/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


termination of the given Bare JBC problem could be proven:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 97 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 1185 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) JBCTerminationSCC
        (8) SCCToIRSProof [SOUND, 4 ms]
        (9) IRSwT
        (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (11) IRSwT
        (12) IRSwTTerminationDigraphProof [EQUIVALENT, 38 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, 0 ms]
        (24) IRSwT
        (25) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (26) IRSwT
        (27) IRSwTTerminationDigraphProof [EQUIVALENT, 54 ms]
        (28) IRSwT
        (29) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (30) IRSwT
        (31) TempFilterProof [SOUND, 47 ms]
        (32) IntTRS
        (33) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (34) AND
            (35) IntTRS
                (36) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
                (37) YES
            (38) IntTRS
                (39) RankingReductionPairProof [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:
f4609_0_imprimer_Load(EOS(STATIC_4609), java.lang.Object(Carre(EOC, i31)), i497, i497) -> f4610_0_imprimer_FieldAccess(EOS(STATIC_4610), java.lang.Object(Carre(EOC, i31)), i497, i497, java.lang.Object(Carre(EOC, i31))) :|: TRUE
f4610_0_imprimer_FieldAccess(EOS(STATIC_4610), java.lang.Object(Carre(EOC, i31)), i497, i497, java.lang.Object(Carre(EOC, i31))) -> f4611_0_imprimer_GE(EOS(STATIC_4611), java.lang.Object(Carre(EOC, i31)), i497, i497, i31) :|: TRUE
f4611_0_imprimer_GE(EOS(STATIC_4611), java.lang.Object(Carre(EOC, i31)), i497, i497, i31) -> f4613_0_imprimer_GE(EOS(STATIC_4613), java.lang.Object(Carre(EOC, i31)), i497, i497, i31) :|: i497 < i31
f4613_0_imprimer_GE(EOS(STATIC_4613), java.lang.Object(Carre(EOC, i31)), i497, i497, i31) -> f4615_0_imprimer_ConstantStackPush(EOS(STATIC_4615), java.lang.Object(Carre(EOC, i31)), i497) :|: i497 < i31
f4615_0_imprimer_ConstantStackPush(EOS(STATIC_4615), java.lang.Object(Carre(EOC, i31)), i497) -> f4617_0_imprimer_Store(EOS(STATIC_4617), java.lang.Object(Carre(EOC, i31)), i497, 0) :|: TRUE
f4617_0_imprimer_Store(EOS(STATIC_4617), java.lang.Object(Carre(EOC, i31)), i497, matching1) -> f4619_0_imprimer_Load(EOS(STATIC_4619), java.lang.Object(Carre(EOC, i31)), i497, 0) :|: TRUE && matching1 = 0
f4619_0_imprimer_Load(EOS(STATIC_4619), java.lang.Object(Carre(EOC, i31)), i497, matching1) -> f4626_0_imprimer_Load(EOS(STATIC_4626), java.lang.Object(Carre(EOC, i31)), i497, 0) :|: TRUE && matching1 = 0
f4626_0_imprimer_Load(EOS(STATIC_4626), java.lang.Object(Carre(EOC, i31)), i497, i499) -> f4633_0_imprimer_Load(EOS(STATIC_4633), java.lang.Object(Carre(EOC, i31)), i497, i499) :|: TRUE
f4633_0_imprimer_Load(EOS(STATIC_4633), java.lang.Object(Carre(EOC, i31)), i497, i502) -> f4645_0_imprimer_Load(EOS(STATIC_4645), java.lang.Object(Carre(EOC, i31)), i497, i502) :|: TRUE
f4645_0_imprimer_Load(EOS(STATIC_4645), java.lang.Object(Carre(EOC, i31)), i497, i507) -> f4646_0_imprimer_Load(EOS(STATIC_4646), java.lang.Object(Carre(EOC, i31)), i497, i507, i507) :|: TRUE
f4646_0_imprimer_Load(EOS(STATIC_4646), java.lang.Object(Carre(EOC, i31)), i497, i507, i507) -> f4647_0_imprimer_FieldAccess(EOS(STATIC_4647), java.lang.Object(Carre(EOC, i31)), i497, i507, i507, java.lang.Object(Carre(EOC, i31))) :|: TRUE
f4647_0_imprimer_FieldAccess(EOS(STATIC_4647), java.lang.Object(Carre(EOC, i31)), i497, i507, i507, java.lang.Object(Carre(EOC, i31))) -> f4648_0_imprimer_GE(EOS(STATIC_4648), java.lang.Object(Carre(EOC, i31)), i497, i507, i507, i31) :|: TRUE
f4648_0_imprimer_GE(EOS(STATIC_4648), java.lang.Object(Carre(EOC, i31)), i497, i507, i507, i31) -> f4649_0_imprimer_GE(EOS(STATIC_4649), java.lang.Object(Carre(EOC, i31)), i497, i507, i507, i31) :|: i507 >= i31
f4648_0_imprimer_GE(EOS(STATIC_4648), java.lang.Object(Carre(EOC, i31)), i497, i507, i507, i31) -> f4650_0_imprimer_GE(EOS(STATIC_4650), java.lang.Object(Carre(EOC, i31)), i497, i507, i507, i31) :|: i507 < i31
f4649_0_imprimer_GE(EOS(STATIC_4649), java.lang.Object(Carre(EOC, i31)), i497, i507, i507, i31) -> f4651_0_imprimer_Inc(EOS(STATIC_4651), java.lang.Object(Carre(EOC, i31)), i497) :|: i507 >= i31
f4651_0_imprimer_Inc(EOS(STATIC_4651), java.lang.Object(Carre(EOC, i31)), i497) -> f4653_0_imprimer_JMP(EOS(STATIC_4653), java.lang.Object(Carre(EOC, i31)), i497 + 1) :|: TRUE
f4653_0_imprimer_JMP(EOS(STATIC_4653), java.lang.Object(Carre(EOC, i31)), i509) -> f4655_0_imprimer_Load(EOS(STATIC_4655), java.lang.Object(Carre(EOC, i31)), i509) :|: TRUE
f4655_0_imprimer_Load(EOS(STATIC_4655), java.lang.Object(Carre(EOC, i31)), i509) -> f4608_0_imprimer_Load(EOS(STATIC_4608), java.lang.Object(Carre(EOC, i31)), i509) :|: TRUE
f4608_0_imprimer_Load(EOS(STATIC_4608), java.lang.Object(Carre(EOC, i31)), i497) -> f4609_0_imprimer_Load(EOS(STATIC_4609), java.lang.Object(Carre(EOC, i31)), i497, i497) :|: TRUE
f4650_0_imprimer_GE(EOS(STATIC_4650), java.lang.Object(Carre(EOC, i31)), i497, i507, i507, i31) -> f4652_0_imprimer_Inc(EOS(STATIC_4652), java.lang.Object(Carre(EOC, i31)), i497, i507) :|: i507 < i31
f4652_0_imprimer_Inc(EOS(STATIC_4652), java.lang.Object(Carre(EOC, i31)), i497, i507) -> f4654_0_imprimer_JMP(EOS(STATIC_4654), java.lang.Object(Carre(EOC, i31)), i497, i507 + 1) :|: TRUE
f4654_0_imprimer_JMP(EOS(STATIC_4654), java.lang.Object(Carre(EOC, i31)), i497, i510) -> f4656_0_imprimer_Load(EOS(STATIC_4656), java.lang.Object(Carre(EOC, i31)), i497, i510) :|: TRUE
f4656_0_imprimer_Load(EOS(STATIC_4656), java.lang.Object(Carre(EOC, i31)), i497, i510) -> f4645_0_imprimer_Load(EOS(STATIC_4645), java.lang.Object(Carre(EOC, i31)), i497, i510) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f4648_0_imprimer_GE(EOS(STATIC_4648), java.lang.Object(Carre(EOC, i31:0)), i497:0, i507:0, i507:0, i31:0) -> f4648_0_imprimer_GE(EOS(STATIC_4648), java.lang.Object(Carre(EOC, i31:0)), i497:0 + 1, 0, 0, i31:0) :|: i497:0 + 1 < i31:0 && i507:0 >= i31:0
f4648_0_imprimer_GE(EOS(STATIC_4648), java.lang.Object(Carre(EOC, i31:0)), i497:0, i507:0, i507:0, i31:0) -> f4648_0_imprimer_GE(EOS(STATIC_4648), java.lang.Object(Carre(EOC, i31:0)), i497:0, i507:0 + 1, i507:0 + 1, i31:0) :|: i507:0 < i31:0
Filtered constant ground arguments:
   f4648_0_imprimer_GE(x1, x2, x3, x4, x5, x6) -> f4648_0_imprimer_GE(x2, x3, x4, x5, x6)
   EOS(x1) -> EOS
   Carre(x1, x2) -> Carre(x2)
Filtered duplicate arguments:
   f4648_0_imprimer_GE(x1, x2, x3, x4, x5) -> f4648_0_imprimer_GE(x1, x2, x4, x5)
Finished conversion. Obtained 2 rules.P rules:
f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i497:0, i507:0, i31:0, i31:0) -> f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i497:0 + 1, 0, i31:0, i31:0) :|: i497:0 + 1 < i31:0 && i507:0 >= i31:0
f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i497:0, i507:0, i31:0, i31:0) -> f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i497:0, i507:0 + 1, i31:0, i31:0) :|: i507:0 < i31:0

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

(9)
Obligation:
Rules:
f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i497:0, i507:0, i31:0, i31:0) -> f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i497:0 + 1, 0, i31:0, i31:0) :|: i497:0 + 1 < i31:0 && i507:0 >= i31:0
f4648_0_imprimer_GE(java.lang.Object(Carre(x)), x1, x2, x, x) -> f4648_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:
f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i497:0, i507:0, i31:0, i31:0) -> f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0)), arith, 0, i31:0, i31:0) :|: i497:0 + 1 < i31:0 && i507:0 >= i31:0 && arith = i497:0 + 1
f4648_0_imprimer_GE(java.lang.Object(Carre(x3)), x4, x5, x3, x3) -> f4648_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) f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i497:0, i507:0, i31:0, i31:0) -> f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0)), arith, 0, i31:0, i31:0) :|: i497:0 + 1 < i31:0 && i507:0 >= i31:0 && arith = i497:0 + 1
(2) f4648_0_imprimer_GE(java.lang.Object(Carre(x3)), x4, x5, x3, x3) -> f4648_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) f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0)), i497:0, i507:0, i31:0, i31:0) -> f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0)), arith, 0, i31:0, i31:0) :|: i497:0 + 1 < i31:0 && i507:0 >= i31:0 && arith = i497:0 + 1
(2) f4648_0_imprimer_GE(java.lang.Object(Carre(x3)), x4, x5, x3, x3) -> f4648_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:
f4648_0_imprimer_GE(java.lang.Object(Carre(x3:0)), x4:0, x5:0, x3:0, x3:0) -> f4648_0_imprimer_GE(java.lang.Object(Carre(x3:0)), x4:0, x5:0 + 1, x3:0, x3:0) :|: x5:0 < x3:0
f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0:0)), i497:0:0, i507:0:0, i31:0:0, i31:0:0) -> f4648_0_imprimer_GE(java.lang.Object(Carre(i31:0:0)), i497:0:0 + 1, 0, i31:0:0, i31:0:0) :|: i497:0:0 + 1 < i31:0:0 && i507:0:0 >= i31:0:0

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

(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f4648_0_imprimer_GE(VARIABLE, VARIABLE, VARIABLE, INTEGER, INTEGER)
java.lang.Object(VARIABLE)
Carre(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(17)
Obligation:
Rules:
f4648_0_imprimer_GE(c, x4:0, x5:0, x3:0, x3:0) -> f4648_0_imprimer_GE(c1, x4:0, c2, x3:0, x3:0) :|: c2 = x5:0 + 1 && (c1 = 0 && c = 0) && x5:0 < x3:0
f4648_0_imprimer_GE(c3, i497:0:0, i507:0:0, i31:0:0, i31:0:0) -> f4648_0_imprimer_GE(c4, c5, c6, i31:0:0, i31:0:0) :|: c6 = 0 && (c5 = i497:0:0 + 1 && (c4 = 0 && c3 = 0)) && (i497:0:0 + 1 < i31:0:0 && i507:0:0 >= i31:0:0)

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

(18) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4648_0_imprimer_GE(x, x1, x2, x3, x4)] = -1 + c*x - x1 + x4

The following rules are decreasing:
f4648_0_imprimer_GE(c3, i497:0:0, i507:0:0, i31:0:0, i31:0:0) -> f4648_0_imprimer_GE(c4, c5, c6, i31:0:0, i31:0:0) :|: c6 = 0 && (c5 = i497:0:0 + 1 && (c4 = 0 && c3 = 0)) && (i497:0:0 + 1 < i31:0:0 && i507:0:0 >= i31:0:0)
The following rules are bounded:
f4648_0_imprimer_GE(c3, i497:0:0, i507:0:0, i31:0:0, i31:0:0) -> f4648_0_imprimer_GE(c4, c5, c6, i31:0:0, i31:0:0) :|: c6 = 0 && (c5 = i497:0:0 + 1 && (c4 = 0 && c3 = 0)) && (i497:0:0 + 1 < i31:0:0 && i507:0:0 >= i31:0:0)

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

(19)
Obligation:
Rules:
f4648_0_imprimer_GE(c, x4:0, x5:0, x3:0, x3:0) -> f4648_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:
[ f4648_0_imprimer_GE ] = -1*f4648_0_imprimer_GE_3 + f4648_0_imprimer_GE_5

The following rules are decreasing:
f4648_0_imprimer_GE(c, x4:0, x5:0, x3:0, x3:0) -> f4648_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:
f4648_0_imprimer_GE(c, x4:0, x5:0, x3:0, x3:0) -> f4648_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:
f4050_0_init_ConstantStackPush(EOS(STATIC_4050), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i348, i348) -> f4065_0_init_GE(EOS(STATIC_4065), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i348, i348, 3) :|: TRUE
f4065_0_init_GE(EOS(STATIC_4065), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i371, matching1) -> f4070_0_init_GE(EOS(STATIC_4070), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i371, 3) :|: TRUE && matching1 = 3
f4070_0_init_GE(EOS(STATIC_4070), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i371, matching1) -> f4073_0_init_ConstantStackPush(EOS(STATIC_4073), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371) :|: i371 < 3 && matching1 = 3
f4073_0_init_ConstantStackPush(EOS(STATIC_4073), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371) -> f4087_0_init_Store(EOS(STATIC_4087), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, 0) :|: TRUE
f4087_0_init_Store(EOS(STATIC_4087), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, matching1) -> f4091_0_init_Load(EOS(STATIC_4091), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, 0) :|: TRUE && matching1 = 0
f4091_0_init_Load(EOS(STATIC_4091), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, matching1) -> f4351_0_init_Load(EOS(STATIC_4351), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, 0) :|: TRUE && matching1 = 0
f4351_0_init_Load(EOS(STATIC_4351), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i398) -> f4395_0_init_Load(EOS(STATIC_4395), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i398) :|: TRUE
f4395_0_init_Load(EOS(STATIC_4395), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i422) -> f4443_0_init_Load(EOS(STATIC_4443), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i422) :|: TRUE
f4443_0_init_Load(EOS(STATIC_4443), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i451) -> f4446_0_init_ConstantStackPush(EOS(STATIC_4446), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i451, i451) :|: TRUE
f4446_0_init_ConstantStackPush(EOS(STATIC_4446), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i451, i451) -> f4449_0_init_GE(EOS(STATIC_4449), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i451, i451, 3) :|: TRUE
f4449_0_init_GE(EOS(STATIC_4449), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, i465, matching1) -> f4452_0_init_GE(EOS(STATIC_4452), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, i465, 3) :|: TRUE && matching1 = 3
f4449_0_init_GE(EOS(STATIC_4449), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i466, i466, matching1) -> f4453_0_init_GE(EOS(STATIC_4453), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i466, i466, 3) :|: TRUE && matching1 = 3
f4452_0_init_GE(EOS(STATIC_4452), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, i465, matching1) -> f4455_0_init_Load(EOS(STATIC_4455), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465) :|: i465 < 3 && matching1 = 3
f4455_0_init_Load(EOS(STATIC_4455), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465) -> f4458_0_init_FieldAccess(EOS(STATIC_4458), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31))))) :|: TRUE
f4458_0_init_FieldAccess(EOS(STATIC_4458), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31))))) -> f4461_0_init_Load(EOS(STATIC_4461), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(ARRAY(i31))) :|: TRUE
f4461_0_init_Load(EOS(STATIC_4461), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(ARRAY(i31))) -> f4464_0_init_ArrayAccess(EOS(STATIC_4464), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(ARRAY(i31)), i371) :|: TRUE
f4464_0_init_ArrayAccess(EOS(STATIC_4464), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(ARRAY(i31)), i371) -> f4466_0_init_ArrayAccess(EOS(STATIC_4466), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(ARRAY(i31)), i371) :|: TRUE
f4466_0_init_ArrayAccess(EOS(STATIC_4466), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(ARRAY(i31)), i371) -> f4469_0_init_Load(EOS(STATIC_4469), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, o1103) :|: i371 < i31
f4469_0_init_Load(EOS(STATIC_4469), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, o1103) -> f4472_0_init_ConstantStackPush(EOS(STATIC_4472), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, o1103, i465) :|: TRUE
f4472_0_init_ConstantStackPush(EOS(STATIC_4472), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, o1103, i465) -> f4474_0_init_ArrayAccess(EOS(STATIC_4474), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, o1103, i465, 0) :|: TRUE
f4474_0_init_ArrayAccess(EOS(STATIC_4474), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(o1109put), i465, matching1) -> f4477_0_init_ArrayAccess(EOS(STATIC_4477), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(o1109put), i465, 0) :|: TRUE && matching1 = 0
f4477_0_init_ArrayAccess(EOS(STATIC_4477), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(ARRAY(i477)), i465, matching1) -> f4481_0_init_ArrayAccess(EOS(STATIC_4481), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(ARRAY(i477)), i465, 0) :|: i477 >= 0 && matching1 = 0
f4481_0_init_ArrayAccess(EOS(STATIC_4481), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(ARRAY(i477)), i465, matching1) -> f4484_0_init_ArrayAccess(EOS(STATIC_4484), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(ARRAY(i477)), i465, 0) :|: TRUE && matching1 = 0
f4484_0_init_ArrayAccess(EOS(STATIC_4484), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465, java.lang.Object(ARRAY(i477)), i465, matching1) -> f4489_0_init_Inc(EOS(STATIC_4489), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465) :|: i465 < i477 && matching1 = 0
f4489_0_init_Inc(EOS(STATIC_4489), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465) -> f4494_0_init_JMP(EOS(STATIC_4494), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i465 + 1) :|: TRUE
f4494_0_init_JMP(EOS(STATIC_4494), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i480) -> f4497_0_init_Load(EOS(STATIC_4497), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i480) :|: TRUE
f4497_0_init_Load(EOS(STATIC_4497), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i480) -> f4443_0_init_Load(EOS(STATIC_4443), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i480) :|: TRUE
f4453_0_init_GE(EOS(STATIC_4453), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371, i466, i466, matching1) -> f4456_0_init_Inc(EOS(STATIC_4456), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371) :|: i466 >= 3 && matching1 = 3
f4456_0_init_Inc(EOS(STATIC_4456), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371) -> f4459_0_init_JMP(EOS(STATIC_4459), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i371 + 1) :|: TRUE
f4459_0_init_JMP(EOS(STATIC_4459), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i467) -> f4462_0_init_Load(EOS(STATIC_4462), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i467) :|: TRUE
f4462_0_init_Load(EOS(STATIC_4462), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i467) -> f4045_0_init_Load(EOS(STATIC_4045), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i467) :|: TRUE
f4045_0_init_Load(EOS(STATIC_4045), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i348) -> f4050_0_init_ConstantStackPush(EOS(STATIC_4050), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31)))), i348, i348) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f4449_0_init_GE(EOS(STATIC_4449), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), i371:0, i465:0, i465:0, 3) -> f4449_0_init_GE(EOS(STATIC_4449), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), i371:0, i465:0 + 1, i465:0 + 1, 3) :|: i465:0 < 3 && i371:0 < i31:0 && i477:0 > i465:0 && i477:0 > -1
f4449_0_init_GE(EOS(STATIC_4449), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), i371:0, i466:0, i466:0, 3) -> f4449_0_init_GE(EOS(STATIC_4449), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), java.lang.Object(Carre(EOC, java.lang.Object(ARRAY(i31:0)))), i371:0 + 1, 0, 0, 3) :|: i466:0 > 2 && i371:0 < 2
Filtered constant ground arguments:
   f4449_0_init_GE(x1, x2, x3, x4, x5, x6, x7) -> f4449_0_init_GE(x2, x3, x4, x5, x6)
   EOS(x1) -> EOS
   Carre(x1, x2) -> Carre(x2)
Filtered duplicate arguments:
   f4449_0_init_GE(x1, x2, x3, x4, x5) -> f4449_0_init_GE(x2, x3, x5)
Finished conversion. Obtained 2 rules.P rules:
f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i371:0, i465:0, i31:0) -> f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i371:0, i465:0 + 1, i31:0) :|: i371:0 < i31:0 && i465:0 < 3 && i477:0 > -1 && i477:0 > i465:0
f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i371:0, i466:0, i31:0) -> f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i371:0 + 1, 0, i31:0) :|: i466:0 > 2 && i371:0 < 2

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

(24)
Obligation:
Rules:
f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i371:0, i465:0, i31:0) -> f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i371:0, i465:0 + 1, i31:0) :|: i371:0 < i31:0 && i465:0 < 3 && i477:0 > -1 && i477:0 > i465:0
f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x)))), x1, x2, x) -> f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x)))), x1 + 1, 0, x) :|: x2 > 2 && x1 < 2

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

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

(26)
Obligation:
Rules:
f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i371:0, i465:0, i31:0) -> f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i371:0, arith, i31:0) :|: i371:0 < i31:0 && i465:0 < 3 && i477:0 > -1 && i477:0 > i465:0 && arith = i465:0 + 1
f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x3)))), x4, x5, x3) -> f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x3)))), x6, 0, x3) :|: x5 > 2 && x4 < 2 && x6 = x4 + 1

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

(27) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i371:0, i465:0, i31:0) -> f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i371:0, arith, i31:0) :|: i371:0 < i31:0 && i465:0 < 3 && i477:0 > -1 && i477:0 > i465:0 && arith = i465:0 + 1
(2) f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x3)))), x4, x5, x3) -> f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x3)))), x6, 0, x3) :|: x5 > 2 && x4 < 2 && x6 = x4 + 1

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

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

(28)
Obligation:

Termination digraph:
Nodes:
(1) f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i371:0, i465:0, i31:0) -> f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0)))), i371:0, arith, i31:0) :|: i371:0 < i31:0 && i465:0 < 3 && i477:0 > -1 && i477:0 > i465:0 && arith = i465:0 + 1
(2) f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x3)))), x4, x5, x3) -> f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x3)))), x6, 0, x3) :|: x5 > 2 && x4 < 2 && x6 = x4 + 1

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

This digraph is fully evaluated!

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(29) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(30)
Obligation:
Rules:
f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x3:0)))), x4:0, x5:0, x3:0) -> f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(x3:0)))), x4:0 + 1, 0, x3:0) :|: x5:0 > 2 && x4:0 < 2
f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0:0)))), i371:0:0, i465:0:0, i31:0:0) -> f4449_0_init_GE(java.lang.Object(Carre(java.lang.Object(ARRAY(i31:0:0)))), i371:0:0, i465:0:0 + 1, i31:0:0) :|: i477:0:0 > -1 && i477:0:0 > i465:0:0 && i465:0:0 < 3 && i371:0:0 < i31:0:0

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(31) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f4449_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:
f4449_0_init_GE(c, x4:0, x5:0, x3:0) -> f4449_0_init_GE(c1, c2, c3, x3:0) :|: c3 = 0 && (c2 = x4:0 + 1 && (c1 = 0 && c = 0)) && (x5:0 > 2 && x4:0 < 2)
f4449_0_init_GE(c4, i371:0:0, i465:0:0, i31:0:0) -> f4449_0_init_GE(c5, i371:0:0, c6, i31:0:0) :|: c6 = i465:0:0 + 1 && (c5 = 0 && c4 = 0) && (i477:0:0 > -1 && i477:0:0 > i465:0:0 && i465:0:0 < 3 && i371:0:0 < i31:0:0)

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(33) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4449_0_init_GE(x, x1, x2, x3)] = c*x - x1 + x3

The following rules are decreasing:
f4449_0_init_GE(c, x4:0, x5:0, x3:0) -> f4449_0_init_GE(c1, c2, c3, x3:0) :|: c3 = 0 && (c2 = x4:0 + 1 && (c1 = 0 && c = 0)) && (x5:0 > 2 && x4:0 < 2)
The following rules are bounded:
f4449_0_init_GE(c4, i371:0:0, i465:0:0, i31:0:0) -> f4449_0_init_GE(c5, i371:0:0, c6, i31:0:0) :|: c6 = i465:0:0 + 1 && (c5 = 0 && c4 = 0) && (i477:0:0 > -1 && i477:0:0 > i465:0:0 && i465:0:0 < 3 && i371:0:0 < i31:0:0)

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(34)
Complex Obligation (AND)

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(35)
Obligation:
Rules:
f4449_0_init_GE(c4, i371:0:0, i465:0:0, i31:0:0) -> f4449_0_init_GE(c5, i371:0:0, c6, i31:0:0) :|: c6 = i465:0:0 + 1 && (c5 = 0 && c4 = 0) && (i477:0:0 > -1 && i477:0:0 > i465:0:0 && i465:0:0 < 3 && i371:0:0 < i31:0:0)

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(36) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f4449_0_init_GE(x, x1, x2, x3)] = 2 + c*x - x2

The following rules are decreasing:
f4449_0_init_GE(c4, i371:0:0, i465:0:0, i31:0:0) -> f4449_0_init_GE(c5, i371:0:0, c6, i31:0:0) :|: c6 = i465:0:0 + 1 && (c5 = 0 && c4 = 0) && (i477:0:0 > -1 && i477:0:0 > i465:0:0 && i465:0:0 < 3 && i371:0:0 < i31:0:0)
The following rules are bounded:
f4449_0_init_GE(c4, i371:0:0, i465:0:0, i31:0:0) -> f4449_0_init_GE(c5, i371:0:0, c6, i31:0:0) :|: c6 = i465:0:0 + 1 && (c5 = 0 && c4 = 0) && (i477:0:0 > -1 && i477:0:0 > i465:0:0 && i465:0:0 < 3 && i371:0:0 < i31:0:0)

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(37)
YES

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(38)
Obligation:
Rules:
f4449_0_init_GE(c, x4:0, x5:0, x3:0) -> f4449_0_init_GE(c1, c2, c3, x3:0) :|: c3 = 0 && (c2 = x4:0 + 1 && (c1 = 0 && c = 0)) && (x5:0 > 2 && x4:0 < 2)

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(39) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f4449_0_init_GE ] = 1/3*f4449_0_init_GE_3

The following rules are decreasing:
f4449_0_init_GE(c, x4:0, x5:0, x3:0) -> f4449_0_init_GE(c1, c2, c3, x3:0) :|: c3 = 0 && (c2 = x4:0 + 1 && (c1 = 0 && c = 0)) && (x5:0 > 2 && x4:0 < 2)

The following rules are bounded:
f4449_0_init_GE(c, x4:0, x5:0, x3:0) -> f4449_0_init_GE(c1, c2, c3, x3:0) :|: c3 = 0 && (c2 = x4:0 + 1 && (c1 = 0 && c = 0)) && (x5:0 > 2 && x4:0 < 2)


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(40)
YES