/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


termination of the given Bare JBC problem could be proven:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 97 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 1029 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 185 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 49 ms]
(12) AND
    (13) IRSwT
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IRSwT
        (16) TempFilterProof [SOUND, 11 ms]
        (17) IntTRS
        (18) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) IRSwT
        (21) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (22) IRSwT
        (23) TempFilterProof [SOUND, 25 ms]
        (24) IntTRS
        (25) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (26) YES


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

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

    public static int fib(int n){
	if (n  < 2) return 1;
	else return fib(n-1) + fib(n-2);	  
    }

    public static int doSum(List x){
	if (x==null) return 1;
	else return fib(x.head) + doSum(x.tail);	
    }

    public static void main(String [] args) {
	Random.args = args;
	List l = List.mk(Random.random()*Random.random());
	//System.out.println(doSum(l));
    }
}



public class List {
    public int head;
    public List tail;

    public List(int head, List tail) {
	this.head = head;
	this.tail = tail;
    }

    public List getTail() {
	return tail;
    }

    public static List mk(int len) {
	List result = null;

	while (len-- > 0)
	    result = new List(Random.random(), result);

	return result;
    }
}

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

  public static int random() {
      if (index >= args.length)
	  return 0;

      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 FibSLR {

    public static int fib(int n){
	if (n  < 2) return 1;
	else return fib(n-1) + fib(n-2);	  
    }

    public static int doSum(List x){
	if (x==null) return 1;
	else return fib(x.head) + doSum(x.tail);	
    }

    public static void main(String [] args) {
	Random.args = args;
	List l = List.mk(Random.random()*Random.random());
	//System.out.println(doSum(l));
    }
}



public class List {
    public int head;
    public List tail;

    public List(int head, List tail) {
	this.head = head;
	this.tail = tail;
    }

    public List getTail() {
	return tail;
    }

    public static List mk(int len) {
	List result = null;

	while (len-- > 0)
	    result = new List(Random.random(), result);

	return result;
    }
}

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

  public static int random() {
      if (index >= args.length)
	  return 0;

      String string = args[index];
      index++;
      return string.length();
  }
}



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

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

(4)
Obligation:
Termination Graph based on JBC Program:
FibSLR.main([Ljava/lang/String;)V: Graph of 231 nodes with 0 SCCs.



List.mk(I)LList;: Graph of 264 nodes with 1 SCC.





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

(5) TerminationGraphToSCCProof (SOUND)
Splitted TerminationGraph to 1 SCCs.
----------------------------------------

(6)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: List.mk(I)LList;
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:

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

(7) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 67 IRulesP rules:
f3370_0_mk_Inc(EOS(STATIC_3370(java.lang.Object(ARRAY(i527)), i528)), i1432, i1432) -> f3386_0_mk_LE(EOS(STATIC_3386(java.lang.Object(ARRAY(i527)), i528)), i1432 + -1, i1432) :|: TRUE
f3386_0_mk_LE(EOS(STATIC_3386(java.lang.Object(ARRAY(i527)), i528)), i1466, i1432) -> f3977_0_mk_LE(EOS(STATIC_3977(java.lang.Object(ARRAY(i527)), i528)), i1466, i1432) :|: TRUE
f3977_0_mk_LE(EOS(STATIC_3977(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1887) -> f3983_0_mk_LE(EOS(STATIC_3983(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1887) :|: TRUE
f3983_0_mk_LE(EOS(STATIC_3983(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1887) -> f3986_0_mk_New(EOS(STATIC_3986(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: i1887 > 0
f3986_0_mk_New(EOS(STATIC_3986(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f3988_0_mk_Duplicate(EOS(STATIC_3988(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f3988_0_mk_Duplicate(EOS(STATIC_3988(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f3991_0_mk_InvokeMethod(EOS(STATIC_3991(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f3991_0_mk_InvokeMethod(EOS(STATIC_3991(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4015_0_random_FieldAccess(EOS(STATIC_4015(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4015_0_random_FieldAccess(EOS(STATIC_4015(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4042_0_random_FieldAccess(EOS(STATIC_4042(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1868) :|: TRUE
f4042_0_random_FieldAccess(EOS(STATIC_4042(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1868) -> f4046_0_random_ArrayLength(EOS(STATIC_4046(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1868, java.lang.Object(ARRAY(i1867))) :|: TRUE
f4046_0_random_ArrayLength(EOS(STATIC_4046(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1868, java.lang.Object(ARRAY(i1867))) -> f4067_0_random_LT(EOS(STATIC_4067(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1868, i1867) :|: i1867 >= 0
f4067_0_random_LT(EOS(STATIC_4067(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1868, i1867) -> f4072_0_random_LT(EOS(STATIC_4072(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1868, i1867) :|: i1868 < i1867
f4067_0_random_LT(EOS(STATIC_4067(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1868, i1867) -> f4074_0_random_LT(EOS(STATIC_4074(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1868, i1867) :|: i1868 >= i1867
f4072_0_random_LT(EOS(STATIC_4072(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1868, i1867) -> f4078_0_random_FieldAccess(EOS(STATIC_4078(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: i1868 < i1867
f4078_0_random_FieldAccess(EOS(STATIC_4078(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4086_0_random_FieldAccess(EOS(STATIC_4086(java.lang.Object(ARRAY(i1867)), i1868)), i1870, java.lang.Object(ARRAY(i1867))) :|: TRUE
f4086_0_random_FieldAccess(EOS(STATIC_4086(java.lang.Object(ARRAY(i1867)), i1868)), i1870, java.lang.Object(ARRAY(i1867))) -> f4094_0_random_ArrayAccess(EOS(STATIC_4094(java.lang.Object(ARRAY(i1867)), i1868)), i1870, java.lang.Object(ARRAY(i1867)), i1868) :|: TRUE
f4094_0_random_ArrayAccess(EOS(STATIC_4094(java.lang.Object(ARRAY(i1867)), i1966)), i1870, java.lang.Object(ARRAY(i1867)), i1966) -> f4102_0_random_ArrayAccess(EOS(STATIC_4102(java.lang.Object(ARRAY(i1867)), i1966)), i1870, java.lang.Object(ARRAY(i1867)), i1966) :|: TRUE
f4102_0_random_ArrayAccess(EOS(STATIC_4102(java.lang.Object(ARRAY(i1867)), i1966)), i1870, java.lang.Object(ARRAY(i1867)), i1966) -> f4105_0_random_ArrayAccess(EOS(STATIC_4105(java.lang.Object(ARRAY(i1867)), i1966)), i1870, java.lang.Object(ARRAY(i1867)), i1966) :|: TRUE
f4105_0_random_ArrayAccess(EOS(STATIC_4105(java.lang.Object(ARRAY(i1867)), i1966)), i1870, java.lang.Object(ARRAY(i1867)), i1966) -> f4113_0_random_Store(EOS(STATIC_4113(java.lang.Object(ARRAY(i1867)), i1966)), i1870, o900) :|: TRUE
f4113_0_random_Store(EOS(STATIC_4113(java.lang.Object(ARRAY(i1867)), i1966)), i1870, o900) -> f4122_0_random_FieldAccess(EOS(STATIC_4122(java.lang.Object(ARRAY(i1867)), i1966)), i1870, o900) :|: TRUE
f4122_0_random_FieldAccess(EOS(STATIC_4122(java.lang.Object(ARRAY(i1867)), i1966)), i1870, o900) -> f4130_0_random_ConstantStackPush(EOS(STATIC_4130(java.lang.Object(ARRAY(i1867)), i1966)), i1870, o900, i1966) :|: TRUE
f4130_0_random_ConstantStackPush(EOS(STATIC_4130(java.lang.Object(ARRAY(i1867)), i1966)), i1870, o900, i1966) -> f4138_0_random_IntArithmetic(EOS(STATIC_4138(java.lang.Object(ARRAY(i1867)), i1966)), i1870, o900, i1966, 1) :|: TRUE
f4138_0_random_IntArithmetic(EOS(STATIC_4138(java.lang.Object(ARRAY(i1867)), i1966)), i1870, o900, i1966, matching1) -> f4149_0_random_FieldAccess(EOS(STATIC_4149(java.lang.Object(ARRAY(i1867)), i1966)), i1870, o900, i1966 + 1) :|: i1966 >= 0 && matching1 = 1
f4149_0_random_FieldAccess(EOS(STATIC_4149(java.lang.Object(ARRAY(i1867)), i1966)), i1870, o900, i1999) -> f4156_0_random_Load(EOS(STATIC_4156(java.lang.Object(ARRAY(i1867)), i1999)), i1870, o900) :|: TRUE
f4156_0_random_Load(EOS(STATIC_4156(java.lang.Object(ARRAY(i1867)), i1999)), i1870, o900) -> f4166_0_random_InvokeMethod(EOS(STATIC_4166(java.lang.Object(ARRAY(i1867)), i1999)), i1870, o900) :|: TRUE
f4166_0_random_InvokeMethod(EOS(STATIC_4166(java.lang.Object(ARRAY(i1867)), i1999)), i1870, java.lang.Object(o934sub)) -> f4170_0_random_InvokeMethod(EOS(STATIC_4170(java.lang.Object(ARRAY(i1867)), i1999)), i1870, java.lang.Object(o934sub)) :|: TRUE
f4170_0_random_InvokeMethod(EOS(STATIC_4170(java.lang.Object(ARRAY(i1867)), i1999)), i1870, java.lang.Object(o937sub)) -> f4177_0_random_InvokeMethod(EOS(STATIC_4177(java.lang.Object(ARRAY(i1867)), i1999)), i1870, java.lang.Object(o937sub)) :|: TRUE
f4177_0_random_InvokeMethod(EOS(STATIC_4177(java.lang.Object(ARRAY(i1867)), i1999)), i1870, java.lang.Object(o937sub)) -> f4191_0_length_Load(EOS(STATIC_4191(java.lang.Object(ARRAY(i1867)), i1999)), i1870, java.lang.Object(o937sub)) :|: TRUE
f4191_0_length_Load(EOS(STATIC_4191(java.lang.Object(ARRAY(i1867)), i1999)), i1870, java.lang.Object(o937sub)) -> f4210_0_length_FieldAccess(EOS(STATIC_4210(java.lang.Object(ARRAY(i1867)), i1999)), i1870, java.lang.Object(o937sub)) :|: TRUE
f4210_0_length_FieldAccess(EOS(STATIC_4210(java.lang.Object(ARRAY(i1867)), i1999)), i1870, java.lang.Object(java.lang.String(EOC, i2078))) -> f4235_0_length_FieldAccess(EOS(STATIC_4235(java.lang.Object(ARRAY(i1867)), i1999)), i1870, java.lang.Object(java.lang.String(EOC, i2078))) :|: TRUE
f4235_0_length_FieldAccess(EOS(STATIC_4235(java.lang.Object(ARRAY(i1867)), i1999)), i1870, java.lang.Object(java.lang.String(EOC, i2078))) -> f4241_0_length_Return(EOS(STATIC_4241(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4241_0_length_Return(EOS(STATIC_4241(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4251_0_random_Return(EOS(STATIC_4251(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4251_0_random_Return(EOS(STATIC_4251(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4258_0_mk_Load(EOS(STATIC_4258(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4258_0_mk_Load(EOS(STATIC_4258(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4264_0_mk_InvokeMethod(EOS(STATIC_4264(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4264_0_mk_InvokeMethod(EOS(STATIC_4264(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4277_0__init__Load(EOS(STATIC_4277(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4277_0__init__Load(EOS(STATIC_4277(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4296_0__init__InvokeMethod(EOS(STATIC_4296(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4296_0__init__InvokeMethod(EOS(STATIC_4296(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4308_0__init__Load(EOS(STATIC_4308(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4308_0__init__Load(EOS(STATIC_4308(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4317_0__init__Load(EOS(STATIC_4317(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4317_0__init__Load(EOS(STATIC_4317(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4330_0__init__FieldAccess(EOS(STATIC_4330(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4330_0__init__FieldAccess(EOS(STATIC_4330(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4343_0__init__Load(EOS(STATIC_4343(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4343_0__init__Load(EOS(STATIC_4343(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4356_0__init__Load(EOS(STATIC_4356(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4356_0__init__Load(EOS(STATIC_4356(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4370_0__init__FieldAccess(EOS(STATIC_4370(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4370_0__init__FieldAccess(EOS(STATIC_4370(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4386_0__init__Return(EOS(STATIC_4386(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4386_0__init__Return(EOS(STATIC_4386(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4398_0_mk_Store(EOS(STATIC_4398(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4398_0_mk_Store(EOS(STATIC_4398(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4434_0_mk_JMP(EOS(STATIC_4434(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4434_0_mk_JMP(EOS(STATIC_4434(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4496_0_mk_Load(EOS(STATIC_4496(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4496_0_mk_Load(EOS(STATIC_4496(java.lang.Object(ARRAY(i1867)), i1999)), i1870) -> f4497_0_mk_Load(EOS(STATIC_4497(java.lang.Object(ARRAY(i1867)), i1999)), i1870) :|: TRUE
f4497_0_mk_Load(EOS(STATIC_4497(java.lang.Object(ARRAY(i2288)), i2289)), i2291) -> f4544_0_mk_Inc(EOS(STATIC_4544(java.lang.Object(ARRAY(i2288)), i2289)), i2291, i2291) :|: TRUE
f4544_0_mk_Inc(EOS(STATIC_4544(java.lang.Object(ARRAY(i2288)), i2289)), i2291, i2291) -> f4584_0_mk_LE(EOS(STATIC_4584(java.lang.Object(ARRAY(i2288)), i2289)), i2291 + -1, i2291) :|: TRUE
f4584_0_mk_LE(EOS(STATIC_4584(java.lang.Object(ARRAY(i2288)), i2289)), i2355, i2291) -> f3977_0_mk_LE(EOS(STATIC_3977(java.lang.Object(ARRAY(i2288)), i2289)), i2355, i2291) :|: TRUE
f4074_0_random_LT(EOS(STATIC_4074(java.lang.Object(ARRAY(i1867)), i1868)), i1870, i1868, i1867) -> f4084_0_random_ConstantStackPush(EOS(STATIC_4084(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: i1868 >= i1867
f4084_0_random_ConstantStackPush(EOS(STATIC_4084(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4089_0_random_Return(EOS(STATIC_4089(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4089_0_random_Return(EOS(STATIC_4089(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4097_0_mk_Load(EOS(STATIC_4097(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4097_0_mk_Load(EOS(STATIC_4097(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4103_0_mk_InvokeMethod(EOS(STATIC_4103(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4103_0_mk_InvokeMethod(EOS(STATIC_4103(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4108_0__init__Load(EOS(STATIC_4108(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4108_0__init__Load(EOS(STATIC_4108(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4126_0__init__InvokeMethod(EOS(STATIC_4126(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4126_0__init__InvokeMethod(EOS(STATIC_4126(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4137_0__init__Load(EOS(STATIC_4137(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4137_0__init__Load(EOS(STATIC_4137(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4143_0__init__Load(EOS(STATIC_4143(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4143_0__init__Load(EOS(STATIC_4143(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4153_0__init__FieldAccess(EOS(STATIC_4153(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4153_0__init__FieldAccess(EOS(STATIC_4153(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4162_0__init__Load(EOS(STATIC_4162(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4162_0__init__Load(EOS(STATIC_4162(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4168_0__init__Load(EOS(STATIC_4168(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4168_0__init__Load(EOS(STATIC_4168(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4173_0__init__FieldAccess(EOS(STATIC_4173(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4173_0__init__FieldAccess(EOS(STATIC_4173(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4190_0__init__Return(EOS(STATIC_4190(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4190_0__init__Return(EOS(STATIC_4190(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4196_0_mk_Store(EOS(STATIC_4196(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4196_0_mk_Store(EOS(STATIC_4196(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4205_0_mk_JMP(EOS(STATIC_4205(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4205_0_mk_JMP(EOS(STATIC_4205(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f4232_0_mk_Load(EOS(STATIC_4232(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f4232_0_mk_Load(EOS(STATIC_4232(java.lang.Object(ARRAY(i1867)), i1868)), i1870) -> f3357_0_mk_Load(EOS(STATIC_3357(java.lang.Object(ARRAY(i1867)), i1868)), i1870) :|: TRUE
f3357_0_mk_Load(EOS(STATIC_3357(java.lang.Object(ARRAY(i527)), i528)), i1432) -> f3370_0_mk_Inc(EOS(STATIC_3370(java.lang.Object(ARRAY(i527)), i528)), i1432, i1432) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f4067_0_random_LT(EOS(STATIC_4067(java.lang.Object(ARRAY(i1867:0)), i1868:0)), i1870:0, i1868:0, i1867:0) -> f4067_0_random_LT(EOS(STATIC_4067(java.lang.Object(ARRAY(i1867:0)), i1868:0 + 1)), i1870:0 - 1, i1868:0 + 1, i1867:0) :|: i1868:0 < i1867:0 && i1868:0 > -1 && i1867:0 > -1 && i1870:0 > 0
f4067_0_random_LT(EOS(STATIC_4067(java.lang.Object(ARRAY(i1867:0)), i1868:0)), i1870:0, i1868:0, i1867:0) -> f4067_0_random_LT(EOS(STATIC_4067(java.lang.Object(ARRAY(i1867:0)), i1868:0)), i1870:0 - 1, i1868:0, i1867:0) :|: i1868:0 >= i1867:0 && i1867:0 > -1 && i1870:0 > 0
Finished conversion. Obtained 2 rules.P rules:
f4067_0_random_LT(i1870:0, i1868:0, i1867:0, i1867:0, i1868:0) -> f4067_0_random_LT(i1870:0 - 1, i1868:0 + 1, i1867:0, i1867:0, i1868:0 + 1) :|: i1868:0 > -1 && i1868:0 < i1867:0 && i1870:0 > 0 && i1867:0 > -1
f4067_0_random_LT(i1870:0, i1868:0, i1867:0, i1867:0, i1868:0) -> f4067_0_random_LT(i1870:0 - 1, i1868:0, i1867:0, i1867:0, i1868:0) :|: i1867:0 > -1 && i1870:0 > 0 && i1868:0 >= i1867:0

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(8)
Obligation:
Rules:
f4067_0_random_LT(i1870:0, i1868:0, i1867:0, i1867:0, i1868:0) -> f4067_0_random_LT(i1870:0 - 1, i1868:0 + 1, i1867:0, i1867:0, i1868:0 + 1) :|: i1868:0 > -1 && i1868:0 < i1867:0 && i1870:0 > 0 && i1867:0 > -1
f4067_0_random_LT(x, x1, x2, x2, x1) -> f4067_0_random_LT(x - 1, x1, x2, x2, x1) :|: x2 > -1 && x > 0 && x1 >= x2

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(9) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
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(10)
Obligation:
Rules:
f4067_0_random_LT(i1870:0, i1868:0, i1867:0, i1867:0, i1868:0) -> f4067_0_random_LT(arith, arith1, i1867:0, i1867:0, arith1) :|: i1868:0 > -1 && i1868:0 < i1867:0 && i1870:0 > 0 && i1867:0 > -1 && arith = i1870:0 - 1 && arith1 = i1868:0 + 1 && arith1 = i1868:0 + 1
f4067_0_random_LT(x3, x4, x5, x5, x4) -> f4067_0_random_LT(x6, x4, x5, x5, x4) :|: x5 > -1 && x3 > 0 && x4 >= x5 && x6 = x3 - 1

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(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f4067_0_random_LT(i1870:0, i1868:0, i1867:0, i1867:0, i1868:0) -> f4067_0_random_LT(arith, arith1, i1867:0, i1867:0, arith1) :|: i1868:0 > -1 && i1868:0 < i1867:0 && i1870:0 > 0 && i1867:0 > -1 && arith = i1870:0 - 1 && arith1 = i1868:0 + 1 && arith1 = i1868:0 + 1
(2) f4067_0_random_LT(x3, x4, x5, x5, x4) -> f4067_0_random_LT(x6, x4, x5, x5, x4) :|: x5 > -1 && x3 > 0 && x4 >= x5 && x6 = x3 - 1

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

This digraph is fully evaluated!
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(12)
Complex Obligation (AND)

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(13)
Obligation:

Termination digraph:
Nodes:
(1) f4067_0_random_LT(i1870:0, i1868:0, i1867:0, i1867:0, i1868:0) -> f4067_0_random_LT(arith, arith1, i1867:0, i1867:0, arith1) :|: i1868:0 > -1 && i1868:0 < i1867:0 && i1870:0 > 0 && i1867:0 > -1 && arith = i1870:0 - 1 && arith1 = i1868:0 + 1 && arith1 = i1868:0 + 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(14) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(15)
Obligation:
Rules:
f4067_0_random_LT(i1870:0:0, i1868:0:0, i1867:0:0, i1867:0:0, i1868:0:0) -> f4067_0_random_LT(i1870:0:0 - 1, i1868:0:0 + 1, i1867:0:0, i1867:0:0, i1868:0:0 + 1) :|: i1870:0:0 > 0 && i1867:0:0 > -1 && i1868:0:0 < i1867:0:0 && i1868:0:0 > -1

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(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f4067_0_random_LT(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(17)
Obligation:
Rules:
f4067_0_random_LT(i1870:0:0, i1868:0:0, i1867:0:0, i1867:0:0, i1868:0:0) -> f4067_0_random_LT(c, c1, i1867:0:0, i1867:0:0, c2) :|: c2 = i1868:0:0 + 1 && (c1 = i1868:0:0 + 1 && c = i1870:0:0 - 1) && (i1870:0:0 > 0 && i1867:0:0 > -1 && i1868:0:0 < i1867:0:0 && i1868:0:0 > -1)

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(18) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f4067_0_random_LT ] = f4067_0_random_LT_1

The following rules are decreasing:
f4067_0_random_LT(i1870:0:0, i1868:0:0, i1867:0:0, i1867:0:0, i1868:0:0) -> f4067_0_random_LT(c, c1, i1867:0:0, i1867:0:0, c2) :|: c2 = i1868:0:0 + 1 && (c1 = i1868:0:0 + 1 && c = i1870:0:0 - 1) && (i1870:0:0 > 0 && i1867:0:0 > -1 && i1868:0:0 < i1867:0:0 && i1868:0:0 > -1)

The following rules are bounded:
f4067_0_random_LT(i1870:0:0, i1868:0:0, i1867:0:0, i1867:0:0, i1868:0:0) -> f4067_0_random_LT(c, c1, i1867:0:0, i1867:0:0, c2) :|: c2 = i1868:0:0 + 1 && (c1 = i1868:0:0 + 1 && c = i1870:0:0 - 1) && (i1870:0:0 > 0 && i1867:0:0 > -1 && i1868:0:0 < i1867:0:0 && i1868:0:0 > -1)


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(19)
YES

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(20)
Obligation:

Termination digraph:
Nodes:
(1) f4067_0_random_LT(x3, x4, x5, x5, x4) -> f4067_0_random_LT(x6, x4, x5, x5, x4) :|: x5 > -1 && x3 > 0 && x4 >= x5 && x6 = x3 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(21) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(22)
Obligation:
Rules:
f4067_0_random_LT(x3:0, x4:0, x5:0, x5:0, x4:0) -> f4067_0_random_LT(x3:0 - 1, x4:0, x5:0, x5:0, x4:0) :|: x5:0 > -1 && x3:0 > 0 && x5:0 <= x4:0

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(23) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f4067_0_random_LT(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(24)
Obligation:
Rules:
f4067_0_random_LT(x3:0, x4:0, x5:0, x5:0, x4:0) -> f4067_0_random_LT(c, x4:0, x5:0, x5:0, x4:0) :|: c = x3:0 - 1 && (x5:0 > -1 && x3:0 > 0 && x5:0 <= x4:0)

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(25) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f4067_0_random_LT ] = f4067_0_random_LT_1

The following rules are decreasing:
f4067_0_random_LT(x3:0, x4:0, x5:0, x5:0, x4:0) -> f4067_0_random_LT(c, x4:0, x5:0, x5:0, x4:0) :|: c = x3:0 - 1 && (x5:0 > -1 && x3:0 > 0 && x5:0 <= x4:0)

The following rules are bounded:
f4067_0_random_LT(x3:0, x4:0, x5:0, x5:0, x4:0) -> f4067_0_random_LT(c, x4:0, x5:0, x5:0, x4:0) :|: c = x3:0 - 1 && (x5:0 > -1 && x3:0 > 0 && x5:0 <= x4:0)


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(26)
YES