Termination proof of /tmp/tmpTAruof/Test12.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇒)

↳2 JBCTerminationGraph

↳3 FIGtoITRSProof (⇒)

↳4 IDP

↳5 IDPNonInfProof (⇒)

↳6 IDP

↳7 IDependencyGraphProof (⇔)

↳8 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_20 (Apple Inc.) Main-Class: Test12

public class Test12 {
    public static void main(String[] args) {
	Random.args = args;

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

	rec(x, y);
    }

    private static void rec(int x, int y) {
	if (x + y > 0) {
	    if (Random.random() * Random.random() > 9)
		rec(x - 1, y);
	    else
		rec(x, y - 1);
	}
    }
}

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:
Test12.main([Ljava/lang/String;)V: Graph of 57 nodes with 0 SCCs.

Test12.rec(II)V: Graph of 384 nodes with 0 SCCs.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 124 rules for P and 285 rules for R.

Combined rules. Obtained 17 rules for P and 32 rules for R.

Filtered ground terms:

6722_0_rec_Load(x1, x2, x3, x4) → 6722_0_rec_Load(x2, x3, x4)
Cond_6794_1_rec_InvokeMethod(x1, x2, x3, x4, x5) → Cond_6794_1_rec_InvokeMethod(x1, x2, x3, x4)
6794_0_random_LT(x1, x2, x3) → 6794_0_random_LT(x2, x3)
6794_1_rec_InvokeMethod(x1, x2, x3, x4) → 6794_1_rec_InvokeMethod(x1, x2, x3)
Cond_6915_1_rec_InvokeMethod(x1, x2, x3, x4, x5) → Cond_6915_1_rec_InvokeMethod(x1, x2, x3, x4)
6915_0_random_IntArithmetic(x1, x2, x3, x4) → 6915_0_random_IntArithmetic(x2, x3)
6915_1_rec_InvokeMethod(x1, x2, x3, x4) → 6915_1_rec_InvokeMethod(x1, x2, x3)
Cond_6847_1_rec_InvokeMethod(x1, x2, x3, x4, x5) → Cond_6847_1_rec_InvokeMethod(x1, x2, x3, x4)
6847_0_random_ArrayAccess(x1, x2, x3) → 6847_0_random_ArrayAccess(x2, x3)
6847_1_rec_InvokeMethod(x1, x2, x3, x4) → 6847_1_rec_InvokeMethod(x1, x2, x3)
Cond_6792_1_rec_InvokeMethod(x1, x2, x3, x4, x5) → Cond_6792_1_rec_InvokeMethod(x1, x2, x3, x4)
6792_0_random_LT(x1, x2, x3) → 6792_0_random_LT(x2, x3)
6792_1_rec_InvokeMethod(x1, x2, x3, x4) → 6792_1_rec_InvokeMethod(x1, x2, x3)
6749_0_random_LT(x1, x2, x3) → 6749_0_random_LT(x2, x3)
7058_0_random_LT(x1, x2, x3) → 7058_0_random_LT(x2, x3)
7349_0_random_IntArithmetic(x1, x2, x3, x4) → 7349_0_random_IntArithmetic(x2, x3)
7211_0_random_ArrayAccess(x1, x2, x3) → 7211_0_random_ArrayAccess(x2, x3)
7057_0_random_LT(x1, x2, x3) → 7057_0_random_LT(x2, x3)
6797_0_random_IntArithmetic(x1, x2, x3, x4) → 6797_0_random_IntArithmetic(x2, x3)
6764_0_random_ArrayAccess(x1, x2, x3) → 6764_0_random_ArrayAccess(x2, x3)
6748_0_random_LT(x1, x2, x3) → 6748_0_random_LT(x2, x3)
Cond_6722_0_rec_Load1(x1, x2, x3, x4, x5) → Cond_6722_0_rec_Load1(x1, x3, x4, x5)
Cond_6722_0_rec_Load(x1, x2, x3, x4, x5) → Cond_6722_0_rec_Load(x1, x3, x4, x5)
7511_0_rec_InvokeMethod(x1, x2, x3, x4) → 7511_0_rec_InvokeMethod(x2, x3, x4)
java.lang.NullPointerException(x1) → java.lang.NullPointerException
8091_0_rec_InvokeMethod(x1, x2, x3, x4, x5) → 8091_0_rec_InvokeMethod(x3, x4, x5)
7957_0_rec_InvokeMethod(x1, x2, x3, x4) → 7957_0_rec_InvokeMethod(x2, x3, x4)
java.lang.ArrayIndexOutOfBoundsException(x1) → java.lang.ArrayIndexOutOfBoundsException
java.lang.IndexOutOfBoundsException(x1) → java.lang.IndexOutOfBoundsException
7951_0_rec_InvokeMethod(x1, x2, x3, x4, x5) → 7951_0_rec_InvokeMethod(x3, x4, x5)
7722_0_rec_InvokeMethod(x1, x2, x3, x4, x5) → 7722_0_rec_InvokeMethod(x3, x4)
7613_0_rec_Return(x1) → 7613_0_rec_Return
7533_0_rec_InvokeMethod(x1, x2, x3, x4, x5) → 7533_0_rec_InvokeMethod(x3, x4)
7472_0_rec_InvokeMethod(x1, x2, x3, x4, x5) → 7472_0_rec_InvokeMethod(x3, x4)
7390_0_rec_InvokeMethod(x1, x2, x3, x4) → 7390_0_rec_InvokeMethod(x3, x4)
7222_0_rec_InvokeMethod(x1, x2, x3, x4) → 7222_0_rec_InvokeMethod(x3, x4)
7174_0_rec_InvokeMethod(x1, x2, x3, x4) → 7174_0_rec_InvokeMethod(x3, x4)
6731_0_rec_Return(x1) → 6731_0_rec_Return

Filtered duplicate args:

6722_0_rec_Load(x1, x2, x3) → 6722_0_rec_Load(x2, x3)
Cond_6722_0_rec_Load1(x1, x2, x3, x4) → Cond_6722_0_rec_Load1(x1, x3, x4)
Cond_6722_0_rec_Load(x1, x2, x3, x4) → Cond_6722_0_rec_Load(x1, x3, x4)

Filtered unneeded arguments:

Cond_7349_1_rec_InvokeMethod(x1, x2, x3, x4, x5) → Cond_7349_1_rec_InvokeMethod(x1, x2, x3, x4)
Cond_7349_1_rec_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_7349_1_rec_InvokeMethod1(x1, x2, x3, x4)
7058_1_rec_InvokeMethod(x1, x2, x3, x4) → 7058_1_rec_InvokeMethod(x1, x2, x3)
Cond_7058_1_rec_InvokeMethod(x1, x2, x3, x4, x5) → Cond_7058_1_rec_InvokeMethod(x1, x2, x3, x4)

Filtered all free variables:

6748_1_rec_InvokeMethod(x1, x2, x3) → 6748_1_rec_InvokeMethod(x2, x3)
6749_1_rec_InvokeMethod(x1, x2, x3) → 6749_1_rec_InvokeMethod(x2, x3)
Cond_6748_1_rec_InvokeMethod(x1, x2, x3, x4) → Cond_6748_1_rec_InvokeMethod(x1, x3, x4)
6764_1_rec_InvokeMethod(x1, x2, x3) → 6764_1_rec_InvokeMethod(x2, x3)
Cond_6764_1_rec_InvokeMethod(x1, x2, x3, x4) → Cond_6764_1_rec_InvokeMethod(x1, x3, x4)
6797_1_rec_InvokeMethod(x1, x2, x3) → 6797_1_rec_InvokeMethod(x2, x3)
Cond_6797_1_rec_InvokeMethod(x1, x2, x3, x4) → Cond_6797_1_rec_InvokeMethod(x1, x3, x4)
7057_1_rec_InvokeMethod(x1, x2, x3, x4) → 7057_1_rec_InvokeMethod(x2, x3, x4)
Cond_6797_1_rec_InvokeMethod1(x1, x2, x3, x4) → Cond_6797_1_rec_InvokeMethod1(x1, x3, x4)
7058_1_rec_InvokeMethod(x1, x2, x3) → 7058_1_rec_InvokeMethod(x2, x3)
Cond_7057_1_rec_InvokeMethod(x1, x2, x3, x4, x5) → Cond_7057_1_rec_InvokeMethod(x1, x3, x4, x5)
7211_1_rec_InvokeMethod(x1, x2, x3, x4) → 7211_1_rec_InvokeMethod(x2, x3, x4)
Cond_7211_1_rec_InvokeMethod(x1, x2, x3, x4, x5) → Cond_7211_1_rec_InvokeMethod(x1, x3, x4, x5)
7349_1_rec_InvokeMethod(x1, x2, x3, x4) → 7349_1_rec_InvokeMethod(x2, x3, x4)
Cond_7349_1_rec_InvokeMethod(x1, x2, x3, x4) → Cond_7349_1_rec_InvokeMethod(x1, x3, x4)
Cond_7349_1_rec_InvokeMethod1(x1, x2, x3, x4) → Cond_7349_1_rec_InvokeMethod1(x1, x3, x4)
Cond_7058_1_rec_InvokeMethod(x1, x2, x3, x4) → Cond_7058_1_rec_InvokeMethod(x1, x3, x4)
Cond_6749_1_rec_InvokeMethod(x1, x2, x3, x4) → Cond_6749_1_rec_InvokeMethod(x1, x3, x4)
6792_1_rec_InvokeMethod(x1, x2, x3) → 6792_1_rec_InvokeMethod(x2, x3)
Cond_6749_1_rec_InvokeMethod1(x1, x2, x3, x4) → Cond_6749_1_rec_InvokeMethod1(x1, x3, x4)
6794_1_rec_InvokeMethod(x1, x2, x3) → 6794_1_rec_InvokeMethod(x2, x3)
Cond_6792_1_rec_InvokeMethod(x1, x2, x3, x4) → Cond_6792_1_rec_InvokeMethod(x1, x3, x4)
6847_1_rec_InvokeMethod(x1, x2, x3) → 6847_1_rec_InvokeMethod(x2, x3)
Cond_6847_1_rec_InvokeMethod(x1, x2, x3, x4) → Cond_6847_1_rec_InvokeMethod(x1, x3, x4)
6915_1_rec_InvokeMethod(x1, x2, x3) → 6915_1_rec_InvokeMethod(x2, x3)
Cond_6915_1_rec_InvokeMethod(x1, x2, x3, x4) → Cond_6915_1_rec_InvokeMethod(x1, x3, x4)
Cond_6794_1_rec_InvokeMethod(x1, x2, x3, x4) → Cond_6794_1_rec_InvokeMethod(x1, x3, x4)

Combined rules. Obtained 5 rules for P and 32 rules for R.

Finished conversion. Obtained 5 rules for P and 32 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

The ITRS R consists of the following rules:
7439_1_rec_InvokeMethod(6731_0_rec_Return, x0, x1) → 7613_0_rec_Return
7439_1_rec_InvokeMethod(7222_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
7439_1_rec_InvokeMethod(7390_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
7439_1_rec_InvokeMethod(7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x1, x3) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x3)
7439_1_rec_InvokeMethod(7533_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
7439_1_rec_InvokeMethod(7613_0_rec_Return, x0, x1) → 7613_0_rec_Return
7439_1_rec_InvokeMethod(7722_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
7439_1_rec_InvokeMethod(7951_0_rec_InvokeMethod(x0, x1, x2), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
7439_1_rec_InvokeMethod(7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x3, x2) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x3, x2)
7439_1_rec_InvokeMethod(8091_0_rec_InvokeMethod(x0, x1, x2), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
7900_1_rec_InvokeMethod(6731_0_rec_Return, x0, x1) → 7613_0_rec_Return
7900_1_rec_InvokeMethod(7222_0_rec_InvokeMethod(x0, x1), x0, x1) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
7900_1_rec_InvokeMethod(7390_0_rec_InvokeMethod(x0, x1), x0, x1) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
7900_1_rec_InvokeMethod(7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x1, x3) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x3)
7900_1_rec_InvokeMethod(7533_0_rec_InvokeMethod(x0, x1), x0, x1) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
7900_1_rec_InvokeMethod(7613_0_rec_Return, x0, x1) → 7613_0_rec_Return
7900_1_rec_InvokeMethod(7722_0_rec_InvokeMethod(x0, x1), x0, x1) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
7900_1_rec_InvokeMethod(7951_0_rec_InvokeMethod(x0, x1, x2), x0, x1) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
7900_1_rec_InvokeMethod(7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x3, x2) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x3, x2)
7900_1_rec_InvokeMethod(8091_0_rec_InvokeMethod(x0, x1, x2), x0, x1) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
6957_1_rec_InvokeMethod(6731_0_rec_Return, x0, x1) → 7613_0_rec_Return
6957_1_rec_InvokeMethod(7174_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
6957_1_rec_InvokeMethod(7222_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
6957_1_rec_InvokeMethod(7390_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
6957_1_rec_InvokeMethod(7472_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
6957_1_rec_InvokeMethod(7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x1, x3) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x3)
6957_1_rec_InvokeMethod(7533_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
6957_1_rec_InvokeMethod(7613_0_rec_Return, x0, x1) → 7613_0_rec_Return
6957_1_rec_InvokeMethod(7722_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
6957_1_rec_InvokeMethod(7951_0_rec_InvokeMethod(x0, x1, x2), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
6957_1_rec_InvokeMethod(7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x3, x2) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x3, x2)
6957_1_rec_InvokeMethod(8091_0_rec_InvokeMethod(x0, x1, x2), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)

The integer pair graph contains the following rules and edges:
(0): 6915_1_REC_INVOKEMETHOD(x4[0], x5[0]) → 6722_0_REC_LOAD(x5[0] - 1, x4[0])
(1): 6722_0_REC_LOAD(x0[1], x1[1]) → COND_6722_0_REC_LOAD(0 < x1[1] + x0[1], x0[1], x1[1])
(2): COND_6722_0_REC_LOAD(TRUE, x0[2], x1[2]) → 6722_0_REC_LOAD(x0[2] - 1, x1[2])
(3): 6722_0_REC_LOAD(x0[3], x1[3]) → COND_6722_0_REC_LOAD1(0 < x1[3] + x0[3], x0[3], x1[3])
(4): COND_6722_0_REC_LOAD1(TRUE, x0[4], x1[4]) → 6722_0_REC_LOAD(x0[4], x1[4] - 1)
(5): 6722_0_REC_LOAD(x0[5], x1[5]) → COND_6722_0_REC_LOAD3(0 < x1[5] + x0[5], x0[5], x1[5])
(6): COND_6722_0_REC_LOAD3(TRUE, x0[6], x1[6]) → 6915_1_REC_INVOKEMETHOD(x1[6], x0[6])

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

(2) -> (3), if ((x0[2] - 1 →^* x0[3])∧(x1[2] →^* x1[3]))

(2) -> (5), if ((x0[2] - 1 →^* x0[5])∧(x1[2] →^* x1[5]))

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

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

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

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

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

(6) -> (0), if ((x1[6] →^* x4[0])∧(x0[6] →^* x5[0]))

The set Q consists of the following terms:
7439_1_rec_InvokeMethod(6731_0_rec_Return, x0, x1)
7439_1_rec_InvokeMethod(7222_0_rec_InvokeMethod(x0, x1), x0, x1)
7439_1_rec_InvokeMethod(7390_0_rec_InvokeMethod(x0, x1), x0, x1)
7439_1_rec_InvokeMethod(7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x1, x3)
7439_1_rec_InvokeMethod(7533_0_rec_InvokeMethod(x0, x1), x0, x1)
7439_1_rec_InvokeMethod(7613_0_rec_Return, x0, x1)
7439_1_rec_InvokeMethod(7722_0_rec_InvokeMethod(x0, x1), x0, x1)
7439_1_rec_InvokeMethod(7951_0_rec_InvokeMethod(x0, x1, x2), x0, x1)
7439_1_rec_InvokeMethod(7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x3, x2)
7439_1_rec_InvokeMethod(8091_0_rec_InvokeMethod(x0, x1, x2), x0, x1)
7900_1_rec_InvokeMethod(6731_0_rec_Return, x0, x1)
7900_1_rec_InvokeMethod(7222_0_rec_InvokeMethod(x0, x1), x0, x1)
7900_1_rec_InvokeMethod(7390_0_rec_InvokeMethod(x0, x1), x0, x1)
7900_1_rec_InvokeMethod(7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x1, x3)
7900_1_rec_InvokeMethod(7533_0_rec_InvokeMethod(x0, x1), x0, x1)
7900_1_rec_InvokeMethod(7613_0_rec_Return, x0, x1)
7900_1_rec_InvokeMethod(7722_0_rec_InvokeMethod(x0, x1), x0, x1)
7900_1_rec_InvokeMethod(7951_0_rec_InvokeMethod(x0, x1, x2), x0, x1)
7900_1_rec_InvokeMethod(7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x3, x2)
7900_1_rec_InvokeMethod(8091_0_rec_InvokeMethod(x0, x1, x2), x0, x1)
6957_1_rec_InvokeMethod(6731_0_rec_Return, x0, x1)
6957_1_rec_InvokeMethod(7174_0_rec_InvokeMethod(x0, x1), x0, x1)
6957_1_rec_InvokeMethod(7222_0_rec_InvokeMethod(x0, x1), x0, x1)
6957_1_rec_InvokeMethod(7390_0_rec_InvokeMethod(x0, x1), x0, x1)
6957_1_rec_InvokeMethod(7472_0_rec_InvokeMethod(x0, x1), x0, x1)
6957_1_rec_InvokeMethod(7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x1, x3)
6957_1_rec_InvokeMethod(7533_0_rec_InvokeMethod(x0, x1), x0, x1)
6957_1_rec_InvokeMethod(7613_0_rec_Return, x0, x1)
6957_1_rec_InvokeMethod(7722_0_rec_InvokeMethod(x0, x1), x0, x1)
6957_1_rec_InvokeMethod(7951_0_rec_InvokeMethod(x0, x1, x2), x0, x1)
6957_1_rec_InvokeMethod(7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x3, x2)
6957_1_rec_InvokeMethod(8091_0_rec_InvokeMethod(x0, x1, x2), x0, x1)

(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 6915_1_REC_INVOKEMETHOD(x4, x5) → 6722_0_REC_LOAD(-(x5, 1), x4) the following chains were created:

We consider the chain 6915_1_REC_INVOKEMETHOD(x4[0], x5[0]) → 6722_0_REC_LOAD(-(x5[0], 1), x4[0]) which results in the following constraint:
(1)    (6915_1_REC_INVOKEMETHOD(x4[0], x5[0])≥NonInfC∧6915_1_REC_INVOKEMETHOD(x4[0], x5[0])≥6722_0_REC_LOAD(-(x5[0], 1), x4[0])∧(U^Increasing(6722_0_REC_LOAD(-(x5[0], 1), x4[0])), ≥))

We simplified constraint (1) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(2)    ((U^Increasing(6722_0_REC_LOAD(-(x5[0], 1), x4[0])), ≥)∧[(-1)bso_33] ≥ 0)

We simplified constraint (2) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(3)    ((U^Increasing(6722_0_REC_LOAD(-(x5[0], 1), x4[0])), ≥)∧[(-1)bso_33] ≥ 0)

We simplified constraint (3) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(4)    ((U^Increasing(6722_0_REC_LOAD(-(x5[0], 1), x4[0])), ≥)∧[(-1)bso_33] ≥ 0)

We simplified constraint (4) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(5)    ((U^Increasing(6722_0_REC_LOAD(-(x5[0], 1), x4[0])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_33] ≥ 0)

For Pair 6722_0_REC_LOAD(x0, x1) → COND_6722_0_REC_LOAD(<(0, +(x1, x0)), x0, x1) the following chains were created:

We consider the chain 6722_0_REC_LOAD(x0[1], x1[1]) → COND_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1]), COND_6722_0_REC_LOAD(TRUE, x0[2], x1[2]) → 6722_0_REC_LOAD(-(x0[2], 1), x1[2]) which results in the following constraint:
(6)    (<(0, +(x1[1], x0[1]))=TRUE∧x0[1]=x0[2]∧x1[1]=x1[2] ⇒ 6722_0_REC_LOAD(x0[1], x1[1])≥NonInfC∧6722_0_REC_LOAD(x0[1], x1[1])≥COND_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])∧(U^Increasing(COND_6722_0_REC_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 ⇒ 6722_0_REC_LOAD(x0[1], x1[1])≥NonInfC∧6722_0_REC_LOAD(x0[1], x1[1])≥COND_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])∧(U^Increasing(COND_6722_0_REC_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_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(2)bni_34 + (-1)Bound*bni_34] + [(2)bni_34]x0[1] + [(2)bni_34]x1[1] ≥ 0∧[1 + (-1)bso_35] ≥ 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_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(2)bni_34 + (-1)Bound*bni_34] + [(2)bni_34]x0[1] + [(2)bni_34]x1[1] ≥ 0∧[1 + (-1)bso_35] ≥ 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_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(2)bni_34 + (-1)Bound*bni_34] + [(2)bni_34]x0[1] + [(2)bni_34]x1[1] ≥ 0∧[1 + (-1)bso_35] ≥ 0)

We simplified constraint (10) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(11)    (x1[1] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(4)bni_34 + (-1)Bound*bni_34] + [(2)bni_34]x1[1] ≥ 0∧[1 + (-1)bso_35] ≥ 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_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(4)bni_34 + (-1)Bound*bni_34] + [(2)bni_34]x1[1] ≥ 0∧[1 + (-1)bso_35] ≥ 0)

(13)    (x1[1] ≥ 0∧x0[1] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(4)bni_34 + (-1)Bound*bni_34] + [(2)bni_34]x1[1] ≥ 0∧[1 + (-1)bso_35] ≥ 0)

For Pair COND_6722_0_REC_LOAD(TRUE, x0, x1) → 6722_0_REC_LOAD(-(x0, 1), x1) the following chains were created:

We consider the chain COND_6722_0_REC_LOAD(TRUE, x0[2], x1[2]) → 6722_0_REC_LOAD(-(x0[2], 1), x1[2]) which results in the following constraint:
(14)    (COND_6722_0_REC_LOAD(TRUE, x0[2], x1[2])≥NonInfC∧COND_6722_0_REC_LOAD(TRUE, x0[2], x1[2])≥6722_0_REC_LOAD(-(x0[2], 1), x1[2])∧(U^Increasing(6722_0_REC_LOAD(-(x0[2], 1), x1[2])), ≥))

We simplified constraint (14) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(15)    ((U^Increasing(6722_0_REC_LOAD(-(x0[2], 1), x1[2])), ≥)∧[1 + (-1)bso_37] ≥ 0)

We simplified constraint (15) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(16)    ((U^Increasing(6722_0_REC_LOAD(-(x0[2], 1), x1[2])), ≥)∧[1 + (-1)bso_37] ≥ 0)

We simplified constraint (16) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(17)    ((U^Increasing(6722_0_REC_LOAD(-(x0[2], 1), x1[2])), ≥)∧[1 + (-1)bso_37] ≥ 0)

We simplified constraint (17) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(18)    ((U^Increasing(6722_0_REC_LOAD(-(x0[2], 1), x1[2])), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_37] ≥ 0)

For Pair 6722_0_REC_LOAD(x0, x1) → COND_6722_0_REC_LOAD1(<(0, +(x1, x0)), x0, x1) the following chains were created:

We consider the chain 6722_0_REC_LOAD(x0[3], x1[3]) → COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3]), COND_6722_0_REC_LOAD1(TRUE, x0[4], x1[4]) → 6722_0_REC_LOAD(x0[4], -(x1[4], 1)) which results in the following constraint:
(19)    (<(0, +(x1[3], x0[3]))=TRUE∧x0[3]=x0[4]∧x1[3]=x1[4] ⇒ 6722_0_REC_LOAD(x0[3], x1[3])≥NonInfC∧6722_0_REC_LOAD(x0[3], x1[3])≥COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])∧(U^Increasing(COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥))

We simplified constraint (19) using rule (IV) which results in the following new constraint:
(20)    (<(0, +(x1[3], x0[3]))=TRUE ⇒ 6722_0_REC_LOAD(x0[3], x1[3])≥NonInfC∧6722_0_REC_LOAD(x0[3], x1[3])≥COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])∧(U^Increasing(COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥))

We simplified constraint (20) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(21)    (x1[3] + [-1] + x0[3] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(2)bni_38 + (-1)Bound*bni_38] + [(2)bni_38]x0[3] + [(2)bni_38]x1[3] ≥ 0∧[1 + (-1)bso_39] ≥ 0)

We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(22)    (x1[3] + [-1] + x0[3] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(2)bni_38 + (-1)Bound*bni_38] + [(2)bni_38]x0[3] + [(2)bni_38]x1[3] ≥ 0∧[1 + (-1)bso_39] ≥ 0)

We simplified constraint (22) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(23)    (x1[3] + [-1] + x0[3] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(2)bni_38 + (-1)Bound*bni_38] + [(2)bni_38]x0[3] + [(2)bni_38]x1[3] ≥ 0∧[1 + (-1)bso_39] ≥ 0)

We simplified constraint (23) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(24)    (x1[3] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(4)bni_38 + (-1)Bound*bni_38] + [(2)bni_38]x1[3] ≥ 0∧[1 + (-1)bso_39] ≥ 0)

We simplified constraint (24) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(25)    (x1[3] ≥ 0∧x0[3] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(4)bni_38 + (-1)Bound*bni_38] + [(2)bni_38]x1[3] ≥ 0∧[1 + (-1)bso_39] ≥ 0)

(26)    (x1[3] ≥ 0∧x0[3] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(4)bni_38 + (-1)Bound*bni_38] + [(2)bni_38]x1[3] ≥ 0∧[1 + (-1)bso_39] ≥ 0)

For Pair COND_6722_0_REC_LOAD1(TRUE, x0, x1) → 6722_0_REC_LOAD(x0, -(x1, 1)) the following chains were created:

We consider the chain COND_6722_0_REC_LOAD1(TRUE, x0[4], x1[4]) → 6722_0_REC_LOAD(x0[4], -(x1[4], 1)) which results in the following constraint:
(27)    (COND_6722_0_REC_LOAD1(TRUE, x0[4], x1[4])≥NonInfC∧COND_6722_0_REC_LOAD1(TRUE, x0[4], x1[4])≥6722_0_REC_LOAD(x0[4], -(x1[4], 1))∧(U^Increasing(6722_0_REC_LOAD(x0[4], -(x1[4], 1))), ≥))

We simplified constraint (27) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(28)    ((U^Increasing(6722_0_REC_LOAD(x0[4], -(x1[4], 1))), ≥)∧[1 + (-1)bso_41] ≥ 0)

We simplified constraint (28) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(29)    ((U^Increasing(6722_0_REC_LOAD(x0[4], -(x1[4], 1))), ≥)∧[1 + (-1)bso_41] ≥ 0)

We simplified constraint (29) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(30)    ((U^Increasing(6722_0_REC_LOAD(x0[4], -(x1[4], 1))), ≥)∧[1 + (-1)bso_41] ≥ 0)

We simplified constraint (30) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(31)    ((U^Increasing(6722_0_REC_LOAD(x0[4], -(x1[4], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_41] ≥ 0)

For Pair 6722_0_REC_LOAD(x0, x1) → COND_6722_0_REC_LOAD3(<(0, +(x1, x0)), x0, x1) the following chains were created:

We consider the chain 6722_0_REC_LOAD(x0[5], x1[5]) → COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5]), COND_6722_0_REC_LOAD3(TRUE, x0[6], x1[6]) → 6915_1_REC_INVOKEMETHOD(x1[6], x0[6]) which results in the following constraint:
(32)    (<(0, +(x1[5], x0[5]))=TRUE∧x0[5]=x0[6]∧x1[5]=x1[6] ⇒ 6722_0_REC_LOAD(x0[5], x1[5])≥NonInfC∧6722_0_REC_LOAD(x0[5], x1[5])≥COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])∧(U^Increasing(COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥))

We simplified constraint (32) using rule (IV) which results in the following new constraint:
(33)    (<(0, +(x1[5], x0[5]))=TRUE ⇒ 6722_0_REC_LOAD(x0[5], x1[5])≥NonInfC∧6722_0_REC_LOAD(x0[5], x1[5])≥COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])∧(U^Increasing(COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥))

We simplified constraint (33) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(34)    (x1[5] + [-1] + x0[5] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(2)bni_42 + (-1)Bound*bni_42] + [(2)bni_42]x0[5] + [(2)bni_42]x1[5] ≥ 0∧[1 + (-1)bso_43] ≥ 0)

We simplified constraint (34) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(35)    (x1[5] + [-1] + x0[5] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(2)bni_42 + (-1)Bound*bni_42] + [(2)bni_42]x0[5] + [(2)bni_42]x1[5] ≥ 0∧[1 + (-1)bso_43] ≥ 0)

We simplified constraint (35) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(36)    (x1[5] + [-1] + x0[5] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(2)bni_42 + (-1)Bound*bni_42] + [(2)bni_42]x0[5] + [(2)bni_42]x1[5] ≥ 0∧[1 + (-1)bso_43] ≥ 0)

We simplified constraint (36) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(37)    (x1[5] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(4)bni_42 + (-1)Bound*bni_42] + [(2)bni_42]x1[5] ≥ 0∧[1 + (-1)bso_43] ≥ 0)

We simplified constraint (37) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(38)    (x1[5] ≥ 0∧x0[5] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(4)bni_42 + (-1)Bound*bni_42] + [(2)bni_42]x1[5] ≥ 0∧[1 + (-1)bso_43] ≥ 0)

(39)    (x1[5] ≥ 0∧x0[5] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(4)bni_42 + (-1)Bound*bni_42] + [(2)bni_42]x1[5] ≥ 0∧[1 + (-1)bso_43] ≥ 0)

For Pair COND_6722_0_REC_LOAD3(TRUE, x0, x1) → 6915_1_REC_INVOKEMETHOD(x1, x0) the following chains were created:

We consider the chain COND_6722_0_REC_LOAD3(TRUE, x0[6], x1[6]) → 6915_1_REC_INVOKEMETHOD(x1[6], x0[6]), 6915_1_REC_INVOKEMETHOD(x4[0], x5[0]) → 6722_0_REC_LOAD(-(x5[0], 1), x4[0]) which results in the following constraint:
(40)    (x1[6]=x4[0]∧x0[6]=x5[0] ⇒ COND_6722_0_REC_LOAD3(TRUE, x0[6], x1[6])≥NonInfC∧COND_6722_0_REC_LOAD3(TRUE, x0[6], x1[6])≥6915_1_REC_INVOKEMETHOD(x1[6], x0[6])∧(U^Increasing(6915_1_REC_INVOKEMETHOD(x1[6], x0[6])), ≥))

We simplified constraint (40) using rule (IV) which results in the following new constraint:
(41)    (COND_6722_0_REC_LOAD3(TRUE, x0[6], x1[6])≥NonInfC∧COND_6722_0_REC_LOAD3(TRUE, x0[6], x1[6])≥6915_1_REC_INVOKEMETHOD(x1[6], x0[6])∧(U^Increasing(6915_1_REC_INVOKEMETHOD(x1[6], x0[6])), ≥))

We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(42)    ((U^Increasing(6915_1_REC_INVOKEMETHOD(x1[6], x0[6])), ≥)∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (42) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(43)    ((U^Increasing(6915_1_REC_INVOKEMETHOD(x1[6], x0[6])), ≥)∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (43) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(44)    ((U^Increasing(6915_1_REC_INVOKEMETHOD(x1[6], x0[6])), ≥)∧[1 + (-1)bso_45] ≥ 0)

We simplified constraint (44) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(45)    ((U^Increasing(6915_1_REC_INVOKEMETHOD(x1[6], x0[6])), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_45] ≥ 0)

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

6915_1_REC_INVOKEMETHOD(x4, x5) → 6722_0_REC_LOAD(-(x5, 1), x4)
- ((U^Increasing(6722_0_REC_LOAD(-(x5[0], 1), x4[0])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_33] ≥ 0)
6722_0_REC_LOAD(x0, x1) → COND_6722_0_REC_LOAD(<(0, +(x1, x0)), x0, x1)
- (x1[1] ≥ 0∧x0[1] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(4)bni_34 + (-1)Bound*bni_34] + [(2)bni_34]x1[1] ≥ 0∧[1 + (-1)bso_35] ≥ 0)
- (x1[1] ≥ 0∧x0[1] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])), ≥)∧[(4)bni_34 + (-1)Bound*bni_34] + [(2)bni_34]x1[1] ≥ 0∧[1 + (-1)bso_35] ≥ 0)
COND_6722_0_REC_LOAD(TRUE, x0, x1) → 6722_0_REC_LOAD(-(x0, 1), x1)
- ((U^Increasing(6722_0_REC_LOAD(-(x0[2], 1), x1[2])), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_37] ≥ 0)
6722_0_REC_LOAD(x0, x1) → COND_6722_0_REC_LOAD1(<(0, +(x1, x0)), x0, x1)
- (x1[3] ≥ 0∧x0[3] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(4)bni_38 + (-1)Bound*bni_38] + [(2)bni_38]x1[3] ≥ 0∧[1 + (-1)bso_39] ≥ 0)
- (x1[3] ≥ 0∧x0[3] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])), ≥)∧[(4)bni_38 + (-1)Bound*bni_38] + [(2)bni_38]x1[3] ≥ 0∧[1 + (-1)bso_39] ≥ 0)
COND_6722_0_REC_LOAD1(TRUE, x0, x1) → 6722_0_REC_LOAD(x0, -(x1, 1))
- ((U^Increasing(6722_0_REC_LOAD(x0[4], -(x1[4], 1))), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_41] ≥ 0)
6722_0_REC_LOAD(x0, x1) → COND_6722_0_REC_LOAD3(<(0, +(x1, x0)), x0, x1)
- (x1[5] ≥ 0∧x0[5] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(4)bni_42 + (-1)Bound*bni_42] + [(2)bni_42]x1[5] ≥ 0∧[1 + (-1)bso_43] ≥ 0)
- (x1[5] ≥ 0∧x0[5] ≥ 0 ⇒ (U^Increasing(COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])), ≥)∧[(4)bni_42 + (-1)Bound*bni_42] + [(2)bni_42]x1[5] ≥ 0∧[1 + (-1)bso_43] ≥ 0)
COND_6722_0_REC_LOAD3(TRUE, x0, x1) → 6915_1_REC_INVOKEMETHOD(x1, x0)
- ((U^Increasing(6915_1_REC_INVOKEMETHOD(x1[6], x0[6])), ≥)∧0 = 0∧0 = 0∧[1 + (-1)bso_45] ≥ 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(7439_1_rec_InvokeMethod(x₁, x₂, x₃)) = [-1]
POL(6731_0_rec_Return) = [-1]
POL(7613_0_rec_Return) = [-1]
POL(7222_0_rec_InvokeMethod(x₁, x₂)) = [-1]
POL(7511_0_rec_InvokeMethod(x₁, x₂, x₃)) = [-1]
POL(java.lang.Object(x₁)) = [-1]
POL(java.lang.Throwable(x₁)) = [-1]
POL(java.lang.Exception(x₁)) = [-1]
POL(java.lang.RuntimeException(x₁)) = [-1]
POL(java.lang.IndexOutOfBoundsException) = [-1]
POL(7390_0_rec_InvokeMethod(x₁, x₂)) = [-1]
POL(java.lang.NullPointerException) = [-1]
POL(7533_0_rec_InvokeMethod(x₁, x₂)) = [-1]
POL(7722_0_rec_InvokeMethod(x₁, x₂)) = [-1]
POL(7951_0_rec_InvokeMethod(x₁, x₂, x₃)) = [-1]
POL(7957_0_rec_InvokeMethod(x₁, x₂, x₃)) = [-1]
POL(8091_0_rec_InvokeMethod(x₁, x₂, x₃)) = [-1]
POL(7900_1_rec_InvokeMethod(x₁, x₂, x₃)) = [-1]
POL(6957_1_rec_InvokeMethod(x₁, x₂, x₃)) = [-1]
POL(7174_0_rec_InvokeMethod(x₁, x₂)) = [-1]
POL(7472_0_rec_InvokeMethod(x₁, x₂)) = [-1]
POL(6915_1_REC_INVOKEMETHOD(x₁, x₂)) = [2]x₁ + [2]x₂
POL(6722_0_REC_LOAD(x₁, x₂)) = [2] + [2]x₁ + [2]x₂
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(1) = [1]
POL(COND_6722_0_REC_LOAD(x₁, x₂, x₃)) = [1] + [2]x₃ + [2]x₂
POL(<(x₁, x₂)) = [-1]
POL(0) = 0
POL(+(x₁, x₂)) = x₁ + x₂
POL(COND_6722_0_REC_LOAD1(x₁, x₂, x₃)) = [1] + [2]x₃ + [2]x₂
POL(COND_6722_0_REC_LOAD3(x₁, x₂, x₃)) = [1] + [2]x₃ + [2]x₂

The following pairs are in P_>:

6722_0_REC_LOAD(x0[1], x1[1]) → COND_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])
COND_6722_0_REC_LOAD(TRUE, x0[2], x1[2]) → 6722_0_REC_LOAD(-(x0[2], 1), x1[2])
6722_0_REC_LOAD(x0[3], x1[3]) → COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])
COND_6722_0_REC_LOAD1(TRUE, x0[4], x1[4]) → 6722_0_REC_LOAD(x0[4], -(x1[4], 1))
6722_0_REC_LOAD(x0[5], x1[5]) → COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])
COND_6722_0_REC_LOAD3(TRUE, x0[6], x1[6]) → 6915_1_REC_INVOKEMETHOD(x1[6], x0[6])

The following pairs are in P_bound:

6722_0_REC_LOAD(x0[1], x1[1]) → COND_6722_0_REC_LOAD(<(0, +(x1[1], x0[1])), x0[1], x1[1])
6722_0_REC_LOAD(x0[3], x1[3]) → COND_6722_0_REC_LOAD1(<(0, +(x1[3], x0[3])), x0[3], x1[3])
6722_0_REC_LOAD(x0[5], x1[5]) → COND_6722_0_REC_LOAD3(<(0, +(x1[5], x0[5])), x0[5], x1[5])

The following pairs are in P_≥:

6915_1_REC_INVOKEMETHOD(x4[0], x5[0]) → 6722_0_REC_LOAD(-(x5[0], 1), x4[0])

There are no usable rules.

(6) 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

The ITRS R consists of the following rules:
7439_1_rec_InvokeMethod(6731_0_rec_Return, x0, x1) → 7613_0_rec_Return
7439_1_rec_InvokeMethod(7222_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
7439_1_rec_InvokeMethod(7390_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
7439_1_rec_InvokeMethod(7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x1, x3) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x3)
7439_1_rec_InvokeMethod(7533_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
7439_1_rec_InvokeMethod(7613_0_rec_Return, x0, x1) → 7613_0_rec_Return
7439_1_rec_InvokeMethod(7722_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
7439_1_rec_InvokeMethod(7951_0_rec_InvokeMethod(x0, x1, x2), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
7439_1_rec_InvokeMethod(7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x3, x2) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x3, x2)
7439_1_rec_InvokeMethod(8091_0_rec_InvokeMethod(x0, x1, x2), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
7900_1_rec_InvokeMethod(6731_0_rec_Return, x0, x1) → 7613_0_rec_Return
7900_1_rec_InvokeMethod(7222_0_rec_InvokeMethod(x0, x1), x0, x1) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
7900_1_rec_InvokeMethod(7390_0_rec_InvokeMethod(x0, x1), x0, x1) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
7900_1_rec_InvokeMethod(7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x1, x3) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x3)
7900_1_rec_InvokeMethod(7533_0_rec_InvokeMethod(x0, x1), x0, x1) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
7900_1_rec_InvokeMethod(7613_0_rec_Return, x0, x1) → 7613_0_rec_Return
7900_1_rec_InvokeMethod(7722_0_rec_InvokeMethod(x0, x1), x0, x1) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
7900_1_rec_InvokeMethod(7951_0_rec_InvokeMethod(x0, x1, x2), x0, x1) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
7900_1_rec_InvokeMethod(7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x3, x2) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x3, x2)
7900_1_rec_InvokeMethod(8091_0_rec_InvokeMethod(x0, x1, x2), x0, x1) → 7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
6957_1_rec_InvokeMethod(6731_0_rec_Return, x0, x1) → 7613_0_rec_Return
6957_1_rec_InvokeMethod(7174_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
6957_1_rec_InvokeMethod(7222_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
6957_1_rec_InvokeMethod(7390_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
6957_1_rec_InvokeMethod(7472_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
6957_1_rec_InvokeMethod(7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x1, x3) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x3)
6957_1_rec_InvokeMethod(7533_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
6957_1_rec_InvokeMethod(7613_0_rec_Return, x0, x1) → 7613_0_rec_Return
6957_1_rec_InvokeMethod(7722_0_rec_InvokeMethod(x0, x1), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)
6957_1_rec_InvokeMethod(7951_0_rec_InvokeMethod(x0, x1, x2), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.IndexOutOfBoundsException)))), x0, x1)
6957_1_rec_InvokeMethod(7957_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x1, x2), x3, x2) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(x0)))), x3, x2)
6957_1_rec_InvokeMethod(8091_0_rec_InvokeMethod(x0, x1, x2), x0, x1) → 7511_0_rec_InvokeMethod(java.lang.Object(java.lang.Throwable(java.lang.Exception(java.lang.RuntimeException(java.lang.NullPointerException)))), x0, x1)

The integer pair graph contains the following rules and edges:
(0): 6915_1_REC_INVOKEMETHOD(x4[0], x5[0]) → 6722_0_REC_LOAD(x5[0] - 1, x4[0])
(2): COND_6722_0_REC_LOAD(TRUE, x0[2], x1[2]) → 6722_0_REC_LOAD(x0[2] - 1, x1[2])
(4): COND_6722_0_REC_LOAD1(TRUE, x0[4], x1[4]) → 6722_0_REC_LOAD(x0[4], x1[4] - 1)
(6): COND_6722_0_REC_LOAD3(TRUE, x0[6], x1[6]) → 6915_1_REC_INVOKEMETHOD(x1[6], x0[6])

(6) -> (0), if ((x1[6] →^* x4[0])∧(x0[6] →^* x5[0]))

(7) IDependencyGraphProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) JBC2FIG (SOUND transformation)

(2) Obligation:

(3) FIGtoITRSProof (SOUND transformation)

(4) Obligation:

(5) IDPNonInfProof (SOUND transformation)

(6) Obligation:

(7) IDependencyGraphProof (EQUIVALENT transformation)

(8) TRUE