/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.jar /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.jar
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


termination of the given Bare JBC problem could be proven:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 426 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 6 ms]
(6) AND
    (7) JBCTerminationSCC
        (8) SCCToQDPProof [SOUND, 122 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) JBCTerminationSCC
        (13) SCCToIRSProof [SOUND, 49 ms]
        (14) IRSwT
        (15) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) IRSwTTerminationDigraphProof [EQUIVALENT, 13 ms]
        (18) IRSwT
        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (20) IRSwT
        (21) TempFilterProof [SOUND, 11 ms]
        (22) IntTRS
        (23) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (24) YES
    (25) JBCTerminationSCC
        (26) SCCToIRSProof [SOUND, 58 ms]
        (27) IRSwT
        (28) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (29) IRSwT
        (30) IRSwTTerminationDigraphProof [EQUIVALENT, 43 ms]
        (31) IRSwT
        (32) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (33) IRSwT
        (34) TempFilterProof [SOUND, 29 ms]
        (35) IntTRS
        (36) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (37) YES


----------------------------------------

(0)
Obligation:
need to prove termination of the following program:
package CyclicAnalysis;

public class CyclicAnalysis {
	CyclicAnalysis field;

	public static void main(String[] args) {
		Random.args = args;
		CyclicAnalysis t = new CyclicAnalysis();
		t.field = new CyclicAnalysis();
		t.field.appendNewCyclicList(Random.random());
		t.appendNewList(Random.random());
		t.length();
	}

	public int length() {
		int length = 1;
		CyclicAnalysis cur = this.field;
		while (cur != null) {
			cur = cur.field;
			length++;
		}
		return length;
	}

	public void appendNewCyclicList(int i) {
		CyclicAnalysis last = this.appendNewList(i);
		last.field = this;
	}

	/**
 	 * @param i number of elements to append
 	 * @return the last list element appended
 	 */
	private CyclicAnalysis appendNewList(int i) {
		this.field = new CyclicAnalysis();
		CyclicAnalysis cur = this.field;
		while (i > 1) {
			i--;
			cur = cur.field = new CyclicAnalysis();
		}
		return cur;
	}
}


package CyclicAnalysis;

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

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



----------------------------------------

(1) BareJBCToJBCProof (EQUIVALENT)
initialized classpath
----------------------------------------

(2)
Obligation:
need to prove termination of the following program:
package CyclicAnalysis;

public class CyclicAnalysis {
	CyclicAnalysis field;

	public static void main(String[] args) {
		Random.args = args;
		CyclicAnalysis t = new CyclicAnalysis();
		t.field = new CyclicAnalysis();
		t.field.appendNewCyclicList(Random.random());
		t.appendNewList(Random.random());
		t.length();
	}

	public int length() {
		int length = 1;
		CyclicAnalysis cur = this.field;
		while (cur != null) {
			cur = cur.field;
			length++;
		}
		return length;
	}

	public void appendNewCyclicList(int i) {
		CyclicAnalysis last = this.appendNewList(i);
		last.field = this;
	}

	/**
 	 * @param i number of elements to append
 	 * @return the last list element appended
 	 */
	private CyclicAnalysis appendNewList(int i) {
		this.field = new CyclicAnalysis();
		CyclicAnalysis cur = this.field;
		while (i > 1) {
			i--;
			cur = cur.field = new CyclicAnalysis();
		}
		return cur;
	}
}


package CyclicAnalysis;

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

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



----------------------------------------

(3) JBCToGraph (EQUIVALENT)
Constructed TerminationGraph.
----------------------------------------

(4)
Obligation:
Termination Graph based on JBC Program:
CyclicAnalysis.CyclicAnalysis.main([Ljava/lang/String;)V: Graph of 299 nodes with 3 SCCs.





----------------------------------------

(5) TerminationGraphToSCCProof (SOUND)
Splitted TerminationGraph to 3 SCCss.
----------------------------------------

(6)
Complex Obligation (AND)

----------------------------------------

(7)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: CyclicAnalysis.CyclicAnalysis.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*CyclicAnalysis.CyclicAnalysis: [field]
*Marker field analysis yielded the following relations that could be markers:

----------------------------------------

(8) SCCToQDPProof (SOUND)
Transformed TerminationGraph SCC to QDP. Log: 
Generated 10 rules for P and 0 rules for R.P rules:
f1242_0_length_NULL(EOS(STATIC_1242), java.lang.Object(o185sub), java.lang.Object(o185sub)) -> f1245_0_length_NULL(EOS(STATIC_1245), java.lang.Object(o185sub), java.lang.Object(o185sub)) :|: TRUE
f1245_0_length_NULL(EOS(STATIC_1245), java.lang.Object(o185sub), java.lang.Object(o185sub)) -> f1248_0_length_Load(EOS(STATIC_1248), java.lang.Object(o185sub)) :|: TRUE
f1248_0_length_Load(EOS(STATIC_1248), java.lang.Object(o185sub)) -> f1252_0_length_FieldAccess(EOS(STATIC_1252), java.lang.Object(o185sub)) :|: TRUE
f1252_0_length_FieldAccess(EOS(STATIC_1252), java.lang.Object(CyclicAnalysis.CyclicAnalysis(EOC, o187))) -> f1255_0_length_FieldAccess(EOS(STATIC_1255), java.lang.Object(CyclicAnalysis.CyclicAnalysis(EOC, o187))) :|: TRUE
f1255_0_length_FieldAccess(EOS(STATIC_1255), java.lang.Object(CyclicAnalysis.CyclicAnalysis(EOC, o187))) -> f1257_0_length_Store(EOS(STATIC_1257), o187) :|: TRUE
f1257_0_length_Store(EOS(STATIC_1257), o187) -> f1259_0_length_Inc(EOS(STATIC_1259), o187) :|: TRUE
f1259_0_length_Inc(EOS(STATIC_1259), o187) -> f1263_0_length_JMP(EOS(STATIC_1263), o187) :|: TRUE
f1263_0_length_JMP(EOS(STATIC_1263), o187) -> f1267_0_length_Load(EOS(STATIC_1267), o187) :|: TRUE
f1267_0_length_Load(EOS(STATIC_1267), o187) -> f1239_0_length_Load(EOS(STATIC_1239), o187) :|: TRUE
f1239_0_length_Load(EOS(STATIC_1239), o183) -> f1242_0_length_NULL(EOS(STATIC_1242), o183, o183) :|: TRUE
R rules:
Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules:
f1242_0_length_NULL(EOS(STATIC_1242), java.lang.Object(CyclicAnalysis.CyclicAnalysis(EOC, o187:0)), java.lang.Object(CyclicAnalysis.CyclicAnalysis(EOC, o187:0))) -> f1242_0_length_NULL(EOS(STATIC_1242), o187:0, o187:0) :|: TRUE
R rules:
Filtered ground terms:
   f1242_0_length_NULL(x1, x2, x3) -> f1242_0_length_NULL(x2, x3)
   EOS(x1) -> EOS
   CyclicAnalysis.CyclicAnalysis(x1, x2) -> CyclicAnalysis.CyclicAnalysis(x2)
Filtered duplicate args:
   f1242_0_length_NULL(x1, x2) -> f1242_0_length_NULL(x2)
Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules:
F1242_0_LENGTH_NULL(java.lang.Object(CyclicAnalysis.CyclicAnalysis(o187:0:0))) -> F1242_0_LENGTH_NULL(o187:0:0) :|: TRUE
R rules:

----------------------------------------

(9)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   F1242_0_LENGTH_NULL(java.lang.Object(CyclicAnalysis.CyclicAnalysis(o187:0:0))) -> F1242_0_LENGTH_NULL(o187:0:0)

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

(10) QDPSizeChangeProof (EQUIVALENT)
By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 

From the DPs we obtained the following set of size-change graphs:
*F1242_0_LENGTH_NULL(java.lang.Object(CyclicAnalysis.CyclicAnalysis(o187:0:0))) -> F1242_0_LENGTH_NULL(o187:0:0)
The graph contains the following edges 1 > 1


----------------------------------------

(11)
YES

----------------------------------------

(12)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: CyclicAnalysis.CyclicAnalysis.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:

*Marker field analysis yielded the following relations that could be markers:

----------------------------------------

(13) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 23 IRulesP rules:
f806_0_appendNewList_ConstantStackPush(EOS(STATIC_806), i96, i96, o128[CyclicAnalysis.field]o126) -> f827_0_appendNewList_LE(EOS(STATIC_827), i96, i96, 1, o128[CyclicAnalysis.field]o126) :|: TRUE
f827_0_appendNewList_LE(EOS(STATIC_827), i107, i107, matching1, o128[CyclicAnalysis.field]o126) -> f834_0_appendNewList_LE(EOS(STATIC_834), i107, i107, 1, o128[CyclicAnalysis.field]o126) :|: TRUE && matching1 = 1
f834_0_appendNewList_LE(EOS(STATIC_834), i107, i107, matching1, o128[CyclicAnalysis.field]o126) -> f891_0_appendNewList_Inc(EOS(STATIC_891), i107, o128[CyclicAnalysis.field]o126) :|: i107 > 1 && matching1 = 1
f891_0_appendNewList_Inc(EOS(STATIC_891), i107, o128[CyclicAnalysis.field]o126) -> f897_0_appendNewList_Load(EOS(STATIC_897), i107 + -1, o128[CyclicAnalysis.field]o126) :|: TRUE
f897_0_appendNewList_Load(EOS(STATIC_897), i110, o128[CyclicAnalysis.field]o126) -> f899_0_appendNewList_New(EOS(STATIC_899), i110, o128[CyclicAnalysis.field]o126) :|: TRUE
f899_0_appendNewList_New(EOS(STATIC_899), i110, o128[CyclicAnalysis.field]o126) -> f904_0_appendNewList_Duplicate(EOS(STATIC_904), i110, o128[CyclicAnalysis.field]o126) :|: TRUE
f904_0_appendNewList_Duplicate(EOS(STATIC_904), i110, o128[CyclicAnalysis.field]o126) -> f908_0_appendNewList_InvokeMethod(EOS(STATIC_908), i110, o128[CyclicAnalysis.field]o126) :|: TRUE
f908_0_appendNewList_InvokeMethod(EOS(STATIC_908), i110, o128[CyclicAnalysis.field]o126) -> f910_0__init__Load(EOS(STATIC_910), i110, o128[CyclicAnalysis.field]o126) :|: TRUE
f910_0__init__Load(EOS(STATIC_910), i110, o128[CyclicAnalysis.field]o126) -> f914_0__init__InvokeMethod(EOS(STATIC_914), i110, o128[CyclicAnalysis.field]o126) :|: TRUE
f914_0__init__InvokeMethod(EOS(STATIC_914), i110, o128[CyclicAnalysis.field]o126) -> f918_0__init__Return(EOS(STATIC_918), i110, o128[CyclicAnalysis.field]o126) :|: TRUE
f918_0__init__Return(EOS(STATIC_918), i110, o128[CyclicAnalysis.field]o126) -> f921_0_appendNewList_Duplicate(EOS(STATIC_921), i110, o128[CyclicAnalysis.field]o126) :|: TRUE
f921_0_appendNewList_Duplicate(EOS(STATIC_921), i110, o128[CyclicAnalysis.field]o126) -> f932_0_appendNewList_FieldAccess(EOS(STATIC_932), i110, o128[CyclicAnalysis.field]o126) :|: TRUE
f932_0_appendNewList_FieldAccess(EOS(STATIC_932), i110, o128[CyclicAnalysis.field]o126) -> f972_0_appendNewList_FieldAccess(EOS(STATIC_972), i110, o128[CyclicAnalysis.field]o126) :|: o128[CyclicAnalysis.field]o126 > 0
f932_0_appendNewList_FieldAccess(EOS(STATIC_932), i110, o148[CyclicAnalysis.field]o148) -> f973_0_appendNewList_FieldAccess(EOS(STATIC_973), i110) :|: TRUE
f972_0_appendNewList_FieldAccess(EOS(STATIC_972), i110, o128[CyclicAnalysis.field]o126) -> f977_0_appendNewList_Store(EOS(STATIC_977), i110, o128[CyclicAnalysis.field]o142) :|: o128[CyclicAnalysis.field]o142 > o128[CyclicAnalysis.field]o126 && o128[CyclicAnalysis.field]o126 >= 0
f977_0_appendNewList_Store(EOS(STATIC_977), i110, o128[CyclicAnalysis.field]o142) -> f994_0_appendNewList_JMP(EOS(STATIC_994), i110, o128[CyclicAnalysis.field]o142) :|: TRUE
f994_0_appendNewList_JMP(EOS(STATIC_994), i110, o128[CyclicAnalysis.field]o142) -> f1015_0_appendNewList_Load(EOS(STATIC_1015), i110, o128[CyclicAnalysis.field]o142) :|: TRUE
f1015_0_appendNewList_Load(EOS(STATIC_1015), i110, o128[CyclicAnalysis.field]o142) -> f801_0_appendNewList_Load(EOS(STATIC_801), i110, o128[CyclicAnalysis.field]o142) :|: TRUE
f801_0_appendNewList_Load(EOS(STATIC_801), i96, o128[CyclicAnalysis.field]o126) -> f806_0_appendNewList_ConstantStackPush(EOS(STATIC_806), i96, i96, o128[CyclicAnalysis.field]o126) :|: TRUE
f973_0_appendNewList_FieldAccess(EOS(STATIC_973), i110) -> f991_0_appendNewList_Store(EOS(STATIC_991), i110) :|: TRUE
f991_0_appendNewList_Store(EOS(STATIC_991), i110) -> f996_0_appendNewList_JMP(EOS(STATIC_996), i110) :|: TRUE
f996_0_appendNewList_JMP(EOS(STATIC_996), i110) -> f1063_0_appendNewList_Load(EOS(STATIC_1063), i110) :|: TRUE
f1063_0_appendNewList_Load(EOS(STATIC_1063), i110) -> f801_0_appendNewList_Load(EOS(STATIC_801), i110, o148[CyclicAnalysis.field]o142) :|: o148[CyclicAnalysis.field]o142 = 1
Combined rules. Obtained 2 IRulesP rules:
f806_0_appendNewList_ConstantStackPush(EOS(STATIC_806), i96:0, i96:0, o128[CyclicAnalysis.field]o126:0) -> f806_0_appendNewList_ConstantStackPush(EOS(STATIC_806), i96:0 - 1, i96:0 - 1, 1) :|: i96:0 > 1
f806_0_appendNewList_ConstantStackPush(EOS(STATIC_806), i96:0, i96:0, o128[CyclicAnalysis.field]o126:0) -> f806_0_appendNewList_ConstantStackPush(EOS(STATIC_806), i96:0 - 1, i96:0 - 1, o128[CyclicAnalysis.field]o142:0) :|: o128[CyclicAnalysis.field]o126:0 > 0 && o128[CyclicAnalysis.field]o142:0 > o128[CyclicAnalysis.field]o126:0 && i96:0 > 1
Filtered constant ground arguments:
   f806_0_appendNewList_ConstantStackPush(x1, x2, x3, x4) -> f806_0_appendNewList_ConstantStackPush(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f806_0_appendNewList_ConstantStackPush(x1, x2, x3) -> f806_0_appendNewList_ConstantStackPush(x2, x3)
Finished conversion. Obtained 2 rules.P rules:
f806_0_appendNewList_ConstantStackPush(i96:0, o128[CyclicAnalysis.field]o126:0) -> f806_0_appendNewList_ConstantStackPush(i96:0 - 1, 1) :|: i96:0 > 1
f806_0_appendNewList_ConstantStackPush(i96:0, o128[CyclicAnalysis.field]o126:0) -> f806_0_appendNewList_ConstantStackPush(i96:0 - 1, o128[CyclicAnalysis.field]o142:0) :|: o128[CyclicAnalysis.field]o142:0 > o128[CyclicAnalysis.field]o126:0 && i96:0 > 1 && o128[CyclicAnalysis.field]o126:0 > 0

----------------------------------------

(14)
Obligation:
Rules:
f806_0_appendNewList_ConstantStackPush(i96:0, o128[CyclicAnalysis.field]o126:0) -> f806_0_appendNewList_ConstantStackPush(i96:0 - 1, 1) :|: i96:0 > 1
f806_0_appendNewList_ConstantStackPush(x, x1) -> f806_0_appendNewList_ConstantStackPush(x - 1, x2) :|: x2 > x1 && x > 1 && x1 > 0

----------------------------------------

(15) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(16)
Obligation:
Rules:
f806_0_appendNewList_ConstantStackPush(i96:0, o128[CyclicAnalysis.field]o126:0) -> f806_0_appendNewList_ConstantStackPush(arith, 1) :|: i96:0 > 1 && arith = i96:0 - 1
f806_0_appendNewList_ConstantStackPush(x3, x4) -> f806_0_appendNewList_ConstantStackPush(x5, x6) :|: x6 > x4 && x3 > 1 && x4 > 0 && x5 = x3 - 1

----------------------------------------

(17) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f806_0_appendNewList_ConstantStackPush(i96:0, o128[CyclicAnalysis.field]o126:0) -> f806_0_appendNewList_ConstantStackPush(arith, 1) :|: i96:0 > 1 && arith = i96:0 - 1
(2) f806_0_appendNewList_ConstantStackPush(x3, x4) -> f806_0_appendNewList_ConstantStackPush(x5, x6) :|: x6 > x4 && x3 > 1 && x4 > 0 && x5 = x3 - 1

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!
----------------------------------------

(18)
Obligation:

Termination digraph:
Nodes:
(1) f806_0_appendNewList_ConstantStackPush(i96:0, o128[CyclicAnalysis.field]o126:0) -> f806_0_appendNewList_ConstantStackPush(arith, 1) :|: i96:0 > 1 && arith = i96:0 - 1
(2) f806_0_appendNewList_ConstantStackPush(x3, x4) -> f806_0_appendNewList_ConstantStackPush(x5, x6) :|: x6 > x4 && x3 > 1 && x4 > 0 && x5 = x3 - 1

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!

----------------------------------------

(19) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(20)
Obligation:
Rules:
f806_0_appendNewList_ConstantStackPush(i96:0:0, o128[CyclicAnalysis.field]o126:0:0) -> f806_0_appendNewList_ConstantStackPush(i96:0:0 - 1, 1) :|: i96:0:0 > 1
f806_0_appendNewList_ConstantStackPush(x3:0, x4:0) -> f806_0_appendNewList_ConstantStackPush(x3:0 - 1, x6:0) :|: x6:0 > x4:0 && x3:0 > 1 && x4:0 > 0

----------------------------------------

(21) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f806_0_appendNewList_ConstantStackPush(INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(22)
Obligation:
Rules:
f806_0_appendNewList_ConstantStackPush(i96:0:0, o128[CyclicAnalysis.field]o126:0:0) -> f806_0_appendNewList_ConstantStackPush(c, c1) :|: c1 = 1 && c = i96:0:0 - 1 && i96:0:0 > 1
f806_0_appendNewList_ConstantStackPush(x3:0, x4:0) -> f806_0_appendNewList_ConstantStackPush(c2, x6:0) :|: c2 = x3:0 - 1 && (x6:0 > x4:0 && x3:0 > 1 && x4:0 > 0)

----------------------------------------

(23) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f806_0_appendNewList_ConstantStackPush(x, x1)] = x

The following rules are decreasing:
f806_0_appendNewList_ConstantStackPush(i96:0:0, o128[CyclicAnalysis.field]o126:0:0) -> f806_0_appendNewList_ConstantStackPush(c, c1) :|: c1 = 1 && c = i96:0:0 - 1 && i96:0:0 > 1
f806_0_appendNewList_ConstantStackPush(x3:0, x4:0) -> f806_0_appendNewList_ConstantStackPush(c2, x6:0) :|: c2 = x3:0 - 1 && (x6:0 > x4:0 && x3:0 > 1 && x4:0 > 0)
The following rules are bounded:
f806_0_appendNewList_ConstantStackPush(i96:0:0, o128[CyclicAnalysis.field]o126:0:0) -> f806_0_appendNewList_ConstantStackPush(c, c1) :|: c1 = 1 && c = i96:0:0 - 1 && i96:0:0 > 1
f806_0_appendNewList_ConstantStackPush(x3:0, x4:0) -> f806_0_appendNewList_ConstantStackPush(c2, x6:0) :|: c2 = x3:0 - 1 && (x6:0 > x4:0 && x3:0 > 1 && x4:0 > 0)

----------------------------------------

(24)
YES

----------------------------------------

(25)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: CyclicAnalysis.CyclicAnalysis.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:

*Marker field analysis yielded the following relations that could be markers:

----------------------------------------

(26) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 23 IRulesP rules:
f377_0_appendNewList_ConstantStackPush(EOS(STATIC_377), i33, i33, o46[CyclicAnalysis.field]o44) -> f378_0_appendNewList_LE(EOS(STATIC_378), i33, i33, 1, o46[CyclicAnalysis.field]o44) :|: TRUE
f378_0_appendNewList_LE(EOS(STATIC_378), i42, i42, matching1, o46[CyclicAnalysis.field]o44) -> f380_0_appendNewList_LE(EOS(STATIC_380), i42, i42, 1, o46[CyclicAnalysis.field]o44) :|: TRUE && matching1 = 1
f380_0_appendNewList_LE(EOS(STATIC_380), i42, i42, matching1, o46[CyclicAnalysis.field]o44) -> f393_0_appendNewList_Inc(EOS(STATIC_393), i42, o46[CyclicAnalysis.field]o44) :|: i42 > 1 && matching1 = 1
f393_0_appendNewList_Inc(EOS(STATIC_393), i42, o46[CyclicAnalysis.field]o44) -> f399_0_appendNewList_Load(EOS(STATIC_399), i42 + -1, o46[CyclicAnalysis.field]o44) :|: TRUE
f399_0_appendNewList_Load(EOS(STATIC_399), i43, o46[CyclicAnalysis.field]o44) -> f405_0_appendNewList_New(EOS(STATIC_405), i43, o46[CyclicAnalysis.field]o44) :|: TRUE
f405_0_appendNewList_New(EOS(STATIC_405), i43, o46[CyclicAnalysis.field]o44) -> f411_0_appendNewList_Duplicate(EOS(STATIC_411), i43, o46[CyclicAnalysis.field]o44) :|: TRUE
f411_0_appendNewList_Duplicate(EOS(STATIC_411), i43, o46[CyclicAnalysis.field]o44) -> f415_0_appendNewList_InvokeMethod(EOS(STATIC_415), i43, o46[CyclicAnalysis.field]o44) :|: TRUE
f415_0_appendNewList_InvokeMethod(EOS(STATIC_415), i43, o46[CyclicAnalysis.field]o44) -> f417_0__init__Load(EOS(STATIC_417), i43, o46[CyclicAnalysis.field]o44) :|: TRUE
f417_0__init__Load(EOS(STATIC_417), i43, o46[CyclicAnalysis.field]o44) -> f462_0__init__InvokeMethod(EOS(STATIC_462), i43, o46[CyclicAnalysis.field]o44) :|: TRUE
f462_0__init__InvokeMethod(EOS(STATIC_462), i43, o46[CyclicAnalysis.field]o44) -> f468_0__init__Return(EOS(STATIC_468), i43, o46[CyclicAnalysis.field]o44) :|: TRUE
f468_0__init__Return(EOS(STATIC_468), i43, o46[CyclicAnalysis.field]o44) -> f476_0_appendNewList_Duplicate(EOS(STATIC_476), i43, o46[CyclicAnalysis.field]o44) :|: TRUE
f476_0_appendNewList_Duplicate(EOS(STATIC_476), i43, o46[CyclicAnalysis.field]o44) -> f479_0_appendNewList_FieldAccess(EOS(STATIC_479), i43, o46[CyclicAnalysis.field]o44) :|: TRUE
f479_0_appendNewList_FieldAccess(EOS(STATIC_479), i43, o46[CyclicAnalysis.field]o44) -> f496_0_appendNewList_FieldAccess(EOS(STATIC_496), i43, o46[CyclicAnalysis.field]o44) :|: o46[CyclicAnalysis.field]o44 > 0
f479_0_appendNewList_FieldAccess(EOS(STATIC_479), i43, o77[CyclicAnalysis.field]o77) -> f497_0_appendNewList_FieldAccess(EOS(STATIC_497), i43) :|: TRUE
f496_0_appendNewList_FieldAccess(EOS(STATIC_496), i43, o46[CyclicAnalysis.field]o44) -> f509_0_appendNewList_Store(EOS(STATIC_509), i43, o46[CyclicAnalysis.field]o60) :|: o46[CyclicAnalysis.field]o60 > o46[CyclicAnalysis.field]o44 && o46[CyclicAnalysis.field]o44 >= 0
f509_0_appendNewList_Store(EOS(STATIC_509), i43, o46[CyclicAnalysis.field]o60) -> f528_0_appendNewList_JMP(EOS(STATIC_528), i43, o46[CyclicAnalysis.field]o60) :|: TRUE
f528_0_appendNewList_JMP(EOS(STATIC_528), i43, o46[CyclicAnalysis.field]o60) -> f565_0_appendNewList_Load(EOS(STATIC_565), i43, o46[CyclicAnalysis.field]o60) :|: TRUE
f565_0_appendNewList_Load(EOS(STATIC_565), i43, o46[CyclicAnalysis.field]o60) -> f376_0_appendNewList_Load(EOS(STATIC_376), i43, o46[CyclicAnalysis.field]o60) :|: TRUE
f376_0_appendNewList_Load(EOS(STATIC_376), i33, o46[CyclicAnalysis.field]o44) -> f377_0_appendNewList_ConstantStackPush(EOS(STATIC_377), i33, i33, o46[CyclicAnalysis.field]o44) :|: TRUE
f497_0_appendNewList_FieldAccess(EOS(STATIC_497), i43) -> f515_0_appendNewList_Store(EOS(STATIC_515), i43) :|: TRUE
f515_0_appendNewList_Store(EOS(STATIC_515), i43) -> f530_0_appendNewList_JMP(EOS(STATIC_530), i43) :|: TRUE
f530_0_appendNewList_JMP(EOS(STATIC_530), i43) -> f569_0_appendNewList_Load(EOS(STATIC_569), i43) :|: TRUE
f569_0_appendNewList_Load(EOS(STATIC_569), i43) -> f376_0_appendNewList_Load(EOS(STATIC_376), i43, o77[CyclicAnalysis.field]o60) :|: o77[CyclicAnalysis.field]o60 = 1
Combined rules. Obtained 2 IRulesP rules:
f377_0_appendNewList_ConstantStackPush(EOS(STATIC_377), i33:0, i33:0, o46[CyclicAnalysis.field]o44:0) -> f377_0_appendNewList_ConstantStackPush(EOS(STATIC_377), i33:0 - 1, i33:0 - 1, o46[CyclicAnalysis.field]o60:0) :|: o46[CyclicAnalysis.field]o44:0 > 0 && o46[CyclicAnalysis.field]o60:0 > o46[CyclicAnalysis.field]o44:0 && i33:0 > 1
f377_0_appendNewList_ConstantStackPush(EOS(STATIC_377), i33:0, i33:0, o46[CyclicAnalysis.field]o44:0) -> f377_0_appendNewList_ConstantStackPush(EOS(STATIC_377), i33:0 - 1, i33:0 - 1, 1) :|: i33:0 > 1
Filtered constant ground arguments:
   f377_0_appendNewList_ConstantStackPush(x1, x2, x3, x4) -> f377_0_appendNewList_ConstantStackPush(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f377_0_appendNewList_ConstantStackPush(x1, x2, x3) -> f377_0_appendNewList_ConstantStackPush(x2, x3)
Finished conversion. Obtained 2 rules.P rules:
f377_0_appendNewList_ConstantStackPush(i33:0, o46[CyclicAnalysis.field]o44:0) -> f377_0_appendNewList_ConstantStackPush(i33:0 - 1, o46[CyclicAnalysis.field]o60:0) :|: o46[CyclicAnalysis.field]o60:0 > o46[CyclicAnalysis.field]o44:0 && i33:0 > 1 && o46[CyclicAnalysis.field]o44:0 > 0
f377_0_appendNewList_ConstantStackPush(i33:0, o46[CyclicAnalysis.field]o44:0) -> f377_0_appendNewList_ConstantStackPush(i33:0 - 1, 1) :|: i33:0 > 1

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(27)
Obligation:
Rules:
f377_0_appendNewList_ConstantStackPush(i33:0, o46[CyclicAnalysis.field]o44:0) -> f377_0_appendNewList_ConstantStackPush(i33:0 - 1, o46[CyclicAnalysis.field]o60:0) :|: o46[CyclicAnalysis.field]o60:0 > o46[CyclicAnalysis.field]o44:0 && i33:0 > 1 && o46[CyclicAnalysis.field]o44:0 > 0
f377_0_appendNewList_ConstantStackPush(x, x1) -> f377_0_appendNewList_ConstantStackPush(x - 1, 1) :|: x > 1

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(28) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(29)
Obligation:
Rules:
f377_0_appendNewList_ConstantStackPush(i33:0, o46[CyclicAnalysis.field]o44:0) -> f377_0_appendNewList_ConstantStackPush(arith, o46[CyclicAnalysis.field]o60:0) :|: o46[CyclicAnalysis.field]o60:0 > o46[CyclicAnalysis.field]o44:0 && i33:0 > 1 && o46[CyclicAnalysis.field]o44:0 > 0 && arith = i33:0 - 1
f377_0_appendNewList_ConstantStackPush(x2, x3) -> f377_0_appendNewList_ConstantStackPush(x4, 1) :|: x2 > 1 && x4 = x2 - 1

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(30) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f377_0_appendNewList_ConstantStackPush(i33:0, o46[CyclicAnalysis.field]o44:0) -> f377_0_appendNewList_ConstantStackPush(arith, o46[CyclicAnalysis.field]o60:0) :|: o46[CyclicAnalysis.field]o60:0 > o46[CyclicAnalysis.field]o44:0 && i33:0 > 1 && o46[CyclicAnalysis.field]o44:0 > 0 && arith = i33:0 - 1
(2) f377_0_appendNewList_ConstantStackPush(x2, x3) -> f377_0_appendNewList_ConstantStackPush(x4, 1) :|: x2 > 1 && x4 = x2 - 1

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!
----------------------------------------

(31)
Obligation:

Termination digraph:
Nodes:
(1) f377_0_appendNewList_ConstantStackPush(i33:0, o46[CyclicAnalysis.field]o44:0) -> f377_0_appendNewList_ConstantStackPush(arith, o46[CyclicAnalysis.field]o60:0) :|: o46[CyclicAnalysis.field]o60:0 > o46[CyclicAnalysis.field]o44:0 && i33:0 > 1 && o46[CyclicAnalysis.field]o44:0 > 0 && arith = i33:0 - 1
(2) f377_0_appendNewList_ConstantStackPush(x2, x3) -> f377_0_appendNewList_ConstantStackPush(x4, 1) :|: x2 > 1 && x4 = x2 - 1

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!

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(32) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(33)
Obligation:
Rules:
f377_0_appendNewList_ConstantStackPush(i33:0:0, o46[CyclicAnalysis.field]o44:0:0) -> f377_0_appendNewList_ConstantStackPush(i33:0:0 - 1, o46[CyclicAnalysis.field]o60:0:0) :|: o46[CyclicAnalysis.field]o60:0:0 > o46[CyclicAnalysis.field]o44:0:0 && i33:0:0 > 1 && o46[CyclicAnalysis.field]o44:0:0 > 0
f377_0_appendNewList_ConstantStackPush(x2:0, x3:0) -> f377_0_appendNewList_ConstantStackPush(x2:0 - 1, 1) :|: x2:0 > 1

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(34) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f377_0_appendNewList_ConstantStackPush(INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(35)
Obligation:
Rules:
f377_0_appendNewList_ConstantStackPush(i33:0:0, o46[CyclicAnalysis.field]o44:0:0) -> f377_0_appendNewList_ConstantStackPush(c, o46[CyclicAnalysis.field]o60:0:0) :|: c = i33:0:0 - 1 && (o46[CyclicAnalysis.field]o60:0:0 > o46[CyclicAnalysis.field]o44:0:0 && i33:0:0 > 1 && o46[CyclicAnalysis.field]o44:0:0 > 0)
f377_0_appendNewList_ConstantStackPush(x2:0, x3:0) -> f377_0_appendNewList_ConstantStackPush(c1, c2) :|: c2 = 1 && c1 = x2:0 - 1 && x2:0 > 1

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(36) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f377_0_appendNewList_ConstantStackPush ] = f377_0_appendNewList_ConstantStackPush_1

The following rules are decreasing:
f377_0_appendNewList_ConstantStackPush(i33:0:0, o46[CyclicAnalysis.field]o44:0:0) -> f377_0_appendNewList_ConstantStackPush(c, o46[CyclicAnalysis.field]o60:0:0) :|: c = i33:0:0 - 1 && (o46[CyclicAnalysis.field]o60:0:0 > o46[CyclicAnalysis.field]o44:0:0 && i33:0:0 > 1 && o46[CyclicAnalysis.field]o44:0:0 > 0)
f377_0_appendNewList_ConstantStackPush(x2:0, x3:0) -> f377_0_appendNewList_ConstantStackPush(c1, c2) :|: c2 = 1 && c1 = x2:0 - 1 && x2:0 > 1

The following rules are bounded:
f377_0_appendNewList_ConstantStackPush(i33:0:0, o46[CyclicAnalysis.field]o44:0:0) -> f377_0_appendNewList_ConstantStackPush(c, o46[CyclicAnalysis.field]o60:0:0) :|: c = i33:0:0 - 1 && (o46[CyclicAnalysis.field]o60:0:0 > o46[CyclicAnalysis.field]o44:0:0 && i33:0:0 > 1 && o46[CyclicAnalysis.field]o44:0:0 > 0)
f377_0_appendNewList_ConstantStackPush(x2:0, x3:0) -> f377_0_appendNewList_ConstantStackPush(c1, c2) :|: c2 = 1 && c1 = x2:0 - 1 && x2:0 > 1


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(37)
YES