/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 392 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) JBCTerminationSCC
        (8) SCCToQDPProof [SOUND, 79 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) JBCTerminationSCC
        (13) SCCToIRSProof [SOUND, 74 ms]
        (14) IRSwT
        (15) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (16) IRSwT
        (17) IRSwTTerminationDigraphProof [EQUIVALENT, 48 ms]
        (18) IRSwT
        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (20) IRSwT
        (21) TempFilterProof [SOUND, 50 ms]
        (22) IntTRS
        (23) PolynomialOrderProcessor [EQUIVALENT, 13 ms]
        (24) YES
    (25) JBCTerminationSCC
        (26) SCCToIRSProof [SOUND, 78 ms]
        (27) IRSwT
        (28) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (29) IRSwT
        (30) IRSwTTerminationDigraphProof [EQUIVALENT, 23 ms]
        (31) IRSwT
        (32) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (33) IRSwT
        (34) TempFilterProof [SOUND, 9 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:
f1177_0_length_NULL(EOS(STATIC_1177), java.lang.Object(o191sub), java.lang.Object(o191sub)) -> f1178_0_length_NULL(EOS(STATIC_1178), java.lang.Object(o191sub), java.lang.Object(o191sub)) :|: TRUE
f1178_0_length_NULL(EOS(STATIC_1178), java.lang.Object(o191sub), java.lang.Object(o191sub)) -> f1180_0_length_Load(EOS(STATIC_1180), java.lang.Object(o191sub)) :|: TRUE
f1180_0_length_Load(EOS(STATIC_1180), java.lang.Object(o191sub)) -> f1184_0_length_FieldAccess(EOS(STATIC_1184), java.lang.Object(o191sub)) :|: TRUE
f1184_0_length_FieldAccess(EOS(STATIC_1184), java.lang.Object(CyclicAnalysis.CyclicAnalysis(EOC, o193))) -> f1188_0_length_FieldAccess(EOS(STATIC_1188), java.lang.Object(CyclicAnalysis.CyclicAnalysis(EOC, o193))) :|: TRUE
f1188_0_length_FieldAccess(EOS(STATIC_1188), java.lang.Object(CyclicAnalysis.CyclicAnalysis(EOC, o193))) -> f1191_0_length_Store(EOS(STATIC_1191), o193) :|: TRUE
f1191_0_length_Store(EOS(STATIC_1191), o193) -> f1193_0_length_Inc(EOS(STATIC_1193), o193) :|: TRUE
f1193_0_length_Inc(EOS(STATIC_1193), o193) -> f1195_0_length_JMP(EOS(STATIC_1195), o193) :|: TRUE
f1195_0_length_JMP(EOS(STATIC_1195), o193) -> f1201_0_length_Load(EOS(STATIC_1201), o193) :|: TRUE
f1201_0_length_Load(EOS(STATIC_1201), o193) -> f1175_0_length_Load(EOS(STATIC_1175), o193) :|: TRUE
f1175_0_length_Load(EOS(STATIC_1175), o188) -> f1177_0_length_NULL(EOS(STATIC_1177), o188, o188) :|: TRUE
R rules:
Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules:
f1177_0_length_NULL(EOS(STATIC_1177), java.lang.Object(CyclicAnalysis.CyclicAnalysis(EOC, o193:0)), java.lang.Object(CyclicAnalysis.CyclicAnalysis(EOC, o193:0))) -> f1177_0_length_NULL(EOS(STATIC_1177), o193:0, o193:0) :|: TRUE
R rules:
Filtered ground terms:
   f1177_0_length_NULL(x1, x2, x3) -> f1177_0_length_NULL(x2, x3)
   EOS(x1) -> EOS
   CyclicAnalysis.CyclicAnalysis(x1, x2) -> CyclicAnalysis.CyclicAnalysis(x2)
Filtered duplicate args:
   f1177_0_length_NULL(x1, x2) -> f1177_0_length_NULL(x2)
Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules:
F1177_0_LENGTH_NULL(java.lang.Object(CyclicAnalysis.CyclicAnalysis(o193:0:0))) -> F1177_0_LENGTH_NULL(o193:0:0) :|: TRUE
R rules:

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

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

   F1177_0_LENGTH_NULL(java.lang.Object(CyclicAnalysis.CyclicAnalysis(o193:0:0))) -> F1177_0_LENGTH_NULL(o193:0:0)

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:
*F1177_0_LENGTH_NULL(java.lang.Object(CyclicAnalysis.CyclicAnalysis(o193:0:0))) -> F1177_0_LENGTH_NULL(o193:0:0)
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:
f899_0_appendNewList_ConstantStackPush(EOS(STATIC_899), i100, i100, o143[CyclicAnalysis.field]o141) -> f914_0_appendNewList_LE(EOS(STATIC_914), i100, i100, 1, o143[CyclicAnalysis.field]o141) :|: TRUE
f914_0_appendNewList_LE(EOS(STATIC_914), i114, i114, matching1, o143[CyclicAnalysis.field]o141) -> f939_0_appendNewList_LE(EOS(STATIC_939), i114, i114, 1, o143[CyclicAnalysis.field]o141) :|: TRUE && matching1 = 1
f939_0_appendNewList_LE(EOS(STATIC_939), i114, i114, matching1, o143[CyclicAnalysis.field]o141) -> f954_0_appendNewList_Inc(EOS(STATIC_954), i114, o143[CyclicAnalysis.field]o141) :|: i114 > 1 && matching1 = 1
f954_0_appendNewList_Inc(EOS(STATIC_954), i114, o143[CyclicAnalysis.field]o141) -> f959_0_appendNewList_Load(EOS(STATIC_959), i114 + -1, o143[CyclicAnalysis.field]o141) :|: TRUE
f959_0_appendNewList_Load(EOS(STATIC_959), i116, o143[CyclicAnalysis.field]o141) -> f961_0_appendNewList_New(EOS(STATIC_961), i116, o143[CyclicAnalysis.field]o141) :|: TRUE
f961_0_appendNewList_New(EOS(STATIC_961), i116, o143[CyclicAnalysis.field]o141) -> f965_0_appendNewList_Duplicate(EOS(STATIC_965), i116, o143[CyclicAnalysis.field]o141) :|: TRUE
f965_0_appendNewList_Duplicate(EOS(STATIC_965), i116, o143[CyclicAnalysis.field]o141) -> f967_0_appendNewList_InvokeMethod(EOS(STATIC_967), i116, o143[CyclicAnalysis.field]o141) :|: TRUE
f967_0_appendNewList_InvokeMethod(EOS(STATIC_967), i116, o143[CyclicAnalysis.field]o141) -> f972_0__init__Load(EOS(STATIC_972), i116, o143[CyclicAnalysis.field]o141) :|: TRUE
f972_0__init__Load(EOS(STATIC_972), i116, o143[CyclicAnalysis.field]o141) -> f979_0__init__InvokeMethod(EOS(STATIC_979), i116, o143[CyclicAnalysis.field]o141) :|: TRUE
f979_0__init__InvokeMethod(EOS(STATIC_979), i116, o143[CyclicAnalysis.field]o141) -> f982_0__init__Return(EOS(STATIC_982), i116, o143[CyclicAnalysis.field]o141) :|: TRUE
f982_0__init__Return(EOS(STATIC_982), i116, o143[CyclicAnalysis.field]o141) -> f984_0_appendNewList_Duplicate(EOS(STATIC_984), i116, o143[CyclicAnalysis.field]o141) :|: TRUE
f984_0_appendNewList_Duplicate(EOS(STATIC_984), i116, o143[CyclicAnalysis.field]o141) -> f988_0_appendNewList_FieldAccess(EOS(STATIC_988), i116, o143[CyclicAnalysis.field]o141) :|: TRUE
f988_0_appendNewList_FieldAccess(EOS(STATIC_988), i116, o143[CyclicAnalysis.field]o141) -> f992_0_appendNewList_FieldAccess(EOS(STATIC_992), i116, o143[CyclicAnalysis.field]o141) :|: o143[CyclicAnalysis.field]o141 > 0
f988_0_appendNewList_FieldAccess(EOS(STATIC_988), i116, o156[CyclicAnalysis.field]o156) -> f993_0_appendNewList_FieldAccess(EOS(STATIC_993), i116) :|: TRUE
f992_0_appendNewList_FieldAccess(EOS(STATIC_992), i116, o143[CyclicAnalysis.field]o141) -> f996_0_appendNewList_Store(EOS(STATIC_996), i116, o143[CyclicAnalysis.field]o152) :|: o143[CyclicAnalysis.field]o152 > o143[CyclicAnalysis.field]o141 && o143[CyclicAnalysis.field]o141 >= 0
f996_0_appendNewList_Store(EOS(STATIC_996), i116, o143[CyclicAnalysis.field]o152) -> f1006_0_appendNewList_JMP(EOS(STATIC_1006), i116, o143[CyclicAnalysis.field]o152) :|: TRUE
f1006_0_appendNewList_JMP(EOS(STATIC_1006), i116, o143[CyclicAnalysis.field]o152) -> f1031_0_appendNewList_Load(EOS(STATIC_1031), i116, o143[CyclicAnalysis.field]o152) :|: TRUE
f1031_0_appendNewList_Load(EOS(STATIC_1031), i116, o143[CyclicAnalysis.field]o152) -> f896_0_appendNewList_Load(EOS(STATIC_896), i116, o143[CyclicAnalysis.field]o152) :|: TRUE
f896_0_appendNewList_Load(EOS(STATIC_896), i100, o143[CyclicAnalysis.field]o141) -> f899_0_appendNewList_ConstantStackPush(EOS(STATIC_899), i100, i100, o143[CyclicAnalysis.field]o141) :|: TRUE
f993_0_appendNewList_FieldAccess(EOS(STATIC_993), i116) -> f1000_0_appendNewList_Store(EOS(STATIC_1000), i116) :|: TRUE
f1000_0_appendNewList_Store(EOS(STATIC_1000), i116) -> f1013_0_appendNewList_JMP(EOS(STATIC_1013), i116) :|: TRUE
f1013_0_appendNewList_JMP(EOS(STATIC_1013), i116) -> f1047_0_appendNewList_Load(EOS(STATIC_1047), i116) :|: TRUE
f1047_0_appendNewList_Load(EOS(STATIC_1047), i116) -> f896_0_appendNewList_Load(EOS(STATIC_896), i116, o156[CyclicAnalysis.field]o152) :|: o156[CyclicAnalysis.field]o152 = 1
Combined rules. Obtained 2 IRulesP rules:
f899_0_appendNewList_ConstantStackPush(EOS(STATIC_899), i100:0, i100:0, o143[CyclicAnalysis.field]o141:0) -> f899_0_appendNewList_ConstantStackPush(EOS(STATIC_899), i100:0 - 1, i100:0 - 1, 1) :|: i100:0 > 1
f899_0_appendNewList_ConstantStackPush(EOS(STATIC_899), i100:0, i100:0, o143[CyclicAnalysis.field]o141:0) -> f899_0_appendNewList_ConstantStackPush(EOS(STATIC_899), i100:0 - 1, i100:0 - 1, o143[CyclicAnalysis.field]o152:0) :|: o143[CyclicAnalysis.field]o141:0 > 0 && o143[CyclicAnalysis.field]o152:0 > o143[CyclicAnalysis.field]o141:0 && i100:0 > 1
Filtered constant ground arguments:
   f899_0_appendNewList_ConstantStackPush(x1, x2, x3, x4) -> f899_0_appendNewList_ConstantStackPush(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f899_0_appendNewList_ConstantStackPush(x1, x2, x3) -> f899_0_appendNewList_ConstantStackPush(x2, x3)
Finished conversion. Obtained 2 rules.P rules:
f899_0_appendNewList_ConstantStackPush(i100:0, o143[CyclicAnalysis.field]o141:0) -> f899_0_appendNewList_ConstantStackPush(i100:0 - 1, 1) :|: i100:0 > 1
f899_0_appendNewList_ConstantStackPush(i100:0, o143[CyclicAnalysis.field]o141:0) -> f899_0_appendNewList_ConstantStackPush(i100:0 - 1, o143[CyclicAnalysis.field]o152:0) :|: o143[CyclicAnalysis.field]o152:0 > o143[CyclicAnalysis.field]o141:0 && i100:0 > 1 && o143[CyclicAnalysis.field]o141:0 > 0

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

(14)
Obligation:
Rules:
f899_0_appendNewList_ConstantStackPush(i100:0, o143[CyclicAnalysis.field]o141:0) -> f899_0_appendNewList_ConstantStackPush(i100:0 - 1, 1) :|: i100:0 > 1
f899_0_appendNewList_ConstantStackPush(x, x1) -> f899_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:
f899_0_appendNewList_ConstantStackPush(i100:0, o143[CyclicAnalysis.field]o141:0) -> f899_0_appendNewList_ConstantStackPush(arith, 1) :|: i100:0 > 1 && arith = i100:0 - 1
f899_0_appendNewList_ConstantStackPush(x3, x4) -> f899_0_appendNewList_ConstantStackPush(x5, x6) :|: x6 > x4 && x3 > 1 && x4 > 0 && x5 = x3 - 1

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

(17) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f899_0_appendNewList_ConstantStackPush(i100:0, o143[CyclicAnalysis.field]o141:0) -> f899_0_appendNewList_ConstantStackPush(arith, 1) :|: i100:0 > 1 && arith = i100:0 - 1
(2) f899_0_appendNewList_ConstantStackPush(x3, x4) -> f899_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) f899_0_appendNewList_ConstantStackPush(i100:0, o143[CyclicAnalysis.field]o141:0) -> f899_0_appendNewList_ConstantStackPush(arith, 1) :|: i100:0 > 1 && arith = i100:0 - 1
(2) f899_0_appendNewList_ConstantStackPush(x3, x4) -> f899_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:
f899_0_appendNewList_ConstantStackPush(x3:0, x4:0) -> f899_0_appendNewList_ConstantStackPush(x3:0 - 1, x6:0) :|: x6:0 > x4:0 && x3:0 > 1 && x4:0 > 0
f899_0_appendNewList_ConstantStackPush(i100:0:0, o143[CyclicAnalysis.field]o141:0:0) -> f899_0_appendNewList_ConstantStackPush(i100:0:0 - 1, 1) :|: i100:0:0 > 1

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

(21) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f899_0_appendNewList_ConstantStackPush(INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(22)
Obligation:
Rules:
f899_0_appendNewList_ConstantStackPush(x3:0, x4:0) -> f899_0_appendNewList_ConstantStackPush(c, x6:0) :|: c = x3:0 - 1 && (x6:0 > x4:0 && x3:0 > 1 && x4:0 > 0)
f899_0_appendNewList_ConstantStackPush(i100:0:0, o143[CyclicAnalysis.field]o141:0:0) -> f899_0_appendNewList_ConstantStackPush(c1, c2) :|: c2 = 1 && c1 = i100:0:0 - 1 && i100:0:0 > 1

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

(23) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f899_0_appendNewList_ConstantStackPush(x, x1)] = x

The following rules are decreasing:
f899_0_appendNewList_ConstantStackPush(x3:0, x4:0) -> f899_0_appendNewList_ConstantStackPush(c, x6:0) :|: c = x3:0 - 1 && (x6:0 > x4:0 && x3:0 > 1 && x4:0 > 0)
f899_0_appendNewList_ConstantStackPush(i100:0:0, o143[CyclicAnalysis.field]o141:0:0) -> f899_0_appendNewList_ConstantStackPush(c1, c2) :|: c2 = 1 && c1 = i100:0:0 - 1 && i100:0:0 > 1
The following rules are bounded:
f899_0_appendNewList_ConstantStackPush(x3:0, x4:0) -> f899_0_appendNewList_ConstantStackPush(c, x6:0) :|: c = x3:0 - 1 && (x6:0 > x4:0 && x3:0 > 1 && x4:0 > 0)
f899_0_appendNewList_ConstantStackPush(i100:0:0, o143[CyclicAnalysis.field]o141:0:0) -> f899_0_appendNewList_ConstantStackPush(c1, c2) :|: c2 = 1 && c1 = i100:0:0 - 1 && i100:0:0 > 1

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

(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:
f382_0_appendNewList_ConstantStackPush(EOS(STATIC_382), i31, i31, o43[CyclicAnalysis.field]o41) -> f383_0_appendNewList_LE(EOS(STATIC_383), i31, i31, 1, o43[CyclicAnalysis.field]o41) :|: TRUE
f383_0_appendNewList_LE(EOS(STATIC_383), i42, i42, matching1, o43[CyclicAnalysis.field]o41) -> f386_0_appendNewList_LE(EOS(STATIC_386), i42, i42, 1, o43[CyclicAnalysis.field]o41) :|: TRUE && matching1 = 1
f386_0_appendNewList_LE(EOS(STATIC_386), i42, i42, matching1, o43[CyclicAnalysis.field]o41) -> f408_0_appendNewList_Inc(EOS(STATIC_408), i42, o43[CyclicAnalysis.field]o41) :|: i42 > 1 && matching1 = 1
f408_0_appendNewList_Inc(EOS(STATIC_408), i42, o43[CyclicAnalysis.field]o41) -> f413_0_appendNewList_Load(EOS(STATIC_413), i42 + -1, o43[CyclicAnalysis.field]o41) :|: TRUE
f413_0_appendNewList_Load(EOS(STATIC_413), i44, o43[CyclicAnalysis.field]o41) -> f417_0_appendNewList_New(EOS(STATIC_417), i44, o43[CyclicAnalysis.field]o41) :|: TRUE
f417_0_appendNewList_New(EOS(STATIC_417), i44, o43[CyclicAnalysis.field]o41) -> f420_0_appendNewList_Duplicate(EOS(STATIC_420), i44, o43[CyclicAnalysis.field]o41) :|: TRUE
f420_0_appendNewList_Duplicate(EOS(STATIC_420), i44, o43[CyclicAnalysis.field]o41) -> f422_0_appendNewList_InvokeMethod(EOS(STATIC_422), i44, o43[CyclicAnalysis.field]o41) :|: TRUE
f422_0_appendNewList_InvokeMethod(EOS(STATIC_422), i44, o43[CyclicAnalysis.field]o41) -> f425_0__init__Load(EOS(STATIC_425), i44, o43[CyclicAnalysis.field]o41) :|: TRUE
f425_0__init__Load(EOS(STATIC_425), i44, o43[CyclicAnalysis.field]o41) -> f468_0__init__InvokeMethod(EOS(STATIC_468), i44, o43[CyclicAnalysis.field]o41) :|: TRUE
f468_0__init__InvokeMethod(EOS(STATIC_468), i44, o43[CyclicAnalysis.field]o41) -> f473_0__init__Return(EOS(STATIC_473), i44, o43[CyclicAnalysis.field]o41) :|: TRUE
f473_0__init__Return(EOS(STATIC_473), i44, o43[CyclicAnalysis.field]o41) -> f481_0_appendNewList_Duplicate(EOS(STATIC_481), i44, o43[CyclicAnalysis.field]o41) :|: TRUE
f481_0_appendNewList_Duplicate(EOS(STATIC_481), i44, o43[CyclicAnalysis.field]o41) -> f488_0_appendNewList_FieldAccess(EOS(STATIC_488), i44, o43[CyclicAnalysis.field]o41) :|: TRUE
f488_0_appendNewList_FieldAccess(EOS(STATIC_488), i44, o43[CyclicAnalysis.field]o41) -> f498_0_appendNewList_FieldAccess(EOS(STATIC_498), i44, o43[CyclicAnalysis.field]o41) :|: o43[CyclicAnalysis.field]o41 > 0
f488_0_appendNewList_FieldAccess(EOS(STATIC_488), i44, o79[CyclicAnalysis.field]o79) -> f499_0_appendNewList_FieldAccess(EOS(STATIC_499), i44) :|: TRUE
f498_0_appendNewList_FieldAccess(EOS(STATIC_498), i44, o43[CyclicAnalysis.field]o41) -> f502_0_appendNewList_Store(EOS(STATIC_502), i44, o43[CyclicAnalysis.field]o62) :|: o43[CyclicAnalysis.field]o62 > o43[CyclicAnalysis.field]o41 && o43[CyclicAnalysis.field]o41 >= 0
f502_0_appendNewList_Store(EOS(STATIC_502), i44, o43[CyclicAnalysis.field]o62) -> f520_0_appendNewList_JMP(EOS(STATIC_520), i44, o43[CyclicAnalysis.field]o62) :|: TRUE
f520_0_appendNewList_JMP(EOS(STATIC_520), i44, o43[CyclicAnalysis.field]o62) -> f542_0_appendNewList_Load(EOS(STATIC_542), i44, o43[CyclicAnalysis.field]o62) :|: TRUE
f542_0_appendNewList_Load(EOS(STATIC_542), i44, o43[CyclicAnalysis.field]o62) -> f381_0_appendNewList_Load(EOS(STATIC_381), i44, o43[CyclicAnalysis.field]o62) :|: TRUE
f381_0_appendNewList_Load(EOS(STATIC_381), i31, o43[CyclicAnalysis.field]o41) -> f382_0_appendNewList_ConstantStackPush(EOS(STATIC_382), i31, i31, o43[CyclicAnalysis.field]o41) :|: TRUE
f499_0_appendNewList_FieldAccess(EOS(STATIC_499), i44) -> f503_0_appendNewList_Store(EOS(STATIC_503), i44) :|: TRUE
f503_0_appendNewList_Store(EOS(STATIC_503), i44) -> f522_0_appendNewList_JMP(EOS(STATIC_522), i44) :|: TRUE
f522_0_appendNewList_JMP(EOS(STATIC_522), i44) -> f550_0_appendNewList_Load(EOS(STATIC_550), i44) :|: TRUE
f550_0_appendNewList_Load(EOS(STATIC_550), i44) -> f381_0_appendNewList_Load(EOS(STATIC_381), i44, o79[CyclicAnalysis.field]o62) :|: o79[CyclicAnalysis.field]o62 = 1
Combined rules. Obtained 2 IRulesP rules:
f382_0_appendNewList_ConstantStackPush(EOS(STATIC_382), i31:0, i31:0, o43[CyclicAnalysis.field]o41:0) -> f382_0_appendNewList_ConstantStackPush(EOS(STATIC_382), i31:0 - 1, i31:0 - 1, 1) :|: i31:0 > 1
f382_0_appendNewList_ConstantStackPush(EOS(STATIC_382), i31:0, i31:0, o43[CyclicAnalysis.field]o41:0) -> f382_0_appendNewList_ConstantStackPush(EOS(STATIC_382), i31:0 - 1, i31:0 - 1, o43[CyclicAnalysis.field]o62:0) :|: o43[CyclicAnalysis.field]o41:0 > 0 && o43[CyclicAnalysis.field]o62:0 > o43[CyclicAnalysis.field]o41:0 && i31:0 > 1
Filtered constant ground arguments:
   f382_0_appendNewList_ConstantStackPush(x1, x2, x3, x4) -> f382_0_appendNewList_ConstantStackPush(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f382_0_appendNewList_ConstantStackPush(x1, x2, x3) -> f382_0_appendNewList_ConstantStackPush(x2, x3)
Finished conversion. Obtained 2 rules.P rules:
f382_0_appendNewList_ConstantStackPush(i31:0, o43[CyclicAnalysis.field]o41:0) -> f382_0_appendNewList_ConstantStackPush(i31:0 - 1, 1) :|: i31:0 > 1
f382_0_appendNewList_ConstantStackPush(i31:0, o43[CyclicAnalysis.field]o41:0) -> f382_0_appendNewList_ConstantStackPush(i31:0 - 1, o43[CyclicAnalysis.field]o62:0) :|: o43[CyclicAnalysis.field]o62:0 > o43[CyclicAnalysis.field]o41:0 && i31:0 > 1 && o43[CyclicAnalysis.field]o41:0 > 0

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(27)
Obligation:
Rules:
f382_0_appendNewList_ConstantStackPush(i31:0, o43[CyclicAnalysis.field]o41:0) -> f382_0_appendNewList_ConstantStackPush(i31:0 - 1, 1) :|: i31:0 > 1
f382_0_appendNewList_ConstantStackPush(x, x1) -> f382_0_appendNewList_ConstantStackPush(x - 1, x2) :|: x2 > x1 && x > 1 && x1 > 0

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

(29)
Obligation:
Rules:
f382_0_appendNewList_ConstantStackPush(i31:0, o43[CyclicAnalysis.field]o41:0) -> f382_0_appendNewList_ConstantStackPush(arith, 1) :|: i31:0 > 1 && arith = i31:0 - 1
f382_0_appendNewList_ConstantStackPush(x3, x4) -> f382_0_appendNewList_ConstantStackPush(x5, x6) :|: x6 > x4 && x3 > 1 && x4 > 0 && x5 = x3 - 1

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(30) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f382_0_appendNewList_ConstantStackPush(i31:0, o43[CyclicAnalysis.field]o41:0) -> f382_0_appendNewList_ConstantStackPush(arith, 1) :|: i31:0 > 1 && arith = i31:0 - 1
(2) f382_0_appendNewList_ConstantStackPush(x3, x4) -> f382_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!
----------------------------------------

(31)
Obligation:

Termination digraph:
Nodes:
(1) f382_0_appendNewList_ConstantStackPush(i31:0, o43[CyclicAnalysis.field]o41:0) -> f382_0_appendNewList_ConstantStackPush(arith, 1) :|: i31:0 > 1 && arith = i31:0 - 1
(2) f382_0_appendNewList_ConstantStackPush(x3, x4) -> f382_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!

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

(33)
Obligation:
Rules:
f382_0_appendNewList_ConstantStackPush(i31:0:0, o43[CyclicAnalysis.field]o41:0:0) -> f382_0_appendNewList_ConstantStackPush(i31:0:0 - 1, 1) :|: i31:0:0 > 1
f382_0_appendNewList_ConstantStackPush(x3:0, x4:0) -> f382_0_appendNewList_ConstantStackPush(x3:0 - 1, x6:0) :|: x6:0 > x4:0 && x3:0 > 1 && x4:0 > 0

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(34) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f382_0_appendNewList_ConstantStackPush(INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(35)
Obligation:
Rules:
f382_0_appendNewList_ConstantStackPush(i31:0:0, o43[CyclicAnalysis.field]o41:0:0) -> f382_0_appendNewList_ConstantStackPush(c, c1) :|: c1 = 1 && c = i31:0:0 - 1 && i31:0:0 > 1
f382_0_appendNewList_ConstantStackPush(x3:0, x4:0) -> f382_0_appendNewList_ConstantStackPush(c2, x6:0) :|: c2 = x3:0 - 1 && (x6:0 > x4:0 && x3:0 > 1 && x4:0 > 0)

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(36) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f382_0_appendNewList_ConstantStackPush ] = f382_0_appendNewList_ConstantStackPush_1

The following rules are decreasing:
f382_0_appendNewList_ConstantStackPush(i31:0:0, o43[CyclicAnalysis.field]o41:0:0) -> f382_0_appendNewList_ConstantStackPush(c, c1) :|: c1 = 1 && c = i31:0:0 - 1 && i31:0:0 > 1
f382_0_appendNewList_ConstantStackPush(x3:0, x4:0) -> f382_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:
f382_0_appendNewList_ConstantStackPush(i31:0:0, o43[CyclicAnalysis.field]o41:0:0) -> f382_0_appendNewList_ConstantStackPush(c, c1) :|: c1 = 1 && c = i31:0:0 - 1 && i31:0:0 > 1
f382_0_appendNewList_ConstantStackPush(x3:0, x4:0) -> f382_0_appendNewList_ConstantStackPush(c2, x6:0) :|: c2 = x3:0 - 1 && (x6:0 > x4:0 && x3:0 > 1 && x4:0 > 0)


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(37)
YES