (__ret : int) {
if (x == 0) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $gereal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $eqref(x : ref, y : ref) returns (__ret : int) {
if (x == y) then 1 else 0
}


// procedure is generated by joogie.
function {:inline true} $cmpint(x : int, y : int) returns (__ret : int) {
if (x < y) then 1 else if (x == y) then 0 else -1
}


// <java.lang.String: int length()>
procedure int$java.lang.String$length$59(__this : ref) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $andint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $andreal($param00 : realVar, $param11 : realVar) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $shlint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $xorint($param00 : int, $param11 : int) returns (__ret : int);



// procedure is generated by joogie.
function {:inline true} $subint(x : int, y : int) returns (__ret : int) {
(x - y)
}