/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


termination of the given Bare JBC problem could be proven:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 1245 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 3 ms]
(6) AND
    (7) JBCTerminationSCC
        (8) SCCToIRSProof [SOUND, 114 ms]
        (9) IRSwT
        (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (11) IRSwT
        (12) IRSwTTerminationDigraphProof [EQUIVALENT, 18 ms]
        (13) IRSwT
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IRSwT
        (16) TempFilterProof [SOUND, 59 ms]
        (17) IntTRS
        (18) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (19) IntTRS
        (20) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) JBCTerminationSCC
        (23) SCCToIRSProof [SOUND, 54 ms]
        (24) IRSwT
        (25) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (26) IRSwT
        (27) IRSwTTerminationDigraphProof [EQUIVALENT, 21 ms]
        (28) IRSwT
        (29) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (30) IRSwT
        (31) TempFilterProof [SOUND, 49 ms]
        (32) IntTRS
        (33) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (34) AND
            (35) IntTRS
                (36) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
                (37) YES
            (38) IntTRS
                (39) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
                (40) YES


----------------------------------------

(0)
Obligation:
need to prove termination of the following program:
class Curseur{
	private int X=0, Y=0, maxX, maxY;
	private boolean torique=false;

	public Curseur(int maxX, int maxY, boolean espaceTorique){
		super();
		this.maxX=maxX;
		this.maxY=maxY;
		this.torique=espaceTorique;		
	}

	public void centrer(){
		
			int cX=maxX/2;
			int cY=maxY/2;
			X=cX;
			Y=cY;
		
	}

	public void haut(){

			Y--;
			if(torique&&Y<0) Y=maxY-1;
	}

	public void bas(){
			Y++;
			if(torique&&Y==maxY) Y=0;
	}

	public void droite(){
			X++;
			if(torique&&X==maxX) X=0;
	}

	public void gauche(){
			X--;
			if(torique&&X<0) X=maxX-1;
	}

	public int getX(){
			return X;
	}

	public int getY(){
			return Y;
	}
	
	public void imprimer(){
	    //System.out.println("Curseur@["+getX()+","+getY()+"]");
	}
}

public class Carre {

	private Curseur curseur=null;
	private int cote=0;

	public Carre(int cote){
		if(cote>1&cote%2==1){
			this.cote=cote; 
		}else{
		    //System.out.println("Cette classe ne genere pas les carres magiques d\'ordre pair.");
		    //System.exit(0);
		}
		this.curseur=new Curseur(cote,cote,true);
	}
	
	private int [][] carre=null;

	public void init(){
		carre=new int[cote][cote];
		int n=0;
		for(int x=0;x<3;x++) for(int y=0;y<3;y++) carre[x][y]=0;
		curseur.centrer();
	}

	public void peupler(){
		curseur.bas();
		int nbre=1;
		int cpteur=1;
		while(cpteur<3){			
			if(!ajouter(nbre,curseur.getX(),curseur.getY())){
				curseur.bas();
				curseur.gauche();
				cpteur++;
			}else{
				cpteur=1;
				curseur.bas();
				curseur.droite();
				nbre++;
			}
		}
	}

	public Curseur curseur(){
		return curseur;
	}

	public int cote(){
		return cote;
	}

	public boolean ajouter(int nombre, int X, int Y){
		if(carre[X][Y]!=0) return false; 
		carre[X][Y]=nombre;
		return true;
	}

	public void imprimer(){
		for(int j=0;j<cote;j++){
			for(int i=0;i<cote;i++){
			    //System.out.print(carre[i][j]+"\t");
			}
			//System.out.println();
		}
	}

	public static void main(String args[]){
	    Random.args = args;
	    Carre carre=new Carre(2*Random.random()+1);
	    carre.init();
	    //carre.peupler();
	    carre.imprimer();
	}
    
}

public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
      if (index >= args.length)
	  return 0;

      String string = args[index];
      index++;
      return string.length();
  }
}



----------------------------------------

(1) BareJBCToJBCProof (EQUIVALENT)
initialized classpath
----------------------------------------

(2)
Obligation:
need to prove termination of the following program:
class Curseur{
	private int X=0, Y=0, maxX, maxY;
	private boolean torique=false;

	public Curseur(int maxX, int maxY, boolean espaceTorique){
		super();
		this.maxX=maxX;
		this.maxY=maxY;
		this.torique=espaceTorique;		
	}

	public void centrer(){
		
			int cX=maxX/2;
			int cY=maxY/2;
			X=cX;
			Y=cY;
		
	}

	public void haut(){

			Y--;
			if(torique&&Y<0) Y=maxY-1;
	}

	public void bas(){
			Y++;
			if(torique&&Y==maxY) Y=0;
	}

	public void droite(){
			X++;
			if(torique&&X==maxX) X=0;
	}

	public void gauche(){
			X--;
			if(torique&&X<0) X=maxX-1;
	}

	public int getX(){
			return X;
	}

	public int getY(){
			return Y;
	}
	
	public void imprimer(){
	    //System.out.println("Curseur@["+getX()+","+getY()+"]");
	}
}

public class Carre {

	private Curseur curseur=null;
	private int cote=0;

	public Carre(int cote){
		if(cote>1&cote%2==1){
			this.cote=cote; 
		}else{
		    //System.out.println("Cette classe ne genere pas les carres magiques d\'ordre pair.");
		    //System.exit(0);
		}
		this.curseur=new Curseur(cote,cote,true);
	}
	
	private int [][] carre=null;

	public void init(){
		carre=new int[cote][cote];
		int n=0;
		for(int x=0;x<3;x++) for(int y=0;y<3;y++) carre[x][y]=0;
		curseur.centrer();
	}

	public void peupler(){
		curseur.bas();
		int nbre=1;
		int cpteur=1;
		while(cpteur<3){			
			if(!ajouter(nbre,curseur.getX(),curseur.getY())){
				curseur.bas();
				curseur.gauche();
				cpteur++;
			}else{
				cpteur=1;
				curseur.bas();
				curseur.droite();
				nbre++;
			}
		}
	}

	public Curseur curseur(){
		return curseur;
	}

	public int cote(){
		return cote;
	}

	public boolean ajouter(int nombre, int X, int Y){
		if(carre[X][Y]!=0) return false; 
		carre[X][Y]=nombre;
		return true;
	}

	public void imprimer(){
		for(int j=0;j<cote;j++){
			for(int i=0;i<cote;i++){
			    //System.out.print(carre[i][j]+"\t");
			}
			//System.out.println();
		}
	}

	public static void main(String args[]){
	    Random.args = args;
	    Carre carre=new Carre(2*Random.random()+1);
	    carre.init();
	    //carre.peupler();
	    carre.imprimer();
	}
    
}

public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
      if (index >= args.length)
	  return 0;

      String string = args[index];
      index++;
      return string.length();
  }
}



----------------------------------------

(3) JBCToGraph (EQUIVALENT)
Constructed TerminationGraph.
----------------------------------------

(4)
Obligation:
Termination Graph based on JBC Program:
Carre.main([Ljava/lang/String;)V: Graph of 630 nodes with 2 SCCs.





----------------------------------------

(5) TerminationGraphToSCCProof (SOUND)
Splitted TerminationGraph to 2 SCCss.
----------------------------------------

(6)
Complex Obligation (AND)

----------------------------------------

(7)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: Carre.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*Carre: [cote]
*Marker field analysis yielded the following relations that could be markers:

----------------------------------------

(8) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 23 IRulesP rules:
f4393_0_imprimer_Load(EOS(STATIC_4393), java.lang.Object(Carre(EOC, i31)), i488, i488) -> f4394_0_imprimer_FieldAccess(EOS(STATIC_4394), java.lang.Object(Carre(EOC, i31)), i488, i488, java.lang.Object(Carre(EOC, i31))) :|: TRUE
f4394_0_imprimer_FieldAccess(EOS(STATIC_4394), java.lang.Object(Carre(EOC, i31)), i488, i488, java.lang.Object(Carre(EOC, i31))) -> f4395_0_imprimer_GE(EOS(STATIC_4395), java.lang.Object(Carre(EOC, i31)), i488, i488, i31) :|: TRUE
f4395_0_imprimer_GE(EOS(STATIC_4395), java.lang.Object(Carre(EOC, i31)), i488, i488, i31) -> f4397_0_imprimer_GE(EOS(STATIC_4397), java.lang.Object(Carre(EOC, i31)), i488, i488, i31) :|: i488 < i31
f4397_0_imprimer_GE(EOS(STATIC_4397), java.lang.Object(Carre(EOC, i31)), i488, i488, i31) -> f4399_0_imprimer_ConstantStackPush(EOS(STATIC_4399), java.lang.Object(Carre(EOC, i31)), i488) :|: i488 < i31
f4399_0_imprimer_ConstantStackPush(EOS(STATIC_4399), java.lang.Object(Carre(EOC, i31)), i488) -> f4401_0_imprimer_Store(EOS(STATIC_4401), java.lang.Object(Carre(EOC, i31)), i488, 0) :|: TRUE
f4401_0_imprimer_Store(EOS(STATIC_4401), java.lang.Object(Carre(EOC, i31)), i488, matching1) -> f4403_0_imprimer_Load(EOS(STATIC_4403), java.lang.Object(Carre(EOC, i31)), i488, 0) :|: TRUE && matching1 = 0
f4403_0_imprimer_Load(EOS(STATIC_4403), java.lang.Object(Carre(EOC, i31)), i488, matching1) -> f4410_0_imprimer_Load(EOS(STATIC_4410), java.lang.Object(Carre(EOC, i31)), i488, 0) :|: TRUE && matching1 = 0
f4410_0_imprimer_Load(EOS(STATIC_4410), java.lang.Object(Carre(EOC, i31)), i488, i490) -> f4417_0_imprimer_Load(EOS(STATIC_4417), java.lang.Object(Carre(EOC, i31)), i488, i490) :|: TRUE
f4417_0_imprimer_Load(EOS(STATIC_4417), java.lang.Object(Carre(EOC, i31)), i488, i493) -> f4429_0_imprimer_Load(EOS(STATIC_4429), java.lang.Object(Carre(EOC, i31)), i488, i493) :|: TRUE
f4429_0_imprimer_Load(EOS(STATIC_4429), java.lang.Object(Carre(EOC, i31)), i488, i498) -> f4430_0_imprimer_Load(EOS(STATIC_4430), java.lang.Object(Carre(EOC, i31)), i488, i498, i498) :|: TRUE
f4430_0_imprimer_Load(EOS(STATIC_4430), java.lang.Object(Carre(EOC, i31)), i488, i498, i498) -> f4431_0_imprimer_FieldAccess(EOS(STATIC_4431), java.lang.Object(Carre(EOC, i31)), i488, i498, i498, java.lang.Object(Carre(EOC, i31))) :|: TRUE
f4431_0_imprimer_FieldAccess(EOS(STATIC_4431), java.lang.Object(Carre(EOC, i31)), i488, i498, i498, java.lang.Object(Carre(EOC, i31))) -> f4432_0_imprimer_GE(EOS(STATIC_4432), java.lang.Object(Carre(EOC, i31)), i488, i498, i498, i31) :|: TRUE
f4432_0_imprimer_GE(EOS(STATIC_4432), java.lang.Object(Carre(EOC, i31)), i488, i498, i498, i31) -> f4433_0_imprimer_GE(EOS(STATIC_4433), java.lang.Object(Carre(EOC, i31)), i488, i498, i498, i31) :|: i498 >= i31
f4432_0_imprimer_GE(EOS(STATIC_4432), java.lang.Object(Carre(EOC, i31)), i488, i498, i498, i31) -> f4434_0_imprimer_GE(EOS(STATIC_4434), java.lang.Object(Carre(EOC, i31)), i488, i498, i498, i31) :|: i498 < i31
f4433_0_imprimer_GE(EOS(STATIC_4433), java.lang.Object(Carre(EOC, i31)), i488, i498, i498, i31) -> f4435_0_imprimer_Inc(EOS(STATIC_4435), java.lang.Object(Carre(EOC, i31)), i488) :|: i498 >= i31
f4435_0_imprimer_Inc(EOS(STATIC_4435), java.lang.Object(Carre(EOC, i31)), i488) -> f4437_0_imprimer_JMP(EOS(STATIC_4437), java.lang.Object(Carre(EOC, i31)), i488 + 1) :|: TRUE
f4437_0_imprimer_JMP(EOS(STATIC_4437), java.lang.Object(Carre(EOC, i31)), i500) -> f4439_0_imprimer_Load(EOS(STATIC_4439), java.lang.Object(Carre(EOC, i31)), i500) :|: TRUE
f4439_0_imprimer_Load(EOS(STATIC_4439), java.lang.Object(Carre(EOC, i31)), i500) -> f4392_0_imprimer_Load(EOS(STATIC_4392), java.lang.Object(Carre(EOC, i31)), i500) :|: TRUE
f4392_0_imprimer_Load(EOS(STATIC_4392), java.lang.Object(Carre(EOC, i31)), i488) -> f4393_0_imprimer_Load(EOS(STATIC_4393), java.lang.Object(Carre(EOC, i31)), i488, i488) :|: TRUE
f4434_0_imprimer_GE(EOS(STATIC_4434), java.lang.Object(Carre(EOC, i31)), i488, i498, i498, i31) -> f4436_0_imprimer_Inc(EOS(STATIC_4436), java.lang.Object(Carre(EOC, i31)), i488, i498) :|: i498 < i31
f4436_0_imprimer_Inc(EOS(STATIC_4436), java.lang.Object(Carre(EOC, i31)), i488, i498) -> f4438_0_imprimer_JMP(EOS(STATIC_4438), java.lang.Object(Carre(EOC, i31)), i488, i498 + 1) :|: TRUE
f4438_0_imprimer_JMP(EOS(STATIC_4438), java.lang.Object(Carre(EOC, i31)), i488, i501) -> f4440_0_imprimer_Load(EOS(STATIC_4440), java.lang.Object(Carre(EOC, i31)), i488, i501) :|: TRUE
f4440_0_imprimer_Load(EOS(STATIC_4440), java.lang.Object(Carre(EOC, i31)), i488, i501) -> f4429_0_imprimer_Load(EOS(STATIC_4429), java.lang.Object(Carre(EOC, i31)), i488, i501) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f4432_0_imprimer_GE(EOS(STATIC_4432), java.lang.Object(Carre(EOC, i31:0)), i488:0, i498:0, i498:0, i31:0) -> f4432_0_imprimer_GE(EOS(STATIC_4432), java.lang.Object(Carre(EOC, i31:0)), i488:0 + 1, 0, 0, i31:0) :|: i488:0 + 1 < i31:0 && i498:0 >= i31:0
f4432_0_imprimer_GE(EOS(STATIC_4432), java.lang.Object(Carre(EOC, i31:0)), i488:0, i498:0, i498:0, i31:0) -> f4432_0_imprimer_GE(EOS(STATIC_4432), java.lang.Object(Carre(EOC, i31:0)), i488:0, i498:0 + 1, i498:0 + 1, i31:0) :|: i498:0 < i31:0
Filtered constant ground arguments:
   f4432_0_imprimer_GE(x1, x2, x3, x4, x5, x6) -> f4432_0_imprimer_GE(x2, x3, x4, x5, x6)
   EOS(x1) -> EOS
   Carre(x1, x2) -> Carre(x2)
Filtered duplicate arguments:
   f4432_0_imprimer_GE(x1, x2, x3, x4, x5) -> f4432_0_imprimer_GE(x1, x2, x4, x5)
Finished conversion. Obtained 2 rules.P rules:
f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i488:0, i498:0, i31:0, i31:0) -> f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i488:0 + 1, 0, i31:0, i31:0) :|: i488:0 + 1 < i31:0 && i498:0 >= i31:0
f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i488:0, i498:0, i31:0, i31:0) -> f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i488:0, i498:0 + 1, i31:0, i31:0) :|: i498:0 < i31:0

----------------------------------------

(9)
Obligation:
Rules:
f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i488:0, i498:0, i31:0, i31:0) -> f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i488:0 + 1, 0, i31:0, i31:0) :|: i488:0 + 1 < i31:0 && i498:0 >= i31:0
f4432_0_imprimer_GE(java.lang.Object(Carre(x)), x1, x2, x, x) -> f4432_0_imprimer_GE(java.lang.Object(Carre(x)), x1, x2 + 1, x, x) :|: x2 < x

----------------------------------------

(10) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(11)
Obligation:
Rules:
f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i488:0, i498:0, i31:0, i31:0) -> f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0)), arith, 0, i31:0, i31:0) :|: i488:0 + 1 < i31:0 && i498:0 >= i31:0 && arith = i488:0 + 1
f4432_0_imprimer_GE(java.lang.Object(Carre(x3)), x4, x5, x3, x3) -> f4432_0_imprimer_GE(java.lang.Object(Carre(x3)), x4, x6, x3, x3) :|: x5 < x3 && x6 = x5 + 1

----------------------------------------

(12) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i488:0, i498:0, i31:0, i31:0) -> f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0)), arith, 0, i31:0, i31:0) :|: i488:0 + 1 < i31:0 && i498:0 >= i31:0 && arith = i488:0 + 1
(2) f4432_0_imprimer_GE(java.lang.Object(Carre(x3)), x4, x5, x3, x3) -> f4432_0_imprimer_GE(java.lang.Object(Carre(x3)), x4, x6, x3, x3) :|: x5 < x3 && x6 = x5 + 1

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!
----------------------------------------

(13)
Obligation:

Termination digraph:
Nodes:
(1) f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i488:0, i498:0, i31:0, i31:0) -> f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0)), arith, 0, i31:0, i31:0) :|: i488:0 + 1 < i31:0 && i498:0 >= i31:0 && arith = i488:0 + 1
(2) f4432_0_imprimer_GE(java.lang.Object(Carre(x3)), x4, x5, x3, x3) -> f4432_0_imprimer_GE(java.lang.Object(Carre(x3)), x4, x6, x3, x3) :|: x5 < x3 && x6 = x5 + 1

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!

----------------------------------------

(14) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(15)
Obligation:
Rules:
f4432_0_imprimer_GE(java.lang.Object(Carre(x3:0)), x4:0, x5:0, x3:0, x3:0) -> f4432_0_imprimer_GE(java.lang.Object(Carre(x3:0)), x4:0, x5:0 + 1, x3:0, x3:0) :|: x5:0 < x3:0
f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0:0)), i488:0:0, i498:0:0, i31:0:0, i31:0:0) -> f4432_0_imprimer_GE(java.lang.Object(Carre(i31:0:0)), i488:0:0 + 1, 0, i31:0:0, i31:0:0) :|: i488:0:0 + 1 < i31:0:0 && i498:0:0 >= i31:0:0

----------------------------------------

(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f4432_0_imprimer_GE(VARIABLE, VARIABLE, VARIABLE, INTEGER, INTEGER)
java.lang.Object(VARIABLE)
Carre(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(17)
Obligation:
Rules:
f4432_0_imprimer_GE(c, x4:0, x5:0, x3:0, x3:0) -> f4432_0_imprimer_GE(c1, x4:0, c2, x3:0, x3:0) :|: c2 = x5:0 + 1 && (c1 = 0 && c = 0) && x5:0 < x3:0
f4432_0_imprimer_GE(c3, i488:0:0, i498:0:0, i31:0:0, i31:0:0) -> f4432_0_imprimer_GE(c4, c5, c6, i31:0:0, i31:0:0) :|: c6 = 0 && (c5 = i488:0:0 + 1 && (c4 = 0 && c3 = 0)) && (i488:0:0 + 1 < i31:0:0 && i498:0:0 >= i31:0:0)

----------------------------------------

(18) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4432_0_imprimer_GE(x, x1, x2, x3, x4)] = -1 + c*x - x1 + x4

The following rules are decreasing:
f4432_0_imprimer_GE(c3, i488:0:0, i498:0:0, i31:0:0, i31:0:0) -> f4432_0_imprimer_GE(c4, c5, c6, i31:0:0, i31:0:0) :|: c6 = 0 && (c5 = i488:0:0 + 1 && (c4 = 0 && c3 = 0)) && (i488:0:0 + 1 < i31:0:0 && i498:0:0 >= i31:0:0)
The following rules are bounded:
f4432_0_imprimer_GE(c3, i488:0:0, i498:0:0, i31:0:0, i31:0:0) -> f4432_0_imprimer_GE(c4, c5, c6, i31:0:0, i31:0:0) :|: c6 = 0 && (c5 = i488:0:0 + 1 && (c4 = 0 && c3 = 0)) && (i488:0:0 + 1 < i31:0:0 && i498:0:0 >= i31:0:0)

----------------------------------------

(19)
Obligation:
Rules:
f4432_0_imprimer_GE(c, x4:0, x5:0, x3:0, x3:0) -> f4432_0_imprimer_GE(c1, x4:0, c2, x3:0, x3:0) :|: c2 = x5:0 + 1 && (c1 = 0 && c = 0) && x5:0 < x3:0

----------------------------------------

(20) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f4432_0_imprimer_GE ] = -1*f4432_0_imprimer_GE_3 + f4432_0_imprimer_GE_5

The following rules are decreasing:
f4432_0_imprimer_GE(c, x4:0, x5:0, x3:0, x3:0) -> f4432_0_imprimer_GE(c1, x4:0, c2, x3:0, x3:0) :|: c2 = x5:0 + 1 && (c1 = 0 && c = 0) && x5:0 < x3:0

The following rules are bounded:
f4432_0_imprimer_GE(c, x4:0, x5:0, x3:0, x3:0) -> f4432_0_imprimer_GE(c1, x4:0, c2, x3:0, x3:0) :|: c2 = x5:0 + 1 && (c1 = 0 && c = 0) && x5:0 < x3:0


----------------------------------------

(21)
YES

----------------------------------------

(22)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: Carre.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*Carre: [carre]
*Marker field analysis yielded the following relations that could be markers:

----------------------------------------

(23) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 32 IRulesP rules:
f3883_0_init_ConstantStackPush(EOS(STATIC_3883), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i354, i354) -> f3894_0_init_GE(EOS(STATIC_3894), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i354, i354, 3) :|: TRUE
f3894_0_init_GE(EOS(STATIC_3894), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i369, matching1) -> f3898_0_init_GE(EOS(STATIC_3898), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i369, 3) :|: TRUE && matching1 = 3
f3898_0_init_GE(EOS(STATIC_3898), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i369, matching1) -> f3900_0_init_ConstantStackPush(EOS(STATIC_3900), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369) :|: i369 < 3 && matching1 = 3
f3900_0_init_ConstantStackPush(EOS(STATIC_3900), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369) -> f3902_0_init_Store(EOS(STATIC_3902), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, 0) :|: TRUE
f3902_0_init_Store(EOS(STATIC_3902), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, matching1) -> f3904_0_init_Load(EOS(STATIC_3904), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, 0) :|: TRUE && matching1 = 0
f3904_0_init_Load(EOS(STATIC_3904), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, matching1) -> f4076_0_init_Load(EOS(STATIC_4076), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, 0) :|: TRUE && matching1 = 0
f4076_0_init_Load(EOS(STATIC_4076), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i387) -> f4179_0_init_Load(EOS(STATIC_4179), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i387) :|: TRUE
f4179_0_init_Load(EOS(STATIC_4179), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i412) -> f4227_0_init_Load(EOS(STATIC_4227), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i412) :|: TRUE
f4227_0_init_Load(EOS(STATIC_4227), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i438) -> f4230_0_init_ConstantStackPush(EOS(STATIC_4230), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i438, i438) :|: TRUE
f4230_0_init_ConstantStackPush(EOS(STATIC_4230), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i438, i438) -> f4233_0_init_GE(EOS(STATIC_4233), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i438, i438, 3) :|: TRUE
f4233_0_init_GE(EOS(STATIC_4233), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, i458, matching1) -> f4236_0_init_GE(EOS(STATIC_4236), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, i458, 3) :|: TRUE && matching1 = 3
f4233_0_init_GE(EOS(STATIC_4233), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i459, i459, matching1) -> f4237_0_init_GE(EOS(STATIC_4237), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i459, i459, 3) :|: TRUE && matching1 = 3
f4236_0_init_GE(EOS(STATIC_4236), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, i458, matching1) -> f4239_0_init_Load(EOS(STATIC_4239), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458) :|: i458 < 3 && matching1 = 3
f4239_0_init_Load(EOS(STATIC_4239), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458) -> f4242_0_init_FieldAccess(EOS(STATIC_4242), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31))))) :|: TRUE
f4242_0_init_FieldAccess(EOS(STATIC_4242), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31))))) -> f4245_0_init_Load(EOS(STATIC_4245), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(ARRAY(i31))) :|: TRUE
f4245_0_init_Load(EOS(STATIC_4245), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(ARRAY(i31))) -> f4248_0_init_ArrayAccess(EOS(STATIC_4248), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(ARRAY(i31)), i369) :|: TRUE
f4248_0_init_ArrayAccess(EOS(STATIC_4248), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(ARRAY(i31)), i369) -> f4250_0_init_ArrayAccess(EOS(STATIC_4250), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(ARRAY(i31)), i369) :|: TRUE
f4250_0_init_ArrayAccess(EOS(STATIC_4250), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(ARRAY(i31)), i369) -> f4253_0_init_Load(EOS(STATIC_4253), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, o1084) :|: i369 < i31
f4253_0_init_Load(EOS(STATIC_4253), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, o1084) -> f4256_0_init_ConstantStackPush(EOS(STATIC_4256), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, o1084, i458) :|: TRUE
f4256_0_init_ConstantStackPush(EOS(STATIC_4256), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, o1084, i458) -> f4258_0_init_ArrayAccess(EOS(STATIC_4258), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, o1084, i458, 0) :|: TRUE
f4258_0_init_ArrayAccess(EOS(STATIC_4258), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(o1090put), i458, matching1) -> f4261_0_init_ArrayAccess(EOS(STATIC_4261), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(o1090put), i458, 0) :|: TRUE && matching1 = 0
f4261_0_init_ArrayAccess(EOS(STATIC_4261), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(ARRAY(i469)), i458, matching1) -> f4265_0_init_ArrayAccess(EOS(STATIC_4265), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(ARRAY(i469)), i458, 0) :|: i469 >= 0 && matching1 = 0
f4265_0_init_ArrayAccess(EOS(STATIC_4265), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(ARRAY(i469)), i458, matching1) -> f4268_0_init_ArrayAccess(EOS(STATIC_4268), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(ARRAY(i469)), i458, 0) :|: TRUE && matching1 = 0
f4268_0_init_ArrayAccess(EOS(STATIC_4268), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458, java.lang.Object(ARRAY(i469)), i458, matching1) -> f4273_0_init_Inc(EOS(STATIC_4273), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458) :|: i458 < i469 && matching1 = 0
f4273_0_init_Inc(EOS(STATIC_4273), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458) -> f4278_0_init_JMP(EOS(STATIC_4278), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i458 + 1) :|: TRUE
f4278_0_init_JMP(EOS(STATIC_4278), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i472) -> f4281_0_init_Load(EOS(STATIC_4281), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i472) :|: TRUE
f4281_0_init_Load(EOS(STATIC_4281), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i472) -> f4227_0_init_Load(EOS(STATIC_4227), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i472) :|: TRUE
f4237_0_init_GE(EOS(STATIC_4237), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369, i459, i459, matching1) -> f4240_0_init_Inc(EOS(STATIC_4240), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369) :|: i459 >= 3 && matching1 = 3
f4240_0_init_Inc(EOS(STATIC_4240), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369) -> f4243_0_init_JMP(EOS(STATIC_4243), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i369 + 1) :|: TRUE
f4243_0_init_JMP(EOS(STATIC_4243), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i460) -> f4246_0_init_Load(EOS(STATIC_4246), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i460) :|: TRUE
f4246_0_init_Load(EOS(STATIC_4246), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i460) -> f3879_0_init_Load(EOS(STATIC_3879), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i460) :|: TRUE
f3879_0_init_Load(EOS(STATIC_3879), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i354) -> f3883_0_init_ConstantStackPush(EOS(STATIC_3883), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i354, i354) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f4233_0_init_GE(EOS(STATIC_4233), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), i369:0, i459:0, i459:0, 3) -> f4233_0_init_GE(EOS(STATIC_4233), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), i369:0 + 1, 0, 0, 3) :|: i459:0 > 2 && i369:0 < 2
f4233_0_init_GE(EOS(STATIC_4233), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), i369:0, i458:0, i458:0, 3) -> f4233_0_init_GE(EOS(STATIC_4233), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), i369:0, i458:0 + 1, i458:0 + 1, 3) :|: i458:0 < 3 && i369:0 < i31:0 && i469:0 > i458:0 && i469:0 > -1
Filtered constant ground arguments:
   f4233_0_init_GE(x1, x2, x3, x4, x5, x6, x7) -> f4233_0_init_GE(x2, x3, x4, x5, x6)
   EOS(x1) -> EOS
   Carre(x1, x2) -> Carre(x2)
Filtered duplicate arguments:
   f4233_0_init_GE(x1, x2, x3, x4, x5) -> f4233_0_init_GE(x2, x3, x5)
Finished conversion. Obtained 2 rules.P rules:
f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i369:0, i459:0, i31:0) -> f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i369:0 + 1, 0, i31:0) :|: i459:0 > 2 && i369:0 < 2
f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i369:0, i458:0, i31:0) -> f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i369:0, i458:0 + 1, i31:0) :|: i369:0 < i31:0 && i458:0 < 3 && i469:0 > -1 && i469:0 > i458:0

----------------------------------------

(24)
Obligation:
Rules:
f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i369:0, i459:0, i31:0) -> f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i369:0 + 1, 0, i31:0) :|: i459:0 > 2 && i369:0 < 2
f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x)))), x1, x2, x) -> f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x)))), x1, x2 + 1, x) :|: x1 < x && x2 < 3 && x3 > -1 && x3 > x2

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(25) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(26)
Obligation:
Rules:
f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i369:0, i459:0, i31:0) -> f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), arith, 0, i31:0) :|: i459:0 > 2 && i369:0 < 2 && arith = i369:0 + 1
f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x4)))), x5, x6, x4) -> f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x4)))), x5, x7, x4) :|: x5 < x4 && x6 < 3 && x8 > -1 && x8 > x6 && x7 = x6 + 1

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(27) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i369:0, i459:0, i31:0) -> f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), arith, 0, i31:0) :|: i459:0 > 2 && i369:0 < 2 && arith = i369:0 + 1
(2) f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x4)))), x5, x6, x4) -> f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x4)))), x5, x7, x4) :|: x5 < x4 && x6 < 3 && x8 > -1 && x8 > x6 && x7 = x6 + 1

Arcs:
(1) -> (2)
(2) -> (1), (2)

This digraph is fully evaluated!
----------------------------------------

(28)
Obligation:

Termination digraph:
Nodes:
(1) f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i369:0, i459:0, i31:0) -> f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), arith, 0, i31:0) :|: i459:0 > 2 && i369:0 < 2 && arith = i369:0 + 1
(2) f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x4)))), x5, x6, x4) -> f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x4)))), x5, x7, x4) :|: x5 < x4 && x6 < 3 && x8 > -1 && x8 > x6 && x7 = x6 + 1

Arcs:
(1) -> (2)
(2) -> (1), (2)

This digraph is fully evaluated!

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(29) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(30)
Obligation:
Rules:
f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0:0)))), i369:0:0, i459:0:0, i31:0:0) -> f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0:0)))), i369:0:0 + 1, 0, i31:0:0) :|: i459:0:0 > 2 && i369:0:0 < 2
f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x4:0)))), x5:0, x6:0, x4:0) -> f4233_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x4:0)))), x5:0, x6:0 + 1, x4:0) :|: x8:0 > -1 && x8:0 > x6:0 && x6:0 < 3 && x5:0 < x4:0

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(31) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f4233_0_init_GE(VARIABLE, INTEGER, VARIABLE, VARIABLE)
java.lang.Object(VARIABLE)
Carre(VARIABLE)
ARRAY(VARIABLE)
Replaced non-predefined constructor symbols by 0.
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(32)
Obligation:
Rules:
f4233_0_init_GE(c, i369:0:0, i459:0:0, i31:0:0) -> f4233_0_init_GE(c1, c2, c3, i31:0:0) :|: c3 = 0 && (c2 = i369:0:0 + 1 && (c1 = 0 && c = 0)) && (i459:0:0 > 2 && i369:0:0 < 2)
f4233_0_init_GE(c4, x5:0, x6:0, x4:0) -> f4233_0_init_GE(c5, x5:0, c6, x4:0) :|: c6 = x6:0 + 1 && (c5 = 0 && c4 = 0) && (x8:0 > -1 && x8:0 > x6:0 && x6:0 < 3 && x5:0 < x4:0)

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(33) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4233_0_init_GE(x, x1, x2, x3)] = c*x - x1 + x3

The following rules are decreasing:
f4233_0_init_GE(c, i369:0:0, i459:0:0, i31:0:0) -> f4233_0_init_GE(c1, c2, c3, i31:0:0) :|: c3 = 0 && (c2 = i369:0:0 + 1 && (c1 = 0 && c = 0)) && (i459:0:0 > 2 && i369:0:0 < 2)
The following rules are bounded:
f4233_0_init_GE(c4, x5:0, x6:0, x4:0) -> f4233_0_init_GE(c5, x5:0, c6, x4:0) :|: c6 = x6:0 + 1 && (c5 = 0 && c4 = 0) && (x8:0 > -1 && x8:0 > x6:0 && x6:0 < 3 && x5:0 < x4:0)

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(34)
Complex Obligation (AND)

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(35)
Obligation:
Rules:
f4233_0_init_GE(c4, x5:0, x6:0, x4:0) -> f4233_0_init_GE(c5, x5:0, c6, x4:0) :|: c6 = x6:0 + 1 && (c5 = 0 && c4 = 0) && (x8:0 > -1 && x8:0 > x6:0 && x6:0 < 3 && x5:0 < x4:0)

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(36) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4233_0_init_GE(x, x1, x2, x3)] = 2 + c*x - x2

The following rules are decreasing:
f4233_0_init_GE(c4, x5:0, x6:0, x4:0) -> f4233_0_init_GE(c5, x5:0, c6, x4:0) :|: c6 = x6:0 + 1 && (c5 = 0 && c4 = 0) && (x8:0 > -1 && x8:0 > x6:0 && x6:0 < 3 && x5:0 < x4:0)
The following rules are bounded:
f4233_0_init_GE(c4, x5:0, x6:0, x4:0) -> f4233_0_init_GE(c5, x5:0, c6, x4:0) :|: c6 = x6:0 + 1 && (c5 = 0 && c4 = 0) && (x8:0 > -1 && x8:0 > x6:0 && x6:0 < 3 && x5:0 < x4:0)

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(37)
YES

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(38)
Obligation:
Rules:
f4233_0_init_GE(c, i369:0:0, i459:0:0, i31:0:0) -> f4233_0_init_GE(c1, c2, c3, i31:0:0) :|: c3 = 0 && (c2 = i369:0:0 + 1 && (c1 = 0 && c = 0)) && (i459:0:0 > 2 && i369:0:0 < 2)

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(39) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4233_0_init_GE(x, x1, x2, x3)] = 1 + c*x - x1

The following rules are decreasing:
f4233_0_init_GE(c, i369:0:0, i459:0:0, i31:0:0) -> f4233_0_init_GE(c1, c2, c3, i31:0:0) :|: c3 = 0 && (c2 = i369:0:0 + 1 && (c1 = 0 && c = 0)) && (i459:0:0 > 2 && i369:0:0 < 2)
The following rules are bounded:
f4233_0_init_GE(c, i369:0:0, i459:0:0, i31:0:0) -> f4233_0_init_GE(c1, c2, c3, i31:0:0) :|: c3 = 0 && (c2 = i369:0:0 + 1 && (c1 = 0 && c = 0)) && (i459:0:0 > 2 && i369:0:0 < 2)

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(40)
YES