(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)=TRUEx0[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])∧(UIncreasing(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)=TRUE169_0_DESCEND_LE(x0[0])≥NonInfC∧169_0_DESCEND_LE(x0[0])≥COND_169_0_DESCEND_LE(>(x0[0], 0), x0[0])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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))∧(UIncreasing(169_0_DESCEND_LE(-(x0[1], 1))), ≥))



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

    (8)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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 ⇒ (UIncreasing(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))
    • ((UIncreasing(169_0_DESCEND_LE(-(x0[1], 1))), ≥)∧0 = 0∧[2 + (-1)bso_15] ≥ 0)




The constraints for P> respective Pbound 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 Pbound.
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 Pbound:

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)=TRUEx0[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])∧(UIncreasing(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)=TRUE69_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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])∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)=TRUE321_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])∧(UIncreasing(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)=TRUE321_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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))∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)))=TRUEx0[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])∧(UIncreasing(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)=TRUE69_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])∧(UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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))∧(UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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)    ((UIncreasing(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 ⇒ (UIncreasing(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 ⇒ (UIncreasing(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)
    • ((UIncreasing(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)
    • ((UIncreasing(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)
    • ((UIncreasing(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)
    • ((UIncreasing(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)
    • ((UIncreasing(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)
    • ((UIncreasing(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)
    • ((UIncreasing(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)
    • ((UIncreasing(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 ⇒ (UIncreasing(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))
    • ((UIncreasing(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 ⇒ (UIncreasing(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))
    • ((UIncreasing(69_0_REC_GE(-(x0[12], 1), -(x0[12], 1))), ≥)∧0 = 0∧0 = 0∧[2 + (-1)bso_100] ≥ 0)




The constraints for P> respective Pbound 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 Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

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 Pbound:

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)1181_0_descend_Return1
92_0_descend_Load(i45)1243_0_descend_Return1
92_0_descend_Load(i59)1256_0_descend_Return1
92_0_descend_Load(i62)1273_0_descend_Return1
92_0_descend_Load(i67)1287_0_descend_Return1
92_0_descend_Load(i70)1300_0_descend_Return1
92_0_descend_Load(i74)1314_0_descend_Return1
92_0_descend_Load(i76)1327_0_descend_Return1
92_0_descend_Load(x0)1169_0_descend_LE(x0)1
169_0_descend_LE(0)1175_0_descend_Return1
169_0_descend_LE(x0)1Cond_169_0_descend_LE(>(x0, 0), x0)1
Cond_169_0_descend_LE(TRUE, x0)1191_1_descend_InvokeMethod(169_0_descend_LE(-(x0, 1)), -(x0, 1))1
191_1_descend_InvokeMethod(175_0_descend_Return, 0)1220_0_descend_Return1
191_1_descend_InvokeMethod(220_0_descend_Return, x0)1220_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


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])

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


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

(18) IDependencyGraphProof (EQUIVALENT transformation)

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

(19) 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:
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:
(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)
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(0): 69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(x1[0] < 100, x0[0], x1[0])

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


(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]))



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)

(20) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(21) 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:
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)
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:
(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)
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(0): 69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(x1[0] < 100, x0[0], x1[0])

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


(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]))



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)

(22) 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 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)) 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:

    (1)    (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))∧(UIncreasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥))



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

    (2)    ((UIncreasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧[(-1)bso_40] ≥ 0)



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

    (3)    ((UIncreasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧[(-1)bso_40] ≥ 0)



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

    (4)    ((UIncreasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧[(-1)bso_40] ≥ 0)



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

    (5)    ((UIncreasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧0 = 0∧[(-1)bso_40] ≥ 0)







For Pair 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]) 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:

    (6)    (>(x0[9], 0)=TRUE321_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])∧(UIncreasing(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 (6) using rules (I), (II), (IV), (DELETE_TRIVIAL_REDUCESTO) which results in the following new constraint:

    (7)    (>(x0[9], 0)=TRUE321_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])∧(UIncreasing(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 (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (8)    (x0[9] + [-1] ≥ 0 ⇒ (UIncreasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]x0[9] ≥ 0∧[(-1)bso_42] ≥ 0)



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

    (9)    (x0[9] + [-1] ≥ 0 ⇒ (UIncreasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]x0[9] ≥ 0∧[(-1)bso_42] ≥ 0)



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

    (10)    (x0[9] + [-1] ≥ 0 ⇒ (UIncreasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]x0[9] ≥ 0∧[(-1)bso_42] ≥ 0)



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

    (11)    (x0[9] ≥ 0 ⇒ (UIncreasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-2)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]x0[9] ≥ 0∧[(-1)bso_42] ≥ 0)







For Pair 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]) 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:

    (12)    (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])∧(UIncreasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥))



    We simplified constraint (12) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (13)    ((UIncreasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧[(-1)bso_44] ≥ 0)



    We simplified constraint (13) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (14)    ((UIncreasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧[(-1)bso_44] ≥ 0)



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

    (15)    ((UIncreasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧[(-1)bso_44] ≥ 0)



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

    (16)    ((UIncreasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧0 = 0∧[(-1)bso_44] ≥ 0)







For Pair 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]) 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:

    (17)    (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])∧(UIncreasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥))



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

    (18)    ((UIncreasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧[(-1)bso_46] ≥ 0)



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

    (19)    ((UIncreasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧[(-1)bso_46] ≥ 0)



    We simplified constraint (19) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (20)    ((UIncreasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧[(-1)bso_46] ≥ 0)



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

    (21)    ((UIncreasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧0 = 0∧[(-1)bso_46] ≥ 0)







For Pair 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]) 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:

    (22)    (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])∧(UIncreasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥))



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

    (23)    ((UIncreasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧[(-1)bso_48] ≥ 0)



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

    (24)    ((UIncreasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧[(-1)bso_48] ≥ 0)



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

    (25)    ((UIncreasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧[(-1)bso_48] ≥ 0)



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

    (26)    ((UIncreasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧0 = 0∧[(-1)bso_48] ≥ 0)







For Pair 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]) 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:

    (27)    (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])∧(UIncreasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥))



    We simplified constraint (27) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (28)    ((UIncreasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧[(-1)bso_50] ≥ 0)



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

    (29)    ((UIncreasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧[(-1)bso_50] ≥ 0)



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

    (30)    ((UIncreasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧[(-1)bso_50] ≥ 0)



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

    (31)    ((UIncreasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧0 = 0∧[(-1)bso_50] ≥ 0)







For Pair 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]) 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:

    (32)    (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])∧(UIncreasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥))



    We simplified constraint (32) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (33)    ((UIncreasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧[(-1)bso_52] ≥ 0)



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

    (34)    ((UIncreasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧[(-1)bso_52] ≥ 0)



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

    (35)    ((UIncreasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧[(-1)bso_52] ≥ 0)



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

    (36)    ((UIncreasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧0 = 0∧[(-1)bso_52] ≥ 0)







For Pair 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]) 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:

    (37)    (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])∧(UIncreasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥))



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

    (38)    ((UIncreasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧[(-1)bso_54] ≥ 0)



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

    (39)    ((UIncreasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧[(-1)bso_54] ≥ 0)



    We simplified constraint (39) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (40)    ((UIncreasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧[(-1)bso_54] ≥ 0)



    We simplified constraint (40) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (41)    ((UIncreasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧0 = 0∧[(-1)bso_54] ≥ 0)







For Pair 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]) 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:

    (42)    (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])∧(UIncreasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥))



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

    (43)    ((UIncreasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧[(-1)bso_56] ≥ 0)



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

    (44)    ((UIncreasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧[(-1)bso_56] ≥ 0)



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

    (45)    ((UIncreasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧[(-1)bso_56] ≥ 0)



    We simplified constraint (45) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (46)    ((UIncreasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧0 = 0∧[(-1)bso_56] ≥ 0)







For Pair 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]) 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:

    (47)    (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])∧(UIncreasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥))



    We simplified constraint (47) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (48)    ((UIncreasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧[(-1)bso_58] ≥ 0)



    We simplified constraint (48) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (49)    ((UIncreasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧[(-1)bso_58] ≥ 0)



    We simplified constraint (49) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (50)    ((UIncreasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧[(-1)bso_58] ≥ 0)



    We simplified constraint (50) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (51)    ((UIncreasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧0 = 0∧[(-1)bso_58] ≥ 0)







For Pair 69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0]) 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:

    (52)    (<(x1[0], 100)=TRUEx0[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])∧(UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥))



    We simplified constraint (52) using rule (IV) which results in the following new constraint:

    (53)    (<(x1[0], 100)=TRUE69_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])∧(UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥))



    We simplified constraint (53) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (54)    ([99] + [-1]x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_59] + [(-1)bni_59]x1[0] ≥ 0∧[1 + (-1)bso_60] ≥ 0)



    We simplified constraint (54) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (55)    ([99] + [-1]x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_59] + [(-1)bni_59]x1[0] ≥ 0∧[1 + (-1)bso_60] ≥ 0)



    We simplified constraint (55) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (56)    ([99] + [-1]x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_59] + [(-1)bni_59]x1[0] ≥ 0∧[1 + (-1)bso_60] ≥ 0)



    We simplified constraint (56) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (57)    ([99] + [-1]x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_59] + [(-1)bni_59]x1[0] ≥ 0∧[1 + (-1)bso_60] ≥ 0)


    (58)    ([99] + x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_59] + [bni_59]x1[0] ≥ 0∧[1 + (-1)bso_60] ≥ 0)







To summarize, we get the following constraints P for the following pairs.
  • 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))
    • ((UIncreasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧0 = 0∧[(-1)bso_40] ≥ 0)

  • 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])
    • (x0[9] ≥ 0 ⇒ (UIncreasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-2)bni_41 + (-1)Bound*bni_41] + [(-1)bni_41]x0[9] ≥ 0∧[(-1)bso_42] ≥ 0)

  • 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])
    • ((UIncreasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧0 = 0∧[(-1)bso_44] ≥ 0)

  • 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])
    • ((UIncreasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧0 = 0∧[(-1)bso_46] ≥ 0)

  • 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])
    • ((UIncreasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧0 = 0∧[(-1)bso_48] ≥ 0)

  • 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])
    • ((UIncreasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧0 = 0∧[(-1)bso_50] ≥ 0)

  • 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])
    • ((UIncreasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧0 = 0∧[(-1)bso_52] ≥ 0)

  • 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])
    • ((UIncreasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧0 = 0∧[(-1)bso_54] ≥ 0)

  • 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])
    • ((UIncreasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧0 = 0∧[(-1)bso_56] ≥ 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])
    • ((UIncreasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧0 = 0∧[(-1)bso_58] ≥ 0)

  • 69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])
    • ([99] + [-1]x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_59] + [(-1)bni_59]x1[0] ≥ 0∧[1 + (-1)bso_60] ≥ 0)
    • ([99] + x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_59] + [bni_59]x1[0] ≥ 0∧[1 + (-1)bso_60] ≥ 0)




The constraints for P> respective Pbound 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 Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(92_0_descend_Load(x1)) = [-1] + [-1]x1   
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) = 0   
POL(300_0_descend_Return) = 0   
POL(314_0_descend_Return) = [1]   
POL(327_0_descend_Return) = [2]   
POL(169_0_descend_LE(x1)) = [2]   
POL(0) = 0   
POL(175_0_descend_Return) = [1]   
POL(Cond_169_0_descend_LE(x1, x2)) = [-1]x2   
POL(>(x1, x2)) = [-1]   
POL(191_1_descend_InvokeMethod(x1, x2)) = [-1] + [-1]x2 + [-1]x1   
POL(-(x1, x2)) = x1 + [-1]x2   
POL(1) = [1]   
POL(220_0_descend_Return) = [-1]   
POL(COND_321_2_REC_INVOKEMETHOD(x1, x2, x3, x4)) = [-1] + [-1]x4   
POL(321_1_test_InvokeMethod(x1, x2)) = [-1] + [-1]x2 + [-1]x1   
POL(69_0_REC_GE(x1, x2)) = [-1]x2   
POL(+(x1, x2)) = x1 + x2   
POL(321_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(309_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(309_1_test_InvokeMethod(x1, x2)) = [-1] + [-1]x2 + [-1]x1   
POL(295_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(295_1_test_InvokeMethod(x1, x2)) = [-1] + [-1]x1   
POL(282_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(282_1_test_InvokeMethod(x1, x2)) = [-1] + [-1]x2 + [-1]x1   
POL(266_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(266_1_test_InvokeMethod(x1, x2)) = [-1] + [2]x2 + [-1]x1   
POL(250_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(250_1_test_InvokeMethod(x1, x2)) = [-1] + [-1]x2 + [-1]x1   
POL(237_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x1 + [-1]x3   
POL(237_1_test_InvokeMethod(x1, x2)) = 0   
POL(92_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1]x1 + [-1]x3   
POL(92_1_test_InvokeMethod(x1, x2)) = [1]   
POL(COND_69_0_REC_GE(x1, x2, x3)) = [-1] + [-1]x3   
POL(<(x1, x2)) = [-1]   
POL(100) = [100]   

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])

The following pairs are in Pbound:

69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])

The following pairs are in P:

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))
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])
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])
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])
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])
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])
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])
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])
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])
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])

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

169_0_descend_LE(0)1175_0_descend_Return1
220_0_descend_Return1191_1_descend_InvokeMethod(175_0_descend_Return, 0)1

(23) 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:
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)
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:
(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)
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])

(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]))



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)

(24) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 10 less nodes.

(25) TRUE

(26) 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:
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)
(12): COND_69_0_REC_GE1(TRUE, x0[12], x1[12]) → 69_0_REC_GE(x0[12] - 1, x0[12] - 1)

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


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


(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]))



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)

(27) IDependencyGraphProof (EQUIVALENT transformation)

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

(28) 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:
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:
(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)
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(0): 69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(x1[0] < 100, x0[0], x1[0])

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


(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]))



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)

(29) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(30) 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:
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)
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:
(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)
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(0): 69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(x1[0] < 100, x0[0], x1[0])

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


(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]))



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)

(31) 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 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)) 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:

    (1)    (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))∧(UIncreasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥))



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

    (2)    ((UIncreasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧[(-1)bso_39] ≥ 0)



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

    (3)    ((UIncreasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧[(-1)bso_39] ≥ 0)



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

    (4)    ((UIncreasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧[(-1)bso_39] ≥ 0)



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

    (5)    ((UIncreasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧0 = 0∧[(-1)bso_39] ≥ 0)







For Pair 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]) 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:

    (6)    (>(x0[9], 0)=TRUE321_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])∧(UIncreasing(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 (6) using rules (I), (II), (IV), (DELETE_TRIVIAL_REDUCESTO) which results in the following new constraint:

    (7)    (>(x0[9], 0)=TRUE321_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])∧(UIncreasing(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 (7) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (8)    (x0[9] + [-1] ≥ 0 ⇒ (UIncreasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]x0[9] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (9)    (x0[9] + [-1] ≥ 0 ⇒ (UIncreasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]x0[9] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (10)    (x0[9] + [-1] ≥ 0 ⇒ (UIncreasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-1)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]x0[9] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (11)    (x0[9] ≥ 0 ⇒ (UIncreasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-2)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]x0[9] ≥ 0∧[(-1)bso_41] ≥ 0)







For Pair 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]) 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:

    (12)    (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])∧(UIncreasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥))



    We simplified constraint (12) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (13)    ((UIncreasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧[(-1)bso_43] ≥ 0)



    We simplified constraint (13) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (14)    ((UIncreasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧[(-1)bso_43] ≥ 0)



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

    (15)    ((UIncreasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧[(-1)bso_43] ≥ 0)



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

    (16)    ((UIncreasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧0 = 0∧[(-1)bso_43] ≥ 0)







For Pair 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]) 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:

    (17)    (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])∧(UIncreasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥))



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

    (18)    ((UIncreasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧[(-1)bso_45] ≥ 0)



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

    (19)    ((UIncreasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧[(-1)bso_45] ≥ 0)



    We simplified constraint (19) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (20)    ((UIncreasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧[(-1)bso_45] ≥ 0)



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

    (21)    ((UIncreasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧0 = 0∧[(-1)bso_45] ≥ 0)







For Pair 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]) 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:

    (22)    (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])∧(UIncreasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥))



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

    (23)    ((UIncreasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧[(-1)bso_47] ≥ 0)



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

    (24)    ((UIncreasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧[(-1)bso_47] ≥ 0)



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

    (25)    ((UIncreasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧[(-1)bso_47] ≥ 0)



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

    (26)    ((UIncreasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧0 = 0∧[(-1)bso_47] ≥ 0)







For Pair 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]) 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:

    (27)    (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])∧(UIncreasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥))



    We simplified constraint (27) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (28)    ((UIncreasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧[(-1)bso_49] ≥ 0)



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

    (29)    ((UIncreasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧[(-1)bso_49] ≥ 0)



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

    (30)    ((UIncreasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧[(-1)bso_49] ≥ 0)



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

    (31)    ((UIncreasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧0 = 0∧[(-1)bso_49] ≥ 0)







For Pair 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]) 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:

    (32)    (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])∧(UIncreasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥))



    We simplified constraint (32) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (33)    ((UIncreasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧[(-1)bso_51] ≥ 0)



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

    (34)    ((UIncreasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧[(-1)bso_51] ≥ 0)



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

    (35)    ((UIncreasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧[(-1)bso_51] ≥ 0)



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

    (36)    ((UIncreasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧0 = 0∧[(-1)bso_51] ≥ 0)







For Pair 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]) 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:

    (37)    (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])∧(UIncreasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥))



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

    (38)    ((UIncreasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧[(-1)bso_53] ≥ 0)



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

    (39)    ((UIncreasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧[(-1)bso_53] ≥ 0)



    We simplified constraint (39) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (40)    ((UIncreasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧[(-1)bso_53] ≥ 0)



    We simplified constraint (40) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (41)    ((UIncreasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧0 = 0∧[(-1)bso_53] ≥ 0)







For Pair 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]) 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:

    (42)    (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])∧(UIncreasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥))



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

    (43)    ((UIncreasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧[1 + (-1)bso_55] ≥ 0)



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

    (44)    ((UIncreasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧[1 + (-1)bso_55] ≥ 0)



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

    (45)    ((UIncreasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧[1 + (-1)bso_55] ≥ 0)



    We simplified constraint (45) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (46)    ((UIncreasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧0 = 0∧[1 + (-1)bso_55] ≥ 0)







For Pair 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]) 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:

    (47)    (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])∧(UIncreasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥))



    We simplified constraint (47) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (48)    ((UIncreasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧[(-1)bso_57] ≥ 0)



    We simplified constraint (48) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (49)    ((UIncreasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧[(-1)bso_57] ≥ 0)



    We simplified constraint (49) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (50)    ((UIncreasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧[(-1)bso_57] ≥ 0)



    We simplified constraint (50) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (51)    ((UIncreasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧0 = 0∧[(-1)bso_57] ≥ 0)







For Pair 69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0]) 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:

    (52)    (<(x1[0], 100)=TRUEx0[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])∧(UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥))



    We simplified constraint (52) using rule (IV) which results in the following new constraint:

    (53)    (<(x1[0], 100)=TRUE69_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])∧(UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥))



    We simplified constraint (53) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (54)    ([99] + [-1]x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]x1[0] ≥ 0∧[(-1)bso_59] ≥ 0)



    We simplified constraint (54) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (55)    ([99] + [-1]x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]x1[0] ≥ 0∧[(-1)bso_59] ≥ 0)



    We simplified constraint (55) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (56)    ([99] + [-1]x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]x1[0] ≥ 0∧[(-1)bso_59] ≥ 0)



    We simplified constraint (56) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (57)    ([99] + x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_58] + [bni_58]x1[0] ≥ 0∧[(-1)bso_59] ≥ 0)


    (58)    ([99] + [-1]x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]x1[0] ≥ 0∧[(-1)bso_59] ≥ 0)







To summarize, we get the following constraints P for the following pairs.
  • 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))
    • ((UIncreasing(69_0_REC_GE(x1[10], +(x0[10], 1))), ≥)∧0 = 0∧[(-1)bso_39] ≥ 0)

  • 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])
    • (x0[9] ≥ 0 ⇒ (UIncreasing(COND_321_2_REC_INVOKEMETHOD(>(x0[9], 0), 321_1_test_InvokeMethod(220_0_descend_Return, x0[9]), x1[9], x0[9])), ≥)∧[(-2)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]x0[9] ≥ 0∧[(-1)bso_41] ≥ 0)

  • 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])
    • ((UIncreasing(321_2_REC_INVOKEMETHOD(321_1_test_InvokeMethod(92_0_descend_Load(x0[8]), x0[8]), x1[8], x0[8])), ≥)∧0 = 0∧[(-1)bso_43] ≥ 0)

  • 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])
    • ((UIncreasing(309_2_REC_INVOKEMETHOD(309_1_test_InvokeMethod(92_0_descend_Load(x0[7]), x0[7]), x1[7], x0[7])), ≥)∧0 = 0∧[(-1)bso_45] ≥ 0)

  • 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])
    • ((UIncreasing(295_2_REC_INVOKEMETHOD(295_1_test_InvokeMethod(92_0_descend_Load(x0[6]), x0[6]), x1[6], x0[6])), ≥)∧0 = 0∧[(-1)bso_47] ≥ 0)

  • 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])
    • ((UIncreasing(282_2_REC_INVOKEMETHOD(282_1_test_InvokeMethod(92_0_descend_Load(x0[5]), x0[5]), x1[5], x0[5])), ≥)∧0 = 0∧[(-1)bso_49] ≥ 0)

  • 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])
    • ((UIncreasing(266_2_REC_INVOKEMETHOD(266_1_test_InvokeMethod(92_0_descend_Load(x0[4]), x0[4]), x1[4], x0[4])), ≥)∧0 = 0∧[(-1)bso_51] ≥ 0)

  • 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])
    • ((UIncreasing(250_2_REC_INVOKEMETHOD(250_1_test_InvokeMethod(92_0_descend_Load(x0[3]), x0[3]), x1[3], x0[3])), ≥)∧0 = 0∧[(-1)bso_53] ≥ 0)

  • 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])
    • ((UIncreasing(237_2_REC_INVOKEMETHOD(237_1_test_InvokeMethod(92_0_descend_Load(x0[2]), x0[2]), x1[2], x0[2])), ≥)∧0 = 0∧[1 + (-1)bso_55] ≥ 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])
    • ((UIncreasing(92_2_REC_INVOKEMETHOD(92_1_test_InvokeMethod(92_0_descend_Load(x1[1]), x1[1]), x0[1], x1[1])), ≥)∧0 = 0∧[(-1)bso_57] ≥ 0)

  • 69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])
    • ([99] + x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_58] + [bni_58]x1[0] ≥ 0∧[(-1)bso_59] ≥ 0)
    • ([99] + [-1]x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (UIncreasing(COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]x1[0] ≥ 0∧[(-1)bso_59] ≥ 0)




The constraints for P> respective Pbound 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 Pbound.
Using the following integer polynomial ordering the resulting constraints can be solved
Polynomial interpretation over integers[POLO]:

POL(TRUE) = 0   
POL(FALSE) = 0   
POL(92_0_descend_Load(x1)) = [-1] + x1   
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) = [2]   
POL(300_0_descend_Return) = [-1]   
POL(314_0_descend_Return) = [2]   
POL(327_0_descend_Return) = [-1]   
POL(169_0_descend_LE(x1)) = [-1] + [-1]x1   
POL(0) = 0   
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)) = [2] + [-1]x2 + [-1]x1   
POL(-(x1, x2)) = x1 + [-1]x2   
POL(1) = [1]   
POL(220_0_descend_Return) = [-1]   
POL(COND_321_2_REC_INVOKEMETHOD(x1, x2, x3, x4)) = [-1] + [-1]x4   
POL(321_1_test_InvokeMethod(x1, x2)) = [-1] + [2]x2 + [-1]x1   
POL(69_0_REC_GE(x1, x2)) = [-1]x2   
POL(+(x1, x2)) = x1 + x2   
POL(321_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(309_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(309_1_test_InvokeMethod(x1, x2)) = [-1] + [-1]x2 + [-1]x1   
POL(295_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(295_1_test_InvokeMethod(x1, x2)) = [-1] + [-1]x2 + [-1]x1   
POL(282_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(282_1_test_InvokeMethod(x1, x2)) = [-1] + [2]x2 + [-1]x1   
POL(266_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(266_1_test_InvokeMethod(x1, x2)) = [-1] + [-1]x2 + [-1]x1   
POL(250_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(250_1_test_InvokeMethod(x1, x2)) = [-1] + [2]x2 + [-1]x1   
POL(237_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1] + [-1]x3   
POL(237_1_test_InvokeMethod(x1, x2)) = [-1] + [-1]x2 + [-1]x1   
POL(92_2_REC_INVOKEMETHOD(x1, x2, x3)) = [-1]x1 + [-1]x3   
POL(92_1_test_InvokeMethod(x1, x2)) = 0   
POL(COND_69_0_REC_GE(x1, x2, x3)) = [-1]x3   
POL(<(x1, x2)) = 0   
POL(100) = [100]   

The following pairs are in P>:

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])

The following pairs are in Pbound:

69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])

The following pairs are in P:

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))
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])
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])
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])
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])
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])
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])
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])
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])
69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(<(x1[0], 100), x0[0], x1[0])

There are no usable rules.

(32) Complex Obligation (AND)

(33) 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:
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)
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:
(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)
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(0): 69_0_REC_GE(x0[0], x1[0]) → COND_69_0_REC_GE(x1[0] < 100, x0[0], x1[0])

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


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


(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]))



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)

(34) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 10 less nodes.

(35) TRUE

(36) 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:
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)
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:
(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)
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])
(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])

(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]))



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)

(37) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 10 less nodes.

(38) TRUE