Termination proof of /tmp/tmpNZFOD

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇒)

↳2 JBCTerminationGraph

↳3 FIGtoITRSProof (⇒)

↳4 AND

    ↳5 IDP

        ↳6 IDPNonInfProof (⇒)

        ↳7 AND

            ↳8 IDP

                ↳9 IDependencyGraphProof (⇔)

                ↳10 TRUE

            ↳11 IDP

                ↳12 IDependencyGraphProof (⇔)

                ↳13 TRUE

    ↳14 IDP

        ↳15 IDPNonInfProof (⇒)

        ↳16 AND

            ↳17 IDP

                ↳18 IDependencyGraphProof (⇔)

                ↳19 IDP

                ↳20 UsableRulesProof (⇔)

                ↳21 IDP

                ↳22 IDPNonInfProof (⇒)

                ↳23 IDP

                ↳24 IDependencyGraphProof (⇔)

                ↳25 TRUE

            ↳26 IDP

                ↳27 IDependencyGraphProof (⇔)

                ↳28 IDP

                ↳29 UsableRulesProof (⇔)

                ↳30 IDP

                ↳31 IDPNonInfProof (⇒)

                ↳32 AND

                    ↳33 IDP

                        ↳34 IDependencyGraphProof (⇔)

                        ↳35 TRUE

                    ↳36 IDP

                        ↳37 IDependencyGraphProof (⇔)

                        ↳38 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_20 (Apple Inc.) Main-Class: Test10

public class Test10 {
    public static void main(String[] args) {
	rec(args.length);
    }

    private static void rec(long l) {
	if (l > 0) {
	    for (int i = (int) l ; i < 100; i++)
		test(i);

	    rec (l - 1);
	}
    }

    private static void test(int i) {
	descend(i);
	descend(i);
	descend(i);
	descend(i);
	descend(i);
	descend(i);
	descend(i);
	descend(i);
    }

    private static void descend(int i) {
	if (i > 0)
	    descend(i - 1);
    }
}

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Test10.main([Ljava/lang/String;)V: Graph of 13 nodes with 0 SCCs.

Test10.rec(J)V: Graph of 83 nodes with 1 SCC.

Test10.descend(I)V: Graph of 17 nodes with 0 SCCs.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Logs:

Log for SCC 0:

Generated 9 rules for P and 7 rules for R.

Combined rules. Obtained 1 rules for P and 3 rules for R.

Filtered ground terms:

169_0_descend_LE(x1, x2, x3) → 169_0_descend_LE(x2, x3)
Cond_169_0_descend_LE(x1, x2, x3, x4) → Cond_169_0_descend_LE(x1, x3, x4)
220_0_descend_Return(x1) → 220_0_descend_Return
175_0_descend_Return(x1) → 175_0_descend_Return

Filtered duplicate args:

169_0_descend_LE(x1, x2) → 169_0_descend_LE(x2)
Cond_169_0_descend_LE(x1, x2, x3) → Cond_169_0_descend_LE(x1, x3)

Combined rules. Obtained 1 rules for P and 3 rules for R.

Finished conversion. Obtained 1 rules for P and 3 rules for R. System has predefined symbols.

Log for SCC 1:

Generated 59 rules for P and 48 rules for R.

Combined rules. Obtained 10 rules for P and 22 rules for R.

Filtered ground terms:

69_0_rec_GE(x1, x2, x3, x4, x5) → 69_0_rec_GE(x2, x3, x4)
Cond_69_0_rec_GE1(x1, x2, x3, x4, x5, x6) → Cond_69_0_rec_GE1(x1, x3, x4, x5)
220_0_descend_Return(x1) → 220_0_descend_Return
321_0_descend_Load(x1, x2) → 321_0_descend_Load(x2)
309_0_descend_Load(x1, x2) → 309_0_descend_Load(x2)
295_0_descend_Load(x1, x2) → 295_0_descend_Load(x2)
282_0_descend_Load(x1, x2) → 282_0_descend_Load(x2)
266_0_descend_Load(x1, x2) → 266_0_descend_Load(x2)
250_0_descend_Load(x1, x2) → 250_0_descend_Load(x2)
237_0_descend_Load(x1, x2) → 237_0_descend_Load(x2)
92_0_descend_Load(x1, x2) → 92_0_descend_Load(x2)
Cond_69_0_rec_GE(x1, x2, x3, x4, x5, x6) → Cond_69_0_rec_GE(x1, x3, x4, x5)
175_0_descend_Return(x1) → 175_0_descend_Return
169_0_descend_LE(x1, x2, x3) → 169_0_descend_LE(x2, x3)
Cond_169_0_descend_LE(x1, x2, x3, x4) → Cond_169_0_descend_LE(x1, x3, x4)
143_0_rec_Return(x1) → 143_0_rec_Return
47_0_rec_Return(x1) → 47_0_rec_Return
327_0_descend_Return(x1) → 327_0_descend_Return
314_0_descend_Return(x1) → 314_0_descend_Return
300_0_descend_Return(x1) → 300_0_descend_Return
287_0_descend_Return(x1) → 287_0_descend_Return
273_0_descend_Return(x1) → 273_0_descend_Return
256_0_descend_Return(x1) → 256_0_descend_Return
243_0_descend_Return(x1) → 243_0_descend_Return
181_0_descend_Return(x1) → 181_0_descend_Return

Filtered duplicate args:

69_0_rec_GE(x1, x2, x3) → 69_0_rec_GE(x1, x3)
Cond_69_0_rec_GE1(x1, x2, x3, x4) → Cond_69_0_rec_GE1(x1, x2, x4)
Cond_321_2_rec_InvokeMethod(x1, x2, x3, x4, x5) → Cond_321_2_rec_InvokeMethod(x1, x2, x3, x5)
321_2_rec_InvokeMethod(x1, x2, x3, x4) → 321_2_rec_InvokeMethod(x1, x2, x4)
309_2_rec_InvokeMethod(x1, x2, x3, x4) → 309_2_rec_InvokeMethod(x1, x2, x4)
309_1_test_InvokeMethod(x1, x2, x3) → 309_1_test_InvokeMethod(x1, x3)
295_2_rec_InvokeMethod(x1, x2, x3, x4) → 295_2_rec_InvokeMethod(x1, x2, x4)
295_1_test_InvokeMethod(x1, x2, x3) → 295_1_test_InvokeMethod(x1, x3)
282_2_rec_InvokeMethod(x1, x2, x3, x4) → 282_2_rec_InvokeMethod(x1, x2, x4)
282_1_test_InvokeMethod(x1, x2, x3) → 282_1_test_InvokeMethod(x1, x3)
266_2_rec_InvokeMethod(x1, x2, x3, x4) → 266_2_rec_InvokeMethod(x1, x2, x4)
266_1_test_InvokeMethod(x1, x2, x3) → 266_1_test_InvokeMethod(x1, x3)
250_2_rec_InvokeMethod(x1, x2, x3, x4) → 250_2_rec_InvokeMethod(x1, x2, x4)
250_1_test_InvokeMethod(x1, x2, x3) → 250_1_test_InvokeMethod(x1, x3)
237_2_rec_InvokeMethod(x1, x2, x3, x4) → 237_2_rec_InvokeMethod(x1, x2, x4)
237_1_test_InvokeMethod(x1, x2, x3) → 237_1_test_InvokeMethod(x1, x3)
92_2_rec_InvokeMethod(x1, x2, x3, x4) → 92_2_rec_InvokeMethod(x1, x2, x4)
92_1_test_InvokeMethod(x1, x2, x3) → 92_1_test_InvokeMethod(x1, x3)
Cond_69_0_rec_GE(x1, x2, x3, x4) → Cond_69_0_rec_GE(x1, x2, x4)
169_0_descend_LE(x1, x2) → 169_0_descend_LE(x2)
Cond_169_0_descend_LE(x1, x2, x3) → Cond_169_0_descend_LE(x1, x3)

Filtered unneeded arguments:

Cond_69_0_rec_GE1(x1, x2, x3) → Cond_69_0_rec_GE1(x1, x2)

Combined rules. Obtained 10 rules for P and 22 rules for R.

Finished conversion. Obtained 10 rules for P and 22 rules for R. System has predefined symbols.

(4) Complex Obligation (AND)

(5) 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:
169_0_descend_LE(0) → 175_0_descend_Return
191_1_descend_InvokeMethod(175_0_descend_Return, 0) → 220_0_descend_Return
191_1_descend_InvokeMethod(220_0_descend_Return, x0) → 220_0_descend_Return

The integer pair graph contains the following rules and edges:
(0): 169_0_DESCEND_LE(x0[0]) → COND_169_0_DESCEND_LE(x0[0] > 0, x0[0])
(1): COND_169_0_DESCEND_LE(TRUE, x0[1]) → 169_0_DESCEND_LE(x0[1] - 1)

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

(1) -> (0), if ((x0[1] - 1 →^* x0[0]))

The set Q consists of the following terms:
169_0_descend_LE(0)
191_1_descend_InvokeMethod(175_0_descend_Return, 0)
191_1_descend_InvokeMethod(220_0_descend_Return, x0)

(6) 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 169_0_DESCEND_LE(x0) → COND_169_0_DESCEND_LE(>(x0, 0), x0) the following chains were created:

We consider the chain 169_0_DESCEND_LE(x0[0]) → COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0]), COND_169_0_DESCEND_LE(TRUE, x0[1]) → 169_0_DESCEND_LE(-(x0[1], 1)) which results in the following constraint:
(1)    (>(x0[0], 0)=TRUE∧x0[0]=x0[1] ⇒ 169_0_DESCEND_LE(x0[0])≥NonInfC∧169_0_DESCEND_LE(x0[0])≥COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0])∧(U^Increasing(COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0])), ≥))

We simplified constraint (1) using rule (IV) which results in the following new constraint:
(2)    (>(x0[0], 0)=TRUE ⇒ 169_0_DESCEND_LE(x0[0])≥NonInfC∧169_0_DESCEND_LE(x0[0])≥COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0])∧(U^Increasing(COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_12] + [(2)bni_12]x0[0] ≥ 0∧[(-1)bso_13] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_12] + [(2)bni_12]x0[0] ≥ 0∧[(-1)bso_13] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] + [-1] ≥ 0 ⇒ (U^Increasing(COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_12] + [(2)bni_12]x0[0] ≥ 0∧[(-1)bso_13] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x0[0] ≥ 0 ⇒ (U^Increasing(COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_12 + (2)bni_12] + [(2)bni_12]x0[0] ≥ 0∧[(-1)bso_13] ≥ 0)

For Pair COND_169_0_DESCEND_LE(TRUE, x0) → 169_0_DESCEND_LE(-(x0, 1)) the following chains were created:

We consider the chain COND_169_0_DESCEND_LE(TRUE, x0[1]) → 169_0_DESCEND_LE(-(x0[1], 1)) which results in the following constraint:
(7)    (COND_169_0_DESCEND_LE(TRUE, x0[1])≥NonInfC∧COND_169_0_DESCEND_LE(TRUE, x0[1])≥169_0_DESCEND_LE(-(x0[1], 1))∧(U^Increasing(169_0_DESCEND_LE(-(x0[1], 1))), ≥))

We simplified constraint (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(8)    ((U^Increasing(169_0_DESCEND_LE(-(x0[1], 1))), ≥)∧[2 + (-1)bso_15] ≥ 0)

We simplified constraint (8) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(9)    ((U^Increasing(169_0_DESCEND_LE(-(x0[1], 1))), ≥)∧[2 + (-1)bso_15] ≥ 0)

We simplified constraint (9) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(10)    ((U^Increasing(169_0_DESCEND_LE(-(x0[1], 1))), ≥)∧[2 + (-1)bso_15] ≥ 0)

We simplified constraint (10) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(11)    ((U^Increasing(169_0_DESCEND_LE(-(x0[1], 1))), ≥)∧0 = 0∧[2 + (-1)bso_15] ≥ 0)

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

169_0_DESCEND_LE(x0) → COND_169_0_DESCEND_LE(>(x0, 0), x0)
- (x0[0] ≥ 0 ⇒ (U^Increasing(COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0])), ≥)∧[(-1)Bound*bni_12 + (2)bni_12] + [(2)bni_12]x0[0] ≥ 0∧[(-1)bso_13] ≥ 0)
COND_169_0_DESCEND_LE(TRUE, x0) → 169_0_DESCEND_LE(-(x0, 1))
- ((U^Increasing(169_0_DESCEND_LE(-(x0[1], 1))), ≥)∧0 = 0∧[2 + (-1)bso_15] ≥ 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(169_0_descend_LE(x₁)) = [-1]
POL(0) = 0
POL(175_0_descend_Return) = [-1]
POL(191_1_descend_InvokeMethod(x₁, x₂)) = [-1]
POL(220_0_descend_Return) = [-1]
POL(169_0_DESCEND_LE(x₁)) = [2]x₁
POL(COND_169_0_DESCEND_LE(x₁, x₂)) = [2]x₂
POL(>(x₁, x₂)) = [-1]
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(1) = [1]

The following pairs are in P_>:

COND_169_0_DESCEND_LE(TRUE, x0[1]) → 169_0_DESCEND_LE(-(x0[1], 1))

The following pairs are in P_bound:

169_0_DESCEND_LE(x0[0]) → COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0])

The following pairs are in P_≥:

169_0_DESCEND_LE(x0[0]) → COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0])

There are no usable rules.

(7) Complex Obligation (AND)

(8) 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:
169_0_descend_LE(0) → 175_0_descend_Return
191_1_descend_InvokeMethod(175_0_descend_Return, 0) → 220_0_descend_Return
191_1_descend_InvokeMethod(220_0_descend_Return, x0) → 220_0_descend_Return

The integer pair graph contains the following rules and edges:
(0): 169_0_DESCEND_LE(x0[0]) → COND_169_0_DESCEND_LE(x0[0] > 0, x0[0])

The set Q consists of the following terms:
169_0_descend_LE(0)
191_1_descend_InvokeMethod(175_0_descend_Return, 0)
191_1_descend_InvokeMethod(220_0_descend_Return, x0)

(9) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(10) TRUE

(11) 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:
169_0_descend_LE(0) → 175_0_descend_Return
191_1_descend_InvokeMethod(175_0_descend_Return, 0) → 220_0_descend_Return
191_1_descend_InvokeMethod(220_0_descend_Return, x0) → 220_0_descend_Return

The integer pair graph contains the following rules and edges:
(1): COND_169_0_DESCEND_LE(TRUE, x0[1]) → 169_0_DESCEND_LE(x0[1] - 1)

The set Q consists of the following terms:
169_0_descend_LE(0)
191_1_descend_InvokeMethod(175_0_descend_Return, 0)
191_1_descend_InvokeMethod(220_0_descend_Return, x0)

(12) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(13) TRUE

(14) 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, Boolean

The ITRS R consists of the following rules:
92_0_descend_Load(i12) → 181_0_descend_Return
92_0_descend_Load(i45) → 243_0_descend_Return
92_0_descend_Load(i59) → 256_0_descend_Return
92_0_descend_Load(i62) → 273_0_descend_Return
92_0_descend_Load(i67) → 287_0_descend_Return
92_0_descend_Load(i70) → 300_0_descend_Return
92_0_descend_Load(i74) → 314_0_descend_Return
92_0_descend_Load(i76) → 327_0_descend_Return
92_0_descend_Load(x0) → 169_0_descend_LE(x0)
97_1_rec_InvokeMethod(47_0_rec_Return, 0) → 143_0_rec_Return
97_1_rec_InvokeMethod(143_0_rec_Return, x0) → 143_0_rec_Return
169_0_descend_LE(0) → 175_0_descend_Return
169_0_descend_LE(x0) → Cond_169_0_descend_LE(x0 > 0, x0)
Cond_169_0_descend_LE(TRUE, x0) → 191_1_descend_InvokeMethod(169_0_descend_LE(x0 - 1), x0 - 1)
191_1_descend_InvokeMethod(175_0_descend_Return, 0) → 220_0_descend_Return
191_1_descend_InvokeMethod(220_0_descend_Return, x0) → 220_0_descend_Return

The integer pair graph contains the following rules and edges:
(0): 69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(x1[0] < 100, x0[0], x1[0])
(1): COND_69_0_REC_GE(TRUE, x0[1], x1[1]) → 92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])
(2): 92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(220_0_descend_Return, x0[2]), x1[2], x0[2]) → 237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])
(3): 237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(220_0_descend_Return, x0[3]), x1[3], x0[3]) → 250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])
(4): 250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(220_0_descend_Return, x0[4]), x1[4], x0[4]) → 266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])
(5): 266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(220_0_descend_Return, x0[5]), x1[5], x0[5]) → 282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])
(6): 282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(220_0_descend_Return, x0[6]), x1[6], x0[6]) → 295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])
(7): 295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(220_0_descend_Return, x0[7]), x1[7], x0[7]) → 309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])
(8): 309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(220_0_descend_Return, x0[8]), x1[8], x0[8]) → 321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])
(9): 321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9]) → COND_321_2_REC_INVOKEMETHOD(x0[9] > 0, 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])
(10): COND_321_2_REC_INVOKEMETHOD(TRUE, 321_1_test_InvokeMethod(220_0_descend_Return, x0[10]), x1[10], x0[10]) → 69_0_REC_GE(x1[10], x0[10] + 1)
(11): 69_0_REC_GE(x0[11], x1[11]) → COND_69_0_REC_GE1(x1[11] >= 100 && x0[11] > 0 && 1 > 0 && 0 < x0[11] - 1, x0[11], x1[11])
(12): COND_69_0_REC_GE1(TRUE, x0[12], x1[12]) → 69_0_REC_GE(x0[12] - 1, x0[12] - 1)

(0) -> (1), if ((x1[0] < 100 →^* TRUE)∧(x0[0] →^* x0[1])∧(x1[0] →^* x1[1]))

(1) -> (2), if ((92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]) →^* 92_1_test_InvokeMethod(220_0_descend_Return, x0[2]))∧(x0[1] →^* x1[2])∧(x1[1] →^* x0[2]))

(2) -> (3), if ((237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]) →^* 237_1_test_InvokeMethod(220_0_descend_Return, x0[3]))∧(x1[2] →^* x1[3])∧(x0[2] →^* x0[3]))

(3) -> (4), if ((250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]) →^* 250_1_test_InvokeMethod(220_0_descend_Return, x0[4]))∧(x1[3] →^* x1[4])∧(x0[3] →^* x0[4]))

(4) -> (5), if ((266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]) →^* 266_1_test_InvokeMethod(220_0_descend_Return, x0[5]))∧(x1[4] →^* x1[5])∧(x0[4] →^* x0[5]))

(5) -> (6), if ((282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]) →^* 282_1_test_InvokeMethod(220_0_descend_Return, x0[6]))∧(x1[5] →^* x1[6])∧(x0[5] →^* x0[6]))

(6) -> (7), if ((295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]) →^* 295_1_test_InvokeMethod(220_0_descend_Return, x0[7]))∧(x1[6] →^* x1[7])∧(x0[6] →^* x0[7]))

(7) -> (8), if ((309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]) →^* 309_1_test_InvokeMethod(220_0_descend_Return, x0[8]))∧(x1[7] →^* x1[8])∧(x0[7] →^* x0[8]))

(8) -> (9), if ((321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]) →^* 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]))∧(x1[8] →^* x1[9])∧(x0[8] →^* x0[9]))

(9) -> (10), if ((x0[9] > 0 →^* TRUE)∧(321_1_test_InvokeMethod(220_0_descend_Return, x0[9]) →^* 321_1_test_InvokeMethod(220_0_descend_Return, x0[10]))∧(x1[9] →^* x1[10])∧(x0[9] →^* x0[10]))

(10) -> (0), if ((x1[10] →^* x0[0])∧(x0[10] + 1 →^* x1[0]))

(10) -> (11), if ((x1[10] →^* x0[11])∧(x0[10] + 1 →^* x1[11]))

(11) -> (12), if ((x1[11] >= 100 && x0[11] > 0 && 1 > 0 && 0 < x0[11] - 1 →^* TRUE)∧(x0[11] →^* x0[12])∧(x1[11] →^* x1[12]))

(12) -> (0), if ((x0[12] - 1 →^* x0[0])∧(x0[12] - 1 →^* x1[0]))

(12) -> (11), if ((x0[12] - 1 →^* x0[11])∧(x0[12] - 1 →^* x1[11]))

The set Q consists of the following terms:
92_0_descend_Load(x0)
97_1_rec_InvokeMethod(47_0_rec_Return, 0)
97_1_rec_InvokeMethod(143_0_rec_Return, x0)
169_0_descend_LE(x0)
Cond_169_0_descend_LE(TRUE, x0)
191_1_descend_InvokeMethod(175_0_descend_Return, 0)
191_1_descend_InvokeMethod(220_0_descend_Return, x0)

(15) 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 69_0_REC_GE(x0, x1) → COND_69_0_REC_GE(<(x1, 100), x0, x1) the following chains were created:

We consider the chain 69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0]), COND_69_0_REC_GE(TRUE, x0[1], x1[1]) → 92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1]) which results in the following constraint:
(1)    (<(x1[0], 100)=TRUE∧x0[0]=x0[1]∧x1[0]=x1[1] ⇒ 69_0_REC_GE(x0[0], x1[0])≥NonInfC∧69_0_REC_GE(x0[0], x1[0])≥COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])∧(U^Increasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥))

We simplified constraint (1) using rule (IV) which results in the following new constraint:
(2)    (<(x1[0], 100)=TRUE ⇒ 69_0_REC_GE(x0[0], x1[0])≥NonInfC∧69_0_REC_GE(x0[0], x1[0])≥COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])∧(U^Increasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    ([99] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)bni_75 + (-1)Bound*bni_75] + [(2)bni_75]x0[0] ≥ 0∧[(-1)bso_76] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    ([99] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)bni_75 + (-1)Bound*bni_75] + [(2)bni_75]x0[0] ≥ 0∧[(-1)bso_76] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    ([99] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)bni_75 + (-1)Bound*bni_75] + [(2)bni_75]x0[0] ≥ 0∧[(-1)bso_76] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    ([99] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(2)bni_75] = 0∧[(-1)bni_75 + (-1)Bound*bni_75] ≥ 0∧0 = 0∧[(-1)bso_76] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(7)    ([99] + x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(2)bni_75] = 0∧[(-1)bni_75 + (-1)Bound*bni_75] ≥ 0∧0 = 0∧[(-1)bso_76] ≥ 0)

(8)    ([99] + [-1]x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(2)bni_75] = 0∧[(-1)bni_75 + (-1)Bound*bni_75] ≥ 0∧0 = 0∧[(-1)bso_76] ≥ 0)

For Pair COND_69_0_REC_GE(TRUE, x0, x1) → 92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1), x1), x0, x1) the following chains were created:

We consider the chain COND_69_0_REC_GE(TRUE, x0[1], x1[1]) → 92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1]) which results in the following constraint:
(9)    (COND_69_0_REC_GE(TRUE, x0[1], x1[1])≥NonInfC∧COND_69_0_REC_GE(TRUE, x0[1], x1[1])≥92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])∧(U^Increasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥))

We simplified constraint (9) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(10)    ((U^Increasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧[(-1)bso_78] ≥ 0)

We simplified constraint (10) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(11)    ((U^Increasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧[(-1)bso_78] ≥ 0)

We simplified constraint (11) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(12)    ((U^Increasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧[(-1)bso_78] ≥ 0)

We simplified constraint (12) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(13)    ((U^Increasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_78] ≥ 0)

For Pair 92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0) the following chains were created:

We consider the chain 92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(220_0_descend_Return, x0[2]), x1[2], x0[2]) → 237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2]) which results in the following constraint:
(14)    (92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(220_0_descend_Return, x0[2]), x1[2], x0[2])≥NonInfC∧92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(220_0_descend_Return, x0[2]), x1[2], x0[2])≥237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])∧(U^Increasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥))

We simplified constraint (14) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(15)    ((U^Increasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧[(-1)bso_80] ≥ 0)

We simplified constraint (15) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(16)    ((U^Increasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧[(-1)bso_80] ≥ 0)

We simplified constraint (16) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(17)    ((U^Increasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧[(-1)bso_80] ≥ 0)

We simplified constraint (17) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(18)    ((U^Increasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_80] ≥ 0)

For Pair 237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0) the following chains were created:

We consider the chain 237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(220_0_descend_Return, x0[3]), x1[3], x0[3]) → 250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3]) which results in the following constraint:
(19)    (237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(220_0_descend_Return, x0[3]), x1[3], x0[3])≥NonInfC∧237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(220_0_descend_Return, x0[3]), x1[3], x0[3])≥250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])∧(U^Increasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥))

We simplified constraint (19) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(20)    ((U^Increasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧[(-1)bso_82] ≥ 0)

We simplified constraint (20) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(21)    ((U^Increasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧[(-1)bso_82] ≥ 0)

We simplified constraint (21) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(22)    ((U^Increasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧[(-1)bso_82] ≥ 0)

We simplified constraint (22) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(23)    ((U^Increasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_82] ≥ 0)

For Pair 250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0) the following chains were created:

We consider the chain 250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(220_0_descend_Return, x0[4]), x1[4], x0[4]) → 266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4]) which results in the following constraint:
(24)    (250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(220_0_descend_Return, x0[4]), x1[4], x0[4])≥NonInfC∧250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(220_0_descend_Return, x0[4]), x1[4], x0[4])≥266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])∧(U^Increasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥))

We simplified constraint (24) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(25)    ((U^Increasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧[(-1)bso_84] ≥ 0)

We simplified constraint (25) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(26)    ((U^Increasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧[(-1)bso_84] ≥ 0)

We simplified constraint (26) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(27)    ((U^Increasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧[(-1)bso_84] ≥ 0)

We simplified constraint (27) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(28)    ((U^Increasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_84] ≥ 0)

For Pair 266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0) the following chains were created:

We consider the chain 266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(220_0_descend_Return, x0[5]), x1[5], x0[5]) → 282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5]) which results in the following constraint:
(29)    (266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(220_0_descend_Return, x0[5]), x1[5], x0[5])≥NonInfC∧266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(220_0_descend_Return, x0[5]), x1[5], x0[5])≥282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])∧(U^Increasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥))

We simplified constraint (29) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(30)    ((U^Increasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧[(-1)bso_86] ≥ 0)

We simplified constraint (30) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(31)    ((U^Increasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧[(-1)bso_86] ≥ 0)

We simplified constraint (31) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(32)    ((U^Increasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧[(-1)bso_86] ≥ 0)

We simplified constraint (32) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(33)    ((U^Increasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_86] ≥ 0)

For Pair 282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0) the following chains were created:

We consider the chain 282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(220_0_descend_Return, x0[6]), x1[6], x0[6]) → 295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6]) which results in the following constraint:
(34)    (282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(220_0_descend_Return, x0[6]), x1[6], x0[6])≥NonInfC∧282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(220_0_descend_Return, x0[6]), x1[6], x0[6])≥295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])∧(U^Increasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥))

We simplified constraint (34) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(35)    ((U^Increasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧[(-1)bso_88] ≥ 0)

We simplified constraint (35) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(36)    ((U^Increasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧[(-1)bso_88] ≥ 0)

We simplified constraint (36) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(37)    ((U^Increasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧[(-1)bso_88] ≥ 0)

We simplified constraint (37) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(38)    ((U^Increasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_88] ≥ 0)

For Pair 295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0) the following chains were created:

We consider the chain 295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(220_0_descend_Return, x0[7]), x1[7], x0[7]) → 309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7]) which results in the following constraint:
(39)    (295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(220_0_descend_Return, x0[7]), x1[7], x0[7])≥NonInfC∧295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(220_0_descend_Return, x0[7]), x1[7], x0[7])≥309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])∧(U^Increasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥))

We simplified constraint (39) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(40)    ((U^Increasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧[(-1)bso_90] ≥ 0)

We simplified constraint (40) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(41)    ((U^Increasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧[(-1)bso_90] ≥ 0)

We simplified constraint (41) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(42)    ((U^Increasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧[(-1)bso_90] ≥ 0)

We simplified constraint (42) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(43)    ((U^Increasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_90] ≥ 0)

For Pair 309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0) the following chains were created:

We consider the chain 309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(220_0_descend_Return, x0[8]), x1[8], x0[8]) → 321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8]) which results in the following constraint:
(44)    (309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(220_0_descend_Return, x0[8]), x1[8], x0[8])≥NonInfC∧309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(220_0_descend_Return, x0[8]), x1[8], x0[8])≥321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])∧(U^Increasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥))

We simplified constraint (44) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(45)    ((U^Increasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧[(-1)bso_92] ≥ 0)

We simplified constraint (45) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(46)    ((U^Increasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧[(-1)bso_92] ≥ 0)

We simplified constraint (46) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(47)    ((U^Increasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧[(-1)bso_92] ≥ 0)

We simplified constraint (47) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(48)    ((U^Increasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_92] ≥ 0)

For Pair 321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → COND_321_2_REC_INVOKEMETHOD(>(x0, 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) the following chains were created:

We consider the chain 321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9]) → COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9]), COND_321_2_REC_INVOKEMETHOD(TRUE, 321_1_test_InvokeMethod(220_0_descend_Return, x0[10]), x1[10], x0[10]) → 69_0_REC_GE(x1[10], +(x0[10], 1)) which results in the following constraint:
(49)    (>(x0[9], 0)=TRUE∧321_1_test_InvokeMethod(220_0_descend_Return, x0[9])=321_1_test_InvokeMethod(220_0_descend_Return, x0[10])∧x1[9]=x1[10]∧x0[9]=x0[10] ⇒ 321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])≥NonInfC∧321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])≥COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])∧(U^Increasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥))

We simplified constraint (49) using rules (I), (II), (IV), (DELETE_TRIVIAL_REDUCESTO) which results in the following new constraint:
(50)    (>(x0[9], 0)=TRUE ⇒ 321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])≥NonInfC∧321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])≥COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])∧(U^Increasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥))

We simplified constraint (50) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(51)    (x0[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-1)bni_93 + (-1)Bound*bni_93] + [(2)bni_93]x1[9] ≥ 0∧[(-1)bso_94] ≥ 0)

We simplified constraint (51) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(52)    (x0[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-1)bni_93 + (-1)Bound*bni_93] + [(2)bni_93]x1[9] ≥ 0∧[(-1)bso_94] ≥ 0)

We simplified constraint (52) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(53)    (x0[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-1)bni_93 + (-1)Bound*bni_93] + [(2)bni_93]x1[9] ≥ 0∧[(-1)bso_94] ≥ 0)

We simplified constraint (53) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(54)    (x0[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(2)bni_93] = 0∧[(-1)bni_93 + (-1)Bound*bni_93] ≥ 0∧0 = 0∧[(-1)bso_94] ≥ 0)

We simplified constraint (54) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(55)    (x0[9] ≥ 0 ⇒ (U^Increasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(2)bni_93] = 0∧[(-1)bni_93 + (-1)Bound*bni_93] ≥ 0∧0 = 0∧[(-1)bso_94] ≥ 0)

For Pair COND_321_2_REC_INVOKEMETHOD(TRUE, 321_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 69_0_REC_GE(x1, +(x0, 1)) the following chains were created:

We consider the chain COND_321_2_REC_INVOKEMETHOD(TRUE, 321_1_test_InvokeMethod(220_0_descend_Return, x0[10]), x1[10], x0[10]) → 69_0_REC_GE(x1[10], +(x0[10], 1)) which results in the following constraint:
(56)    (COND_321_2_REC_INVOKEMETHOD(TRUE, 321_1_test_InvokeMethod(220_0_descend_Return, x0[10]), x1[10], x0[10])≥NonInfC∧COND_321_2_REC_INVOKEMETHOD(TRUE, 321_1_test_InvokeMethod(220_0_descend_Return, x0[10]), x1[10], x0[10])≥69_0_REC_GE(x1[10], +(x0[10], 1))∧(U^Increasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥))

We simplified constraint (56) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(57)    ((U^Increasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧[(-1)bso_96] ≥ 0)

We simplified constraint (57) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(58)    ((U^Increasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧[(-1)bso_96] ≥ 0)

We simplified constraint (58) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(59)    ((U^Increasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧[(-1)bso_96] ≥ 0)

We simplified constraint (59) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(60)    ((U^Increasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_96] ≥ 0)

For Pair 69_0_REC_GE(x0, x1) → COND_69_0_REC_GE1(&&(&&(&&(>=(x1, 100), >(x0, 0)), >(1, 0)), <(0, -(x0, 1))), x0, x1) the following chains were created:

We consider the chain 69_0_REC_GE(x0[11], x1[11]) → COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11]), COND_69_0_REC_GE1(TRUE, x0[12], x1[12]) → 69_0_REC_GE(-(x0[12], 1), -(x0[12], 1)) which results in the following constraint:
(61)    (&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1)))=TRUE∧x0[11]=x0[12]∧x1[11]=x1[12] ⇒ 69_0_REC_GE(x0[11], x1[11])≥NonInfC∧69_0_REC_GE(x0[11], x1[11])≥COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11])∧(U^Increasing(COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11])), ≥))

We simplified constraint (61) using rules (IV), (IDP_CONSTANT_FOLD), (DELETE_TRIVIAL_REDUCESTO), (IDP_BOOLEAN) which results in the following new constraint:
(62)    (<(0, -(x0[11], 1))=TRUE∧>=(x1[11], 100)=TRUE∧>(x0[11], 0)=TRUE ⇒ 69_0_REC_GE(x0[11], x1[11])≥NonInfC∧69_0_REC_GE(x0[11], x1[11])≥COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11])∧(U^Increasing(COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11])), ≥))

We simplified constraint (62) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(63)    (x0[11] + [-2] ≥ 0∧x1[11] + [-100] ≥ 0∧x0[11] + [-1] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11])), ≥)∧[(-1)bni_97 + (-1)Bound*bni_97] + [(2)bni_97]x0[11] ≥ 0∧[(-1)bso_98] ≥ 0)

We simplified constraint (63) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(64)    (x0[11] + [-2] ≥ 0∧x1[11] + [-100] ≥ 0∧x0[11] + [-1] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11])), ≥)∧[(-1)bni_97 + (-1)Bound*bni_97] + [(2)bni_97]x0[11] ≥ 0∧[(-1)bso_98] ≥ 0)

We simplified constraint (64) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(65)    (x0[11] + [-2] ≥ 0∧x1[11] + [-100] ≥ 0∧x0[11] + [-1] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11])), ≥)∧[(-1)bni_97 + (-1)Bound*bni_97] + [(2)bni_97]x0[11] ≥ 0∧[(-1)bso_98] ≥ 0)

We simplified constraint (65) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(66)    (x0[11] ≥ 0∧x1[11] + [-100] ≥ 0∧[1] + x0[11] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11])), ≥)∧[(3)bni_97 + (-1)Bound*bni_97] + [(2)bni_97]x0[11] ≥ 0∧[(-1)bso_98] ≥ 0)

We simplified constraint (66) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(67)    (x0[11] ≥ 0∧x1[11] ≥ 0∧[1] + x0[11] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11])), ≥)∧[(3)bni_97 + (-1)Bound*bni_97] + [(2)bni_97]x0[11] ≥ 0∧[(-1)bso_98] ≥ 0)

For Pair COND_69_0_REC_GE1(TRUE, x0, x1) → 69_0_REC_GE(-(x0, 1), -(x0, 1)) the following chains were created:

We consider the chain COND_69_0_REC_GE1(TRUE, x0[12], x1[12]) → 69_0_REC_GE(-(x0[12], 1), -(x0[12], 1)) which results in the following constraint:
(68)    (COND_69_0_REC_GE1(TRUE, x0[12], x1[12])≥NonInfC∧COND_69_0_REC_GE1(TRUE, x0[12], x1[12])≥69_0_REC_GE(-(x0[12], 1), -(x0[12], 1))∧(U^Increasing(69_0_REC_GE(-(x0[12], 1), -(x0[12], 1))), ≥))

We simplified constraint (68) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(69)    ((U^Increasing(69_0_REC_GE(-(x0[12], 1), -(x0[12], 1))), ≥)∧[2 + (-1)bso_100] ≥ 0)

We simplified constraint (69) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(70)    ((U^Increasing(69_0_REC_GE(-(x0[12], 1), -(x0[12], 1))), ≥)∧[2 + (-1)bso_100] ≥ 0)

We simplified constraint (70) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(71)    ((U^Increasing(69_0_REC_GE(-(x0[12], 1), -(x0[12], 1))), ≥)∧[2 + (-1)bso_100] ≥ 0)

We simplified constraint (71) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(72)    ((U^Increasing(69_0_REC_GE(-(x0[12], 1), -(x0[12], 1))), ≥)∧0 = 0∧0 = 0∧[2 + (-1)bso_100] ≥ 0)

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

69_0_REC_GE(x0, x1) → COND_69_0_REC_GE(<(x1, 100), x0, x1)
- ([99] + x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(2)bni_75] = 0∧[(-1)bni_75 + (-1)Bound*bni_75] ≥ 0∧0 = 0∧[(-1)bso_76] ≥ 0)
- ([99] + [-1]x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(2)bni_75] = 0∧[(-1)bni_75 + (-1)Bound*bni_75] ≥ 0∧0 = 0∧[(-1)bso_76] ≥ 0)
COND_69_0_REC_GE(TRUE, x0, x1) → 92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1), x1), x0, x1)
- ((U^Increasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_78] ≥ 0)
92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0)
- ((U^Increasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_80] ≥ 0)
237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0)
- ((U^Increasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_82] ≥ 0)
250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0)
- ((U^Increasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_84] ≥ 0)
266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0)
- ((U^Increasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_86] ≥ 0)
282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0)
- ((U^Increasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_88] ≥ 0)
295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0)
- ((U^Increasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_90] ≥ 0)
309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0), x0), x1, x0)
- ((U^Increasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧0 = 0∧0 = 0∧[(-1)bso_92] ≥ 0)
321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → COND_321_2_REC_INVOKEMETHOD(>(x0, 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0)
- (x0[9] ≥ 0 ⇒ (U^Increasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(2)bni_93] = 0∧[(-1)bni_93 + (-1)Bound*bni_93] ≥ 0∧0 = 0∧[(-1)bso_94] ≥ 0)
COND_321_2_REC_INVOKEMETHOD(TRUE, 321_1_test_InvokeMethod(220_0_descend_Return, x0), x1, x0) → 69_0_REC_GE(x1, +(x0, 1))
- ((U^Increasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧0 = 0∧0 = 0∧[(-1)bso_96] ≥ 0)
69_0_REC_GE(x0, x1) → COND_69_0_REC_GE1(&&(&&(&&(>=(x1, 100), >(x0, 0)), >(1, 0)), <(0, -(x0, 1))), x0, x1)
- (x0[11] ≥ 0∧x1[11] ≥ 0∧[1] + x0[11] ≥ 0 ⇒ (U^Increasing(COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11])), ≥)∧[(3)bni_97 + (-1)Bound*bni_97] + [(2)bni_97]x0[11] ≥ 0∧[(-1)bso_98] ≥ 0)
COND_69_0_REC_GE1(TRUE, x0, x1) → 69_0_REC_GE(-(x0, 1), -(x0, 1))
- ((U^Increasing(69_0_REC_GE(-(x0[12], 1), -(x0[12], 1))), ≥)∧0 = 0∧0 = 0∧[2 + (-1)bso_100] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(92_0_descend_Load(x₁)) = [-1]
POL(181_0_descend_Return) = [-1]
POL(243_0_descend_Return) = [-1]
POL(256_0_descend_Return) = [-1]
POL(273_0_descend_Return) = [-1]
POL(287_0_descend_Return) = [-1]
POL(300_0_descend_Return) = [-1]
POL(314_0_descend_Return) = [-1]
POL(327_0_descend_Return) = [-1]
POL(169_0_descend_LE(x₁)) = [-1]
POL(97_1_rec_InvokeMethod(x₁, x₂)) = [-1]
POL(47_0_rec_Return) = [-1]
POL(0) = 0
POL(143_0_rec_Return) = [-1]
POL(175_0_descend_Return) = [-1]
POL(Cond_169_0_descend_LE(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(191_1_descend_InvokeMethod(x₁, x₂)) = [-1]
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(1) = [1]
POL(220_0_descend_Return) = [-1]
POL(69_0_REC_GE(x₁, x₂)) = [-1] + [2]x₁
POL(COND_69_0_REC_GE(x₁, x₂, x₃)) = [-1] + [2]x₂
POL(<(x₁, x₂)) = [-1]
POL(100) = [100]
POL(92_2_REC_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [-1]x₁ + [2]x₂
POL(92_1_test_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₁
POL(237_2_REC_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [-1]x₁ + [2]x₂
POL(237_1_test_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₁
POL(250_2_REC_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [-1]x₁ + [2]x₂
POL(250_1_test_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₁
POL(266_2_REC_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [2]x₂
POL(266_1_test_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(282_2_REC_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [-1]x₁ + [2]x₂
POL(282_1_test_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₁
POL(295_2_REC_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [2]x₂
POL(295_1_test_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(309_2_REC_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + [-1]x₁ + [2]x₂
POL(309_1_test_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₁
POL(321_2_REC_INVOKEMETHOD(x₁, x₂, x₃)) = [-1] + x₁ + [2]x₂
POL(321_1_test_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₁
POL(COND_321_2_REC_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + [2]x₃ + x₂
POL(+(x₁, x₂)) = x₁ + x₂
POL(COND_69_0_REC_GE1(x₁, x₂, x₃)) = [-1] + [2]x₂
POL(&&(x₁, x₂)) = [-1]
POL(>=(x₁, x₂)) = [-1]

The following pairs are in P_>:

COND_69_0_REC_GE1(TRUE, x0[12], x1[12]) → 69_0_REC_GE(-(x0[12], 1), -(x0[12], 1))

The following pairs are in P_bound:

69_0_REC_GE(x0[11], x1[11]) → COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11])

The following pairs are in P_≥:

69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])
COND_69_0_REC_GE(TRUE, x0[1], x1[1]) → 92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])
92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(220_0_descend_Return, x0[2]), x1[2], x0[2]) → 237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])
237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(220_0_descend_Return, x0[3]), x1[3], x0[3]) → 250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])
250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(220_0_descend_Return, x0[4]), x1[4], x0[4]) → 266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])
266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(220_0_descend_Return, x0[5]), x1[5], x0[5]) → 282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])
282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(220_0_descend_Return, x0[6]), x1[6], x0[6]) → 295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])
295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(220_0_descend_Return, x0[7]), x1[7], x0[7]) → 309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])
309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(220_0_descend_Return, x0[8]), x1[8], x0[8]) → 321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])
321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9]) → COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])
COND_321_2_REC_INVOKEMETHOD(TRUE, 321_1_test_InvokeMethod(220_0_descend_Return, x0[10]), x1[10], x0[10]) → 69_0_REC_GE(x1[10], +(x0[10], 1))
69_0_REC_GE(x0[11], x1[11]) → COND_69_0_REC_GE1(&&(&&(&&(>=(x1[11], 100), >(x0[11], 0)), >(1, 0)), <(0, -(x0[11], 1))), x0[11], x1[11])

At least the following rules have been oriented under context sensitive arithmetic replacement:

92_0_descend_Load(i12)¹ ↔ 181_0_descend_Return¹
92_0_descend_Load(i45)¹ ↔ 243_0_descend_Return¹
92_0_descend_Load(i59)¹ ↔ 256_0_descend_Return¹
92_0_descend_Load(i62)¹ ↔ 273_0_descend_Return¹
92_0_descend_Load(i67)¹ ↔ 287_0_descend_Return¹
92_0_descend_Load(i70)¹ ↔ 300_0_descend_Return¹
92_0_descend_Load(i74)¹ ↔ 314_0_descend_Return¹
92_0_descend_Load(i76)¹ ↔ 327_0_descend_Return¹
92_0_descend_Load(x0)¹ ↔ 169_0_descend_LE(x0)¹
169_0_descend_LE(0)¹ ↔ 175_0_descend_Return¹
169_0_descend_LE(x0)¹ ↔ Cond_169_0_descend_LE(>(x0, 0), x0)¹
Cond_169_0_descend_LE(TRUE, x0)¹ ↔ 191_1_descend_InvokeMethod(169_0_descend_LE(-(x0, 1)), -(x0, 1))¹
191_1_descend_InvokeMethod(175_0_descend_Return, 0)¹ ↔ 220_0_descend_Return¹
191_1_descend_InvokeMethod(220_0_descend_Return, x0)¹ ↔ 220_0_descend_Return¹

(16) Complex Obligation (AND)

(17) 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