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 



var java.lang.String$lp$$rp$$Random$args254 : [int]ref;
var int$Random$index0 : int;


// 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);



	 //  @line: 2
// <AProVEMathRecursive: void main(java.lang.String[])>
procedure void$AProVEMathRecursive$main$2229($param_0 : [int]ref)
  modifies java.lang.String$lp$$rp$$Random$args254, $stringSize;
 {
var i16 : int;
var i04 : int;
var r02 : [int]ref;

 //temp local variables 
var $freshlocal0 : int;

Block17:
	r02 := $param_0;
	 //  @line: 3
	java.lang.String$lp$$rp$$Random$args254 := r02;
	 //  @line: 4
	 call i04 := int$Random$random$2232();
	 //  @line: 5
	 call i16 := int$Random$random$2232();
	 //  @line: 6
	 call $freshlocal0 := int$AProVEMathRecursive$power$2230((i04), (i16));
	 return;
}


// 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)
}


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



// 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: 5
// <Random: int random()>
procedure int$Random$random$2232() returns (__ret : int)
  modifies $stringSize, int$Random$index0;
 {
var $i529 : int;
var $r121 : [int]ref;
var $i428 : int;
var $i327 : int;
var $i022 : int;
var $i123 : int;
var $r225 : [int]ref;
var $i224 : int;
var r026 : ref;
	 //  @line: 6
Block37:
	 //  @line: 6
	$r121 := java.lang.String$lp$$rp$$Random$args254;
	 //  @line: 6
	$i123 := $refArrSize[$r121[$arrSizeIdx]];
	 //  @line: 6
	$i022 := int$Random$index0;
	 goto Block38;
	 //  @line: 6
Block38:
	 goto Block39, Block41;
	 //  @line: 6
Block39:
	 assume ($gtint(($i123), ($i022))==1);
	 goto Block40;
	 //  @line: 6
Block41:
	 //  @line: 6
	 assume ($negInt(($gtint(($i123), ($i022))))==1);
	 //  @line: 7
	__ret := 0;
	 return;
	 //  @line: 9
Block40:
	 //  @line: 9
	$r225 := java.lang.String$lp$$rp$$Random$args254;
	 goto Block42;
	 //  @line: 9
Block42:
	 //  @line: 9
	$i224 := int$Random$index0;
	 assert ($geint(($i224), (0))==1);
	 assert ($ltint(($i224), ($refArrSize[$r225[$arrSizeIdx]]))==1);
	 //  @line: 9
	r026 := $r225[$i224];
	 //  @line: 10
	$i327 := int$Random$index0;
	 //  @line: 10
	$i428 := $addint(($i327), (1));
	 //  @line: 10
	int$Random$index0 := $i428;
	 goto Block43;
	 //  @line: 11
Block43:
	 goto Block46, Block44;
	 //  @line: 11
Block46:
	 //  @line: 11
	 assume ($negInt(($neref((r026), ($null))))==1);
	 //  @line: 12
	__ret := 0;
	 return;
	 //  @line: 11
Block44:
	 assume ($neref((r026), ($null))==1);
	 goto Block45;
	 //  @line: 14
Block45:
	$i529 := $stringSize[r026];
	 goto Block47;
	 //  @line: 14
Block47:
	 //  @line: 14
	__ret := $i529;
	 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);



	 //  @line: 2
// <Random: void <clinit>()>
procedure void$Random$$la$clinit$ra$$2233()
  modifies int$Random$index0;
 {
	 //  @line: 3
Block48:
	 //  @line: 3
	int$Random$index0 := 0;
	 return;
}


// 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
}


// 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);



// <Random: void <init>()>
procedure void$Random$$la$init$ra$$2231(__this : ref)  requires ($neref((__this), ($null))==1);
 {
var r020 : ref;
Block36:
	r020 := __this;
	 assert ($neref((r020), ($null))==1);
	 //  @line: 1
	 call void$java.lang.Object$$la$init$ra$$28((r020));
	 return;
}


// 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);



// 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);



// 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
}


	 //  @line: 9
// <AProVEMathRecursive: int power(int,int)>
procedure int$AProVEMathRecursive$power$2230($param_0 : int, $param_1 : int) returns (__ret : int) {
var $i1019 : int;
var $i615 : int;
var i18 : int;
var $i817 : int;
var $i514 : int;
var i213 : int;
var $i918 : int;
var $i716 : int;
var i09 : int;
var $i310 : int;
var $i411 : int;
Block18:
	i09 := $param_0;
	i18 := $param_1;
	 goto Block19;
	 //  @line: 10
Block19:
	 goto Block20, Block22;
	 //  @line: 10
Block20:
	 assume ($gtint((i18), (0))==1);
	 goto Block21;
	 //  @line: 10
Block22:
	 //  @line: 10
	 assume ($negInt(($gtint((i18), (0))))==1);
	 //  @line: 11
	__ret := 1;
	 return;
	 //  @line: 12
Block21:
	 goto Block25, Block23;
	 //  @line: 12
Block25:
	 //  @line: 12
	 assume ($negInt(($neint((i18), (1))))==1);
	 goto Block26;
	 //  @line: 12
Block23:
	 assume ($neint((i18), (1))==1);
	 goto Block24;
	 //  @line: 13
Block26:
	 //  @line: 13
	__ret := i09;
	 return;
	 //  @line: 14
Block24:
	 goto Block27, Block29;
	 //  @line: 14
Block27:
	 assume ($neint((i09), (2))==1);
	 goto Block28;
	 //  @line: 14
Block29:
	 //  @line: 14
	 assume ($negInt(($neint((i09), (2))))==1);
	 goto Block30;
	 //  @line: 16
Block28:
	 //  @line: 16
	$i310 := $modint((i18), (2));
	 goto Block31;
	 //  @line: 15
Block30:
	 //  @line: 15
	$i918 := $subint((i18), (1));
	 //  @line: 15
	$i1019 := $shlint((i09), ($i918));
	 //  @line: 15
	__ret := $i1019;
	 return;
	 //  @line: 16
Block31:
	 goto Block32, Block34;
	 //  @line: 16
Block32:
	 assume ($neint(($i310), (1))==1);
	 goto Block33;
	 //  @line: 16
Block34:
	 //  @line: 16
	 assume ($negInt(($neint(($i310), (1))))==1);
	 //  @line: 17
	$i615 := $subint((i18), (1));
	 //  @line: 17
	 call $i716 := int$AProVEMathRecursive$power$2230((i09), ($i615));
	 //  @line: 17
	$i817 := $mulint((i09), ($i716));
	 //  @line: 17
	__ret := $i817;
	 return;
	 //  @line: 19
Block33:
	 assert ($neint((2), (0))==1);
	 //  @line: 19
	$i411 := $divint((i18), (2));
	 goto Block35;
	 //  @line: 19
Block35:
	 //  @line: 19
	 call i213 := int$AProVEMathRecursive$power$2230((i09), ($i411));
	 //  @line: 20
	$i514 := $mulint((i213), (i213));
	 //  @line: 20
	__ret := $i514;
	 return;
}


// 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);



// <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} $eqref(x : ref, y : ref) returns (__ret : int) {
if (x == y) then 1 else 0
}


// <AProVEMathRecursive: void <init>()>
procedure void$AProVEMathRecursive$$la$init$ra$$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} $cmpint(x : int, y : int) returns (__ret : int) {
if (x < y) then 1 else if (x == y) then 0 else -1
}


// 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)
}