Termination proof of /tmp/tmpyaMK5E/AlternatingGrowReduce2.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBCToGraph (⇒, 140 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToSCCProof (⇒, 0 ms)

↳4 AND

    ↳5 JBCTerminationSCC

        ↳6 SCCToIDPv1Proof (⇒, 60 ms)

        ↳7 IDP

        ↳8 IDPNonInfProof (⇒, 140 ms)

        ↳9 AND

            ↳10 IDP

                ↳11 IDependencyGraphProof (⇔, 0 ms)

                ↳12 TRUE

            ↳13 IDP

                ↳14 IDependencyGraphProof (⇔, 0 ms)

                ↳15 TRUE

    ↳16 JBCTerminationSCC

        ↳17 SCCToIDPv1Proof (⇒, 350 ms)

        ↳18 IDP

        ↳19 IDPtoQDPProof (⇒, 20 ms)

        ↳20 QDP

        ↳21 QDPOrderProof (⇔, 0 ms)

        ↳22 QDP

        ↳23 DependencyGraphProof (⇔, 0 ms)

        ↳24 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_25 (Sun Microsystems Inc.) Main-Class: AlternatingGrowReduce2/AlternatingGrowReduce2

package AlternatingGrowReduce2;

public class AlternatingGrowReduce2 {
	AlternatingGrowReduce2 next;

	public static void main(String[] argv) {
		Random.args = argv;
		AlternatingGrowReduce2 list = createList(Random.random());

		int mode = 0;
		while (list != null) {
			if (mode == 0) {
				list = list.next;
			} else if (mode == 1) {
				list = new AlternatingGrowReduce2(list);
			} else if (mode > 1) {
				list = list.next;
			}

			mode++;
			if (mode > 2) {
				mode = 0;
			}
		}
	}

	public AlternatingGrowReduce2(AlternatingGrowReduce2 old) {
		this.next = old;
	}

	public static AlternatingGrowReduce2 createList(int length) {
		AlternatingGrowReduce2 res = new AlternatingGrowReduce2(null);
		while (length > 0) {
			res = new AlternatingGrowReduce2(res);
			length--;
		}
		return res;
	}
}


package AlternatingGrowReduce2;

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:
AlternatingGrowReduce2.AlternatingGrowReduce2.main([Ljava/lang/String;)V: Graph of 163 nodes with 1 SCC.

AlternatingGrowReduce2.AlternatingGrowReduce2.createList(I)LAlternatingGrowReduce2/AlternatingGrowReduce2;: Graph of 33 nodes with 1 SCC.

(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: AlternatingGrowReduce2.AlternatingGrowReduce2.createList(I)LAlternatingGrowReduce2/AlternatingGrowReduce2;
SCC calls the following helper methods:
Performed SCC analyses: UsedFieldsAnalysis

(6) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 17 rules for P and 0 rules for R.

P rules:
327_0_createList_LE(EOS(STATIC_327), i37, i37) → 333_0_createList_LE(EOS(STATIC_333), i37, i37)
333_0_createList_LE(EOS(STATIC_333), i37, i37) → 339_0_createList_New(EOS(STATIC_339), i37) | >(i37, 0)
339_0_createList_New(EOS(STATIC_339), i37) → 346_0_createList_Duplicate(EOS(STATIC_346), i37)
346_0_createList_Duplicate(EOS(STATIC_346), i37) → 352_0_createList_Load(EOS(STATIC_352), i37)
352_0_createList_Load(EOS(STATIC_352), i37) → 370_0_createList_InvokeMethod(EOS(STATIC_370), i37)
370_0_createList_InvokeMethod(EOS(STATIC_370), i37) → 379_0_<init>_Load(EOS(STATIC_379), i37)
379_0_<init>_Load(EOS(STATIC_379), i37) → 384_0_<init>_InvokeMethod(EOS(STATIC_384), i37)
384_0_<init>_InvokeMethod(EOS(STATIC_384), i37) → 388_0_<init>_Load(EOS(STATIC_388), i37)
388_0_<init>_Load(EOS(STATIC_388), i37) → 391_0_<init>_Load(EOS(STATIC_391), i37)
391_0_<init>_Load(EOS(STATIC_391), i37) → 395_0_<init>_FieldAccess(EOS(STATIC_395), i37)
395_0_<init>_FieldAccess(EOS(STATIC_395), i37) → 399_0_<init>_Return(EOS(STATIC_399), i37)
399_0_<init>_Return(EOS(STATIC_399), i37) → 404_0_createList_Store(EOS(STATIC_404), i37)
404_0_createList_Store(EOS(STATIC_404), i37) → 408_0_createList_Inc(EOS(STATIC_408), i37)
408_0_createList_Inc(EOS(STATIC_408), i37) → 412_0_createList_JMP(EOS(STATIC_412), +(i37, -1)) | >(i37, 0)
412_0_createList_JMP(EOS(STATIC_412), i52) → 417_0_createList_Load(EOS(STATIC_417), i52)
417_0_createList_Load(EOS(STATIC_417), i52) → 320_0_createList_Load(EOS(STATIC_320), i52)
320_0_createList_Load(EOS(STATIC_320), i29) → 327_0_createList_LE(EOS(STATIC_327), i29, i29)
R rules:

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

P rules:
327_0_createList_LE(EOS(STATIC_327), x0, x0) → 327_0_createList_LE(EOS(STATIC_327), +(x0, -1), +(x0, -1)) | >(x0, 0)
R rules:

Filtered ground terms:

327_0_createList_LE(x1, x2, x3) → 327_0_createList_LE(x2, x3)
EOS(x1) → EOS
Cond_327_0_createList_LE(x1, x2, x3, x4) → Cond_327_0_createList_LE(x1, x3, x4)

Filtered duplicate args:

327_0_createList_LE(x1, x2) → 327_0_createList_LE(x2)
Cond_327_0_createList_LE(x1, x2, x3) → Cond_327_0_createList_LE(x1, x3)

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

P rules:
327_0_createList_LE(x0) → 327_0_createList_LE(+(x0, -1)) | >(x0, 0)
R rules:

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

P rules:
327_0_CREATELIST_LE(x0) → COND_327_0_CREATELIST_LE(>(x0, 0), x0)
COND_327_0_CREATELIST_LE(TRUE, x0) → 327_0_CREATELIST_LE(+(x0, -1))
R rules:

(7) Obligation:

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

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 327_0_CREATELIST_LE(x0[0]) → COND_327_0_CREATELIST_LE(x0[0] > 0, x0[0])
(1): COND_327_0_CREATELIST_LE(TRUE, x0[1]) → 327_0_CREATELIST_LE(x0[1] + -1)

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

(1) -> (0), if (x0[1] + -1 →^* x0[0])

The set Q is empty.

(8) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpCand1ShapeHeuristic@7fc17ff9 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 327_0_CREATELIST_LE(x0) → COND_327_0_CREATELIST_LE(>(x0, 0), x0) the following chains were created:

We consider the chain 327_0_CREATELIST_LE(x0[0]) → COND_327_0_CREATELIST_LE(>(x0[0], 0), x0[0]), COND_327_0_CREATELIST_LE(TRUE, x0[1]) → 327_0_CREATELIST_LE(+(x0[1], -1)) which results in the following constraint:
(1)    (>(x0[0], 0)=TRUE∧x0[0]=x0[1] ⇒ 327_0_CREATELIST_LE(x0[0])≥NonInfC∧327_0_CREATELIST_LE(x0[0])≥COND_327_0_CREATELIST_LE(>(x0[0], 0), x0[0])∧(U^Increasing(COND_327_0_CREATELIST_LE(>(x0[0], 0), x0[0])), ≥))

We simplified constraint (1) using rule (IV) which results in the following new constraint:
(2)    (>(x0[0], 0)=TRUE ⇒ 327_0_CREATELIST_LE(x0[0])≥NonInfC∧327_0_CREATELIST_LE(x0[0])≥COND_327_0_CREATELIST_LE(>(x0[0], 0), x0[0])∧(U^Increasing(COND_327_0_CREATELIST_LE(>(x0[0], 0), x0[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_327_0_CREATELIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_327_0_CREATELIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_327_0_CREATELIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x0[0] ≥ 0 ⇒ (U^Increasing(COND_327_0_CREATELIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8 + (2)bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)

For Pair COND_327_0_CREATELIST_LE(TRUE, x0) → 327_0_CREATELIST_LE(+(x0, -1)) the following chains were created:

We consider the chain COND_327_0_CREATELIST_LE(TRUE, x0[1]) → 327_0_CREATELIST_LE(+(x0[1], -1)) which results in the following constraint:
(7)    (COND_327_0_CREATELIST_LE(TRUE, x0[1])≥NonInfC∧COND_327_0_CREATELIST_LE(TRUE, x0[1])≥327_0_CREATELIST_LE(+(x0[1], -1))∧(U^Increasing(327_0_CREATELIST_LE(+(x0[1], -1))), ≥))

We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(8)    ((U^Increasing(327_0_CREATELIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(9)    ((U^Increasing(327_0_CREATELIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(10)    ((U^Increasing(327_0_CREATELIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧[2 + (-1)bso_11] ≥ 0)

We simplified constraint (10) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(11)    ((U^Increasing(327_0_CREATELIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧0 = 0∧[2 + (-1)bso_11] ≥ 0)

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

327_0_CREATELIST_LE(x0) → COND_327_0_CREATELIST_LE(>(x0, 0), x0)
- (x0[0] ≥ 0 ⇒ (U^Increasing(COND_327_0_CREATELIST_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_8 + (2)bni_8] + [(2)bni_8]x0[0] ≥ 0∧[(-1)bso_9] ≥ 0)
COND_327_0_CREATELIST_LE(TRUE, x0) → 327_0_CREATELIST_LE(+(x0, -1))
- ((U^Increasing(327_0_CREATELIST_LE(+(x0[1], -1))), ≥)∧[bni_10] = 0∧0 = 0∧[2 + (-1)bso_11] ≥ 0)

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

POL(TRUE) = 0
POL(FALSE) = 0
POL(327_0_CREATELIST_LE(x₁)) = [2]x₁
POL(COND_327_0_CREATELIST_LE(x₁, x₂)) = [2]x₂
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(+(x₁, x₂)) = x₁ + x₂
POL(-1) = [-1]

The following pairs are in P_>:

COND_327_0_CREATELIST_LE(TRUE, x0[1]) → 327_0_CREATELIST_LE(+(x0[1], -1))

The following pairs are in P_bound:

327_0_CREATELIST_LE(x0[0]) → COND_327_0_CREATELIST_LE(>(x0[0], 0), x0[0])

The following pairs are in P_≥:

327_0_CREATELIST_LE(x0[0]) → COND_327_0_CREATELIST_LE(>(x0[0], 0), x0[0])

There are no usable rules.

(9) Complex Obligation (AND)

(10) Obligation:

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

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 327_0_CREATELIST_LE(x0[0]) → COND_327_0_CREATELIST_LE(x0[0] > 0, x0[0])

The set Q is empty.

(11) IDependencyGraphProof (EQUIVALENT transformation)

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

(12) TRUE

(13) Obligation:

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

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

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(1): COND_327_0_CREATELIST_LE(TRUE, x0[1]) → 327_0_CREATELIST_LE(x0[1] + -1)

The set Q is empty.

(14) IDependencyGraphProof (EQUIVALENT transformation)

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

(15) TRUE

(16) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: AlternatingGrowReduce2.AlternatingGrowReduce2.main([Ljava/lang/String;)V
SCC calls the following helper methods:
Performed SCC analyses: UsedFieldsAnalysis

(17) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 56 rules for P and 0 rules for R.

P rules:
511_0_main_NULL(EOS(STATIC_511), java.lang.Object(o98sub), i58, java.lang.Object(o98sub)) → 513_0_main_NULL(EOS(STATIC_513), java.lang.Object(o98sub), i58, java.lang.Object(o98sub))
513_0_main_NULL(EOS(STATIC_513), java.lang.Object(o98sub), i58, java.lang.Object(o98sub)) → 516_0_main_Load(EOS(STATIC_516), java.lang.Object(o98sub), i58)
516_0_main_Load(EOS(STATIC_516), java.lang.Object(o98sub), i58) → 520_0_main_NE(EOS(STATIC_520), java.lang.Object(o98sub), i58, i58)
520_0_main_NE(EOS(STATIC_520), java.lang.Object(o98sub), i61, i61) → 523_0_main_NE(EOS(STATIC_523), java.lang.Object(o98sub), i61, i61)
520_0_main_NE(EOS(STATIC_520), java.lang.Object(o98sub), matching1, matching2) → 524_0_main_NE(EOS(STATIC_524), java.lang.Object(o98sub), 0, 0) | &&(=(matching1, 0), =(matching2, 0))
523_0_main_NE(EOS(STATIC_523), java.lang.Object(o98sub), i61, i61) → 526_0_main_Load(EOS(STATIC_526), java.lang.Object(o98sub), i61) | >(i61, 0)
526_0_main_Load(EOS(STATIC_526), java.lang.Object(o98sub), i61) → 529_0_main_ConstantStackPush(EOS(STATIC_529), java.lang.Object(o98sub), i61, i61)
529_0_main_ConstantStackPush(EOS(STATIC_529), java.lang.Object(o98sub), i61, i61) → 533_0_main_NE(EOS(STATIC_533), java.lang.Object(o98sub), i61, i61, 1)
533_0_main_NE(EOS(STATIC_533), java.lang.Object(o98sub), matching1, matching2, matching3) → 536_0_main_NE(EOS(STATIC_536), java.lang.Object(o98sub), 1, 1, 1) | &&(&&(=(matching1, 1), =(matching2, 1)), =(matching3, 1))
533_0_main_NE(EOS(STATIC_533), java.lang.Object(o98sub), matching1, matching2, matching3) → 538_0_main_NE(EOS(STATIC_538), java.lang.Object(o98sub), 2, 2, 1) | &&(&&(=(matching1, 2), =(matching2, 2)), =(matching3, 1))
536_0_main_NE(EOS(STATIC_536), java.lang.Object(o98sub), matching1, matching2, matching3) → 541_0_main_New(EOS(STATIC_541), java.lang.Object(o98sub), 1) | &&(&&(=(matching1, 1), =(matching2, 1)), =(matching3, 1))
541_0_main_New(EOS(STATIC_541), java.lang.Object(o98sub), matching1) → 547_0_main_Duplicate(EOS(STATIC_547), java.lang.Object(o98sub), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) | =(matching1, 1)
547_0_main_Duplicate(EOS(STATIC_547), java.lang.Object(o98sub), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) → 553_0_main_Load(EOS(STATIC_553), java.lang.Object(o98sub), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) | =(matching1, 1)
553_0_main_Load(EOS(STATIC_553), java.lang.Object(o98sub), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) → 559_0_main_InvokeMethod(EOS(STATIC_559), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub)) | =(matching1, 1)
559_0_main_InvokeMethod(EOS(STATIC_559), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub)) → 563_0_<init>_Load(EOS(STATIC_563), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub)) | =(matching1, 1)
563_0_<init>_Load(EOS(STATIC_563), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub)) → 575_0_<init>_InvokeMethod(EOS(STATIC_575), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) | =(matching1, 1)
575_0_<init>_InvokeMethod(EOS(STATIC_575), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) → 580_0_<init>_Load(EOS(STATIC_580), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub)) | =(matching1, 1)
580_0_<init>_Load(EOS(STATIC_580), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub)) → 584_0_<init>_Load(EOS(STATIC_584), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub), java.lang.Object(o98sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) | =(matching1, 1)
584_0_<init>_Load(EOS(STATIC_584), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub), java.lang.Object(o98sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) → 589_0_<init>_FieldAccess(EOS(STATIC_589), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub)) | =(matching1, 1)
589_0_<init>_FieldAccess(EOS(STATIC_589), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o98sub)) → 595_0_<init>_Return(EOS(STATIC_595), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), java.lang.Object(o98sub)) | =(matching1, 1)
595_0_<init>_Return(EOS(STATIC_595), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), java.lang.Object(o98sub)) → 600_0_main_Store(EOS(STATIC_600), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub)))) | =(matching1, 1)
600_0_main_Store(EOS(STATIC_600), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub)))) → 604_0_main_JMP(EOS(STATIC_604), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), 1) | =(matching1, 1)
604_0_main_JMP(EOS(STATIC_604), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), matching1) → 609_0_main_Inc(EOS(STATIC_609), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), 1) | =(matching1, 1)
609_0_main_Inc(EOS(STATIC_609), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), matching1) → 615_0_main_Load(EOS(STATIC_615), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), 2) | =(matching1, 1)
615_0_main_Load(EOS(STATIC_615), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), matching1) → 622_0_main_ConstantStackPush(EOS(STATIC_622), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), 2, 2) | =(matching1, 2)
622_0_main_ConstantStackPush(EOS(STATIC_622), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), matching1, matching2) → 625_0_main_LE(EOS(STATIC_625), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), 2, 2, 2) | &&(=(matching1, 2), =(matching2, 2))
625_0_main_LE(EOS(STATIC_625), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), matching1, matching2, matching3) → 628_0_main_Load(EOS(STATIC_628), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), 2) | &&(&&(=(matching1, 2), =(matching2, 2)), =(matching3, 2))
628_0_main_Load(EOS(STATIC_628), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), matching1) → 508_0_main_Load(EOS(STATIC_508), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o98sub))), 2) | =(matching1, 2)
508_0_main_Load(EOS(STATIC_508), o92, i58) → 511_0_main_NULL(EOS(STATIC_511), o92, i58, o92)
538_0_main_NE(EOS(STATIC_538), java.lang.Object(o98sub), matching1, matching2, matching3) → 543_0_main_Load(EOS(STATIC_543), java.lang.Object(o98sub), 2) | &&(&&(=(matching1, 2), =(matching2, 2)), =(matching3, 1))
543_0_main_Load(EOS(STATIC_543), java.lang.Object(o98sub), matching1) → 549_0_main_ConstantStackPush(EOS(STATIC_549), java.lang.Object(o98sub), 2, 2) | =(matching1, 2)
549_0_main_ConstantStackPush(EOS(STATIC_549), java.lang.Object(o98sub), matching1, matching2) → 555_0_main_LE(EOS(STATIC_555), java.lang.Object(o98sub), 2, 2, 1) | &&(=(matching1, 2), =(matching2, 2))
555_0_main_LE(EOS(STATIC_555), java.lang.Object(o98sub), matching1, matching2, matching3) → 561_0_main_Load(EOS(STATIC_561), java.lang.Object(o98sub), 2) | &&(&&(=(matching1, 2), =(matching2, 2)), =(matching3, 1))
561_0_main_Load(EOS(STATIC_561), java.lang.Object(o98sub), matching1) → 565_0_main_FieldAccess(EOS(STATIC_565), 2, java.lang.Object(o98sub)) | =(matching1, 2)
565_0_main_FieldAccess(EOS(STATIC_565), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o107))) → 570_0_main_FieldAccess(EOS(STATIC_570), 2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o107))) | =(matching1, 2)
570_0_main_FieldAccess(EOS(STATIC_570), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o107))) → 577_0_main_Store(EOS(STATIC_577), 2, o107) | =(matching1, 2)
577_0_main_Store(EOS(STATIC_577), matching1, o107) → 582_0_main_Inc(EOS(STATIC_582), o107, 2) | =(matching1, 2)
582_0_main_Inc(EOS(STATIC_582), o107, matching1) → 587_0_main_Load(EOS(STATIC_587), o107) | =(matching1, 2)
587_0_main_Load(EOS(STATIC_587), o107) → 592_0_main_ConstantStackPush(EOS(STATIC_592), o107)
592_0_main_ConstantStackPush(EOS(STATIC_592), o107) → 598_0_main_LE(EOS(STATIC_598), o107, 2)
598_0_main_LE(EOS(STATIC_598), o107, matching1) → 602_0_main_ConstantStackPush(EOS(STATIC_602), o107) | =(matching1, 2)
602_0_main_ConstantStackPush(EOS(STATIC_602), o107) → 606_0_main_Store(EOS(STATIC_606), o107, 0)
606_0_main_Store(EOS(STATIC_606), o107, matching1) → 611_0_main_JMP(EOS(STATIC_611), o107, 0) | =(matching1, 0)
611_0_main_JMP(EOS(STATIC_611), o107, matching1) → 618_0_main_Load(EOS(STATIC_618), o107, 0) | =(matching1, 0)
618_0_main_Load(EOS(STATIC_618), o107, matching1) → 508_0_main_Load(EOS(STATIC_508), o107, 0) | =(matching1, 0)
524_0_main_NE(EOS(STATIC_524), java.lang.Object(o98sub), matching1, matching2) → 527_0_main_Load(EOS(STATIC_527), java.lang.Object(o98sub), 0) | &&(=(matching1, 0), =(matching2, 0))
527_0_main_Load(EOS(STATIC_527), java.lang.Object(o98sub), matching1) → 531_0_main_FieldAccess(EOS(STATIC_531), 0, java.lang.Object(o98sub)) | =(matching1, 0)
531_0_main_FieldAccess(EOS(STATIC_531), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o102))) → 535_0_main_FieldAccess(EOS(STATIC_535), 0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o102))) | =(matching1, 0)
535_0_main_FieldAccess(EOS(STATIC_535), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o102))) → 539_0_main_Store(EOS(STATIC_539), 0, o102) | =(matching1, 0)
539_0_main_Store(EOS(STATIC_539), matching1, o102) → 545_0_main_JMP(EOS(STATIC_545), o102, 0) | =(matching1, 0)
545_0_main_JMP(EOS(STATIC_545), o102, matching1) → 551_0_main_Inc(EOS(STATIC_551), o102, 0) | =(matching1, 0)
551_0_main_Inc(EOS(STATIC_551), o102, matching1) → 556_0_main_Load(EOS(STATIC_556), o102, 1) | =(matching1, 0)
556_0_main_Load(EOS(STATIC_556), o102, matching1) → 562_0_main_ConstantStackPush(EOS(STATIC_562), o102, 1, 1) | =(matching1, 1)
562_0_main_ConstantStackPush(EOS(STATIC_562), o102, matching1, matching2) → 567_0_main_LE(EOS(STATIC_567), o102, 1, 1) | &&(=(matching1, 1), =(matching2, 1))
567_0_main_LE(EOS(STATIC_567), o102, matching1, matching2) → 573_0_main_Load(EOS(STATIC_573), o102, 1) | &&(=(matching1, 1), =(matching2, 1))
573_0_main_Load(EOS(STATIC_573), o102, matching1) → 508_0_main_Load(EOS(STATIC_508), o102, 1) | =(matching1, 1)
R rules:

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

P rules:
511_0_main_NULL(EOS(STATIC_511), java.lang.Object(x0), 1, java.lang.Object(x0)) → 511_0_main_NULL(EOS(STATIC_511), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(x0))), 2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(x0))))
511_0_main_NULL(EOS(STATIC_511), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, x0)), 2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, x0))) → 511_0_main_NULL(EOS(STATIC_511), x0, 0, x0)
511_0_main_NULL(EOS(STATIC_511), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, x0)), 0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, x0))) → 511_0_main_NULL(EOS(STATIC_511), x0, 1, x0)
R rules:

Filtered ground terms:

511_0_main_NULL(x1, x2, x3, x4) → 511_0_main_NULL(x2, x3, x4)
EOS(x1) → EOS
AlternatingGrowReduce2.AlternatingGrowReduce2(x1, x2) → AlternatingGrowReduce2.AlternatingGrowReduce2(x2)

Filtered duplicate args:

511_0_main_NULL(x1, x2, x3) → 511_0_main_NULL(x2, x3)

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

P rules:
511_0_main_NULL(1, java.lang.Object(x0)) → 511_0_main_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(java.lang.Object(x0))))
511_0_main_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0))) → 511_0_main_NULL(0, x0)
511_0_main_NULL(0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0))) → 511_0_main_NULL(1, x0)
R rules:

Finished conversion. Obtained 3 rules for P and 0 rules for R. System has no predefined symbols.

P rules:
511_0_MAIN_NULL(1, java.lang.Object(x0)) → 511_0_MAIN_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(java.lang.Object(x0))))
511_0_MAIN_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0))) → 511_0_MAIN_NULL(0, x0)
511_0_MAIN_NULL(0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0))) → 511_0_MAIN_NULL(1, x0)
R rules:

(18) Obligation:

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

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

The following domains are used:
none

R is empty.

The integer pair graph contains the following rules and edges:
(0): 511_0_MAIN_NULL(1, java.lang.Object(x0[0])) → 511_0_MAIN_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(java.lang.Object(x0[0]))))
(1): 511_0_MAIN_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0[1]))) → 511_0_MAIN_NULL(0, x0[1])
(2): 511_0_MAIN_NULL(0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0[2]))) → 511_0_MAIN_NULL(1, x0[2])

(0) -> (0), if (2 →^* 1∧java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(java.lang.Object(x0[0]))) →^* java.lang.Object(x0[0]'))

(0) -> (1), if java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(java.lang.Object(x0[0]))) →^* java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0[1]))

(0) -> (2), if (2 →^* 0∧java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(java.lang.Object(x0[0]))) →^* java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0[2])))

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

(1) -> (1), if (0 →^* 2∧x0[1] →^* java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0[1]')))

(1) -> (2), if x0[1] →^* java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0[2]))

(2) -> (0), if x0[2] →^* java.lang.Object(x0[0])

(2) -> (1), if (1 →^* 2∧x0[2] →^* java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0[1])))

(2) -> (2), if (1 →^* 0∧x0[2] →^* java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0[2]')))

The set Q is empty.

(19) IDPtoQDPProof (SOUND transformation)

Represented integers and predefined function symbols by Terms

(20) Obligation:

Q DP problem:
The TRS P consists of the following rules:

511_0_MAIN_NULL(pos(s(01)), java.lang.Object(x0[0])) → 511_0_MAIN_NULL(pos(s(s(01))), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(java.lang.Object(x0[0]))))
511_0_MAIN_NULL(pos(s(s(01))), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0[1]))) → 511_0_MAIN_NULL(pos(01), x0[1])
511_0_MAIN_NULL(pos(01), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0[2]))) → 511_0_MAIN_NULL(pos(s(01)), x0[2])

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(21) QDPOrderProof (EQUIVALENT transformation)

We use the reduction pair processor [LPAR04].

The following pairs can be oriented strictly and are deleted.

511_0_MAIN_NULL(pos(s(s(01))), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0[1]))) → 511_0_MAIN_NULL(pos(01), x0[1])

The remaining pairs can at least be oriented weakly.
Used ordering: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) :

POL(511_0_MAIN_NULL(x₁, x₂)) = 0 +
[ 1, 1 ]

· x₁ +
[ 1, 0 ]

· x₂

POL(pos(x₁)) =
/ 1 \

\ 1 /

+
/ 0 1 \

\ 0 0 /

· x₁

POL(s(x₁)) =
/ 0 \

\ 1 /

+
/ 0 0 \

\ 1 0 /

· x₁

POL(01) =
/ 1 \

\ 1 /

POL(java.lang.Object(x₁)) =
/ 0 \

\ 0 /

+
/ 0 1 \

\ 0 0 /

· x₁

POL(AlternatingGrowReduce2.AlternatingGrowReduce2(x₁)) =
/ 0 \

\ 1 /

+
/ 0 0 \

\ 1 0 /

· x₁

The following usable rules [FROCOS05] were oriented: none

(22) Obligation:

Q DP problem:
The TRS P consists of the following rules:

511_0_MAIN_NULL(pos(s(01)), java.lang.Object(x0[0])) → 511_0_MAIN_NULL(pos(s(s(01))), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(java.lang.Object(x0[0]))))
511_0_MAIN_NULL(pos(01), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(x0[2]))) → 511_0_MAIN_NULL(pos(s(01)), x0[2])

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.

(23) DependencyGraphProof (EQUIVALENT transformation)

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

(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) IDependencyGraphProof (EQUIVALENT transformation)

(15) TRUE

(16) Obligation:

(17) SCCToIDPv1Proof (SOUND transformation)

(18) Obligation:

(19) IDPtoQDPProof (SOUND transformation)

(20) Obligation:

(21) QDPOrderProof (EQUIVALENT transformation)

(22) Obligation:

(23) DependencyGraphProof (EQUIVALENT transformation)

(24) TRUE