Termination of the given JBC could be proven:

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_20 (Apple Inc.) Main-Class: Test11

public class Test11 {
    public static void main(String[] args) {
	Random.args = args;

	int x = args.length * 100, y = args.length * 200 / 13;

	while (x + y > 0) {
	    if (Random.random() * Random.random() > 9)
		x--;
	    else
		y--;
	}
    }
}

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) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Test11.main([Ljava/lang/String;)V: Graph of 331 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

---

Log for SCC 0:

Generated 108 rules for P and 190 rules for R.

Combined rules. Obtained 17 rules for P and 0 rules for R.

Filtered ground terms:

5887_0_main_Load(x1, x2, x3, x4) → 5887_0_main_Load(x2, x3, x4)
5954_0_random_LT(x1, x2, x3) → 5954_0_random_LT(x2, x3)
6091_0_random_IntArithmetic(x1, x2, x3, x4) → 6091_0_random_IntArithmetic(x2, x3)
6012_0_random_ArrayAccess(x1, x2, x3) → 6012_0_random_ArrayAccess(x2, x3)
5952_0_random_LT(x1, x2, x3) → 5952_0_random_LT(x2, x3)
5905_0_random_LT(x1, x2, x3) → 5905_0_random_LT(x2, x3)
6286_0_random_LT(x1, x2, x3) → 6286_0_random_LT(x2, x3)
6591_0_random_IntArithmetic(x1, x2, x3, x4) → 6591_0_random_IntArithmetic(x2, x3)
6442_0_random_ArrayAccess(x1, x2, x3) → 6442_0_random_ArrayAccess(x2, x3)
6283_0_random_LT(x1, x2, x3) → 6283_0_random_LT(x2, x3)
5957_0_random_IntArithmetic(x1, x2, x3, x4) → 5957_0_random_IntArithmetic(x2, x3)
5924_0_random_ArrayAccess(x1, x2, x3) → 5924_0_random_ArrayAccess(x2, x3)
5904_0_random_LT(x1, x2, x3) → 5904_0_random_LT(x2, x3)
Cond_5887_0_main_Load1(x1, x2, x3, x4, x5) → Cond_5887_0_main_Load1(x1, x3, x4, x5)
Cond_5887_0_main_Load(x1, x2, x3, x4, x5) → Cond_5887_0_main_Load(x1, x3, x4, x5)

Filtered duplicate args:

5887_0_main_Load(x1, x2, x3) → 5887_0_main_Load(x2, x3)
Cond_5887_0_main_Load1(x1, x2, x3, x4) → Cond_5887_0_main_Load1(x1, x3, x4)
Cond_5887_0_main_Load(x1, x2, x3, x4) → Cond_5887_0_main_Load(x1, x3, x4)

Filtered unneeded arguments:

Cond_6591_1_main_InvokeMethod(x1, x2, x3, x4, x5) → Cond_6591_1_main_InvokeMethod(x1, x2, x3, x4)
Cond_6591_1_main_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_6591_1_main_InvokeMethod1(x1, x2, x3, x4)
6286_1_main_InvokeMethod(x1, x2, x3, x4) → 6286_1_main_InvokeMethod(x1, x2, x3)
Cond_6286_1_main_InvokeMethod(x1, x2, x3, x4, x5) → Cond_6286_1_main_InvokeMethod(x1, x2, x3, x4)

Filtered all free variables:

5904_1_main_InvokeMethod(x1, x2, x3) → 5904_1_main_InvokeMethod(x2, x3)
5905_1_main_InvokeMethod(x1, x2, x3) → 5905_1_main_InvokeMethod(x2, x3)
Cond_5904_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_5904_1_main_InvokeMethod(x1, x3, x4)
5924_1_main_InvokeMethod(x1, x2, x3) → 5924_1_main_InvokeMethod(x2, x3)
Cond_5924_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_5924_1_main_InvokeMethod(x1, x3, x4)
5957_1_main_InvokeMethod(x1, x2, x3) → 5957_1_main_InvokeMethod(x2, x3)
Cond_5957_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_5957_1_main_InvokeMethod(x1, x3, x4)
6283_1_main_InvokeMethod(x1, x2, x3, x4) → 6283_1_main_InvokeMethod(x2, x3, x4)
Cond_5957_1_main_InvokeMethod1(x1, x2, x3, x4) → Cond_5957_1_main_InvokeMethod1(x1, x3, x4)
6286_1_main_InvokeMethod(x1, x2, x3) → 6286_1_main_InvokeMethod(x2, x3)
Cond_6283_1_main_InvokeMethod(x1, x2, x3, x4, x5) → Cond_6283_1_main_InvokeMethod(x1, x3, x4, x5)
6442_1_main_InvokeMethod(x1, x2, x3, x4) → 6442_1_main_InvokeMethod(x2, x3, x4)
Cond_6442_1_main_InvokeMethod(x1, x2, x3, x4, x5) → Cond_6442_1_main_InvokeMethod(x1, x3, x4, x5)
6591_1_main_InvokeMethod(x1, x2, x3, x4) → 6591_1_main_InvokeMethod(x2, x3, x4)
Cond_6591_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_6591_1_main_InvokeMethod(x1, x3, x4)
Cond_6591_1_main_InvokeMethod1(x1, x2, x3, x4) → Cond_6591_1_main_InvokeMethod1(x1, x3, x4)
Cond_6286_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_6286_1_main_InvokeMethod(x1, x3, x4)
Cond_5905_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_5905_1_main_InvokeMethod(x1, x3, x4)
5952_1_main_InvokeMethod(x1, x2, x3) → 5952_1_main_InvokeMethod(x2, x3)
Cond_5905_1_main_InvokeMethod1(x1, x2, x3, x4) → Cond_5905_1_main_InvokeMethod1(x1, x3, x4)
5954_1_main_InvokeMethod(x1, x2, x3) → 5954_1_main_InvokeMethod(x2, x3)
Cond_5952_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_5952_1_main_InvokeMethod(x1, x3, x4)
6012_1_main_InvokeMethod(x1, x2, x3) → 6012_1_main_InvokeMethod(x2, x3)
Cond_6012_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_6012_1_main_InvokeMethod(x1, x3, x4)
6091_1_main_InvokeMethod(x1, x2, x3) → 6091_1_main_InvokeMethod(x2, x3)
Cond_6091_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_6091_1_main_InvokeMethod(x1, x3, x4)
Cond_5954_1_main_InvokeMethod(x1, x2, x3, x4) → Cond_5954_1_main_InvokeMethod(x1, x3, x4)

Combined rules. Obtained 6 rules for P and 0 rules for R.

Finished conversion. Obtained 6 rules for P and 0 rules for R. System has predefined symbols.

(4) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
||	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 6091_1_MAIN_INVOKEMETHOD(x4[0], x5[0]) → 5887_0_MAIN_LOAD(x5[0] + -1, x4[0])
(1): 5887_0_MAIN_LOAD(x0[1], x1[1]) → COND_5887_0_MAIN_LOAD(0 < x1[1] + x0[1], x0[1], x1[1])
(2): COND_5887_0_MAIN_LOAD(TRUE, x0[2], x1[2]) → 6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2])
(3): 5887_0_MAIN_LOAD(x0[3], x1[3]) → COND_5887_0_MAIN_LOAD1(0 < x1[3] + x0[3], x0[3], x1[3])
(4): COND_5887_0_MAIN_LOAD1(TRUE, x0[4], x1[4]) → 5887_0_MAIN_LOAD(x0[4] + -1, x1[4])
(5): 5887_0_MAIN_LOAD(x0[5], x1[5]) → COND_5887_0_MAIN_LOAD2(0 < x1[5] + x0[5], x0[5], x1[5])
(6): COND_5887_0_MAIN_LOAD2(TRUE, x0[6], x1[6]) → 5887_0_MAIN_LOAD(x0[6], x1[6] + -1)

(0) -> (1), if ((x5[0] + -1 →^* x0[1])∧(x4[0] →^* x1[1]))

(0) -> (3), if ((x5[0] + -1 →^* x0[3])∧(x4[0] →^* x1[3]))

(0) -> (5), if ((x5[0] + -1 →^* x0[5])∧(x4[0] →^* x1[5]))

(1) -> (2), if ((0 < x1[1] + x0[1] →^* TRUE)∧(x0[1] →^* x0[2])∧(x1[1] →^* x1[2]))

(2) -> (0), if ((x1[2] →^* x4[0])∧(x0[2] →^* x5[0]))

(3) -> (4), if ((0 < x1[3] + x0[3] →^* TRUE)∧(x0[3] →^* x0[4])∧(x1[3] →^* x1[4]))

(4) -> (1), if ((x0[4] + -1 →^* x0[1])∧(x1[4] →^* x1[1]))

(4) -> (3), if ((x0[4] + -1 →^* x0[3])∧(x1[4] →^* x1[3]))

(4) -> (5), if ((x0[4] + -1 →^* x0[5])∧(x1[4] →^* x1[5]))

(5) -> (6), if ((0 < x1[5] + x0[5] →^* TRUE)∧(x0[5] →^* x0[6])∧(x1[5] →^* x1[6]))

(6) -> (1), if ((x0[6] →^* x0[1])∧(x1[6] + -1 →^* x1[1]))

(6) -> (3), if ((x0[6] →^* x0[3])∧(x1[6] + -1 →^* x1[3]))

(6) -> (5), if ((x0[6] →^* x0[5])∧(x1[6] + -1 →^* x1[5]))

The set Q is empty.

(5) IDPNonInfProof (SOUND transformation)

The constraints were generated the following way:
The DP Problem is simplified using the Induction Calculus [NONINF] with the following steps:
Note that final constraints are written in bold face.


For Pair 6091_1_MAIN_INVOKEMETHOD(x4, x5) → 5887_0_MAIN_LOAD(+(x5, -1), x4) the following chains were created:

• We consider the chain 6091_1_MAIN_INVOKEMETHOD(x4[0], x5[0]) → 5887_0_MAIN_LOAD(+(x5[0], -1), x4[0]) which results in the following constraint:
  

  (1)    (6091_1_MAIN_INVOKEMETHOD(x4[0], x5[0])≥NonInfC∧6091_1_MAIN_INVOKEMETHOD(x4[0], x5[0])≥5887_0_MAIN_LOAD(+(x5[0], -1), x4[0])∧(U^Increasing(5887_0_MAIN_LOAD(+(x5[0], -1), x4[0])), ≥))

  
  
  We simplified constraint (1) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (2)    ((U^Increasing(5887_0_MAIN_LOAD(+(x5[0], -1), x4[0])), ≥)∧[(-1)bso_12] ≥ 0)

  
  
  We simplified constraint (2) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (3)    ((U^Increasing(5887_0_MAIN_LOAD(+(x5[0], -1), x4[0])), ≥)∧[(-1)bso_12] ≥ 0)

  
  
  We simplified constraint (3) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (4)    ((U^Increasing(5887_0_MAIN_LOAD(+(x5[0], -1), x4[0])), ≥)∧[(-1)bso_12] ≥ 0)

  
  
  We simplified constraint (4) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (5)    ((U^Increasing(5887_0_MAIN_LOAD(+(x5[0], -1), x4[0])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_12] ≥ 0)

  
  
  

For Pair 5887_0_MAIN_LOAD(x0, x1) → COND_5887_0_MAIN_LOAD(<(0, +(x1, x0)), x0, x1) the following chains were created:

• We consider the chain 5887_0_MAIN_LOAD(x0[1], x1[1]) → COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1]), COND_5887_0_MAIN_LOAD(TRUE, x0[2], x1[2]) → 6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2]) which results in the following constraint:
  

  (6)    (<(0, +(x1[1], x0[1]))=TRUE∧x0[1]=x0[2]∧x1[1]=x1[2] ⇒ 5887_0_MAIN_LOAD(x0[1], x1[1])≥NonInfC∧5887_0_MAIN_LOAD(x0[1], x1[1])≥COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])∧(U^Increasing(COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥))

  
  
  We simplified constraint (6) using rule (IV) which results in the following new constraint:
  

  (7)    (<(0, +(x1[1], x0[1]))=TRUE ⇒ 5887_0_MAIN_LOAD(x0[1], x1[1])≥NonInfC∧5887_0_MAIN_LOAD(x0[1], x1[1])≥COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])∧(U^Increasing(COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥))

  
  
  We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (8)    (x1[1] + [-1] + x0[1] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[bni_13 + (-1)Bound*bni_13] + [bni_13]x0[1] + [bni_13]x1[1] ≥ 0∧[(-1)bso_14] ≥ 0)

  
  
  We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (9)    (x1[1] + [-1] + x0[1] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[bni_13 + (-1)Bound*bni_13] + [bni_13]x0[1] + [bni_13]x1[1] ≥ 0∧[(-1)bso_14] ≥ 0)

  
  
  We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (10)    (x1[1] + [-1] + x0[1] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[bni_13 + (-1)Bound*bni_13] + [bni_13]x0[1] + [bni_13]x1[1] ≥ 0∧[(-1)bso_14] ≥ 0)

  
  
  We simplified constraint (10) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (11)    (x1[1] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(2)bni_13 + (-1)Bound*bni_13] + [bni_13]x1[1] ≥ 0∧[(-1)bso_14] ≥ 0)

  
  
  We simplified constraint (11) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (12)    (x1[1] ≥ 0∧x0[1] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(2)bni_13 + (-1)Bound*bni_13] + [bni_13]x1[1] ≥ 0∧[(-1)bso_14] ≥ 0)

  
  

  (13)    (x1[1] ≥ 0∧x0[1] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(2)bni_13 + (-1)Bound*bni_13] + [bni_13]x1[1] ≥ 0∧[(-1)bso_14] ≥ 0)

  
  
  

For Pair COND_5887_0_MAIN_LOAD(TRUE, x0, x1) → 6091_1_MAIN_INVOKEMETHOD(x1, x0) the following chains were created:

• We consider the chain COND_5887_0_MAIN_LOAD(TRUE, x0[2], x1[2]) → 6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2]), 6091_1_MAIN_INVOKEMETHOD(x4[0], x5[0]) → 5887_0_MAIN_LOAD(+(x5[0], -1), x4[0]) which results in the following constraint:
  

  (14)    (x1[2]=x4[0]∧x0[2]=x5[0] ⇒ COND_5887_0_MAIN_LOAD(TRUE, x0[2], x1[2])≥NonInfC∧COND_5887_0_MAIN_LOAD(TRUE, x0[2], x1[2])≥6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2])∧(U^Increasing(6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2])), ≥))

  
  
  We simplified constraint (14) using rule (IV) which results in the following new constraint:
  

  (15)    (COND_5887_0_MAIN_LOAD(TRUE, x0[2], x1[2])≥NonInfC∧COND_5887_0_MAIN_LOAD(TRUE, x0[2], x1[2])≥6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2])∧(U^Increasing(6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2])), ≥))

  
  
  We simplified constraint (15) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (16)    ((U^Increasing(6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2])), ≥)∧[1 + (-1)bso_16] ≥ 0)

  
  
  We simplified constraint (16) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (17)    ((U^Increasing(6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2])), ≥)∧[1 + (-1)bso_16] ≥ 0)

  
  
  We simplified constraint (17) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (18)    ((U^Increasing(6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2])), ≥)∧[1 + (-1)bso_16] ≥ 0)

  
  
  We simplified constraint (18) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (19)    ((U^Increasing(6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2])), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_16] ≥ 0)

  
  
  

For Pair 5887_0_MAIN_LOAD(x0, x1) → COND_5887_0_MAIN_LOAD1(<(0, +(x1, x0)), x0, x1) the following chains were created:

• We consider the chain 5887_0_MAIN_LOAD(x0[3], x1[3]) → COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3]), COND_5887_0_MAIN_LOAD1(TRUE, x0[4], x1[4]) → 5887_0_MAIN_LOAD(+(x0[4], -1), x1[4]) which results in the following constraint:
  

  (20)    (<(0, +(x1[3], x0[3]))=TRUE∧x0[3]=x0[4]∧x1[3]=x1[4] ⇒ 5887_0_MAIN_LOAD(x0[3], x1[3])≥NonInfC∧5887_0_MAIN_LOAD(x0[3], x1[3])≥COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])∧(U^Increasing(COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥))

  
  
  We simplified constraint (20) using rule (IV) which results in the following new constraint:
  

  (21)    (<(0, +(x1[3], x0[3]))=TRUE ⇒ 5887_0_MAIN_LOAD(x0[3], x1[3])≥NonInfC∧5887_0_MAIN_LOAD(x0[3], x1[3])≥COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])∧(U^Increasing(COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥))

  
  
  We simplified constraint (21) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (22)    (x1[3] + [-1] + x0[3] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[bni_17 + (-1)Bound*bni_17] + [bni_17]x0[3] + [bni_17]x1[3] ≥ 0∧[(-1)bso_18] ≥ 0)

  
  
  We simplified constraint (22) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (23)    (x1[3] + [-1] + x0[3] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[bni_17 + (-1)Bound*bni_17] + [bni_17]x0[3] + [bni_17]x1[3] ≥ 0∧[(-1)bso_18] ≥ 0)

  
  
  We simplified constraint (23) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (24)    (x1[3] + [-1] + x0[3] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[bni_17 + (-1)Bound*bni_17] + [bni_17]x0[3] + [bni_17]x1[3] ≥ 0∧[(-1)bso_18] ≥ 0)

  
  
  We simplified constraint (24) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (25)    (x1[3] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(2)bni_17 + (-1)Bound*bni_17] + [bni_17]x1[3] ≥ 0∧[(-1)bso_18] ≥ 0)

  
  
  We simplified constraint (25) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (26)    (x1[3] ≥ 0∧x0[3] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(2)bni_17 + (-1)Bound*bni_17] + [bni_17]x1[3] ≥ 0∧[(-1)bso_18] ≥ 0)

  
  

  (27)    (x1[3] ≥ 0∧x0[3] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(2)bni_17 + (-1)Bound*bni_17] + [bni_17]x1[3] ≥ 0∧[(-1)bso_18] ≥ 0)

  
  
  

For Pair COND_5887_0_MAIN_LOAD1(TRUE, x0, x1) → 5887_0_MAIN_LOAD(+(x0, -1), x1) the following chains were created:

• We consider the chain COND_5887_0_MAIN_LOAD1(TRUE, x0[4], x1[4]) → 5887_0_MAIN_LOAD(+(x0[4], -1), x1[4]) which results in the following constraint:
  

  (28)    (COND_5887_0_MAIN_LOAD1(TRUE, x0[4], x1[4])≥NonInfC∧COND_5887_0_MAIN_LOAD1(TRUE, x0[4], x1[4])≥5887_0_MAIN_LOAD(+(x0[4], -1), x1[4])∧(U^Increasing(5887_0_MAIN_LOAD(+(x0[4], -1), x1[4])), ≥))

  
  
  We simplified constraint (28) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (29)    ((U^Increasing(5887_0_MAIN_LOAD(+(x0[4], -1), x1[4])), ≥)∧[1 + (-1)bso_20] ≥ 0)

  
  
  We simplified constraint (29) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (30)    ((U^Increasing(5887_0_MAIN_LOAD(+(x0[4], -1), x1[4])), ≥)∧[1 + (-1)bso_20] ≥ 0)

  
  
  We simplified constraint (30) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (31)    ((U^Increasing(5887_0_MAIN_LOAD(+(x0[4], -1), x1[4])), ≥)∧[1 + (-1)bso_20] ≥ 0)

  
  
  We simplified constraint (31) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (32)    ((U^Increasing(5887_0_MAIN_LOAD(+(x0[4], -1), x1[4])), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_20] ≥ 0)

  
  
  

For Pair 5887_0_MAIN_LOAD(x0, x1) → COND_5887_0_MAIN_LOAD2(<(0, +(x1, x0)), x0, x1) the following chains were created:

• We consider the chain 5887_0_MAIN_LOAD(x0[5], x1[5]) → COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5]), COND_5887_0_MAIN_LOAD2(TRUE, x0[6], x1[6]) → 5887_0_MAIN_LOAD(x0[6], +(x1[6], -1)) which results in the following constraint:
  

  (33)    (<(0, +(x1[5], x0[5]))=TRUE∧x0[5]=x0[6]∧x1[5]=x1[6] ⇒ 5887_0_MAIN_LOAD(x0[5], x1[5])≥NonInfC∧5887_0_MAIN_LOAD(x0[5], x1[5])≥COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])∧(U^Increasing(COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥))

  
  
  We simplified constraint (33) using rule (IV) which results in the following new constraint:
  

  (34)    (<(0, +(x1[5], x0[5]))=TRUE ⇒ 5887_0_MAIN_LOAD(x0[5], x1[5])≥NonInfC∧5887_0_MAIN_LOAD(x0[5], x1[5])≥COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])∧(U^Increasing(COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥))

  
  
  We simplified constraint (34) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (35)    (x1[5] + [-1] + x0[5] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[bni_21 + (-1)Bound*bni_21] + [bni_21]x0[5] + [bni_21]x1[5] ≥ 0∧[(-1)bso_22] ≥ 0)

  
  
  We simplified constraint (35) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (36)    (x1[5] + [-1] + x0[5] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[bni_21 + (-1)Bound*bni_21] + [bni_21]x0[5] + [bni_21]x1[5] ≥ 0∧[(-1)bso_22] ≥ 0)

  
  
  We simplified constraint (36) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (37)    (x1[5] + [-1] + x0[5] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[bni_21 + (-1)Bound*bni_21] + [bni_21]x0[5] + [bni_21]x1[5] ≥ 0∧[(-1)bso_22] ≥ 0)

  
  
  We simplified constraint (37) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
  

  (38)    (x1[5] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(2)bni_21 + (-1)Bound*bni_21] + [bni_21]x1[5] ≥ 0∧[(-1)bso_22] ≥ 0)

  
  
  We simplified constraint (38) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
  

  (39)    (x1[5] ≥ 0∧x0[5] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(2)bni_21 + (-1)Bound*bni_21] + [bni_21]x1[5] ≥ 0∧[(-1)bso_22] ≥ 0)

  
  

  (40)    (x1[5] ≥ 0∧x0[5] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(2)bni_21 + (-1)Bound*bni_21] + [bni_21]x1[5] ≥ 0∧[(-1)bso_22] ≥ 0)

  
  
  

For Pair COND_5887_0_MAIN_LOAD2(TRUE, x0, x1) → 5887_0_MAIN_LOAD(x0, +(x1, -1)) the following chains were created:

• We consider the chain COND_5887_0_MAIN_LOAD2(TRUE, x0[6], x1[6]) → 5887_0_MAIN_LOAD(x0[6], +(x1[6], -1)) which results in the following constraint:
  

  (41)    (COND_5887_0_MAIN_LOAD2(TRUE, x0[6], x1[6])≥NonInfC∧COND_5887_0_MAIN_LOAD2(TRUE, x0[6], x1[6])≥5887_0_MAIN_LOAD(x0[6], +(x1[6], -1))∧(U^Increasing(5887_0_MAIN_LOAD(x0[6], +(x1[6], -1))), ≥))

  
  
  We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
  

  (42)    ((U^Increasing(5887_0_MAIN_LOAD(x0[6], +(x1[6], -1))), ≥)∧[1 + (-1)bso_24] ≥ 0)

  
  
  We simplified constraint (42) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
  

  (43)    ((U^Increasing(5887_0_MAIN_LOAD(x0[6], +(x1[6], -1))), ≥)∧[1 + (-1)bso_24] ≥ 0)

  
  
  We simplified constraint (43) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
  

  (44)    ((U^Increasing(5887_0_MAIN_LOAD(x0[6], +(x1[6], -1))), ≥)∧[1 + (-1)bso_24] ≥ 0)

  
  
  We simplified constraint (44) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
  

  (45)    ((U^Increasing(5887_0_MAIN_LOAD(x0[6], +(x1[6], -1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_24] ≥ 0)

  
  
  

To summarize, we get the following constraints P_≥ for the following pairs.

• 6091_1_MAIN_INVOKEMETHOD(x4, x5) → 5887_0_MAIN_LOAD(+(x5, -1), x4)
  
  • ((U^Increasing(5887_0_MAIN_LOAD(+(x5[0], -1), x4[0])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_12] ≥ 0)
    
  
  
• 5887_0_MAIN_LOAD(x0, x1) → COND_5887_0_MAIN_LOAD(<(0, +(x1, x0)), x0, x1)
  
  • (x1[1] ≥ 0∧x0[1] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(2)bni_13 + (-1)Bound*bni_13] + [bni_13]x1[1] ≥ 0∧[(-1)bso_14] ≥ 0)
    
  • (x1[1] ≥ 0∧x0[1] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(2)bni_13 + (-1)Bound*bni_13] + [bni_13]x1[1] ≥ 0∧[(-1)bso_14] ≥ 0)
    
  
  
• COND_5887_0_MAIN_LOAD(TRUE, x0, x1) → 6091_1_MAIN_INVOKEMETHOD(x1, x0)
  
  • ((U^Increasing(6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2])), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_16] ≥ 0)
    
  
  
• 5887_0_MAIN_LOAD(x0, x1) → COND_5887_0_MAIN_LOAD1(<(0, +(x1, x0)), x0, x1)
  
  • (x1[3] ≥ 0∧x0[3] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(2)bni_17 + (-1)Bound*bni_17] + [bni_17]x1[3] ≥ 0∧[(-1)bso_18] ≥ 0)
    
  • (x1[3] ≥ 0∧x0[3] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(2)bni_17 + (-1)Bound*bni_17] + [bni_17]x1[3] ≥ 0∧[(-1)bso_18] ≥ 0)
    
  
  
• COND_5887_0_MAIN_LOAD1(TRUE, x0, x1) → 5887_0_MAIN_LOAD(+(x0, -1), x1)
  
  • ((U^Increasing(5887_0_MAIN_LOAD(+(x0[4], -1), x1[4])), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_20] ≥ 0)
    
  
  
• 5887_0_MAIN_LOAD(x0, x1) → COND_5887_0_MAIN_LOAD2(<(0, +(x1, x0)), x0, x1)
  
  • (x1[5] ≥ 0∧x0[5] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(2)bni_21 + (-1)Bound*bni_21] + [bni_21]x1[5] ≥ 0∧[(-1)bso_22] ≥ 0)
    
  • (x1[5] ≥ 0∧x0[5] ≥ 0 ⇒ (U^Increasing(COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(2)bni_21 + (-1)Bound*bni_21] + [bni_21]x1[5] ≥ 0∧[(-1)bso_22] ≥ 0)
    
  
  
• COND_5887_0_MAIN_LOAD2(TRUE, x0, x1) → 5887_0_MAIN_LOAD(x0, +(x1, -1))
  
  • ((U^Increasing(5887_0_MAIN_LOAD(x0[6], +(x1[6], -1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_24] ≥ 0)
    
  
  

The constraints for P_> respective P_bound are constructed from P_≥ where we just replace every occurence of "t ≥ s" in P_≥ by "t > s" respective "t ≥ c". Here c stands for the fresh constant used for P_bound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(6091_1_MAIN_INVOKEMETHOD(x₁, x₂)) = x₁ + x₂   
POL(5887_0_MAIN_LOAD(x₁, x₂)) = [1] + x₁ + x₂   
POL(+(x₁, x₂)) = x₁ + x₂   
POL(-1) = [-1]   
POL(COND_5887_0_MAIN_LOAD(x₁, x₂, x₃)) = [1] + x₃ + x₂   
POL(<(x₁, x₂)) = [-1]   
POL(0) = 0   
POL(COND_5887_0_MAIN_LOAD1(x₁, x₂, x₃)) = [1] + x₃ + x₂   
POL(COND_5887_0_MAIN_LOAD2(x₁, x₂, x₃)) = [1] + x₃ + x₂   

The following pairs are in P_>:

COND_5887_0_MAIN_LOAD(TRUE, x0[2], x1[2]) → 6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2])
COND_5887_0_MAIN_LOAD1(TRUE, x0[4], x1[4]) → 5887_0_MAIN_LOAD(+(x0[4], -1), x1[4])
COND_5887_0_MAIN_LOAD2(TRUE, x0[6], x1[6]) → 5887_0_MAIN_LOAD(x0[6], +(x1[6], -1))

The following pairs are in P_bound:

5887_0_MAIN_LOAD(x0[1], x1[1]) → COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])
5887_0_MAIN_LOAD(x0[3], x1[3]) → COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])
5887_0_MAIN_LOAD(x0[5], x1[5]) → COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])

The following pairs are in P_≥:

6091_1_MAIN_INVOKEMETHOD(x4[0], x5[0]) → 5887_0_MAIN_LOAD(+(x5[0], -1), x4[0])
5887_0_MAIN_LOAD(x0[1], x1[1]) → COND_5887_0_MAIN_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])
5887_0_MAIN_LOAD(x0[3], x1[3]) → COND_5887_0_MAIN_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])
5887_0_MAIN_LOAD(x0[5], x1[5]) → COND_5887_0_MAIN_LOAD2(<(0, +(x1[5], x0[5])), x0[5], x1[5])

There are no usable rules.

(6) Complex Obligation (AND)

(7) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
||	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 6091_1_MAIN_INVOKEMETHOD(x4[0], x5[0]) → 5887_0_MAIN_LOAD(x5[0] + -1, x4[0])
(1): 5887_0_MAIN_LOAD(x0[1], x1[1]) → COND_5887_0_MAIN_LOAD(0 < x1[1] + x0[1], x0[1], x1[1])
(3): 5887_0_MAIN_LOAD(x0[3], x1[3]) → COND_5887_0_MAIN_LOAD1(0 < x1[3] + x0[3], x0[3], x1[3])
(5): 5887_0_MAIN_LOAD(x0[5], x1[5]) → COND_5887_0_MAIN_LOAD2(0 < x1[5] + x0[5], x0[5], x1[5])

(0) -> (1), if ((x5[0] + -1 →^* x0[1])∧(x4[0] →^* x1[1]))

(0) -> (3), if ((x5[0] + -1 →^* x0[3])∧(x4[0] →^* x1[3]))

(0) -> (5), if ((x5[0] + -1 →^* x0[5])∧(x4[0] →^* x1[5]))

The set Q is empty.

(8) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 4 less nodes.

(9) TRUE

(10) Obligation:

IDP problem:
The following function symbols are pre-defined:

!=	~	Neq: (Integer, Integer) -> Boolean
*	~	Mul: (Integer, Integer) -> Integer
>=	~	Ge: (Integer, Integer) -> Boolean
-1	~	UnaryMinus: (Integer) -> Integer
|	~	Bwor: (Integer, Integer) -> Integer
/	~	Div: (Integer, Integer) -> Integer
=	~	Eq: (Integer, Integer) -> Boolean
	~	Bwxor: (Integer, Integer) -> Integer
||	~	Lor: (Boolean, Boolean) -> Boolean
!	~	Lnot: (Boolean) -> Boolean
<	~	Lt: (Integer, Integer) -> Boolean
-	~	Sub: (Integer, Integer) -> Integer
<=	~	Le: (Integer, Integer) -> Boolean
>	~	Gt: (Integer, Integer) -> Boolean
~	~	Bwnot: (Integer) -> Integer
%	~	Mod: (Integer, Integer) -> Integer
&	~	Bwand: (Integer, Integer) -> Integer
+	~	Add: (Integer, Integer) -> Integer
&&	~	Land: (Boolean, Boolean) -> Boolean

The following domains are used:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 6091_1_MAIN_INVOKEMETHOD(x4[0], x5[0]) → 5887_0_MAIN_LOAD(x5[0] + -1, x4[0])
(2): COND_5887_0_MAIN_LOAD(TRUE, x0[2], x1[2]) → 6091_1_MAIN_INVOKEMETHOD(x1[2], x0[2])
(4): COND_5887_0_MAIN_LOAD1(TRUE, x0[4], x1[4]) → 5887_0_MAIN_LOAD(x0[4] + -1, x1[4])
(6): COND_5887_0_MAIN_LOAD2(TRUE, x0[6], x1[6]) → 5887_0_MAIN_LOAD(x0[6], x1[6] + -1)

(2) -> (0), if ((x1[2] →^* x4[0])∧(x0[2] →^* x5[0]))

The set Q is empty.

(11) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 4 less nodes.

(12) TRUE