/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 608 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) JBCTerminationSCC
        (8) SCCToIRSProof [SOUND, 55 ms]
        (9) IRSwT
        (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (11) IRSwT
        (12) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms]
        (13) IRSwT
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IRSwT
        (16) TempFilterProof [SOUND, 35 ms]
        (17) IntTRS
        (18) RankingReductionPairProof [EQUIVALENT, 18 ms]
        (19) YES
    (20) JBCTerminationSCC
        (21) SCCToIRSProof [SOUND, 147 ms]
        (22) IRSwT
        (23) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (24) IRSwT
        (25) IRSwTTerminationDigraphProof [EQUIVALENT, 7 ms]
        (26) IRSwT
        (27) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (28) IRSwT
        (29) TempFilterProof [SOUND, 29 ms]
        (30) IRSwT
        (31) IRSwTToQDPProof [SOUND, 0 ms]
        (32) QDP
        (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (34) YES
    (35) JBCTerminationSCC
        (36) SCCToIRSProof [SOUND, 82 ms]
        (37) IRSwT
        (38) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (39) IRSwT
        (40) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms]
        (41) IRSwT
        (42) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (43) IRSwT
        (44) TempFilterProof [SOUND, 17 ms]
        (45) IntTRS
        (46) PolynomialOrderProcessor [EQUIVALENT, 5 ms]
        (47) YES


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

(0)
Obligation:
need to prove termination of the following program:
public class ListContentTail{

  public static void main(String[] args) {
    Random.args = args;
    IntList l = IntList.createIntList();

    int m = IntList.nth(Random.random(),l);

    while (m > 0) {

      l = l.next;
      m = IntList.nth(Random.random(),l);
    }
  }
}

class IntList {
  int value;
  IntList next;

  public IntList(int value, IntList next) {
    this.value = value;
    this.next = next;
  }

  public static IntList createIntList() {

    int i = Random.random();
    IntList l = null;

    while (i > 0) {
      l = new IntList(Random.random(), l);
      i--;
    }

    return l;
  }

  public static int nth(int n, IntList l){

    while (n > 1 && l != null) {
      n--;
      l = l.next;
    }

    if (l == null) return 0;
    else           return l.value;
  }





}






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

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



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

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

(2)
Obligation:
need to prove termination of the following program:
public class ListContentTail{

  public static void main(String[] args) {
    Random.args = args;
    IntList l = IntList.createIntList();

    int m = IntList.nth(Random.random(),l);

    while (m > 0) {

      l = l.next;
      m = IntList.nth(Random.random(),l);
    }
  }
}

class IntList {
  int value;
  IntList next;

  public IntList(int value, IntList next) {
    this.value = value;
    this.next = next;
  }

  public static IntList createIntList() {

    int i = Random.random();
    IntList l = null;

    while (i > 0) {
      l = new IntList(Random.random(), l);
      i--;
    }

    return l;
  }

  public static int nth(int n, IntList l){

    while (n > 1 && l != null) {
      n--;
      l = l.next;
    }

    if (l == null) return 0;
    else           return l.value;
  }





}






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

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



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

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

(4)
Obligation:
Termination Graph based on JBC Program:
ListContentTail.main([Ljava/lang/String;)V: Graph of 256 nodes with 2 SCCs.



IntList.createIntList()LIntList;: Graph of 187 nodes with 1 SCC.





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

(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: IntList.createIntList()LIntList;
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*java.lang.String: [count]
*Marker field analysis yielded the following relations that could be markers:

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

(8) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 39 IRulesP rules:
f1478_0_createIntList_LE(EOS(STATIC_1478(java.lang.Object(ARRAY(i6)))), i249, i249) -> f1494_0_createIntList_LE(EOS(STATIC_1494(java.lang.Object(ARRAY(i6)))), i249, i249) :|: TRUE
f1494_0_createIntList_LE(EOS(STATIC_1494(java.lang.Object(ARRAY(i6)))), i249, i249) -> f1510_0_createIntList_New(EOS(STATIC_1510(java.lang.Object(ARRAY(i6)))), i249) :|: i249 > 0
f1510_0_createIntList_New(EOS(STATIC_1510(java.lang.Object(ARRAY(i6)))), i249) -> f1524_0_createIntList_Duplicate(EOS(STATIC_1524(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1524_0_createIntList_Duplicate(EOS(STATIC_1524(java.lang.Object(ARRAY(i6)))), i249) -> f1542_0_createIntList_InvokeMethod(EOS(STATIC_1542(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1542_0_createIntList_InvokeMethod(EOS(STATIC_1542(java.lang.Object(ARRAY(i6)))), i249) -> f1552_0_random_FieldAccess(EOS(STATIC_1552(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1552_0_random_FieldAccess(EOS(STATIC_1552(java.lang.Object(ARRAY(i6)))), i249) -> f1580_0_random_FieldAccess(EOS(STATIC_1580(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(ARRAY(i6))) :|: TRUE
f1580_0_random_FieldAccess(EOS(STATIC_1580(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(ARRAY(i6))) -> f1583_0_random_ArrayAccess(EOS(STATIC_1583(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(ARRAY(i6))) :|: TRUE
f1583_0_random_ArrayAccess(EOS(STATIC_1583(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(ARRAY(i6))) -> f1585_0_random_ArrayAccess(EOS(STATIC_1585(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(ARRAY(i6))) :|: TRUE
f1585_0_random_ArrayAccess(EOS(STATIC_1585(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(ARRAY(i6))) -> f1589_0_random_Store(EOS(STATIC_1589(java.lang.Object(ARRAY(i6)))), i249, o211) :|: TRUE
f1589_0_random_Store(EOS(STATIC_1589(java.lang.Object(ARRAY(i6)))), i249, o211) -> f1598_0_random_FieldAccess(EOS(STATIC_1598(java.lang.Object(ARRAY(i6)))), i249, o211) :|: TRUE
f1598_0_random_FieldAccess(EOS(STATIC_1598(java.lang.Object(ARRAY(i6)))), i249, o211) -> f1602_0_random_ConstantStackPush(EOS(STATIC_1602(java.lang.Object(ARRAY(i6)))), i249, o211) :|: TRUE
f1602_0_random_ConstantStackPush(EOS(STATIC_1602(java.lang.Object(ARRAY(i6)))), i249, o211) -> f1608_0_random_IntArithmetic(EOS(STATIC_1608(java.lang.Object(ARRAY(i6)))), i249, o211) :|: TRUE
f1608_0_random_IntArithmetic(EOS(STATIC_1608(java.lang.Object(ARRAY(i6)))), i249, o211) -> f1619_0_random_FieldAccess(EOS(STATIC_1619(java.lang.Object(ARRAY(i6)))), i249, o211) :|: TRUE
f1619_0_random_FieldAccess(EOS(STATIC_1619(java.lang.Object(ARRAY(i6)))), i249, o211) -> f1626_0_random_Load(EOS(STATIC_1626(java.lang.Object(ARRAY(i6)))), i249, o211) :|: TRUE
f1626_0_random_Load(EOS(STATIC_1626(java.lang.Object(ARRAY(i6)))), i249, o211) -> f1642_0_random_InvokeMethod(EOS(STATIC_1642(java.lang.Object(ARRAY(i6)))), i249, o211) :|: TRUE
f1642_0_random_InvokeMethod(EOS(STATIC_1642(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(o216sub)) -> f1649_0_random_InvokeMethod(EOS(STATIC_1649(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(o216sub)) :|: TRUE
f1649_0_random_InvokeMethod(EOS(STATIC_1649(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(o217sub)) -> f1652_0_random_InvokeMethod(EOS(STATIC_1652(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(o217sub)) :|: TRUE
f1652_0_random_InvokeMethod(EOS(STATIC_1652(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(o217sub)) -> f1667_0_length_Load(EOS(STATIC_1667(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(o217sub)) :|: TRUE
f1667_0_length_Load(EOS(STATIC_1667(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(o217sub)) -> f1693_0_length_FieldAccess(EOS(STATIC_1693(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(o217sub)) :|: TRUE
f1693_0_length_FieldAccess(EOS(STATIC_1693(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(java.lang.String(EOC, i296))) -> f1705_0_length_FieldAccess(EOS(STATIC_1705(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(java.lang.String(EOC, i296))) :|: TRUE
f1705_0_length_FieldAccess(EOS(STATIC_1705(java.lang.Object(ARRAY(i6)))), i249, java.lang.Object(java.lang.String(EOC, i296))) -> f1716_0_length_Return(EOS(STATIC_1716(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1716_0_length_Return(EOS(STATIC_1716(java.lang.Object(ARRAY(i6)))), i249) -> f1728_0_random_Return(EOS(STATIC_1728(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1728_0_random_Return(EOS(STATIC_1728(java.lang.Object(ARRAY(i6)))), i249) -> f1743_0_createIntList_Load(EOS(STATIC_1743(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1743_0_createIntList_Load(EOS(STATIC_1743(java.lang.Object(ARRAY(i6)))), i249) -> f1755_0_createIntList_InvokeMethod(EOS(STATIC_1755(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1755_0_createIntList_InvokeMethod(EOS(STATIC_1755(java.lang.Object(ARRAY(i6)))), i249) -> f1763_0__init__Load(EOS(STATIC_1763(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1763_0__init__Load(EOS(STATIC_1763(java.lang.Object(ARRAY(i6)))), i249) -> f1785_0__init__InvokeMethod(EOS(STATIC_1785(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1785_0__init__InvokeMethod(EOS(STATIC_1785(java.lang.Object(ARRAY(i6)))), i249) -> f1792_0__init__Load(EOS(STATIC_1792(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1792_0__init__Load(EOS(STATIC_1792(java.lang.Object(ARRAY(i6)))), i249) -> f1799_0__init__Load(EOS(STATIC_1799(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1799_0__init__Load(EOS(STATIC_1799(java.lang.Object(ARRAY(i6)))), i249) -> f1809_0__init__FieldAccess(EOS(STATIC_1809(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1809_0__init__FieldAccess(EOS(STATIC_1809(java.lang.Object(ARRAY(i6)))), i249) -> f1815_0__init__Load(EOS(STATIC_1815(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1815_0__init__Load(EOS(STATIC_1815(java.lang.Object(ARRAY(i6)))), i249) -> f1821_0__init__Load(EOS(STATIC_1821(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1821_0__init__Load(EOS(STATIC_1821(java.lang.Object(ARRAY(i6)))), i249) -> f1837_0__init__FieldAccess(EOS(STATIC_1837(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1837_0__init__FieldAccess(EOS(STATIC_1837(java.lang.Object(ARRAY(i6)))), i249) -> f1850_0__init__Return(EOS(STATIC_1850(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1850_0__init__Return(EOS(STATIC_1850(java.lang.Object(ARRAY(i6)))), i249) -> f1872_0_createIntList_Store(EOS(STATIC_1872(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1872_0_createIntList_Store(EOS(STATIC_1872(java.lang.Object(ARRAY(i6)))), i249) -> f1889_0_createIntList_Inc(EOS(STATIC_1889(java.lang.Object(ARRAY(i6)))), i249) :|: TRUE
f1889_0_createIntList_Inc(EOS(STATIC_1889(java.lang.Object(ARRAY(i6)))), i249) -> f1898_0_createIntList_JMP(EOS(STATIC_1898(java.lang.Object(ARRAY(i6)))), i249 + -1) :|: TRUE
f1898_0_createIntList_JMP(EOS(STATIC_1898(java.lang.Object(ARRAY(i6)))), i324) -> f1907_0_createIntList_Load(EOS(STATIC_1907(java.lang.Object(ARRAY(i6)))), i324) :|: TRUE
f1907_0_createIntList_Load(EOS(STATIC_1907(java.lang.Object(ARRAY(i6)))), i324) -> f1424_0_createIntList_Load(EOS(STATIC_1424(java.lang.Object(ARRAY(i6)))), i324) :|: TRUE
f1424_0_createIntList_Load(EOS(STATIC_1424(java.lang.Object(ARRAY(i6)))), i209) -> f1478_0_createIntList_LE(EOS(STATIC_1478(java.lang.Object(ARRAY(i6)))), i209, i209) :|: TRUE
Combined rules. Obtained 1 IRulesP rules:
f1478_0_createIntList_LE(EOS(STATIC_1478(java.lang.Object(ARRAY(i6:0)))), i249:0, i249:0) -> f1478_0_createIntList_LE(EOS(STATIC_1478(java.lang.Object(ARRAY(i6:0)))), i249:0 - 1, i249:0 - 1) :|: i249:0 > 0
Filtered duplicate arguments:
   f1478_0_createIntList_LE(x1, x2, x3) -> f1478_0_createIntList_LE(x1, x3)
Filtered unneeded arguments:
   f1478_0_createIntList_LE(x1, x2) -> f1478_0_createIntList_LE(x2)
Finished conversion. Obtained 1 rules.P rules:
f1478_0_createIntList_LE(i249:0) -> f1478_0_createIntList_LE(i249:0 - 1) :|: i249:0 > 0

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

(9)
Obligation:
Rules:
f1478_0_createIntList_LE(i249:0) -> f1478_0_createIntList_LE(i249:0 - 1) :|: i249:0 > 0

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

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

(11)
Obligation:
Rules:
f1478_0_createIntList_LE(i249:0) -> f1478_0_createIntList_LE(arith) :|: i249:0 > 0 && arith = i249:0 - 1

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

(12) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1478_0_createIntList_LE(i249:0) -> f1478_0_createIntList_LE(arith) :|: i249:0 > 0 && arith = i249:0 - 1

Arcs:
(1) -> (1)

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

(13)
Obligation:

Termination digraph:
Nodes:
(1) f1478_0_createIntList_LE(i249:0) -> f1478_0_createIntList_LE(arith) :|: i249:0 > 0 && arith = i249:0 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(15)
Obligation:
Rules:
f1478_0_createIntList_LE(i249:0:0) -> f1478_0_createIntList_LE(i249:0:0 - 1) :|: i249:0:0 > 0

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

(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1478_0_createIntList_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(17)
Obligation:
Rules:
f1478_0_createIntList_LE(i249:0:0) -> f1478_0_createIntList_LE(c) :|: c = i249:0:0 - 1 && i249:0:0 > 0

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

(18) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f1478_0_createIntList_LE ] = f1478_0_createIntList_LE_1

The following rules are decreasing:
f1478_0_createIntList_LE(i249:0:0) -> f1478_0_createIntList_LE(c) :|: c = i249:0:0 - 1 && i249:0:0 > 0

The following rules are bounded:
f1478_0_createIntList_LE(i249:0:0) -> f1478_0_createIntList_LE(c) :|: c = i249:0:0 - 1 && i249:0:0 > 0


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

(19)
YES

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

(20)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: ListContentTail.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*IntList: [next, value]
*java.lang.String: [count]
*Marker field analysis yielded the following relations that could be markers:

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

(21) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 66 IRulesP rules:
f2115_0_main_LE(EOS(STATIC_2115(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o270, i374) -> f2118_0_main_LE(EOS(STATIC_2118(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o270, i374) :|: TRUE
f2118_0_main_LE(EOS(STATIC_2118(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o270, i374) -> f2120_0_main_Load(EOS(STATIC_2120(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o270) :|: i374 > 0
f2120_0_main_Load(EOS(STATIC_2120(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o270) -> f2122_0_main_FieldAccess(EOS(STATIC_2122(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o270) :|: TRUE
f2122_0_main_FieldAccess(EOS(STATIC_2122(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), java.lang.Object(o286sub)) -> f2123_0_main_FieldAccess(EOS(STATIC_2123(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), java.lang.Object(o286sub)) :|: TRUE
f2123_0_main_FieldAccess(EOS(STATIC_2123(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), java.lang.Object(IntList(EOC, o288, i375))) -> f2125_0_main_FieldAccess(EOS(STATIC_2125(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), java.lang.Object(IntList(EOC, o288, i375))) :|: TRUE
f2125_0_main_FieldAccess(EOS(STATIC_2125(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), java.lang.Object(IntList(EOC, o288, i375))) -> f2127_0_main_Store(EOS(STATIC_2127(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288) :|: TRUE
f2127_0_main_Store(EOS(STATIC_2127(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288) -> f2128_0_main_InvokeMethod(EOS(STATIC_2128(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288) :|: TRUE
f2128_0_main_InvokeMethod(EOS(STATIC_2128(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288) -> f2130_0_random_FieldAccess(EOS(STATIC_2130(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288) :|: TRUE
f2130_0_random_FieldAccess(EOS(STATIC_2130(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288) -> f2132_0_random_FieldAccess(EOS(STATIC_2132(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(ARRAY(i265))) :|: TRUE
f2132_0_random_FieldAccess(EOS(STATIC_2132(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(ARRAY(i265))) -> f2135_0_random_ArrayAccess(EOS(STATIC_2135(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(ARRAY(i265))) :|: TRUE
f2135_0_random_ArrayAccess(EOS(STATIC_2135(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(ARRAY(i265))) -> f2139_0_random_ArrayAccess(EOS(STATIC_2139(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(ARRAY(i265))) :|: TRUE
f2139_0_random_ArrayAccess(EOS(STATIC_2139(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(ARRAY(i265))) -> f2143_0_random_Store(EOS(STATIC_2143(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) :|: TRUE
f2143_0_random_Store(EOS(STATIC_2143(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) -> f2151_0_random_FieldAccess(EOS(STATIC_2151(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) :|: TRUE
f2151_0_random_FieldAccess(EOS(STATIC_2151(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) -> f2156_0_random_ConstantStackPush(EOS(STATIC_2156(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) :|: TRUE
f2156_0_random_ConstantStackPush(EOS(STATIC_2156(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) -> f2161_0_random_IntArithmetic(EOS(STATIC_2161(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) :|: TRUE
f2161_0_random_IntArithmetic(EOS(STATIC_2161(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) -> f2169_0_random_FieldAccess(EOS(STATIC_2169(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) :|: TRUE
f2169_0_random_FieldAccess(EOS(STATIC_2169(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) -> f2175_0_random_Load(EOS(STATIC_2175(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) :|: TRUE
f2175_0_random_Load(EOS(STATIC_2175(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) -> f2186_0_random_InvokeMethod(EOS(STATIC_2186(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, o290) :|: TRUE
f2186_0_random_InvokeMethod(EOS(STATIC_2186(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(o303sub)) -> f2192_0_random_InvokeMethod(EOS(STATIC_2192(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(o303sub)) :|: TRUE
f2192_0_random_InvokeMethod(EOS(STATIC_2192(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(o304sub)) -> f2205_0_random_InvokeMethod(EOS(STATIC_2205(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(o304sub)) :|: TRUE
f2205_0_random_InvokeMethod(EOS(STATIC_2205(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(o304sub)) -> f2215_0_length_Load(EOS(STATIC_2215(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(o304sub)) :|: TRUE
f2215_0_length_Load(EOS(STATIC_2215(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(o304sub)) -> f2236_0_length_FieldAccess(EOS(STATIC_2236(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(o304sub)) :|: TRUE
f2236_0_length_FieldAccess(EOS(STATIC_2236(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(java.lang.String(EOC, i392))) -> f2247_0_length_FieldAccess(EOS(STATIC_2247(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(java.lang.String(EOC, i392))) :|: i392 >= 0
f2247_0_length_FieldAccess(EOS(STATIC_2247(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, java.lang.Object(java.lang.String(EOC, i392))) -> f2255_0_length_Return(EOS(STATIC_2255(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, i392) :|: TRUE
f2255_0_length_Return(EOS(STATIC_2255(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, i392) -> f2262_0_random_Return(EOS(STATIC_2262(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, i392) :|: TRUE
f2262_0_random_Return(EOS(STATIC_2262(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, i392) -> f2270_0_main_Load(EOS(STATIC_2270(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, i392) :|: TRUE
f2270_0_main_Load(EOS(STATIC_2270(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, i392) -> f2277_0_main_InvokeMethod(EOS(STATIC_2277(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, i392, o288) :|: TRUE
f2277_0_main_InvokeMethod(EOS(STATIC_2277(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, i392, o288) -> f2285_0_nth_Load(EOS(STATIC_2285(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, i392, o288) :|: TRUE
f2285_0_nth_Load(EOS(STATIC_2285(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, i392, o288) -> f2513_0_nth_Load(EOS(STATIC_2513(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o288, i392, o288) :|: TRUE
f2513_0_nth_Load(EOS(STATIC_2513(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i456, o362) -> f2517_0_nth_ConstantStackPush(EOS(STATIC_2517(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i456, o362, i456) :|: TRUE
f2517_0_nth_ConstantStackPush(EOS(STATIC_2517(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i456, o362, i456) -> f2522_0_nth_LE(EOS(STATIC_2522(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i456, o362, i456, 1) :|: TRUE
f2522_0_nth_LE(EOS(STATIC_2522(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i470, o362, i470, matching1) -> f2529_0_nth_LE(EOS(STATIC_2529(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i470, o362, i470, 1) :|: TRUE && matching1 = 1
f2522_0_nth_LE(EOS(STATIC_2522(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, o362, i471, matching1) -> f2530_0_nth_LE(EOS(STATIC_2530(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, o362, i471, 1) :|: TRUE && matching1 = 1
f2529_0_nth_LE(EOS(STATIC_2529(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i470, o362, i470, matching1) -> f2539_0_nth_Load(EOS(STATIC_2539(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, o362) :|: i470 <= 1 && matching1 = 1
f2539_0_nth_Load(EOS(STATIC_2539(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, o362) -> f2550_0_nth_NONNULL(EOS(STATIC_2550(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, o362, o362) :|: TRUE
f2550_0_nth_NONNULL(EOS(STATIC_2550(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, java.lang.Object(o381sub), java.lang.Object(o381sub)) -> f2554_0_nth_NONNULL(EOS(STATIC_2554(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, java.lang.Object(o381sub), java.lang.Object(o381sub)) :|: TRUE
f2550_0_nth_NONNULL(EOS(STATIC_2550(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, NULL, NULL) -> f2555_0_nth_NONNULL(EOS(STATIC_2555(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, NULL, NULL) :|: TRUE
f2554_0_nth_NONNULL(EOS(STATIC_2554(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, java.lang.Object(o381sub), java.lang.Object(o381sub)) -> f2561_0_nth_Load(EOS(STATIC_2561(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, java.lang.Object(o381sub)) :|: TRUE
f2561_0_nth_Load(EOS(STATIC_2561(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, java.lang.Object(o381sub)) -> f2567_0_nth_FieldAccess(EOS(STATIC_2567(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, java.lang.Object(o381sub)) :|: TRUE
f2567_0_nth_FieldAccess(EOS(STATIC_2567(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, java.lang.Object(IntList(EOC, o392, i491))) -> f2573_0_nth_FieldAccess(EOS(STATIC_2573(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, java.lang.Object(IntList(EOC, o392, i491))) :|: TRUE
f2573_0_nth_FieldAccess(EOS(STATIC_2573(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, java.lang.Object(IntList(EOC, o392, i491))) -> f2589_0_nth_Return(EOS(STATIC_2589(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i491) :|: TRUE
f2589_0_nth_Return(EOS(STATIC_2589(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i491) -> f2616_0_main_Store(EOS(STATIC_2616(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i491) :|: TRUE
f2616_0_main_Store(EOS(STATIC_2616(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i491) -> f2622_0_main_JMP(EOS(STATIC_2622(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i491) :|: TRUE
f2622_0_main_JMP(EOS(STATIC_2622(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i491) -> f2692_0_main_Load(EOS(STATIC_2692(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i491) :|: TRUE
f2692_0_main_Load(EOS(STATIC_2692(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i491) -> f2113_0_main_Load(EOS(STATIC_2113(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i491) :|: TRUE
f2113_0_main_Load(EOS(STATIC_2113(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o270, i366) -> f2115_0_main_LE(EOS(STATIC_2115(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o270, i366) :|: TRUE
f2555_0_nth_NONNULL(EOS(STATIC_2555(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, NULL, NULL) -> f2564_0_nth_ConstantStackPush(EOS(STATIC_2564(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363) :|: TRUE
f2564_0_nth_ConstantStackPush(EOS(STATIC_2564(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363) -> f2569_0_nth_Return(EOS(STATIC_2569(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, 0) :|: TRUE
f2569_0_nth_Return(EOS(STATIC_2569(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, matching1) -> f2575_0_main_Store(EOS(STATIC_2575(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, 0) :|: TRUE && matching1 = 0
f2575_0_main_Store(EOS(STATIC_2575(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, matching1) -> f2616_0_main_Store(EOS(STATIC_2616(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, 0) :|: TRUE && matching1 = 0
f2530_0_nth_LE(EOS(STATIC_2530(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, o362, i471, matching1) -> f2543_0_nth_Load(EOS(STATIC_2543(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, o362) :|: i471 > 1 && matching1 = 1
f2543_0_nth_Load(EOS(STATIC_2543(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, o362) -> f2552_0_nth_NULL(EOS(STATIC_2552(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, o362, o362) :|: TRUE
f2552_0_nth_NULL(EOS(STATIC_2552(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, java.lang.Object(o384sub), java.lang.Object(o384sub)) -> f2557_0_nth_NULL(EOS(STATIC_2557(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, java.lang.Object(o384sub), java.lang.Object(o384sub)) :|: TRUE
f2552_0_nth_NULL(EOS(STATIC_2552(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, NULL, NULL) -> f2558_0_nth_NULL(EOS(STATIC_2558(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, NULL, NULL) :|: TRUE
f2557_0_nth_NULL(EOS(STATIC_2557(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, java.lang.Object(o384sub), java.lang.Object(o384sub)) -> f2565_0_nth_Inc(EOS(STATIC_2565(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, java.lang.Object(o384sub)) :|: TRUE
f2565_0_nth_Inc(EOS(STATIC_2565(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, java.lang.Object(o384sub)) -> f2570_0_nth_Load(EOS(STATIC_2570(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471 + -1, java.lang.Object(o384sub)) :|: TRUE
f2570_0_nth_Load(EOS(STATIC_2570(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i490, java.lang.Object(o384sub)) -> f2578_0_nth_FieldAccess(EOS(STATIC_2578(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i490, java.lang.Object(o384sub)) :|: TRUE
f2578_0_nth_FieldAccess(EOS(STATIC_2578(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i490, java.lang.Object(IntList(EOC, o399, i497))) -> f2595_0_nth_FieldAccess(EOS(STATIC_2595(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i490, java.lang.Object(IntList(EOC, o399, i497))) :|: TRUE
f2595_0_nth_FieldAccess(EOS(STATIC_2595(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i490, java.lang.Object(IntList(EOC, o399, i497))) -> f2620_0_nth_Store(EOS(STATIC_2620(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i490, o399) :|: TRUE
f2620_0_nth_Store(EOS(STATIC_2620(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i490, o399) -> f2624_0_nth_JMP(EOS(STATIC_2624(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i490, o399) :|: TRUE
f2624_0_nth_JMP(EOS(STATIC_2624(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i490, o399) -> f2693_0_nth_Load(EOS(STATIC_2693(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i490, o399) :|: TRUE
f2693_0_nth_Load(EOS(STATIC_2693(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i490, o399) -> f2513_0_nth_Load(EOS(STATIC_2513(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i490, o399) :|: TRUE
f2558_0_nth_NULL(EOS(STATIC_2558(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, i471, NULL, NULL) -> f2566_0_nth_Load(EOS(STATIC_2566(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, NULL) :|: TRUE
f2566_0_nth_Load(EOS(STATIC_2566(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, NULL) -> f2571_0_nth_NONNULL(EOS(STATIC_2571(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, NULL, NULL) :|: TRUE
f2571_0_nth_NONNULL(EOS(STATIC_2571(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363, NULL, NULL) -> f2586_0_nth_ConstantStackPush(EOS(STATIC_2586(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363) :|: TRUE
f2586_0_nth_ConstantStackPush(EOS(STATIC_2586(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363) -> f2564_0_nth_ConstantStackPush(EOS(STATIC_2564(java.lang.Object(ARRAY(i265)))), java.lang.Object(ARRAY(i265)), o363) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f2522_0_nth_LE(EOS(STATIC_2522(java.lang.Object(ARRAY(i265:0)))), java.lang.Object(ARRAY(i265:0)), o363:0, i471:0, java.lang.Object(IntList(EOC, o399:0, i497:0)), i471:0, 1) -> f2522_0_nth_LE(EOS(STATIC_2522(java.lang.Object(ARRAY(i265:0)))), java.lang.Object(ARRAY(i265:0)), o363:0, i471:0 - 1, o399:0, i471:0 - 1, 1) :|: i471:0 > 1
f2522_0_nth_LE(EOS(STATIC_2522(java.lang.Object(ARRAY(i265:0)))), java.lang.Object(ARRAY(i265:0)), java.lang.Object(IntList(EOC, o288:0, i375:0)), i470:0, java.lang.Object(IntList(EOC, o392:0, i491:0)), i470:0, 1) -> f2522_0_nth_LE(EOS(STATIC_2522(java.lang.Object(ARRAY(i265:0)))), java.lang.Object(ARRAY(i265:0)), o288:0, i392:0, o288:0, i392:0, 1) :|: i491:0 > 0 && i392:0 > -1 && i470:0 < 2
Filtered constant ground arguments:
   f2522_0_nth_LE(x1, x2, x3, x4, x5, x6, x7) -> f2522_0_nth_LE(x1, x2, x3, x4, x5, x6)
   IntList(x1, x2, x3) -> IntList(x2, x3)
Filtered duplicate arguments:
   f2522_0_nth_LE(x1, x2, x3, x4, x5, x6) -> f2522_0_nth_LE(x1, x2, x3, x5, x6)
Filtered unneeded arguments:
   f2522_0_nth_LE(x1, x2, x3, x4, x5) -> f2522_0_nth_LE(x3, x4, x5)
Finished conversion. Obtained 2 rules.P rules:
f2522_0_nth_LE(o363:0, java.lang.Object(IntList(o399:0, i497:0)), i471:0) -> f2522_0_nth_LE(o363:0, o399:0, i471:0 - 1) :|: i471:0 > 1
f2522_0_nth_LE(java.lang.Object(IntList(o288:0, i375:0)), java.lang.Object(IntList(o392:0, i491:0)), i470:0) -> f2522_0_nth_LE(o288:0, o288:0, i392:0) :|: i392:0 > -1 && i470:0 < 2 && i491:0 > 0

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

(22)
Obligation:
Rules:
f2522_0_nth_LE(o363:0, java.lang.Object(IntList(o399:0, i497:0)), i471:0) -> f2522_0_nth_LE(o363:0, o399:0, i471:0 - 1) :|: i471:0 > 1
f2522_0_nth_LE(java.lang.Object(IntList(o288:0, i375:0)), java.lang.Object(IntList(o392:0, i491:0)), i470:0) -> f2522_0_nth_LE(o288:0, o288:0, i392:0) :|: i392:0 > -1 && i470:0 < 2 && i491:0 > 0

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

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

(24)
Obligation:
Rules:
f2522_0_nth_LE(o363:0, java.lang.Object(IntList(o399:0, i497:0)), i471:0) -> f2522_0_nth_LE(o363:0, o399:0, arith) :|: i471:0 > 1 && arith = i471:0 - 1
f2522_0_nth_LE(java.lang.Object(IntList(o288:0, i375:0)), java.lang.Object(IntList(o392:0, i491:0)), i470:0) -> f2522_0_nth_LE(o288:0, o288:0, i392:0) :|: i392:0 > -1 && i470:0 < 2 && i491:0 > 0

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

(25) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f2522_0_nth_LE(o363:0, java.lang.Object(IntList(o399:0, i497:0)), i471:0) -> f2522_0_nth_LE(o363:0, o399:0, arith) :|: i471:0 > 1 && arith = i471:0 - 1
(2) f2522_0_nth_LE(java.lang.Object(IntList(o288:0, i375:0)), java.lang.Object(IntList(o392:0, i491:0)), i470:0) -> f2522_0_nth_LE(o288:0, o288:0, i392:0) :|: i392:0 > -1 && i470:0 < 2 && i491:0 > 0

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

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

(26)
Obligation:

Termination digraph:
Nodes:
(1) f2522_0_nth_LE(o363:0, java.lang.Object(IntList(o399:0, i497:0)), i471:0) -> f2522_0_nth_LE(o363:0, o399:0, arith) :|: i471:0 > 1 && arith = i471:0 - 1
(2) f2522_0_nth_LE(java.lang.Object(IntList(o288:0, i375:0)), java.lang.Object(IntList(o392:0, i491:0)), i470:0) -> f2522_0_nth_LE(o288:0, o288:0, i392:0) :|: i392:0 > -1 && i470:0 < 2 && i491:0 > 0

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

This digraph is fully evaluated!

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

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

(28)
Obligation:
Rules:
f2522_0_nth_LE(o363:0:0, java.lang.Object(IntList(o399:0:0, i497:0:0)), i471:0:0) -> f2522_0_nth_LE(o363:0:0, o399:0:0, i471:0:0 - 1) :|: i471:0:0 > 1
f2522_0_nth_LE(java.lang.Object(IntList(o288:0:0, i375:0:0)), java.lang.Object(IntList(o392:0:0, i491:0:0)), i470:0:0) -> f2522_0_nth_LE(o288:0:0, o288:0:0, i392:0:0) :|: i392:0:0 > -1 && i470:0:0 < 2 && i491:0:0 > 0

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

(29) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f2522_0_nth_LE(VARIABLE, VARIABLE, INTEGER)
java.lang.Object(VARIABLE)
IntList(VARIABLE, VARIABLE)
Removed predefined arithmetic.
----------------------------------------

(30)
Obligation:
Rules:
f2522_0_nth_LE(o363:0:0, java.lang.Object(IntList(o399:0:0, i497:0:0))) -> f2522_0_nth_LE(o363:0:0, o399:0:0)
f2522_0_nth_LE(java.lang.Object(IntList(o288:0:0, i375:0:0)), java.lang.Object(IntList(o392:0:0, i491:0:0))) -> f2522_0_nth_LE(o288:0:0, o288:0:0)

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

(31) IRSwTToQDPProof (SOUND)
Removed the integers and created a QDP-Problem.
----------------------------------------

(32)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   f2522_0_nth_LE(o363:0:0, java.lang.Object(IntList(o399:0:0, i497:0:0))) -> f2522_0_nth_LE(o363:0:0, o399:0:0)
   f2522_0_nth_LE(java.lang.Object(IntList(o288:0:0, i375:0:0)), java.lang.Object(IntList(o392:0:0, i491:0:0))) -> f2522_0_nth_LE(o288:0:0, o288:0:0)

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

(33) 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:
*f2522_0_nth_LE(o363:0:0, java.lang.Object(IntList(o399:0:0, i497:0:0))) -> f2522_0_nth_LE(o363:0:0, o399:0:0)
The graph contains the following edges 1 >= 1, 2 > 2


*f2522_0_nth_LE(java.lang.Object(IntList(o288:0:0, i375:0:0)), java.lang.Object(IntList(o392:0:0, i491:0:0))) -> f2522_0_nth_LE(o288:0:0, o288:0:0)
The graph contains the following edges 1 > 1, 1 > 2


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

(34)
YES

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

(35)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: ListContentTail.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*IntList: [next]
*Marker field analysis yielded the following relations that could be markers:

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

(36) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 14 IRulesP rules:
f2040_0_nth_ConstantStackPush(EOS(STATIC_2040), i358, o269, i358) -> f2042_0_nth_LE(EOS(STATIC_2042), i358, o269, i358, 1) :|: TRUE
f2042_0_nth_LE(EOS(STATIC_2042), i362, o269, i362, matching1) -> f2044_0_nth_LE(EOS(STATIC_2044), i362, o269, i362, 1) :|: TRUE && matching1 = 1
f2044_0_nth_LE(EOS(STATIC_2044), i362, o269, i362, matching1) -> f2047_0_nth_Load(EOS(STATIC_2047), i362, o269) :|: i362 > 1 && matching1 = 1
f2047_0_nth_Load(EOS(STATIC_2047), i362, o269) -> f2052_0_nth_NULL(EOS(STATIC_2052), i362, o269, o269) :|: TRUE
f2052_0_nth_NULL(EOS(STATIC_2052), i362, java.lang.Object(o275sub), java.lang.Object(o275sub)) -> f2056_0_nth_NULL(EOS(STATIC_2056), i362, java.lang.Object(o275sub), java.lang.Object(o275sub)) :|: TRUE
f2056_0_nth_NULL(EOS(STATIC_2056), i362, java.lang.Object(o275sub), java.lang.Object(o275sub)) -> f2060_0_nth_Inc(EOS(STATIC_2060), i362, java.lang.Object(o275sub)) :|: TRUE
f2060_0_nth_Inc(EOS(STATIC_2060), i362, java.lang.Object(o275sub)) -> f2068_0_nth_Load(EOS(STATIC_2068), i362 + -1, java.lang.Object(o275sub)) :|: TRUE
f2068_0_nth_Load(EOS(STATIC_2068), i364, java.lang.Object(o275sub)) -> f2078_0_nth_FieldAccess(EOS(STATIC_2078), i364, java.lang.Object(o275sub)) :|: TRUE
f2078_0_nth_FieldAccess(EOS(STATIC_2078), i364, java.lang.Object(IntList(EOC, o282))) -> f2085_0_nth_FieldAccess(EOS(STATIC_2085), i364, java.lang.Object(IntList(EOC, o282))) :|: TRUE
f2085_0_nth_FieldAccess(EOS(STATIC_2085), i364, java.lang.Object(IntList(EOC, o282))) -> f2112_0_nth_Store(EOS(STATIC_2112), i364, o282) :|: TRUE
f2112_0_nth_Store(EOS(STATIC_2112), i364, o282) -> f2114_0_nth_JMP(EOS(STATIC_2114), i364, o282) :|: TRUE
f2114_0_nth_JMP(EOS(STATIC_2114), i364, o282) -> f2116_0_nth_Load(EOS(STATIC_2116), i364, o282) :|: TRUE
f2116_0_nth_Load(EOS(STATIC_2116), i364, o282) -> f2038_0_nth_Load(EOS(STATIC_2038), i364, o282) :|: TRUE
f2038_0_nth_Load(EOS(STATIC_2038), i358, o269) -> f2040_0_nth_ConstantStackPush(EOS(STATIC_2040), i358, o269, i358) :|: TRUE
Combined rules. Obtained 1 IRulesP rules:
f2040_0_nth_ConstantStackPush(EOS(STATIC_2040), i358:0, java.lang.Object(IntList(EOC, o282:0)), i358:0) -> f2040_0_nth_ConstantStackPush(EOS(STATIC_2040), i358:0 - 1, o282:0, i358:0 - 1) :|: i358:0 > 1
Filtered constant ground arguments:
   f2040_0_nth_ConstantStackPush(x1, x2, x3, x4) -> f2040_0_nth_ConstantStackPush(x2, x3, x4)
   EOS(x1) -> EOS
   IntList(x1, x2) -> IntList(x2)
Filtered duplicate arguments:
   f2040_0_nth_ConstantStackPush(x1, x2, x3) -> f2040_0_nth_ConstantStackPush(x2, x3)
Finished conversion. Obtained 1 rules.P rules:
f2040_0_nth_ConstantStackPush(java.lang.Object(IntList(o282:0)), i358:0) -> f2040_0_nth_ConstantStackPush(o282:0, i358:0 - 1) :|: i358:0 > 1

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

(37)
Obligation:
Rules:
f2040_0_nth_ConstantStackPush(java.lang.Object(IntList(o282:0)), i358:0) -> f2040_0_nth_ConstantStackPush(o282:0, i358:0 - 1) :|: i358:0 > 1

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

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

(39)
Obligation:
Rules:
f2040_0_nth_ConstantStackPush(java.lang.Object(IntList(o282:0)), i358:0) -> f2040_0_nth_ConstantStackPush(o282:0, arith) :|: i358:0 > 1 && arith = i358:0 - 1

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

(40) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f2040_0_nth_ConstantStackPush(java.lang.Object(IntList(o282:0)), i358:0) -> f2040_0_nth_ConstantStackPush(o282:0, arith) :|: i358:0 > 1 && arith = i358:0 - 1

Arcs:
(1) -> (1)

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

(41)
Obligation:

Termination digraph:
Nodes:
(1) f2040_0_nth_ConstantStackPush(java.lang.Object(IntList(o282:0)), i358:0) -> f2040_0_nth_ConstantStackPush(o282:0, arith) :|: i358:0 > 1 && arith = i358:0 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(43)
Obligation:
Rules:
f2040_0_nth_ConstantStackPush(java.lang.Object(IntList(o282:0:0)), i358:0:0) -> f2040_0_nth_ConstantStackPush(o282:0:0, i358:0:0 - 1) :|: i358:0:0 > 1

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

(44) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f2040_0_nth_ConstantStackPush(VARIABLE, INTEGER)
java.lang.Object(VARIABLE)
IntList(VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(45)
Obligation:
Rules:
f2040_0_nth_ConstantStackPush(c, i358:0:0) -> f2040_0_nth_ConstantStackPush(o282:0:0, c1) :|: c1 = i358:0:0 - 1 && c = 0 && i358:0:0 > 1

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

(46) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f2040_0_nth_ConstantStackPush(x, x1)] = x1

The following rules are decreasing:
f2040_0_nth_ConstantStackPush(c, i358:0:0) -> f2040_0_nth_ConstantStackPush(o282:0:0, c1) :|: c1 = i358:0:0 - 1 && c = 0 && i358:0:0 > 1
The following rules are bounded:
f2040_0_nth_ConstantStackPush(c, i358:0:0) -> f2040_0_nth_ConstantStackPush(o282:0:0, c1) :|: c1 = i358:0:0 - 1 && c = 0 && i358:0:0 > 1

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

(47)
YES