Termination proof of /tmp/tmp3JQS4-/PastaA10.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBC2FIG (⇐)

↳2 FIGraph

↳3 FIGtoITRSProof (⇐)

↳4 ITRS

↳5 ITRStoIDPProof (⇔)

↳6 IDP

↳7 UsableRulesProof (⇔)

↳8 IDP

↳9 IDPNonInfProof (⇐)

↳10 AND

    ↳11 IDP

        ↳12 IDependencyGraphProof (⇔)

        ↳13 TRUE

    ↳14 IDP

        ↳15 IDependencyGraphProof (⇔)

        ↳16 TRUE

(0) Obligation:

JBC Problem based on JBC Program:

No human-readable program information known.

Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaA10

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Graph of 169 nodes with 1 SCC.

(3) FIGtoITRSProof (SOUND transformation)

Transformed FIGraph to ITRS rules

(4) Obligation:

ITRS 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 TRS R consists of the following rules:
Load524(i12, i44) → Cond_Load524(i12 >= 0 && i12 < i44 && i12 + 1 > 0, i12, i44)
Cond_Load524(TRUE, i12, i44) → Load524(i12 + 1, i44)
Load524(i12, i44) → Cond_Load5241(i44 >= 0 && i12 > i44, i12, i44)
Cond_Load5241(TRUE, i12, i44) → Load524(i12, i44 + 1)
The set Q consists of the following terms:
Load524(x0, x1)
Cond_Load524(TRUE, x0, x1)
Cond_Load5241(TRUE, x0, x1)

(5) ITRStoIDPProof (EQUIVALENT transformation)

Added dependency pairs

(6) Obligation:

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

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

The following domains are used:

Boolean, Integer

The ITRS R consists of the following rules:
Load524(i12, i44) → Cond_Load524(i12 >= 0 && i12 < i44 && i12 + 1 > 0, i12, i44)
Cond_Load524(TRUE, i12, i44) → Load524(i12 + 1, i44)
Load524(i12, i44) → Cond_Load5241(i44 >= 0 && i12 > i44, i12, i44)
Cond_Load5241(TRUE, i12, i44) → Load524(i12, i44 + 1)

The integer pair graph contains the following rules and edges:
(0): LOAD524(i12[0], i44[0]) → COND_LOAD524(i12[0] >= 0 && i12[0] < i44[0] && i12[0] + 1 > 0, i12[0], i44[0])
(1): COND_LOAD524(TRUE, i12[1], i44[1]) → LOAD524(i12[1] + 1, i44[1])
(2): LOAD524(i12[2], i44[2]) → COND_LOAD5241(i44[2] >= 0 && i12[2] > i44[2], i12[2], i44[2])
(3): COND_LOAD5241(TRUE, i12[3], i44[3]) → LOAD524(i12[3], i44[3] + 1)

(0) -> (1), if ((i44[0] →^* i44[1])∧(i12[0] →^* i12[1])∧(i12[0] >= 0 && i12[0] < i44[0] && i12[0] + 1 > 0 →^* TRUE))

(1) -> (0), if ((i44[1] →^* i44[0])∧(i12[1] + 1 →^* i12[0]))

(1) -> (2), if ((i12[1] + 1 →^* i12[2])∧(i44[1] →^* i44[2]))

(2) -> (3), if ((i44[2] →^* i44[3])∧(i12[2] →^* i12[3])∧(i44[2] >= 0 && i12[2] > i44[2] →^* TRUE))

(3) -> (0), if ((i44[3] + 1 →^* i44[0])∧(i12[3] →^* i12[0]))

(3) -> (2), if ((i44[3] + 1 →^* i44[2])∧(i12[3] →^* i12[2]))

The set Q consists of the following terms:
Load524(x0, x1)
Cond_Load524(TRUE, x0, x1)
Cond_Load5241(TRUE, x0, x1)

(7) 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.

(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:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD524(i12[0], i44[0]) → COND_LOAD524(i12[0] >= 0 && i12[0] < i44[0] && i12[0] + 1 > 0, i12[0], i44[0])
(1): COND_LOAD524(TRUE, i12[1], i44[1]) → LOAD524(i12[1] + 1, i44[1])
(2): LOAD524(i12[2], i44[2]) → COND_LOAD5241(i44[2] >= 0 && i12[2] > i44[2], i12[2], i44[2])
(3): COND_LOAD5241(TRUE, i12[3], i44[3]) → LOAD524(i12[3], i44[3] + 1)

(0) -> (1), if ((i44[0] →^* i44[1])∧(i12[0] →^* i12[1])∧(i12[0] >= 0 && i12[0] < i44[0] && i12[0] + 1 > 0 →^* TRUE))

(1) -> (0), if ((i44[1] →^* i44[0])∧(i12[1] + 1 →^* i12[0]))

(1) -> (2), if ((i12[1] + 1 →^* i12[2])∧(i44[1] →^* i44[2]))

(2) -> (3), if ((i44[2] →^* i44[3])∧(i12[2] →^* i12[3])∧(i44[2] >= 0 && i12[2] > i44[2] →^* TRUE))

(3) -> (0), if ((i44[3] + 1 →^* i44[0])∧(i12[3] →^* i12[0]))

(3) -> (2), if ((i44[3] + 1 →^* i44[2])∧(i12[3] →^* i12[2]))

The set Q consists of the following terms:
Load524(x0, x1)
Cond_Load524(TRUE, x0, x1)
Cond_Load5241(TRUE, x0, x1)

(9) 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 LOAD524(i12, i44) → COND_LOAD524(&&(&&(>=(i12, 0), <(i12, i44)), >(+(i12, 1), 0)), i12, i44) the following chains were created:

We consider the chain LOAD524(i12[0], i44[0]) → COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0]), COND_LOAD524(TRUE, i12[1], i44[1]) → LOAD524(+(i12[1], 1), i44[1]) which results in the following constraint:
(1)    (i44[0]=i44[1]∧i12[0]=i12[1]∧&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0))=TRUE ⇒ LOAD524(i12[0], i44[0])≥NonInfC∧LOAD524(i12[0], i44[0])≥COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0])∧(U^Increasing(COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0])), ≥))

We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>(+(i12[0], 1), 0)=TRUE∧>=(i12[0], 0)=TRUE∧<(i12[0], i44[0])=TRUE ⇒ LOAD524(i12[0], i44[0])≥NonInfC∧LOAD524(i12[0], i44[0])≥COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0])∧(U^Increasing(COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[0] + [-1] + [-1]i12[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]max{i12[0] + [-1]i44[0], [-1]i12[0] + i44[0]} ≥ 0∧[(-1)bso_16] + max{i12[0] + [-1]i44[0], [-1]i12[0] + i44[0]} + [-1]max{i12[0] + [-1]i44[0], [-1]i12[0] + i44[0]} ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[0] + [-1] + [-1]i12[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]max{i12[0] + [-1]i44[0], [-1]i12[0] + i44[0]} ≥ 0∧[(-1)bso_16] + max{i12[0] + [-1]i44[0], [-1]i12[0] + i44[0]} + [-1]max{i12[0] + [-1]i44[0], [-1]i12[0] + i44[0]} ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[0] + [-1] + [-1]i12[0] ≥ 0∧[-1] + [-2]i12[0] + [2]i44[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i12[0] + [bni_15]i44[0] ≥ 0∧[(-1)bso_16] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[0] ≥ 0∧[1] + [2]i44[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]i44[0] ≥ 0∧[(-1)bso_16] ≥ 0)

We simplified constraint (6) using rule (IDP_POLY_GCD) which results in the following new constraint:
(7)    (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[0] ≥ 0∧i44[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]i44[0] ≥ 0∧[(-1)bso_16] ≥ 0)

For Pair COND_LOAD524(TRUE, i12, i44) → LOAD524(+(i12, 1), i44) the following chains were created:

We consider the chain COND_LOAD524(TRUE, i12[1], i44[1]) → LOAD524(+(i12[1], 1), i44[1]), LOAD524(i12[0], i44[0]) → COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0]), COND_LOAD524(TRUE, i12[1], i44[1]) → LOAD524(+(i12[1], 1), i44[1]) which results in the following constraint:
(8)    (i44[1]=i44[0]∧+(i12[1], 1)=i12[0]∧i44[0]=i44[1]1∧i12[0]=i12[1]1∧&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0))=TRUE ⇒ COND_LOAD524(TRUE, i12[1]1, i44[1]1)≥NonInfC∧COND_LOAD524(TRUE, i12[1]1, i44[1]1)≥LOAD524(+(i12[1]1, 1), i44[1]1)∧(U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥))

We simplified constraint (8) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:
(9)    (>(+(+(i12[1], 1), 1), 0)=TRUE∧>=(+(i12[1], 1), 0)=TRUE∧<(+(i12[1], 1), i44[0])=TRUE ⇒ COND_LOAD524(TRUE, +(i12[1], 1), i44[0])≥NonInfC∧COND_LOAD524(TRUE, +(i12[1], 1), i44[0])≥LOAD524(+(+(i12[1], 1), 1), i44[0])∧(U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥))

We simplified constraint (9) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(10)    (i12[1] + [1] ≥ 0∧i12[1] + [1] ≥ 0∧i44[0] + [-2] + [-1]i12[1] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]max{[1] + i12[1] + [-1]i44[0], [-1] + [-1]i12[1] + i44[0]} ≥ 0∧[(-1)bso_18] + max{[1] + i12[1] + [-1]i44[0], [-1] + [-1]i12[1] + i44[0]} + [-1]max{[2] + i12[1] + [-1]i44[0], [-2] + [-1]i12[1] + i44[0]} ≥ 0)

We simplified constraint (10) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(11)    (i12[1] + [1] ≥ 0∧i12[1] + [1] ≥ 0∧i44[0] + [-2] + [-1]i12[1] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]max{[1] + i12[1] + [-1]i44[0], [-1] + [-1]i12[1] + i44[0]} ≥ 0∧[(-1)bso_18] + max{[1] + i12[1] + [-1]i44[0], [-1] + [-1]i12[1] + i44[0]} + [-1]max{[2] + i12[1] + [-1]i44[0], [-2] + [-1]i12[1] + i44[0]} ≥ 0)

We simplified constraint (11) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraints:
(12)    (i12[1] + [1] ≥ 0∧i12[1] + [1] ≥ 0∧i44[0] + [-2] + [-1]i12[1] ≥ 0∧[-3] + [-2]i12[1] + [2]i44[0] ≥ 0∧[4] + [2]i12[1] + [-2]i44[0] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥)∧[(-2)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i12[1] + [bni_17]i44[0] ≥ 0∧[-3 + (-1)bso_18] + [-2]i12[1] + [2]i44[0] ≥ 0)

(13)    (i12[1] + [1] ≥ 0∧i12[1] + [1] ≥ 0∧i44[0] + [-2] + [-1]i12[1] ≥ 0∧[-3] + [-2]i12[1] + [2]i44[0] ≥ 0∧[-5] + [-2]i12[1] + [2]i44[0] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥)∧[(-2)bni_17 + (-1)Bound*bni_17] + [(-1)bni_17]i12[1] + [bni_17]i44[0] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    (i44[0] + [-1] + [-1]i12[1] ≥ 0∧i44[0] + [-1] + [-1]i12[1] ≥ 0∧i12[1] ≥ 0∧[1] + [2]i12[1] ≥ 0∧[-2]i12[1] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥)∧[(-1)Bound*bni_17] + [bni_17]i12[1] ≥ 0∧[1 + (-1)bso_18] + [2]i12[1] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(15)    (i44[0] + [-1] + [-1]i12[1] ≥ 0∧i44[0] + [-1] + [-1]i12[1] ≥ 0∧i12[1] ≥ 0∧[1] + [2]i12[1] ≥ 0∧[-1] + [2]i12[1] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥)∧[(-1)Bound*bni_17] + [bni_17]i12[1] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (14) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(16)    (i44[0] + [-1]i12[1] ≥ 0∧i44[0] + [-1]i12[1] ≥ 0∧i12[1] ≥ 0∧[1] + [2]i12[1] ≥ 0∧[-2]i12[1] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥)∧[(-1)Bound*bni_17] + [bni_17]i12[1] ≥ 0∧[1 + (-1)bso_18] + [2]i12[1] ≥ 0)

We simplified constraint (16) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(17)    (i44[0] ≥ 0∧i44[0] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥)∧[(-1)Bound*bni_17] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (15) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(18)    (i44[0] ≥ 0∧i44[0] ≥ 0∧i12[1] ≥ 0∧[1] + [2]i12[1] ≥ 0∧[-1] + [2]i12[1] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥)∧[(-1)Bound*bni_17] + [bni_17]i12[1] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (18) using rule (IDP_POLY_GCD) which results in the following new constraint:
(19)    (i44[0] ≥ 0∧i44[0] ≥ 0∧i12[1] ≥ 0∧i12[1] ≥ 0∧i12[1] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥)∧[(-1)Bound*bni_17] + [bni_17]i12[1] ≥ 0∧[1 + (-1)bso_18] ≥ 0)
We consider the chain COND_LOAD5241(TRUE, i12[3], i44[3]) → LOAD524(i12[3], +(i44[3], 1)), LOAD524(i12[0], i44[0]) → COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0]), COND_LOAD524(TRUE, i12[1], i44[1]) → LOAD524(+(i12[1], 1), i44[1]) which results in the following constraint:
(20)    (+(i44[3], 1)=i44[0]∧i12[3]=i12[0]∧i44[0]=i44[1]∧i12[0]=i12[1]∧&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0))=TRUE ⇒ COND_LOAD524(TRUE, i12[1], i44[1])≥NonInfC∧COND_LOAD524(TRUE, i12[1], i44[1])≥LOAD524(+(i12[1], 1), i44[1])∧(U^Increasing(LOAD524(+(i12[1], 1), i44[1])), ≥))

We simplified constraint (20) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:
(21)    (>(+(i12[0], 1), 0)=TRUE∧>=(i12[0], 0)=TRUE∧<(i12[0], +(i44[3], 1))=TRUE ⇒ COND_LOAD524(TRUE, i12[0], +(i44[3], 1))≥NonInfC∧COND_LOAD524(TRUE, i12[0], +(i44[3], 1))≥LOAD524(+(i12[0], 1), +(i44[3], 1))∧(U^Increasing(LOAD524(+(i12[1], 1), i44[1])), ≥))

We simplified constraint (21) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(22)    (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[3] + [-1]i12[0] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1], 1), i44[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]max{[-1] + i12[0] + [-1]i44[3], [1] + [-1]i12[0] + i44[3]} ≥ 0∧[(-1)bso_18] + max{[-1] + i12[0] + [-1]i44[3], [1] + [-1]i12[0] + i44[3]} + [-1]max{i12[0] + [-1]i44[3], [-1]i12[0] + i44[3]} ≥ 0)

We simplified constraint (22) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(23)    (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[3] + [-1]i12[0] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1], 1), i44[1])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]max{[-1] + i12[0] + [-1]i44[3], [1] + [-1]i12[0] + i44[3]} ≥ 0∧[(-1)bso_18] + max{[-1] + i12[0] + [-1]i44[3], [1] + [-1]i12[0] + i44[3]} + [-1]max{i12[0] + [-1]i44[3], [-1]i12[0] + i44[3]} ≥ 0)

We simplified constraint (23) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraints:
(24)    (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[3] + [-1]i12[0] ≥ 0∧[1] + [-2]i12[0] + [2]i44[3] ≥ 0∧[2]i12[0] + [-2]i44[3] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1], 1), i44[1])), ≥)∧[(-1)Bound*bni_17] + [(-1)bni_17]i12[0] + [bni_17]i44[3] ≥ 0∧[1 + (-1)bso_18] + [-2]i12[0] + [2]i44[3] ≥ 0)

(25)    (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[3] + [-1]i12[0] ≥ 0∧[1] + [-2]i12[0] + [2]i44[3] ≥ 0∧[-1] + [-2]i12[0] + [2]i44[3] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1], 1), i44[1])), ≥)∧[(-1)Bound*bni_17] + [(-1)bni_17]i12[0] + [bni_17]i44[3] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (24) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(26)    (i44[3] + i12[0] ≥ 0∧i44[3] + i12[0] ≥ 0∧[-1]i12[0] ≥ 0∧[1] + [-2]i12[0] ≥ 0∧[2]i12[0] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1], 1), i44[1])), ≥)∧[(-1)Bound*bni_17] + [(-1)bni_17]i12[0] ≥ 0∧[1 + (-1)bso_18] + [-2]i12[0] ≥ 0)

We simplified constraint (25) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(27)    (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[3] ≥ 0∧[1] + [2]i44[3] ≥ 0∧[-1] + [2]i44[3] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1], 1), i44[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]i44[3] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (26) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(28)    (i44[3] ≥ 0∧i44[3] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1], 1), i44[1])), ≥)∧[(-1)Bound*bni_17] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

We simplified constraint (27) using rule (IDP_POLY_GCD) which results in the following new constraint:
(29)    (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[3] ≥ 0∧i44[3] ≥ 0∧i44[3] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1], 1), i44[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]i44[3] ≥ 0∧[1 + (-1)bso_18] ≥ 0)

For Pair LOAD524(i12, i44) → COND_LOAD5241(&&(>=(i44, 0), >(i12, i44)), i12, i44) the following chains were created:

We consider the chain LOAD524(i12[2], i44[2]) → COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2]), COND_LOAD5241(TRUE, i12[3], i44[3]) → LOAD524(i12[3], +(i44[3], 1)) which results in the following constraint:
(30)    (i44[2]=i44[3]∧i12[2]=i12[3]∧&&(>=(i44[2], 0), >(i12[2], i44[2]))=TRUE ⇒ LOAD524(i12[2], i44[2])≥NonInfC∧LOAD524(i12[2], i44[2])≥COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2])∧(U^Increasing(COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2])), ≥))

We simplified constraint (30) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(31)    (>=(i44[2], 0)=TRUE∧>(i12[2], i44[2])=TRUE ⇒ LOAD524(i12[2], i44[2])≥NonInfC∧LOAD524(i12[2], i44[2])≥COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2])∧(U^Increasing(COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2])), ≥))

We simplified constraint (31) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(32)    (i44[2] ≥ 0∧i12[2] + [-1] + [-1]i44[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2])), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]max{i12[2] + [-1]i44[2], [-1]i12[2] + i44[2]} ≥ 0∧[(-1)bso_20] + max{i12[2] + [-1]i44[2], [-1]i12[2] + i44[2]} + [-1]max{i12[2] + [-1]i44[2], [-1]i12[2] + i44[2]} ≥ 0)

We simplified constraint (32) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(33)    (i44[2] ≥ 0∧i12[2] + [-1] + [-1]i44[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2])), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]max{i12[2] + [-1]i44[2], [-1]i12[2] + i44[2]} ≥ 0∧[(-1)bso_20] + max{i12[2] + [-1]i44[2], [-1]i12[2] + i44[2]} + [-1]max{i12[2] + [-1]i44[2], [-1]i12[2] + i44[2]} ≥ 0)

We simplified constraint (33) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(34)    (i44[2] ≥ 0∧i12[2] + [-1] + [-1]i44[2] ≥ 0∧[2]i12[2] + [-2]i44[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2])), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]i12[2] + [(-1)bni_19]i44[2] ≥ 0∧[(-1)bso_20] ≥ 0)

We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(35)    (i44[2] ≥ 0∧i12[2] ≥ 0∧[2] + [2]i12[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2])), ≥)∧[(-1)Bound*bni_19] + [bni_19]i12[2] ≥ 0∧[(-1)bso_20] ≥ 0)

We simplified constraint (35) using rule (IDP_POLY_GCD) which results in the following new constraint:
(36)    (i44[2] ≥ 0∧i12[2] ≥ 0∧[1] + i12[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2])), ≥)∧[(-1)Bound*bni_19] + [bni_19]i12[2] ≥ 0∧[(-1)bso_20] ≥ 0)

For Pair COND_LOAD5241(TRUE, i12, i44) → LOAD524(i12, +(i44, 1)) the following chains were created:

We consider the chain COND_LOAD524(TRUE, i12[1], i44[1]) → LOAD524(+(i12[1], 1), i44[1]), LOAD524(i12[2], i44[2]) → COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2]), COND_LOAD5241(TRUE, i12[3], i44[3]) → LOAD524(i12[3], +(i44[3], 1)) which results in the following constraint:
(37)    (+(i12[1], 1)=i12[2]∧i44[1]=i44[2]∧i44[2]=i44[3]∧i12[2]=i12[3]∧&&(>=(i44[2], 0), >(i12[2], i44[2]))=TRUE ⇒ COND_LOAD5241(TRUE, i12[3], i44[3])≥NonInfC∧COND_LOAD5241(TRUE, i12[3], i44[3])≥LOAD524(i12[3], +(i44[3], 1))∧(U^Increasing(LOAD524(i12[3], +(i44[3], 1))), ≥))

We simplified constraint (37) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:
(38)    (>=(i44[2], 0)=TRUE∧>(+(i12[1], 1), i44[2])=TRUE ⇒ COND_LOAD5241(TRUE, +(i12[1], 1), i44[2])≥NonInfC∧COND_LOAD5241(TRUE, +(i12[1], 1), i44[2])≥LOAD524(+(i12[1], 1), +(i44[2], 1))∧(U^Increasing(LOAD524(i12[3], +(i44[3], 1))), ≥))

We simplified constraint (38) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(39)    (i44[2] ≥ 0∧i12[1] + [-1]i44[2] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3], +(i44[3], 1))), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]max{[1] + i12[1] + [-1]i44[2], [-1] + [-1]i12[1] + i44[2]} ≥ 0∧[(-1)bso_22] + max{[1] + i12[1] + [-1]i44[2], [-1] + [-1]i12[1] + i44[2]} + [-1]max{i12[1] + [-1]i44[2], [-1]i12[1] + i44[2]} ≥ 0)

We simplified constraint (39) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(40)    (i44[2] ≥ 0∧i12[1] + [-1]i44[2] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3], +(i44[3], 1))), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]max{[1] + i12[1] + [-1]i44[2], [-1] + [-1]i12[1] + i44[2]} ≥ 0∧[(-1)bso_22] + max{[1] + i12[1] + [-1]i44[2], [-1] + [-1]i12[1] + i44[2]} + [-1]max{i12[1] + [-1]i44[2], [-1]i12[1] + i44[2]} ≥ 0)

We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(41)    (i44[2] ≥ 0∧i12[1] + [-1]i44[2] ≥ 0∧[2] + [2]i12[1] + [-2]i44[2] ≥ 0∧[2]i12[1] + [-2]i44[2] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3], +(i44[3], 1))), ≥)∧[(-1)Bound*bni_21] + [bni_21]i12[1] + [(-1)bni_21]i44[2] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

We simplified constraint (41) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(42)    (i44[2] ≥ 0∧i12[1] ≥ 0∧[2] + [2]i12[1] ≥ 0∧[2]i12[1] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3], +(i44[3], 1))), ≥)∧[(-1)Bound*bni_21] + [bni_21]i12[1] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

We simplified constraint (42) using rule (IDP_POLY_GCD) which results in the following new constraint:
(43)    (i44[2] ≥ 0∧i12[1] ≥ 0∧[1] + i12[1] ≥ 0∧i12[1] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3], +(i44[3], 1))), ≥)∧[(-1)Bound*bni_21] + [bni_21]i12[1] ≥ 0∧[1 + (-1)bso_22] ≥ 0)
We consider the chain COND_LOAD5241(TRUE, i12[3], i44[3]) → LOAD524(i12[3], +(i44[3], 1)), LOAD524(i12[2], i44[2]) → COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2]), COND_LOAD5241(TRUE, i12[3], i44[3]) → LOAD524(i12[3], +(i44[3], 1)) which results in the following constraint:
(44)    (+(i44[3], 1)=i44[2]∧i12[3]=i12[2]∧i44[2]=i44[3]1∧i12[2]=i12[3]1∧&&(>=(i44[2], 0), >(i12[2], i44[2]))=TRUE ⇒ COND_LOAD5241(TRUE, i12[3]1, i44[3]1)≥NonInfC∧COND_LOAD5241(TRUE, i12[3]1, i44[3]1)≥LOAD524(i12[3]1, +(i44[3]1, 1))∧(U^Increasing(LOAD524(i12[3]1, +(i44[3]1, 1))), ≥))

We simplified constraint (44) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:
(45)    (>=(+(i44[3], 1), 0)=TRUE∧>(i12[2], +(i44[3], 1))=TRUE ⇒ COND_LOAD5241(TRUE, i12[2], +(i44[3], 1))≥NonInfC∧COND_LOAD5241(TRUE, i12[2], +(i44[3], 1))≥LOAD524(i12[2], +(+(i44[3], 1), 1))∧(U^Increasing(LOAD524(i12[3]1, +(i44[3]1, 1))), ≥))

We simplified constraint (45) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(46)    (i44[3] + [1] ≥ 0∧i12[2] + [-2] + [-1]i44[3] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3]1, +(i44[3]1, 1))), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]max{[-1] + i12[2] + [-1]i44[3], [1] + [-1]i12[2] + i44[3]} ≥ 0∧[(-1)bso_22] + max{[-1] + i12[2] + [-1]i44[3], [1] + [-1]i12[2] + i44[3]} + [-1]max{[-2] + i12[2] + [-1]i44[3], [2] + [-1]i12[2] + i44[3]} ≥ 0)

We simplified constraint (46) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(47)    (i44[3] + [1] ≥ 0∧i12[2] + [-2] + [-1]i44[3] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3]1, +(i44[3]1, 1))), ≥)∧[(-1)bni_21 + (-1)Bound*bni_21] + [bni_21]max{[-1] + i12[2] + [-1]i44[3], [1] + [-1]i12[2] + i44[3]} ≥ 0∧[(-1)bso_22] + max{[-1] + i12[2] + [-1]i44[3], [1] + [-1]i12[2] + i44[3]} + [-1]max{[-2] + i12[2] + [-1]i44[3], [2] + [-1]i12[2] + i44[3]} ≥ 0)

We simplified constraint (47) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(48)    (i44[3] + [1] ≥ 0∧i12[2] + [-2] + [-1]i44[3] ≥ 0∧[-2] + [2]i12[2] + [-2]i44[3] ≥ 0∧[-4] + [2]i12[2] + [-2]i44[3] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3]1, +(i44[3]1, 1))), ≥)∧[(-2)bni_21 + (-1)Bound*bni_21] + [bni_21]i12[2] + [(-1)bni_21]i44[3] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

We simplified constraint (48) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(49)    (i12[2] + [-1] + [-1]i44[3] ≥ 0∧i44[3] ≥ 0∧[2] + [2]i44[3] ≥ 0∧[2]i44[3] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3]1, +(i44[3]1, 1))), ≥)∧[(-1)Bound*bni_21] + [bni_21]i44[3] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

We simplified constraint (49) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(50)    (i12[2] ≥ 0∧i44[3] ≥ 0∧[2] + [2]i44[3] ≥ 0∧[2]i44[3] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3]1, +(i44[3]1, 1))), ≥)∧[(-1)Bound*bni_21] + [bni_21]i44[3] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

We simplified constraint (50) using rule (IDP_POLY_GCD) which results in the following new constraint:
(51)    (i12[2] ≥ 0∧i44[3] ≥ 0∧[1] + i44[3] ≥ 0∧i44[3] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3]1, +(i44[3]1, 1))), ≥)∧[(-1)Bound*bni_21] + [bni_21]i44[3] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

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

LOAD524(i12, i44) → COND_LOAD524(&&(&&(>=(i12, 0), <(i12, i44)), >(+(i12, 1), 0)), i12, i44)
- (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[0] ≥ 0∧i44[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0])), ≥)∧[(-1)Bound*bni_15] + [bni_15]i44[0] ≥ 0∧[(-1)bso_16] ≥ 0)
COND_LOAD524(TRUE, i12, i44) → LOAD524(+(i12, 1), i44)
- (i44[0] ≥ 0∧i44[0] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥)∧[(-1)Bound*bni_17] ≥ 0∧[1 + (-1)bso_18] ≥ 0)
- (i44[0] ≥ 0∧i44[0] ≥ 0∧i12[1] ≥ 0∧i12[1] ≥ 0∧i12[1] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1]1, 1), i44[1]1)), ≥)∧[(-1)Bound*bni_17] + [bni_17]i12[1] ≥ 0∧[1 + (-1)bso_18] ≥ 0)
- (i44[3] ≥ 0∧i44[3] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1], 1), i44[1])), ≥)∧[(-1)Bound*bni_17] ≥ 0∧[1 + (-1)bso_18] ≥ 0)
- (i12[0] ≥ 0∧i12[0] ≥ 0∧i44[3] ≥ 0∧i44[3] ≥ 0∧i44[3] ≥ 0 ⇒ (U^Increasing(LOAD524(+(i12[1], 1), i44[1])), ≥)∧[(-1)Bound*bni_17] + [bni_17]i44[3] ≥ 0∧[1 + (-1)bso_18] ≥ 0)
LOAD524(i12, i44) → COND_LOAD5241(&&(>=(i44, 0), >(i12, i44)), i12, i44)
- (i44[2] ≥ 0∧i12[2] ≥ 0∧[1] + i12[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2])), ≥)∧[(-1)Bound*bni_19] + [bni_19]i12[2] ≥ 0∧[(-1)bso_20] ≥ 0)
COND_LOAD5241(TRUE, i12, i44) → LOAD524(i12, +(i44, 1))
- (i44[2] ≥ 0∧i12[1] ≥ 0∧[1] + i12[1] ≥ 0∧i12[1] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3], +(i44[3], 1))), ≥)∧[(-1)Bound*bni_21] + [bni_21]i12[1] ≥ 0∧[1 + (-1)bso_22] ≥ 0)
- (i12[2] ≥ 0∧i44[3] ≥ 0∧[1] + i44[3] ≥ 0∧i44[3] ≥ 0 ⇒ (U^Increasing(LOAD524(i12[3]1, +(i44[3]1, 1))), ≥)∧[(-1)Bound*bni_21] + [bni_21]i44[3] ≥ 0∧[1 + (-1)bso_22] ≥ 0)

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

POL(TRUE) = 0
POL(FALSE) = 0
POL(LOAD524(x₁, x₂)) = [-1] + max{x₁ + [-1]x₂, [-1]x₁ + x₂}
POL(COND_LOAD524(x₁, x₂, x₃)) = [-1] + max{x₂ + [-1]x₃, [-1]x₂ + x₃}
POL(&&(x₁, x₂)) = [-1]
POL(>=(x₁, x₂)) = [-1]
POL(0) = 0
POL(<(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(+(x₁, x₂)) = x₁ + x₂
POL(1) = [1]
POL(COND_LOAD5241(x₁, x₂, x₃)) = [-1] + max{x₂ + [-1]x₃, [-1]x₂ + x₃}

The following pairs are in P_>:

COND_LOAD524(TRUE, i12[1], i44[1]) → LOAD524(+(i12[1], 1), i44[1])
COND_LOAD5241(TRUE, i12[3], i44[3]) → LOAD524(i12[3], +(i44[3], 1))

The following pairs are in P_bound:

LOAD524(i12[0], i44[0]) → COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0])
COND_LOAD524(TRUE, i12[1], i44[1]) → LOAD524(+(i12[1], 1), i44[1])
LOAD524(i12[2], i44[2]) → COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2])
COND_LOAD5241(TRUE, i12[3], i44[3]) → LOAD524(i12[3], +(i44[3], 1))

The following pairs are in P_≥:

LOAD524(i12[0], i44[0]) → COND_LOAD524(&&(&&(>=(i12[0], 0), <(i12[0], i44[0])), >(+(i12[0], 1), 0)), i12[0], i44[0])
LOAD524(i12[2], i44[2]) → COND_LOAD5241(&&(>=(i44[2], 0), >(i12[2], i44[2])), i12[2], i44[2])

There are no usable rules.

(10) Complex Obligation (AND)

(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:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD524(i12[0], i44[0]) → COND_LOAD524(i12[0] >= 0 && i12[0] < i44[0] && i12[0] + 1 > 0, i12[0], i44[0])
(2): LOAD524(i12[2], i44[2]) → COND_LOAD5241(i44[2] >= 0 && i12[2] > i44[2], i12[2], i44[2])

The set Q consists of the following terms:
Load524(x0, x1)
Cond_Load524(TRUE, x0, x1)
Cond_Load5241(TRUE, x0, x1)

(12) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.

(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:
none

R is empty.

The integer pair graph is empty.

The set Q consists of the following terms:
Load524(x0, x1)
Cond_Load524(TRUE, x0, x1)
Cond_Load5241(TRUE, x0, x1)

(15) IDependencyGraphProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) JBC2FIG (SOUND transformation)

(2) Obligation:

(3) FIGtoITRSProof (SOUND transformation)

(4) Obligation:

(5) ITRStoIDPProof (EQUIVALENT transformation)

(6) Obligation:

(7) UsableRulesProof (EQUIVALENT transformation)

(8) Obligation:

(9) IDPNonInfProof (SOUND transformation)

(10) Complex Obligation (AND)

(11) Obligation:

(12) IDependencyGraphProof (EQUIVALENT transformation)

(13) TRUE

(14) Obligation:

(15) IDependencyGraphProof (EQUIVALENT transformation)

(16) TRUE