Termination proof of /tmp/tmpK1Pd1Z/CyclicList.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBCToGraph (⇒, 430 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToSCCProof (⇒, 0 ms)

↳4 AND

    ↳5 JBCTerminationSCC

        ↳6 SCCToIDPv1Proof (⇒, 120 ms)

        ↳7 IDP

        ↳8 IDPNonInfProof (⇒, 1210 ms)

        ↳9 AND

            ↳10 IDP

                ↳11 IDependencyGraphProof (⇔, 0 ms)

                ↳12 TRUE

            ↳13 IDP

                ↳14 IDPNonInfProof (⇒, 210 ms)

                ↳15 IDP

                ↳16 IDependencyGraphProof (⇔, 0 ms)

                ↳17 TRUE

    ↳18 JBCTerminationSCC

        ↳19 SCCToIDPv1Proof (⇒, 40 ms)

        ↳20 IDP

        ↳21 IDPNonInfProof (⇒, 130 ms)

        ↳22 AND

            ↳23 IDP

                ↳24 IDependencyGraphProof (⇔, 0 ms)

                ↳25 TRUE

            ↳26 IDP

                ↳27 IDependencyGraphProof (⇔, 0 ms)

                ↳28 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_20 (Sun Microsystems Inc.) Main-Class: CyclicList

/**
 * This class represents a list. The function get(n) can be used to access
 * the n-th element. 
 * @author Marc Brockschmidt
 */
public class CyclicList {
	/**
	 * A reference to the next list element.
	 */
	private CyclicList next;
	
	public static void main(String[] args) {
		CyclicList list = CyclicList.create(args.length);
		list.get(args[0].length());
	}
	
	/**
	 * Create a new list element.
	 * @param n a reference to the next element.
	 */
	public CyclicList(final CyclicList n) {
		this.next = n;
	}
	
	/**
	 * Create a new cyclical list of a length l.
	 * @param l some length
	 * @return cyclical list of length max(1, l)
	 */
	public static CyclicList create(int x) {
		CyclicList last, current;
		last = current = new CyclicList(null);
		while (--x > 0)
			current = new CyclicList(current);
		return last.next = current;
	}

	public CyclicList get(int n) {
		CyclicList cur = this;
		while (--n > 0) {
			cur = cur.next;
		}
		return cur;
	}	
}

(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
CyclicList.main([Ljava/lang/String;)V: Graph of 246 nodes with 2 SCCs.

(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 2 SCCss.

(4) Complex Obligation (AND)

(5) Obligation:

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

(6) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 18 rules for P and 0 rules for R.

P rules:
897_0_get_Load(EOS(STATIC_897), java.lang.Object(o338sub0), i221, o3370) → 912_0_get_LE(EOS(STATIC_912), java.lang.Object(o338sub0), i221, o3370, i221)
912_0_get_LE(EOS(STATIC_912), java.lang.Object(o338sub0), i234, o3370, i234) → 926_0_get_LE(EOS(STATIC_926), java.lang.Object(o338sub0), i234, o3370, i234)
926_0_get_LE(EOS(STATIC_926), java.lang.Object(o338sub0), i234, o3370, i234) → 941_0_get_Load(EOS(STATIC_941), java.lang.Object(o338sub0), i234, o3370) | >(i234, 0)
941_0_get_Load(EOS(STATIC_941), java.lang.Object(o338sub0), i234, o3370) → 960_0_get_FieldAccess(EOS(STATIC_960), java.lang.Object(o338sub0), i234, o3370)
960_0_get_FieldAccess(EOS(STATIC_960), java.lang.Object(o338sub0), i234, java.lang.Object(o406sub0)) → 974_0_get_FieldAccess(EOS(STATIC_974), java.lang.Object(o338sub0), i234, java.lang.Object(o406sub0))
974_0_get_FieldAccess(EOS(STATIC_974), java.lang.Object(o338sub0), i234, java.lang.Object(o406sub0)) → 989_0_get_FieldAccess(EOS(STATIC_989), java.lang.Object(o338sub0), i234, java.lang.Object(o406sub0))
974_0_get_FieldAccess(EOS(STATIC_974), java.lang.Object(o338sub0), i234, java.lang.Object(o338sub0)) → 991_0_get_FieldAccess(EOS(STATIC_991), java.lang.Object(o338sub0), i234, java.lang.Object(o338sub0))
989_0_get_FieldAccess(EOS(STATIC_989), java.lang.Object(o338sub0), i234, java.lang.Object(CyclicList(EOC, o4202125997956))) → 999_0_get_FieldAccess(EOS(STATIC_999), java.lang.Object(o338sub0), i234, java.lang.Object(CyclicList(EOC, o4202125997956)))
999_0_get_FieldAccess(EOS(STATIC_999), java.lang.Object(o338sub0), i234, java.lang.Object(CyclicList(EOC, o4202125997956))) → 1005_0_get_Store(EOS(STATIC_1005), java.lang.Object(o338sub0), i234, o4200)
1005_0_get_Store(EOS(STATIC_1005), java.lang.Object(o338sub0), i234, o4200) → 1010_0_get_JMP(EOS(STATIC_1010), java.lang.Object(o338sub0), i234, o4200)
1010_0_get_JMP(EOS(STATIC_1010), java.lang.Object(o338sub0), i234, o4200) → 1018_0_get_Inc(EOS(STATIC_1018), java.lang.Object(o338sub0), i234, o4200)
1018_0_get_Inc(EOS(STATIC_1018), java.lang.Object(o338sub0), i234, o4200) → 883_0_get_Inc(EOS(STATIC_883), java.lang.Object(o338sub0), i234, o4200)
883_0_get_Inc(EOS(STATIC_883), java.lang.Object(o338sub0), i207, o3370) → 897_0_get_Load(EOS(STATIC_897), java.lang.Object(o338sub0), +(i207, -1), o3370) | >=(i207, 0)
991_0_get_FieldAccess(EOS(STATIC_991), java.lang.Object(CyclicList(EOC, o4222125998669)), i234, java.lang.Object(CyclicList(EOC, o4222125998669))) → 1001_0_get_FieldAccess(EOS(STATIC_1001), java.lang.Object(CyclicList(EOC, o4222125998669)), i234, java.lang.Object(CyclicList(EOC, o4222125998669)))
1001_0_get_FieldAccess(EOS(STATIC_1001), java.lang.Object(CyclicList(EOC, o4222125998669)), i234, java.lang.Object(CyclicList(EOC, o4222125998669))) → 1008_0_get_Store(EOS(STATIC_1008), java.lang.Object(CyclicList(EOC, o4222125998669)), i234, o4220)
1008_0_get_Store(EOS(STATIC_1008), java.lang.Object(CyclicList(EOC, o4222125998669)), i234, o4220) → 1012_0_get_JMP(EOS(STATIC_1012), java.lang.Object(CyclicList(EOC, o4222125998669)), i234, o4220)
1012_0_get_JMP(EOS(STATIC_1012), java.lang.Object(CyclicList(EOC, o4222125998669)), i234, o4220) → 1019_0_get_Inc(EOS(STATIC_1019), java.lang.Object(CyclicList(EOC, o4222125998669)), i234, o4220)
1019_0_get_Inc(EOS(STATIC_1019), java.lang.Object(CyclicList(EOC, o4222125998669)), i234, o4220) → 883_0_get_Inc(EOS(STATIC_883), java.lang.Object(CyclicList(EOC, o4222125998669)), i234, o4220)
R rules:

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

P rules:
897_0_get_Load(EOS(STATIC_897), java.lang.Object(x0), x1, java.lang.Object(CyclicList(EOC, x2))) → 897_0_get_Load(EOS(STATIC_897), java.lang.Object(x0), +(x1, -1), x3) | >(x1, 0)
897_0_get_Load(EOS(STATIC_897), java.lang.Object(CyclicList(EOC, x0)), x1, java.lang.Object(CyclicList(EOC, x0))) → 897_0_get_Load(EOS(STATIC_897), java.lang.Object(CyclicList(EOC, x0)), +(x1, -1), x2) | >(x1, 0)
R rules:

Filtered ground terms:

897_0_get_Load(x1, x2, x3, x4) → 897_0_get_Load(x2, x3, x4)
CyclicList(x1, x2) → CyclicList(x2)
EOS(x1) → EOS
Cond_897_0_get_Load1(x1, x2, x3, x4, x5, x6) → Cond_897_0_get_Load1(x1, x3, x4, x5, x6)
Cond_897_0_get_Load(x1, x2, x3, x4, x5, x6) → Cond_897_0_get_Load(x1, x3, x4, x5, x6)

Filtered duplicate args:

Cond_897_0_get_Load1(x1, x2, x3, x4, x5) → Cond_897_0_get_Load1(x1, x3, x4, x5)

Filtered unneeded arguments:

Cond_897_0_get_Load(x1, x2, x3, x4, x5) → Cond_897_0_get_Load(x1, x2, x3, x5)
Cond_897_0_get_Load1(x1, x2, x3, x4) → Cond_897_0_get_Load1(x1, x2, x4)

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

P rules:
897_0_get_Load(java.lang.Object(x0), x1, java.lang.Object(CyclicList(x2))) → 897_0_get_Load(java.lang.Object(x0), +(x1, -1), x3) | >(x1, 0)
897_0_get_Load(java.lang.Object(CyclicList(x0)), x1, java.lang.Object(CyclicList(x0))) → 897_0_get_Load(java.lang.Object(CyclicList(x0)), +(x1, -1), x2) | >(x1, 0)
R rules:

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

P rules:
897_0_GET_LOAD(java.lang.Object(x0), x1, java.lang.Object(CyclicList(x2))) → COND_897_0_GET_LOAD(>(x1, 0), java.lang.Object(x0), x1, java.lang.Object(CyclicList(x2)), x3)
COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0), x1, java.lang.Object(CyclicList(x2)), x3) → 897_0_GET_LOAD(java.lang.Object(x0), +(x1, -1), x3)
897_0_GET_LOAD(java.lang.Object(CyclicList(x0)), x1, java.lang.Object(CyclicList(x0))) → COND_897_0_GET_LOAD1(>(x1, 0), java.lang.Object(CyclicList(x0)), x1, java.lang.Object(CyclicList(x0)), x2)
COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0)), x1, java.lang.Object(CyclicList(x0)), x2) → 897_0_GET_LOAD(java.lang.Object(CyclicList(x0)), +(x1, -1), x2)
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): 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(x1[0] > 0, java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])
(1): COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), x1[1] + -1, x3[1])
(2): 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2]))) → COND_897_0_GET_LOAD1(x1[2] > 0, java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])
(3): COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3]) → 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), x1[3] + -1, x2[3])

(0) -> (1), if (x1[0] > 0 ∧java.lang.Object(x0[0]) →^* java.lang.Object(x0[1])∧x1[0] →^* x1[1]∧java.lang.Object(CyclicList(x2[0])) →^* java.lang.Object(CyclicList(x2[1]))∧x3[0] →^* x3[1])

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

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

(2) -> (3), if (x1[2] > 0 ∧java.lang.Object(CyclicList(x0[2])) →^* java.lang.Object(CyclicList(x0[3]))∧x1[2] →^* x1[3]∧x2[2] →^* x2[3])

(3) -> (0), if (java.lang.Object(CyclicList(x0[3])) →^* java.lang.Object(x0[0])∧x1[3] + -1 →^* x1[0]∧x2[3] →^* java.lang.Object(CyclicList(x2[0])))

(3) -> (2), if (java.lang.Object(CyclicList(x0[3])) →^* java.lang.Object(CyclicList(x0[2]))∧x1[3] + -1 →^* x1[2]∧x2[3] →^* java.lang.Object(CyclicList(x0[2])))

The set Q is empty.

(8) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@606e685a 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 897_0_GET_LOAD(java.lang.Object(x0), x1, java.lang.Object(CyclicList(x2))) → COND_897_0_GET_LOAD(>(x1, 0), java.lang.Object(x0), x1, java.lang.Object(CyclicList(x2)), x3) the following chains were created:

We consider the chain COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1]), 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0]), COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1]) which results in the following constraint:
(1)    (java.lang.Object(x0[1])=java.lang.Object(x0[0])∧+(x1[1], -1)=x1[0]∧x3[1]=java.lang.Object(CyclicList(x2[0]))∧>(x1[0], 0)=TRUE∧java.lang.Object(x0[0])=java.lang.Object(x0[1]1)∧x1[0]=x1[1]1∧java.lang.Object(CyclicList(x2[0]))=java.lang.Object(CyclicList(x2[1]1))∧x3[0]=x3[1]1 ⇒ 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])))≥NonInfC∧897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])))≥COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])∧(U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥))

We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
(2)    (>(+(x1[1], -1), 0)=TRUE ⇒ 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), java.lang.Object(CyclicList(x2[0])))≥NonInfC∧897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), java.lang.Object(CyclicList(x2[0])))≥COND_897_0_GET_LOAD(>(+(x1[1], -1), 0), java.lang.Object(x0[1]), +(x1[1], -1), java.lang.Object(CyclicList(x2[0])), x3[0])∧(U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x1[1] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[1] + [(-2)bni_24]x0[1] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x1[1] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[1] + [(-2)bni_24]x0[1] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x1[1] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[1] + [(-2)bni_24]x0[1] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (x1[1] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧0 = 0∧[(-2)bni_24] = 0∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x1[1] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧0 = 0∧[(-2)bni_24] = 0∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_25] ≥ 0)
We consider the chain COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3]) → 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3]), 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0]), COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1]) which results in the following constraint:
(8)    (java.lang.Object(CyclicList(x0[3]))=java.lang.Object(x0[0])∧+(x1[3], -1)=x1[0]∧x2[3]=java.lang.Object(CyclicList(x2[0]))∧>(x1[0], 0)=TRUE∧java.lang.Object(x0[0])=java.lang.Object(x0[1])∧x1[0]=x1[1]∧java.lang.Object(CyclicList(x2[0]))=java.lang.Object(CyclicList(x2[1]))∧x3[0]=x3[1] ⇒ 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])))≥NonInfC∧897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])))≥COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])∧(U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥))

We simplified constraint (8) using rules (I), (II), (III), (IV) which results in the following new constraint:
(9)    (>(+(x1[3], -1), 0)=TRUE ⇒ 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), java.lang.Object(CyclicList(x2[0])))≥NonInfC∧897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), java.lang.Object(CyclicList(x2[0])))≥COND_897_0_GET_LOAD(>(+(x1[3], -1), 0), java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), java.lang.Object(CyclicList(x2[0])), x3[0])∧(U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥))

We simplified constraint (9) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(10)    (x1[3] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[3] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (10) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(11)    (x1[3] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[3] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (11) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(12)    (x1[3] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[3] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (12) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(13)    (x1[3] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧0 = 0∧0 = 0∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    (x1[3] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧0 = 0∧0 = 0∧[(3)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_25] ≥ 0)

For Pair COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0), x1, java.lang.Object(CyclicList(x2)), x3) → 897_0_GET_LOAD(java.lang.Object(x0), +(x1, -1), x3) the following chains were created:

We consider the chain 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0]), COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1]), 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0]) which results in the following constraint:
(15)    (>(x1[0], 0)=TRUE∧java.lang.Object(x0[0])=java.lang.Object(x0[1])∧x1[0]=x1[1]∧java.lang.Object(CyclicList(x2[0]))=java.lang.Object(CyclicList(x2[1]))∧x3[0]=x3[1]∧java.lang.Object(x0[1])=java.lang.Object(x0[0]1)∧+(x1[1], -1)=x1[0]1∧x3[1]=java.lang.Object(CyclicList(x2[0]1)) ⇒ COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1])≥NonInfC∧COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1])≥897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])∧(U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥))

We simplified constraint (15) using rules (I), (II), (III), (IV) which results in the following new constraint:
(16)    (>(x1[0], 0)=TRUE ⇒ COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), java.lang.Object(CyclicList(x2[0]1)))≥NonInfC∧COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), java.lang.Object(CyclicList(x2[0]1)))≥897_0_GET_LOAD(java.lang.Object(x0[0]), +(x1[0], -1), java.lang.Object(CyclicList(x2[0]1)))∧(U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥))

We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(17)    (x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧[(-1)Bound*bni_26] + [bni_26]x1[0] + [(-2)bni_26]x0[0] ≥ 0∧[1 + (-1)bso_27] ≥ 0)

We simplified constraint (17) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(18)    (x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧[(-1)Bound*bni_26] + [bni_26]x1[0] + [(-2)bni_26]x0[0] ≥ 0∧[1 + (-1)bso_27] ≥ 0)

We simplified constraint (18) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(19)    (x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧[(-1)Bound*bni_26] + [bni_26]x1[0] + [(-2)bni_26]x0[0] ≥ 0∧[1 + (-1)bso_27] ≥ 0)

We simplified constraint (19) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(20)    (x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧0 = 0∧0 = 0∧[(-2)bni_26] = 0∧[(-1)Bound*bni_26] + [bni_26]x1[0] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_27] ≥ 0)

We simplified constraint (20) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(21)    (x1[0] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧0 = 0∧0 = 0∧[(-2)bni_26] = 0∧[(-1)Bound*bni_26 + bni_26] + [bni_26]x1[0] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_27] ≥ 0)
We consider the chain 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0]), COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1]), 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2]))) → COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2]) which results in the following constraint:
(22)    (>(x1[0], 0)=TRUE∧java.lang.Object(x0[0])=java.lang.Object(x0[1])∧x1[0]=x1[1]∧java.lang.Object(CyclicList(x2[0]))=java.lang.Object(CyclicList(x2[1]))∧x3[0]=x3[1]∧java.lang.Object(x0[1])=java.lang.Object(CyclicList(x0[2]))∧+(x1[1], -1)=x1[2]∧x3[1]=java.lang.Object(CyclicList(x0[2])) ⇒ COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1])≥NonInfC∧COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1])≥897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])∧(U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥))

We simplified constraint (22) using rules (I), (II), (III), (IV) which results in the following new constraint:
(23)    (>(x1[0], 0)=TRUE ⇒ COND_897_0_GET_LOAD(TRUE, java.lang.Object(CyclicList(x0[2])), x1[0], java.lang.Object(CyclicList(x2[0])), java.lang.Object(CyclicList(x0[2])))≥NonInfC∧COND_897_0_GET_LOAD(TRUE, java.lang.Object(CyclicList(x0[2])), x1[0], java.lang.Object(CyclicList(x2[0])), java.lang.Object(CyclicList(x0[2])))≥897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), +(x1[0], -1), java.lang.Object(CyclicList(x0[2])))∧(U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥))

We simplified constraint (23) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(24)    (x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧[(2)bni_26 + (-1)Bound*bni_26] + [bni_26]x1[0] ≥ 0∧[1 + (-1)bso_27] ≥ 0)

We simplified constraint (24) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(25)    (x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧[(2)bni_26 + (-1)Bound*bni_26] + [bni_26]x1[0] ≥ 0∧[1 + (-1)bso_27] ≥ 0)

We simplified constraint (25) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(26)    (x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧[(2)bni_26 + (-1)Bound*bni_26] + [bni_26]x1[0] ≥ 0∧[1 + (-1)bso_27] ≥ 0)

We simplified constraint (26) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(27)    (x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧0 = 0∧0 = 0∧[(2)bni_26 + (-1)Bound*bni_26] + [bni_26]x1[0] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_27] ≥ 0)

We simplified constraint (27) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(28)    (x1[0] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧0 = 0∧0 = 0∧[(3)bni_26 + (-1)Bound*bni_26] + [bni_26]x1[0] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_27] ≥ 0)

For Pair 897_0_GET_LOAD(java.lang.Object(CyclicList(x0)), x1, java.lang.Object(CyclicList(x0))) → COND_897_0_GET_LOAD1(>(x1, 0), java.lang.Object(CyclicList(x0)), x1, java.lang.Object(CyclicList(x0)), x2) the following chains were created:

We consider the chain COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1]), 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2]))) → COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2]), COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3]) → 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3]) which results in the following constraint:
(29)    (java.lang.Object(x0[1])=java.lang.Object(CyclicList(x0[2]))∧+(x1[1], -1)=x1[2]∧x3[1]=java.lang.Object(CyclicList(x0[2]))∧>(x1[2], 0)=TRUE∧java.lang.Object(CyclicList(x0[2]))=java.lang.Object(CyclicList(x0[3]))∧x1[2]=x1[3]∧x2[2]=x2[3] ⇒ 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])))≥NonInfC∧897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])))≥COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])∧(U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥))

We simplified constraint (29) using rules (I), (II), (III), (IV) which results in the following new constraint:
(30)    (>(+(x1[1], -1), 0)=TRUE ⇒ 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), +(x1[1], -1), java.lang.Object(CyclicList(x0[2])))≥NonInfC∧897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), +(x1[1], -1), java.lang.Object(CyclicList(x0[2])))≥COND_897_0_GET_LOAD1(>(+(x1[1], -1), 0), java.lang.Object(CyclicList(x0[2])), +(x1[1], -1), java.lang.Object(CyclicList(x0[2])), x2[2])∧(U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥))

We simplified constraint (30) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(31)    (x1[1] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]x1[1] ≥ 0∧[(-1)bso_29] ≥ 0)

We simplified constraint (31) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(32)    (x1[1] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]x1[1] ≥ 0∧[(-1)bso_29] ≥ 0)

We simplified constraint (32) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(33)    (x1[1] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]x1[1] ≥ 0∧[(-1)bso_29] ≥ 0)

We simplified constraint (33) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(34)    (x1[1] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥)∧0 = 0∧[bni_28 + (-1)Bound*bni_28] + [bni_28]x1[1] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)

We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(35)    (x1[1] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥)∧0 = 0∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[1] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)
We consider the chain COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3]) → 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3]), 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2]))) → COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2]), COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3]) → 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3]) which results in the following constraint:
(36)    (java.lang.Object(CyclicList(x0[3]))=java.lang.Object(CyclicList(x0[2]))∧+(x1[3], -1)=x1[2]∧x2[3]=java.lang.Object(CyclicList(x0[2]))∧>(x1[2], 0)=TRUE∧java.lang.Object(CyclicList(x0[2]))=java.lang.Object(CyclicList(x0[3]1))∧x1[2]=x1[3]1∧x2[2]=x2[3]1 ⇒ 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])))≥NonInfC∧897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])))≥COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])∧(U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥))

We simplified constraint (36) using rules (I), (II), (III), (IV) which results in the following new constraint:
(37)    (>(+(x1[3], -1), 0)=TRUE ⇒ 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), java.lang.Object(CyclicList(x0[3])))≥NonInfC∧897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), java.lang.Object(CyclicList(x0[3])))≥COND_897_0_GET_LOAD1(>(+(x1[3], -1), 0), java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), java.lang.Object(CyclicList(x0[3])), x2[2])∧(U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥))

We simplified constraint (37) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(38)    (x1[3] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]x1[3] ≥ 0∧[(-1)bso_29] ≥ 0)

We simplified constraint (38) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(39)    (x1[3] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]x1[3] ≥ 0∧[(-1)bso_29] ≥ 0)

We simplified constraint (39) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(40)    (x1[3] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]x1[3] ≥ 0∧[(-1)bso_29] ≥ 0)

We simplified constraint (40) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(41)    (x1[3] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥)∧0 = 0∧[bni_28 + (-1)Bound*bni_28] + [bni_28]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)

We simplified constraint (41) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(42)    (x1[3] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥)∧0 = 0∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)

For Pair COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0)), x1, java.lang.Object(CyclicList(x0)), x2) → 897_0_GET_LOAD(java.lang.Object(CyclicList(x0)), +(x1, -1), x2) the following chains were created:

We consider the chain 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2]))) → COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2]), COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3]) → 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3]), 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0]) which results in the following constraint:
(43)    (>(x1[2], 0)=TRUE∧java.lang.Object(CyclicList(x0[2]))=java.lang.Object(CyclicList(x0[3]))∧x1[2]=x1[3]∧x2[2]=x2[3]∧java.lang.Object(CyclicList(x0[3]))=java.lang.Object(x0[0])∧+(x1[3], -1)=x1[0]∧x2[3]=java.lang.Object(CyclicList(x2[0])) ⇒ COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3])≥NonInfC∧COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3])≥897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])∧(U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥))

We simplified constraint (43) using rules (I), (II), (III), (IV) which results in the following new constraint:
(44)    (>(x1[2], 0)=TRUE ⇒ COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), java.lang.Object(CyclicList(x2[0])))≥NonInfC∧COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), java.lang.Object(CyclicList(x2[0])))≥897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), +(x1[2], -1), java.lang.Object(CyclicList(x2[0])))∧(U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥))

We simplified constraint (44) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(45)    (x1[2] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥)∧[(2)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

We simplified constraint (45) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(46)    (x1[2] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥)∧[(2)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

We simplified constraint (46) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(47)    (x1[2] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥)∧[(2)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

We simplified constraint (47) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(48)    (x1[2] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥)∧0 = 0∧0 = 0∧[(2)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_31] ≥ 0)

We simplified constraint (48) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(49)    (x1[2] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥)∧0 = 0∧0 = 0∧[(3)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_31] ≥ 0)
We consider the chain 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2]))) → COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2]), COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3]) → 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3]), 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2]))) → COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2]) which results in the following constraint:
(50)    (>(x1[2], 0)=TRUE∧java.lang.Object(CyclicList(x0[2]))=java.lang.Object(CyclicList(x0[3]))∧x1[2]=x1[3]∧x2[2]=x2[3]∧java.lang.Object(CyclicList(x0[3]))=java.lang.Object(CyclicList(x0[2]1))∧+(x1[3], -1)=x1[2]1∧x2[3]=java.lang.Object(CyclicList(x0[2]1)) ⇒ COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3])≥NonInfC∧COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3])≥897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])∧(U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥))

We simplified constraint (50) using rules (I), (II), (III), (IV) which results in the following new constraint:
(51)    (>(x1[2], 0)=TRUE ⇒ COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), java.lang.Object(CyclicList(x0[2])))≥NonInfC∧COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), java.lang.Object(CyclicList(x0[2])))≥897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), +(x1[2], -1), java.lang.Object(CyclicList(x0[2])))∧(U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥))

We simplified constraint (51) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(52)    (x1[2] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥)∧[(2)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

We simplified constraint (52) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(53)    (x1[2] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥)∧[(2)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

We simplified constraint (53) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(54)    (x1[2] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥)∧[(2)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] ≥ 0∧[1 + (-1)bso_31] ≥ 0)

We simplified constraint (54) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(55)    (x1[2] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥)∧0 = 0∧[(2)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] ≥ 0∧0 = 0∧[1 + (-1)bso_31] ≥ 0)

We simplified constraint (55) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(56)    (x1[2] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥)∧0 = 0∧[(3)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] ≥ 0∧0 = 0∧[1 + (-1)bso_31] ≥ 0)

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

897_0_GET_LOAD(java.lang.Object(x0), x1, java.lang.Object(CyclicList(x2))) → COND_897_0_GET_LOAD(>(x1, 0), java.lang.Object(x0), x1, java.lang.Object(CyclicList(x2)), x3)
- (x1[1] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧0 = 0∧[(-2)bni_24] = 0∧[bni_24 + (-1)Bound*bni_24] + [bni_24]x1[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_25] ≥ 0)
- (x1[3] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧0 = 0∧0 = 0∧[(3)bni_24 + (-1)Bound*bni_24] + [bni_24]x1[3] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_25] ≥ 0)
COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0), x1, java.lang.Object(CyclicList(x2)), x3) → 897_0_GET_LOAD(java.lang.Object(x0), +(x1, -1), x3)
- (x1[0] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧0 = 0∧0 = 0∧[(-2)bni_26] = 0∧[(-1)Bound*bni_26 + bni_26] + [bni_26]x1[0] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_27] ≥ 0)
- (x1[0] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧0 = 0∧0 = 0∧[(3)bni_26 + (-1)Bound*bni_26] + [bni_26]x1[0] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_27] ≥ 0)
897_0_GET_LOAD(java.lang.Object(CyclicList(x0)), x1, java.lang.Object(CyclicList(x0))) → COND_897_0_GET_LOAD1(>(x1, 0), java.lang.Object(CyclicList(x0)), x1, java.lang.Object(CyclicList(x0)), x2)
- (x1[1] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥)∧0 = 0∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[1] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)
- (x1[3] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])), ≥)∧0 = 0∧[(3)bni_28 + (-1)Bound*bni_28] + [bni_28]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_29] ≥ 0)
COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0)), x1, java.lang.Object(CyclicList(x0)), x2) → 897_0_GET_LOAD(java.lang.Object(CyclicList(x0)), +(x1, -1), x2)
- (x1[2] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥)∧0 = 0∧0 = 0∧[(3)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_31] ≥ 0)
- (x1[2] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])), ≥)∧0 = 0∧[(3)bni_30 + (-1)Bound*bni_30] + [bni_30]x1[2] ≥ 0∧0 = 0∧[1 + (-1)bso_31] ≥ 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) = [2]
POL(FALSE) = 0
POL(897_0_GET_LOAD(x₁, x₂, x₃)) = [1] + [-1]x₃ + x₂ + [2]x₁
POL(java.lang.Object(x₁)) = [-1]x₁
POL(CyclicList(x₁)) = [-1]
POL(COND_897_0_GET_LOAD(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₄ + x₃ + [2]x₂
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(+(x₁, x₂)) = x₁ + x₂
POL(-1) = [-1]
POL(COND_897_0_GET_LOAD1(x₁, x₂, x₃, x₄, x₅)) = x₄ + x₃ + x₂

The following pairs are in P_>:

COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])
COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3]) → 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])

The following pairs are in P_bound:

897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2]))) → COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])
COND_897_0_GET_LOAD1(TRUE, java.lang.Object(CyclicList(x0[3])), x1[3], java.lang.Object(CyclicList(x0[3])), x2[3]) → 897_0_GET_LOAD(java.lang.Object(CyclicList(x0[3])), +(x1[3], -1), x2[3])

The following pairs are in P_≥:

897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])
897_0_GET_LOAD(java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2]))) → COND_897_0_GET_LOAD1(>(x1[2], 0), java.lang.Object(CyclicList(x0[2])), x1[2], java.lang.Object(CyclicList(x0[2])), x2[2])

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

(11) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.

(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

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

The set Q is empty.

(14) 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@606e685a 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 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0]) the following chains were created:

We consider the chain COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1]), 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0]), COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1]) which results in the following constraint:
(1)    (java.lang.Object(x0[1])=java.lang.Object(x0[0])∧+(x1[1], -1)=x1[0]∧x3[1]=java.lang.Object(CyclicList(x2[0]))∧>(x1[0], 0)=TRUE∧java.lang.Object(x0[0])=java.lang.Object(x0[1]1)∧x1[0]=x1[1]1∧java.lang.Object(CyclicList(x2[0]))=java.lang.Object(CyclicList(x2[1]1))∧x3[0]=x3[1]1 ⇒ 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])))≥NonInfC∧897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])))≥COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])∧(U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥))

We simplified constraint (1) using rules (I), (II), (III), (IV) which results in the following new constraint:
(2)    (>(+(x1[1], -1), 0)=TRUE ⇒ 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), java.lang.Object(CyclicList(x2[0])))≥NonInfC∧897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), java.lang.Object(CyclicList(x2[0])))≥COND_897_0_GET_LOAD(>(+(x1[1], -1), 0), java.lang.Object(x0[1]), +(x1[1], -1), java.lang.Object(CyclicList(x2[0])), x3[0])∧(U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x1[1] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[1] ≥ 0∧[1 + (-1)bso_19] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x1[1] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[1] ≥ 0∧[1 + (-1)bso_19] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x1[1] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[1] ≥ 0∧[1 + (-1)bso_19] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (x1[1] + [-2] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧0 = 0∧0 = 0∧[bni_18 + (-1)Bound*bni_18] + [bni_18]x1[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_19] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x1[1] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧0 = 0∧0 = 0∧[(3)bni_18 + (-1)Bound*bni_18] + [bni_18]x1[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_19] ≥ 0)

For Pair COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1]) the following chains were created:

We consider the chain 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0]), COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1]), 897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0]) which results in the following constraint:
(8)    (>(x1[0], 0)=TRUE∧java.lang.Object(x0[0])=java.lang.Object(x0[1])∧x1[0]=x1[1]∧java.lang.Object(CyclicList(x2[0]))=java.lang.Object(CyclicList(x2[1]))∧x3[0]=x3[1]∧java.lang.Object(x0[1])=java.lang.Object(x0[0]1)∧+(x1[1], -1)=x1[0]1∧x3[1]=java.lang.Object(CyclicList(x2[0]1)) ⇒ COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1])≥NonInfC∧COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1])≥897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])∧(U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥))

We simplified constraint (8) using rules (I), (II), (III), (IV) which results in the following new constraint:
(9)    (>(x1[0], 0)=TRUE ⇒ COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), java.lang.Object(CyclicList(x2[0]1)))≥NonInfC∧COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), java.lang.Object(CyclicList(x2[0]1)))≥897_0_GET_LOAD(java.lang.Object(x0[0]), +(x1[0], -1), java.lang.Object(CyclicList(x2[0]1)))∧(U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥))

We simplified constraint (9) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(10)    (x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[0] ≥ 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (10) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(11)    (x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[0] ≥ 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (11) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(12)    (x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[0] ≥ 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (12) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(13)    (x1[0] + [-1] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[bni_20 + (-1)Bound*bni_20] + [bni_20]x1[0] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    (x1[0] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(2)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[0] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_21] ≥ 0)

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

897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])
- (x1[1] ≥ 0 ⇒ (U^Increasing(COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])), ≥)∧0 = 0∧0 = 0∧[(3)bni_18 + (-1)Bound*bni_18] + [bni_18]x1[1] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_19] ≥ 0)
COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])
- (x1[0] ≥ 0 ⇒ (U^Increasing(897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(2)bni_20 + (-1)Bound*bni_20] + [bni_20]x1[0] ≥ 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_21] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(897_0_GET_LOAD(x₁, x₂, x₃)) = [1] + x₂ + [-1]x₁
POL(java.lang.Object(x₁)) = [-1]
POL(CyclicList(x₁)) = [2] + [-1]x₁
POL(COND_897_0_GET_LOAD(x₁, x₂, x₃, x₄, x₅)) = [2] + x₄ + x₃
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(+(x₁, x₂)) = x₁ + x₂
POL(-1) = [-1]

The following pairs are in P_>:

897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])

The following pairs are in P_bound:

897_0_GET_LOAD(java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0]))) → COND_897_0_GET_LOAD(>(x1[0], 0), java.lang.Object(x0[0]), x1[0], java.lang.Object(CyclicList(x2[0])), x3[0])
COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])

The following pairs are in P_≥:

COND_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), +(x1[1], -1), x3[1])

There are no usable rules.

(15) 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_897_0_GET_LOAD(TRUE, java.lang.Object(x0[1]), x1[1], java.lang.Object(CyclicList(x2[1])), x3[1]) → 897_0_GET_LOAD(java.lang.Object(x0[1]), x1[1] + -1, x3[1])

The set Q is empty.

(16) IDependencyGraphProof (EQUIVALENT transformation)

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

(17) TRUE

(18) Obligation:

(19) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 17 rules for P and 0 rules for R.

P rules:
182_0_create_Load(EOS(STATIC_182), i23) → 185_0_create_LE(EOS(STATIC_185), i23, i23)
185_0_create_LE(EOS(STATIC_185), i27, i27) → 189_0_create_LE(EOS(STATIC_189), i27, i27)
189_0_create_LE(EOS(STATIC_189), i27, i27) → 193_0_create_New(EOS(STATIC_193), i27) | >(i27, 0)
193_0_create_New(EOS(STATIC_193), i27) → 197_0_create_Duplicate(EOS(STATIC_197), i27)
197_0_create_Duplicate(EOS(STATIC_197), i27) → 202_0_create_Load(EOS(STATIC_202), i27)
202_0_create_Load(EOS(STATIC_202), i27) → 209_0_create_InvokeMethod(EOS(STATIC_209), i27)
209_0_create_InvokeMethod(EOS(STATIC_209), i27) → 216_0_<init>_Load(EOS(STATIC_216), i27)
216_0_<init>_Load(EOS(STATIC_216), i27) → 232_0_<init>_InvokeMethod(EOS(STATIC_232), i27)
232_0_<init>_InvokeMethod(EOS(STATIC_232), i27) → 246_0_<init>_Load(EOS(STATIC_246), i27)
246_0_<init>_Load(EOS(STATIC_246), i27) → 254_0_<init>_Load(EOS(STATIC_254), i27)
254_0_<init>_Load(EOS(STATIC_254), i27) → 266_0_<init>_FieldAccess(EOS(STATIC_266), i27)
266_0_<init>_FieldAccess(EOS(STATIC_266), i27) → 279_0_<init>_Return(EOS(STATIC_279), i27)
279_0_<init>_Return(EOS(STATIC_279), i27) → 292_0_create_Store(EOS(STATIC_292), i27)
292_0_create_Store(EOS(STATIC_292), i27) → 320_0_create_JMP(EOS(STATIC_320), i27)
320_0_create_JMP(EOS(STATIC_320), i27) → 345_0_create_Inc(EOS(STATIC_345), i27)
345_0_create_Inc(EOS(STATIC_345), i27) → 179_0_create_Inc(EOS(STATIC_179), i27)
179_0_create_Inc(EOS(STATIC_179), i20) → 182_0_create_Load(EOS(STATIC_182), +(i20, -1)) | >=(i20, 0)
R rules:

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

P rules:
182_0_create_Load(EOS(STATIC_182), x0) → 182_0_create_Load(EOS(STATIC_182), +(x0, -1)) | >(x0, 0)
R rules:

Filtered ground terms:

182_0_create_Load(x1, x2) → 182_0_create_Load(x2)
EOS(x1) → EOS
Cond_182_0_create_Load(x1, x2, x3) → Cond_182_0_create_Load(x1, x3)

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

P rules:
182_0_create_Load(x0) → 182_0_create_Load(+(x0, -1)) | >(x0, 0)
R rules:

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

P rules:
182_0_CREATE_LOAD(x0) → COND_182_0_CREATE_LOAD(>(x0, 0), x0)
COND_182_0_CREATE_LOAD(TRUE, x0) → 182_0_CREATE_LOAD(+(x0, -1))
R rules:

(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:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 182_0_CREATE_LOAD(x0[0]) → COND_182_0_CREATE_LOAD(x0[0] > 0, x0[0])
(1): COND_182_0_CREATE_LOAD(TRUE, x0[1]) → 182_0_CREATE_LOAD(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.

(21) 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@70851e2b 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 182_0_CREATE_LOAD(x0) → COND_182_0_CREATE_LOAD(>(x0, 0), x0) the following chains were created:

We consider the chain 182_0_CREATE_LOAD(x0[0]) → COND_182_0_CREATE_LOAD(>(x0[0], 0), x0[0]), COND_182_0_CREATE_LOAD(TRUE, x0[1]) → 182_0_CREATE_LOAD(+(x0[1], -1)) which results in the following constraint:
(1)    (>(x0[0], 0)=TRUE∧x0[0]=x0[1] ⇒ 182_0_CREATE_LOAD(x0[0])≥NonInfC∧182_0_CREATE_LOAD(x0[0])≥COND_182_0_CREATE_LOAD(>(x0[0], 0), x0[0])∧(U^Increasing(COND_182_0_CREATE_LOAD(>(x0[0], 0), x0[0])), ≥))

We simplified constraint (1) using rule (IV) which results in the following new constraint:
(2)    (>(x0[0], 0)=TRUE ⇒ 182_0_CREATE_LOAD(x0[0])≥NonInfC∧182_0_CREATE_LOAD(x0[0])≥COND_182_0_CREATE_LOAD(>(x0[0], 0), x0[0])∧(U^Increasing(COND_182_0_CREATE_LOAD(>(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_182_0_CREATE_LOAD(>(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_182_0_CREATE_LOAD(>(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_182_0_CREATE_LOAD(>(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_182_0_CREATE_LOAD(>(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_182_0_CREATE_LOAD(TRUE, x0) → 182_0_CREATE_LOAD(+(x0, -1)) the following chains were created:

We consider the chain COND_182_0_CREATE_LOAD(TRUE, x0[1]) → 182_0_CREATE_LOAD(+(x0[1], -1)) which results in the following constraint:
(7)    (COND_182_0_CREATE_LOAD(TRUE, x0[1])≥NonInfC∧COND_182_0_CREATE_LOAD(TRUE, x0[1])≥182_0_CREATE_LOAD(+(x0[1], -1))∧(U^Increasing(182_0_CREATE_LOAD(+(x0[1], -1))), ≥))

We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(8)    ((U^Increasing(182_0_CREATE_LOAD(+(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(182_0_CREATE_LOAD(+(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(182_0_CREATE_LOAD(+(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(182_0_CREATE_LOAD(+(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.

182_0_CREATE_LOAD(x0) → COND_182_0_CREATE_LOAD(>(x0, 0), x0)
- (x0[0] ≥ 0 ⇒ (U^Increasing(COND_182_0_CREATE_LOAD(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8 + (2)bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)
COND_182_0_CREATE_LOAD(TRUE, x0) → 182_0_CREATE_LOAD(+(x0, -1))
- ((U^Increasing(182_0_CREATE_LOAD(+(x0[1], -1))), ≥)∧[bni_10] = 0∧0 = 0∧[2 + (-1)bso_11] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(182_0_CREATE_LOAD(x₁)) = [2]x₁
POL(COND_182_0_CREATE_LOAD(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_182_0_CREATE_LOAD(TRUE, x0[1]) → 182_0_CREATE_LOAD(+(x0[1], -1))

The following pairs are in P_bound:

182_0_CREATE_LOAD(x0[0]) → COND_182_0_CREATE_LOAD(>(x0[0], 0), x0[0])

The following pairs are in P_≥:

182_0_CREATE_LOAD(x0[0]) → COND_182_0_CREATE_LOAD(>(x0[0], 0), x0[0])

There are no usable rules.

(22) Complex Obligation (AND)

(23) 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): 182_0_CREATE_LOAD(x0[0]) → COND_182_0_CREATE_LOAD(x0[0] > 0, x0[0])

The set Q is empty.

(24) IDependencyGraphProof (EQUIVALENT transformation)

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

(25) TRUE

(26) 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_182_0_CREATE_LOAD(TRUE, x0[1]) → 182_0_CREATE_LOAD(x0[1] + -1)

The set Q is empty.

(27) 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) Complex Obligation (AND)

(5) Obligation:

(6) SCCToIDPv1Proof (SOUND transformation)

(7) Obligation:

(8) IDPNonInfProof (SOUND transformation)

(9) Complex Obligation (AND)

(10) Obligation:

(11) IDependencyGraphProof (EQUIVALENT transformation)

(12) TRUE

(13) Obligation:

(14) IDPNonInfProof (SOUND transformation)

(15) Obligation:

(16) IDependencyGraphProof (EQUIVALENT transformation)

(17) TRUE

(18) Obligation:

(19) SCCToIDPv1Proof (SOUND transformation)

(20) Obligation:

(21) IDPNonInfProof (SOUND transformation)

(22) Complex Obligation (AND)

(23) Obligation:

(24) IDependencyGraphProof (EQUIVALENT transformation)

(25) TRUE

(26) Obligation:

(27) IDependencyGraphProof (EQUIVALENT transformation)

(28) TRUE