Termination proof of /tmp/tmpjHzI4Q/ListContentTail.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBCToGraph (⇒, 720 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToSCCProof (⇒, 0 ms)

↳4 AND

    ↳5 JBCTerminationSCC

        ↳6 SCCToIDPv1Proof (⇒, 150 ms)

        ↳7 IDP

        ↳8 IDPNonInfProof (⇒, 120 ms)

        ↳9 AND

            ↳10 IDP

                ↳11 IDependencyGraphProof (⇔, 0 ms)

                ↳12 TRUE

            ↳13 IDP

                ↳14 IDependencyGraphProof (⇔, 0 ms)

                ↳15 TRUE

    ↳16 JBCTerminationSCC

        ↳17 SCCToIDPv1Proof (⇒, 560 ms)

        ↳18 IDP

        ↳19 IDPNonInfProof (⇒, 1380 ms)

        ↳20 IDP

        ↳21 IDependencyGraphProof (⇔, 0 ms)

        ↳22 IDP

        ↳23 IDPNonInfProof (⇒, 580 ms)

        ↳24 IDP

        ↳25 IDPNonInfProof (⇒, 190 ms)

        ↳26 IDP

        ↳27 IDependencyGraphProof (⇔, 0 ms)

        ↳28 TRUE

    ↳29 JBCTerminationSCC

        ↳30 SCCToIDPv1Proof (⇒, 150 ms)

        ↳31 IDP

        ↳32 IDPNonInfProof (⇒, 130 ms)

        ↳33 AND

            ↳34 IDP

                ↳35 IDependencyGraphProof (⇔, 0 ms)

                ↳36 TRUE

            ↳37 IDP

                ↳38 IDependencyGraphProof (⇔, 0 ms)

                ↳39 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: ListContentTail

public class ListContentTail{

  public static void main(String[] args) {
    Random.args = args;
    IntList l = IntList.createIntList();

    int m = IntList.nth(Random.random(),l);

    while (m > 0) {

      l = l.next;
      m = IntList.nth(Random.random(),l);
    }
  }
}

class IntList {
  int value;
  IntList next;

  public IntList(int value, IntList next) {
    this.value = value;
    this.next = next;
  }

  public static IntList createIntList() {

    int i = Random.random();
    IntList l = null;

    while (i > 0) {
      l = new IntList(Random.random(), l);
      i--;
    }

    return l;
  }

  public static int nth(int n, IntList l){

    while (n > 1 && l != null) {
      n--;
      l = l.next;
    }

    if (l == null) return 0;
    else           return l.value;
  }





}






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

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}

(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
ListContentTail.main([Ljava/lang/String;)V: Graph of 311 nodes with 2 SCCs.

IntList.createIntList()LIntList;: Graph of 163 nodes with 1 SCC.

(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 3 SCCss.

(4) Complex Obligation (AND)

(5) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: IntList.createIntList()LIntList;
SCC calls the following helper methods:
Performed SCC analyses: UsedFieldsAnalysis

(6) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 38 rules for P and 0 rules for R.

P rules:
1813_0_createIntList_LE(EOS(STATIC_1813), i479, i479) → 1826_0_createIntList_LE(EOS(STATIC_1826), i479, i479)
1826_0_createIntList_LE(EOS(STATIC_1826), i479, i479) → 1839_0_createIntList_New(EOS(STATIC_1839), i479) | >(i479, 0)
1839_0_createIntList_New(EOS(STATIC_1839), i479) → 1848_0_createIntList_Duplicate(EOS(STATIC_1848), i479)
1848_0_createIntList_Duplicate(EOS(STATIC_1848), i479) → 1861_0_createIntList_InvokeMethod(EOS(STATIC_1861), i479)
1861_0_createIntList_InvokeMethod(EOS(STATIC_1861), i479) → 1868_0_random_FieldAccess(EOS(STATIC_1868), i479)
1868_0_random_FieldAccess(EOS(STATIC_1868), i479) → 1879_0_random_FieldAccess(EOS(STATIC_1879), i479)
1879_0_random_FieldAccess(EOS(STATIC_1879), i479) → 1883_0_random_ArrayAccess(EOS(STATIC_1883), i479)
1883_0_random_ArrayAccess(EOS(STATIC_1883), i479) → 1890_0_random_ArrayAccess(EOS(STATIC_1890), i479)
1890_0_random_ArrayAccess(EOS(STATIC_1890), i479) → 1898_0_random_Store(EOS(STATIC_1898), i479, o764)
1898_0_random_Store(EOS(STATIC_1898), i479, o764) → 1906_0_random_FieldAccess(EOS(STATIC_1906), i479, o764)
1906_0_random_FieldAccess(EOS(STATIC_1906), i479, o764) → 1915_0_random_ConstantStackPush(EOS(STATIC_1915), i479, o764)
1915_0_random_ConstantStackPush(EOS(STATIC_1915), i479, o764) → 1927_0_random_IntArithmetic(EOS(STATIC_1927), i479, o764)
1927_0_random_IntArithmetic(EOS(STATIC_1927), i479, o764) → 1937_0_random_FieldAccess(EOS(STATIC_1937), i479, o764)
1937_0_random_FieldAccess(EOS(STATIC_1937), i479, o764) → 1948_0_random_Load(EOS(STATIC_1948), i479, o764)
1948_0_random_Load(EOS(STATIC_1948), i479, o764) → 1962_0_random_InvokeMethod(EOS(STATIC_1962), i479, o764)
1962_0_random_InvokeMethod(EOS(STATIC_1962), i479, java.lang.Object(o811sub)) → 1971_0_random_InvokeMethod(EOS(STATIC_1971), i479, java.lang.Object(o811sub))
1971_0_random_InvokeMethod(EOS(STATIC_1971), i479, java.lang.Object(o811sub)) → 1986_0_length_Load(EOS(STATIC_1986), i479, java.lang.Object(o811sub), java.lang.Object(o811sub))
1986_0_length_Load(EOS(STATIC_1986), i479, java.lang.Object(o811sub), java.lang.Object(o811sub)) → 2000_0_length_FieldAccess(EOS(STATIC_2000), i479, java.lang.Object(o811sub), java.lang.Object(o811sub))
2000_0_length_FieldAccess(EOS(STATIC_2000), i479, java.lang.Object(java.lang.String(o829sub, i546)), java.lang.Object(java.lang.String(o829sub, i546))) → 2005_0_length_FieldAccess(EOS(STATIC_2005), i479, java.lang.Object(java.lang.String(o829sub, i546)), java.lang.Object(java.lang.String(o829sub, i546))) | &&(>=(i546, 0), >=(i547, 0))
2005_0_length_FieldAccess(EOS(STATIC_2005), i479, java.lang.Object(java.lang.String(o829sub, i546)), java.lang.Object(java.lang.String(o829sub, i546))) → 2013_0_length_Return(EOS(STATIC_2013), i479, java.lang.Object(java.lang.String(o829sub, i546)))
2013_0_length_Return(EOS(STATIC_2013), i479, java.lang.Object(java.lang.String(o829sub, i546))) → 2021_0_random_Return(EOS(STATIC_2021), i479)
2021_0_random_Return(EOS(STATIC_2021), i479) → 2026_0_createIntList_Load(EOS(STATIC_2026), i479)
2026_0_createIntList_Load(EOS(STATIC_2026), i479) → 2034_0_createIntList_InvokeMethod(EOS(STATIC_2034), i479)
2034_0_createIntList_InvokeMethod(EOS(STATIC_2034), i479) → 2042_0_<init>_Load(EOS(STATIC_2042), i479)
2042_0_<init>_Load(EOS(STATIC_2042), i479) → 2053_0_<init>_InvokeMethod(EOS(STATIC_2053), i479)
2053_0_<init>_InvokeMethod(EOS(STATIC_2053), i479) → 2062_0_<init>_Load(EOS(STATIC_2062), i479)
2062_0_<init>_Load(EOS(STATIC_2062), i479) → 2069_0_<init>_Load(EOS(STATIC_2069), i479)
2069_0_<init>_Load(EOS(STATIC_2069), i479) → 2077_0_<init>_FieldAccess(EOS(STATIC_2077), i479)
2077_0_<init>_FieldAccess(EOS(STATIC_2077), i479) → 2085_0_<init>_Load(EOS(STATIC_2085), i479)
2085_0_<init>_Load(EOS(STATIC_2085), i479) → 2095_0_<init>_Load(EOS(STATIC_2095), i479)
2095_0_<init>_Load(EOS(STATIC_2095), i479) → 2103_0_<init>_FieldAccess(EOS(STATIC_2103), i479)
2103_0_<init>_FieldAccess(EOS(STATIC_2103), i479) → 2111_0_<init>_Return(EOS(STATIC_2111), i479)
2111_0_<init>_Return(EOS(STATIC_2111), i479) → 2121_0_createIntList_Store(EOS(STATIC_2121), i479)
2121_0_createIntList_Store(EOS(STATIC_2121), i479) → 2135_0_createIntList_Inc(EOS(STATIC_2135), i479)
2135_0_createIntList_Inc(EOS(STATIC_2135), i479) → 2146_0_createIntList_JMP(EOS(STATIC_2146), +(i479, -1)) | >(i479, 0)
2146_0_createIntList_JMP(EOS(STATIC_2146), i593) → 2161_0_createIntList_Load(EOS(STATIC_2161), i593)
2161_0_createIntList_Load(EOS(STATIC_2161), i593) → 1799_0_createIntList_Load(EOS(STATIC_1799), i593)
1799_0_createIntList_Load(EOS(STATIC_1799), i472) → 1813_0_createIntList_LE(EOS(STATIC_1813), i472, i472)
R rules:

Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.

P rules:
1813_0_createIntList_LE(EOS(STATIC_1813), x0, x0) → 1813_0_createIntList_LE(EOS(STATIC_1813), +(x0, -1), +(x0, -1)) | >(x0, 0)
R rules:

Filtered ground terms:

1813_0_createIntList_LE(x1, x2, x3) → 1813_0_createIntList_LE(x2, x3)
EOS(x1) → EOS
Cond_1813_0_createIntList_LE(x1, x2, x3, x4) → Cond_1813_0_createIntList_LE(x1, x3, x4)

Filtered duplicate args:

1813_0_createIntList_LE(x1, x2) → 1813_0_createIntList_LE(x2)
Cond_1813_0_createIntList_LE(x1, x2, x3) → Cond_1813_0_createIntList_LE(x1, x3)

Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.

P rules:
1813_0_createIntList_LE(x0) → 1813_0_createIntList_LE(+(x0, -1)) | >(x0, 0)
R rules:

Finished conversion. Obtained 2 rules for P and 0 rules for R. System has predefined symbols.

P rules:
1813_0_CREATEINTLIST_LE(x0) → COND_1813_0_CREATEINTLIST_LE(>(x0, 0), x0)
COND_1813_0_CREATEINTLIST_LE(TRUE, x0) → 1813_0_CREATEINTLIST_LE(+(x0, -1))
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:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 1813_0_CREATEINTLIST_LE(x0[0]) → COND_1813_0_CREATEINTLIST_LE(x0[0] > 0, x0[0])
(1): COND_1813_0_CREATEINTLIST_LE(TRUE, x0[1]) → 1813_0_CREATEINTLIST_LE(x0[1] + -1)

(0) -> (1), if (x0[0] > 0 ∧x0[0] →^* x0[1])

(1) -> (0), if (x0[1] + -1 →^* x0[0])

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.IdpCand1ShapeHeuristic@1c29b5a1 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 1813_0_CREATEINTLIST_LE(x0) → COND_1813_0_CREATEINTLIST_LE(>(x0, 0), x0) the following chains were created:

We consider the chain 1813_0_CREATEINTLIST_LE(x0[0]) → COND_1813_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0]), COND_1813_0_CREATEINTLIST_LE(TRUE, x0[1]) → 1813_0_CREATEINTLIST_LE(+(x0[1], -1)) which results in the following constraint:
(1)    (>(x0[0], 0)=TRUE∧x0[0]=x0[1] ⇒ 1813_0_CREATEINTLIST_LE(x0[0])≥NonInfC∧1813_0_CREATEINTLIST_LE(x0[0])≥COND_1813_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])∧(U^Increasing(COND_1813_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥))

We simplified constraint (1) using rule (IV) which results in the following new constraint:
(2)    (>(x0[0], 0)=TRUE ⇒ 1813_0_CREATEINTLIST_LE(x0[0])≥NonInfC∧1813_0_CREATEINTLIST_LE(x0[0])≥COND_1813_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])∧(U^Increasing(COND_1813_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1813_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1813_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1813_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x0[0] ≥ 0 ⇒ (U^Increasing(COND_1813_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8 + (2)bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

For Pair COND_1813_0_CREATEINTLIST_LE(TRUE, x0) → 1813_0_CREATEINTLIST_LE(+(x0, -1)) the following chains were created:

We consider the chain COND_1813_0_CREATEINTLIST_LE(TRUE, x0[1]) → 1813_0_CREATEINTLIST_LE(+(x0[1], -1)) which results in the following constraint:
(7)    (COND_1813_0_CREATEINTLIST_LE(TRUE, x0[1])≥NonInfC∧COND_1813_0_CREATEINTLIST_LE(TRUE, x0[1])≥1813_0_CREATEINTLIST_LE(+(x0[1], -1))∧(U^Increasing(1813_0_CREATEINTLIST_LE(+(x0[1], -1))), ≥))

We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(8)    ((U^Increasing(1813_0_CREATEINTLIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(9)    ((U^Increasing(1813_0_CREATEINTLIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(10)    ((U^Increasing(1813_0_CREATEINTLIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

We simplified constraint (10) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(11)    ((U^Increasing(1813_0_CREATEINTLIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧0 = 0∧[2 + (-1)bso_11] ≥ 0)

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

1813_0_CREATEINTLIST_LE(x0) → COND_1813_0_CREATEINTLIST_LE(>(x0, 0), x0)
- (x0[0] ≥ 0 ⇒ (U^Increasing(COND_1813_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8 + (2)bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)
COND_1813_0_CREATEINTLIST_LE(TRUE, x0) → 1813_0_CREATEINTLIST_LE(+(x0, -1))
- ((U^Increasing(1813_0_CREATEINTLIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧0 = 0∧[2 + (-1)bso_11] ≥ 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(1813_0_CREATEINTLIST_LE(x₁)) = [2]x₁
POL(COND_1813_0_CREATEINTLIST_LE(x₁, x₂)) = [2]x₂
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(+(x₁, x₂)) = x₁ + x₂
POL(-1) = [-1]

The following pairs are in P_>:

COND_1813_0_CREATEINTLIST_LE(TRUE, x0[1]) → 1813_0_CREATEINTLIST_LE(+(x0[1], -1))

The following pairs are in P_bound:

1813_0_CREATEINTLIST_LE(x0[0]) → COND_1813_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])

The following pairs are in P_≥:

1813_0_CREATEINTLIST_LE(x0[0]) → COND_1813_0_CREATEINTLIST_LE(>(x0[0], 0), x0[0])

There are no usable rules.

(9) Complex Obligation (AND)

(10) 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

R is empty.

The integer pair graph contains the following rules and edges:
(0): 1813_0_CREATEINTLIST_LE(x0[0]) → COND_1813_0_CREATEINTLIST_LE(x0[0] > 0, x0[0])

The set Q is empty.

(11) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(12) TRUE

(13) 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

R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_1813_0_CREATEINTLIST_LE(TRUE, x0[1]) → 1813_0_CREATEINTLIST_LE(x0[1] + -1)

The set Q is empty.

(14) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(15) TRUE

(16) Obligation:

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

(17) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 80 rules for P and 0 rules for R.

P rules:
1975_0_main_LE(EOS(STATIC_1975), o740, i530) → 1992_0_main_LE(EOS(STATIC_1992), o740, i530)
1992_0_main_LE(EOS(STATIC_1992), o740, i530) → 1998_0_main_Load(EOS(STATIC_1998), o740) | >(i530, 0)
1998_0_main_Load(EOS(STATIC_1998), o740) → 2004_0_main_FieldAccess(EOS(STATIC_2004), o740)
2004_0_main_FieldAccess(EOS(STATIC_2004), java.lang.Object(o833sub)) → 2010_0_main_FieldAccess(EOS(STATIC_2010), java.lang.Object(o833sub))
2010_0_main_FieldAccess(EOS(STATIC_2010), java.lang.Object(IntList(EOC, o836, i552))) → 2017_0_main_FieldAccess(EOS(STATIC_2017), java.lang.Object(IntList(EOC, o836, i552)))
2017_0_main_FieldAccess(EOS(STATIC_2017), java.lang.Object(IntList(EOC, o836, i552))) → 2023_0_main_Store(EOS(STATIC_2023), o836)
2023_0_main_Store(EOS(STATIC_2023), o836) → 2032_0_main_InvokeMethod(EOS(STATIC_2032), o836)
2032_0_main_InvokeMethod(EOS(STATIC_2032), o836) → 2039_0_random_FieldAccess(EOS(STATIC_2039), o836)
2039_0_random_FieldAccess(EOS(STATIC_2039), o836) → 2052_0_random_FieldAccess(EOS(STATIC_2052), o836)
2052_0_random_FieldAccess(EOS(STATIC_2052), o836) → 2059_0_random_ArrayAccess(EOS(STATIC_2059), o836)
2059_0_random_ArrayAccess(EOS(STATIC_2059), o836) → 2065_0_random_ArrayAccess(EOS(STATIC_2065), o836)
2065_0_random_ArrayAccess(EOS(STATIC_2065), o836) → 2075_0_random_Store(EOS(STATIC_2075), o836, o870)
2075_0_random_Store(EOS(STATIC_2075), o836, o870) → 2081_0_random_FieldAccess(EOS(STATIC_2081), o836, o870)
2081_0_random_FieldAccess(EOS(STATIC_2081), o836, o870) → 2090_0_random_ConstantStackPush(EOS(STATIC_2090), o836, o870)
2090_0_random_ConstantStackPush(EOS(STATIC_2090), o836, o870) → 2100_0_random_IntArithmetic(EOS(STATIC_2100), o836, o870)
2100_0_random_IntArithmetic(EOS(STATIC_2100), o836, o870) → 2108_0_random_FieldAccess(EOS(STATIC_2108), o836, o870)
2108_0_random_FieldAccess(EOS(STATIC_2108), o836, o870) → 2115_0_random_Load(EOS(STATIC_2115), o836, o870)
2115_0_random_Load(EOS(STATIC_2115), o836, o870) → 2130_0_random_InvokeMethod(EOS(STATIC_2130), o836, o870)
2130_0_random_InvokeMethod(EOS(STATIC_2130), o836, java.lang.Object(o933sub)) → 2141_0_random_InvokeMethod(EOS(STATIC_2141), o836, java.lang.Object(o933sub))
2141_0_random_InvokeMethod(EOS(STATIC_2141), o836, java.lang.Object(o933sub)) → 2152_0_length_Load(EOS(STATIC_2152), o836, java.lang.Object(o933sub), java.lang.Object(o933sub))
2152_0_length_Load(EOS(STATIC_2152), o836, java.lang.Object(o933sub), java.lang.Object(o933sub)) → 2180_0_length_FieldAccess(EOS(STATIC_2180), o836, java.lang.Object(o933sub), java.lang.Object(o933sub))
2180_0_length_FieldAccess(EOS(STATIC_2180), o836, java.lang.Object(java.lang.String(o970sub, i616)), java.lang.Object(java.lang.String(o970sub, i616))) → 2189_0_length_FieldAccess(EOS(STATIC_2189), o836, java.lang.Object(java.lang.String(o970sub, i616)), java.lang.Object(java.lang.String(o970sub, i616))) | &&(>=(i616, 0), >=(i617, 0))
2189_0_length_FieldAccess(EOS(STATIC_2189), o836, java.lang.Object(java.lang.String(o970sub, i616)), java.lang.Object(java.lang.String(o970sub, i616))) → 2200_0_length_Return(EOS(STATIC_2200), o836, java.lang.Object(java.lang.String(o970sub, i616)), i616)
2200_0_length_Return(EOS(STATIC_2200), o836, java.lang.Object(java.lang.String(o970sub, i616)), i616) → 2209_0_random_Return(EOS(STATIC_2209), o836, i616)
2209_0_random_Return(EOS(STATIC_2209), o836, i616) → 2215_0_main_Load(EOS(STATIC_2215), o836, i616)
2215_0_main_Load(EOS(STATIC_2215), o836, i616) → 2232_0_main_InvokeMethod(EOS(STATIC_2232), o836, i616, o836)
2232_0_main_InvokeMethod(EOS(STATIC_2232), o836, i616, o836) → 2243_0_nth_Load(EOS(STATIC_2243), o836, i616, o836, i616, o836)
2243_0_nth_Load(EOS(STATIC_2243), o836, i616, o836, i616, o836) → 2395_0_nth_Load(EOS(STATIC_2395), o836, i616, o836, i616, o836)
2395_0_nth_Load(EOS(STATIC_2395), o1162, i662, o1162, i661, o1161) → 2400_0_nth_ConstantStackPush(EOS(STATIC_2400), o1162, i662, o1162, i661, o1161, i661)
2400_0_nth_ConstantStackPush(EOS(STATIC_2400), o1162, i662, o1162, i661, o1161, i661) → 2406_0_nth_LE(EOS(STATIC_2406), o1162, i662, o1162, i661, o1161, i661, 1)
2406_0_nth_LE(EOS(STATIC_2406), o1162, i662, o1162, i673, o1161, i673, matching1) → 2410_0_nth_LE(EOS(STATIC_2410), o1162, i662, o1162, i673, o1161, i673, 1) | =(matching1, 1)
2406_0_nth_LE(EOS(STATIC_2406), o1162, i662, o1162, i674, o1161, i674, matching1) → 2411_0_nth_LE(EOS(STATIC_2411), o1162, i662, o1162, i674, o1161, i674, 1) | =(matching1, 1)
2410_0_nth_LE(EOS(STATIC_2410), o1162, i662, o1162, i673, o1161, i673, matching1) → 2415_0_nth_Load(EOS(STATIC_2415), o1162, i662, o1162, o1161) | &&(<=(i673, 1), =(matching1, 1))
2415_0_nth_Load(EOS(STATIC_2415), o1162, i662, o1162, o1161) → 2420_0_nth_NONNULL(EOS(STATIC_2420), o1162, i662, o1162, o1161, o1161)
2420_0_nth_NONNULL(EOS(STATIC_2420), o1162, i662, o1162, java.lang.Object(o1199sub), java.lang.Object(o1199sub)) → 2425_0_nth_NONNULL(EOS(STATIC_2425), o1162, i662, o1162, java.lang.Object(o1199sub), java.lang.Object(o1199sub))
2420_0_nth_NONNULL(EOS(STATIC_2420), o1162, i662, o1162, NULL, NULL) → 2426_0_nth_NONNULL(EOS(STATIC_2426), o1162, i662, o1162, NULL, NULL)
2425_0_nth_NONNULL(EOS(STATIC_2425), o1162, i662, o1162, java.lang.Object(o1199sub), java.lang.Object(o1199sub)) → 2431_0_nth_Load(EOS(STATIC_2431), o1162, i662, o1162, java.lang.Object(o1199sub))
2431_0_nth_Load(EOS(STATIC_2431), o1162, i662, o1162, java.lang.Object(o1199sub)) → 2441_0_nth_FieldAccess(EOS(STATIC_2441), o1162, i662, o1162, java.lang.Object(o1199sub))
2441_0_nth_FieldAccess(EOS(STATIC_2441), o1162, i662, o1162, java.lang.Object(o1199sub)) → 2448_0_nth_FieldAccess(EOS(STATIC_2448), o1162, i662, o1162, java.lang.Object(o1199sub))
2441_0_nth_FieldAccess(EOS(STATIC_2441), java.lang.Object(o1199sub), i662, java.lang.Object(o1199sub), java.lang.Object(o1199sub)) → 2449_0_nth_FieldAccess(EOS(STATIC_2449), java.lang.Object(o1199sub), i662, java.lang.Object(o1199sub), java.lang.Object(o1199sub))
2448_0_nth_FieldAccess(EOS(STATIC_2448), o1162, i662, o1162, java.lang.Object(IntList(EOC, o1226, i686))) → 2459_0_nth_FieldAccess(EOS(STATIC_2459), o1162, i662, o1162, java.lang.Object(IntList(EOC, o1226, i686)))
2459_0_nth_FieldAccess(EOS(STATIC_2459), o1162, i662, o1162, java.lang.Object(IntList(EOC, o1226, i686))) → 2467_0_nth_Return(EOS(STATIC_2467), o1162, i662, o1162, i686)
2467_0_nth_Return(EOS(STATIC_2467), o1162, i662, o1162, i686) → 2477_0_main_Store(EOS(STATIC_2477), o1162, i686)
2477_0_main_Store(EOS(STATIC_2477), o1162, i686) → 2485_0_main_JMP(EOS(STATIC_2485), o1162, i686)
2485_0_main_JMP(EOS(STATIC_2485), o1162, i686) → 2494_0_main_Load(EOS(STATIC_2494), o1162, i686)
2494_0_main_Load(EOS(STATIC_2494), o1162, i686) → 1965_0_main_Load(EOS(STATIC_1965), o1162, i686)
1965_0_main_Load(EOS(STATIC_1965), o740, i501) → 1975_0_main_LE(EOS(STATIC_1975), o740, i501)
2449_0_nth_FieldAccess(EOS(STATIC_2449), java.lang.Object(IntList(EOC, o1228, i687)), i662, java.lang.Object(IntList(EOC, o1228, i687)), java.lang.Object(IntList(EOC, o1228, i687))) → 2460_0_nth_FieldAccess(EOS(STATIC_2460), java.lang.Object(IntList(EOC, o1228, i687)), i662, java.lang.Object(IntList(EOC, o1228, i687)), java.lang.Object(IntList(EOC, o1228, i687)))
2460_0_nth_FieldAccess(EOS(STATIC_2460), java.lang.Object(IntList(EOC, o1228, i687)), i662, java.lang.Object(IntList(EOC, o1228, i687)), java.lang.Object(IntList(EOC, o1228, i687))) → 2470_0_nth_Return(EOS(STATIC_2470), java.lang.Object(IntList(EOC, o1228, i687)), i662, java.lang.Object(IntList(EOC, o1228, i687)), i687)
2470_0_nth_Return(EOS(STATIC_2470), java.lang.Object(IntList(EOC, o1228, i687)), i662, java.lang.Object(IntList(EOC, o1228, i687)), i687) → 2479_0_main_Store(EOS(STATIC_2479), java.lang.Object(IntList(EOC, o1228, i687)), i687)
2479_0_main_Store(EOS(STATIC_2479), java.lang.Object(IntList(EOC, o1228, i687)), i687) → 2487_0_main_JMP(EOS(STATIC_2487), java.lang.Object(IntList(EOC, o1228, i687)), i687)
2487_0_main_JMP(EOS(STATIC_2487), java.lang.Object(IntList(EOC, o1228, i687)), i687) → 2496_0_main_Load(EOS(STATIC_2496), java.lang.Object(IntList(EOC, o1228, i687)), i687)
2496_0_main_Load(EOS(STATIC_2496), java.lang.Object(IntList(EOC, o1228, i687)), i687) → 1965_0_main_Load(EOS(STATIC_1965), java.lang.Object(IntList(EOC, o1228, i687)), i687)
2426_0_nth_NONNULL(EOS(STATIC_2426), o1162, i662, o1162, NULL, NULL) → 2433_0_nth_ConstantStackPush(EOS(STATIC_2433), o1162, i662, o1162, NULL)
2433_0_nth_ConstantStackPush(EOS(STATIC_2433), o1162, i662, o1162, NULL) → 2457_0_nth_ConstantStackPush(EOS(STATIC_2457), o1162, i662, o1162, NULL)
2457_0_nth_ConstantStackPush(EOS(STATIC_2457), o1162, i662, o1162, NULL) → 2465_0_nth_Return(EOS(STATIC_2465), o1162, i662, o1162, NULL, 0)
2465_0_nth_Return(EOS(STATIC_2465), o1162, i662, o1162, NULL, matching1) → 2475_0_main_Store(EOS(STATIC_2475), o1162, 0) | =(matching1, 0)
2475_0_main_Store(EOS(STATIC_2475), o1162, matching1) → 2477_0_main_Store(EOS(STATIC_2477), o1162, 0) | =(matching1, 0)
2411_0_nth_LE(EOS(STATIC_2411), o1162, i662, o1162, i674, o1161, i674, matching1) → 2416_0_nth_Load(EOS(STATIC_2416), o1162, i662, o1162, i674, o1161) | &&(>(i674, 1), =(matching1, 1))
2416_0_nth_Load(EOS(STATIC_2416), o1162, i662, o1162, i674, o1161) → 2423_0_nth_NULL(EOS(STATIC_2423), o1162, i662, o1162, i674, o1161, o1161)
2423_0_nth_NULL(EOS(STATIC_2423), o1162, i662, o1162, i674, java.lang.Object(o1200sub), java.lang.Object(o1200sub)) → 2428_0_nth_NULL(EOS(STATIC_2428), o1162, i662, o1162, i674, java.lang.Object(o1200sub), java.lang.Object(o1200sub))
2423_0_nth_NULL(EOS(STATIC_2423), o1162, i662, o1162, i674, NULL, NULL) → 2429_0_nth_NULL(EOS(STATIC_2429), o1162, i662, o1162, i674, NULL, NULL)
2428_0_nth_NULL(EOS(STATIC_2428), o1162, i662, o1162, i674, java.lang.Object(o1200sub), java.lang.Object(o1200sub)) → 2435_0_nth_Inc(EOS(STATIC_2435), o1162, i662, o1162, i674, java.lang.Object(o1200sub))
2435_0_nth_Inc(EOS(STATIC_2435), o1162, i662, o1162, i674, java.lang.Object(o1200sub)) → 2444_0_nth_Load(EOS(STATIC_2444), o1162, i662, o1162, +(i674, -1), java.lang.Object(o1200sub)) | >(i674, 0)
2444_0_nth_Load(EOS(STATIC_2444), o1162, i662, o1162, i682, java.lang.Object(o1200sub)) → 2454_0_nth_FieldAccess(EOS(STATIC_2454), o1162, i662, o1162, i682, java.lang.Object(o1200sub))
2454_0_nth_FieldAccess(EOS(STATIC_2454), o1162, i662, o1162, i682, java.lang.Object(o1200sub)) → 2462_0_nth_FieldAccess(EOS(STATIC_2462), o1162, i662, o1162, i682, java.lang.Object(o1200sub))
2454_0_nth_FieldAccess(EOS(STATIC_2454), java.lang.Object(o1200sub), i662, java.lang.Object(o1200sub), i682, java.lang.Object(o1200sub)) → 2464_0_nth_FieldAccess(EOS(STATIC_2464), java.lang.Object(o1200sub), i662, java.lang.Object(o1200sub), i682, java.lang.Object(o1200sub))
2462_0_nth_FieldAccess(EOS(STATIC_2462), o1162, i662, o1162, i682, java.lang.Object(IntList(EOC, o1239, i689))) → 2472_0_nth_FieldAccess(EOS(STATIC_2472), o1162, i662, o1162, i682, java.lang.Object(IntList(EOC, o1239, i689)))
2472_0_nth_FieldAccess(EOS(STATIC_2472), o1162, i662, o1162, i682, java.lang.Object(IntList(EOC, o1239, i689))) → 2481_0_nth_Store(EOS(STATIC_2481), o1162, i662, o1162, i682, o1239)
2481_0_nth_Store(EOS(STATIC_2481), o1162, i662, o1162, i682, o1239) → 2489_0_nth_JMP(EOS(STATIC_2489), o1162, i662, o1162, i682, o1239)
2489_0_nth_JMP(EOS(STATIC_2489), o1162, i662, o1162, i682, o1239) → 2499_0_nth_Load(EOS(STATIC_2499), o1162, i662, o1162, i682, o1239)
2499_0_nth_Load(EOS(STATIC_2499), o1162, i662, o1162, i682, o1239) → 2395_0_nth_Load(EOS(STATIC_2395), o1162, i662, o1162, i682, o1239)
2464_0_nth_FieldAccess(EOS(STATIC_2464), java.lang.Object(IntList(EOC, o1241, i690)), i662, java.lang.Object(IntList(EOC, o1241, i690)), i682, java.lang.Object(IntList(EOC, o1241, i690))) → 2473_0_nth_FieldAccess(EOS(STATIC_2473), java.lang.Object(IntList(EOC, o1241, i690)), i662, java.lang.Object(IntList(EOC, o1241, i690)), i682, java.lang.Object(IntList(EOC, o1241, i690)))
2473_0_nth_FieldAccess(EOS(STATIC_2473), java.lang.Object(IntList(EOC, o1241, i690)), i662, java.lang.Object(IntList(EOC, o1241, i690)), i682, java.lang.Object(IntList(EOC, o1241, i690))) → 2483_0_nth_Store(EOS(STATIC_2483), java.lang.Object(IntList(EOC, o1241, i690)), i662, java.lang.Object(IntList(EOC, o1241, i690)), i682, o1241)
2483_0_nth_Store(EOS(STATIC_2483), java.lang.Object(IntList(EOC, o1241, i690)), i662, java.lang.Object(IntList(EOC, o1241, i690)), i682, o1241) → 2492_0_nth_JMP(EOS(STATIC_2492), java.lang.Object(IntList(EOC, o1241, i690)), i662, java.lang.Object(IntList(EOC, o1241, i690)), i682, o1241)
2492_0_nth_JMP(EOS(STATIC_2492), java.lang.Object(IntList(EOC, o1241, i690)), i662, java.lang.Object(IntList(EOC, o1241, i690)), i682, o1241) → 2502_0_nth_Load(EOS(STATIC_2502), java.lang.Object(IntList(EOC, o1241, i690)), i662, java.lang.Object(IntList(EOC, o1241, i690)), i682, o1241)
2502_0_nth_Load(EOS(STATIC_2502), java.lang.Object(IntList(EOC, o1241, i690)), i662, java.lang.Object(IntList(EOC, o1241, i690)), i682, o1241) → 2395_0_nth_Load(EOS(STATIC_2395), java.lang.Object(IntList(EOC, o1241, i690)), i662, java.lang.Object(IntList(EOC, o1241, i690)), i682, o1241)
2429_0_nth_NULL(EOS(STATIC_2429), o1162, i662, o1162, i674, NULL, NULL) → 2437_0_nth_Load(EOS(STATIC_2437), o1162, i662, o1162, NULL)
2437_0_nth_Load(EOS(STATIC_2437), o1162, i662, o1162, NULL) → 2446_0_nth_NONNULL(EOS(STATIC_2446), o1162, i662, o1162, NULL, NULL)
2446_0_nth_NONNULL(EOS(STATIC_2446), o1162, i662, o1162, NULL, NULL) → 2457_0_nth_ConstantStackPush(EOS(STATIC_2457), o1162, i662, o1162, NULL)
R rules:

Combined rules. Obtained 5 conditional rules for P and 0 conditional rules for R.

P rules:
2406_0_nth_LE(EOS(STATIC_2406), java.lang.Object(IntList(EOC, x0, x1)), x2, java.lang.Object(IntList(EOC, x0, x1)), x3, java.lang.Object(IntList(EOC, x4, x5)), x3, 1) → 2406_0_nth_LE(EOS(STATIC_2406), x0, x7, x0, x7, x0, x7, 1) | &&(&&(>(+(x7, 1), 0), >(x5, 0)), <=(x3, 1))
2406_0_nth_LE(EOS(STATIC_2406), java.lang.Object(IntList(EOC, x0, x1)), x2, java.lang.Object(IntList(EOC, x0, x1)), x3, java.lang.Object(IntList(EOC, x0, x1)), x3, 1) → 2406_0_nth_LE(EOS(STATIC_2406), x0, x5, x0, x5, x0, x5, 1) | &&(&&(>(+(x5, 1), 0), <=(x3, 1)), >(x1, 0))
2406_0_nth_LE(EOS(STATIC_2406), java.lang.Object(IntList(EOC, x0, x1)), x2, java.lang.Object(IntList(EOC, x0, x1)), x3, NULL, x3, x4) → 2406_0_nth_LE(EOS(STATIC_2406), x0, x5, x0, x5, x0, x5, 1) | FALSE
2406_0_nth_LE(EOS(STATIC_2406), x0, x1, x0, x2, java.lang.Object(IntList(EOC, x3, x4)), x2, 1) → 2406_0_nth_LE(EOS(STATIC_2406), x0, x1, x0, +(x2, -1), x3, +(x2, -1), 1) | >(x2, 1)
2406_0_nth_LE(EOS(STATIC_2406), java.lang.Object(IntList(EOC, x0, x1)), x2, java.lang.Object(IntList(EOC, x0, x1)), x3, java.lang.Object(IntList(EOC, x0, x1)), x3, 1) → 2406_0_nth_LE(EOS(STATIC_2406), java.lang.Object(IntList(EOC, x0, x1)), x2, java.lang.Object(IntList(EOC, x0, x1)), +(x3, -1), x0, +(x3, -1), 1) | >(x3, 1)
R rules:

Filtered ground terms:

2406_0_nth_LE(x1, x2, x3, x4, x5, x6, x7, x8) → 2406_0_nth_LE(x2, x3, x4, x5, x6, x7)
IntList(x1, x2, x3) → IntList(x2, x3)
EOS(x1) → EOS
Cond_2406_0_nth_LE3(x1, x2, x3, x4, x5, x6, x7, x8, x9) → Cond_2406_0_nth_LE3(x1, x3, x4, x5, x6, x7, x8)
Cond_2406_0_nth_LE2(x1, x2, x3, x4, x5, x6, x7, x8, x9) → Cond_2406_0_nth_LE2(x1, x3, x4, x5, x6, x7, x8)
Cond_2406_0_nth_LE1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) → Cond_2406_0_nth_LE1(x1, x3, x4, x5, x6, x7, x8, x10)
Cond_2406_0_nth_LE(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10) → Cond_2406_0_nth_LE(x1, x3, x4, x5, x6, x7, x8, x10)

Filtered duplicate args:

2406_0_nth_LE(x1, x2, x3, x4, x5, x6) → 2406_0_nth_LE(x2, x3, x5, x6)
Cond_2406_0_nth_LE(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_2406_0_nth_LE(x1, x3, x4, x6, x7, x8)
Cond_2406_0_nth_LE1(x1, x2, x3, x4, x5, x6, x7, x8) → Cond_2406_0_nth_LE1(x1, x3, x6, x7, x8)
Cond_2406_0_nth_LE2(x1, x2, x3, x4, x5, x6, x7) → Cond_2406_0_nth_LE2(x1, x3, x4, x6, x7)
Cond_2406_0_nth_LE3(x1, x2, x3, x4, x5, x6, x7) → Cond_2406_0_nth_LE3(x1, x3, x6, x7)

Filtered unneeded arguments:

2406_0_nth_LE(x1, x2, x3, x4) → 2406_0_nth_LE(x2, x3, x4)
Cond_2406_0_nth_LE(x1, x2, x3, x4, x5, x6) → Cond_2406_0_nth_LE(x1, x3, x6)
Cond_2406_0_nth_LE1(x1, x2, x3, x4, x5) → Cond_2406_0_nth_LE1(x1, x3, x5)
Cond_2406_0_nth_LE2(x1, x2, x3, x4, x5) → Cond_2406_0_nth_LE2(x1, x3, x4, x5)
Cond_2406_0_nth_LE3(x1, x2, x3, x4) → Cond_2406_0_nth_LE3(x1, x3, x4)

Combined rules. Obtained 4 conditional rules for P and 0 conditional rules for R.

P rules:
2406_0_nth_LE(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x4, x5)), x3) → 2406_0_nth_LE(x0, x0, x7) | &&(&&(>(x7, -1), >(x5, 0)), <=(x3, 1))
2406_0_nth_LE(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3) → 2406_0_nth_LE(x0, x0, x5) | &&(&&(>(x5, -1), <=(x3, 1)), >(x1, 0))
2406_0_nth_LE(x0, java.lang.Object(IntList(x3, x4)), x2) → 2406_0_nth_LE(x0, x3, +(x2, -1)) | >(x2, 1)
2406_0_nth_LE(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3) → 2406_0_nth_LE(java.lang.Object(IntList(x0, x1)), x0, +(x3, -1)) | >(x3, 1)
R rules:

Finished conversion. Obtained 8 rules for P and 0 rules for R. System has predefined symbols.

P rules:
2406_0_NTH_LE(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x4, x5)), x3) → COND_2406_0_NTH_LE(&&(&&(>(x7, -1), >(x5, 0)), <=(x3, 1)), java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x4, x5)), x3, x7)
COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x4, x5)), x3, x7) → 2406_0_NTH_LE(x0, x0, x7)
2406_0_NTH_LE(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3) → COND_2406_0_NTH_LE1(&&(&&(>(x5, -1), <=(x3, 1)), >(x1, 0)), java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3, x5)
COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3, x5) → 2406_0_NTH_LE(x0, x0, x5)
2406_0_NTH_LE(x0, java.lang.Object(IntList(x3, x4)), x2) → COND_2406_0_NTH_LE2(>(x2, 1), x0, java.lang.Object(IntList(x3, x4)), x2)
COND_2406_0_NTH_LE2(TRUE, x0, java.lang.Object(IntList(x3, x4)), x2) → 2406_0_NTH_LE(x0, x3, +(x2, -1))
2406_0_NTH_LE(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3) → COND_2406_0_NTH_LE3(>(x3, 1), java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3)
COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3) → 2406_0_NTH_LE(java.lang.Object(IntList(x0, x1)), x0, +(x3, -1))
R rules:

(18) 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): 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0]) → COND_2406_0_NTH_LE(x7[0] > -1 && x5[0] > 0 && x3[0] <= 1, java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])
(1): COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[1], x1[1])), java.lang.Object(IntList(x4[1], x5[1])), x3[1], x7[1]) → 2406_0_NTH_LE(x0[1], x0[1], x7[1])
(2): 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2]) → COND_2406_0_NTH_LE1(x5[2] > -1 && x3[2] <= 1 && x1[2] > 0, java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])
(3): COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[3], x1[3])), java.lang.Object(IntList(x0[3], x1[3])), x3[3], x5[3]) → 2406_0_NTH_LE(x0[3], x0[3], x5[3])
(4): 2406_0_NTH_LE(x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4]) → COND_2406_0_NTH_LE2(x2[4] > 1, x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])
(5): COND_2406_0_NTH_LE2(TRUE, x0[5], java.lang.Object(IntList(x3[5], x4[5])), x2[5]) → 2406_0_NTH_LE(x0[5], x3[5], x2[5] + -1)
(6): 2406_0_NTH_LE(java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6]) → COND_2406_0_NTH_LE3(x3[6] > 1, java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])
(7): COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0[7], x1[7])), java.lang.Object(IntList(x0[7], x1[7])), x3[7]) → 2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], x3[7] + -1)

(0) -> (1), if (x7[0] > -1 && x5[0] > 0 && x3[0] <= 1 ∧java.lang.Object(IntList(x0[0], x1[0])) →^* java.lang.Object(IntList(x0[1], x1[1]))∧java.lang.Object(IntList(x4[0], x5[0])) →^* java.lang.Object(IntList(x4[1], x5[1]))∧x3[0] →^* x3[1]∧x7[0] →^* x7[1])

(1) -> (0), if (x0[1] →^* java.lang.Object(IntList(x0[0], x1[0]))∧x0[1] →^* java.lang.Object(IntList(x4[0], x5[0]))∧x7[1] →^* x3[0])

(1) -> (2), if (x0[1] →^* java.lang.Object(IntList(x0[2], x1[2]))∧x7[1] →^* x3[2])

(1) -> (4), if (x0[1] →^* x0[4]∧x0[1] →^* java.lang.Object(IntList(x3[4], x4[4]))∧x7[1] →^* x2[4])

(1) -> (6), if (x0[1] →^* java.lang.Object(IntList(x0[6], x1[6]))∧x7[1] →^* x3[6])

(2) -> (3), if (x5[2] > -1 && x3[2] <= 1 && x1[2] > 0 ∧java.lang.Object(IntList(x0[2], x1[2])) →^* java.lang.Object(IntList(x0[3], x1[3]))∧x3[2] →^* x3[3]∧x5[2] →^* x5[3])

(3) -> (0), if (x0[3] →^* java.lang.Object(IntList(x0[0], x1[0]))∧x0[3] →^* java.lang.Object(IntList(x4[0], x5[0]))∧x5[3] →^* x3[0])

(3) -> (2), if (x0[3] →^* java.lang.Object(IntList(x0[2], x1[2]))∧x5[3] →^* x3[2])

(3) -> (4), if (x0[3] →^* x0[4]∧x0[3] →^* java.lang.Object(IntList(x3[4], x4[4]))∧x5[3] →^* x2[4])

(3) -> (6), if (x0[3] →^* java.lang.Object(IntList(x0[6], x1[6]))∧x5[3] →^* x3[6])

(4) -> (5), if (x2[4] > 1 ∧x0[4] →^* x0[5]∧java.lang.Object(IntList(x3[4], x4[4])) →^* java.lang.Object(IntList(x3[5], x4[5]))∧x2[4] →^* x2[5])

(5) -> (0), if (x0[5] →^* java.lang.Object(IntList(x0[0], x1[0]))∧x3[5] →^* java.lang.Object(IntList(x4[0], x5[0]))∧x2[5] + -1 →^* x3[0])

(5) -> (2), if (x0[5] →^* java.lang.Object(IntList(x0[2], x1[2]))∧x3[5] →^* java.lang.Object(IntList(x0[2], x1[2]))∧x2[5] + -1 →^* x3[2])

(5) -> (4), if (x0[5] →^* x0[4]∧x3[5] →^* java.lang.Object(IntList(x3[4], x4[4]))∧x2[5] + -1 →^* x2[4])

(5) -> (6), if (x0[5] →^* java.lang.Object(IntList(x0[6], x1[6]))∧x3[5] →^* java.lang.Object(IntList(x0[6], x1[6]))∧x2[5] + -1 →^* x3[6])

(6) -> (7), if (x3[6] > 1 ∧java.lang.Object(IntList(x0[6], x1[6])) →^* java.lang.Object(IntList(x0[7], x1[7]))∧x3[6] →^* x3[7])

(7) -> (0), if (java.lang.Object(IntList(x0[7], x1[7])) →^* java.lang.Object(IntList(x0[0], x1[0]))∧x0[7] →^* java.lang.Object(IntList(x4[0], x5[0]))∧x3[7] + -1 →^* x3[0])

(7) -> (2), if (java.lang.Object(IntList(x0[7], x1[7])) →^* java.lang.Object(IntList(x0[2], x1[2]))∧x0[7] →^* java.lang.Object(IntList(x0[2], x1[2]))∧x3[7] + -1 →^* x3[2])

(7) -> (4), if (java.lang.Object(IntList(x0[7], x1[7])) →^* x0[4]∧x0[7] →^* java.lang.Object(IntList(x3[4], x4[4]))∧x3[7] + -1 →^* x2[4])

(7) -> (6), if (java.lang.Object(IntList(x0[7], x1[7])) →^* java.lang.Object(IntList(x0[6], x1[6]))∧x0[7] →^* java.lang.Object(IntList(x0[6], x1[6]))∧x3[7] + -1 →^* x3[6])

The set Q is empty.

(19) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: true Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@54639901 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 2406_0_NTH_LE(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x4, x5)), x3) → COND_2406_0_NTH_LE(&&(&&(>(x7, -1), >(x5, 0)), <=(x3, 1)), java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x4, x5)), x3, x7) the following chains were created:

We consider the chain COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[1], x1[1])), java.lang.Object(IntList(x4[1], x5[1])), x3[1], x7[1]) → 2406_0_NTH_LE(x0[1], x0[1], x7[1]), 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0]) → COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0]), COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[1], x1[1])), java.lang.Object(IntList(x4[1], x5[1])), x3[1], x7[1]) → 2406_0_NTH_LE(x0[1], x0[1], x7[1]) which results in the following constraint:
(1)    (x0[1]=java.lang.Object(IntList(x0[0], x1[0]))∧x0[1]=java.lang.Object(IntList(x4[0], x5[0]))∧x7[1]=x3[0]∧&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1))=TRUE∧java.lang.Object(IntList(x0[0], x1[0]))=java.lang.Object(IntList(x0[1]1, x1[1]1))∧java.lang.Object(IntList(x4[0], x5[0]))=java.lang.Object(IntList(x4[1]1, x5[1]1))∧x3[0]=x3[1]1∧x7[0]=x7[1]1 ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0])≥COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])∧(U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥))

We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
(2)    (&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1))=TRUE ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x5[0])), java.lang.Object(IntList(x0[0], x5[0])), x3[0])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x5[0])), java.lang.Object(IntList(x0[0], x5[0])), x3[0])≥COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x5[0])), java.lang.Object(IntList(x0[0], x5[0])), x3[0], x7[0])∧(U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x0[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x0[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x0[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧[bni_32] ≥ 0∧[(-1)Bound*bni_32] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_33] ≥ 0)
We consider the chain COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[3], x1[3])), java.lang.Object(IntList(x0[3], x1[3])), x3[3], x5[3]) → 2406_0_NTH_LE(x0[3], x0[3], x5[3]), 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0]) → COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0]), COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[1], x1[1])), java.lang.Object(IntList(x4[1], x5[1])), x3[1], x7[1]) → 2406_0_NTH_LE(x0[1], x0[1], x7[1]) which results in the following constraint:
(7)    (x0[3]=java.lang.Object(IntList(x0[0], x1[0]))∧x0[3]=java.lang.Object(IntList(x4[0], x5[0]))∧x5[3]=x3[0]∧&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1))=TRUE∧java.lang.Object(IntList(x0[0], x1[0]))=java.lang.Object(IntList(x0[1], x1[1]))∧java.lang.Object(IntList(x4[0], x5[0]))=java.lang.Object(IntList(x4[1], x5[1]))∧x3[0]=x3[1]∧x7[0]=x7[1] ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0])≥COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])∧(U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥))

We simplified constraint (7) using rules (I), (II), (III), (IV) which results in the following new constraint:
(8)    (&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1))=TRUE ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x5[0])), java.lang.Object(IntList(x0[0], x5[0])), x3[0])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x5[0])), java.lang.Object(IntList(x0[0], x5[0])), x3[0])≥COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x5[0])), java.lang.Object(IntList(x0[0], x5[0])), x3[0], x7[0])∧(U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥))

We simplified constraint (8) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(9)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x0[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (9) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(10)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x0[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (10) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(11)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x0[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (11) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(12)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧[bni_32] ≥ 0∧[(-1)Bound*bni_32] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_33] ≥ 0)
We consider the chain COND_2406_0_NTH_LE2(TRUE, x0[5], java.lang.Object(IntList(x3[5], x4[5])), x2[5]) → 2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1)), 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0]) → COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0]), COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[1], x1[1])), java.lang.Object(IntList(x4[1], x5[1])), x3[1], x7[1]) → 2406_0_NTH_LE(x0[1], x0[1], x7[1]) which results in the following constraint:
(13)    (x0[5]=java.lang.Object(IntList(x0[0], x1[0]))∧x3[5]=java.lang.Object(IntList(x4[0], x5[0]))∧+(x2[5], -1)=x3[0]∧&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1))=TRUE∧java.lang.Object(IntList(x0[0], x1[0]))=java.lang.Object(IntList(x0[1], x1[1]))∧java.lang.Object(IntList(x4[0], x5[0]))=java.lang.Object(IntList(x4[1], x5[1]))∧x3[0]=x3[1]∧x7[0]=x7[1] ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0])≥COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])∧(U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥))

We simplified constraint (13) using rules (I), (II), (III), (IV) which results in the following new constraint:
(14)    (&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(+(x2[5], -1), 1))=TRUE ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), +(x2[5], -1))≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), +(x2[5], -1))≥COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(+(x2[5], -1), 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), +(x2[5], -1), x7[0])∧(U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥))

We simplified constraint (14) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(15)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x0[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (15) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(16)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x0[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (16) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(17)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧[(-1)Bound*bni_32] + [bni_32]x0[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (17) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(18)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[bni_32] ≥ 0∧[(-1)Bound*bni_32] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_33] ≥ 0)
We consider the chain COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0[7], x1[7])), java.lang.Object(IntList(x0[7], x1[7])), x3[7]) → 2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1)), 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0]) → COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0]), COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[1], x1[1])), java.lang.Object(IntList(x4[1], x5[1])), x3[1], x7[1]) → 2406_0_NTH_LE(x0[1], x0[1], x7[1]) which results in the following constraint:
(19)    (java.lang.Object(IntList(x0[7], x1[7]))=java.lang.Object(IntList(x0[0], x1[0]))∧x0[7]=java.lang.Object(IntList(x4[0], x5[0]))∧+(x3[7], -1)=x3[0]∧&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1))=TRUE∧java.lang.Object(IntList(x0[0], x1[0]))=java.lang.Object(IntList(x0[1], x1[1]))∧java.lang.Object(IntList(x4[0], x5[0]))=java.lang.Object(IntList(x4[1], x5[1]))∧x3[0]=x3[1]∧x7[0]=x7[1] ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0])≥COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])∧(U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥))

We simplified constraint (19) using rules (I), (II), (III), (IV) which results in the following new constraint:
(20)    (&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(+(x3[7], -1), 1))=TRUE ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(java.lang.Object(IntList(x4[0], x5[0])), x1[7])), java.lang.Object(IntList(x4[0], x5[0])), +(x3[7], -1))≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(java.lang.Object(IntList(x4[0], x5[0])), x1[7])), java.lang.Object(IntList(x4[0], x5[0])), +(x3[7], -1))≥COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(+(x3[7], -1), 1)), java.lang.Object(IntList(java.lang.Object(IntList(x4[0], x5[0])), x1[7])), java.lang.Object(IntList(x4[0], x5[0])), +(x3[7], -1), x7[0])∧(U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥))

We simplified constraint (20) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(21)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧[bni_32 + (-1)Bound*bni_32] + [bni_32]x4[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(22)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧[bni_32 + (-1)Bound*bni_32] + [bni_32]x4[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (22) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(23)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧[bni_32 + (-1)Bound*bni_32] + [bni_32]x4[0] ≥ 0∧[(-1)bso_33] ≥ 0)

We simplified constraint (23) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(24)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧0 ≥ 0∧[bni_32] ≥ 0∧0 ≥ 0∧[bni_32 + (-1)Bound*bni_32] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_33] ≥ 0)

For Pair COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x4, x5)), x3, x7) → 2406_0_NTH_LE(x0, x0, x7) the following chains were created:

We consider the chain 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0]) → COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0]), COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[1], x1[1])), java.lang.Object(IntList(x4[1], x5[1])), x3[1], x7[1]) → 2406_0_NTH_LE(x0[1], x0[1], x7[1]) which results in the following constraint:
(25)    (&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1))=TRUE∧java.lang.Object(IntList(x0[0], x1[0]))=java.lang.Object(IntList(x0[1], x1[1]))∧java.lang.Object(IntList(x4[0], x5[0]))=java.lang.Object(IntList(x4[1], x5[1]))∧x3[0]=x3[1]∧x7[0]=x7[1] ⇒ COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[1], x1[1])), java.lang.Object(IntList(x4[1], x5[1])), x3[1], x7[1])≥NonInfC∧COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[1], x1[1])), java.lang.Object(IntList(x4[1], x5[1])), x3[1], x7[1])≥2406_0_NTH_LE(x0[1], x0[1], x7[1])∧(U^Increasing(2406_0_NTH_LE(x0[1], x0[1], x7[1])), ≥))

We simplified constraint (25) using rules (I), (II), (III) which results in the following new constraint:
(26)    (&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1))=TRUE ⇒ COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])≥NonInfC∧COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])≥2406_0_NTH_LE(x0[0], x0[0], x7[0])∧(U^Increasing(2406_0_NTH_LE(x0[1], x0[1], x7[1])), ≥))

We simplified constraint (26) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(27)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[1], x0[1], x7[1])), ≥)∧[(-1)Bound*bni_34] + [bni_34]x0[0] ≥ 0∧[1 + (-1)bso_35] ≥ 0)

We simplified constraint (27) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(28)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[1], x0[1], x7[1])), ≥)∧[(-1)Bound*bni_34] + [bni_34]x0[0] ≥ 0∧[1 + (-1)bso_35] ≥ 0)

We simplified constraint (28) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(29)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[1], x0[1], x7[1])), ≥)∧[(-1)Bound*bni_34] + [bni_34]x0[0] ≥ 0∧[1 + (-1)bso_35] ≥ 0)

We simplified constraint (29) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(30)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[1], x0[1], x7[1])), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[bni_34] ≥ 0∧[(-1)Bound*bni_34] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_35] ≥ 0)

For Pair 2406_0_NTH_LE(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3) → COND_2406_0_NTH_LE1(&&(&&(>(x5, -1), <=(x3, 1)), >(x1, 0)), java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3, x5) the following chains were created:

We consider the chain COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[1], x1[1])), java.lang.Object(IntList(x4[1], x5[1])), x3[1], x7[1]) → 2406_0_NTH_LE(x0[1], x0[1], x7[1]), 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2]) → COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2]), COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[3], x1[3])), java.lang.Object(IntList(x0[3], x1[3])), x3[3], x5[3]) → 2406_0_NTH_LE(x0[3], x0[3], x5[3]) which results in the following constraint:
(31)    (x0[1]=java.lang.Object(IntList(x0[2], x1[2]))∧x7[1]=x3[2]∧&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0))=TRUE∧java.lang.Object(IntList(x0[2], x1[2]))=java.lang.Object(IntList(x0[3], x1[3]))∧x3[2]=x3[3]∧x5[2]=x5[3] ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2])≥COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])∧(U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥))

We simplified constraint (31) using rules (I), (II), (III), (IV) which results in the following new constraint:
(32)    (&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0))=TRUE ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2])≥COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])∧(U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥))

We simplified constraint (32) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(33)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧[(-1)Bound*bni_36] + [bni_36]x0[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (33) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(34)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧[(-1)Bound*bni_36] + [bni_36]x0[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (34) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(35)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧[(-1)Bound*bni_36] + [bni_36]x0[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (35) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(36)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧0 ≥ 0∧0 ≥ 0∧[bni_36] ≥ 0∧[(-1)Bound*bni_36] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_37] ≥ 0)
We consider the chain COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[3], x1[3])), java.lang.Object(IntList(x0[3], x1[3])), x3[3], x5[3]) → 2406_0_NTH_LE(x0[3], x0[3], x5[3]), 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2]) → COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2]), COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[3], x1[3])), java.lang.Object(IntList(x0[3], x1[3])), x3[3], x5[3]) → 2406_0_NTH_LE(x0[3], x0[3], x5[3]) which results in the following constraint:
(37)    (x0[3]=java.lang.Object(IntList(x0[2], x1[2]))∧x5[3]=x3[2]∧&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0))=TRUE∧java.lang.Object(IntList(x0[2], x1[2]))=java.lang.Object(IntList(x0[3]1, x1[3]1))∧x3[2]=x3[3]1∧x5[2]=x5[3]1 ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2])≥COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])∧(U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥))

We simplified constraint (37) using rules (I), (II), (III), (IV) which results in the following new constraint:
(38)    (&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0))=TRUE ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2])≥COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])∧(U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥))

We simplified constraint (38) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(39)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧[(-1)Bound*bni_36] + [bni_36]x0[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (39) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(40)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧[(-1)Bound*bni_36] + [bni_36]x0[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(41)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧[(-1)Bound*bni_36] + [bni_36]x0[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (41) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(42)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧0 ≥ 0∧0 ≥ 0∧[bni_36] ≥ 0∧[(-1)Bound*bni_36] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_37] ≥ 0)
We consider the chain COND_2406_0_NTH_LE2(TRUE, x0[5], java.lang.Object(IntList(x3[5], x4[5])), x2[5]) → 2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1)), 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2]) → COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2]), COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[3], x1[3])), java.lang.Object(IntList(x0[3], x1[3])), x3[3], x5[3]) → 2406_0_NTH_LE(x0[3], x0[3], x5[3]) which results in the following constraint:
(43)    (x0[5]=java.lang.Object(IntList(x0[2], x1[2]))∧x3[5]=java.lang.Object(IntList(x0[2], x1[2]))∧+(x2[5], -1)=x3[2]∧&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0))=TRUE∧java.lang.Object(IntList(x0[2], x1[2]))=java.lang.Object(IntList(x0[3], x1[3]))∧x3[2]=x3[3]∧x5[2]=x5[3] ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2])≥COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])∧(U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥))

We simplified constraint (43) using rules (I), (II), (III), (IV) which results in the following new constraint:
(44)    (&&(&&(>(x5[2], -1), <=(+(x2[5], -1), 1)), >(x1[2], 0))=TRUE ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), +(x2[5], -1))≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), +(x2[5], -1))≥COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(+(x2[5], -1), 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), +(x2[5], -1), x5[2])∧(U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥))

We simplified constraint (44) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(45)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧[(-1)Bound*bni_36] + [bni_36]x0[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (45) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(46)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧[(-1)Bound*bni_36] + [bni_36]x0[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (46) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(47)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧[(-1)Bound*bni_36] + [bni_36]x0[2] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (47) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(48)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧0 ≥ 0∧[bni_36] ≥ 0∧[(-1)Bound*bni_36] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_37] ≥ 0)
We consider the chain COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0[7], x1[7])), java.lang.Object(IntList(x0[7], x1[7])), x3[7]) → 2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1)), 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2]) → COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2]), COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[3], x1[3])), java.lang.Object(IntList(x0[3], x1[3])), x3[3], x5[3]) → 2406_0_NTH_LE(x0[3], x0[3], x5[3]) which results in the following constraint:
(49)    (java.lang.Object(IntList(x0[7], x1[7]))=java.lang.Object(IntList(x0[2], x1[2]))∧x0[7]=java.lang.Object(IntList(x0[2], x1[2]))∧+(x3[7], -1)=x3[2]∧&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0))=TRUE∧java.lang.Object(IntList(x0[2], x1[2]))=java.lang.Object(IntList(x0[3], x1[3]))∧x3[2]=x3[3]∧x5[2]=x5[3] ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2])≥COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])∧(U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥))

We simplified constraint (49) using rules (I), (II), (III), (IV) which results in the following new constraint:
(50)    (&&(&&(>(x5[2], -1), <=(+(x3[7], -1), 1)), >(x1[2], 0))=TRUE ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(java.lang.Object(IntList(x0[7], x1[2])), x1[2])), java.lang.Object(IntList(java.lang.Object(IntList(x0[7], x1[2])), x1[2])), +(x3[7], -1))≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(java.lang.Object(IntList(x0[7], x1[2])), x1[2])), java.lang.Object(IntList(java.lang.Object(IntList(x0[7], x1[2])), x1[2])), +(x3[7], -1))≥COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(+(x3[7], -1), 1)), >(x1[2], 0)), java.lang.Object(IntList(java.lang.Object(IntList(x0[7], x1[2])), x1[2])), java.lang.Object(IntList(java.lang.Object(IntList(x0[7], x1[2])), x1[2])), +(x3[7], -1), x5[2])∧(U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥))

We simplified constraint (50) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(51)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧[bni_36 + (-1)Bound*bni_36] + [bni_36]x0[7] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (51) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(52)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧[bni_36 + (-1)Bound*bni_36] + [bni_36]x0[7] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (52) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(53)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧[bni_36 + (-1)Bound*bni_36] + [bni_36]x0[7] ≥ 0∧[(-1)bso_37] ≥ 0)

We simplified constraint (53) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(54)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧0 ≥ 0∧[bni_36] ≥ 0∧[bni_36 + (-1)Bound*bni_36] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_37] ≥ 0)

For Pair COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3, x5) → 2406_0_NTH_LE(x0, x0, x5) the following chains were created:

We consider the chain 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2]) → COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2]), COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[3], x1[3])), java.lang.Object(IntList(x0[3], x1[3])), x3[3], x5[3]) → 2406_0_NTH_LE(x0[3], x0[3], x5[3]) which results in the following constraint:
(55)    (&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0))=TRUE∧java.lang.Object(IntList(x0[2], x1[2]))=java.lang.Object(IntList(x0[3], x1[3]))∧x3[2]=x3[3]∧x5[2]=x5[3] ⇒ COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[3], x1[3])), java.lang.Object(IntList(x0[3], x1[3])), x3[3], x5[3])≥NonInfC∧COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[3], x1[3])), java.lang.Object(IntList(x0[3], x1[3])), x3[3], x5[3])≥2406_0_NTH_LE(x0[3], x0[3], x5[3])∧(U^Increasing(2406_0_NTH_LE(x0[3], x0[3], x5[3])), ≥))

We simplified constraint (55) using rules (I), (II), (III) which results in the following new constraint:
(56)    (&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0))=TRUE ⇒ COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])≥NonInfC∧COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])≥2406_0_NTH_LE(x0[2], x0[2], x5[2])∧(U^Increasing(2406_0_NTH_LE(x0[3], x0[3], x5[3])), ≥))

We simplified constraint (56) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(57)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[3], x0[3], x5[3])), ≥)∧[(-1)Bound*bni_38] + [bni_38]x0[2] ≥ 0∧[1 + (-1)bso_39] ≥ 0)

We simplified constraint (57) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(58)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[3], x0[3], x5[3])), ≥)∧[(-1)Bound*bni_38] + [bni_38]x0[2] ≥ 0∧[1 + (-1)bso_39] ≥ 0)

We simplified constraint (58) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(59)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[3], x0[3], x5[3])), ≥)∧[(-1)Bound*bni_38] + [bni_38]x0[2] ≥ 0∧[1 + (-1)bso_39] ≥ 0)

We simplified constraint (59) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(60)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[3], x0[3], x5[3])), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[bni_38] ≥ 0∧[(-1)Bound*bni_38] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_39] ≥ 0)

For Pair 2406_0_NTH_LE(x0, java.lang.Object(IntList(x3, x4)), x2) → COND_2406_0_NTH_LE2(>(x2, 1), x0, java.lang.Object(IntList(x3, x4)), x2) the following chains were created:

We consider the chain 2406_0_NTH_LE(x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4]) → COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4]), COND_2406_0_NTH_LE2(TRUE, x0[5], java.lang.Object(IntList(x3[5], x4[5])), x2[5]) → 2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1)) which results in the following constraint:
(61)    (>(x2[4], 1)=TRUE∧x0[4]=x0[5]∧java.lang.Object(IntList(x3[4], x4[4]))=java.lang.Object(IntList(x3[5], x4[5]))∧x2[4]=x2[5] ⇒ 2406_0_NTH_LE(x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])≥NonInfC∧2406_0_NTH_LE(x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])≥COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])∧(U^Increasing(COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])), ≥))

We simplified constraint (61) using rules (I), (II), (IV) which results in the following new constraint:
(62)    (>(x2[4], 1)=TRUE ⇒ 2406_0_NTH_LE(x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])≥NonInfC∧2406_0_NTH_LE(x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])≥COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])∧(U^Increasing(COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])), ≥))

We simplified constraint (62) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(63)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]x0[4] ≥ 0∧[(-1)bso_41] ≥ 0)

We simplified constraint (63) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(64)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]x0[4] ≥ 0∧[(-1)bso_41] ≥ 0)

We simplified constraint (64) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(65)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [bni_40]x0[4] ≥ 0∧[(-1)bso_41] ≥ 0)

We simplified constraint (65) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(66)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[bni_40] ≥ 0∧[(-1)bni_40 + (-1)Bound*bni_40] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_41] ≥ 0)

For Pair COND_2406_0_NTH_LE2(TRUE, x0, java.lang.Object(IntList(x3, x4)), x2) → 2406_0_NTH_LE(x0, x3, +(x2, -1)) the following chains were created:

We consider the chain 2406_0_NTH_LE(x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4]) → COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4]), COND_2406_0_NTH_LE2(TRUE, x0[5], java.lang.Object(IntList(x3[5], x4[5])), x2[5]) → 2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1)) which results in the following constraint:
(67)    (>(x2[4], 1)=TRUE∧x0[4]=x0[5]∧java.lang.Object(IntList(x3[4], x4[4]))=java.lang.Object(IntList(x3[5], x4[5]))∧x2[4]=x2[5] ⇒ COND_2406_0_NTH_LE2(TRUE, x0[5], java.lang.Object(IntList(x3[5], x4[5])), x2[5])≥NonInfC∧COND_2406_0_NTH_LE2(TRUE, x0[5], java.lang.Object(IntList(x3[5], x4[5])), x2[5])≥2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1))∧(U^Increasing(2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1))), ≥))

We simplified constraint (67) using rules (I), (II), (III) which results in the following new constraint:
(68)    (>(x2[4], 1)=TRUE ⇒ COND_2406_0_NTH_LE2(TRUE, x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])≥NonInfC∧COND_2406_0_NTH_LE2(TRUE, x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])≥2406_0_NTH_LE(x0[4], x3[4], +(x2[4], -1))∧(U^Increasing(2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1))), ≥))

We simplified constraint (68) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(69)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1))), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]x0[4] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (69) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(70)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1))), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]x0[4] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (70) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(71)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1))), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [bni_42]x0[4] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (71) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(72)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1))), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[bni_42] ≥ 0∧[(-1)bni_42 + (-1)Bound*bni_42] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_43] ≥ 0)

For Pair 2406_0_NTH_LE(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3) → COND_2406_0_NTH_LE3(>(x3, 1), java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3) the following chains were created:

We consider the chain 2406_0_NTH_LE(java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6]) → COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6]), COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0[7], x1[7])), java.lang.Object(IntList(x0[7], x1[7])), x3[7]) → 2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1)) which results in the following constraint:
(73)    (>(x3[6], 1)=TRUE∧java.lang.Object(IntList(x0[6], x1[6]))=java.lang.Object(IntList(x0[7], x1[7]))∧x3[6]=x3[7] ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])≥COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])∧(U^Increasing(COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])), ≥))

We simplified constraint (73) using rules (I), (II), (IV) which results in the following new constraint:
(74)    (>(x3[6], 1)=TRUE ⇒ 2406_0_NTH_LE(java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])≥NonInfC∧2406_0_NTH_LE(java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])≥COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])∧(U^Increasing(COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])), ≥))

We simplified constraint (74) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(75)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[6] ≥ 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (75) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(76)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[6] ≥ 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (76) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(77)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])), ≥)∧[(-1)Bound*bni_44] + [bni_44]x0[6] ≥ 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (77) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(78)    (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])), ≥)∧0 ≥ 0∧0 ≥ 0∧[bni_44] ≥ 0∧[(-1)Bound*bni_44] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_45] ≥ 0)

For Pair COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3) → 2406_0_NTH_LE(java.lang.Object(IntList(x0, x1)), x0, +(x3, -1)) the following chains were created:

We consider the chain 2406_0_NTH_LE(java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6]) → COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6]), COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0[7], x1[7])), java.lang.Object(IntList(x0[7], x1[7])), x3[7]) → 2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1)) which results in the following constraint:
(79)    (>(x3[6], 1)=TRUE∧java.lang.Object(IntList(x0[6], x1[6]))=java.lang.Object(IntList(x0[7], x1[7]))∧x3[6]=x3[7] ⇒ COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0[7], x1[7])), java.lang.Object(IntList(x0[7], x1[7])), x3[7])≥NonInfC∧COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0[7], x1[7])), java.lang.Object(IntList(x0[7], x1[7])), x3[7])≥2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1))∧(U^Increasing(2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1))), ≥))

We simplified constraint (79) using rules (I), (II), (III) which results in the following new constraint:
(80)    (>(x3[6], 1)=TRUE ⇒ COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])≥NonInfC∧COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])≥2406_0_NTH_LE(java.lang.Object(IntList(x0[6], x1[6])), x0[6], +(x3[6], -1))∧(U^Increasing(2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1))), ≥))

We simplified constraint (80) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(81)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1))), ≥)∧[(-1)Bound*bni_46] + [bni_46]x0[6] ≥ 0∧[(-1)bso_47] ≥ 0)

We simplified constraint (81) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(82)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1))), ≥)∧[(-1)Bound*bni_46] + [bni_46]x0[6] ≥ 0∧[(-1)bso_47] ≥ 0)

We simplified constraint (82) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(83)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1))), ≥)∧[(-1)Bound*bni_46] + [bni_46]x0[6] ≥ 0∧[(-1)bso_47] ≥ 0)

We simplified constraint (83) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(84)    (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1))), ≥)∧0 ≥ 0∧0 ≥ 0∧[bni_46] ≥ 0∧[(-1)Bound*bni_46] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_47] ≥ 0)

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

2406_0_NTH_LE(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x4, x5)), x3) → COND_2406_0_NTH_LE(&&(&&(>(x7, -1), >(x5, 0)), <=(x3, 1)), java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x4, x5)), x3, x7)
- (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧[bni_32] ≥ 0∧[(-1)Bound*bni_32] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_33] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧[bni_32] ≥ 0∧[(-1)Bound*bni_32] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_33] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[bni_32] ≥ 0∧[(-1)Bound*bni_32] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_33] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])), ≥)∧0 ≥ 0∧[bni_32] ≥ 0∧0 ≥ 0∧[bni_32 + (-1)Bound*bni_32] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_33] ≥ 0)
COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x4, x5)), x3, x7) → 2406_0_NTH_LE(x0, x0, x7)
- (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[1], x0[1], x7[1])), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[bni_34] ≥ 0∧[(-1)Bound*bni_34] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_35] ≥ 0)
2406_0_NTH_LE(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3) → COND_2406_0_NTH_LE1(&&(&&(>(x5, -1), <=(x3, 1)), >(x1, 0)), java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3, x5)
- (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧0 ≥ 0∧0 ≥ 0∧[bni_36] ≥ 0∧[(-1)Bound*bni_36] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_37] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧0 ≥ 0∧0 ≥ 0∧[bni_36] ≥ 0∧[(-1)Bound*bni_36] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_37] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧0 ≥ 0∧[bni_36] ≥ 0∧[(-1)Bound*bni_36] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_37] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])), ≥)∧0 ≥ 0∧[bni_36] ≥ 0∧[bni_36 + (-1)Bound*bni_36] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_37] ≥ 0)
COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3, x5) → 2406_0_NTH_LE(x0, x0, x5)
- (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[3], x0[3], x5[3])), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[bni_38] ≥ 0∧[(-1)Bound*bni_38] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_39] ≥ 0)
2406_0_NTH_LE(x0, java.lang.Object(IntList(x3, x4)), x2) → COND_2406_0_NTH_LE2(>(x2, 1), x0, java.lang.Object(IntList(x3, x4)), x2)
- (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[bni_40] ≥ 0∧[(-1)bni_40 + (-1)Bound*bni_40] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_41] ≥ 0)
COND_2406_0_NTH_LE2(TRUE, x0, java.lang.Object(IntList(x3, x4)), x2) → 2406_0_NTH_LE(x0, x3, +(x2, -1))
- (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1))), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[bni_42] ≥ 0∧[(-1)bni_42 + (-1)Bound*bni_42] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_43] ≥ 0)
2406_0_NTH_LE(java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3) → COND_2406_0_NTH_LE3(>(x3, 1), java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3)
- (0 ≥ 0 ⇒ (U^Increasing(COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])), ≥)∧0 ≥ 0∧0 ≥ 0∧[bni_44] ≥ 0∧[(-1)Bound*bni_44] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_45] ≥ 0)
COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0, x1)), java.lang.Object(IntList(x0, x1)), x3) → 2406_0_NTH_LE(java.lang.Object(IntList(x0, x1)), x0, +(x3, -1))
- (0 ≥ 0 ⇒ (U^Increasing(2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1))), ≥)∧0 ≥ 0∧0 ≥ 0∧[bni_46] ≥ 0∧[(-1)Bound*bni_46] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_47] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(2406_0_NTH_LE(x₁, x₂, x₃)) = [-1] + x₁
POL(java.lang.Object(x₁)) = [1] + x₁
POL(IntList(x₁, x₂)) = x₁
POL(COND_2406_0_NTH_LE(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₂ + x₁
POL(&&(x₁, x₂)) = 0
POL(>(x₁, x₂)) = 0
POL(-1) = 0
POL(0) = 0
POL(<=(x₁, x₂)) = 0
POL(1) = 0
POL(COND_2406_0_NTH_LE1(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₃ + [2]x₂ + [2]x₁
POL(COND_2406_0_NTH_LE2(x₁, x₂, x₃, x₄)) = [-1] + x₂
POL(+(x₁, x₂)) = 0
POL(COND_2406_0_NTH_LE3(x₁, x₂, x₃, x₄)) = [-1] + [2]x₃ + [-1]x₂

The following pairs are in P_>:

COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[1], x1[1])), java.lang.Object(IntList(x4[1], x5[1])), x3[1], x7[1]) → 2406_0_NTH_LE(x0[1], x0[1], x7[1])
COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[3], x1[3])), java.lang.Object(IntList(x0[3], x1[3])), x3[3], x5[3]) → 2406_0_NTH_LE(x0[3], x0[3], x5[3])

The following pairs are in P_bound:

2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0]) → COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])
COND_2406_0_NTH_LE(TRUE, java.lang.Object(IntList(x0[1], x1[1])), java.lang.Object(IntList(x4[1], x5[1])), x3[1], x7[1]) → 2406_0_NTH_LE(x0[1], x0[1], x7[1])
2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2]) → COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])
COND_2406_0_NTH_LE1(TRUE, java.lang.Object(IntList(x0[3], x1[3])), java.lang.Object(IntList(x0[3], x1[3])), x3[3], x5[3]) → 2406_0_NTH_LE(x0[3], x0[3], x5[3])
2406_0_NTH_LE(x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4]) → COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])
COND_2406_0_NTH_LE2(TRUE, x0[5], java.lang.Object(IntList(x3[5], x4[5])), x2[5]) → 2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1))
2406_0_NTH_LE(java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6]) → COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])
COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0[7], x1[7])), java.lang.Object(IntList(x0[7], x1[7])), x3[7]) → 2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1))

The following pairs are in P_≥:

2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0]) → COND_2406_0_NTH_LE(&&(&&(>(x7[0], -1), >(x5[0], 0)), <=(x3[0], 1)), java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])
2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2]) → COND_2406_0_NTH_LE1(&&(&&(>(x5[2], -1), <=(x3[2], 1)), >(x1[2], 0)), java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])
2406_0_NTH_LE(x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4]) → COND_2406_0_NTH_LE2(>(x2[4], 1), x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])
COND_2406_0_NTH_LE2(TRUE, x0[5], java.lang.Object(IntList(x3[5], x4[5])), x2[5]) → 2406_0_NTH_LE(x0[5], x3[5], +(x2[5], -1))
2406_0_NTH_LE(java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6]) → COND_2406_0_NTH_LE3(>(x3[6], 1), java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])
COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0[7], x1[7])), java.lang.Object(IntList(x0[7], x1[7])), x3[7]) → 2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], +(x3[7], -1))

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

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

(20) 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): 2406_0_NTH_LE(java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0]) → COND_2406_0_NTH_LE(x7[0] > -1 && x5[0] > 0 && x3[0] <= 1, java.lang.Object(IntList(x0[0], x1[0])), java.lang.Object(IntList(x4[0], x5[0])), x3[0], x7[0])
(2): 2406_0_NTH_LE(java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2]) → COND_2406_0_NTH_LE1(x5[2] > -1 && x3[2] <= 1 && x1[2] > 0, java.lang.Object(IntList(x0[2], x1[2])), java.lang.Object(IntList(x0[2], x1[2])), x3[2], x5[2])
(4): 2406_0_NTH_LE(x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4]) → COND_2406_0_NTH_LE2(x2[4] > 1, x0[4], java.lang.Object(IntList(x3[4], x4[4])), x2[4])
(5): COND_2406_0_NTH_LE2(TRUE, x0[5], java.lang.Object(IntList(x3[5], x4[5])), x2[5]) → 2406_0_NTH_LE(x0[5], x3[5], x2[5] + -1)
(6): 2406_0_NTH_LE(java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6]) → COND_2406_0_NTH_LE3(x3[6] > 1, java.lang.Object(IntList(x0[6], x1[6])), java.lang.Object(IntList(x0[6], x1[6])), x3[6])
(7): COND_2406_0_NTH_LE3(TRUE, java.lang.Object(IntList(x0[7], x1[7])), java.lang.Object(IntList(x0[7], x1[7])), x3[7]) → 2406_0_NTH_LE(java.lang.Object(IntList(x0[7], x1[7])), x0[7], x3[7] + -1)