Termination proof of /tmp/tmpUFJ1yl/PastaC9.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBCToGraph (⇒, 930 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToSCCProof (⇒, 0 ms)

↳4 JBCTerminationSCC

↳5 SCCToIDPv1Proof (⇒, 170 ms)

↳6 IDP

↳7 IDPNonInfProof (⇒, 670 ms)

↳8 IDP

↳9 IDependencyGraphProof (⇔, 0 ms)

↳10 IDP

↳11 IDPNonInfProof (⇒, 160 ms)

↳12 IDP

↳13 IDependencyGraphProof (⇔, 0 ms)

↳14 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaC9

/**
 * Example taken from "A Term Rewriting Approach to the Automated Termination
 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
 * and converted to Java.
 */

public class PastaC9 {
    public static void main(String[] args) {
        Random.args = args;
        int x = Random.random();
        int y = Random.random();

        while (x > 0 && y > 0) {
            if (Random.random() < 42) {
                x--;
                y = Random.random();
            } else {
                y--;
            }
        }
    } 
}


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:
PastaC9.main([Ljava/lang/String;)V: Graph of 322 nodes with 1 SCC.

(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 1 SCCs.

(4) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: PastaC9.main([Ljava/lang/String;)V
SCC calls the following helper methods:
Performed SCC analyses: UsedFieldsAnalysis

(5) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 54 rules for P and 0 rules for R.

P rules:
1005_0_main_LE(EOS(STATIC_1005), i385, i376, i385) → 1007_0_main_LE(EOS(STATIC_1007), i385, i376, i385)
1007_0_main_LE(EOS(STATIC_1007), i385, i376, i385) → 1011_0_main_Load(EOS(STATIC_1011), i385, i376) | >(i385, 0)
1011_0_main_Load(EOS(STATIC_1011), i385, i376) → 1014_0_main_LE(EOS(STATIC_1014), i385, i376, i376)
1014_0_main_LE(EOS(STATIC_1014), i385, i387, i387) → 1017_0_main_LE(EOS(STATIC_1017), i385, i387, i387)
1017_0_main_LE(EOS(STATIC_1017), i385, i387, i387) → 1022_0_main_InvokeMethod(EOS(STATIC_1022), i385, i387) | >(i387, 0)
1022_0_main_InvokeMethod(EOS(STATIC_1022), i385, i387) → 1025_0_random_FieldAccess(EOS(STATIC_1025), i385, i387)
1025_0_random_FieldAccess(EOS(STATIC_1025), i385, i387) → 1027_0_random_FieldAccess(EOS(STATIC_1027), i385, i387)
1027_0_random_FieldAccess(EOS(STATIC_1027), i385, i387) → 1030_0_random_ArrayAccess(EOS(STATIC_1030), i385, i387)
1030_0_random_ArrayAccess(EOS(STATIC_1030), i385, i387) → 1032_0_random_ArrayAccess(EOS(STATIC_1032), i385, i387)
1032_0_random_ArrayAccess(EOS(STATIC_1032), i385, i387) → 1035_0_random_Store(EOS(STATIC_1035), i385, i387, o272)
1035_0_random_Store(EOS(STATIC_1035), i385, i387, o272) → 1039_0_random_FieldAccess(EOS(STATIC_1039), i385, i387, o272)
1039_0_random_FieldAccess(EOS(STATIC_1039), i385, i387, o272) → 1042_0_random_ConstantStackPush(EOS(STATIC_1042), i385, i387, o272)
1042_0_random_ConstantStackPush(EOS(STATIC_1042), i385, i387, o272) → 1046_0_random_IntArithmetic(EOS(STATIC_1046), i385, i387, o272)
1046_0_random_IntArithmetic(EOS(STATIC_1046), i385, i387, o272) → 1050_0_random_FieldAccess(EOS(STATIC_1050), i385, i387, o272)
1050_0_random_FieldAccess(EOS(STATIC_1050), i385, i387, o272) → 1052_0_random_Load(EOS(STATIC_1052), i385, i387, o272)
1052_0_random_Load(EOS(STATIC_1052), i385, i387, o272) → 1062_0_random_InvokeMethod(EOS(STATIC_1062), i385, i387, o272)
1062_0_random_InvokeMethod(EOS(STATIC_1062), i385, i387, java.lang.Object(o290sub)) → 1065_0_random_InvokeMethod(EOS(STATIC_1065), i385, i387, java.lang.Object(o290sub))
1065_0_random_InvokeMethod(EOS(STATIC_1065), i385, i387, java.lang.Object(o290sub)) → 1069_0_length_Load(EOS(STATIC_1069), i385, i387, java.lang.Object(o290sub), java.lang.Object(o290sub))
1069_0_length_Load(EOS(STATIC_1069), i385, i387, java.lang.Object(o290sub), java.lang.Object(o290sub)) → 1077_0_length_FieldAccess(EOS(STATIC_1077), i385, i387, java.lang.Object(o290sub), java.lang.Object(o290sub))
1077_0_length_FieldAccess(EOS(STATIC_1077), i385, i387, java.lang.Object(java.lang.String(o298sub, i423)), java.lang.Object(java.lang.String(o298sub, i423))) → 1078_0_length_FieldAccess(EOS(STATIC_1078), i385, i387, java.lang.Object(java.lang.String(o298sub, i423)), java.lang.Object(java.lang.String(o298sub, i423))) | &&(>=(i423, 0), >=(i424, 0))
1078_0_length_FieldAccess(EOS(STATIC_1078), i385, i387, java.lang.Object(java.lang.String(o298sub, i423)), java.lang.Object(java.lang.String(o298sub, i423))) → 1085_0_length_Return(EOS(STATIC_1085), i385, i387, java.lang.Object(java.lang.String(o298sub, i423)), i423)
1085_0_length_Return(EOS(STATIC_1085), i385, i387, java.lang.Object(java.lang.String(o298sub, i423)), i423) → 1091_0_random_Return(EOS(STATIC_1091), i385, i387, i423)
1091_0_random_Return(EOS(STATIC_1091), i385, i387, i423) → 1093_0_main_ConstantStackPush(EOS(STATIC_1093), i385, i387, i423)
1093_0_main_ConstantStackPush(EOS(STATIC_1093), i385, i387, i423) → 1101_0_main_GE(EOS(STATIC_1101), i385, i387, i423, 42)
1101_0_main_GE(EOS(STATIC_1101), i385, i387, i439, matching1) → 1107_0_main_GE(EOS(STATIC_1107), i385, i387, i439, 42) | =(matching1, 42)
1101_0_main_GE(EOS(STATIC_1101), i385, i387, i440, matching1) → 1108_0_main_GE(EOS(STATIC_1108), i385, i387, i440, 42) | =(matching1, 42)
1107_0_main_GE(EOS(STATIC_1107), i385, i387, i439, matching1) → 1113_0_main_Inc(EOS(STATIC_1113), i385) | &&(<(i439, 42), =(matching1, 42))
1113_0_main_Inc(EOS(STATIC_1113), i385) → 1121_0_main_InvokeMethod(EOS(STATIC_1121), +(i385, -1)) | >(i385, 0)
1121_0_main_InvokeMethod(EOS(STATIC_1121), i446) → 1131_0_random_FieldAccess(EOS(STATIC_1131), i446)
1131_0_random_FieldAccess(EOS(STATIC_1131), i446) → 1451_0_random_FieldAccess(EOS(STATIC_1451), i446)
1451_0_random_FieldAccess(EOS(STATIC_1451), i446) → 1462_0_random_ArrayAccess(EOS(STATIC_1462), i446)
1462_0_random_ArrayAccess(EOS(STATIC_1462), i446) → 1470_0_random_ArrayAccess(EOS(STATIC_1470), i446)
1470_0_random_ArrayAccess(EOS(STATIC_1470), i446) → 1479_0_random_Store(EOS(STATIC_1479), i446, o482)
1479_0_random_Store(EOS(STATIC_1479), i446, o482) → 1490_0_random_FieldAccess(EOS(STATIC_1490), i446, o482)
1490_0_random_FieldAccess(EOS(STATIC_1490), i446, o482) → 1497_0_random_ConstantStackPush(EOS(STATIC_1497), i446, o482)
1497_0_random_ConstantStackPush(EOS(STATIC_1497), i446, o482) → 1508_0_random_IntArithmetic(EOS(STATIC_1508), i446, o482)
1508_0_random_IntArithmetic(EOS(STATIC_1508), i446, o482) → 1516_0_random_FieldAccess(EOS(STATIC_1516), i446, o482)
1516_0_random_FieldAccess(EOS(STATIC_1516), i446, o482) → 1523_0_random_Load(EOS(STATIC_1523), i446, o482)
1523_0_random_Load(EOS(STATIC_1523), i446, o482) → 1537_0_random_InvokeMethod(EOS(STATIC_1537), i446, o482)
1537_0_random_InvokeMethod(EOS(STATIC_1537), i446, java.lang.Object(o540sub)) → 1542_0_random_InvokeMethod(EOS(STATIC_1542), i446, java.lang.Object(o540sub))
1542_0_random_InvokeMethod(EOS(STATIC_1542), i446, java.lang.Object(o540sub)) → 1549_0_length_Load(EOS(STATIC_1549), i446, java.lang.Object(o540sub), java.lang.Object(o540sub))
1549_0_length_Load(EOS(STATIC_1549), i446, java.lang.Object(o540sub), java.lang.Object(o540sub)) → 1564_0_length_FieldAccess(EOS(STATIC_1564), i446, java.lang.Object(o540sub), java.lang.Object(o540sub))
1564_0_length_FieldAccess(EOS(STATIC_1564), i446, java.lang.Object(java.lang.String(o561sub, i726)), java.lang.Object(java.lang.String(o561sub, i726))) → 1566_0_length_FieldAccess(EOS(STATIC_1566), i446, java.lang.Object(java.lang.String(o561sub, i726)), java.lang.Object(java.lang.String(o561sub, i726))) | &&(>=(i726, 0), >=(i727, 0))
1566_0_length_FieldAccess(EOS(STATIC_1566), i446, java.lang.Object(java.lang.String(o561sub, i726)), java.lang.Object(java.lang.String(o561sub, i726))) → 1573_0_length_Return(EOS(STATIC_1573), i446, java.lang.Object(java.lang.String(o561sub, i726)), i726)
1573_0_length_Return(EOS(STATIC_1573), i446, java.lang.Object(java.lang.String(o561sub, i726)), i726) → 1577_0_random_Return(EOS(STATIC_1577), i446, i726)
1577_0_random_Return(EOS(STATIC_1577), i446, i726) → 1578_0_main_Store(EOS(STATIC_1578), i446, i726)
1578_0_main_Store(EOS(STATIC_1578), i446, i726) → 1583_0_main_JMP(EOS(STATIC_1583), i446, i726)
1583_0_main_JMP(EOS(STATIC_1583), i446, i726) → 1592_0_main_Load(EOS(STATIC_1592), i446, i726)
1592_0_main_Load(EOS(STATIC_1592), i446, i726) → 1000_0_main_Load(EOS(STATIC_1000), i446, i726)
1000_0_main_Load(EOS(STATIC_1000), i375, i376) → 1005_0_main_LE(EOS(STATIC_1005), i375, i376, i375)
1108_0_main_GE(EOS(STATIC_1108), i385, i387, i440, matching1) → 1115_0_main_Inc(EOS(STATIC_1115), i385, i387) | &&(>=(i440, 42), =(matching1, 42))
1115_0_main_Inc(EOS(STATIC_1115), i385, i387) → 1123_0_main_JMP(EOS(STATIC_1123), i385, +(i387, -1)) | >(i387, 0)
1123_0_main_JMP(EOS(STATIC_1123), i385, i447) → 1140_0_main_Load(EOS(STATIC_1140), i385, i447)
1140_0_main_Load(EOS(STATIC_1140), i385, i447) → 1000_0_main_Load(EOS(STATIC_1000), i385, i447)
R rules:

Combined rules. Obtained 2 conditional rules for P and 0 conditional rules for R.

P rules:
1005_0_main_LE(EOS(STATIC_1005), x0, x1, x0) → 1005_0_main_LE(EOS(STATIC_1005), +(x0, -1), x2, +(x0, -1)) | &&(&&(>(+(x2, 1), 0), >(x1, 0)), >(x0, 0))
1005_0_main_LE(EOS(STATIC_1005), x0, x1, x0) → 1005_0_main_LE(EOS(STATIC_1005), x0, +(x1, -1), x0) | &&(>(x1, 0), >(x0, 0))
R rules:

Filtered ground terms:

1005_0_main_LE(x1, x2, x3, x4) → 1005_0_main_LE(x2, x3, x4)
EOS(x1) → EOS
Cond_1005_0_main_LE1(x1, x2, x3, x4, x5) → Cond_1005_0_main_LE1(x1, x3, x4, x5)
Cond_1005_0_main_LE(x1, x2, x3, x4, x5, x6) → Cond_1005_0_main_LE(x1, x3, x4, x5, x6)

Filtered duplicate args:

1005_0_main_LE(x1, x2, x3) → 1005_0_main_LE(x2, x3)
Cond_1005_0_main_LE(x1, x2, x3, x4, x5) → Cond_1005_0_main_LE(x1, x3, x4, x5)
Cond_1005_0_main_LE1(x1, x2, x3, x4) → Cond_1005_0_main_LE1(x1, x3, x4)

Filtered unneeded arguments:

Cond_1005_0_main_LE(x1, x2, x3, x4) → Cond_1005_0_main_LE(x1, x3, x4)

Combined rules. Obtained 2 conditional rules for P and 0 conditional rules for R.

P rules:
1005_0_main_LE(x1, x0) → 1005_0_main_LE(x2, +(x0, -1)) | &&(&&(>(x2, -1), >(x1, 0)), >(x0, 0))
1005_0_main_LE(x1, x0) → 1005_0_main_LE(+(x1, -1), x0) | &&(>(x1, 0), >(x0, 0))
R rules:

Finished conversion. Obtained 4 rules for P and 0 rules for R. System has predefined symbols.

P rules:
1005_0_MAIN_LE(x1, x0) → COND_1005_0_MAIN_LE(&&(&&(>(x2, -1), >(x1, 0)), >(x0, 0)), x1, x0, x2)
COND_1005_0_MAIN_LE(TRUE, x1, x0, x2) → 1005_0_MAIN_LE(x2, +(x0, -1))
1005_0_MAIN_LE(x1, x0) → COND_1005_0_MAIN_LE1(&&(>(x1, 0), >(x0, 0)), x1, x0)
COND_1005_0_MAIN_LE1(TRUE, x1, x0) → 1005_0_MAIN_LE(+(x1, -1), x0)
R rules:

(6) 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): 1005_0_MAIN_LE(x1[0], x0[0]) → COND_1005_0_MAIN_LE(x2[0] > -1 && x1[0] > 0 && x0[0] > 0, x1[0], x0[0], x2[0])
(1): COND_1005_0_MAIN_LE(TRUE, x1[1], x0[1], x2[1]) → 1005_0_MAIN_LE(x2[1], x0[1] + -1)
(2): 1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(x1[2] > 0 && x0[2] > 0, x1[2], x0[2])
(3): COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(x1[3] + -1, x0[3])

(0) -> (1), if (x2[0] > -1 && x1[0] > 0 && x0[0] > 0 ∧x1[0] →^* x1[1]∧x0[0] →^* x0[1]∧x2[0] →^* x2[1])

(1) -> (0), if (x2[1] →^* x1[0]∧x0[1] + -1 →^* x0[0])

(1) -> (2), if (x2[1] →^* x1[2]∧x0[1] + -1 →^* x0[2])

(2) -> (3), if (x1[2] > 0 && x0[2] > 0 ∧x1[2] →^* x1[3]∧x0[2] →^* x0[3])

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

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

The set Q is empty.

(7) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@7571ccae 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 1005_0_MAIN_LE(x1, x0) → COND_1005_0_MAIN_LE(&&(&&(>(x2, -1), >(x1, 0)), >(x0, 0)), x1, x0, x2) the following chains were created:

We consider the chain COND_1005_0_MAIN_LE(TRUE, x1[1], x0[1], x2[1]) → 1005_0_MAIN_LE(x2[1], +(x0[1], -1)), 1005_0_MAIN_LE(x1[0], x0[0]) → COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0]), COND_1005_0_MAIN_LE(TRUE, x1[1], x0[1], x2[1]) → 1005_0_MAIN_LE(x2[1], +(x0[1], -1)) which results in the following constraint:
(1)    (x2[1]=x1[0]∧+(x0[1], -1)=x0[0]∧&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0))=TRUE∧x1[0]=x1[1]1∧x0[0]=x0[1]1∧x2[0]=x2[1]1 ⇒ 1005_0_MAIN_LE(x1[0], x0[0])≥NonInfC∧1005_0_MAIN_LE(x1[0], x0[0])≥COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])∧(U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥))

We simplified constraint (1) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>(+(x0[1], -1), 0)=TRUE∧>(x2[0], -1)=TRUE∧>(x1[0], 0)=TRUE ⇒ 1005_0_MAIN_LE(x1[0], +(x0[1], -1))≥NonInfC∧1005_0_MAIN_LE(x1[0], +(x0[1], -1))≥COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(+(x0[1], -1), 0)), x1[0], +(x0[1], -1), x2[0])∧(U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[1] + [-2] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥)∧[(-2)bni_17 + (-1)Bound*bni_17] + [bni_17]x0[1] ≥ 0∧[(-1)bso_18] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[1] + [-2] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥)∧[(-2)bni_17 + (-1)Bound*bni_17] + [bni_17]x0[1] ≥ 0∧[(-1)bso_18] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[1] + [-2] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥)∧[(-2)bni_17 + (-1)Bound*bni_17] + [bni_17]x0[1] ≥ 0∧[(-1)bso_18] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x0[1] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x0[1] ≥ 0∧[(-1)bso_18] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x0[1] ≥ 0∧x2[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x0[1] ≥ 0∧[(-1)bso_18] ≥ 0)
We consider the chain COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(+(x1[3], -1), x0[3]), 1005_0_MAIN_LE(x1[0], x0[0]) → COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0]), COND_1005_0_MAIN_LE(TRUE, x1[1], x0[1], x2[1]) → 1005_0_MAIN_LE(x2[1], +(x0[1], -1)) which results in the following constraint:
(8)    (+(x1[3], -1)=x1[0]∧x0[3]=x0[0]∧&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0))=TRUE∧x1[0]=x1[1]∧x0[0]=x0[1]∧x2[0]=x2[1] ⇒ 1005_0_MAIN_LE(x1[0], x0[0])≥NonInfC∧1005_0_MAIN_LE(x1[0], x0[0])≥COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])∧(U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥))

We simplified constraint (8) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(9)    (>(x0[0], 0)=TRUE∧>(x2[0], -1)=TRUE∧>(+(x1[3], -1), 0)=TRUE ⇒ 1005_0_MAIN_LE(+(x1[3], -1), x0[0])≥NonInfC∧1005_0_MAIN_LE(+(x1[3], -1), x0[0])≥COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(+(x1[3], -1), 0)), >(x0[0], 0)), +(x1[3], -1), x0[0], x2[0])∧(U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥))

We simplified constraint (9) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(10)    (x0[0] + [-1] ≥ 0∧x2[0] ≥ 0∧x1[3] + [-2] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x0[0] ≥ 0∧[(-1)bso_18] ≥ 0)

We simplified constraint (10) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(11)    (x0[0] + [-1] ≥ 0∧x2[0] ≥ 0∧x1[3] + [-2] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x0[0] ≥ 0∧[(-1)bso_18] ≥ 0)

We simplified constraint (11) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(12)    (x0[0] + [-1] ≥ 0∧x2[0] ≥ 0∧x1[3] + [-2] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]x0[0] ≥ 0∧[(-1)bso_18] ≥ 0)

We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(13)    (x0[0] ≥ 0∧x2[0] ≥ 0∧x1[3] + [-2] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x0[0] ≥ 0∧[(-1)bso_18] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    (x0[0] ≥ 0∧x2[0] ≥ 0∧x1[3] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x0[0] ≥ 0∧[(-1)bso_18] ≥ 0)

For Pair COND_1005_0_MAIN_LE(TRUE, x1, x0, x2) → 1005_0_MAIN_LE(x2, +(x0, -1)) the following chains were created:

We consider the chain 1005_0_MAIN_LE(x1[0], x0[0]) → COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0]), COND_1005_0_MAIN_LE(TRUE, x1[1], x0[1], x2[1]) → 1005_0_MAIN_LE(x2[1], +(x0[1], -1)), 1005_0_MAIN_LE(x1[0], x0[0]) → COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0]) which results in the following constraint:
(15)    (&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0))=TRUE∧x1[0]=x1[1]∧x0[0]=x0[1]∧x2[0]=x2[1]∧x2[1]=x1[0]1∧+(x0[1], -1)=x0[0]1 ⇒ COND_1005_0_MAIN_LE(TRUE, x1[1], x0[1], x2[1])≥NonInfC∧COND_1005_0_MAIN_LE(TRUE, x1[1], x0[1], x2[1])≥1005_0_MAIN_LE(x2[1], +(x0[1], -1))∧(U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥))

We simplified constraint (15) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(16)    (>(x0[0], 0)=TRUE∧>(x2[0], -1)=TRUE∧>(x1[0], 0)=TRUE ⇒ COND_1005_0_MAIN_LE(TRUE, x1[0], x0[0], x2[0])≥NonInfC∧COND_1005_0_MAIN_LE(TRUE, x1[0], x0[0], x2[0])≥1005_0_MAIN_LE(x2[0], +(x0[0], -1))∧(U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥))

We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(17)    (x0[0] + [-1] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]x0[0] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (17) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(18)    (x0[0] + [-1] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]x0[0] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (18) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(19)    (x0[0] + [-1] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]x0[0] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (19) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(20)    (x0[0] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]x0[0] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (20) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(21)    (x0[0] ≥ 0∧x2[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]x0[0] ≥ 0∧[1 + (-1)bso_20] ≥ 0)
We consider the chain 1005_0_MAIN_LE(x1[0], x0[0]) → COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0]), COND_1005_0_MAIN_LE(TRUE, x1[1], x0[1], x2[1]) → 1005_0_MAIN_LE(x2[1], +(x0[1], -1)), 1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2]) which results in the following constraint:
(22)    (&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0))=TRUE∧x1[0]=x1[1]∧x0[0]=x0[1]∧x2[0]=x2[1]∧x2[1]=x1[2]∧+(x0[1], -1)=x0[2] ⇒ COND_1005_0_MAIN_LE(TRUE, x1[1], x0[1], x2[1])≥NonInfC∧COND_1005_0_MAIN_LE(TRUE, x1[1], x0[1], x2[1])≥1005_0_MAIN_LE(x2[1], +(x0[1], -1))∧(U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥))

We simplified constraint (22) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(23)    (>(x0[0], 0)=TRUE∧>(x2[0], -1)=TRUE∧>(x1[0], 0)=TRUE ⇒ COND_1005_0_MAIN_LE(TRUE, x1[0], x0[0], x2[0])≥NonInfC∧COND_1005_0_MAIN_LE(TRUE, x1[0], x0[0], x2[0])≥1005_0_MAIN_LE(x2[0], +(x0[0], -1))∧(U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥))

We simplified constraint (23) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(24)    (x0[0] + [-1] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]x0[0] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (24) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(25)    (x0[0] + [-1] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]x0[0] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (25) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(26)    (x0[0] + [-1] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]x0[0] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (26) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(27)    (x0[0] ≥ 0∧x2[0] ≥ 0∧x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]x0[0] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (27) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(28)    (x0[0] ≥ 0∧x2[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]x0[0] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

For Pair 1005_0_MAIN_LE(x1, x0) → COND_1005_0_MAIN_LE1(&&(>(x1, 0), >(x0, 0)), x1, x0) the following chains were created:

We consider the chain 1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2]), COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(+(x1[3], -1), x0[3]) which results in the following constraint:
(29)    (&&(>(x1[2], 0), >(x0[2], 0))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3] ⇒ 1005_0_MAIN_LE(x1[2], x0[2])≥NonInfC∧1005_0_MAIN_LE(x1[2], x0[2])≥COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])∧(U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥))

We simplified constraint (29) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(30)    (>(x1[2], 0)=TRUE∧>(x0[2], 0)=TRUE ⇒ 1005_0_MAIN_LE(x1[2], x0[2])≥NonInfC∧1005_0_MAIN_LE(x1[2], x0[2])≥COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])∧(U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥))

We simplified constraint (30) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(31)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]x0[2] ≥ 0∧[(-1)bso_22] ≥ 0)

We simplified constraint (31) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(32)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]x0[2] ≥ 0∧[(-1)bso_22] ≥ 0)

We simplified constraint (32) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(33)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]x0[2] ≥ 0∧[(-1)bso_22] ≥ 0)

We simplified constraint (33) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(34)    (x1[2] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]x0[2] ≥ 0∧[(-1)bso_22] ≥ 0)

We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(35)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥)∧[(-1)Bound*bni_21] + [bni_21]x0[2] ≥ 0∧[(-1)bso_22] ≥ 0)

For Pair COND_1005_0_MAIN_LE1(TRUE, x1, x0) → 1005_0_MAIN_LE(+(x1, -1), x0) the following chains were created:

We consider the chain 1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2]), COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(+(x1[3], -1), x0[3]), 1005_0_MAIN_LE(x1[0], x0[0]) → COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0]) which results in the following constraint:
(36)    (&&(>(x1[2], 0), >(x0[2], 0))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧+(x1[3], -1)=x1[0]∧x0[3]=x0[0] ⇒ COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3])≥NonInfC∧COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3])≥1005_0_MAIN_LE(+(x1[3], -1), x0[3])∧(U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥))

We simplified constraint (36) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(37)    (>(x1[2], 0)=TRUE∧>(x0[2], 0)=TRUE ⇒ COND_1005_0_MAIN_LE1(TRUE, x1[2], x0[2])≥NonInfC∧COND_1005_0_MAIN_LE1(TRUE, x1[2], x0[2])≥1005_0_MAIN_LE(+(x1[2], -1), x0[2])∧(U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥))

We simplified constraint (37) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(38)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] ≥ 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (38) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(39)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] ≥ 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (39) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(40)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] ≥ 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (40) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(41)    (x1[2] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] ≥ 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (41) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(42)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)Bound*bni_23] + [bni_23]x0[2] ≥ 0∧[(-1)bso_24] ≥ 0)
We consider the chain 1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2]), COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(+(x1[3], -1), x0[3]), 1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2]) which results in the following constraint:
(43)    (&&(>(x1[2], 0), >(x0[2], 0))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧+(x1[3], -1)=x1[2]1∧x0[3]=x0[2]1 ⇒ COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3])≥NonInfC∧COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3])≥1005_0_MAIN_LE(+(x1[3], -1), x0[3])∧(U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥))

We simplified constraint (43) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(44)    (>(x1[2], 0)=TRUE∧>(x0[2], 0)=TRUE ⇒ COND_1005_0_MAIN_LE1(TRUE, x1[2], x0[2])≥NonInfC∧COND_1005_0_MAIN_LE1(TRUE, x1[2], x0[2])≥1005_0_MAIN_LE(+(x1[2], -1), x0[2])∧(U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥))

We simplified constraint (44) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(45)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] ≥ 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (45) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(46)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] ≥ 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (46) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(47)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] ≥ 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (47) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(48)    (x1[2] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)bni_23 + (-1)Bound*bni_23] + [bni_23]x0[2] ≥ 0∧[(-1)bso_24] ≥ 0)

We simplified constraint (48) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(49)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)Bound*bni_23] + [bni_23]x0[2] ≥ 0∧[(-1)bso_24] ≥ 0)

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

1005_0_MAIN_LE(x1, x0) → COND_1005_0_MAIN_LE(&&(&&(>(x2, -1), >(x1, 0)), >(x0, 0)), x1, x0, x2)
- (x0[1] ≥ 0∧x2[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x0[1] ≥ 0∧[(-1)bso_18] ≥ 0)
- (x0[0] ≥ 0∧x2[0] ≥ 0∧x1[3] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])), ≥)∧[(-1)Bound*bni_17] + [bni_17]x0[0] ≥ 0∧[(-1)bso_18] ≥ 0)
COND_1005_0_MAIN_LE(TRUE, x1, x0, x2) → 1005_0_MAIN_LE(x2, +(x0, -1))
- (x0[0] ≥ 0∧x2[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]x0[0] ≥ 0∧[1 + (-1)bso_20] ≥ 0)
- (x0[0] ≥ 0∧x2[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(x2[1], +(x0[1], -1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]x0[0] ≥ 0∧[1 + (-1)bso_20] ≥ 0)
1005_0_MAIN_LE(x1, x0) → COND_1005_0_MAIN_LE1(&&(>(x1, 0), >(x0, 0)), x1, x0)
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥)∧[(-1)Bound*bni_21] + [bni_21]x0[2] ≥ 0∧[(-1)bso_22] ≥ 0)
COND_1005_0_MAIN_LE1(TRUE, x1, x0) → 1005_0_MAIN_LE(+(x1, -1), x0)
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)Bound*bni_23] + [bni_23]x0[2] ≥ 0∧[(-1)bso_24] ≥ 0)
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)Bound*bni_23] + [bni_23]x0[2] ≥ 0∧[(-1)bso_24] ≥ 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) = [3]
POL(1005_0_MAIN_LE(x₁, x₂)) = [-1] + x₂
POL(COND_1005_0_MAIN_LE(x₁, x₂, x₃, x₄)) = [-1] + x₃
POL(&&(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(-1) = [-1]
POL(0) = 0
POL(+(x₁, x₂)) = x₁ + x₂
POL(COND_1005_0_MAIN_LE1(x₁, x₂, x₃)) = [-1] + x₃

The following pairs are in P_>:

COND_1005_0_MAIN_LE(TRUE, x1[1], x0[1], x2[1]) → 1005_0_MAIN_LE(x2[1], +(x0[1], -1))

The following pairs are in P_bound:

1005_0_MAIN_LE(x1[0], x0[0]) → COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])
COND_1005_0_MAIN_LE(TRUE, x1[1], x0[1], x2[1]) → 1005_0_MAIN_LE(x2[1], +(x0[1], -1))
1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])
COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(+(x1[3], -1), x0[3])

The following pairs are in P_≥:

1005_0_MAIN_LE(x1[0], x0[0]) → COND_1005_0_MAIN_LE(&&(&&(>(x2[0], -1), >(x1[0], 0)), >(x0[0], 0)), x1[0], x0[0], x2[0])
1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])
COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(+(x1[3], -1), x0[3])

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

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

(8) 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): 1005_0_MAIN_LE(x1[0], x0[0]) → COND_1005_0_MAIN_LE(x2[0] > -1 && x1[0] > 0 && x0[0] > 0, x1[0], x0[0], x2[0])
(2): 1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(x1[2] > 0 && x0[2] > 0, x1[2], x0[2])
(3): COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(x1[3] + -1, x0[3])

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

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

(2) -> (3), if (x1[2] > 0 && x0[2] > 0 ∧x1[2] →^* x1[3]∧x0[2] →^* x0[3])

The set Q is empty.

(9) IDependencyGraphProof (EQUIVALENT transformation)

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

(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, Boolean

R is empty.

The integer pair graph contains the following rules and edges:
(3): COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(x1[3] + -1, x0[3])
(2): 1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(x1[2] > 0 && x0[2] > 0, x1[2], x0[2])

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

(2) -> (3), if (x1[2] > 0 && x0[2] > 0 ∧x1[2] →^* x1[3]∧x0[2] →^* x0[3])

The set Q is empty.

(11) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@7571ccae 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 COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(+(x1[3], -1), x0[3]) the following chains were created:

We consider the chain 1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2]), COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(+(x1[3], -1), x0[3]), 1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2]) which results in the following constraint:
(1)    (&&(>(x1[2], 0), >(x0[2], 0))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧+(x1[3], -1)=x1[2]1∧x0[3]=x0[2]1 ⇒ COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3])≥NonInfC∧COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3])≥1005_0_MAIN_LE(+(x1[3], -1), x0[3])∧(U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥))

We simplified constraint (1) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>(x1[2], 0)=TRUE∧>(x0[2], 0)=TRUE ⇒ COND_1005_0_MAIN_LE1(TRUE, x1[2], x0[2])≥NonInfC∧COND_1005_0_MAIN_LE1(TRUE, x1[2], x0[2])≥1005_0_MAIN_LE(+(x1[2], -1), x0[2])∧(U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)bni_12 + (-1)Bound*bni_12] + [bni_12]x0[2] + [bni_12]x1[2] ≥ 0∧[(-1)bso_13] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)bni_12 + (-1)Bound*bni_12] + [bni_12]x0[2] + [bni_12]x1[2] ≥ 0∧[(-1)bso_13] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)bni_12 + (-1)Bound*bni_12] + [bni_12]x0[2] + [bni_12]x1[2] ≥ 0∧[(-1)bso_13] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x1[2] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)Bound*bni_12] + [bni_12]x0[2] + [bni_12]x1[2] ≥ 0∧[(-1)bso_13] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)Bound*bni_12 + bni_12] + [bni_12]x0[2] + [bni_12]x1[2] ≥ 0∧[(-1)bso_13] ≥ 0)

For Pair 1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2]) the following chains were created:

We consider the chain 1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2]), COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(+(x1[3], -1), x0[3]) which results in the following constraint:
(8)    (&&(>(x1[2], 0), >(x0[2], 0))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3] ⇒ 1005_0_MAIN_LE(x1[2], x0[2])≥NonInfC∧1005_0_MAIN_LE(x1[2], x0[2])≥COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])∧(U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥))

We simplified constraint (8) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(9)    (>(x1[2], 0)=TRUE∧>(x0[2], 0)=TRUE ⇒ 1005_0_MAIN_LE(x1[2], x0[2])≥NonInfC∧1005_0_MAIN_LE(x1[2], x0[2])≥COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])∧(U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥))

We simplified constraint (9) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(10)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥)∧[(-1)Bound*bni_14] + [bni_14]x0[2] + [bni_14]x1[2] ≥ 0∧[1 + (-1)bso_15] ≥ 0)

We simplified constraint (10) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(11)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥)∧[(-1)Bound*bni_14] + [bni_14]x0[2] + [bni_14]x1[2] ≥ 0∧[1 + (-1)bso_15] ≥ 0)

We simplified constraint (11) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(12)    (x1[2] + [-1] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥)∧[(-1)Bound*bni_14] + [bni_14]x0[2] + [bni_14]x1[2] ≥ 0∧[1 + (-1)bso_15] ≥ 0)

We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(13)    (x1[2] ≥ 0∧x0[2] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥)∧[(-1)Bound*bni_14 + bni_14] + [bni_14]x0[2] + [bni_14]x1[2] ≥ 0∧[1 + (-1)bso_15] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥)∧[(-1)Bound*bni_14 + (2)bni_14] + [bni_14]x0[2] + [bni_14]x1[2] ≥ 0∧[1 + (-1)bso_15] ≥ 0)

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

COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(+(x1[3], -1), x0[3])
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(1005_0_MAIN_LE(+(x1[3], -1), x0[3])), ≥)∧[(-1)Bound*bni_12 + bni_12] + [bni_12]x0[2] + [bni_12]x1[2] ≥ 0∧[(-1)bso_13] ≥ 0)
1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])
- (x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])), ≥)∧[(-1)Bound*bni_14 + (2)bni_14] + [bni_14]x0[2] + [bni_14]x1[2] ≥ 0∧[1 + (-1)bso_15] ≥ 0)

POL(TRUE) = [3]
POL(FALSE) = [3]
POL(COND_1005_0_MAIN_LE1(x₁, x₂, x₃)) = [-1] + x₃ + x₂
POL(1005_0_MAIN_LE(x₁, x₂)) = x₂ + x₁
POL(+(x₁, x₂)) = x₁ + x₂
POL(-1) = [-1]
POL(&&(x₁, x₂)) = [2]
POL(>(x₁, x₂)) = [-1]
POL(0) = 0

The following pairs are in P_>:

1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])

The following pairs are in P_bound:

COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(+(x1[3], -1), x0[3])
1005_0_MAIN_LE(x1[2], x0[2]) → COND_1005_0_MAIN_LE1(&&(>(x1[2], 0), >(x0[2], 0)), x1[2], x0[2])

The following pairs are in P_≥:

COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(+(x1[3], -1), x0[3])

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

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

(12) 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:
(3): COND_1005_0_MAIN_LE1(TRUE, x1[3], x0[3]) → 1005_0_MAIN_LE(x1[3] + -1, x0[3])

The set Q is empty.

(13) IDependencyGraphProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) JBCToGraph (SOUND transformation)

(2) Obligation:

(3) TerminationGraphToSCCProof (SOUND transformation)

(4) Obligation:

(5) SCCToIDPv1Proof (SOUND transformation)

(6) Obligation:

(7) IDPNonInfProof (SOUND transformation)

(8) Obligation:

(9) IDependencyGraphProof (EQUIVALENT transformation)

(10) Obligation:

(11) IDPNonInfProof (SOUND transformation)

(12) Obligation:

(13) IDependencyGraphProof (EQUIVALENT transformation)

(14) TRUE