Termination proof of /tmp/tmph6

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

/**
 * Example taken from "A Term Rewriting Approach to the Automated Termination
 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
 * and converted to Java.
 */

public class PastaA10 {
    public static void main(String[] args) {
        Random.args = args;
        int x = Random.random();
        int y = Random.random();

        while (x != y) {
            if (x > y) {
                y++;
            } else {
                x++;
            }
        }
    }
}


public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}

(1) JBC2FIG (SOUND transformation)

Constructed FIGraph.

(2) Obligation:

FIGraph based on JBC Program:
Graph of 192 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:
Load1069(i14, i53) → Cond_Load1069(i14 < i53, i14, i53)
Cond_Load1069(TRUE, i14, i53) → Load1069(i14 + 1, i53)
Load1069(i14, i53) → Cond_Load10691(i14 > i53, i14, i53)
Cond_Load10691(TRUE, i14, i53) → Load1069(i14, i53 + 1)
The set Q consists of the following terms:
Load1069(x0, x1)
Cond_Load1069(TRUE, x0, x1)
Cond_Load10691(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:

Integer

The ITRS R consists of the following rules:
Load1069(i14, i53) → Cond_Load1069(i14 < i53, i14, i53)
Cond_Load1069(TRUE, i14, i53) → Load1069(i14 + 1, i53)
Load1069(i14, i53) → Cond_Load10691(i14 > i53, i14, i53)
Cond_Load10691(TRUE, i14, i53) → Load1069(i14, i53 + 1)

The integer pair graph contains the following rules and edges:
(0): LOAD1069(i14[0], i53[0]) → COND_LOAD1069(i14[0] < i53[0], i14[0], i53[0])
(1): COND_LOAD1069(TRUE, i14[1], i53[1]) → LOAD1069(i14[1] + 1, i53[1])
(2): LOAD1069(i14[2], i53[2]) → COND_LOAD10691(i14[2] > i53[2], i14[2], i53[2])
(3): COND_LOAD10691(TRUE, i14[3], i53[3]) → LOAD1069(i14[3], i53[3] + 1)

(0) -> (1), if ((i14[0] < i53[0] →^* TRUE)∧(i53[0] →^* i53[1])∧(i14[0] →^* i14[1]))

(1) -> (0), if ((i14[1] + 1 →^* i14[0])∧(i53[1] →^* i53[0]))

(1) -> (2), if ((i14[1] + 1 →^* i14[2])∧(i53[1] →^* i53[2]))

(2) -> (3), if ((i14[2] →^* i14[3])∧(i53[2] →^* i53[3])∧(i14[2] > i53[2] →^* TRUE))

(3) -> (0), if ((i53[3] + 1 →^* i53[0])∧(i14[3] →^* i14[0]))

(3) -> (2), if ((i53[3] + 1 →^* i53[2])∧(i14[3] →^* i14[2]))

The set Q consists of the following terms:
Load1069(x0, x1)
Cond_Load1069(TRUE, x0, x1)
Cond_Load10691(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:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1069(i14[0], i53[0]) → COND_LOAD1069(i14[0] < i53[0], i14[0], i53[0])
(1): COND_LOAD1069(TRUE, i14[1], i53[1]) → LOAD1069(i14[1] + 1, i53[1])
(2): LOAD1069(i14[2], i53[2]) → COND_LOAD10691(i14[2] > i53[2], i14[2], i53[2])
(3): COND_LOAD10691(TRUE, i14[3], i53[3]) → LOAD1069(i14[3], i53[3] + 1)

(0) -> (1), if ((i14[0] < i53[0] →^* TRUE)∧(i53[0] →^* i53[1])∧(i14[0] →^* i14[1]))

(1) -> (0), if ((i14[1] + 1 →^* i14[0])∧(i53[1] →^* i53[0]))

(1) -> (2), if ((i14[1] + 1 →^* i14[2])∧(i53[1] →^* i53[2]))

(2) -> (3), if ((i14[2] →^* i14[3])∧(i53[2] →^* i53[3])∧(i14[2] > i53[2] →^* TRUE))

(3) -> (0), if ((i53[3] + 1 →^* i53[0])∧(i14[3] →^* i14[0]))

(3) -> (2), if ((i53[3] + 1 →^* i53[2])∧(i14[3] →^* i14[2]))

The set Q consists of the following terms:
Load1069(x0, x1)
Cond_Load1069(TRUE, x0, x1)
Cond_Load10691(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 LOAD1069(i14, i53) → COND_LOAD1069(<(i14, i53), i14, i53) the following chains were created:

We consider the chain LOAD1069(i14[0], i53[0]) → COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0]), COND_LOAD1069(TRUE, i14[1], i53[1]) → LOAD1069(+(i14[1], 1), i53[1]) which results in the following constraint:
(1)    (<(i14[0], i53[0])=TRUE∧i53[0]=i53[1]∧i14[0]=i14[1] ⇒ LOAD1069(i14[0], i53[0])≥NonInfC∧LOAD1069(i14[0], i53[0])≥COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])∧(U^Increasing(COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])), ≥))

We simplified constraint (1) using rule (IV) which results in the following new constraint:
(2)    (<(i14[0], i53[0])=TRUE ⇒ LOAD1069(i14[0], i53[0])≥NonInfC∧LOAD1069(i14[0], i53[0])≥COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])∧(U^Increasing(COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (i53[0] + [-1] + [-1]i14[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]max{i14[0] + [-1]i53[0], [-1]i14[0] + i53[0]} ≥ 0∧[(-1)bso_14] + max{i14[0] + [-1]i53[0], [-1]i14[0] + i53[0]} + [-1]max{i14[0] + [-1]i53[0], [-1]i14[0] + i53[0]} ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (i53[0] + [-1] + [-1]i14[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]max{i14[0] + [-1]i53[0], [-1]i14[0] + i53[0]} ≥ 0∧[(-1)bso_14] + max{i14[0] + [-1]i53[0], [-1]i14[0] + i53[0]} + [-1]max{i14[0] + [-1]i53[0], [-1]i14[0] + i53[0]} ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (i53[0] + [-1] + [-1]i14[0] ≥ 0∧[-1] + [-2]i14[0] + [2]i53[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [(-1)bni_13]i14[0] + [bni_13]i53[0] ≥ 0∧[(-1)bso_14] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (i53[0] ≥ 0∧[1] + [2]i53[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])), ≥)∧[(-1)Bound*bni_13] + [bni_13]i53[0] ≥ 0∧[(-1)bso_14] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(7)    (i53[0] ≥ 0∧[1] + [2]i53[0] ≥ 0∧i14[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])), ≥)∧[(-1)Bound*bni_13] + [bni_13]i53[0] ≥ 0∧[(-1)bso_14] ≥ 0)

(8)    (i53[0] ≥ 0∧[1] + [2]i53[0] ≥ 0∧i14[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])), ≥)∧[(-1)Bound*bni_13] + [bni_13]i53[0] ≥ 0∧[(-1)bso_14] ≥ 0)

We simplified constraint (7) using rule (IDP_POLY_GCD) which results in the following new constraint:
(9)    (i53[0] ≥ 0∧i14[0] ≥ 0∧i53[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])), ≥)∧[(-1)Bound*bni_13] + [bni_13]i53[0] ≥ 0∧[(-1)bso_14] ≥ 0)

We simplified constraint (8) using rule (IDP_POLY_GCD) which results in the following new constraint:
(10)    (i53[0] ≥ 0∧i14[0] ≥ 0∧i53[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])), ≥)∧[(-1)Bound*bni_13] + [bni_13]i53[0] ≥ 0∧[(-1)bso_14] ≥ 0)

For Pair COND_LOAD1069(TRUE, i14, i53) → LOAD1069(+(i14, 1), i53) the following chains were created:

We consider the chain COND_LOAD1069(TRUE, i14[1], i53[1]) → LOAD1069(+(i14[1], 1), i53[1]), LOAD1069(i14[0], i53[0]) → COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0]), COND_LOAD1069(TRUE, i14[1], i53[1]) → LOAD1069(+(i14[1], 1), i53[1]) which results in the following constraint:
(11)    (+(i14[1], 1)=i14[0]∧i53[1]=i53[0]∧<(i14[0], i53[0])=TRUE∧i53[0]=i53[1]1∧i14[0]=i14[1]1 ⇒ COND_LOAD1069(TRUE, i14[1]1, i53[1]1)≥NonInfC∧COND_LOAD1069(TRUE, i14[1]1, i53[1]1)≥LOAD1069(+(i14[1]1, 1), i53[1]1)∧(U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥))

We simplified constraint (11) using rule (III) which results in the following new constraint:
(12)    (<(+(i14[1], 1), i53[0])=TRUE ⇒ COND_LOAD1069(TRUE, +(i14[1], 1), i53[0])≥NonInfC∧COND_LOAD1069(TRUE, +(i14[1], 1), i53[0])≥LOAD1069(+(+(i14[1], 1), 1), i53[0])∧(U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥))

We simplified constraint (12) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(13)    (i53[0] + [-2] + [-1]i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]max{[1] + i14[1] + [-1]i53[0], [-1] + [-1]i14[1] + i53[0]} ≥ 0∧[(-1)bso_16] + max{[1] + i14[1] + [-1]i53[0], [-1] + [-1]i14[1] + i53[0]} + [-1]max{[2] + i14[1] + [-1]i53[0], [-2] + [-1]i14[1] + i53[0]} ≥ 0)

We simplified constraint (13) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(14)    (i53[0] + [-2] + [-1]i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]max{[1] + i14[1] + [-1]i53[0], [-1] + [-1]i14[1] + i53[0]} ≥ 0∧[(-1)bso_16] + max{[1] + i14[1] + [-1]i53[0], [-1] + [-1]i14[1] + i53[0]} + [-1]max{[2] + i14[1] + [-1]i53[0], [-2] + [-1]i14[1] + i53[0]} ≥ 0)

We simplified constraint (14) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraints:
(15)    (i53[0] + [-2] + [-1]i14[1] ≥ 0∧[-3] + [-2]i14[1] + [2]i53[0] ≥ 0∧[4] + [2]i14[1] + [-2]i53[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i14[1] + [bni_15]i53[0] ≥ 0∧[-3 + (-1)bso_16] + [-2]i14[1] + [2]i53[0] ≥ 0)

(16)    (i53[0] + [-2] + [-1]i14[1] ≥ 0∧[-3] + [-2]i14[1] + [2]i53[0] ≥ 0∧[-5] + [-2]i14[1] + [2]i53[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-2)bni_15 + (-1)Bound*bni_15] + [(-1)bni_15]i14[1] + [bni_15]i53[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (15) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(17)    (i53[0] ≥ 0∧[1] + [2]i53[0] ≥ 0∧[-2]i53[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[0] ≥ 0∧[1 + (-1)bso_16] + [2]i53[0] ≥ 0)

We simplified constraint (16) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(18)    (i53[0] ≥ 0∧[1] + [2]i53[0] ≥ 0∧[-1] + [2]i53[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (17) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(19)    (0 ≥ 0∧[1] ≥ 0∧0 ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (19) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(20)    (0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

(21)    (0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (18) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(22)    (i53[0] ≥ 0∧[1] + [2]i53[0] ≥ 0∧[-1] + [2]i53[0] ≥ 0∧i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

(23)    (i53[0] ≥ 0∧[1] + [2]i53[0] ≥ 0∧[-1] + [2]i53[0] ≥ 0∧i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (22) using rule (IDP_POLY_GCD) which results in the following new constraint:
(24)    (i53[0] ≥ 0∧i14[1] ≥ 0∧i53[0] ≥ 0∧i53[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (23) using rule (IDP_POLY_GCD) which results in the following new constraint:
(25)    (i53[0] ≥ 0∧i14[1] ≥ 0∧i53[0] ≥ 0∧i53[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
We consider the chain COND_LOAD10691(TRUE, i14[3], i53[3]) → LOAD1069(i14[3], +(i53[3], 1)), LOAD1069(i14[0], i53[0]) → COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0]), COND_LOAD1069(TRUE, i14[1], i53[1]) → LOAD1069(+(i14[1], 1), i53[1]) which results in the following constraint:
(26)    (+(i53[3], 1)=i53[0]∧i14[3]=i14[0]∧<(i14[0], i53[0])=TRUE∧i53[0]=i53[1]∧i14[0]=i14[1] ⇒ COND_LOAD1069(TRUE, i14[1], i53[1])≥NonInfC∧COND_LOAD1069(TRUE, i14[1], i53[1])≥LOAD1069(+(i14[1], 1), i53[1])∧(U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥))

We simplified constraint (26) using rule (III) which results in the following new constraint:
(27)    (<(i14[0], +(i53[3], 1))=TRUE ⇒ COND_LOAD1069(TRUE, i14[0], +(i53[3], 1))≥NonInfC∧COND_LOAD1069(TRUE, i14[0], +(i53[3], 1))≥LOAD1069(+(i14[0], 1), +(i53[3], 1))∧(U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥))

We simplified constraint (27) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(28)    (i53[3] + [-1]i14[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]max{[-1] + i14[0] + [-1]i53[3], [1] + [-1]i14[0] + i53[3]} ≥ 0∧[(-1)bso_16] + max{[-1] + i14[0] + [-1]i53[3], [1] + [-1]i14[0] + i53[3]} + [-1]max{i14[0] + [-1]i53[3], [-1]i14[0] + i53[3]} ≥ 0)

We simplified constraint (28) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(29)    (i53[3] + [-1]i14[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]max{[-1] + i14[0] + [-1]i53[3], [1] + [-1]i14[0] + i53[3]} ≥ 0∧[(-1)bso_16] + max{[-1] + i14[0] + [-1]i53[3], [1] + [-1]i14[0] + i53[3]} + [-1]max{i14[0] + [-1]i53[3], [-1]i14[0] + i53[3]} ≥ 0)

We simplified constraint (29) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraints:
(30)    (i53[3] + [-1]i14[0] ≥ 0∧[1] + [-2]i14[0] + [2]i53[3] ≥ 0∧[2]i14[0] + [-2]i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] + [(-1)bni_15]i14[0] + [bni_15]i53[3] ≥ 0∧[1 + (-1)bso_16] + [-2]i14[0] + [2]i53[3] ≥ 0)

(31)    (i53[3] + [-1]i14[0] ≥ 0∧[1] + [-2]i14[0] + [2]i53[3] ≥ 0∧[-1] + [-2]i14[0] + [2]i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] + [(-1)bni_15]i14[0] + [bni_15]i53[3] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (30) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(32)    (i53[3] ≥ 0∧[1] + [2]i53[3] ≥ 0∧[-2]i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[3] ≥ 0∧[1 + (-1)bso_16] + [2]i53[3] ≥ 0)

We simplified constraint (31) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(33)    (i53[3] ≥ 0∧[1] + [2]i53[3] ≥ 0∧[-1] + [2]i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[3] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (32) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(34)    (0 ≥ 0∧[1] ≥ 0∧0 ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(35)    (0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧i14[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

(36)    (0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧i14[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (33) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(37)    (i53[3] ≥ 0∧[1] + [2]i53[3] ≥ 0∧[-1] + [2]i53[3] ≥ 0∧i14[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[3] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

(38)    (i53[3] ≥ 0∧[1] + [2]i53[3] ≥ 0∧[-1] + [2]i53[3] ≥ 0∧i14[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[3] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (37) using rule (IDP_POLY_GCD) which results in the following new constraint:
(39)    (i53[3] ≥ 0∧i14[0] ≥ 0∧i53[3] ≥ 0∧i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[3] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

We simplified constraint (38) using rule (IDP_POLY_GCD) which results in the following new constraint:
(40)    (i53[3] ≥ 0∧i14[0] ≥ 0∧i53[3] ≥ 0∧i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[3] ≥ 0∧[1 + (-1)bso_16] ≥ 0)

For Pair LOAD1069(i14, i53) → COND_LOAD10691(>(i14, i53), i14, i53) the following chains were created:

We consider the chain LOAD1069(i14[2], i53[2]) → COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2]), COND_LOAD10691(TRUE, i14[3], i53[3]) → LOAD1069(i14[3], +(i53[3], 1)) which results in the following constraint:
(41)    (i14[2]=i14[3]∧i53[2]=i53[3]∧>(i14[2], i53[2])=TRUE ⇒ LOAD1069(i14[2], i53[2])≥NonInfC∧LOAD1069(i14[2], i53[2])≥COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])∧(U^Increasing(COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])), ≥))

We simplified constraint (41) using rule (IV) which results in the following new constraint:
(42)    (>(i14[2], i53[2])=TRUE ⇒ LOAD1069(i14[2], i53[2])≥NonInfC∧LOAD1069(i14[2], i53[2])≥COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])∧(U^Increasing(COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])), ≥))

We simplified constraint (42) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(43)    (i14[2] + [-1] + [-1]i53[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]max{i14[2] + [-1]i53[2], [-1]i14[2] + i53[2]} ≥ 0∧[(-1)bso_18] + max{i14[2] + [-1]i53[2], [-1]i14[2] + i53[2]} + [-1]max{i14[2] + [-1]i53[2], [-1]i14[2] + i53[2]} ≥ 0)

We simplified constraint (43) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(44)    (i14[2] + [-1] + [-1]i53[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]max{i14[2] + [-1]i53[2], [-1]i14[2] + i53[2]} ≥ 0∧[(-1)bso_18] + max{i14[2] + [-1]i53[2], [-1]i14[2] + i53[2]} + [-1]max{i14[2] + [-1]i53[2], [-1]i14[2] + i53[2]} ≥ 0)

We simplified constraint (44) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(45)    (i14[2] + [-1] + [-1]i53[2] ≥ 0∧[2]i14[2] + [-2]i53[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])), ≥)∧[(-1)bni_17 + (-1)Bound*bni_17] + [bni_17]i14[2] + [(-1)bni_17]i53[2] ≥ 0∧[(-1)bso_18] ≥ 0)

We simplified constraint (45) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(46)    (i14[2] ≥ 0∧[2] + [2]i14[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])), ≥)∧[(-1)Bound*bni_17] + [bni_17]i14[2] ≥ 0∧[(-1)bso_18] ≥ 0)

We simplified constraint (46) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(47)    (i14[2] ≥ 0∧[2] + [2]i14[2] ≥ 0∧i53[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])), ≥)∧[(-1)Bound*bni_17] + [bni_17]i14[2] ≥ 0∧[(-1)bso_18] ≥ 0)

(48)    (i14[2] ≥ 0∧[2] + [2]i14[2] ≥ 0∧i53[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])), ≥)∧[(-1)Bound*bni_17] + [bni_17]i14[2] ≥ 0∧[(-1)bso_18] ≥ 0)

We simplified constraint (47) using rule (IDP_POLY_GCD) which results in the following new constraint:
(49)    (i14[2] ≥ 0∧i53[2] ≥ 0∧[1] + i14[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])), ≥)∧[(-1)Bound*bni_17] + [bni_17]i14[2] ≥ 0∧[(-1)bso_18] ≥ 0)

We simplified constraint (48) using rule (IDP_POLY_GCD) which results in the following new constraint:
(50)    (i14[2] ≥ 0∧i53[2] ≥ 0∧[1] + i14[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])), ≥)∧[(-1)Bound*bni_17] + [bni_17]i14[2] ≥ 0∧[(-1)bso_18] ≥ 0)

For Pair COND_LOAD10691(TRUE, i14, i53) → LOAD1069(i14, +(i53, 1)) the following chains were created:

We consider the chain COND_LOAD1069(TRUE, i14[1], i53[1]) → LOAD1069(+(i14[1], 1), i53[1]), LOAD1069(i14[2], i53[2]) → COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2]), COND_LOAD10691(TRUE, i14[3], i53[3]) → LOAD1069(i14[3], +(i53[3], 1)) which results in the following constraint:
(51)    (+(i14[1], 1)=i14[2]∧i53[1]=i53[2]∧i14[2]=i14[3]∧i53[2]=i53[3]∧>(i14[2], i53[2])=TRUE ⇒ COND_LOAD10691(TRUE, i14[3], i53[3])≥NonInfC∧COND_LOAD10691(TRUE, i14[3], i53[3])≥LOAD1069(i14[3], +(i53[3], 1))∧(U^Increasing(LOAD1069(i14[3], +(i53[3], 1))), ≥))

We simplified constraint (51) using rule (III) which results in the following new constraint:
(52)    (>(+(i14[1], 1), i53[2])=TRUE ⇒ COND_LOAD10691(TRUE, +(i14[1], 1), i53[2])≥NonInfC∧COND_LOAD10691(TRUE, +(i14[1], 1), i53[2])≥LOAD1069(+(i14[1], 1), +(i53[2], 1))∧(U^Increasing(LOAD1069(i14[3], +(i53[3], 1))), ≥))

We simplified constraint (52) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(53)    (i14[1] + [-1]i53[2] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3], +(i53[3], 1))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]max{[1] + i14[1] + [-1]i53[2], [-1] + [-1]i14[1] + i53[2]} ≥ 0∧[(-1)bso_20] + max{[1] + i14[1] + [-1]i53[2], [-1] + [-1]i14[1] + i53[2]} + [-1]max{i14[1] + [-1]i53[2], [-1]i14[1] + i53[2]} ≥ 0)

We simplified constraint (53) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(54)    (i14[1] + [-1]i53[2] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3], +(i53[3], 1))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]max{[1] + i14[1] + [-1]i53[2], [-1] + [-1]i14[1] + i53[2]} ≥ 0∧[(-1)bso_20] + max{[1] + i14[1] + [-1]i53[2], [-1] + [-1]i14[1] + i53[2]} + [-1]max{i14[1] + [-1]i53[2], [-1]i14[1] + i53[2]} ≥ 0)

We simplified constraint (54) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(55)    (i14[1] + [-1]i53[2] ≥ 0∧[2] + [2]i14[1] + [-2]i53[2] ≥ 0∧[2]i14[1] + [-2]i53[2] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3], +(i53[3], 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[1] + [(-1)bni_19]i53[2] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (55) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(56)    (i14[1] ≥ 0∧[2] + [2]i14[1] ≥ 0∧[2]i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3], +(i53[3], 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[1] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (56) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(57)    (i14[1] ≥ 0∧[2] + [2]i14[1] ≥ 0∧[2]i14[1] ≥ 0∧i53[2] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3], +(i53[3], 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[1] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

(58)    (i14[1] ≥ 0∧[2] + [2]i14[1] ≥ 0∧[2]i14[1] ≥ 0∧i53[2] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3], +(i53[3], 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[1] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (57) using rule (IDP_POLY_GCD) which results in the following new constraint:
(59)    (i14[1] ≥ 0∧i53[2] ≥ 0∧[1] + i14[1] ≥ 0∧i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3], +(i53[3], 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[1] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (58) using rule (IDP_POLY_GCD) which results in the following new constraint:
(60)    (i14[1] ≥ 0∧i53[2] ≥ 0∧[1] + i14[1] ≥ 0∧i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3], +(i53[3], 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[1] ≥ 0∧[1 + (-1)bso_20] ≥ 0)
We consider the chain COND_LOAD10691(TRUE, i14[3], i53[3]) → LOAD1069(i14[3], +(i53[3], 1)), LOAD1069(i14[2], i53[2]) → COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2]), COND_LOAD10691(TRUE, i14[3], i53[3]) → LOAD1069(i14[3], +(i53[3], 1)) which results in the following constraint:
(61)    (+(i53[3], 1)=i53[2]∧i14[3]=i14[2]∧i14[2]=i14[3]1∧i53[2]=i53[3]1∧>(i14[2], i53[2])=TRUE ⇒ COND_LOAD10691(TRUE, i14[3]1, i53[3]1)≥NonInfC∧COND_LOAD10691(TRUE, i14[3]1, i53[3]1)≥LOAD1069(i14[3]1, +(i53[3]1, 1))∧(U^Increasing(LOAD1069(i14[3]1, +(i53[3]1, 1))), ≥))

We simplified constraint (61) using rule (III) which results in the following new constraint:
(62)    (>(i14[2], +(i53[3], 1))=TRUE ⇒ COND_LOAD10691(TRUE, i14[2], +(i53[3], 1))≥NonInfC∧COND_LOAD10691(TRUE, i14[2], +(i53[3], 1))≥LOAD1069(i14[2], +(+(i53[3], 1), 1))∧(U^Increasing(LOAD1069(i14[3]1, +(i53[3]1, 1))), ≥))

We simplified constraint (62) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(63)    (i14[2] + [-2] + [-1]i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3]1, +(i53[3]1, 1))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]max{[-1] + i14[2] + [-1]i53[3], [1] + [-1]i14[2] + i53[3]} ≥ 0∧[(-1)bso_20] + max{[-1] + i14[2] + [-1]i53[3], [1] + [-1]i14[2] + i53[3]} + [-1]max{[-2] + i14[2] + [-1]i53[3], [2] + [-1]i14[2] + i53[3]} ≥ 0)

We simplified constraint (63) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(64)    (i14[2] + [-2] + [-1]i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3]1, +(i53[3]1, 1))), ≥)∧[(-1)bni_19 + (-1)Bound*bni_19] + [bni_19]max{[-1] + i14[2] + [-1]i53[3], [1] + [-1]i14[2] + i53[3]} ≥ 0∧[(-1)bso_20] + max{[-1] + i14[2] + [-1]i53[3], [1] + [-1]i14[2] + i53[3]} + [-1]max{[-2] + i14[2] + [-1]i53[3], [2] + [-1]i14[2] + i53[3]} ≥ 0)

We simplified constraint (64) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(65)    (i14[2] + [-2] + [-1]i53[3] ≥ 0∧[-2] + [2]i14[2] + [-2]i53[3] ≥ 0∧[-4] + [2]i14[2] + [-2]i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3]1, +(i53[3]1, 1))), ≥)∧[(-2)bni_19 + (-1)Bound*bni_19] + [bni_19]i14[2] + [(-1)bni_19]i53[3] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (65) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(66)    (i14[2] ≥ 0∧[2] + [2]i14[2] ≥ 0∧[2]i14[2] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3]1, +(i53[3]1, 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[2] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (66) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(67)    (i14[2] ≥ 0∧[2] + [2]i14[2] ≥ 0∧[2]i14[2] ≥ 0∧i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3]1, +(i53[3]1, 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[2] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

(68)    (i14[2] ≥ 0∧[2] + [2]i14[2] ≥ 0∧[2]i14[2] ≥ 0∧i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3]1, +(i53[3]1, 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[2] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (67) using rule (IDP_POLY_GCD) which results in the following new constraint:
(69)    (i14[2] ≥ 0∧i53[3] ≥ 0∧[1] + i14[2] ≥ 0∧i14[2] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3]1, +(i53[3]1, 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[2] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

We simplified constraint (68) using rule (IDP_POLY_GCD) which results in the following new constraint:
(70)    (i14[2] ≥ 0∧i53[3] ≥ 0∧[1] + i14[2] ≥ 0∧i14[2] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3]1, +(i53[3]1, 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[2] ≥ 0∧[1 + (-1)bso_20] ≥ 0)

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

LOAD1069(i14, i53) → COND_LOAD1069(<(i14, i53), i14, i53)
- (i53[0] ≥ 0∧i14[0] ≥ 0∧i53[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])), ≥)∧[(-1)Bound*bni_13] + [bni_13]i53[0] ≥ 0∧[(-1)bso_14] ≥ 0)
- (i53[0] ≥ 0∧i14[0] ≥ 0∧i53[0] ≥ 0 ⇒ (U^Increasing(COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])), ≥)∧[(-1)Bound*bni_13] + [bni_13]i53[0] ≥ 0∧[(-1)bso_14] ≥ 0)
COND_LOAD1069(TRUE, i14, i53) → LOAD1069(+(i14, 1), i53)
- (0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
- (0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
- (i53[0] ≥ 0∧i14[1] ≥ 0∧i53[0] ≥ 0∧i53[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
- (i53[0] ≥ 0∧i14[1] ≥ 0∧i53[0] ≥ 0∧i53[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1]1, 1), i53[1]1)), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[0] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
- (0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧i14[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
- (0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧i14[0] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
- (i53[3] ≥ 0∧i14[0] ≥ 0∧i53[3] ≥ 0∧i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[3] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
- (i53[3] ≥ 0∧i14[0] ≥ 0∧i53[3] ≥ 0∧i53[3] ≥ 0 ⇒ (U^Increasing(LOAD1069(+(i14[1], 1), i53[1])), ≥)∧[(-1)Bound*bni_15] + [bni_15]i53[3] ≥ 0∧[1 + (-1)bso_16] ≥ 0)
LOAD1069(i14, i53) → COND_LOAD10691(>(i14, i53), i14, i53)
- (i14[2] ≥ 0∧i53[2] ≥ 0∧[1] + i14[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])), ≥)∧[(-1)Bound*bni_17] + [bni_17]i14[2] ≥ 0∧[(-1)bso_18] ≥ 0)
- (i14[2] ≥ 0∧i53[2] ≥ 0∧[1] + i14[2] ≥ 0 ⇒ (U^Increasing(COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])), ≥)∧[(-1)Bound*bni_17] + [bni_17]i14[2] ≥ 0∧[(-1)bso_18] ≥ 0)
COND_LOAD10691(TRUE, i14, i53) → LOAD1069(i14, +(i53, 1))
- (i14[1] ≥ 0∧i53[2] ≥ 0∧[1] + i14[1] ≥ 0∧i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3], +(i53[3], 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[1] ≥ 0∧[1 + (-1)bso_20] ≥ 0)
- (i14[1] ≥ 0∧i53[2] ≥ 0∧[1] + i14[1] ≥ 0∧i14[1] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3], +(i53[3], 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[1] ≥ 0∧[1 + (-1)bso_20] ≥ 0)
- (i14[2] ≥ 0∧i53[3] ≥ 0∧[1] + i14[2] ≥ 0∧i14[2] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3]1, +(i53[3]1, 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[2] ≥ 0∧[1 + (-1)bso_20] ≥ 0)
- (i14[2] ≥ 0∧i53[3] ≥ 0∧[1] + i14[2] ≥ 0∧i14[2] ≥ 0 ⇒ (U^Increasing(LOAD1069(i14[3]1, +(i53[3]1, 1))), ≥)∧[(-1)Bound*bni_19] + [bni_19]i14[2] ≥ 0∧[1 + (-1)bso_20] ≥ 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(LOAD1069(x₁, x₂)) = [-1] + max{x₁ + [-1]x₂, [-1]x₁ + x₂}
POL(COND_LOAD1069(x₁, x₂, x₃)) = [-1] + max{x₂ + [-1]x₃, [-1]x₂ + x₃}
POL(<(x₁, x₂)) = [-1]
POL(+(x₁, x₂)) = x₁ + x₂
POL(1) = [1]
POL(COND_LOAD10691(x₁, x₂, x₃)) = [-1] + max{x₂ + [-1]x₃, [-1]x₂ + x₃}
POL(>(x₁, x₂)) = [-1]

The following pairs are in P_>:

COND_LOAD1069(TRUE, i14[1], i53[1]) → LOAD1069(+(i14[1], 1), i53[1])
COND_LOAD10691(TRUE, i14[3], i53[3]) → LOAD1069(i14[3], +(i53[3], 1))

The following pairs are in P_bound:

LOAD1069(i14[0], i53[0]) → COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])
COND_LOAD1069(TRUE, i14[1], i53[1]) → LOAD1069(+(i14[1], 1), i53[1])
LOAD1069(i14[2], i53[2]) → COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[2])
COND_LOAD10691(TRUE, i14[3], i53[3]) → LOAD1069(i14[3], +(i53[3], 1))

The following pairs are in P_≥:

LOAD1069(i14[0], i53[0]) → COND_LOAD1069(<(i14[0], i53[0]), i14[0], i53[0])
LOAD1069(i14[2], i53[2]) → COND_LOAD10691(>(i14[2], i53[2]), i14[2], i53[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:

Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1069(i14[0], i53[0]) → COND_LOAD1069(i14[0] < i53[0], i14[0], i53[0])
(2): LOAD1069(i14[2], i53[2]) → COND_LOAD10691(i14[2] > i53[2], i14[2], i53[2])

The set Q consists of the following terms:
Load1069(x0, x1)
Cond_Load1069(TRUE, x0, x1)
Cond_Load10691(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:
Load1069(x0, x1)
Cond_Load1069(TRUE, x0, x1)
Cond_Load10691(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