/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 975 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 123 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 80 ms]
(12) AND
    (13) IRSwT
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IRSwT
        (16) TempFilterProof [SOUND, 12 ms]
        (17) IntTRS
        (18) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (19) YES
    (20) IRSwT
        (21) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (22) IRSwT
        (23) TempFilterProof [SOUND, 10 ms]
        (24) IntTRS
        (25) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (26) YES


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

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

    public static int factorial(int n){
	if (n  < 1) return 1;
	else return n*factorial(n-1);	  
    }

    public static int doSum(List x){
	if (x==null) return 0;
	else return factorial(x.head) + doSum(x.tail);	
    }

    public static void main(String [] args) {
	Random.args = args;
	List l = List.mk(3*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 FactSLR {

    public static int factorial(int n){
	if (n  < 1) return 1;
	else return n*factorial(n-1);	  
    }

    public static int doSum(List x){
	if (x==null) return 0;
	else return factorial(x.head) + doSum(x.tail);	
    }

    public static void main(String [] args) {
	Random.args = args;
	List l = List.mk(3*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:
FactSLR.main([Ljava/lang/String;)V: Graph of 141 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:
f2692_0_mk_Inc(EOS(STATIC_2692(java.lang.Object(ARRAY(i423)), i424)), i1276, i1276) -> f2698_0_mk_LE(EOS(STATIC_2698(java.lang.Object(ARRAY(i423)), i424)), i1276 + -1, i1276) :|: TRUE
f2698_0_mk_LE(EOS(STATIC_2698(java.lang.Object(ARRAY(i423)), i424)), i1308, i1276) -> f3228_0_mk_LE(EOS(STATIC_3228(java.lang.Object(ARRAY(i423)), i424)), i1308, i1276) :|: TRUE
f3228_0_mk_LE(EOS(STATIC_3228(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1710) -> f3230_0_mk_LE(EOS(STATIC_3230(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1710) :|: TRUE
f3230_0_mk_LE(EOS(STATIC_3230(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1710) -> f3232_0_mk_New(EOS(STATIC_3232(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: i1710 > 0
f3232_0_mk_New(EOS(STATIC_3232(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3234_0_mk_Duplicate(EOS(STATIC_3234(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3234_0_mk_Duplicate(EOS(STATIC_3234(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3236_0_mk_InvokeMethod(EOS(STATIC_3236(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3236_0_mk_InvokeMethod(EOS(STATIC_3236(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3242_0_random_FieldAccess(EOS(STATIC_3242(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3242_0_random_FieldAccess(EOS(STATIC_3242(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3255_0_random_FieldAccess(EOS(STATIC_3255(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1691) :|: TRUE
f3255_0_random_FieldAccess(EOS(STATIC_3255(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1691) -> f3256_0_random_ArrayLength(EOS(STATIC_3256(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1691, java.lang.Object(ARRAY(i1690))) :|: TRUE
f3256_0_random_ArrayLength(EOS(STATIC_3256(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1691, java.lang.Object(ARRAY(i1690))) -> f3268_0_random_LT(EOS(STATIC_3268(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1691, i1690) :|: i1690 >= 0
f3268_0_random_LT(EOS(STATIC_3268(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1691, i1690) -> f3274_0_random_LT(EOS(STATIC_3274(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1691, i1690) :|: i1691 < i1690
f3268_0_random_LT(EOS(STATIC_3268(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1691, i1690) -> f3275_0_random_LT(EOS(STATIC_3275(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1691, i1690) :|: i1691 >= i1690
f3274_0_random_LT(EOS(STATIC_3274(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1691, i1690) -> f3281_0_random_FieldAccess(EOS(STATIC_3281(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: i1691 < i1690
f3281_0_random_FieldAccess(EOS(STATIC_3281(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3288_0_random_FieldAccess(EOS(STATIC_3288(java.lang.Object(ARRAY(i1690)), i1691)), i1693, java.lang.Object(ARRAY(i1690))) :|: TRUE
f3288_0_random_FieldAccess(EOS(STATIC_3288(java.lang.Object(ARRAY(i1690)), i1691)), i1693, java.lang.Object(ARRAY(i1690))) -> f3290_0_random_ArrayAccess(EOS(STATIC_3290(java.lang.Object(ARRAY(i1690)), i1691)), i1693, java.lang.Object(ARRAY(i1690)), i1691) :|: TRUE
f3290_0_random_ArrayAccess(EOS(STATIC_3290(java.lang.Object(ARRAY(i1690)), i1762)), i1693, java.lang.Object(ARRAY(i1690)), i1762) -> f3293_0_random_ArrayAccess(EOS(STATIC_3293(java.lang.Object(ARRAY(i1690)), i1762)), i1693, java.lang.Object(ARRAY(i1690)), i1762) :|: TRUE
f3293_0_random_ArrayAccess(EOS(STATIC_3293(java.lang.Object(ARRAY(i1690)), i1762)), i1693, java.lang.Object(ARRAY(i1690)), i1762) -> f3296_0_random_ArrayAccess(EOS(STATIC_3296(java.lang.Object(ARRAY(i1690)), i1762)), i1693, java.lang.Object(ARRAY(i1690)), i1762) :|: TRUE
f3296_0_random_ArrayAccess(EOS(STATIC_3296(java.lang.Object(ARRAY(i1690)), i1762)), i1693, java.lang.Object(ARRAY(i1690)), i1762) -> f3299_0_random_Store(EOS(STATIC_3299(java.lang.Object(ARRAY(i1690)), i1762)), i1693, o801) :|: TRUE
f3299_0_random_Store(EOS(STATIC_3299(java.lang.Object(ARRAY(i1690)), i1762)), i1693, o801) -> f3302_0_random_FieldAccess(EOS(STATIC_3302(java.lang.Object(ARRAY(i1690)), i1762)), i1693, o801) :|: TRUE
f3302_0_random_FieldAccess(EOS(STATIC_3302(java.lang.Object(ARRAY(i1690)), i1762)), i1693, o801) -> f3305_0_random_ConstantStackPush(EOS(STATIC_3305(java.lang.Object(ARRAY(i1690)), i1762)), i1693, o801, i1762) :|: TRUE
f3305_0_random_ConstantStackPush(EOS(STATIC_3305(java.lang.Object(ARRAY(i1690)), i1762)), i1693, o801, i1762) -> f3308_0_random_IntArithmetic(EOS(STATIC_3308(java.lang.Object(ARRAY(i1690)), i1762)), i1693, o801, i1762, 1) :|: TRUE
f3308_0_random_IntArithmetic(EOS(STATIC_3308(java.lang.Object(ARRAY(i1690)), i1762)), i1693, o801, i1762, matching1) -> f3312_0_random_FieldAccess(EOS(STATIC_3312(java.lang.Object(ARRAY(i1690)), i1762)), i1693, o801, i1762 + 1) :|: i1762 >= 0 && matching1 = 1
f3312_0_random_FieldAccess(EOS(STATIC_3312(java.lang.Object(ARRAY(i1690)), i1762)), i1693, o801, i1791) -> f3315_0_random_Load(EOS(STATIC_3315(java.lang.Object(ARRAY(i1690)), i1791)), i1693, o801) :|: TRUE
f3315_0_random_Load(EOS(STATIC_3315(java.lang.Object(ARRAY(i1690)), i1791)), i1693, o801) -> f3318_0_random_InvokeMethod(EOS(STATIC_3318(java.lang.Object(ARRAY(i1690)), i1791)), i1693, o801) :|: TRUE
f3318_0_random_InvokeMethod(EOS(STATIC_3318(java.lang.Object(ARRAY(i1690)), i1791)), i1693, java.lang.Object(o834sub)) -> f3322_0_random_InvokeMethod(EOS(STATIC_3322(java.lang.Object(ARRAY(i1690)), i1791)), i1693, java.lang.Object(o834sub)) :|: TRUE
f3322_0_random_InvokeMethod(EOS(STATIC_3322(java.lang.Object(ARRAY(i1690)), i1791)), i1693, java.lang.Object(o837sub)) -> f3326_0_random_InvokeMethod(EOS(STATIC_3326(java.lang.Object(ARRAY(i1690)), i1791)), i1693, java.lang.Object(o837sub)) :|: TRUE
f3326_0_random_InvokeMethod(EOS(STATIC_3326(java.lang.Object(ARRAY(i1690)), i1791)), i1693, java.lang.Object(o837sub)) -> f3341_0_length_Load(EOS(STATIC_3341(java.lang.Object(ARRAY(i1690)), i1791)), i1693, java.lang.Object(o837sub)) :|: TRUE
f3341_0_length_Load(EOS(STATIC_3341(java.lang.Object(ARRAY(i1690)), i1791)), i1693, java.lang.Object(o837sub)) -> f3361_0_length_FieldAccess(EOS(STATIC_3361(java.lang.Object(ARRAY(i1690)), i1791)), i1693, java.lang.Object(o837sub)) :|: TRUE
f3361_0_length_FieldAccess(EOS(STATIC_3361(java.lang.Object(ARRAY(i1690)), i1791)), i1693, java.lang.Object(java.lang.String(EOC, i1876))) -> f3386_0_length_FieldAccess(EOS(STATIC_3386(java.lang.Object(ARRAY(i1690)), i1791)), i1693, java.lang.Object(java.lang.String(EOC, i1876))) :|: TRUE
f3386_0_length_FieldAccess(EOS(STATIC_3386(java.lang.Object(ARRAY(i1690)), i1791)), i1693, java.lang.Object(java.lang.String(EOC, i1876))) -> f3389_0_length_Return(EOS(STATIC_3389(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3389_0_length_Return(EOS(STATIC_3389(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3398_0_random_Return(EOS(STATIC_3398(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3398_0_random_Return(EOS(STATIC_3398(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3408_0_mk_Load(EOS(STATIC_3408(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3408_0_mk_Load(EOS(STATIC_3408(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3418_0_mk_InvokeMethod(EOS(STATIC_3418(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3418_0_mk_InvokeMethod(EOS(STATIC_3418(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3426_0__init__Load(EOS(STATIC_3426(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3426_0__init__Load(EOS(STATIC_3426(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3451_0__init__InvokeMethod(EOS(STATIC_3451(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3451_0__init__InvokeMethod(EOS(STATIC_3451(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3472_0__init__Load(EOS(STATIC_3472(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3472_0__init__Load(EOS(STATIC_3472(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3483_0__init__Load(EOS(STATIC_3483(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3483_0__init__Load(EOS(STATIC_3483(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3494_0__init__FieldAccess(EOS(STATIC_3494(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3494_0__init__FieldAccess(EOS(STATIC_3494(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3507_0__init__Load(EOS(STATIC_3507(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3507_0__init__Load(EOS(STATIC_3507(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3517_0__init__Load(EOS(STATIC_3517(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3517_0__init__Load(EOS(STATIC_3517(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3530_0__init__FieldAccess(EOS(STATIC_3530(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3530_0__init__FieldAccess(EOS(STATIC_3530(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3539_0__init__Return(EOS(STATIC_3539(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3539_0__init__Return(EOS(STATIC_3539(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3552_0_mk_Store(EOS(STATIC_3552(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3552_0_mk_Store(EOS(STATIC_3552(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3573_0_mk_JMP(EOS(STATIC_3573(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3573_0_mk_JMP(EOS(STATIC_3573(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3663_0_mk_Load(EOS(STATIC_3663(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3663_0_mk_Load(EOS(STATIC_3663(java.lang.Object(ARRAY(i1690)), i1791)), i1693) -> f3664_0_mk_Load(EOS(STATIC_3664(java.lang.Object(ARRAY(i1690)), i1791)), i1693) :|: TRUE
f3664_0_mk_Load(EOS(STATIC_3664(java.lang.Object(ARRAY(i2077)), i2078)), i2080) -> f3725_0_mk_Inc(EOS(STATIC_3725(java.lang.Object(ARRAY(i2077)), i2078)), i2080, i2080) :|: TRUE
f3725_0_mk_Inc(EOS(STATIC_3725(java.lang.Object(ARRAY(i2077)), i2078)), i2080, i2080) -> f3761_0_mk_LE(EOS(STATIC_3761(java.lang.Object(ARRAY(i2077)), i2078)), i2080 + -1, i2080) :|: TRUE
f3761_0_mk_LE(EOS(STATIC_3761(java.lang.Object(ARRAY(i2077)), i2078)), i2146, i2080) -> f3228_0_mk_LE(EOS(STATIC_3228(java.lang.Object(ARRAY(i2077)), i2078)), i2146, i2080) :|: TRUE
f3275_0_random_LT(EOS(STATIC_3275(java.lang.Object(ARRAY(i1690)), i1691)), i1693, i1691, i1690) -> f3287_0_random_ConstantStackPush(EOS(STATIC_3287(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: i1691 >= i1690
f3287_0_random_ConstantStackPush(EOS(STATIC_3287(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3289_0_random_Return(EOS(STATIC_3289(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3289_0_random_Return(EOS(STATIC_3289(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3291_0_mk_Load(EOS(STATIC_3291(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3291_0_mk_Load(EOS(STATIC_3291(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3294_0_mk_InvokeMethod(EOS(STATIC_3294(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3294_0_mk_InvokeMethod(EOS(STATIC_3294(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3298_0__init__Load(EOS(STATIC_3298(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3298_0__init__Load(EOS(STATIC_3298(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3303_0__init__InvokeMethod(EOS(STATIC_3303(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3303_0__init__InvokeMethod(EOS(STATIC_3303(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3307_0__init__Load(EOS(STATIC_3307(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3307_0__init__Load(EOS(STATIC_3307(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3310_0__init__Load(EOS(STATIC_3310(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3310_0__init__Load(EOS(STATIC_3310(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3313_0__init__FieldAccess(EOS(STATIC_3313(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3313_0__init__FieldAccess(EOS(STATIC_3313(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3317_0__init__Load(EOS(STATIC_3317(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3317_0__init__Load(EOS(STATIC_3317(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3320_0__init__Load(EOS(STATIC_3320(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3320_0__init__Load(EOS(STATIC_3320(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3324_0__init__FieldAccess(EOS(STATIC_3324(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3324_0__init__FieldAccess(EOS(STATIC_3324(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3339_0__init__Return(EOS(STATIC_3339(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3339_0__init__Return(EOS(STATIC_3339(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3344_0_mk_Store(EOS(STATIC_3344(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3344_0_mk_Store(EOS(STATIC_3344(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3352_0_mk_JMP(EOS(STATIC_3352(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3352_0_mk_JMP(EOS(STATIC_3352(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f3385_0_mk_Load(EOS(STATIC_3385(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f3385_0_mk_Load(EOS(STATIC_3385(java.lang.Object(ARRAY(i1690)), i1691)), i1693) -> f2687_0_mk_Load(EOS(STATIC_2687(java.lang.Object(ARRAY(i1690)), i1691)), i1693) :|: TRUE
f2687_0_mk_Load(EOS(STATIC_2687(java.lang.Object(ARRAY(i423)), i424)), i1276) -> f2692_0_mk_Inc(EOS(STATIC_2692(java.lang.Object(ARRAY(i423)), i424)), i1276, i1276) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f3268_0_random_LT(EOS(STATIC_3268(java.lang.Object(ARRAY(i1690:0)), i1691:0)), i1693:0, i1691:0, i1690:0) -> f3268_0_random_LT(EOS(STATIC_3268(java.lang.Object(ARRAY(i1690:0)), i1691:0 + 1)), i1693:0 - 1, i1691:0 + 1, i1690:0) :|: i1691:0 < i1690:0 && i1691:0 > -1 && i1690:0 > -1 && i1693:0 > 0
f3268_0_random_LT(EOS(STATIC_3268(java.lang.Object(ARRAY(i1690:0)), i1691:0)), i1693:0, i1691:0, i1690:0) -> f3268_0_random_LT(EOS(STATIC_3268(java.lang.Object(ARRAY(i1690:0)), i1691:0)), i1693:0 - 1, i1691:0, i1690:0) :|: i1691:0 >= i1690:0 && i1690:0 > -1 && i1693:0 > 0
Finished conversion. Obtained 2 rules.P rules:
f3268_0_random_LT(i1693:0, i1691:0, i1690:0, i1690:0, i1691:0) -> f3268_0_random_LT(i1693:0 - 1, i1691:0 + 1, i1690:0, i1690:0, i1691:0 + 1) :|: i1691:0 > -1 && i1691:0 < i1690:0 && i1693:0 > 0 && i1690:0 > -1
f3268_0_random_LT(i1693:0, i1691:0, i1690:0, i1690:0, i1691:0) -> f3268_0_random_LT(i1693:0 - 1, i1691:0, i1690:0, i1690:0, i1691:0) :|: i1690:0 > -1 && i1693:0 > 0 && i1691:0 >= i1690:0

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(8)
Obligation:
Rules:
f3268_0_random_LT(i1693:0, i1691:0, i1690:0, i1690:0, i1691:0) -> f3268_0_random_LT(i1693:0 - 1, i1691:0 + 1, i1690:0, i1690:0, i1691:0 + 1) :|: i1691:0 > -1 && i1691:0 < i1690:0 && i1693:0 > 0 && i1690:0 > -1
f3268_0_random_LT(x, x1, x2, x2, x1) -> f3268_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 %).
----------------------------------------

(10)
Obligation:
Rules:
f3268_0_random_LT(i1693:0, i1691:0, i1690:0, i1690:0, i1691:0) -> f3268_0_random_LT(arith, arith1, i1690:0, i1690:0, arith1) :|: i1691:0 > -1 && i1691:0 < i1690:0 && i1693:0 > 0 && i1690:0 > -1 && arith = i1693:0 - 1 && arith1 = i1691:0 + 1 && arith1 = i1691:0 + 1
f3268_0_random_LT(x3, x4, x5, x5, x4) -> f3268_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) f3268_0_random_LT(i1693:0, i1691:0, i1690:0, i1690:0, i1691:0) -> f3268_0_random_LT(arith, arith1, i1690:0, i1690:0, arith1) :|: i1691:0 > -1 && i1691:0 < i1690:0 && i1693:0 > 0 && i1690:0 > -1 && arith = i1693:0 - 1 && arith1 = i1691:0 + 1 && arith1 = i1691:0 + 1
(2) f3268_0_random_LT(x3, x4, x5, x5, x4) -> f3268_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) f3268_0_random_LT(i1693:0, i1691:0, i1690:0, i1690:0, i1691:0) -> f3268_0_random_LT(arith, arith1, i1690:0, i1690:0, arith1) :|: i1691:0 > -1 && i1691:0 < i1690:0 && i1693:0 > 0 && i1690:0 > -1 && arith = i1693:0 - 1 && arith1 = i1691:0 + 1 && arith1 = i1691:0 + 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(15)
Obligation:
Rules:
f3268_0_random_LT(i1693:0:0, i1691:0:0, i1690:0:0, i1690:0:0, i1691:0:0) -> f3268_0_random_LT(i1693:0:0 - 1, i1691:0:0 + 1, i1690:0:0, i1690:0:0, i1691:0:0 + 1) :|: i1693:0:0 > 0 && i1690:0:0 > -1 && i1691:0:0 < i1690:0:0 && i1691:0:0 > -1

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(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f3268_0_random_LT(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(17)
Obligation:
Rules:
f3268_0_random_LT(i1693:0:0, i1691:0:0, i1690:0:0, i1690:0:0, i1691:0:0) -> f3268_0_random_LT(c, c1, i1690:0:0, i1690:0:0, c2) :|: c2 = i1691:0:0 + 1 && (c1 = i1691:0:0 + 1 && c = i1693:0:0 - 1) && (i1693:0:0 > 0 && i1690:0:0 > -1 && i1691:0:0 < i1690:0:0 && i1691:0:0 > -1)

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(18) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f3268_0_random_LT(x, x1, x2, x3, x4)] = -x1 + x2

The following rules are decreasing:
f3268_0_random_LT(i1693:0:0, i1691:0:0, i1690:0:0, i1690:0:0, i1691:0:0) -> f3268_0_random_LT(c, c1, i1690:0:0, i1690:0:0, c2) :|: c2 = i1691:0:0 + 1 && (c1 = i1691:0:0 + 1 && c = i1693:0:0 - 1) && (i1693:0:0 > 0 && i1690:0:0 > -1 && i1691:0:0 < i1690:0:0 && i1691:0:0 > -1)
The following rules are bounded:
f3268_0_random_LT(i1693:0:0, i1691:0:0, i1690:0:0, i1690:0:0, i1691:0:0) -> f3268_0_random_LT(c, c1, i1690:0:0, i1690:0:0, c2) :|: c2 = i1691:0:0 + 1 && (c1 = i1691:0:0 + 1 && c = i1693:0:0 - 1) && (i1693:0:0 > 0 && i1690:0:0 > -1 && i1691:0:0 < i1690:0:0 && i1691:0:0 > -1)

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(19)
YES

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(20)
Obligation:

Termination digraph:
Nodes:
(1) f3268_0_random_LT(x3, x4, x5, x5, x4) -> f3268_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.
----------------------------------------

(22)
Obligation:
Rules:
f3268_0_random_LT(x3:0, x4:0, x5:0, x5:0, x4:0) -> f3268_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: 
f3268_0_random_LT(INTEGER, INTEGER, INTEGER, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(24)
Obligation:
Rules:
f3268_0_random_LT(x3:0, x4:0, x5:0, x5:0, x4:0) -> f3268_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) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f3268_0_random_LT(x, x1, x2, x3, x4)] = x

The following rules are decreasing:
f3268_0_random_LT(x3:0, x4:0, x5:0, x5:0, x4:0) -> f3268_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:
f3268_0_random_LT(x3:0, x4:0, x5:0, x5:0, x4:0) -> f3268_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