Termination proof of /tmp/tmpZFSNZR/TriTas.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBCToGraph (⇒, 2228 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToSCCProof (⇒, 5 ms)

↳4 AND

    ↳5 JBCTerminationSCC

        ↳6 SCCToIDPv1Proof (⇒, 403 ms)

        ↳7 IDP

        ↳8 IDPNonInfProof (⇒, 3519 ms)

        ↳9 IDP

        ↳10 IDependencyGraphProof (⇔, 0 ms)

        ↳11 TRUE

    ↳12 JBCTerminationSCC

        ↳13 SCCToIntTRSProof (⇒, 92 ms)

        ↳14 intTRS

        ↳15 PolynomialOrderProcessor (⇔, 3 ms)

        ↳16 YES

    ↳17 JBCTerminationSCC

        ↳18 SCCToIntTRSProof (⇒, 531 ms)

        ↳19 intTRS

        ↳20 PolynomialOrderProcessor (⇔, 0 ms)

        ↳21 YES

    ↳22 JBCTerminationSCC

        ↳23 SCCToIDPv1Proof (⇒, 1080 ms)

        ↳24 IDP

        ↳25 IDPNonInfProof (⇒, 689 ms)

        ↳26 AND

            ↳27 IDP

                ↳28 IDependencyGraphProof (⇔, 0 ms)

                ↳29 TRUE

            ↳30 IDP

                ↳31 IDependencyGraphProof (⇔, 0 ms)

                ↳32 TRUE

    ↳33 JBCTerminationSCC

        ↳34 SCCToIntTRSProof (⇒, 100 ms)

        ↳35 intTRS

        ↳36 PolynomialOrderProcessor (⇔, 0 ms)

        ↳37 YES

(0) Obligation:

JBC Problem based on JBC Program:

public class TriTas {
    static int N; 
    static int[] a; 
    static int nTas = 0; 

    static void Ajouter(int v) {
	int i,j;
	nTas++; 
	i = nTas - 1; 
	while (i > 0 && a[(i - 1)/2] <= v){
	    a[i] = a[(i - 1)/2]; 
	    j = (i - 1)/2;
	    if (j >= i) break; else i = j;
	}
	a[i] = v;
    }

    static int Maximum() {
	return a[0]; 
    }

    static void Supprimer() {
	int i, j, v;
	a[0] = a[nTas - 1]; 
	nTas--; 
	i = 0; v = a[0];
	while (2 * i + 1 < nTas)
	    {
		j = 2*i + 1; 
		if (j + 1 < nTas)
		    if (a[j + 1] > a[j]) 
			j++;
		if (v >= a[j]) break;
		a[i] = a[j]; 
		i = j;
	    }
	a[i] = v;
    }

    static void HeapSort(){
	int i, v;
	nTas = 0; 
	for (i = 0; i < N; i++)
	    Ajouter(a[i]); 
	for (i = N - 1; i >= 0; i--)
	    { 
		v = Maximum(); 
		Supprimer(); 
		a[i]=v;
	    }
    }

    public static void main(String[] args){
	Random.args = args;
	N = args.length;
	a = new int[N];
	for (int i = 0; i < N; i++)
	    a[i] = Random.random();
	//for (int i = 0; i < N; i++)
	//    System.out.print(a[i]+" ");
	//System.out.println();
	HeapSort();
	//for (int i = 0; i < N; i++)
	//    System.out.print(a[i]+" ");
	//System.out.println();
    }
}

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) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
TriTas.main([Ljava/lang/String;)V: Graph of 216 nodes with 1 SCC.

TriTas.HeapSort()V: Graph of 162 nodes with 2 SCCs.

TriTas.Ajouter(I)V: Graph of 213 nodes with 1 SCC.

TriTas.Supprimer()V: Graph of 286 nodes with 1 SCC.

(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 5 SCCss.

(4) Complex Obligation (AND)

(5) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: TriTas.Supprimer()V
SCC calls the following helper methods:
Performed SCC analyses:

Used field analysis yielded the following read fields:
Marker field analysis yielded the following relations that could be markers:

(6) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 61 rules for P and 0 rules for R.

P rules:
f11075_0_Supprimer_Load(EOS(STATIC_11075(i1756)), i2440, i1245, matching1) → f11077_0_Supprimer_IntArithmetic(EOS(STATIC_11077(i1756)), i2440, i1245, 2, i2440) | =(matching1, 2)
f11077_0_Supprimer_IntArithmetic(EOS(STATIC_11077(i1756)), i2440, i1245, matching1, i2440) → f11078_0_Supprimer_ConstantStackPush(EOS(STATIC_11078(i1756)), i2440, i1245, *(2, i2440)) | =(matching1, 2)
f11078_0_Supprimer_ConstantStackPush(EOS(STATIC_11078(i1756)), i2440, i1245, i2442) → f11080_0_Supprimer_IntArithmetic(EOS(STATIC_11080(i1756)), i2440, i1245, i2442, 1)
f11080_0_Supprimer_IntArithmetic(EOS(STATIC_11080(i1756)), i2440, i1245, i2442, matching1) → f11082_0_Supprimer_FieldAccess(EOS(STATIC_11082(i1756)), i2440, i1245, +(i2442, 1)) | &&(>=(i2442, 0), =(matching1, 1))
f11082_0_Supprimer_FieldAccess(EOS(STATIC_11082(i1756)), i2440, i1245, i2444) → f11084_0_Supprimer_GE(EOS(STATIC_11084(i1756)), i2440, i1245, i2444, i1756)
f11084_0_Supprimer_GE(EOS(STATIC_11084(i1756)), i2440, i1245, i2444, i1756) → f11087_0_Supprimer_GE(EOS(STATIC_11087(i1756)), i2440, i1245, i2444, i1756)
f11087_0_Supprimer_GE(EOS(STATIC_11087(i1756)), i2440, i1245, i2444, i1756) → f11091_0_Supprimer_ConstantStackPush(EOS(STATIC_11091(i1756)), i2440, i1245) | <(i2444, i1756)
f11091_0_Supprimer_ConstantStackPush(EOS(STATIC_11091(i1756)), i2440, i1245) → f11094_0_Supprimer_Load(EOS(STATIC_11094(i1756)), i2440, i1245, 2)
f11094_0_Supprimer_Load(EOS(STATIC_11094(i1756)), i2440, i1245, matching1) → f11097_0_Supprimer_IntArithmetic(EOS(STATIC_11097(i1756)), i2440, i1245, 2, i2440) | =(matching1, 2)
f11097_0_Supprimer_IntArithmetic(EOS(STATIC_11097(i1756)), i2440, i1245, matching1, i2440) → f11101_0_Supprimer_ConstantStackPush(EOS(STATIC_11101(i1756)), i2440, i1245, *(2, i2440)) | =(matching1, 2)
f11101_0_Supprimer_ConstantStackPush(EOS(STATIC_11101(i1756)), i2440, i1245, i2445) → f11105_0_Supprimer_IntArithmetic(EOS(STATIC_11105(i1756)), i2440, i1245, i2445, 1)
f11105_0_Supprimer_IntArithmetic(EOS(STATIC_11105(i1756)), i2440, i1245, i2445, matching1) → f11111_0_Supprimer_Store(EOS(STATIC_11111(i1756)), i2440, i1245, +(i2445, 1)) | &&(>=(i2445, 0), =(matching1, 1))
f11111_0_Supprimer_Store(EOS(STATIC_11111(i1756)), i2440, i1245, i2446) → f11115_0_Supprimer_Load(EOS(STATIC_11115(i1756)), i2440, i2446, i1245)
f11115_0_Supprimer_Load(EOS(STATIC_11115(i1756)), i2440, i2446, i1245) → f11137_0_Supprimer_ConstantStackPush(EOS(STATIC_11137(i1756)), i2440, i2446, i1245, i2446)
f11137_0_Supprimer_ConstantStackPush(EOS(STATIC_11137(i1756)), i2440, i2446, i1245, i2446) → f11141_0_Supprimer_IntArithmetic(EOS(STATIC_11141(i1756)), i2440, i2446, i1245, i2446, 1)
f11141_0_Supprimer_IntArithmetic(EOS(STATIC_11141(i1756)), i2440, i2446, i1245, i2446, matching1) → f11143_0_Supprimer_FieldAccess(EOS(STATIC_11143(i1756)), i2440, i2446, i1245, +(i2446, 1)) | &&(>(i2446, 0), =(matching1, 1))
f11143_0_Supprimer_FieldAccess(EOS(STATIC_11143(i1756)), i2440, i2446, i1245, i2465) → f11156_0_Supprimer_GE(EOS(STATIC_11156(i1756)), i2440, i2446, i1245, i2465, i1756)
f11156_0_Supprimer_GE(EOS(STATIC_11156(i1756)), i2440, i2446, i1245, i2465, i1756) → f11161_0_Supprimer_GE(EOS(STATIC_11161(i1756)), i2440, i2446, i1245, i2465, i1756)
f11156_0_Supprimer_GE(EOS(STATIC_11156(i1756)), i2440, i2446, i1245, i2465, i1756) → f11162_0_Supprimer_GE(EOS(STATIC_11162(i1756)), i2440, i2446, i1245, i2465, i1756)
f11161_0_Supprimer_GE(EOS(STATIC_11161(i1756)), i2440, i2446, i1245, i2465, i1756) → f11165_0_Supprimer_Load(EOS(STATIC_11165(i1756)), i2440, i2446, i1245) | >=(i2465, i1756)
f11165_0_Supprimer_Load(EOS(STATIC_11165(i1756)), i2440, i2446, i1245) → f11326_0_Supprimer_Load(EOS(STATIC_11326(i1756)), i2440, i2446, i1245)
f11326_0_Supprimer_Load(EOS(STATIC_11326(i1756)), i2440, i2446, i1245) → f11345_0_Supprimer_FieldAccess(EOS(STATIC_11345(i1756)), i2440, i2446, i1245, i1245)
f11345_0_Supprimer_FieldAccess(EOS(STATIC_11345(i1756)), i2440, i2446, i1245, i1245) → f11354_0_Supprimer_Load(EOS(STATIC_11354(i1756)), i2440, i2446, i1245, i1245, java.lang.Object(ARRAY(i1755)))
f11354_0_Supprimer_Load(EOS(STATIC_11354(i1756)), i2440, i2446, i1245, i1245, java.lang.Object(ARRAY(i1755))) → f11383_0_Supprimer_ArrayAccess(EOS(STATIC_11383(i1756)), i2440, i2446, i1245, i1245, java.lang.Object(ARRAY(i1755)), i2446)
f11383_0_Supprimer_ArrayAccess(EOS(STATIC_11383(i1756)), i2440, i2446, i1245, i1245, java.lang.Object(ARRAY(i1755)), i2446) → f11397_0_Supprimer_ArrayAccess(EOS(STATIC_11397(i1756)), i2440, i2446, i1245, i1245, java.lang.Object(ARRAY(i1755)), i2446)
f11397_0_Supprimer_ArrayAccess(EOS(STATIC_11397(i1756)), i2440, i2446, i1245, i1245, java.lang.Object(ARRAY(i1755)), i2446) → f11407_0_Supprimer_LT(EOS(STATIC_11407(i1756)), i2440, i2446, i1245, i1245, i2546) | <(i2446, i1755)
f11407_0_Supprimer_LT(EOS(STATIC_11407(i1756)), i2440, i2446, i1245, i1245, i2546) → f11427_0_Supprimer_LT(EOS(STATIC_11427(i1756)), i2440, i2446, i1245, i1245, i2546)
f11427_0_Supprimer_LT(EOS(STATIC_11427(i1756)), i2440, i2446, i1245, i1245, i2546) → f11441_0_Supprimer_FieldAccess(EOS(STATIC_11441(i1756)), i2440, i2446, i1245) | <(i1245, i2546)
f11441_0_Supprimer_FieldAccess(EOS(STATIC_11441(i1756)), i2440, i2446, i1245) → f11458_0_Supprimer_Load(EOS(STATIC_11458(i1756)), i2440, i2446, i1245, java.lang.Object(ARRAY(i1755)))
f11458_0_Supprimer_Load(EOS(STATIC_11458(i1756)), i2440, i2446, i1245, java.lang.Object(ARRAY(i1755))) → f11474_0_Supprimer_FieldAccess(EOS(STATIC_11474(i1756)), i2446, i1245, java.lang.Object(ARRAY(i1755)), i2440)
f11474_0_Supprimer_FieldAccess(EOS(STATIC_11474(i1756)), i2446, i1245, java.lang.Object(ARRAY(i1755)), i2440) → f11493_0_Supprimer_Load(EOS(STATIC_11493(i1756)), i2446, i1245, java.lang.Object(ARRAY(i1755)), i2440, java.lang.Object(ARRAY(i1755)))
f11493_0_Supprimer_Load(EOS(STATIC_11493(i1756)), i2446, i1245, java.lang.Object(ARRAY(i1755)), i2440, java.lang.Object(ARRAY(i1755))) → f11511_0_Supprimer_ArrayAccess(EOS(STATIC_11511(i1756)), i2446, i1245, java.lang.Object(ARRAY(i1755)), i2440, java.lang.Object(ARRAY(i1755)), i2446)
f11511_0_Supprimer_ArrayAccess(EOS(STATIC_11511(i1756)), i2446, i1245, java.lang.Object(ARRAY(i1755)), i2440, java.lang.Object(ARRAY(i1755)), i2446) → f11523_0_Supprimer_ArrayAccess(EOS(STATIC_11523(i1756)), i2446, i1245, java.lang.Object(ARRAY(i1755)), i2440, java.lang.Object(ARRAY(i1755)), i2446)
f11523_0_Supprimer_ArrayAccess(EOS(STATIC_11523(i1756)), i2446, i1245, java.lang.Object(ARRAY(i1755)), i2440, java.lang.Object(ARRAY(i1755)), i2446) → f11544_0_Supprimer_ArrayAccess(EOS(STATIC_11544(i1756)), i2446, i1245, java.lang.Object(ARRAY(i1755)), i2440) | <(i2446, i1755)
f11544_0_Supprimer_ArrayAccess(EOS(STATIC_11544(i1756)), i2446, i1245, java.lang.Object(ARRAY(i1755)), i2440) → f11584_0_Supprimer_ArrayAccess(EOS(STATIC_11584(i1756)), i2446, i1245, java.lang.Object(ARRAY(i1755)), i2440)
f11584_0_Supprimer_ArrayAccess(EOS(STATIC_11584(i1756)), i2446, i1245, java.lang.Object(ARRAY(i1755)), i2440) → f11612_0_Supprimer_Load(EOS(STATIC_11612(i1756)), i2446, i1245) | <(i2440, i1755)
f11612_0_Supprimer_Load(EOS(STATIC_11612(i1756)), i2446, i1245) → f11681_0_Supprimer_Store(EOS(STATIC_11681(i1756)), i1245, i2446)
f11681_0_Supprimer_Store(EOS(STATIC_11681(i1756)), i1245, i2446) → f11726_0_Supprimer_JMP(EOS(STATIC_11726(i1756)), i2446, i1245)
f11726_0_Supprimer_JMP(EOS(STATIC_11726(i1756)), i2446, i1245) → f11770_0_Supprimer_ConstantStackPush(EOS(STATIC_11770(i1756)), i2446, i1245)
f11770_0_Supprimer_ConstantStackPush(EOS(STATIC_11770(i1756)), i2446, i1245) → f11063_0_Supprimer_ConstantStackPush(EOS(STATIC_11063(i1756)), i2446, i1245)
f11063_0_Supprimer_ConstantStackPush(EOS(STATIC_11063(i1756)), i2440, i1245) → f11075_0_Supprimer_Load(EOS(STATIC_11075(i1756)), i2440, i1245, 2)
f11162_0_Supprimer_GE(EOS(STATIC_11162(i1756)), i2440, i2446, i1245, i2465, i1756) → f11167_0_Supprimer_FieldAccess(EOS(STATIC_11167(i1756)), i2440, i2446, i1245) | <(i2465, i1756)
f11167_0_Supprimer_FieldAccess(EOS(STATIC_11167(i1756)), i2440, i2446, i1245) → f11183_0_Supprimer_Load(EOS(STATIC_11183(i1756)), i2440, i2446, i1245, java.lang.Object(ARRAY(i1755)))
f11183_0_Supprimer_Load(EOS(STATIC_11183(i1756)), i2440, i2446, i1245, java.lang.Object(ARRAY(i1755))) → f11190_0_Supprimer_ConstantStackPush(EOS(STATIC_11190(i1756)), i2440, i2446, i1245, java.lang.Object(ARRAY(i1755)), i2446)
f11190_0_Supprimer_ConstantStackPush(EOS(STATIC_11190(i1756)), i2440, i2446, i1245, java.lang.Object(ARRAY(i1755)), i2446) → f11195_0_Supprimer_IntArithmetic(EOS(STATIC_11195(i1756)), i2440, i2446, i1245, java.lang.Object(ARRAY(i1755)), i2446, 1)
f11195_0_Supprimer_IntArithmetic(EOS(STATIC_11195(i1756)), i2440, i2446, i1245, java.lang.Object(ARRAY(i1755)), i2446, matching1) → f11210_0_Supprimer_ArrayAccess(EOS(STATIC_11210(i1756)), i2440, i2446, i1245, java.lang.Object(ARRAY(i1755)), +(i2446, 1)) | &&(>(i2446, 0), =(matching1, 1))
f11210_0_Supprimer_ArrayAccess(EOS(STATIC_11210(i1756)), i2440, i2446, i1245, java.lang.Object(ARRAY(i1755)), i2480) → f11220_0_Supprimer_ArrayAccess(EOS(STATIC_11220(i1756)), i2440, i2446, i1245, java.lang.Object(ARRAY(i1755)), i2480)
f11220_0_Supprimer_ArrayAccess(EOS(STATIC_11220(i1756)), i2440, i2446, i1245, java.lang.Object(ARRAY(i1755)), i2480) → f11227_0_Supprimer_FieldAccess(EOS(STATIC_11227(i1756)), i2440, i2446, i1245, i2482) | <(i2480, i1755)
f11227_0_Supprimer_FieldAccess(EOS(STATIC_11227(i1756)), i2440, i2446, i1245, i2482) → f11257_0_Supprimer_Load(EOS(STATIC_11257(i1756)), i2440, i2446, i1245, i2482, java.lang.Object(ARRAY(i1755)))
f11257_0_Supprimer_Load(EOS(STATIC_11257(i1756)), i2440, i2446, i1245, i2482, java.lang.Object(ARRAY(i1755))) → f11275_0_Supprimer_ArrayAccess(EOS(STATIC_11275(i1756)), i2440, i2446, i1245, i2482, java.lang.Object(ARRAY(i1755)), i2446)
f11275_0_Supprimer_ArrayAccess(EOS(STATIC_11275(i1756)), i2440, i2446, i1245, i2482, java.lang.Object(ARRAY(i1755)), i2446) → f11285_0_Supprimer_ArrayAccess(EOS(STATIC_11285(i1756)), i2440, i2446, i1245, i2482, java.lang.Object(ARRAY(i1755)), i2446)
f11285_0_Supprimer_ArrayAccess(EOS(STATIC_11285(i1756)), i2440, i2446, i1245, i2482, java.lang.Object(ARRAY(i1755)), i2446) → f11298_0_Supprimer_LE(EOS(STATIC_11298(i1756)), i2440, i2446, i1245, i2482, i2509) | <(i2446, i1755)
f11298_0_Supprimer_LE(EOS(STATIC_11298(i1756)), i2440, i2446, i1245, i2482, i2509) → f11308_0_Supprimer_LE(EOS(STATIC_11308(i1756)), i2440, i2446, i1245, i2482, i2509)
f11298_0_Supprimer_LE(EOS(STATIC_11298(i1756)), i2440, i2446, i1245, i2482, i2509) → f11309_0_Supprimer_LE(EOS(STATIC_11309(i1756)), i2440, i2446, i1245, i2482, i2509)
f11308_0_Supprimer_LE(EOS(STATIC_11308(i1756)), i2440, i2446, i1245, i2482, i2509) → f11326_0_Supprimer_Load(EOS(STATIC_11326(i1756)), i2440, i2446, i1245) | <=(i2482, i2509)
f11309_0_Supprimer_LE(EOS(STATIC_11309(i1756)), i2440, i2446, i1245, i2482, i2509) → f11329_0_Supprimer_Inc(EOS(STATIC_11329(i1756)), i2440, i2446, i1245) | >(i2482, i2509)
f11329_0_Supprimer_Inc(EOS(STATIC_11329(i1756)), i2440, i2446, i1245) → f11348_0_Supprimer_Load(EOS(STATIC_11348(i1756)), i2440, +(i2446, 1), i1245) | >(i2446, 0)
f11348_0_Supprimer_Load(EOS(STATIC_11348(i1756)), i2440, i2520, i1245) → f11357_0_Supprimer_FieldAccess(EOS(STATIC_11357(i1756)), i2440, i2520, i1245, i1245)
f11357_0_Supprimer_FieldAccess(EOS(STATIC_11357(i1756)), i2440, i2520, i1245, i1245) → f11386_0_Supprimer_Load(EOS(STATIC_11386(i1756)), i2440, i2520, i1245, i1245, java.lang.Object(ARRAY(i1755)))
f11386_0_Supprimer_Load(EOS(STATIC_11386(i1756)), i2440, i2520, i1245, i1245, java.lang.Object(ARRAY(i1755))) → f11403_0_Supprimer_ArrayAccess(EOS(STATIC_11403(i1756)), i2440, i2520, i1245, i1245, java.lang.Object(ARRAY(i1755)), i2520)
f11403_0_Supprimer_ArrayAccess(EOS(STATIC_11403(i1756)), i2440, i2520, i1245, i1245, java.lang.Object(ARRAY(i1755)), i2520) → f11383_0_Supprimer_ArrayAccess(EOS(STATIC_11383(i1756)), i2440, i2520, i1245, i1245, java.lang.Object(ARRAY(i1755)), i2520)
R rules:

Combined rules. Obtained 3 conditional rules for P and 0 conditional rules for R.

P rules:
f11075_0_Supprimer_Load(EOS(STATIC_11075(x0)), x1, x2, 2) → f11075_0_Supprimer_Load(EOS(STATIC_11075(x0)), +(*(2, x1), 1), x2, 2) | &&(&&(>(x0, +(*(2, x1), 1)), <=(x0, +(*(2, x1), 2))), >=(*(2, x1), 0))
f11075_0_Supprimer_Load(EOS(STATIC_11075(x0)), x1, x2, 2) → f11075_0_Supprimer_Load(EOS(STATIC_11075(x0)), +(*(2, x1), 1), x2, 2) | &&(&&(>(x0, +(*(2, x1), 2)), >(x0, +(*(2, x1), 1))), >=(*(2, x1), 0))
f11075_0_Supprimer_Load(EOS(STATIC_11075(x0)), x1, x2, 2) → f11075_0_Supprimer_Load(EOS(STATIC_11075(x0)), +(*(2, x1), 2), x2, 2) | &&(&&(>(x0, +(*(2, x1), 2)), >(x0, +(*(2, x1), 1))), >=(*(2, x1), 0))
R rules:

Filtered ground terms:

f11075_0_Supprimer_Load(x1, x2, x3, x4) → f11075_0_Supprimer_Load(x1, x2, x3)
Cond_f11075_0_Supprimer_Load(x1, x2, x3, x4, x5) → Cond_f11075_0_Supprimer_Load(x1, x2, x3, x4)
Cond_f11075_0_Supprimer_Load1(x1, x2, x3, x4, x5) → Cond_f11075_0_Supprimer_Load1(x1, x2, x3, x4)
Cond_f11075_0_Supprimer_Load2(x1, x2, x3, x4, x5) → Cond_f11075_0_Supprimer_Load2(x1, x2, x3, x4)

Filtered unneeded arguments:

Cond_f11075_0_Supprimer_Load(x1, x2, x3, x4) → Cond_f11075_0_Supprimer_Load(x1, x2, x3)
Cond_f11075_0_Supprimer_Load1(x1, x2, x3, x4) → Cond_f11075_0_Supprimer_Load1(x1, x2, x3)
Cond_f11075_0_Supprimer_Load2(x1, x2, x3, x4) → Cond_f11075_0_Supprimer_Load2(x1, x2, x3)
f11075_0_Supprimer_Load(x1, x2, x3) → f11075_0_Supprimer_Load(x1, x2)

Combined rules. Obtained 3 conditional rules for P and 0 conditional rules for R.

P rules:
F11075_0_SUPPRIMER_LOAD(EOS(STATIC_11075(x0)), x1) → F11075_0_SUPPRIMER_LOAD(EOS(STATIC_11075(x0)), +(*(2, x1), 1)) | &&(&&(>(x0, +(*(2, x1), 1)), >=(*(2, x1), 0)), <=(x0, +(*(2, x1), 2)))
F11075_0_SUPPRIMER_LOAD(EOS(STATIC_11075(x0)), x1) → F11075_0_SUPPRIMER_LOAD(EOS(STATIC_11075(x0)), +(*(2, x1), 1)) | &&(&&(>(x0, +(*(2, x1), 2)), >=(*(2, x1), 0)), >(x0, +(*(2, x1), 1)))
F11075_0_SUPPRIMER_LOAD(EOS(STATIC_11075(x0)), x1) → F11075_0_SUPPRIMER_LOAD(EOS(STATIC_11075(x0)), +(*(2, x1), 2)) | &&(&&(>(x0, +(*(2, x1), 2)), >=(*(2, x1), 0)), >(x0, +(*(2, x1), 1)))
R rules:

Finished conversion. Obtained 6 rules for P and 0 rules for R. System has predefined symbols.

P rules:
F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), x1) → COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0, +(*(2, x1), 1)), >=(*(2, x1), 0)), <=(x0, +(*(2, x1), 2))), EOS(STATIC_11075(x0)), x1)
COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0)), x1) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), +(*(2, x1), 1))
F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), x1) → COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0, +(*(2, x1), 2)), >=(*(2, x1), 0)), >(x0, +(*(2, x1), 1))), EOS(STATIC_11075(x0)), x1)
COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0)), x1) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), +(*(2, x1), 1))
F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), x1) → COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0, +(*(2, x1), 2)), >=(*(2, x1), 0)), >(x0, +(*(2, x1), 1))), EOS(STATIC_11075(x0)), x1)
COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0)), x1) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), +(*(2, x1), 2))
R rules:

(7) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0]) → COND_F11075_0_SUPPRIMER_LOAD(x0[0] > 2 * x1[0] + 1 && 2 * x1[0] >= 0 && x0[0] <= 2 * x1[0] + 2, EOS(STATIC_11075(x0[0])), x1[0])
(1): COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), 2 * x1[1] + 1)
(2): F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2]) → COND_F11075_0_SUPPRIMER_LOAD1(x0[2] > 2 * x1[2] + 2 && 2 * x1[2] >= 0 && x0[2] > 2 * x1[2] + 1, EOS(STATIC_11075(x0[2])), x1[2])
(3): COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), 2 * x1[3] + 1)
(4): F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4]) → COND_F11075_0_SUPPRIMER_LOAD2(x0[4] > 2 * x1[4] + 2 && 2 * x1[4] >= 0 && x0[4] > 2 * x1[4] + 1, EOS(STATIC_11075(x0[4])), x1[4])
(5): COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), 2 * x1[5] + 2)

(0) -> (1), if (x0[0] > 2 * x1[0] + 1 && 2 * x1[0] >= 0 && x0[0] <= 2 * x1[0] + 2 ∧EOS(STATIC_11075(x0[0])) →^* EOS(STATIC_11075(x0[1]))∧x1[0] →^* x1[1])

(1) -> (0), if (EOS(STATIC_11075(x0[1])) →^* EOS(STATIC_11075(x0[0]))∧2 * x1[1] + 1 →^* x1[0])

(1) -> (2), if (EOS(STATIC_11075(x0[1])) →^* EOS(STATIC_11075(x0[2]))∧2 * x1[1] + 1 →^* x1[2])

(1) -> (4), if (EOS(STATIC_11075(x0[1])) →^* EOS(STATIC_11075(x0[4]))∧2 * x1[1] + 1 →^* x1[4])

(2) -> (3), if (x0[2] > 2 * x1[2] + 2 && 2 * x1[2] >= 0 && x0[2] > 2 * x1[2] + 1 ∧EOS(STATIC_11075(x0[2])) →^* EOS(STATIC_11075(x0[3]))∧x1[2] →^* x1[3])

(3) -> (0), if (EOS(STATIC_11075(x0[3])) →^* EOS(STATIC_11075(x0[0]))∧2 * x1[3] + 1 →^* x1[0])

(3) -> (2), if (EOS(STATIC_11075(x0[3])) →^* EOS(STATIC_11075(x0[2]))∧2 * x1[3] + 1 →^* x1[2])

(3) -> (4), if (EOS(STATIC_11075(x0[3])) →^* EOS(STATIC_11075(x0[4]))∧2 * x1[3] + 1 →^* x1[4])

(4) -> (5), if (x0[4] > 2 * x1[4] + 2 && 2 * x1[4] >= 0 && x0[4] > 2 * x1[4] + 1 ∧EOS(STATIC_11075(x0[4])) →^* EOS(STATIC_11075(x0[5]))∧x1[4] →^* x1[5])

(5) -> (0), if (EOS(STATIC_11075(x0[5])) →^* EOS(STATIC_11075(x0[0]))∧2 * x1[5] + 2 →^* x1[0])

(5) -> (2), if (EOS(STATIC_11075(x0[5])) →^* EOS(STATIC_11075(x0[2]))∧2 * x1[5] + 2 →^* x1[2])

(5) -> (4), if (EOS(STATIC_11075(x0[5])) →^* EOS(STATIC_11075(x0[4]))∧2 * x1[5] + 2 →^* x1[4])

The set Q is empty.

(8) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@11d60023 Constraint Generator: NonInfConstraintGenerator: PathGenerator: MetricPathGenerator: Max Left Steps: 1 Max Right Steps: 1

The constraints were generated the following way:
The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
Note that final constraints are written in bold face.

For Pair F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), x1) → COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0, +(*(2, x1), 1)), >=(*(2, x1), 0)), <=(x0, +(*(2, x1), 2))), EOS(STATIC_11075(x0)), x1) the following chains were created:

We consider the chain F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0]) → COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0]), COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1)) which results in the following constraint:
(1)    (&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2)))=TRUE∧EOS(STATIC_11075(x0[0]))=EOS(STATIC_11075(x0[1]))∧x1[0]=x1[1] ⇒ F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0])≥NonInfC∧F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0])≥COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])∧(U^Increasing(COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (<=(x0[0], +(*(2, x1[0]), 2))=TRUE∧>(x0[0], +(*(2, x1[0]), 1))=TRUE∧>=(*(2, x1[0]), 0)=TRUE ⇒ F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0])≥NonInfC∧F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0])≥COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])∧(U^Increasing(COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    ([2]x1[0] + [2] + [-1]x0[0] ≥ 0∧x0[0] + [-2] + [-2]x1[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])), ≥)∧[bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x1[0] + [bni_26]x0[0] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    ([2]x1[0] + [2] + [-1]x0[0] ≥ 0∧x0[0] + [-2] + [-2]x1[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])), ≥)∧[bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x1[0] + [bni_26]x0[0] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    ([2]x1[0] + [2] + [-1]x0[0] ≥ 0∧x0[0] + [-2] + [-2]x1[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])), ≥)∧[bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x1[0] + [bni_26]x0[0] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    ([-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])), ≥)∧[(3)bni_26 + (-1)Bound*bni_26] + [bni_26]x1[0] + [bni_26]x0[0] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (0 ≥ 0∧0 ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])), ≥)∧[(3)bni_26 + (-1)Bound*bni_26] + [bni_26]x1[0] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (7) using rule (IDP_POLY_GCD) which results in the following new constraint:
(8)    (0 ≥ 0∧0 ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])), ≥)∧[(3)bni_26 + (-1)Bound*bni_26] + [bni_26]x1[0] ≥ 0∧[(-1)bso_27] ≥ 0)

For Pair COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0)), x1) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), +(*(2, x1), 1)) the following chains were created:

We consider the chain F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0]) → COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0]), COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1)), F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0]) → COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0]) which results in the following constraint:
(9)    (&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2)))=TRUE∧EOS(STATIC_11075(x0[0]))=EOS(STATIC_11075(x0[1]))∧x1[0]=x1[1]∧EOS(STATIC_11075(x0[1]))=EOS(STATIC_11075(x0[0]1))∧+(*(2, x1[1]), 1)=x1[0]1 ⇒ COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥))

We simplified constraint (9) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(10)    (<=(x0[0], +(*(2, x1[0]), 2))=TRUE∧>(x0[0], +(*(2, x1[0]), 1))=TRUE∧>=(*(2, x1[0]), 0)=TRUE ⇒ COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[0])), x1[0])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[0])), x1[0])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), +(*(2, x1[0]), 1))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥))

We simplified constraint (10) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(11)    ([2]x1[0] + [2] + [-1]x0[0] ≥ 0∧x0[0] + [-2] + [-2]x1[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x1[0] + [bni_28]x0[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (11) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(12)    ([2]x1[0] + [2] + [-1]x0[0] ≥ 0∧x0[0] + [-2] + [-2]x1[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x1[0] + [bni_28]x0[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (12) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(13)    ([2]x1[0] + [2] + [-1]x0[0] ≥ 0∧x0[0] + [-2] + [-2]x1[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x1[0] + [bni_28]x0[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    ([-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[0] + [bni_28]x0[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (14) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(15)    (0 ≥ 0∧0 ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (15) using rule (IDP_POLY_GCD) which results in the following new constraint:
(16)    (0 ≥ 0∧0 ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)
We consider the chain F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0]) → COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0]), COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1)), F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2]) → COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2]) which results in the following constraint:
(17)    (&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2)))=TRUE∧EOS(STATIC_11075(x0[0]))=EOS(STATIC_11075(x0[1]))∧x1[0]=x1[1]∧EOS(STATIC_11075(x0[1]))=EOS(STATIC_11075(x0[2]))∧+(*(2, x1[1]), 1)=x1[2] ⇒ COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥))

We simplified constraint (17) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(18)    (<=(x0[0], +(*(2, x1[0]), 2))=TRUE∧>(x0[0], +(*(2, x1[0]), 1))=TRUE∧>=(*(2, x1[0]), 0)=TRUE ⇒ COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[0])), x1[0])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[0])), x1[0])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), +(*(2, x1[0]), 1))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥))

We simplified constraint (18) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(19)    ([2]x1[0] + [2] + [-1]x0[0] ≥ 0∧x0[0] + [-2] + [-2]x1[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x1[0] + [bni_28]x0[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (19) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(20)    ([2]x1[0] + [2] + [-1]x0[0] ≥ 0∧x0[0] + [-2] + [-2]x1[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x1[0] + [bni_28]x0[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (20) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(21)    ([2]x1[0] + [2] + [-1]x0[0] ≥ 0∧x0[0] + [-2] + [-2]x1[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x1[0] + [bni_28]x0[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (21) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(22)    ([-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[0] + [bni_28]x0[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (22) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(23)    (0 ≥ 0∧0 ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (23) using rule (IDP_POLY_GCD) which results in the following new constraint:
(24)    (0 ≥ 0∧0 ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)
We consider the chain F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0]) → COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0]), COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1)), F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4]) → COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4]) which results in the following constraint:
(25)    (&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2)))=TRUE∧EOS(STATIC_11075(x0[0]))=EOS(STATIC_11075(x0[1]))∧x1[0]=x1[1]∧EOS(STATIC_11075(x0[1]))=EOS(STATIC_11075(x0[4]))∧+(*(2, x1[1]), 1)=x1[4] ⇒ COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥))

We simplified constraint (25) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(26)    (<=(x0[0], +(*(2, x1[0]), 2))=TRUE∧>(x0[0], +(*(2, x1[0]), 1))=TRUE∧>=(*(2, x1[0]), 0)=TRUE ⇒ COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[0])), x1[0])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[0])), x1[0])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), +(*(2, x1[0]), 1))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥))

We simplified constraint (26) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(27)    ([2]x1[0] + [2] + [-1]x0[0] ≥ 0∧x0[0] + [-2] + [-2]x1[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x1[0] + [bni_28]x0[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (27) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(28)    ([2]x1[0] + [2] + [-1]x0[0] ≥ 0∧x0[0] + [-2] + [-2]x1[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x1[0] + [bni_28]x0[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (28) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(29)    ([2]x1[0] + [2] + [-1]x0[0] ≥ 0∧x0[0] + [-2] + [-2]x1[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]x1[0] + [bni_28]x0[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (29) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(30)    ([-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[0] + [bni_28]x0[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (30) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(31)    (0 ≥ 0∧0 ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

We simplified constraint (31) using rule (IDP_POLY_GCD) which results in the following new constraint:
(32)    (0 ≥ 0∧0 ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)

For Pair F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), x1) → COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0, +(*(2, x1), 2)), >=(*(2, x1), 0)), >(x0, +(*(2, x1), 1))), EOS(STATIC_11075(x0)), x1) the following chains were created:

We consider the chain F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2]) → COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2]), COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1)) which results in the following constraint:
(33)    (&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1)))=TRUE∧EOS(STATIC_11075(x0[2]))=EOS(STATIC_11075(x0[3]))∧x1[2]=x1[3] ⇒ F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2])≥NonInfC∧F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2])≥COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])∧(U^Increasing(COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])), ≥))

We simplified constraint (33) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(34)    (>(x0[2], +(*(2, x1[2]), 1))=TRUE∧>(x0[2], +(*(2, x1[2]), 2))=TRUE∧>=(*(2, x1[2]), 0)=TRUE ⇒ F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2])≥NonInfC∧F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2])≥COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])∧(U^Increasing(COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])), ≥))

We simplified constraint (34) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(35)    (x0[2] + [-2] + [-2]x1[2] ≥ 0∧x0[2] + [-3] + [-2]x1[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])), ≥)∧[bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]x1[2] + [bni_30]x0[2] ≥ 0∧[(-1)bso_31] ≥ 0)

We simplified constraint (35) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(36)    (x0[2] + [-2] + [-2]x1[2] ≥ 0∧x0[2] + [-3] + [-2]x1[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])), ≥)∧[bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]x1[2] + [bni_30]x0[2] ≥ 0∧[(-1)bso_31] ≥ 0)

We simplified constraint (36) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(37)    (x0[2] + [-2] + [-2]x1[2] ≥ 0∧x0[2] + [-3] + [-2]x1[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])), ≥)∧[bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]x1[2] + [bni_30]x0[2] ≥ 0∧[(-1)bso_31] ≥ 0)

We simplified constraint (37) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(38)    (x0[2] ≥ 0∧[-1] + x0[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])), ≥)∧[(3)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] + [bni_30]x0[2] ≥ 0∧[(-1)bso_31] ≥ 0)

We simplified constraint (38) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(39)    ([1] + x0[2] ≥ 0∧x0[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])), ≥)∧[(4)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] + [bni_30]x0[2] ≥ 0∧[(-1)bso_31] ≥ 0)

We simplified constraint (39) using rule (IDP_POLY_GCD) which results in the following new constraint:
(40)    ([1] + x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])), ≥)∧[(4)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] + [bni_30]x0[2] ≥ 0∧[(-1)bso_31] ≥ 0)

For Pair COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0)), x1) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), +(*(2, x1), 1)) the following chains were created:

We consider the chain F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2]) → COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2]), COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1)), F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0]) → COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0]) which results in the following constraint:
(41)    (&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1)))=TRUE∧EOS(STATIC_11075(x0[2]))=EOS(STATIC_11075(x0[3]))∧x1[2]=x1[3]∧EOS(STATIC_11075(x0[3]))=EOS(STATIC_11075(x0[0]))∧+(*(2, x1[3]), 1)=x1[0] ⇒ COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥))

We simplified constraint (41) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(42)    (>(x0[2], +(*(2, x1[2]), 1))=TRUE∧>(x0[2], +(*(2, x1[2]), 2))=TRUE∧>=(*(2, x1[2]), 0)=TRUE ⇒ COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[2])), x1[2])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[2])), x1[2])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), +(*(2, x1[2]), 1))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥))

We simplified constraint (42) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(43)    (x0[2] + [-2] + [-2]x1[2] ≥ 0∧x0[2] + [-3] + [-2]x1[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (43) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(44)    (x0[2] + [-2] + [-2]x1[2] ≥ 0∧x0[2] + [-3] + [-2]x1[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (44) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(45)    (x0[2] + [-2] + [-2]x1[2] ≥ 0∧x0[2] + [-3] + [-2]x1[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (45) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(46)    (x0[2] ≥ 0∧[-1] + x0[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[(3)bni_32 + (-1)Bound*bni_32] + [bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (46) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(47)    ([1] + x0[2] ≥ 0∧x0[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[(4)bni_32 + (-1)Bound*bni_32] + [bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (47) using rule (IDP_POLY_GCD) which results in the following new constraint:
(48)    ([1] + x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[(4)bni_32 + (-1)Bound*bni_32] + [bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)
We consider the chain F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2]) → COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2]), COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1)), F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2]) → COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2]) which results in the following constraint:
(49)    (&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1)))=TRUE∧EOS(STATIC_11075(x0[2]))=EOS(STATIC_11075(x0[3]))∧x1[2]=x1[3]∧EOS(STATIC_11075(x0[3]))=EOS(STATIC_11075(x0[2]1))∧+(*(2, x1[3]), 1)=x1[2]1 ⇒ COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥))

We simplified constraint (49) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(50)    (>(x0[2], +(*(2, x1[2]), 1))=TRUE∧>(x0[2], +(*(2, x1[2]), 2))=TRUE∧>=(*(2, x1[2]), 0)=TRUE ⇒ COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[2])), x1[2])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[2])), x1[2])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), +(*(2, x1[2]), 1))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥))

We simplified constraint (50) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(51)    (x0[2] + [-2] + [-2]x1[2] ≥ 0∧x0[2] + [-3] + [-2]x1[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (51) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(52)    (x0[2] + [-2] + [-2]x1[2] ≥ 0∧x0[2] + [-3] + [-2]x1[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (52) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(53)    (x0[2] + [-2] + [-2]x1[2] ≥ 0∧x0[2] + [-3] + [-2]x1[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (53) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(54)    (x0[2] ≥ 0∧[-1] + x0[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[(3)bni_32 + (-1)Bound*bni_32] + [bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (54) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(55)    ([1] + x0[2] ≥ 0∧x0[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[(4)bni_32 + (-1)Bound*bni_32] + [bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (55) using rule (IDP_POLY_GCD) which results in the following new constraint:
(56)    ([1] + x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[(4)bni_32 + (-1)Bound*bni_32] + [bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)
We consider the chain F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2]) → COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2]), COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1)), F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4]) → COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4]) which results in the following constraint:
(57)    (&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1)))=TRUE∧EOS(STATIC_11075(x0[2]))=EOS(STATIC_11075(x0[3]))∧x1[2]=x1[3]∧EOS(STATIC_11075(x0[3]))=EOS(STATIC_11075(x0[4]))∧+(*(2, x1[3]), 1)=x1[4] ⇒ COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥))

We simplified constraint (57) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(58)    (>(x0[2], +(*(2, x1[2]), 1))=TRUE∧>(x0[2], +(*(2, x1[2]), 2))=TRUE∧>=(*(2, x1[2]), 0)=TRUE ⇒ COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[2])), x1[2])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[2])), x1[2])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), +(*(2, x1[2]), 1))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥))

We simplified constraint (58) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(59)    (x0[2] + [-2] + [-2]x1[2] ≥ 0∧x0[2] + [-3] + [-2]x1[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (59) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(60)    (x0[2] + [-2] + [-2]x1[2] ≥ 0∧x0[2] + [-3] + [-2]x1[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (60) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(61)    (x0[2] + [-2] + [-2]x1[2] ≥ 0∧x0[2] + [-3] + [-2]x1[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[bni_32 + (-1)Bound*bni_32] + [(-1)bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (61) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(62)    (x0[2] ≥ 0∧[-1] + x0[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[(3)bni_32 + (-1)Bound*bni_32] + [bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (62) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(63)    ([1] + x0[2] ≥ 0∧x0[2] ≥ 0∧[2]x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[(4)bni_32 + (-1)Bound*bni_32] + [bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

We simplified constraint (63) using rule (IDP_POLY_GCD) which results in the following new constraint:
(64)    ([1] + x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[(4)bni_32 + (-1)Bound*bni_32] + [bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)

For Pair F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), x1) → COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0, +(*(2, x1), 2)), >=(*(2, x1), 0)), >(x0, +(*(2, x1), 1))), EOS(STATIC_11075(x0)), x1) the following chains were created:

We consider the chain F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4]) → COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4]), COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2)) which results in the following constraint:
(65)    (&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1)))=TRUE∧EOS(STATIC_11075(x0[4]))=EOS(STATIC_11075(x0[5]))∧x1[4]=x1[5] ⇒ F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4])≥NonInfC∧F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4])≥COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])∧(U^Increasing(COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])), ≥))

We simplified constraint (65) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(66)    (>(x0[4], +(*(2, x1[4]), 1))=TRUE∧>(x0[4], +(*(2, x1[4]), 2))=TRUE∧>=(*(2, x1[4]), 0)=TRUE ⇒ F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4])≥NonInfC∧F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4])≥COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])∧(U^Increasing(COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])), ≥))

We simplified constraint (66) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(67)    (x0[4] + [-2] + [-2]x1[4] ≥ 0∧x0[4] + [-3] + [-2]x1[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])), ≥)∧[bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x1[4] + [bni_34]x0[4] ≥ 0∧[(-1)bso_35] ≥ 0)

We simplified constraint (67) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(68)    (x0[4] + [-2] + [-2]x1[4] ≥ 0∧x0[4] + [-3] + [-2]x1[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])), ≥)∧[bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x1[4] + [bni_34]x0[4] ≥ 0∧[(-1)bso_35] ≥ 0)

We simplified constraint (68) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(69)    (x0[4] + [-2] + [-2]x1[4] ≥ 0∧x0[4] + [-3] + [-2]x1[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])), ≥)∧[bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x1[4] + [bni_34]x0[4] ≥ 0∧[(-1)bso_35] ≥ 0)

We simplified constraint (69) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(70)    (x0[4] ≥ 0∧[-1] + x0[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [bni_34]x1[4] + [bni_34]x0[4] ≥ 0∧[(-1)bso_35] ≥ 0)

We simplified constraint (70) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(71)    ([1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])), ≥)∧[(4)bni_34 + (-1)Bound*bni_34] + [bni_34]x1[4] + [bni_34]x0[4] ≥ 0∧[(-1)bso_35] ≥ 0)

We simplified constraint (71) using rule (IDP_POLY_GCD) which results in the following new constraint:
(72)    ([1] + x0[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])), ≥)∧[(4)bni_34 + (-1)Bound*bni_34] + [bni_34]x1[4] + [bni_34]x0[4] ≥ 0∧[(-1)bso_35] ≥ 0)

For Pair COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0)), x1) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), +(*(2, x1), 2)) the following chains were created:

We consider the chain F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4]) → COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4]), COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2)), F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0]) → COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0]) which results in the following constraint:
(73)    (&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1)))=TRUE∧EOS(STATIC_11075(x0[4]))=EOS(STATIC_11075(x0[5]))∧x1[4]=x1[5]∧EOS(STATIC_11075(x0[5]))=EOS(STATIC_11075(x0[0]))∧+(*(2, x1[5]), 2)=x1[0] ⇒ COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥))

We simplified constraint (73) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(74)    (>(x0[4], +(*(2, x1[4]), 1))=TRUE∧>(x0[4], +(*(2, x1[4]), 2))=TRUE∧>=(*(2, x1[4]), 0)=TRUE ⇒ COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[4])), x1[4])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[4])), x1[4])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), +(*(2, x1[4]), 2))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥))

We simplified constraint (74) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(75)    (x0[4] + [-2] + [-2]x1[4] ≥ 0∧x0[4] + [-3] + [-2]x1[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (75) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(76)    (x0[4] + [-2] + [-2]x1[4] ≥ 0∧x0[4] + [-3] + [-2]x1[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (76) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(77)    (x0[4] + [-2] + [-2]x1[4] ≥ 0∧x0[4] + [-3] + [-2]x1[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (77) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(78)    (x0[4] ≥ 0∧[-1] + x0[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[(3)bni_36 + (-1)Bound*bni_36] + [bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (78) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(79)    ([1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (79) using rule (IDP_POLY_GCD) which results in the following new constraint:
(80)    ([1] + x0[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)
We consider the chain F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4]) → COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4]), COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2)), F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2]) → COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2]) which results in the following constraint:
(81)    (&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1)))=TRUE∧EOS(STATIC_11075(x0[4]))=EOS(STATIC_11075(x0[5]))∧x1[4]=x1[5]∧EOS(STATIC_11075(x0[5]))=EOS(STATIC_11075(x0[2]))∧+(*(2, x1[5]), 2)=x1[2] ⇒ COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥))

We simplified constraint (81) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(82)    (>(x0[4], +(*(2, x1[4]), 1))=TRUE∧>(x0[4], +(*(2, x1[4]), 2))=TRUE∧>=(*(2, x1[4]), 0)=TRUE ⇒ COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[4])), x1[4])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[4])), x1[4])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), +(*(2, x1[4]), 2))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥))

We simplified constraint (82) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(83)    (x0[4] + [-2] + [-2]x1[4] ≥ 0∧x0[4] + [-3] + [-2]x1[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (83) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(84)    (x0[4] + [-2] + [-2]x1[4] ≥ 0∧x0[4] + [-3] + [-2]x1[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (84) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(85)    (x0[4] + [-2] + [-2]x1[4] ≥ 0∧x0[4] + [-3] + [-2]x1[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (85) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(86)    (x0[4] ≥ 0∧[-1] + x0[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[(3)bni_36 + (-1)Bound*bni_36] + [bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (86) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(87)    ([1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (87) using rule (IDP_POLY_GCD) which results in the following new constraint:
(88)    ([1] + x0[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)
We consider the chain F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4]) → COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4]), COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2)), F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4]) → COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4]) which results in the following constraint:
(89)    (&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1)))=TRUE∧EOS(STATIC_11075(x0[4]))=EOS(STATIC_11075(x0[5]))∧x1[4]=x1[5]∧EOS(STATIC_11075(x0[5]))=EOS(STATIC_11075(x0[4]1))∧+(*(2, x1[5]), 2)=x1[4]1 ⇒ COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥))

We simplified constraint (89) using rules (I), (II), (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(90)    (>(x0[4], +(*(2, x1[4]), 1))=TRUE∧>(x0[4], +(*(2, x1[4]), 2))=TRUE∧>=(*(2, x1[4]), 0)=TRUE ⇒ COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[4])), x1[4])≥NonInfC∧COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[4])), x1[4])≥F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), +(*(2, x1[4]), 2))∧(U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥))

We simplified constraint (90) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(91)    (x0[4] + [-2] + [-2]x1[4] ≥ 0∧x0[4] + [-3] + [-2]x1[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (91) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(92)    (x0[4] + [-2] + [-2]x1[4] ≥ 0∧x0[4] + [-3] + [-2]x1[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (92) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(93)    (x0[4] + [-2] + [-2]x1[4] ≥ 0∧x0[4] + [-3] + [-2]x1[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (93) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(94)    (x0[4] ≥ 0∧[-1] + x0[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[(3)bni_36 + (-1)Bound*bni_36] + [bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (94) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(95)    ([1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

We simplified constraint (95) using rule (IDP_POLY_GCD) which results in the following new constraint:
(96)    ([1] + x0[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

To summarize, we get the following constraints P_≥ for the following pairs.

F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), x1) → COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0, +(*(2, x1), 1)), >=(*(2, x1), 0)), <=(x0, +(*(2, x1), 2))), EOS(STATIC_11075(x0)), x1)
- (0 ≥ 0∧0 ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])), ≥)∧[(3)bni_26 + (-1)Bound*bni_26] + [bni_26]x1[0] ≥ 0∧[(-1)bso_27] ≥ 0)
COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0)), x1) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), +(*(2, x1), 1))
- (0 ≥ 0∧0 ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)
- (0 ≥ 0∧0 ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)
- (0 ≥ 0∧0 ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))), ≥)∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[0] ≥ 0∧[1 + (-1)bso_29] + x1[0] ≥ 0)
F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), x1) → COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0, +(*(2, x1), 2)), >=(*(2, x1), 0)), >(x0, +(*(2, x1), 1))), EOS(STATIC_11075(x0)), x1)
- ([1] + x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])), ≥)∧[(4)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] + [bni_30]x0[2] ≥ 0∧[(-1)bso_31] ≥ 0)
COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0)), x1) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), +(*(2, x1), 1))
- ([1] + x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[(4)bni_32 + (-1)Bound*bni_32] + [bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)
- ([1] + x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[(4)bni_32 + (-1)Bound*bni_32] + [bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)
- ([1] + x0[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))), ≥)∧[(4)bni_32 + (-1)Bound*bni_32] + [bni_32]x1[2] + [bni_32]x0[2] ≥ 0∧[1 + (-1)bso_33] + x1[2] ≥ 0)
F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), x1) → COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0, +(*(2, x1), 2)), >=(*(2, x1), 0)), >(x0, +(*(2, x1), 1))), EOS(STATIC_11075(x0)), x1)
- ([1] + x0[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])), ≥)∧[(4)bni_34 + (-1)Bound*bni_34] + [bni_34]x1[4] + [bni_34]x0[4] ≥ 0∧[(-1)bso_35] ≥ 0)
COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0)), x1) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0)), +(*(2, x1), 2))
- ([1] + x0[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)
- ([1] + x0[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)
- ([1] + x0[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x1[4] + [bni_36]x0[4] ≥ 0∧[2 + (-1)bso_37] + x1[4] ≥ 0)

The constraints for P_> respective P_bound are constructed from P_≥ where we just replace every occurence of "t ≥ s" in P_≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for P_bound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0
POL(FALSE) = 0
POL(F11075_0_SUPPRIMER_LOAD'(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(EOS(x₁)) = [-1] + x₁
POL(STATIC_11075(x₁)) = [-1] + [-1]x₁
POL(COND_F11075_0_SUPPRIMER_LOAD(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂
POL(&&(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(+(x₁, x₂)) = x₁ + x₂
POL(*(x₁, x₂)) = x₁·x₂
POL(2) = [2]
POL(1) = [1]
POL(>=(x₁, x₂)) = [-1]
POL(0) = 0
POL(<=(x₁, x₂)) = [-1]
POL(COND_F11075_0_SUPPRIMER_LOAD1(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂
POL(COND_F11075_0_SUPPRIMER_LOAD2(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂

The following pairs are in P_>:

COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))
COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))
COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))

The following pairs are in P_bound:

F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0]) → COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])
COND_F11075_0_SUPPRIMER_LOAD(TRUE, EOS(STATIC_11075(x0[1])), x1[1]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[1])), +(*(2, x1[1]), 1))
F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2]) → COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])
COND_F11075_0_SUPPRIMER_LOAD1(TRUE, EOS(STATIC_11075(x0[3])), x1[3]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[3])), +(*(2, x1[3]), 1))
F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4]) → COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])
COND_F11075_0_SUPPRIMER_LOAD2(TRUE, EOS(STATIC_11075(x0[5])), x1[5]) → F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[5])), +(*(2, x1[5]), 2))

The following pairs are in P_≥:

F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[0])), x1[0]) → COND_F11075_0_SUPPRIMER_LOAD(&&(&&(>(x0[0], +(*(2, x1[0]), 1)), >=(*(2, x1[0]), 0)), <=(x0[0], +(*(2, x1[0]), 2))), EOS(STATIC_11075(x0[0])), x1[0])
F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[2])), x1[2]) → COND_F11075_0_SUPPRIMER_LOAD1(&&(&&(>(x0[2], +(*(2, x1[2]), 2)), >=(*(2, x1[2]), 0)), >(x0[2], +(*(2, x1[2]), 1))), EOS(STATIC_11075(x0[2])), x1[2])
F11075_0_SUPPRIMER_LOAD'(EOS(STATIC_11075(x0[4])), x1[4]) → COND_F11075_0_SUPPRIMER_LOAD2(&&(&&(>(x0[4], +(*(2, x1[4]), 2)), >=(*(2, x1[4]), 0)), >(x0[4], +(*(2, x1[4]), 1))), EOS(STATIC_11075(x0[4])), x1[4])

At least the following rules have been oriented under context sensitive arithmetic replacement:

TRUE¹ → &&(TRUE, TRUE)¹
FALSE¹ → &&(TRUE, FALSE)¹
FALSE¹ → &&(FALSE, TRUE)¹
FALSE¹ → &&(FALSE, FALSE)¹

(9) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Boolean, Integer

(10) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(11) TRUE

(12) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: TriTas.Ajouter(I)V
SCC calls the following helper methods:
Performed SCC analyses:

Used field analysis yielded the following read fields:
Marker field analysis yielded the following relations that could be markers:

(13) SCCToIntTRSProof (SOUND transformation)

Transformed FIGraph SCCs to intTRSs. Log:

Generated rules. Obtained 40 IRules

P rules:
f4539_0_Ajouter_LE(EOS, i342, i342, i836, i836) → f4563_0_Ajouter_LE(EOS, i342, i342, i836, i836)
f4563_0_Ajouter_LE(EOS, i342, i342, i836, i836) → f4577_0_Ajouter_FieldAccess(EOS, i342, i342, i836) | >(i836, 0)
f4577_0_Ajouter_FieldAccess(EOS, i342, i342, i836) → f4587_0_Ajouter_Load(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)))
f4587_0_Ajouter_Load(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339))) → f4605_0_Ajouter_ConstantStackPush(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f4605_0_Ajouter_ConstantStackPush(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f4627_0_Ajouter_IntArithmetic(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, 1)
f4627_0_Ajouter_IntArithmetic(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, matching1) → f4735_0_Ajouter_ConstantStackPush(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), -(i836, 1)) | &&(>(i836, 0), =(matching1, 1))
f4735_0_Ajouter_ConstantStackPush(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i862) → f4788_0_Ajouter_IntArithmetic(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i862, 2)
f4788_0_Ajouter_IntArithmetic(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i862, matching1) → f4816_0_Ajouter_ArrayAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), /(i862, 2)) | =(matching1, 2)
f4816_0_Ajouter_ArrayAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f4846_0_Ajouter_ArrayAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f4846_0_Ajouter_ArrayAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f4882_0_Ajouter_Load(EOS, i342, i342, i836, i886) | <(i877, i339)
f4882_0_Ajouter_Load(EOS, i342, i342, i836, i886) → f4956_0_Ajouter_GT(EOS, i342, i342, i836, i886, i342)
f4956_0_Ajouter_GT(EOS, i342, i342, i836, i886, i342) → f5001_0_Ajouter_GT(EOS, i342, i342, i836, i886, i342)
f5001_0_Ajouter_GT(EOS, i342, i342, i836, i886, i342) → f5047_0_Ajouter_FieldAccess(EOS, i342, i342, i836) | <=(i886, i342)
f5047_0_Ajouter_FieldAccess(EOS, i342, i342, i836) → f5115_0_Ajouter_Load(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)))
f5115_0_Ajouter_Load(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339))) → f5167_0_Ajouter_FieldAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f5167_0_Ajouter_FieldAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f5230_0_Ajouter_Load(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)))
f5230_0_Ajouter_Load(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339))) → f5289_0_Ajouter_ConstantStackPush(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i836)
f5289_0_Ajouter_ConstantStackPush(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i836) → f5341_0_Ajouter_IntArithmetic(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i836, 1)
f5341_0_Ajouter_IntArithmetic(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i836, matching1) → f5465_0_Ajouter_ConstantStackPush(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), -(i836, 1)) | &&(>(i836, 0), =(matching1, 1))
f5465_0_Ajouter_ConstantStackPush(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1072) → f5803_0_Ajouter_IntArithmetic(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1072, 2)
f5803_0_Ajouter_IntArithmetic(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1072, matching1) → f5882_0_Ajouter_ArrayAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), /(i1072, 2)) | =(matching1, 2)
f5882_0_Ajouter_ArrayAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f5961_0_Ajouter_ArrayAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f5961_0_Ajouter_ArrayAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f6069_0_Ajouter_ArrayAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) | <(i1129, i339)
f6069_0_Ajouter_ArrayAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f6118_0_Ajouter_ArrayAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f6118_0_Ajouter_ArrayAccess(EOS, i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f6195_0_Ajouter_Load(EOS, i342, i342, i836) | <(i836, i339)
f6195_0_Ajouter_Load(EOS, i342, i342, i836) → f6317_0_Ajouter_ConstantStackPush(EOS, i342, i342, i836, i836)
f6317_0_Ajouter_ConstantStackPush(EOS, i342, i342, i836, i836) → f6397_0_Ajouter_IntArithmetic(EOS, i342, i342, i836, i836, 1)
f6397_0_Ajouter_IntArithmetic(EOS, i342, i342, i836, i836, matching1) → f6501_0_Ajouter_ConstantStackPush(EOS, i342, i342, i836, -(i836, 1)) | &&(>(i836, 0), =(matching1, 1))
f6501_0_Ajouter_ConstantStackPush(EOS, i342, i342, i836, i1205) → f6634_0_Ajouter_IntArithmetic(EOS, i342, i342, i836, i1205, 2)
f6634_0_Ajouter_IntArithmetic(EOS, i342, i342, i836, i1205, matching1) → f6739_0_Ajouter_Store(EOS, i342, i342, i836, /(i1205, 2)) | =(matching1, 2)
f6739_0_Ajouter_Store(EOS, i342, i342, i836, i1228) → f6838_0_Ajouter_Load(EOS, i342, i342, i836, i1228)
f6838_0_Ajouter_Load(EOS, i342, i342, i836, i1228) → f6895_0_Ajouter_Load(EOS, i342, i342, i836, i1228, i1228)
f6895_0_Ajouter_Load(EOS, i342, i342, i836, i1228, i1228) → f6942_0_Ajouter_LT(EOS, i342, i342, i836, i1228, i1228, i836)
f6942_0_Ajouter_LT(EOS, i342, i342, i836, i1228, i1228, i836) → f7004_0_Ajouter_LT(EOS, i342, i342, i836, i1228, i1228, i836)
f7004_0_Ajouter_LT(EOS, i342, i342, i836, i1228, i1228, i836) → f7105_0_Ajouter_Load(EOS, i342, i342, i1228) | <(i1228, i836)
f7105_0_Ajouter_Load(EOS, i342, i342, i1228) → f7260_0_Ajouter_Store(EOS, i342, i342, i1228)
f7260_0_Ajouter_Store(EOS, i342, i342, i1228) → f7362_0_Ajouter_JMP(EOS, i342, i342, i1228)
f7362_0_Ajouter_JMP(EOS, i342, i342, i1228) → f7408_0_Ajouter_Load(EOS, i342, i342, i1228)
f7408_0_Ajouter_Load(EOS, i342, i342, i1228) → f4477_0_Ajouter_Load(EOS, i342, i342, i1228)
f4477_0_Ajouter_Load(EOS, i342, i342, i804) → f4539_0_Ajouter_LE(EOS, i342, i342, i804, i804)

Combined rules. Obtained 1 IRules

P rules:
f4539_0_Ajouter_LE(EOS, x0, x0, x1, x1) → f4539_0_Ajouter_LE(EOS, x0, x0, /(-(x1, 1), 2), /(-(x1, 1), 2)) | &&(>(x1, 0), <(/(-(x1, 1), 2), x1))

Filtered ground terms:

f4539_0_Ajouter_LE(x1, x2, x3, x4, x5) → f4539_0_Ajouter_LE(x2, x3, x4, x5)
Cond_f4539_0_Ajouter_LE(x1, x2, x3, x4, x5, x6) → Cond_f4539_0_Ajouter_LE(x1, x3, x4, x5, x6)

Filtered duplicate terms:

f4539_0_Ajouter_LE(x1, x2, x3, x4) → f4539_0_Ajouter_LE(x2, x4)
Cond_f4539_0_Ajouter_LE(x1, x2, x3, x4, x5) → Cond_f4539_0_Ajouter_LE(x1, x3, x5)

Filtered unneeded terms:

Cond_f4539_0_Ajouter_LE(x1, x2, x3) → Cond_f4539_0_Ajouter_LE(x1, x3)
f4539_0_Ajouter_LE(x1, x2) → f4539_0_Ajouter_LE(x2)

Prepared 1 rules for path length conversion:

P rules:
f4539_0_Ajouter_LE(x1) → f4539_0_Ajouter_LE(/(-(x1, 1), 2)) | &&(>(x1, 0), <(/(-(x1, 1), 2), x1))

Finished conversion. Obtained 2 rules.

P rules:
f4539_0_Ajouter_LE(x0) → f4539_0_Ajouter_LE'(x0) | &&(>(x0, 0), >(x0, div))
f4539_0_Ajouter_LE'(x0) → f4539_0_Ajouter_LE(arith) | &&(&&(&&(&&(&&(>(x0, div), >(x0, 0)), >=(-(-(x0, 1), *(2, div)), 0)), <(-(-(x0, 1), *(2, div)), 2)), <(-(-(x0, 1), *(2, arith)), 2)), >=(-(-(x0, 1), *(2, arith)), 0))

(14) Obligation:

Rules:
f4539_0_Ajouter_LE(x0) → f4539_0_Ajouter_LE'(x0) | &&(>(x0, 0), >(x0, div))
f4539_0_Ajouter_LE'(x0) → f4539_0_Ajouter_LE(arith) | &&(&&(&&(&&(&&(>(x0, div), >(x0, 0)), >=(-(-(x0, 1), *(2, div)), 0)), <(-(-(x0, 1), *(2, div)), 2)), <(-(-(x0, 1), *(2, arith)), 2)), >=(-(-(x0, 1), *(2, arith)), 0))

(15) PolynomialOrderProcessor (EQUIVALENT transformation)

Found the following polynomial interpretation:

[f4539_0_Ajouter_LE(x6)] = 1 + 2·x6
[f4539_0_Ajouter_LE'(x9)] = 2·x9

Therefore the following rule(s) have been dropped:

f4539_0_Ajouter_LE(x0) → f4539_0_Ajouter_LE'(x0) | &&(>(x0, 0), >(x0, x1))
f4539_0_Ajouter_LE'(x2) → f4539_0_Ajouter_LE(x3) | &&(&&(&&(&&(&&(>(x2, x4), >(x2, 0)), >=(-(-(x2, 1), *(2, x4)), 0)), <(-(-(x2, 1), *(2, x4)), 2)), <(-(-(x2, 1), *(2, x3)), 2)), >=(-(-(x2, 1), *(2, x3)), 0))

(16) YES

(17) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: TriTas.HeapSort()V
SCC calls the following helper methods: TriTas.Supprimer()V
Performed SCC analyses:

Used field analysis yielded the following read fields:
Marker field analysis yielded the following relations that could be markers:

(18) SCCToIntTRSProof (SOUND transformation)

Transformed FIGraph SCCs to intTRSs. Log:

Generated rules. Obtained 24 IRules

P rules:
f7938_0_HeapSort_LT(EOS, i1488, i1488) → f7957_0_HeapSort_LT(EOS, i1488, i1488)
f7957_0_HeapSort_LT(EOS, i1488, i1488) → f8017_0_HeapSort_InvokeMethod(EOS, i1488) | >=(i1488, 0)
f8017_0_HeapSort_InvokeMethod(EOS, i1488) → f8040_0_Maximum_FieldAccess(EOS, i1488)
f8040_0_Maximum_FieldAccess(EOS, i1488) → f8115_0_Maximum_ConstantStackPush(EOS, i1488, java.lang.Object(ARRAY(i1467)))
f8115_0_Maximum_ConstantStackPush(EOS, i1488, java.lang.Object(ARRAY(i1467))) → f8141_0_Maximum_ArrayAccess(EOS, i1488, java.lang.Object(ARRAY(i1467)), 0)
f8141_0_Maximum_ArrayAccess(EOS, i1488, java.lang.Object(ARRAY(i1531)), matching1) → f8156_0_Maximum_ArrayAccess(EOS, i1488, java.lang.Object(ARRAY(i1531)), 0) | =(matching1, 0)
f8156_0_Maximum_ArrayAccess(EOS, i1488, java.lang.Object(ARRAY(i1531)), matching1) → f8212_0_Maximum_Return(EOS, i1488) | &&(<(0, i1531), =(matching1, 0))
f8212_0_Maximum_Return(EOS, i1488) → f8222_0_HeapSort_Store(EOS, i1488)
f8222_0_HeapSort_Store(EOS, i1488) → f8238_0_HeapSort_InvokeMethod(EOS, i1488)
f8238_0_HeapSort_InvokeMethod(EOS, i1488) → f8248_0_Supprimer_FieldAccess(EOS)
f8238_0_HeapSort_InvokeMethod(EOS, i1488) → f8248_1_Supprimer_FieldAccess(EOS, i1488)
f8248_0_Supprimer_FieldAccess(EOS) → f8321_0_Supprimer_FieldAccess(EOS)
f11660_0_Supprimer_Return(EOS, i1488) → f9261_0_Supprimer_Return(EOS, i1488)
f9261_0_Supprimer_Return(EOS, i1488) → f9272_0_HeapSort_FieldAccess(EOS, i1488)
f9272_0_HeapSort_FieldAccess(EOS, i1488) → f9306_0_HeapSort_Load(EOS, i1488, java.lang.Object(ARRAY(i1797)))
f9306_0_HeapSort_Load(EOS, i1488, java.lang.Object(ARRAY(i1797))) → f9328_0_HeapSort_Load(EOS, i1488, java.lang.Object(ARRAY(i1797)), i1488)
f9328_0_HeapSort_Load(EOS, i1488, java.lang.Object(ARRAY(i1797)), i1488) → f9335_0_HeapSort_ArrayAccess(EOS, i1488, java.lang.Object(ARRAY(i1797)), i1488)
f9335_0_HeapSort_ArrayAccess(EOS, i1488, java.lang.Object(ARRAY(i1797)), i1488) → f9341_0_HeapSort_ArrayAccess(EOS, i1488, java.lang.Object(ARRAY(i1797)), i1488)
f9341_0_HeapSort_ArrayAccess(EOS, i1488, java.lang.Object(ARRAY(i1797)), i1488) → f9344_0_HeapSort_Inc(EOS, i1488) | <(i1488, i1797)
f9344_0_HeapSort_Inc(EOS, i1488) → f9352_0_HeapSort_JMP(EOS, +(i1488, -1)) | >=(i1488, 0)
f9352_0_HeapSort_JMP(EOS, i1823) → f9368_0_HeapSort_Load(EOS, i1823)
f9368_0_HeapSort_Load(EOS, i1823) → f7895_0_HeapSort_Load(EOS, i1823)
f7895_0_HeapSort_Load(EOS, i1470) → f7938_0_HeapSort_LT(EOS, i1470, i1470)
f8248_1_Supprimer_FieldAccess(EOS, i1488) → f11660_0_Supprimer_Return(EOS, i1488)

Combined rules. Obtained 2 IRules

P rules:
f11660_0_Supprimer_Return(EOS, x0) → f8321_0_Supprimer_FieldAccess(EOS) | >(+(x0, 1), 1)
f11660_0_Supprimer_Return(EOS, x0) → f11660_0_Supprimer_Return(EOS, -(x0, 1)) | >(+(x0, 1), 1)

Filtered ground terms:

f11660_0_Supprimer_Return(x1, x2) → f11660_0_Supprimer_Return(x2)
Cond_f11660_0_Supprimer_Return(x1, x2, x3) → Cond_f11660_0_Supprimer_Return(x1, x3)
f8321_0_Supprimer_FieldAccess(x1) → f8321_0_Supprimer_FieldAccess
Cond_f11660_0_Supprimer_Return1(x1, x2, x3) → Cond_f11660_0_Supprimer_Return1(x1, x3)

Filtered unneeded terms:

Cond_f11660_0_Supprimer_Return(x1, x2) → Cond_f11660_0_Supprimer_Return(x1)

Prepared 2 rules for path length conversion:

P rules:
f11660_0_Supprimer_Return(x0) → f8321_0_Supprimer_FieldAccess | >(+(x0, 1), 1)
f11660_0_Supprimer_Return(x0) → f11660_0_Supprimer_Return(-(x0, 1)) | >(+(x0, 1), 1)

Finished conversion. Obtained 1 rules.

P rules:
f11660_0_Supprimer_Return(x1) → f11660_0_Supprimer_Return(-(x1, 1)) | >(x1, 0)

(19) Obligation:

Rules:
f11660_0_Supprimer_Return(x1) → f11660_0_Supprimer_Return(-(x1, 1)) | >(x1, 0)

(20) PolynomialOrderProcessor (EQUIVALENT transformation)

Found the following polynomial interpretation:

[f11660_0_Supprimer_Return(x2)] = x2

Therefore the following rule(s) have been dropped:

f11660_0_Supprimer_Return(x0) → f11660_0_Supprimer_Return(-(x0, 1)) | >(x0, 0)

(21) YES

(22) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: TriTas.HeapSort()V
SCC calls the following helper methods: TriTas.Ajouter(I)V
Performed SCC analyses:

Used field analysis yielded the following read fields:
Marker field analysis yielded the following relations that could be markers:

(23) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 20 rules for P and 210 rules for R.

P rules:
f5116_0_HeapSort_FieldAccess(EOS(STATIC_5116(i950)), i953, i953) → f5122_0_HeapSort_GE(EOS(STATIC_5122(i950)), i953, i953, i950)
f5122_0_HeapSort_GE(EOS(STATIC_5122(i950)), i953, i953, i950) → f5131_0_HeapSort_GE(EOS(STATIC_5131(i950)), i953, i953, i950)
f5131_0_HeapSort_GE(EOS(STATIC_5131(i950)), i953, i953, i950) → f5163_0_HeapSort_FieldAccess(EOS(STATIC_5163(i950)), i953) | <(i953, i950)
f5163_0_HeapSort_FieldAccess(EOS(STATIC_5163(i950)), i953) → f5179_0_HeapSort_Load(EOS(STATIC_5179(i950)), i953, java.lang.Object(ARRAY(i950)))
f5179_0_HeapSort_Load(EOS(STATIC_5179(i950)), i953, java.lang.Object(ARRAY(i950))) → f5200_0_HeapSort_ArrayAccess(EOS(STATIC_5200(i950)), i953, java.lang.Object(ARRAY(i950)), i953)
f5200_0_HeapSort_ArrayAccess(EOS(STATIC_5200(i950)), i953, java.lang.Object(ARRAY(i950)), i953) → f5232_0_HeapSort_ArrayAccess(EOS(STATIC_5232(i950)), i953, java.lang.Object(ARRAY(i950)), i953)
f5232_0_HeapSort_ArrayAccess(EOS(STATIC_5232(i950)), i953, java.lang.Object(ARRAY(i950)), i953) → f5250_0_HeapSort_InvokeMethod(EOS(STATIC_5250(i950)), i953, i1001) | <(i953, i950)
f5250_0_HeapSort_InvokeMethod(EOS(STATIC_5250(i950)), i953, i1001) → f5290_1_HeapSort_InvokeMethod(f5290_0_Ajouter_FieldAccess(EOS(STATIC_5290(i950)), i1001, i1001), i953, i1001)
f5290_0_Ajouter_FieldAccess(EOS(STATIC_5290(i950)), i1001, i1001) → f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(i950)), i1001, i1001)
f5544_0_Ajouter_Return(EOS(STATIC_5544(i1055)), i953, i1053) → f5716_0_Ajouter_Return(EOS(STATIC_5716(i1055)), i953, i1053)
f5716_0_Ajouter_Return(EOS(STATIC_5716(i1100)), i953, i1103) → f5846_0_HeapSort_Inc(EOS(STATIC_5846(i1100)), i953)
f5846_0_HeapSort_Inc(EOS(STATIC_5846(i1100)), i953) → f5901_0_HeapSort_JMP(EOS(STATIC_5901(i1100)), +(i953, 1)) | >=(i953, 0)
f5901_0_HeapSort_JMP(EOS(STATIC_5901(i1100)), i1134) → f5950_0_HeapSort_Load(EOS(STATIC_5950(i1100)), i1134)
f5950_0_HeapSort_Load(EOS(STATIC_5950(i1100)), i1134) → f5069_0_HeapSort_Load(EOS(STATIC_5069(i1100)), i1134)
f5069_0_HeapSort_Load(EOS(STATIC_5069(i950)), i953) → f5116_0_HeapSort_FieldAccess(EOS(STATIC_5116(i950)), i953, i953)
f5715_0_Ajouter_Return(EOS(STATIC_5715(i1065)), i953, i1063) → f5716_0_Ajouter_Return(EOS(STATIC_5716(i1065)), i953, i1063)
f7858_0_Ajouter_Return(EOS(STATIC_7858(i1440)), i953, i1438) → f5716_0_Ajouter_Return(EOS(STATIC_5716(i1440)), i953, i1438)
f5290_1_HeapSort_InvokeMethod(f4806_0_Ajouter_Return(EOS(STATIC_4806(i1055)), i1053), i953, i1053) → f5544_0_Ajouter_Return(EOS(STATIC_5544(i1055)), i953, i1053)
f5290_1_HeapSort_InvokeMethod(f5320_0_Ajouter_Return(EOS(STATIC_5320(i1065)), i1063), i953, i1063) → f5715_0_Ajouter_Return(EOS(STATIC_5715(i1065)), i953, i1063)
f5290_1_HeapSort_InvokeMethod(f7598_0_Ajouter_Return(EOS(STATIC_7598(i1440)), i1438), i953, i1438) → f7858_0_Ajouter_Return(EOS(STATIC_7858(i1440)), i953, i1438)
R rules:
f5290_0_Ajouter_FieldAccess(EOS(STATIC_5290(i950)), i1001, i1001) → f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(i950)), i1001, i1001)
f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(i950)), i1001, i1001) → f2463_0_Ajouter_FieldAccess(EOS(STATIC_2463(i950)), i1001, i1001)
f2463_0_Ajouter_FieldAccess(EOS(STATIC_2463(i339)), i342, i342) → f2567_0_Ajouter_ConstantStackPush(EOS(STATIC_2567(i339)), i342, i342, i340)
f2567_0_Ajouter_ConstantStackPush(EOS(STATIC_2567(i339)), i342, i342, i340) → f2574_0_Ajouter_IntArithmetic(EOS(STATIC_2574(i339)), i342, i342, i340, 1)
f2574_0_Ajouter_IntArithmetic(EOS(STATIC_2574(i339)), i342, i342, i340, matching1) → f2578_0_Ajouter_FieldAccess(EOS(STATIC_2578(i339)), i342, i342, +(i340, 1)) | =(matching1, 1)
f2578_0_Ajouter_FieldAccess(EOS(STATIC_2578(i339)), i342, i342, i355) → f2583_0_Ajouter_FieldAccess(EOS(STATIC_2583(i339)), i342, i342)
f2583_0_Ajouter_FieldAccess(EOS(STATIC_2583(i339)), i342, i342) → f2591_0_Ajouter_ConstantStackPush(EOS(STATIC_2591(i339)), i342, i342, i355)
f2591_0_Ajouter_ConstantStackPush(EOS(STATIC_2591(i339)), i342, i342, i355) → f2596_0_Ajouter_IntArithmetic(EOS(STATIC_2596(i339)), i342, i342, i355, 1)
f2596_0_Ajouter_IntArithmetic(EOS(STATIC_2596(i339)), i342, i342, i355, matching1) → f2603_0_Ajouter_Store(EOS(STATIC_2603(i339)), i342, i342, -(i355, 1)) | =(matching1, 1)
f2603_0_Ajouter_Store(EOS(STATIC_2603(i339)), i342, i342, i357) → f2611_0_Ajouter_Load(EOS(STATIC_2611(i339)), i342, i342, i357)
f2611_0_Ajouter_Load(EOS(STATIC_2611(i339)), i342, i342, i357) → f4477_0_Ajouter_Load(EOS(STATIC_4477(i339)), i342, i342, i357)
f4477_0_Ajouter_Load(EOS(STATIC_4477(i339)), i342, i342, i804) → f4539_0_Ajouter_LE(EOS(STATIC_4539(i339)), i342, i342, i804, i804)
f4539_0_Ajouter_LE(EOS(STATIC_4539(i339)), i342, i342, i835, i835) → f4562_0_Ajouter_LE(EOS(STATIC_4562(i339)), i342, i342, i835, i835)
f4539_0_Ajouter_LE(EOS(STATIC_4539(i339)), i342, i342, i836, i836) → f4563_0_Ajouter_LE(EOS(STATIC_4563(i339)), i342, i342, i836, i836)
f4562_0_Ajouter_LE(EOS(STATIC_4562(i339)), i342, i342, i835, i835) → f4570_0_Ajouter_FieldAccess(EOS(STATIC_4570(i339)), i342, i342, i835) | <=(i835, 0)
f4563_0_Ajouter_LE(EOS(STATIC_4563(i339)), i342, i342, i836, i836) → f4577_0_Ajouter_FieldAccess(EOS(STATIC_4577(i339)), i342, i342, i836) | >(i836, 0)
f4570_0_Ajouter_FieldAccess(EOS(STATIC_4570(i339)), i342, i342, i835) → f4581_0_Ajouter_Load(EOS(STATIC_4581(i339)), i342, i342, i835, java.lang.Object(ARRAY(i339)))
f4577_0_Ajouter_FieldAccess(EOS(STATIC_4577(i339)), i342, i342, i836) → f4587_0_Ajouter_Load(EOS(STATIC_4587(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)))
f4581_0_Ajouter_Load(EOS(STATIC_4581(i339)), i342, i342, i835, java.lang.Object(ARRAY(i339))) → f4593_0_Ajouter_Load(EOS(STATIC_4593(i339)), i342, i342, java.lang.Object(ARRAY(i339)), i835)
f4587_0_Ajouter_Load(EOS(STATIC_4587(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339))) → f4605_0_Ajouter_ConstantStackPush(EOS(STATIC_4605(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f4593_0_Ajouter_Load(EOS(STATIC_4593(i339)), i342, i342, java.lang.Object(ARRAY(i339)), i835) → f4613_0_Ajouter_ArrayAccess(EOS(STATIC_4613(i339)), i342, java.lang.Object(ARRAY(i339)), i835, i342)
f4605_0_Ajouter_ConstantStackPush(EOS(STATIC_4605(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f4627_0_Ajouter_IntArithmetic(EOS(STATIC_4627(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, 1)
f4613_0_Ajouter_ArrayAccess(EOS(STATIC_4613(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f4648_0_Ajouter_ArrayAccess(EOS(STATIC_4648(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f4613_0_Ajouter_ArrayAccess(EOS(STATIC_4613(i339)), i342, java.lang.Object(ARRAY(i339)), matching1, i342) → f4649_0_Ajouter_ArrayAccess(EOS(STATIC_4649(i339)), i342, java.lang.Object(ARRAY(i339)), 0, i342) | =(matching1, 0)
f4627_0_Ajouter_IntArithmetic(EOS(STATIC_4627(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, matching1) → f4735_0_Ajouter_ConstantStackPush(EOS(STATIC_4735(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), -(i836, 1)) | &&(>(i836, 0), =(matching1, 1))
f4648_0_Ajouter_ArrayAccess(EOS(STATIC_4648(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f4755_0__init__Load(EOS(STATIC_4755(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) | <=(i854, -1)
f4649_0_Ajouter_ArrayAccess(EOS(STATIC_4649(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f4778_0_Ajouter_ArrayAccess(EOS(STATIC_4778(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f4649_0_Ajouter_ArrayAccess(EOS(STATIC_4649(i871)), i342, java.lang.Object(ARRAY(i871)), matching1, i342) → f4779_0_Ajouter_ArrayAccess(EOS(STATIC_4779(i871)), i342, java.lang.Object(ARRAY(i871)), 0, i342) | =(matching1, 0)
f4735_0_Ajouter_ConstantStackPush(EOS(STATIC_4735(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i862) → f4788_0_Ajouter_IntArithmetic(EOS(STATIC_4788(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i862, 2)
f4755_0__init__Load(EOS(STATIC_4755(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f4824_0__init__InvokeMethod(EOS(STATIC_4824(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f4778_0_Ajouter_ArrayAccess(EOS(STATIC_4778(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f4802_0__init__Load(EOS(STATIC_4802(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | &&(&&(>=(0, 0), <=(i870, 0)), =(matching1, 0))
f4779_0_Ajouter_ArrayAccess(EOS(STATIC_4779(i871)), i342, java.lang.Object(ARRAY(i871)), matching1, i342) → f4806_0_Ajouter_Return(EOS(STATIC_4806(i871)), i342) | &&(<(0, i871), =(matching1, 0))
f4788_0_Ajouter_IntArithmetic(EOS(STATIC_4788(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i862, matching1) → f4816_0_Ajouter_ArrayAccess(EOS(STATIC_4816(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), /(i862, 2)) | =(matching1, 2)
f4802_0__init__Load(EOS(STATIC_4802(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f4869_0__init__InvokeMethod(EOS(STATIC_4869(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f4806_0_Ajouter_Return(EOS(STATIC_4806(i871)), i342) → f5320_0_Ajouter_Return(EOS(STATIC_5320(i871)), i342)
f4816_0_Ajouter_ArrayAccess(EOS(STATIC_4816(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f4846_0_Ajouter_ArrayAccess(EOS(STATIC_4846(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f4816_0_Ajouter_ArrayAccess(EOS(STATIC_4816(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f4847_0_Ajouter_ArrayAccess(EOS(STATIC_4847(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f4824_0__init__InvokeMethod(EOS(STATIC_4824(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f4863_0__init__Load(EOS(STATIC_4863(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f4846_0_Ajouter_ArrayAccess(EOS(STATIC_4846(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f4882_0_Ajouter_Load(EOS(STATIC_4882(i339)), i342, i342, i836, i886) | <(i877, i339)
f4847_0_Ajouter_ArrayAccess(EOS(STATIC_4847(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f4903_0__init__Load(EOS(STATIC_4903(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) | >=(i877, i339)
f4863_0__init__Load(EOS(STATIC_4863(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f4983_0__init__InvokeMethod(EOS(STATIC_4983(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f4869_0__init__InvokeMethod(EOS(STATIC_4869(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f4931_0__init__Load(EOS(STATIC_4931(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f4882_0_Ajouter_Load(EOS(STATIC_4882(i339)), i342, i342, i836, i886) → f4956_0_Ajouter_GT(EOS(STATIC_4956(i339)), i342, i342, i836, i886, i342)
f4903_0__init__Load(EOS(STATIC_4903(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f5013_0__init__InvokeMethod(EOS(STATIC_5013(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f4931_0__init__Load(EOS(STATIC_4931(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f5028_0__init__InvokeMethod(EOS(STATIC_5028(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f4956_0_Ajouter_GT(EOS(STATIC_4956(i339)), i342, i342, i836, i886, i342) → f5000_0_Ajouter_GT(EOS(STATIC_5000(i339)), i342, i342, i836, i886, i342)
f4956_0_Ajouter_GT(EOS(STATIC_4956(i339)), i342, i342, i836, i886, i342) → f5001_0_Ajouter_GT(EOS(STATIC_5001(i339)), i342, i342, i836, i886, i342)
f4983_0__init__InvokeMethod(EOS(STATIC_4983(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f5020_0__init__Load(EOS(STATIC_5020(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f5000_0_Ajouter_GT(EOS(STATIC_5000(i339)), i342, i342, i836, i886, i342) → f5042_0_Ajouter_FieldAccess(EOS(STATIC_5042(i339)), i342, i342, i836) | >(i886, i342)
f5001_0_Ajouter_GT(EOS(STATIC_5001(i339)), i342, i342, i836, i886, i342) → f5047_0_Ajouter_FieldAccess(EOS(STATIC_5047(i339)), i342, i342, i836) | <=(i886, i342)
f5013_0__init__InvokeMethod(EOS(STATIC_5013(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f5057_0__init__Load(EOS(STATIC_5057(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f5020_0__init__Load(EOS(STATIC_5020(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f5128_0__init__InvokeMethod(EOS(STATIC_5128(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f5028_0__init__InvokeMethod(EOS(STATIC_5028(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f5093_0__init__Load(EOS(STATIC_5093(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f5042_0_Ajouter_FieldAccess(EOS(STATIC_5042(i339)), i342, i342, i836) → f7272_0_Ajouter_FieldAccess(EOS(STATIC_7272(i339)), i342, i342, i836)
f5047_0_Ajouter_FieldAccess(EOS(STATIC_5047(i339)), i342, i342, i836) → f5115_0_Ajouter_Load(EOS(STATIC_5115(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)))
f5057_0__init__Load(EOS(STATIC_5057(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f5177_0__init__InvokeMethod(EOS(STATIC_5177(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f5093_0__init__Load(EOS(STATIC_5093(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f5198_0__init__InvokeMethod(EOS(STATIC_5198(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f5115_0_Ajouter_Load(EOS(STATIC_5115(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339))) → f5167_0_Ajouter_FieldAccess(EOS(STATIC_5167(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f5128_0__init__InvokeMethod(EOS(STATIC_5128(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f5181_0__init__Load(EOS(STATIC_5181(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f5167_0_Ajouter_FieldAccess(EOS(STATIC_5167(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f5230_0_Ajouter_Load(EOS(STATIC_5230(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)))
f5177_0__init__InvokeMethod(EOS(STATIC_5177(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f5241_0__init__Load(EOS(STATIC_5241(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f5181_0__init__Load(EOS(STATIC_5181(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f5306_0__init__InvokeMethod(EOS(STATIC_5306(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f5198_0__init__InvokeMethod(EOS(STATIC_5198(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f5255_0__init__Load(EOS(STATIC_5255(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f5230_0_Ajouter_Load(EOS(STATIC_5230(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339))) → f5289_0_Ajouter_ConstantStackPush(EOS(STATIC_5289(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i836)
f5241_0__init__Load(EOS(STATIC_5241(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f5361_0__init__InvokeMethod(EOS(STATIC_5361(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f5255_0__init__Load(EOS(STATIC_5255(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f5387_0__init__InvokeMethod(EOS(STATIC_5387(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f5289_0_Ajouter_ConstantStackPush(EOS(STATIC_5289(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i836) → f5341_0_Ajouter_IntArithmetic(EOS(STATIC_5341(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i836, 1)
f5306_0__init__InvokeMethod(EOS(STATIC_5306(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f5377_0__init__Load(EOS(STATIC_5377(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f5320_0_Ajouter_Return(EOS(STATIC_5320(i339)), i342) → f7598_0_Ajouter_Return(EOS(STATIC_7598(i339)), i342)
f5341_0_Ajouter_IntArithmetic(EOS(STATIC_5341(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i836, matching1) → f5465_0_Ajouter_ConstantStackPush(EOS(STATIC_5465(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), -(i836, 1)) | &&(>(i836, 0), =(matching1, 1))
f5361_0__init__InvokeMethod(EOS(STATIC_5361(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f5469_0__init__Load(EOS(STATIC_5469(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f5377_0__init__Load(EOS(STATIC_5377(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f5816_0__init__InvokeMethod(EOS(STATIC_5816(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f5387_0__init__InvokeMethod(EOS(STATIC_5387(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f5542_0__init__Load(EOS(STATIC_5542(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f5465_0_Ajouter_ConstantStackPush(EOS(STATIC_5465(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1072) → f5803_0_Ajouter_IntArithmetic(EOS(STATIC_5803(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1072, 2)
f5469_0__init__Load(EOS(STATIC_5469(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f5898_0__init__InvokeMethod(EOS(STATIC_5898(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f5542_0__init__Load(EOS(STATIC_5542(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f5934_0__init__InvokeMethod(EOS(STATIC_5934(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f5803_0_Ajouter_IntArithmetic(EOS(STATIC_5803(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1072, matching1) → f5882_0_Ajouter_ArrayAccess(EOS(STATIC_5882(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), /(i1072, 2)) | =(matching1, 2)
f5816_0__init__InvokeMethod(EOS(STATIC_5816(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f5929_0__init__Load(EOS(STATIC_5929(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f5882_0_Ajouter_ArrayAccess(EOS(STATIC_5882(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f5961_0_Ajouter_ArrayAccess(EOS(STATIC_5961(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f5882_0_Ajouter_ArrayAccess(EOS(STATIC_5882(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f5963_0_Ajouter_ArrayAccess(EOS(STATIC_5963(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f5898_0__init__InvokeMethod(EOS(STATIC_5898(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f5994_0__init__Load(EOS(STATIC_5994(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f5929_0__init__Load(EOS(STATIC_5929(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f6008_0__init__Load(EOS(STATIC_6008(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f5934_0__init__InvokeMethod(EOS(STATIC_5934(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f6045_0__init__Load(EOS(STATIC_6045(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f5961_0_Ajouter_ArrayAccess(EOS(STATIC_5961(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f6069_0_Ajouter_ArrayAccess(EOS(STATIC_6069(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) | <(i1129, i339)
f5963_0_Ajouter_ArrayAccess(EOS(STATIC_5963(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f6076_0__init__Load(EOS(STATIC_6076(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) | >=(i1129, i339)
f5994_0__init__Load(EOS(STATIC_5994(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f6153_0__init__InvokeMethod(EOS(STATIC_6153(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f6008_0__init__Load(EOS(STATIC_6008(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f6087_0__init__FieldAccess(EOS(STATIC_6087(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f6045_0__init__Load(EOS(STATIC_6045(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f6098_0__init__Load(EOS(STATIC_6098(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f6069_0_Ajouter_ArrayAccess(EOS(STATIC_6069(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f6118_0_Ajouter_ArrayAccess(EOS(STATIC_6118(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f6069_0_Ajouter_ArrayAccess(EOS(STATIC_6069(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f6119_0_Ajouter_ArrayAccess(EOS(STATIC_6119(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f6076_0__init__Load(EOS(STATIC_6076(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f6235_0__init__InvokeMethod(EOS(STATIC_6235(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f6087_0__init__FieldAccess(EOS(STATIC_6087(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f6164_0__init__Load(EOS(STATIC_6164(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f6098_0__init__Load(EOS(STATIC_6098(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f6177_0__init__FieldAccess(EOS(STATIC_6177(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f6118_0_Ajouter_ArrayAccess(EOS(STATIC_6118(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f6195_0_Ajouter_Load(EOS(STATIC_6195(i339)), i342, i342, i836) | <(i836, i339)
f6119_0_Ajouter_ArrayAccess(EOS(STATIC_6119(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f6204_0__init__Load(EOS(STATIC_6204(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) | >=(i836, i339)
f6153_0__init__InvokeMethod(EOS(STATIC_6153(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f6254_0__init__Load(EOS(STATIC_6254(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f6164_0__init__Load(EOS(STATIC_6164(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f6276_0__init__InvokeMethod(EOS(STATIC_6276(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f6177_0__init__FieldAccess(EOS(STATIC_6177(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f6292_0__init__Load(EOS(STATIC_6292(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f6195_0_Ajouter_Load(EOS(STATIC_6195(i339)), i342, i342, i836) → f6317_0_Ajouter_ConstantStackPush(EOS(STATIC_6317(i339)), i342, i342, i836, i836)
f6204_0__init__Load(EOS(STATIC_6204(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f6430_0__init__InvokeMethod(EOS(STATIC_6430(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f6235_0__init__InvokeMethod(EOS(STATIC_6235(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f6333_0__init__Load(EOS(STATIC_6333(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f6254_0__init__Load(EOS(STATIC_6254(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f6347_0__init__Load(EOS(STATIC_6347(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f6276_0__init__InvokeMethod(EOS(STATIC_6276(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f6362_0__init__StackPop(EOS(STATIC_6362(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f6292_0__init__Load(EOS(STATIC_6292(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f6378_0__init__InvokeMethod(EOS(STATIC_6378(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f6317_0_Ajouter_ConstantStackPush(EOS(STATIC_6317(i339)), i342, i342, i836, i836) → f6397_0_Ajouter_IntArithmetic(EOS(STATIC_6397(i339)), i342, i342, i836, i836, 1)
f6333_0__init__Load(EOS(STATIC_6333(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f6535_0__init__InvokeMethod(EOS(STATIC_6535(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f6347_0__init__Load(EOS(STATIC_6347(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f6457_0__init__FieldAccess(EOS(STATIC_6457(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f6362_0__init__StackPop(EOS(STATIC_6362(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f6467_0__init__Return(EOS(STATIC_6467(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f6378_0__init__InvokeMethod(EOS(STATIC_6378(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f6479_0__init__StackPop(EOS(STATIC_6479(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f6397_0_Ajouter_IntArithmetic(EOS(STATIC_6397(i339)), i342, i342, i836, i836, matching1) → f6501_0_Ajouter_ConstantStackPush(EOS(STATIC_6501(i339)), i342, i342, i836, -(i836, 1)) | &&(>(i836, 0), =(matching1, 1))
f6430_0__init__InvokeMethod(EOS(STATIC_6430(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f6515_0__init__Load(EOS(STATIC_6515(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f6457_0__init__FieldAccess(EOS(STATIC_6457(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f6563_0__init__Load(EOS(STATIC_6563(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f6467_0__init__Return(EOS(STATIC_6467(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f6577_0__init__Return(EOS(STATIC_6577(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f6479_0__init__StackPop(EOS(STATIC_6479(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f6590_0__init__Return(EOS(STATIC_6590(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f6501_0_Ajouter_ConstantStackPush(EOS(STATIC_6501(i339)), i342, i342, i836, i1205) → f6634_0_Ajouter_IntArithmetic(EOS(STATIC_6634(i339)), i342, i342, i836, i1205, 2)
f6515_0__init__Load(EOS(STATIC_6515(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f6763_0__init__InvokeMethod(EOS(STATIC_6763(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f6535_0__init__InvokeMethod(EOS(STATIC_6535(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f6654_0__init__Load(EOS(STATIC_6654(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f6563_0__init__Load(EOS(STATIC_6563(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f6690_0__init__InvokeMethod(EOS(STATIC_6690(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f6577_0__init__Return(EOS(STATIC_6577(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f6705_0__init__Return(EOS(STATIC_6705(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f6590_0__init__Return(EOS(STATIC_6590(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f6720_0__init__Return(EOS(STATIC_6720(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f6634_0_Ajouter_IntArithmetic(EOS(STATIC_6634(i339)), i342, i342, i836, i1205, matching1) → f6739_0_Ajouter_Store(EOS(STATIC_6739(i339)), i342, i342, i836, /(i1205, 2)) | =(matching1, 2)
f6654_0__init__Load(EOS(STATIC_6654(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f6861_0__init__InvokeMethod(EOS(STATIC_6861(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f6690_0__init__InvokeMethod(EOS(STATIC_6690(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f6784_0__init__StackPop(EOS(STATIC_6784(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f6705_0__init__Return(EOS(STATIC_6705(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f6791_0__init__Return(EOS(STATIC_6791(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f6720_0__init__Return(EOS(STATIC_6720(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f6798_0__init__Return(EOS(STATIC_6798(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f6739_0_Ajouter_Store(EOS(STATIC_6739(i339)), i342, i342, i836, i1228) → f6838_0_Ajouter_Load(EOS(STATIC_6838(i339)), i342, i342, i836, i1228)
f6763_0__init__InvokeMethod(EOS(STATIC_6763(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f6844_0__init__Load(EOS(STATIC_6844(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f6784_0__init__StackPop(EOS(STATIC_6784(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f6869_0__init__Return(EOS(STATIC_6869(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f6791_0__init__Return(EOS(STATIC_6791(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f6874_0__init__Return(EOS(STATIC_6874(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f6798_0__init__Return(EOS(STATIC_6798(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f6877_0__init__Return(EOS(STATIC_6877(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f6838_0_Ajouter_Load(EOS(STATIC_6838(i339)), i342, i342, i836, i1228) → f6895_0_Ajouter_Load(EOS(STATIC_6895(i339)), i342, i342, i836, i1228, i1228)
f6844_0__init__Load(EOS(STATIC_6844(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f6963_0__init__InvokeMethod(EOS(STATIC_6963(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f6861_0__init__InvokeMethod(EOS(STATIC_6861(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f6900_0__init__Load(EOS(STATIC_6900(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f6869_0__init__Return(EOS(STATIC_6869(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f6909_0__init__Return(EOS(STATIC_6909(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f6874_0__init__Return(EOS(STATIC_6874(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342) → f6913_0_Ajouter_ArrayAccess(EOS(STATIC_6913(i339)), i342, java.lang.Object(ARRAY(i339)), i854, i342)
f6877_0__init__Return(EOS(STATIC_6877(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f6919_0__init__Return(EOS(STATIC_6919(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f6895_0_Ajouter_Load(EOS(STATIC_6895(i339)), i342, i342, i836, i1228, i1228) → f6942_0_Ajouter_LT(EOS(STATIC_6942(i339)), i342, i342, i836, i1228, i1228, i836)
f6900_0__init__Load(EOS(STATIC_6900(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f7027_0__init__InvokeMethod(EOS(STATIC_7027(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f6909_0__init__Return(EOS(STATIC_6909(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f6977_0__init__Return(EOS(STATIC_6977(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f6919_0__init__Return(EOS(STATIC_6919(i870)), i342, java.lang.Object(ARRAY(i870)), matching1, i342) → f6985_0_Ajouter_ArrayAccess(EOS(STATIC_6985(i870)), i342, java.lang.Object(ARRAY(i870)), 0, i342) | =(matching1, 0)
f6942_0_Ajouter_LT(EOS(STATIC_6942(i339)), i342, i342, i836, i1228, i1228, i836) → f7004_0_Ajouter_LT(EOS(STATIC_7004(i339)), i342, i342, i836, i1228, i1228, i836)
f6942_0_Ajouter_LT(EOS(STATIC_6942(i339)), i342, i342, i836, i1228, i1228, i836) → f7005_0_Ajouter_LT(EOS(STATIC_7005(i339)), i342, i342, i836, i1228, i1228, i836)
f6963_0__init__InvokeMethod(EOS(STATIC_6963(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f7008_0__init__Load(EOS(STATIC_7008(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f6977_0__init__Return(EOS(STATIC_6977(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f7048_0__init__Return(EOS(STATIC_7048(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f7004_0_Ajouter_LT(EOS(STATIC_7004(i339)), i342, i342, i836, i1228, i1228, i836) → f7105_0_Ajouter_Load(EOS(STATIC_7105(i339)), i342, i342, i1228) | <(i1228, i836)
f7005_0_Ajouter_LT(EOS(STATIC_7005(i339)), i342, i342, i836, i1228, i1228, i836) → f7120_0_Ajouter_JMP(EOS(STATIC_7120(i339)), i342, i342, i836) | >=(i1228, i836)
f7008_0__init__Load(EOS(STATIC_7008(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f7305_0__init__InvokeMethod(EOS(STATIC_7305(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f7027_0__init__InvokeMethod(EOS(STATIC_7027(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f7150_0__init__Load(EOS(STATIC_7150(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f7048_0__init__Return(EOS(STATIC_7048(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f7174_0__init__Return(EOS(STATIC_7174(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f7105_0_Ajouter_Load(EOS(STATIC_7105(i339)), i342, i342, i1228) → f7260_0_Ajouter_Store(EOS(STATIC_7260(i339)), i342, i342, i1228)
f7120_0_Ajouter_JMP(EOS(STATIC_7120(i339)), i342, i342, i836) → f7272_0_Ajouter_FieldAccess(EOS(STATIC_7272(i339)), i342, i342, i836)
f7150_0__init__Load(EOS(STATIC_7150(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f7392_0__init__InvokeMethod(EOS(STATIC_7392(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f7174_0__init__Return(EOS(STATIC_7174(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877) → f7354_0_Ajouter_ArrayAccess(EOS(STATIC_7354(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i877)
f7260_0_Ajouter_Store(EOS(STATIC_7260(i339)), i342, i342, i1228) → f7362_0_Ajouter_JMP(EOS(STATIC_7362(i339)), i342, i342, i1228)
f7272_0_Ajouter_FieldAccess(EOS(STATIC_7272(i339)), i342, i342, i836) → f7368_0_Ajouter_Load(EOS(STATIC_7368(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)))
f7305_0__init__InvokeMethod(EOS(STATIC_7305(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f7371_0__init__Load(EOS(STATIC_7371(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f7362_0_Ajouter_JMP(EOS(STATIC_7362(i339)), i342, i342, i1228) → f7408_0_Ajouter_Load(EOS(STATIC_7408(i339)), i342, i342, i1228)
f7368_0_Ajouter_Load(EOS(STATIC_7368(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339))) → f7412_0_Ajouter_Load(EOS(STATIC_7412(i339)), i342, i342, java.lang.Object(ARRAY(i339)), i836)
f7371_0__init__Load(EOS(STATIC_7371(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f7482_0__init__InvokeMethod(EOS(STATIC_7482(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f7392_0__init__InvokeMethod(EOS(STATIC_7392(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f7435_0__init__Load(EOS(STATIC_7435(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f7408_0_Ajouter_Load(EOS(STATIC_7408(i339)), i342, i342, i1228) → f4477_0_Ajouter_Load(EOS(STATIC_4477(i339)), i342, i342, i1228)
f7412_0_Ajouter_Load(EOS(STATIC_7412(i339)), i342, i342, java.lang.Object(ARRAY(i339)), i836) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f7435_0__init__Load(EOS(STATIC_7435(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f7507_0__init__Load(EOS(STATIC_7507(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f7514_0_Ajouter_ArrayAccess(EOS(STATIC_7514(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f7515_0_Ajouter_ArrayAccess(EOS(STATIC_7515(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f7482_0__init__InvokeMethod(EOS(STATIC_7482(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f7562_0__init__Load(EOS(STATIC_7562(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f7507_0__init__Load(EOS(STATIC_7507(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f7587_0__init__FieldAccess(EOS(STATIC_7587(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f7514_0_Ajouter_ArrayAccess(EOS(STATIC_7514(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f7598_0_Ajouter_Return(EOS(STATIC_7598(i339)), i342) | <(i836, i339)
f7515_0_Ajouter_ArrayAccess(EOS(STATIC_7515(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f7604_0__init__Load(EOS(STATIC_7604(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) | >=(i836, i339)
f7562_0__init__Load(EOS(STATIC_7562(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f7624_0__init__Load(EOS(STATIC_7624(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f7587_0__init__FieldAccess(EOS(STATIC_7587(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f7647_0__init__Load(EOS(STATIC_7647(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f7604_0__init__Load(EOS(STATIC_7604(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f7773_0__init__InvokeMethod(EOS(STATIC_7773(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f7624_0__init__Load(EOS(STATIC_7624(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f7693_0__init__FieldAccess(EOS(STATIC_7693(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f7647_0__init__Load(EOS(STATIC_7647(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f7709_0__init__InvokeMethod(EOS(STATIC_7709(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f7693_0__init__FieldAccess(EOS(STATIC_7693(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f7801_0__init__Load(EOS(STATIC_7801(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f7709_0__init__InvokeMethod(EOS(STATIC_7709(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f7843_0__init__StackPop(EOS(STATIC_7843(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f7773_0__init__InvokeMethod(EOS(STATIC_7773(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f7848_0__init__Load(EOS(STATIC_7848(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f7801_0__init__Load(EOS(STATIC_7801(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f7877_0__init__InvokeMethod(EOS(STATIC_7877(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f7843_0__init__StackPop(EOS(STATIC_7843(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f7912_0__init__Return(EOS(STATIC_7912(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f7848_0__init__Load(EOS(STATIC_7848(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f7986_0__init__InvokeMethod(EOS(STATIC_7986(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f7877_0__init__InvokeMethod(EOS(STATIC_7877(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f7932_0__init__StackPop(EOS(STATIC_7932(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f7912_0__init__Return(EOS(STATIC_7912(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f7951_0__init__Return(EOS(STATIC_7951(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f7932_0__init__StackPop(EOS(STATIC_7932(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f8011_0__init__Return(EOS(STATIC_8011(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f7951_0__init__Return(EOS(STATIC_7951(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f8028_0__init__Return(EOS(STATIC_8028(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f7986_0__init__InvokeMethod(EOS(STATIC_7986(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8035_0__init__Load(EOS(STATIC_8035(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8011_0__init__Return(EOS(STATIC_8011(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f8054_0__init__Return(EOS(STATIC_8054(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f8028_0__init__Return(EOS(STATIC_8028(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f8090_0__init__Return(EOS(STATIC_8090(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f8035_0__init__Load(EOS(STATIC_8035(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8188_0__init__InvokeMethod(EOS(STATIC_8188(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8054_0__init__Return(EOS(STATIC_8054(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f8135_0__init__Return(EOS(STATIC_8135(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f8090_0__init__Return(EOS(STATIC_8090(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f8150_0__init__Return(EOS(STATIC_8150(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f8135_0__init__Return(EOS(STATIC_8135(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f8207_0__init__Return(EOS(STATIC_8207(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f8150_0__init__Return(EOS(STATIC_8150(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129) → f8215_0_Ajouter_ArrayAccess(EOS(STATIC_8215(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836, java.lang.Object(ARRAY(i339)), i1129)
f8188_0__init__InvokeMethod(EOS(STATIC_8188(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8220_0__init__Load(EOS(STATIC_8220(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8207_0__init__Return(EOS(STATIC_8207(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f8229_0__init__Return(EOS(STATIC_8229(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f8220_0__init__Load(EOS(STATIC_8220(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8317_0__init__InvokeMethod(EOS(STATIC_8317(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8229_0__init__Return(EOS(STATIC_8229(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836) → f8243_0_Ajouter_ArrayAccess(EOS(STATIC_8243(i339)), i342, i342, i836, java.lang.Object(ARRAY(i339)), i836)
f8317_0__init__InvokeMethod(EOS(STATIC_8317(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8327_0__init__Load(EOS(STATIC_8327(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8327_0__init__Load(EOS(STATIC_8327(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8400_0__init__InvokeMethod(EOS(STATIC_8400(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8400_0__init__InvokeMethod(EOS(STATIC_8400(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8424_0__init__Load(EOS(STATIC_8424(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8424_0__init__Load(EOS(STATIC_8424(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8445_0__init__Load(EOS(STATIC_8445(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8445_0__init__Load(EOS(STATIC_8445(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8556_0__init__FieldAccess(EOS(STATIC_8556(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8556_0__init__FieldAccess(EOS(STATIC_8556(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8585_0__init__Load(EOS(STATIC_8585(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8585_0__init__Load(EOS(STATIC_8585(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8607_0__init__InvokeMethod(EOS(STATIC_8607(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8607_0__init__InvokeMethod(EOS(STATIC_8607(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8642_0__init__StackPop(EOS(STATIC_8642(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8642_0__init__StackPop(EOS(STATIC_8642(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8664_0__init__Return(EOS(STATIC_8664(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8664_0__init__Return(EOS(STATIC_8664(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8694_0__init__Return(EOS(STATIC_8694(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8694_0__init__Return(EOS(STATIC_8694(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8735_0__init__Return(EOS(STATIC_8735(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8735_0__init__Return(EOS(STATIC_8735(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8771_0__init__Return(EOS(STATIC_8771(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8771_0__init__Return(EOS(STATIC_8771(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8796_0__init__Return(EOS(STATIC_8796(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)
f8796_0__init__Return(EOS(STATIC_8796(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342) → f8814_0_Ajouter_ArrayAccess(EOS(STATIC_8814(i339)), i342, java.lang.Object(ARRAY(i339)), i836, i342)

Combined rules. Obtained 3 conditional rules for P and 11 conditional rules for R.

P rules:
f5290_1_HeapSort_InvokeMethod(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0)), x1), x2, x1) → f5290_1_HeapSort_InvokeMethod(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0)), x3, x3), +(x2, 1), x3) | &&(>(+(x2, 1), 0), <(+(x2, 1), x0))
f5290_1_HeapSort_InvokeMethod(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0)), x1), x2, x1) → f5290_1_HeapSort_InvokeMethod(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0)), x3, x3), +(x2, 1), x3) | &&(>(+(x2, 1), 0), <(+(x2, 1), x0))
f5290_1_HeapSort_InvokeMethod(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)), x1), x2, x1) → f5290_1_HeapSort_InvokeMethod(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0)), x3, x3), +(x2, 1), x3) | &&(>(+(x2, 1), 0), <(+(x2, 1), x0))
R rules:
f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0)), x1, x1) → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1, x1, -(x2, 1), -(x2, 1))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1, x1, 0, 0) → f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)), x1) | >(x0, 0)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1, x1, x2, x2) → f6913_0_Ajouter_ArrayAccess(EOS(STATIC_6913(x0)), x1, java.lang.Object(ARRAY(x0)), x2, x1) | &&(<=(x2, -1), <=(x2, 0))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1, x1, 0, 0) → f6985_0_Ajouter_ArrayAccess(EOS(STATIC_6985(x0)), x1, java.lang.Object(ARRAY(x0)), 0, x1) | <=(x0, 0)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1, x1, x2, x2) → f7354_0_Ajouter_ArrayAccess(EOS(STATIC_7354(x0)), x1, x1, x2, java.lang.Object(ARRAY(x0)), /(-(x2, 1), 2)) | &&(>(x2, 0), >=(/(-(x2, 1), 2), x0))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1, x1, x2, x2) → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1, x1, /(-(x2, 1), 2), /(-(x2, 1), 2)) | &&(&&(&&(>(x2, 0), <(x2, x0)), <(/(-(x2, 1), 2), x2)), <(/(-(x2, 1), 2), x0))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1, x1, x2, x2) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), x1, java.lang.Object(ARRAY(x0)), x2, x1) | &&(>(x2, 0), <(/(-(x2, 1), 2), x0))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1, x1, x2, x2) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), x1, java.lang.Object(ARRAY(x0)), x2, x1) | &&(&&(&&(>(x2, 0), <(x2, x0)), >=(/(-(x2, 1), 2), x2)), <(/(-(x2, 1), 2), x0))
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), x1, java.lang.Object(ARRAY(x0)), x2, x1) → f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)), x1) | <(x2, x0)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1, x1, x2, x2) → f8243_0_Ajouter_ArrayAccess(EOS(STATIC_8243(x0)), x1, x1, x2, java.lang.Object(ARRAY(x0)), x2) | &&(&&(>=(x2, x0), >(x2, 0)), <(/(-(x2, 1), 2), x0))
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), x1, java.lang.Object(ARRAY(x0)), x2, x1) → f8814_0_Ajouter_ArrayAccess(EOS(STATIC_8814(x0)), x1, java.lang.Object(ARRAY(x0)), x2, x1) | >=(x2, x0)

Filtered ground terms:

Cond_f4539_0_Ajouter_LE(x1, x2, x3, x4, x5, x6) → Cond_f4539_0_Ajouter_LE(x1, x2, x3, x4)
Cond_f4539_0_Ajouter_LE2(x1, x2, x3, x4, x5, x6) → Cond_f4539_0_Ajouter_LE2(x1, x2, x3, x4)
f6985_0_Ajouter_ArrayAccess(x1, x2, x3, x4, x5) → f6985_0_Ajouter_ArrayAccess(x1, x2, x3, x5)

Filtered unneeded arguments:

f5290_1_HeapSort_InvokeMethod(x1, x2, x3) → f5290_1_HeapSort_InvokeMethod(x1, x2)
Cond_f5290_1_HeapSort_InvokeMethod(x1, x2, x3, x4, x5) → Cond_f5290_1_HeapSort_InvokeMethod(x1, x2, x3, x5)
Cond_f5290_1_HeapSort_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_f5290_1_HeapSort_InvokeMethod1(x1, x2, x3, x5)
Cond_f5290_1_HeapSort_InvokeMethod2(x1, x2, x3, x4, x5) → Cond_f5290_1_HeapSort_InvokeMethod2(x1, x2, x3, x5)
Cond_f4539_0_Ajouter_LE1(x1, x2, x3, x4, x5, x6) → Cond_f4539_0_Ajouter_LE1(x1, x3, x4, x5, x6)
Cond_f4539_0_Ajouter_LE2(x1, x2, x3, x4) → Cond_f4539_0_Ajouter_LE2(x1, x3, x4)
Cond_f4539_0_Ajouter_LE3(x1, x2, x3, x4, x5, x6) → Cond_f4539_0_Ajouter_LE3(x1, x3, x4, x5, x6)
Cond_f7463_0_Ajouter_ArrayAccess(x1, x2, x3, x4, x5, x6) → Cond_f7463_0_Ajouter_ArrayAccess(x1, x2, x3, x4, x6)
Cond_f4539_0_Ajouter_LE7(x1, x2, x3, x4, x5, x6) → Cond_f4539_0_Ajouter_LE7(x1, x3, x4, x5, x6)
Cond_f7463_0_Ajouter_ArrayAccess1(x1, x2, x3, x4, x5, x6) → Cond_f7463_0_Ajouter_ArrayAccess1(x1, x3, x6)
f4806_0_Ajouter_Return(x1, x2) → f4806_0_Ajouter_Return(x1)
f5320_0_Ajouter_Return(x1, x2) → f5320_0_Ajouter_Return(x1)
f7598_0_Ajouter_Return(x1, x2) → f7598_0_Ajouter_Return(x1)

Filtered duplicate args:

f5311_0_Ajouter_FieldAccess(x1, x2, x3) → f5311_0_Ajouter_FieldAccess(x1, x3)
f4539_0_Ajouter_LE(x1, x2, x3, x4, x5) → f4539_0_Ajouter_LE(x1, x3, x5)
Cond_f4539_0_Ajouter_LE(x1, x2, x3, x4) → Cond_f4539_0_Ajouter_LE(x1, x2, x4)
Cond_f4539_0_Ajouter_LE1(x1, x2, x3, x4, x5) → Cond_f4539_0_Ajouter_LE1(x1, x3, x5)
f6913_0_Ajouter_ArrayAccess(x1, x2, x3, x4, x5) → f6913_0_Ajouter_ArrayAccess(x1, x3, x4, x5)
Cond_f4539_0_Ajouter_LE2(x1, x2, x3) → Cond_f4539_0_Ajouter_LE2(x1, x3)
f6985_0_Ajouter_ArrayAccess(x1, x2, x3, x4) → f6985_0_Ajouter_ArrayAccess(x1, x3, x4)
Cond_f4539_0_Ajouter_LE3(x1, x2, x3, x4, x5) → Cond_f4539_0_Ajouter_LE3(x1, x3, x5)
f7354_0_Ajouter_ArrayAccess(x1, x2, x3, x4, x5, x6) → f7354_0_Ajouter_ArrayAccess(x1, x3, x5, x6)
Cond_f4539_0_Ajouter_LE4(x1, x2, x3, x4, x5, x6) → Cond_f4539_0_Ajouter_LE4(x1, x2, x4, x6)
Cond_f4539_0_Ajouter_LE5(x1, x2, x3, x4, x5, x6) → Cond_f4539_0_Ajouter_LE5(x1, x2, x4, x6)
f7463_0_Ajouter_ArrayAccess(x1, x2, x3, x4, x5) → f7463_0_Ajouter_ArrayAccess(x1, x3, x4, x5)
Cond_f4539_0_Ajouter_LE6(x1, x2, x3, x4, x5, x6) → Cond_f4539_0_Ajouter_LE6(x1, x2, x4, x6)
Cond_f7463_0_Ajouter_ArrayAccess(x1, x2, x3, x4, x5) → Cond_f7463_0_Ajouter_ArrayAccess(x1, x2, x4, x5)
Cond_f4539_0_Ajouter_LE7(x1, x2, x3, x4, x5) → Cond_f4539_0_Ajouter_LE7(x1, x3, x5)
f8243_0_Ajouter_ArrayAccess(x1, x2, x3, x4, x5, x6) → f8243_0_Ajouter_ArrayAccess(x1, x3, x5, x6)
Cond_f7463_0_Ajouter_ArrayAccess1(x1, x2, x3) → Cond_f7463_0_Ajouter_ArrayAccess1(x1, x3)
f8814_0_Ajouter_ArrayAccess(x1, x2, x3, x4, x5) → f8814_0_Ajouter_ArrayAccess(x1, x3, x4, x5)

Filtered unneeded arguments:

Cond_f5290_1_HeapSort_InvokeMethod(x1, x2, x3, x4) → Cond_f5290_1_HeapSort_InvokeMethod(x1, x2, x3)
Cond_f5290_1_HeapSort_InvokeMethod1(x1, x2, x3, x4) → Cond_f5290_1_HeapSort_InvokeMethod1(x1, x2, x3)
Cond_f5290_1_HeapSort_InvokeMethod2(x1, x2, x3, x4) → Cond_f5290_1_HeapSort_InvokeMethod2(x1, x2, x3)
f4539_0_Ajouter_LE(x1, x2, x3) → f4539_0_Ajouter_LE(x1, x3)
Cond_f4539_0_Ajouter_LE(x1, x2, x3) → Cond_f4539_0_Ajouter_LE(x1, x2)
Cond_f4539_0_Ajouter_LE1(x1, x2, x3) → Cond_f4539_0_Ajouter_LE1(x1)
Cond_f4539_0_Ajouter_LE2(x1, x2) → Cond_f4539_0_Ajouter_LE2(x1)
Cond_f4539_0_Ajouter_LE3(x1, x2, x3) → Cond_f4539_0_Ajouter_LE3(x1)
Cond_f4539_0_Ajouter_LE4(x1, x2, x3, x4) → Cond_f4539_0_Ajouter_LE4(x1, x2, x4)
Cond_f4539_0_Ajouter_LE5(x1, x2, x3, x4) → Cond_f4539_0_Ajouter_LE5(x1, x2, x4)
Cond_f4539_0_Ajouter_LE6(x1, x2, x3, x4) → Cond_f4539_0_Ajouter_LE6(x1, x2, x4)
Cond_f7463_0_Ajouter_ArrayAccess(x1, x2, x3, x4) → Cond_f7463_0_Ajouter_ArrayAccess(x1, x2, x3)
Cond_f4539_0_Ajouter_LE7(x1, x2, x3) → Cond_f4539_0_Ajouter_LE7(x1)
Cond_f7463_0_Ajouter_ArrayAccess1(x1, x2) → Cond_f7463_0_Ajouter_ArrayAccess1(x1)
f7463_0_Ajouter_ArrayAccess(x1, x2, x3, x4) → f7463_0_Ajouter_ArrayAccess(x1, x2, x3)
f5311_0_Ajouter_FieldAccess(x1, x2) → f5311_0_Ajouter_FieldAccess(x1)

Combined rules. Obtained 3 conditional rules for P and 11 conditional rules for R.

P rules:
F5290_1_HEAPSORT_INVOKEMETHOD(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0))), x2) → F5290_1_HEAPSORT_INVOKEMETHOD(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))), +(x2, 1)) | &&(<(+(x2, 1), x0), >(x2, -1))
F5290_1_HEAPSORT_INVOKEMETHOD(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0))), x2) → F5290_1_HEAPSORT_INVOKEMETHOD(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))), +(x2, 1)) | &&(<(+(x2, 1), x0), >(x2, -1))
F5290_1_HEAPSORT_INVOKEMETHOD(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0))), x2) → F5290_1_HEAPSORT_INVOKEMETHOD(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))), +(x2, 1)) | &&(<(+(x2, 1), x0), >(x2, -1))
R rules:
f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))) → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), -(x2, 1))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), 0) → f7598_0_Ajouter_Return(EOS(STATIC_7598(x0))) | >(x0, 0)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → f6913_0_Ajouter_ArrayAccess(EOS(STATIC_6913(x0)), java.lang.Object(ARRAY(x0)), x2, x1) | &&(<=(x2, -1), <=(x2, 0))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), 0) → f6985_0_Ajouter_ArrayAccess(EOS(STATIC_6985(x0)), java.lang.Object(ARRAY(x0)), x1) | <=(x0, 0)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → f7354_0_Ajouter_ArrayAccess(EOS(STATIC_7354(x0)), x1, java.lang.Object(ARRAY(x0)), /(-(x2, 1), 2)) | &&(>=(/(-(x2, 1), 2), x0), >(x2, 0))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), /(-(x2, 1), 2)) | &&(&&(&&(>(x2, 0), <(x2, x0)), <(/(-(x2, 1), 2), x0)), <(/(-(x2, 1), 2), x2))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) | &&(<(/(-(x2, 1), 2), x0), >(x2, 0))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) | &&(&&(&&(>(x2, 0), <(x2, x0)), <(/(-(x2, 1), 2), x0)), >=(/(-(x2, 1), 2), x2))
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → f7598_0_Ajouter_Return(EOS(STATIC_7598(x0))) | <(x2, x0)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → f8243_0_Ajouter_ArrayAccess(EOS(STATIC_8243(x0)), x1, java.lang.Object(ARRAY(x0)), x2) | &&(&&(>=(x2, x0), <(/(-(x2, 1), 2), x0)), >(x2, 0))
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → f8814_0_Ajouter_ArrayAccess(EOS(STATIC_8814(x0)), java.lang.Object(ARRAY(x0)), x2, x1) | >=(x2, x0)

Finished conversion. Obtained 6 rules for P and 21 rules for R. System has predefined symbols.

P rules:
F5290_1_HEAPSORT_INVOKEMETHOD'(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0))), x2) → COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2, 1), x0), >(x2, -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0))), x2)
COND_F5290_1_HEAPSORT_INVOKEMETHOD(TRUE, f4806_0_Ajouter_Return(EOS(STATIC_4806(x0))), x2) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))), +(x2, 1))
F5290_1_HEAPSORT_INVOKEMETHOD'(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0))), x2) → COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2, 1), x0), >(x2, -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0))), x2)
COND_F5290_1_HEAPSORT_INVOKEMETHOD1(TRUE, f5320_0_Ajouter_Return(EOS(STATIC_5320(x0))), x2) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))), +(x2, 1))
F5290_1_HEAPSORT_INVOKEMETHOD'(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0))), x2) → COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2, 1), x0), >(x2, -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0))), x2)
COND_F5290_1_HEAPSORT_INVOKEMETHOD2(TRUE, f7598_0_Ajouter_Return(EOS(STATIC_7598(x0))), x2) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))), +(x2, 1))
R rules:
f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))) → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), -(x2, 1))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), 0) → Cond_f4539_0_Ajouter_LE(>(x0, 0), EOS(STATIC_4539(x0)), 0)
Cond_f4539_0_Ajouter_LE(TRUE, EOS(STATIC_4539(x0)), 0) → f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE1(&&(<=(x2, -1), <=(x2, 0)), EOS(STATIC_4539(x0)), x2, x1)
Cond_f4539_0_Ajouter_LE1(TRUE, EOS(STATIC_4539(x0)), x2, x1) → f6913_0_Ajouter_ArrayAccess(EOS(STATIC_6913(x0)), java.lang.Object(ARRAY(x0)), x2, x1)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), 0) → Cond_f4539_0_Ajouter_LE2(<=(x0, 0), EOS(STATIC_4539(x0)), 0, x1)
Cond_f4539_0_Ajouter_LE2(TRUE, EOS(STATIC_4539(x0)), 0, x1) → f6985_0_Ajouter_ArrayAccess(EOS(STATIC_6985(x0)), java.lang.Object(ARRAY(x0)), x1)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE3(&&(>=(/(-(x2, 1), 2), x0), >(x2, 0)), EOS(STATIC_4539(x0)), x2, x1)
Cond_f4539_0_Ajouter_LE3(TRUE, EOS(STATIC_4539(x0)), x2, x1) → f7354_0_Ajouter_ArrayAccess(EOS(STATIC_7354(x0)), x1, java.lang.Object(ARRAY(x0)), /(-(x2, 1), 2))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE4(&&(&&(&&(>(x2, 0), <(x2, x0)), <(/(-(x2, 1), 2), x0)), <(/(-(x2, 1), 2), x2)), EOS(STATIC_4539(x0)), x2)
Cond_f4539_0_Ajouter_LE4(TRUE, EOS(STATIC_4539(x0)), x2) → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), /(-(x2, 1), 2))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE5(&&(<(/(-(x2, 1), 2), x0), >(x2, 0)), EOS(STATIC_4539(x0)), x2)
Cond_f4539_0_Ajouter_LE5(TRUE, EOS(STATIC_4539(x0)), x2) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE6(&&(&&(&&(>(x2, 0), <(x2, x0)), <(/(-(x2, 1), 2), x0)), >=(/(-(x2, 1), 2), x2)), EOS(STATIC_4539(x0)), x2)
Cond_f4539_0_Ajouter_LE6(TRUE, EOS(STATIC_4539(x0)), x2) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → Cond_f7463_0_Ajouter_ArrayAccess(<(x2, x0), EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)
Cond_f7463_0_Ajouter_ArrayAccess(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE7(&&(&&(>=(x2, x0), <(/(-(x2, 1), 2), x0)), >(x2, 0)), EOS(STATIC_4539(x0)), x2, x1)
Cond_f4539_0_Ajouter_LE7(TRUE, EOS(STATIC_4539(x0)), x2, x1) → f8243_0_Ajouter_ArrayAccess(EOS(STATIC_8243(x0)), x1, java.lang.Object(ARRAY(x0)), x2)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → Cond_f7463_0_Ajouter_ArrayAccess1(>=(x2, x0), EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2, x1)
Cond_f7463_0_Ajouter_ArrayAccess1(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2, x1) → f8814_0_Ajouter_ArrayAccess(EOS(STATIC_8814(x0)), java.lang.Object(ARRAY(x0)), x2, x1)

(24) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Integer, Boolean

The ITRS R consists of the following rules:
f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))) → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2 - 1)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), 0) → Cond_f4539_0_Ajouter_LE(x0 > 0, EOS(STATIC_4539(x0)), 0)
Cond_f4539_0_Ajouter_LE(TRUE, EOS(STATIC_4539(x0)), 0) → f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE1(x2 <= -1 && x2 <= 0, EOS(STATIC_4539(x0)), x2, x1)
Cond_f4539_0_Ajouter_LE1(TRUE, EOS(STATIC_4539(x0)), x2, x1) → f6913_0_Ajouter_ArrayAccess(EOS(STATIC_6913(x0)), java.lang.Object(ARRAY(x0)), x2, x1)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), 0) → Cond_f4539_0_Ajouter_LE2(x0 <= 0, EOS(STATIC_4539(x0)), 0, x1)
Cond_f4539_0_Ajouter_LE2(TRUE, EOS(STATIC_4539(x0)), 0, x1) → f6985_0_Ajouter_ArrayAccess(EOS(STATIC_6985(x0)), java.lang.Object(ARRAY(x0)), x1)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE3(x2 - 1 / 2 >= x0 && x2 > 0, EOS(STATIC_4539(x0)), x2, x1)
Cond_f4539_0_Ajouter_LE3(TRUE, EOS(STATIC_4539(x0)), x2, x1) → f7354_0_Ajouter_ArrayAccess(EOS(STATIC_7354(x0)), x1, java.lang.Object(ARRAY(x0)), x2 - 1 / 2)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE4(x2 > 0 && x2 < x0 && x2 - 1 / 2 < x0 && x2 - 1 / 2 < x2, EOS(STATIC_4539(x0)), x2)
Cond_f4539_0_Ajouter_LE4(TRUE, EOS(STATIC_4539(x0)), x2) → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2 - 1 / 2)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE5(x2 - 1 / 2 < x0 && x2 > 0, EOS(STATIC_4539(x0)), x2)
Cond_f4539_0_Ajouter_LE5(TRUE, EOS(STATIC_4539(x0)), x2) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE6(x2 > 0 && x2 < x0 && x2 - 1 / 2 < x0 && x2 - 1 / 2 >= x2, EOS(STATIC_4539(x0)), x2)
Cond_f4539_0_Ajouter_LE6(TRUE, EOS(STATIC_4539(x0)), x2) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → Cond_f7463_0_Ajouter_ArrayAccess(x2 < x0, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)
Cond_f7463_0_Ajouter_ArrayAccess(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE7(x2 >= x0 && x2 - 1 / 2 < x0 && x2 > 0, EOS(STATIC_4539(x0)), x2, x1)
Cond_f4539_0_Ajouter_LE7(TRUE, EOS(STATIC_4539(x0)), x2, x1) → f8243_0_Ajouter_ArrayAccess(EOS(STATIC_8243(x0)), x1, java.lang.Object(ARRAY(x0)), x2)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → Cond_f7463_0_Ajouter_ArrayAccess1(x2 >= x0, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2, x1)
Cond_f7463_0_Ajouter_ArrayAccess1(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2, x1) → f8814_0_Ajouter_ArrayAccess(EOS(STATIC_8814(x0)), java.lang.Object(ARRAY(x0)), x2, x1)

The integer pair graph contains the following rules and edges:
(0): F5290_1_HEAPSORT_INVOKEMETHOD'(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD(x2[0] + 1 < x0[0] && x2[0] > -1, f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])
(1): COND_F5290_1_HEAPSORT_INVOKEMETHOD(TRUE, f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[1]))), x2[1]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))), x2[1] + 1)
(2): F5290_1_HEAPSORT_INVOKEMETHOD'(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD1(x2[2] + 1 < x0[2] && x2[2] > -1, f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])
(3): COND_F5290_1_HEAPSORT_INVOKEMETHOD1(TRUE, f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[3]))), x2[3]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))), x2[3] + 1)
(4): F5290_1_HEAPSORT_INVOKEMETHOD'(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD2(x2[4] + 1 < x0[4] && x2[4] > -1, f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])
(5): COND_F5290_1_HEAPSORT_INVOKEMETHOD2(TRUE, f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[5]))), x2[5]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))), x2[5] + 1)

(0) -> (1), if (x2[0] + 1 < x0[0] && x2[0] > -1 ∧f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))) →^* f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[1])))∧x2[0] →^* x2[1])

(1) -> (0), if (f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))) →^* f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0])))∧x2[1] + 1 →^* x2[0])

(1) -> (2), if (f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))) →^* f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2])))∧x2[1] + 1 →^* x2[2])

(1) -> (4), if (f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))) →^* f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4])))∧x2[1] + 1 →^* x2[4])

(2) -> (3), if (x2[2] + 1 < x0[2] && x2[2] > -1 ∧f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))) →^* f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[3])))∧x2[2] →^* x2[3])

(3) -> (0), if (f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))) →^* f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0])))∧x2[3] + 1 →^* x2[0])

(3) -> (2), if (f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))) →^* f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2])))∧x2[3] + 1 →^* x2[2])

(3) -> (4), if (f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))) →^* f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4])))∧x2[3] + 1 →^* x2[4])

(4) -> (5), if (x2[4] + 1 < x0[4] && x2[4] > -1 ∧f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))) →^* f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[5])))∧x2[4] →^* x2[5])

(5) -> (0), if (f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))) →^* f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0])))∧x2[5] + 1 →^* x2[0])

(5) -> (2), if (f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))) →^* f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2])))∧x2[5] + 1 →^* x2[2])

(5) -> (4), if (f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))) →^* f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4])))∧x2[5] + 1 →^* x2[4])

The set Q consists of the following terms:
f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0)))
Cond_f4539_0_Ajouter_LE(TRUE, EOS(STATIC_4539(x0)), 0)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1)
Cond_f4539_0_Ajouter_LE1(TRUE, EOS(STATIC_4539(x0)), x1, x2)
Cond_f4539_0_Ajouter_LE2(TRUE, EOS(STATIC_4539(x0)), 0, x1)
Cond_f4539_0_Ajouter_LE3(TRUE, EOS(STATIC_4539(x0)), x1, x2)
Cond_f4539_0_Ajouter_LE4(TRUE, EOS(STATIC_4539(x0)), x1)
Cond_f4539_0_Ajouter_LE5(TRUE, EOS(STATIC_4539(x0)), x1)
Cond_f4539_0_Ajouter_LE6(TRUE, EOS(STATIC_4539(x0)), x1)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x1)
Cond_f7463_0_Ajouter_ArrayAccess(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x1)
Cond_f4539_0_Ajouter_LE7(TRUE, EOS(STATIC_4539(x0)), x1, x2)
Cond_f7463_0_Ajouter_ArrayAccess1(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x1, x2)

(25) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpCand1ShapeHeuristic@344de769 Constraint Generator: NonInfConstraintGenerator: PathGenerator: MetricPathGenerator: Max Left Steps: 0 Max Right Steps: 0

The constraints were generated the following way:
The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
Note that final constraints are written in bold face.

For Pair F5290_1_HEAPSORT_INVOKEMETHOD'(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0))), x2) → COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2, 1), x0), >(x2, -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0))), x2) the following chains were created:

We consider the chain F5290_1_HEAPSORT_INVOKEMETHOD'(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0]), COND_F5290_1_HEAPSORT_INVOKEMETHOD(TRUE, f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[1]))), x2[1]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))), +(x2[1], 1)) which results in the following constraint:
(1)    (&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1))=TRUE∧f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0])))=f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[1])))∧x2[0]=x2[1] ⇒ F5290_1_HEAPSORT_INVOKEMETHOD'(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])≥NonInfC∧F5290_1_HEAPSORT_INVOKEMETHOD'(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])≥COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])∧(U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (<(+(x2[0], 1), x0[0])=TRUE∧>(x2[0], -1)=TRUE ⇒ F5290_1_HEAPSORT_INVOKEMETHOD'(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])≥NonInfC∧F5290_1_HEAPSORT_INVOKEMETHOD'(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])≥COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])∧(U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] + [-2] + [-1]x2[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]x2[0] + [bni_49]x0[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] + [-2] + [-1]x2[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]x2[0] + [bni_49]x0[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] + [-2] + [-1]x2[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]x2[0] + [bni_49]x0[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])), ≥)∧[bni_49 + (-1)Bound*bni_49] + [bni_49]x0[0] ≥ 0∧[(-1)bso_50] ≥ 0)

For Pair COND_F5290_1_HEAPSORT_INVOKEMETHOD(TRUE, f4806_0_Ajouter_Return(EOS(STATIC_4806(x0))), x2) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))), +(x2, 1)) the following chains were created:

We consider the chain COND_F5290_1_HEAPSORT_INVOKEMETHOD(TRUE, f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[1]))), x2[1]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))), +(x2[1], 1)) which results in the following constraint:
(7)    (COND_F5290_1_HEAPSORT_INVOKEMETHOD(TRUE, f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[1]))), x2[1])≥NonInfC∧COND_F5290_1_HEAPSORT_INVOKEMETHOD(TRUE, f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[1]))), x2[1])≥F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))), +(x2[1], 1))∧(U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))), +(x2[1], 1))), ≥))

We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(8)    ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))), +(x2[1], 1))), ≥)∧[bni_51] = 0∧[1 + (-1)bso_52] ≥ 0)

We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(9)    ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))), +(x2[1], 1))), ≥)∧[bni_51] = 0∧[1 + (-1)bso_52] ≥ 0)

We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(10)    ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))), +(x2[1], 1))), ≥)∧[bni_51] = 0∧[1 + (-1)bso_52] ≥ 0)

We simplified constraint (10) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(11)    ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))), +(x2[1], 1))), ≥)∧[bni_51] = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_52] ≥ 0)

For Pair F5290_1_HEAPSORT_INVOKEMETHOD'(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0))), x2) → COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2, 1), x0), >(x2, -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0))), x2) the following chains were created:

We consider the chain F5290_1_HEAPSORT_INVOKEMETHOD'(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2]), COND_F5290_1_HEAPSORT_INVOKEMETHOD1(TRUE, f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[3]))), x2[3]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))), +(x2[3], 1)) which results in the following constraint:
(12)    (&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1))=TRUE∧f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2])))=f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[3])))∧x2[2]=x2[3] ⇒ F5290_1_HEAPSORT_INVOKEMETHOD'(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])≥NonInfC∧F5290_1_HEAPSORT_INVOKEMETHOD'(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])≥COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])∧(U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])), ≥))

We simplified constraint (12) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(13)    (<(+(x2[2], 1), x0[2])=TRUE∧>(x2[2], -1)=TRUE ⇒ F5290_1_HEAPSORT_INVOKEMETHOD'(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])≥NonInfC∧F5290_1_HEAPSORT_INVOKEMETHOD'(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])≥COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])∧(U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])), ≥))

We simplified constraint (13) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(14)    (x0[2] + [-2] + [-1]x2[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]x2[2] + [bni_53]x0[2] ≥ 0∧[(-1)bso_54] ≥ 0)

We simplified constraint (14) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(15)    (x0[2] + [-2] + [-1]x2[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]x2[2] + [bni_53]x0[2] ≥ 0∧[(-1)bso_54] ≥ 0)

We simplified constraint (15) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(16)    (x0[2] + [-2] + [-1]x2[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]x2[2] + [bni_53]x0[2] ≥ 0∧[(-1)bso_54] ≥ 0)

We simplified constraint (16) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(17)    (x0[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])), ≥)∧[bni_53 + (-1)Bound*bni_53] + [bni_53]x0[2] ≥ 0∧[(-1)bso_54] ≥ 0)

For Pair COND_F5290_1_HEAPSORT_INVOKEMETHOD1(TRUE, f5320_0_Ajouter_Return(EOS(STATIC_5320(x0))), x2) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))), +(x2, 1)) the following chains were created:

We consider the chain COND_F5290_1_HEAPSORT_INVOKEMETHOD1(TRUE, f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[3]))), x2[3]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))), +(x2[3], 1)) which results in the following constraint:
(18)    (COND_F5290_1_HEAPSORT_INVOKEMETHOD1(TRUE, f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[3]))), x2[3])≥NonInfC∧COND_F5290_1_HEAPSORT_INVOKEMETHOD1(TRUE, f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[3]))), x2[3])≥F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))), +(x2[3], 1))∧(U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))), +(x2[3], 1))), ≥))

We simplified constraint (18) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(19)    ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))), +(x2[3], 1))), ≥)∧[bni_55] = 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (19) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(20)    ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))), +(x2[3], 1))), ≥)∧[bni_55] = 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (20) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(21)    ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))), +(x2[3], 1))), ≥)∧[bni_55] = 0∧[1 + (-1)bso_56] ≥ 0)

We simplified constraint (21) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(22)    ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))), +(x2[3], 1))), ≥)∧[bni_55] = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_56] ≥ 0)

For Pair F5290_1_HEAPSORT_INVOKEMETHOD'(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0))), x2) → COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2, 1), x0), >(x2, -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0))), x2) the following chains were created:

We consider the chain F5290_1_HEAPSORT_INVOKEMETHOD'(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4]), COND_F5290_1_HEAPSORT_INVOKEMETHOD2(TRUE, f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[5]))), x2[5]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))), +(x2[5], 1)) which results in the following constraint:
(23)    (&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1))=TRUE∧f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4])))=f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[5])))∧x2[4]=x2[5] ⇒ F5290_1_HEAPSORT_INVOKEMETHOD'(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])≥NonInfC∧F5290_1_HEAPSORT_INVOKEMETHOD'(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])≥COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])∧(U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])), ≥))

We simplified constraint (23) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(24)    (<(+(x2[4], 1), x0[4])=TRUE∧>(x2[4], -1)=TRUE ⇒ F5290_1_HEAPSORT_INVOKEMETHOD'(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])≥NonInfC∧F5290_1_HEAPSORT_INVOKEMETHOD'(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])≥COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])∧(U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])), ≥))

We simplified constraint (24) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(25)    (x0[4] + [-2] + [-1]x2[4] ≥ 0∧x2[4] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] + [(-1)bni_57]x2[4] + [bni_57]x0[4] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (25) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(26)    (x0[4] + [-2] + [-1]x2[4] ≥ 0∧x2[4] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] + [(-1)bni_57]x2[4] + [bni_57]x0[4] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (26) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(27)    (x0[4] + [-2] + [-1]x2[4] ≥ 0∧x2[4] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] + [(-1)bni_57]x2[4] + [bni_57]x0[4] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (27) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(28)    (x0[4] ≥ 0∧x2[4] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])), ≥)∧[bni_57 + (-1)Bound*bni_57] + [bni_57]x0[4] ≥ 0∧[(-1)bso_58] ≥ 0)

For Pair COND_F5290_1_HEAPSORT_INVOKEMETHOD2(TRUE, f7598_0_Ajouter_Return(EOS(STATIC_7598(x0))), x2) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))), +(x2, 1)) the following chains were created:

We consider the chain COND_F5290_1_HEAPSORT_INVOKEMETHOD2(TRUE, f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[5]))), x2[5]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))), +(x2[5], 1)) which results in the following constraint:
(29)    (COND_F5290_1_HEAPSORT_INVOKEMETHOD2(TRUE, f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[5]))), x2[5])≥NonInfC∧COND_F5290_1_HEAPSORT_INVOKEMETHOD2(TRUE, f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[5]))), x2[5])≥F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))), +(x2[5], 1))∧(U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))), +(x2[5], 1))), ≥))

We simplified constraint (29) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(30)    ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))), +(x2[5], 1))), ≥)∧[bni_59] = 0∧[1 + (-1)bso_60] ≥ 0)

We simplified constraint (30) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(31)    ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))), +(x2[5], 1))), ≥)∧[bni_59] = 0∧[1 + (-1)bso_60] ≥ 0)

We simplified constraint (31) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(32)    ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))), +(x2[5], 1))), ≥)∧[bni_59] = 0∧[1 + (-1)bso_60] ≥ 0)

We simplified constraint (32) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(33)    ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))), +(x2[5], 1))), ≥)∧[bni_59] = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_60] ≥ 0)

To summarize, we get the following constraints P_≥ for the following pairs.

F5290_1_HEAPSORT_INVOKEMETHOD'(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0))), x2) → COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2, 1), x0), >(x2, -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0))), x2)
- (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])), ≥)∧[bni_49 + (-1)Bound*bni_49] + [bni_49]x0[0] ≥ 0∧[(-1)bso_50] ≥ 0)
COND_F5290_1_HEAPSORT_INVOKEMETHOD(TRUE, f4806_0_Ajouter_Return(EOS(STATIC_4806(x0))), x2) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))), +(x2, 1))
- ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))), +(x2[1], 1))), ≥)∧[bni_51] = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_52] ≥ 0)
F5290_1_HEAPSORT_INVOKEMETHOD'(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0))), x2) → COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2, 1), x0), >(x2, -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0))), x2)
- (x0[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])), ≥)∧[bni_53 + (-1)Bound*bni_53] + [bni_53]x0[2] ≥ 0∧[(-1)bso_54] ≥ 0)
COND_F5290_1_HEAPSORT_INVOKEMETHOD1(TRUE, f5320_0_Ajouter_Return(EOS(STATIC_5320(x0))), x2) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))), +(x2, 1))
- ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))), +(x2[3], 1))), ≥)∧[bni_55] = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_56] ≥ 0)
F5290_1_HEAPSORT_INVOKEMETHOD'(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0))), x2) → COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2, 1), x0), >(x2, -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0))), x2)
- (x0[4] ≥ 0∧x2[4] ≥ 0 ⇒ (U^Increasing(COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])), ≥)∧[bni_57 + (-1)Bound*bni_57] + [bni_57]x0[4] ≥ 0∧[(-1)bso_58] ≥ 0)
COND_F5290_1_HEAPSORT_INVOKEMETHOD2(TRUE, f7598_0_Ajouter_Return(EOS(STATIC_7598(x0))), x2) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))), +(x2, 1))
- ((U^Increasing(F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))), +(x2[5], 1))), ≥)∧[bni_59] = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_60] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(f5311_0_Ajouter_FieldAccess(x₁)) = x₁
POL(EOS(x₁)) = x₁
POL(STATIC_5311(x₁)) = x₁
POL(f4539_0_Ajouter_LE(x₁, x₂)) = x₁
POL(STATIC_4539(x₁)) = x₁
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(1) = [1]
POL(0) = 0
POL(Cond_f4539_0_Ajouter_LE(x₁, x₂, x₃)) = x₂
POL(>(x₁, x₂)) = [-1]
POL(f7598_0_Ajouter_Return(x₁)) = x₁
POL(STATIC_7598(x₁)) = x₁
POL(Cond_f4539_0_Ajouter_LE1(x₁, x₂, x₃, x₄)) = [-1] + x₂
POL(&&(x₁, x₂)) = [-1]
POL(<=(x₁, x₂)) = [-1]
POL(-1) = [-1]
POL(f6913_0_Ajouter_ArrayAccess(x₁, x₂, x₃, x₄)) = [-1] + [2]x₂ + [-1]x₁
POL(STATIC_6913(x₁)) = x₁
POL(java.lang.Object(x₁)) = x₁
POL(ARRAY(x₁)) = x₁
POL(Cond_f4539_0_Ajouter_LE2(x₁, x₂, x₃, x₄)) = [-1] + x₂
POL(f6985_0_Ajouter_ArrayAccess(x₁, x₂, x₃)) = [-1] + [2]x₂ + [-1]x₁
POL(STATIC_6985(x₁)) = x₁
POL(Cond_f4539_0_Ajouter_LE3(x₁, x₂, x₃, x₄)) = x₂
POL(>=(x₁, x₂)) = [-1]
POL(2) = [2]
POL(f7354_0_Ajouter_ArrayAccess(x₁, x₂, x₃, x₄)) = [-1] + x₃
POL(STATIC_7354(x₁)) = x₁
POL(Cond_f4539_0_Ajouter_LE4(x₁, x₂, x₃)) = x₂
POL(<(x₁, x₂)) = [-1]
POL(Cond_f4539_0_Ajouter_LE5(x₁, x₂, x₃)) = x₂
POL(f7463_0_Ajouter_ArrayAccess(x₁, x₂, x₃)) = x₂
POL(STATIC_7463(x₁)) = x₁
POL(Cond_f4539_0_Ajouter_LE6(x₁, x₂, x₃)) = x₂
POL(Cond_f7463_0_Ajouter_ArrayAccess(x₁, x₂, x₃, x₄)) = x₃
POL(Cond_f4539_0_Ajouter_LE7(x₁, x₂, x₃, x₄)) = [-1] + x₂
POL(f8243_0_Ajouter_ArrayAccess(x₁, x₂, x₃, x₄)) = [-1] + [2]x₃ + [-1]x₁
POL(STATIC_8243(x₁)) = x₁
POL(Cond_f7463_0_Ajouter_ArrayAccess1(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₃
POL(f8814_0_Ajouter_ArrayAccess(x₁, x₂, x₃, x₄)) = [-1] + x₂
POL(STATIC_8814(x₁)) = x₁
POL(F5290_1_HEAPSORT_INVOKEMETHOD'(x₁, x₂)) = [-1] + [-1]x₂ + x₁
POL(f4806_0_Ajouter_Return(x₁)) = x₁
POL(STATIC_4806(x₁)) = x₁
POL(COND_F5290_1_HEAPSORT_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [-1]x₃ + x₂
POL(+(x₁, x₂)) = x₁ + x₂
POL(f5320_0_Ajouter_Return(x₁)) = x₁
POL(STATIC_5320(x₁)) = x₁
POL(COND_F5290_1_HEAPSORT_INVOKEMETHOD1(x₁, x₂, x₃)) = [-1] + [-1]x₃ + x₂
POL(COND_F5290_1_HEAPSORT_INVOKEMETHOD2(x₁, x₂, x₃)) = [-1] + [-1]x₃ + x₂

Polynomial Interpretations with Context Sensitive Arithemetic Replacement
POL(Term^CSAR-Mode @ Context)

POL(/(x₁, 2)¹ @ {f4539_0_Ajouter_LE_2/1}) = max{x₁, [-1]x₁} + [-1]
POL(/(x₁, 2)¹ @ {f7354_0_Ajouter_ArrayAccess_4/3}) = [-1]max{x₁, [-1]x₁} + [1]

The following pairs are in P_>:

COND_F5290_1_HEAPSORT_INVOKEMETHOD(TRUE, f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[1]))), x2[1]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))), +(x2[1], 1))
COND_F5290_1_HEAPSORT_INVOKEMETHOD1(TRUE, f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[3]))), x2[3]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))), +(x2[3], 1))
COND_F5290_1_HEAPSORT_INVOKEMETHOD2(TRUE, f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[5]))), x2[5]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))), +(x2[5], 1))

The following pairs are in P_bound:

F5290_1_HEAPSORT_INVOKEMETHOD'(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])
F5290_1_HEAPSORT_INVOKEMETHOD'(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])
F5290_1_HEAPSORT_INVOKEMETHOD'(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])

The following pairs are in P_≥:

F5290_1_HEAPSORT_INVOKEMETHOD'(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD(&&(<(+(x2[0], 1), x0[0]), >(x2[0], -1)), f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])
F5290_1_HEAPSORT_INVOKEMETHOD'(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD1(&&(<(+(x2[2], 1), x0[2]), >(x2[2], -1)), f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])
F5290_1_HEAPSORT_INVOKEMETHOD'(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD2(&&(<(+(x2[4], 1), x0[4]), >(x2[4], -1)), f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])

At least the following rules have been oriented under context sensitive arithmetic replacement:

f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0)))¹ → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), -(x2, 1))¹
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), 0)¹ → Cond_f4539_0_Ajouter_LE(>(x0, 0), EOS(STATIC_4539(x0)), 0)¹
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2)¹ → Cond_f4539_0_Ajouter_LE1(&&(<=(x2, -1), <=(x2, 0)), EOS(STATIC_4539(x0)), x2, x1)¹
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), 0)¹ → Cond_f4539_0_Ajouter_LE2(<=(x0, 0), EOS(STATIC_4539(x0)), 0, x1)¹
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2)¹ → Cond_f4539_0_Ajouter_LE3(&&(>=(/(-(x2, 1), 2), x0), >(x2, 0)), EOS(STATIC_4539(x0)), x2, x1)¹
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2)¹ → Cond_f4539_0_Ajouter_LE4(&&(&&(&&(>(x2, 0), <(x2, x0)), <(/(-(x2, 1), 2), x0)), <(/(-(x2, 1), 2), x2)), EOS(STATIC_4539(x0)), x2)¹
Cond_f4539_0_Ajouter_LE4(TRUE, EOS(STATIC_4539(x0)), x2)¹ → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), /(-(x2, 1), 2))¹
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2)¹ ↔ Cond_f4539_0_Ajouter_LE5(&&(<(/(-(x2, 1), 2), x0), >(x2, 0)), EOS(STATIC_4539(x0)), x2)¹
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2)¹ ↔ Cond_f4539_0_Ajouter_LE6(&&(&&(&&(>(x2, 0), <(x2, x0)), <(/(-(x2, 1), 2), x0)), >=(/(-(x2, 1), 2), x2)), EOS(STATIC_4539(x0)), x2)¹
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2)¹ → Cond_f4539_0_Ajouter_LE7(&&(&&(>=(x2, x0), <(/(-(x2, 1), 2), x0)), >(x2, 0)), EOS(STATIC_4539(x0)), x2, x1)¹
/¹ →
Cond_f4539_0_Ajouter_LE(TRUE, EOS(STATIC_4539(x0)), 0)¹ ↔ f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)))¹
Cond_f4539_0_Ajouter_LE1(TRUE, EOS(STATIC_4539(x0)), x2, x1)¹ → f6913_0_Ajouter_ArrayAccess(EOS(STATIC_6913(x0)), java.lang.Object(ARRAY(x0)), x2, x1)¹
Cond_f4539_0_Ajouter_LE2(TRUE, EOS(STATIC_4539(x0)), 0, x1)¹ ↔ f6985_0_Ajouter_ArrayAccess(EOS(STATIC_6985(x0)), java.lang.Object(ARRAY(x0)), x1)¹
Cond_f4539_0_Ajouter_LE3(TRUE, EOS(STATIC_4539(x0)), x2, x1)¹ → f7354_0_Ajouter_ArrayAccess(EOS(STATIC_7354(x0)), x1, java.lang.Object(ARRAY(x0)), /(-(x2, 1), 2))¹
Cond_f4539_0_Ajouter_LE5(TRUE, EOS(STATIC_4539(x0)), x2)¹ → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)¹
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)¹ ↔ Cond_f7463_0_Ajouter_ArrayAccess(<(x2, x0), EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)¹
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)¹ → Cond_f7463_0_Ajouter_ArrayAccess1(>=(x2, x0), EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2, x1)¹
Cond_f4539_0_Ajouter_LE6(TRUE, EOS(STATIC_4539(x0)), x2)¹ → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)¹
Cond_f7463_0_Ajouter_ArrayAccess(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)¹ ↔ f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)))¹
Cond_f4539_0_Ajouter_LE7(TRUE, EOS(STATIC_4539(x0)), x2, x1)¹ ↔ f8243_0_Ajouter_ArrayAccess(EOS(STATIC_8243(x0)), x1, java.lang.Object(ARRAY(x0)), x2)¹
Cond_f7463_0_Ajouter_ArrayAccess1(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2, x1)¹ ↔ f8814_0_Ajouter_ArrayAccess(EOS(STATIC_8814(x0)), java.lang.Object(ARRAY(x0)), x2, x1)¹

(26) Complex Obligation (AND)

(27) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Integer, Boolean

The ITRS R consists of the following rules:
f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))) → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2 - 1)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), 0) → Cond_f4539_0_Ajouter_LE(x0 > 0, EOS(STATIC_4539(x0)), 0)
Cond_f4539_0_Ajouter_LE(TRUE, EOS(STATIC_4539(x0)), 0) → f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE1(x2 <= -1 && x2 <= 0, EOS(STATIC_4539(x0)), x2, x1)
Cond_f4539_0_Ajouter_LE1(TRUE, EOS(STATIC_4539(x0)), x2, x1) → f6913_0_Ajouter_ArrayAccess(EOS(STATIC_6913(x0)), java.lang.Object(ARRAY(x0)), x2, x1)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), 0) → Cond_f4539_0_Ajouter_LE2(x0 <= 0, EOS(STATIC_4539(x0)), 0, x1)
Cond_f4539_0_Ajouter_LE2(TRUE, EOS(STATIC_4539(x0)), 0, x1) → f6985_0_Ajouter_ArrayAccess(EOS(STATIC_6985(x0)), java.lang.Object(ARRAY(x0)), x1)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE3(x2 - 1 / 2 >= x0 && x2 > 0, EOS(STATIC_4539(x0)), x2, x1)
Cond_f4539_0_Ajouter_LE3(TRUE, EOS(STATIC_4539(x0)), x2, x1) → f7354_0_Ajouter_ArrayAccess(EOS(STATIC_7354(x0)), x1, java.lang.Object(ARRAY(x0)), x2 - 1 / 2)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE4(x2 > 0 && x2 < x0 && x2 - 1 / 2 < x0 && x2 - 1 / 2 < x2, EOS(STATIC_4539(x0)), x2)
Cond_f4539_0_Ajouter_LE4(TRUE, EOS(STATIC_4539(x0)), x2) → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2 - 1 / 2)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE5(x2 - 1 / 2 < x0 && x2 > 0, EOS(STATIC_4539(x0)), x2)
Cond_f4539_0_Ajouter_LE5(TRUE, EOS(STATIC_4539(x0)), x2) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE6(x2 > 0 && x2 < x0 && x2 - 1 / 2 < x0 && x2 - 1 / 2 >= x2, EOS(STATIC_4539(x0)), x2)
Cond_f4539_0_Ajouter_LE6(TRUE, EOS(STATIC_4539(x0)), x2) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → Cond_f7463_0_Ajouter_ArrayAccess(x2 < x0, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)
Cond_f7463_0_Ajouter_ArrayAccess(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE7(x2 >= x0 && x2 - 1 / 2 < x0 && x2 > 0, EOS(STATIC_4539(x0)), x2, x1)
Cond_f4539_0_Ajouter_LE7(TRUE, EOS(STATIC_4539(x0)), x2, x1) → f8243_0_Ajouter_ArrayAccess(EOS(STATIC_8243(x0)), x1, java.lang.Object(ARRAY(x0)), x2)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → Cond_f7463_0_Ajouter_ArrayAccess1(x2 >= x0, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2, x1)
Cond_f7463_0_Ajouter_ArrayAccess1(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2, x1) → f8814_0_Ajouter_ArrayAccess(EOS(STATIC_8814(x0)), java.lang.Object(ARRAY(x0)), x2, x1)

The integer pair graph contains the following rules and edges:
(0): F5290_1_HEAPSORT_INVOKEMETHOD'(f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD(x2[0] + 1 < x0[0] && x2[0] > -1, f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[0]))), x2[0])
(2): F5290_1_HEAPSORT_INVOKEMETHOD'(f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD1(x2[2] + 1 < x0[2] && x2[2] > -1, f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[2]))), x2[2])
(4): F5290_1_HEAPSORT_INVOKEMETHOD'(f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4]) → COND_F5290_1_HEAPSORT_INVOKEMETHOD2(x2[4] + 1 < x0[4] && x2[4] > -1, f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[4]))), x2[4])

The set Q consists of the following terms:
f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0)))
Cond_f4539_0_Ajouter_LE(TRUE, EOS(STATIC_4539(x0)), 0)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1)
Cond_f4539_0_Ajouter_LE1(TRUE, EOS(STATIC_4539(x0)), x1, x2)
Cond_f4539_0_Ajouter_LE2(TRUE, EOS(STATIC_4539(x0)), 0, x1)
Cond_f4539_0_Ajouter_LE3(TRUE, EOS(STATIC_4539(x0)), x1, x2)
Cond_f4539_0_Ajouter_LE4(TRUE, EOS(STATIC_4539(x0)), x1)
Cond_f4539_0_Ajouter_LE5(TRUE, EOS(STATIC_4539(x0)), x1)
Cond_f4539_0_Ajouter_LE6(TRUE, EOS(STATIC_4539(x0)), x1)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x1)
Cond_f7463_0_Ajouter_ArrayAccess(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x1)
Cond_f4539_0_Ajouter_LE7(TRUE, EOS(STATIC_4539(x0)), x1, x2)
Cond_f7463_0_Ajouter_ArrayAccess1(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x1, x2)

(28) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(29) TRUE

(30) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
\|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
\|\|	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Integer, Boolean

The ITRS R consists of the following rules:
f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0))) → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2 - 1)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), 0) → Cond_f4539_0_Ajouter_LE(x0 > 0, EOS(STATIC_4539(x0)), 0)
Cond_f4539_0_Ajouter_LE(TRUE, EOS(STATIC_4539(x0)), 0) → f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE1(x2 <= -1 && x2 <= 0, EOS(STATIC_4539(x0)), x2, x1)
Cond_f4539_0_Ajouter_LE1(TRUE, EOS(STATIC_4539(x0)), x2, x1) → f6913_0_Ajouter_ArrayAccess(EOS(STATIC_6913(x0)), java.lang.Object(ARRAY(x0)), x2, x1)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), 0) → Cond_f4539_0_Ajouter_LE2(x0 <= 0, EOS(STATIC_4539(x0)), 0, x1)
Cond_f4539_0_Ajouter_LE2(TRUE, EOS(STATIC_4539(x0)), 0, x1) → f6985_0_Ajouter_ArrayAccess(EOS(STATIC_6985(x0)), java.lang.Object(ARRAY(x0)), x1)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE3(x2 - 1 / 2 >= x0 && x2 > 0, EOS(STATIC_4539(x0)), x2, x1)
Cond_f4539_0_Ajouter_LE3(TRUE, EOS(STATIC_4539(x0)), x2, x1) → f7354_0_Ajouter_ArrayAccess(EOS(STATIC_7354(x0)), x1, java.lang.Object(ARRAY(x0)), x2 - 1 / 2)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE4(x2 > 0 && x2 < x0 && x2 - 1 / 2 < x0 && x2 - 1 / 2 < x2, EOS(STATIC_4539(x0)), x2)
Cond_f4539_0_Ajouter_LE4(TRUE, EOS(STATIC_4539(x0)), x2) → f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2 - 1 / 2)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE5(x2 - 1 / 2 < x0 && x2 > 0, EOS(STATIC_4539(x0)), x2)
Cond_f4539_0_Ajouter_LE5(TRUE, EOS(STATIC_4539(x0)), x2) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE6(x2 > 0 && x2 < x0 && x2 - 1 / 2 < x0 && x2 - 1 / 2 >= x2, EOS(STATIC_4539(x0)), x2)
Cond_f4539_0_Ajouter_LE6(TRUE, EOS(STATIC_4539(x0)), x2) → f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → Cond_f7463_0_Ajouter_ArrayAccess(x2 < x0, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2)
Cond_f7463_0_Ajouter_ArrayAccess(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → f7598_0_Ajouter_Return(EOS(STATIC_7598(x0)))
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x2) → Cond_f4539_0_Ajouter_LE7(x2 >= x0 && x2 - 1 / 2 < x0 && x2 > 0, EOS(STATIC_4539(x0)), x2, x1)
Cond_f4539_0_Ajouter_LE7(TRUE, EOS(STATIC_4539(x0)), x2, x1) → f8243_0_Ajouter_ArrayAccess(EOS(STATIC_8243(x0)), x1, java.lang.Object(ARRAY(x0)), x2)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2) → Cond_f7463_0_Ajouter_ArrayAccess1(x2 >= x0, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2, x1)
Cond_f7463_0_Ajouter_ArrayAccess1(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x2, x1) → f8814_0_Ajouter_ArrayAccess(EOS(STATIC_8814(x0)), java.lang.Object(ARRAY(x0)), x2, x1)

The integer pair graph contains the following rules and edges:
(1): COND_F5290_1_HEAPSORT_INVOKEMETHOD(TRUE, f4806_0_Ajouter_Return(EOS(STATIC_4806(x0[1]))), x2[1]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[1]))), x2[1] + 1)
(3): COND_F5290_1_HEAPSORT_INVOKEMETHOD1(TRUE, f5320_0_Ajouter_Return(EOS(STATIC_5320(x0[3]))), x2[3]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[3]))), x2[3] + 1)
(5): COND_F5290_1_HEAPSORT_INVOKEMETHOD2(TRUE, f7598_0_Ajouter_Return(EOS(STATIC_7598(x0[5]))), x2[5]) → F5290_1_HEAPSORT_INVOKEMETHOD'(f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0[5]))), x2[5] + 1)

The set Q consists of the following terms:
f5311_0_Ajouter_FieldAccess(EOS(STATIC_5311(x0)))
Cond_f4539_0_Ajouter_LE(TRUE, EOS(STATIC_4539(x0)), 0)
f4539_0_Ajouter_LE(EOS(STATIC_4539(x0)), x1)
Cond_f4539_0_Ajouter_LE1(TRUE, EOS(STATIC_4539(x0)), x1, x2)
Cond_f4539_0_Ajouter_LE2(TRUE, EOS(STATIC_4539(x0)), 0, x1)
Cond_f4539_0_Ajouter_LE3(TRUE, EOS(STATIC_4539(x0)), x1, x2)
Cond_f4539_0_Ajouter_LE4(TRUE, EOS(STATIC_4539(x0)), x1)
Cond_f4539_0_Ajouter_LE5(TRUE, EOS(STATIC_4539(x0)), x1)
Cond_f4539_0_Ajouter_LE6(TRUE, EOS(STATIC_4539(x0)), x1)
f7463_0_Ajouter_ArrayAccess(EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x1)
Cond_f7463_0_Ajouter_ArrayAccess(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x1)
Cond_f4539_0_Ajouter_LE7(TRUE, EOS(STATIC_4539(x0)), x1, x2)
Cond_f7463_0_Ajouter_ArrayAccess1(TRUE, EOS(STATIC_7463(x0)), java.lang.Object(ARRAY(x0)), x1, x2)

(31) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(32) TRUE

(33) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: TriTas.main([Ljava/lang/String;)V
SCC calls the following helper methods:
Performed SCC analyses:

Used field analysis yielded the following read fields:
- java.lang.String: [count]
Marker field analysis yielded the following relations that could be markers:

(34) SCCToIntTRSProof (SOUND transformation)

Transformed FIGraph SCCs to intTRSs. Log:

Generated rules. Obtained 43 IRules

P rules:
f4165_0_main_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, i686) → f4172_0_main_GE(EOS, java.lang.Object(ARRAY(i27)), i686, i686, i27)
f4172_0_main_GE(EOS, java.lang.Object(ARRAY(i27)), i686, i686, i27) → f4179_0_main_GE(EOS, java.lang.Object(ARRAY(i27)), i686, i686, i27)
f4179_0_main_GE(EOS, java.lang.Object(ARRAY(i27)), i686, i686, i27) → f4206_0_main_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686) | <(i686, i27)
f4206_0_main_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686) → f4224_0_main_Load(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)))
f4224_0_main_Load(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27))) → f4290_0_main_InvokeMethod(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686)
f4290_0_main_InvokeMethod(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686) → f4311_0_random_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686)
f4311_0_random_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686) → f4352_0_random_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, i685)
f4352_0_random_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, i685) → f4368_0_random_ArrayLength(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, i685, java.lang.Object(ARRAY(i27)))
f4368_0_random_ArrayLength(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, i685, java.lang.Object(ARRAY(i27))) → f4395_0_random_LT(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, i685, i27) | >=(i27, 0)
f4395_0_random_LT(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, i685, i27) → f4397_0_random_LT(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, i685, i27)
f4395_0_random_LT(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, i685, i27) → f4398_0_random_LT(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, i685, i27)
f4397_0_random_LT(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, i685, i27) → f4404_0_random_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686) | <(i685, i27)
f4404_0_random_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686) → f4414_0_random_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)))
f4414_0_random_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27))) → f4426_0_random_ArrayAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i685)
f4426_0_random_ArrayAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i685) → f4460_0_random_ArrayAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i685)
f4460_0_random_ArrayAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i685) → f4512_0_random_Store(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715)
f4512_0_random_Store(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715) → f4543_0_random_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715)
f4543_0_random_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715) → f4585_0_random_ConstantStackPush(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715, i685)
f4585_0_random_ConstantStackPush(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715, i685) → f4617_0_random_IntArithmetic(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715, i685, 1)
f4617_0_random_IntArithmetic(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715, i685, matching1) → f4784_0_random_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715, +(i685, 1)) | &&(>=(i685, 0), =(matching1, 1))
f4784_0_random_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715, i872) → f4804_0_random_Load(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715)
f4804_0_random_Load(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715) → f4829_0_random_InvokeMethod(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, o715)
f4829_0_random_InvokeMethod(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(o756sub)) → f4850_0_random_InvokeMethod(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(o756sub))
f4850_0_random_InvokeMethod(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(o756sub)) → f4887_0_length_Load(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(o756sub), java.lang.Object(o756sub))
f4887_0_length_Load(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(o756sub), java.lang.Object(o756sub)) → f5017_0_length_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(o756sub), java.lang.Object(o756sub))
f5017_0_length_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(java.lang.String(o814sub, i947)), java.lang.Object(java.lang.String(o814sub, i947))) → f5053_0_length_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(java.lang.String(o814sub, i947)), java.lang.Object(java.lang.String(o814sub, i947)))
f5053_0_length_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(java.lang.String(o814sub, i947)), java.lang.Object(java.lang.String(o814sub, i947))) → f5111_0_length_Return(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(java.lang.String(o814sub, i947)))
f5111_0_length_Return(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(java.lang.String(o814sub, i947))) → f5148_0_random_Return(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686)
f5148_0_random_Return(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686) → f5187_0_main_ArrayAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686)
f5187_0_main_ArrayAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686) → f5245_0_main_ArrayAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686)
f5245_0_main_ArrayAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686) → f5293_0_main_Inc(EOS, java.lang.Object(ARRAY(i27)), i686) | <(i686, i27)
f5293_0_main_Inc(EOS, java.lang.Object(ARRAY(i27)), i686) → f5337_0_main_JMP(EOS, java.lang.Object(ARRAY(i27)), +(i686, 1)) | >=(i686, 0)
f5337_0_main_JMP(EOS, java.lang.Object(ARRAY(i27)), i1024) → f5408_0_main_Load(EOS, java.lang.Object(ARRAY(i27)), i1024)
f5408_0_main_Load(EOS, java.lang.Object(ARRAY(i27)), i1024) → f4105_0_main_Load(EOS, java.lang.Object(ARRAY(i27)), i1024)
f4105_0_main_Load(EOS, java.lang.Object(ARRAY(i27)), i686) → f4165_0_main_FieldAccess(EOS, java.lang.Object(ARRAY(i27)), i686, i686)
f4398_0_random_LT(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686, i685, i27) → f4407_0_random_ConstantStackPush(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686) | >=(i685, i27)
f4407_0_random_ConstantStackPush(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686) → f4421_0_random_Return(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686)
f4421_0_random_Return(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686) → f4442_0_main_ArrayAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686)
f4442_0_main_ArrayAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686) → f4505_0_main_ArrayAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686)
f4505_0_main_ArrayAccess(EOS, java.lang.Object(ARRAY(i27)), i686, java.lang.Object(ARRAY(i27)), i686) → f4529_0_main_Inc(EOS, java.lang.Object(ARRAY(i27)), i686) | <(i686, i27)
f4529_0_main_Inc(EOS, java.lang.Object(ARRAY(i27)), i686) → f4575_0_main_JMP(EOS, java.lang.Object(ARRAY(i27)), +(i686, 1)) | >=(i686, 0)
f4575_0_main_JMP(EOS, java.lang.Object(ARRAY(i27)), i837) → f4600_0_main_Load(EOS, java.lang.Object(ARRAY(i27)), i837)
f4600_0_main_Load(EOS, java.lang.Object(ARRAY(i27)), i837) → f4105_0_main_Load(EOS, java.lang.Object(ARRAY(i27)), i837)

Combined rules. Obtained 1 IRules

P rules:
f4165_0_main_FieldAccess(EOS, java.lang.Object(ARRAY(x0)), x1, x1) → f4165_0_main_FieldAccess(EOS, java.lang.Object(ARRAY(x0)), +(x1, 1), +(x1, 1)) | &&(&&(>(+(x1, 1), 0), <(x1, x0)), >(+(x0, 1), 0))

Filtered ground terms:

f4165_0_main_FieldAccess(x1, x2, x3, x4) → f4165_0_main_FieldAccess(x2, x3, x4)
Cond_f4165_0_main_FieldAccess(x1, x2, x3, x4, x5) → Cond_f4165_0_main_FieldAccess(x1, x3, x4, x5)

Filtered duplicate terms:

f4165_0_main_FieldAccess(x1, x2, x3) → f4165_0_main_FieldAccess(x1, x3)
Cond_f4165_0_main_FieldAccess(x1, x2, x3, x4) → Cond_f4165_0_main_FieldAccess(x1, x2, x4)

Prepared 1 rules for path length conversion:

P rules:
f4165_0_main_FieldAccess(java.lang.Object(ARRAY(x0)), x1, x0) → f4165_0_main_FieldAccess(java.lang.Object(ARRAY(x0)), +(x1, 1), x0) | &&(&&(>(+(x1, 1), 0), <(x1, x0)), >(+(x0, 1), 0))

Finished conversion. Obtained 1 rules.

P rules:
f4165_0_main_FieldAccess(v5, x1, x0) → f4165_0_main_FieldAccess(v6, +(x1, 1), x0) | &&(&&(&&(&&(&&(>(x1, -1), <(x1, x0)), >(x0, -1)), >(+(v6, 1), 1)), <=(v6, v5)), >(+(v5, 1), 1))

(35) Obligation:

Rules:
f4165_0_main_FieldAccess(v5, x1, x0) → f4165_0_main_FieldAccess(v6, +(x1, 1), x0) | &&(&&(&&(&&(&&(>(x1, -1), <(x1, x0)), >(x0, -1)), >(+(v6, 1), 1)), <=(v6, v5)), >(+(v5, 1), 1))

(36) PolynomialOrderProcessor (EQUIVALENT transformation)

Found the following polynomial interpretation:

[f4165_0_main_FieldAccess(x5, x7, x9)] = -x7 + x9

Therefore the following rule(s) have been dropped:

f4165_0_main_FieldAccess(x0, x1, x2) → f4165_0_main_FieldAccess(x3, +(x1, 1), x2) | &&(&&(&&(&&(&&(>(x1, -1), <(x1, x2)), >(x2, -1)), >(+(x3, 1), 1)), <=(x3, x0)), >(+(x0, 1), 1))

(0) Obligation:

(1) JBCToGraph (SOUND transformation)

(2) Obligation:

(3) TerminationGraphToSCCProof (SOUND transformation)

(4) Complex Obligation (AND)

(5) Obligation:

(6) SCCToIDPv1Proof (SOUND transformation)

(7) Obligation:

(8) IDPNonInfProof (SOUND transformation)

(9) Obligation:

(10) IDependencyGraphProof (EQUIVALENT transformation)

(11) TRUE

(12) Obligation:

(13) SCCToIntTRSProof (SOUND transformation)

(14) Obligation:

(15) PolynomialOrderProcessor (EQUIVALENT transformation)

(16) YES

(17) Obligation:

(18) SCCToIntTRSProof (SOUND transformation)

(19) Obligation:

(20) PolynomialOrderProcessor (EQUIVALENT transformation)

(21) YES

(22) Obligation:

(23) SCCToIDPv1Proof (SOUND transformation)

(24) Obligation:

(25) IDPNonInfProof (SOUND transformation)

(26) Complex Obligation (AND)

(27) Obligation:

(28) IDependencyGraphProof (EQUIVALENT transformation)

(29) TRUE

(30) Obligation:

(31) IDependencyGraphProof (EQUIVALENT transformation)

(32) TRUE

(33) Obligation:

(34) SCCToIntTRSProof (SOUND transformation)

(35) Obligation:

(36) PolynomialOrderProcessor (EQUIVALENT transformation)

(37) YES