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 IDP
        ↳14 IDPNonInfProof (⇐)
        ↳15 AND
            ↳16 IDP
                ↳17 IDependencyGraphProof (⇔)
                ↳18 IDP
                ↳19 IDPNonInfProof (⇐)
                ↳20 AND
                    ↳21 IDP
                        ↳22 IDependencyGraphProof (⇔)
                        ↳23 TRUE
                    ↳24 IDP
                        ↳25 IDependencyGraphProof (⇔)
                        ↳26 TRUE
            ↳27 IDP
                ↳28 IDependencyGraphProof (⇔)
                ↳29 TRUE
    ↳30 IDP
        ↳31 IDependencyGraphProof (⇔)
        ↳32 IDP
        ↳33 IDPNonInfProof (⇐)
        ↳34 AND
            ↳35 IDP
                ↳36 IDependencyGraphProof (⇔)
                ↳37 IDP
                ↳38 IDPNonInfProof (⇐)
                ↳39 AND
                    ↳40 IDP
                        ↳41 IDependencyGraphProof (⇔)
                        ↳42 TRUE
                    ↳43 IDP
                        ↳44 IDependencyGraphProof (⇔)
                        ↳45 TRUE
            ↳46 IDP
                ↳47 IDependencyGraphProof (⇔)
                ↳48 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaB13 
/**
 * 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 PastaB13 {
    public static void main(String[] args) {
        Random.args = args;
        int x = Random.random();
        int y = Random.random();
        int z = Random.random();

        while (x > z || y > z) {
            if (x > z) {
                x--;
            } else if (y > z) {
                y--;
            } else {
                continue;
            }
        }
    }
}


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 265 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:
Load1328(i14, i29, i59) → Cond_Load1328(i29 > i59 && i14 <= i59, i14, i29, i59)
Cond_Load1328(TRUE, i14, i29, i59) → Load1411(i14, i29, i59)
Load1411(i14, i29, i59) → Cond_Load1411(i29 <= i59 && i14 <= i59, i14, i29, i59)
Cond_Load1411(TRUE, i14, i29, i59) → Load1328(i14, i29, i59)
Load1328(i14, i29, i59) → Cond_Load13281(i29 <= i59 && i14 <= i59 && i14 > i59, i14, i29, i59)
Cond_Load13281(TRUE, i14, i29, i59) → Load1328(i14, i29, i59)
Load1411(i14, i29, i59) → Cond_Load14111(i29 > i59 && i14 <= i59, i14, i29, i59)
Cond_Load14111(TRUE, i14, i29, i59) → Load1328(i14, i29 + -1, i59)
Load1328(i14, i29, i59) → Cond_Load13282(i29 > i59 && i14 <= i59 && i14 > i59, i14, i29, i59)
Cond_Load13282(TRUE, i14, i29, i59) → Load1328(i14, i29 + -1, i59)
Load1411(i14, i29, i59) → Cond_Load14112(i14 > i59, i14, i29, i59)
Cond_Load14112(TRUE, i14, i29, i59) → Load1328(i14 + -1, i29, i59)
Load1328(i14, i29, i59) → Cond_Load13283(i14 > i59, i14, i29, i59)
Cond_Load13283(TRUE, i14, i29, i59) → Load1328(i14 + -1, i29, i59)
The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(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:
Load1328(i14, i29, i59) → Cond_Load1328(i29 > i59 && i14 <= i59, i14, i29, i59)
Cond_Load1328(TRUE, i14, i29, i59) → Load1411(i14, i29, i59)
Load1411(i14, i29, i59) → Cond_Load1411(i29 <= i59 && i14 <= i59, i14, i29, i59)
Cond_Load1411(TRUE, i14, i29, i59) → Load1328(i14, i29, i59)
Load1328(i14, i29, i59) → Cond_Load13281(i29 <= i59 && i14 <= i59 && i14 > i59, i14, i29, i59)
Cond_Load13281(TRUE, i14, i29, i59) → Load1328(i14, i29, i59)
Load1411(i14, i29, i59) → Cond_Load14111(i29 > i59 && i14 <= i59, i14, i29, i59)
Cond_Load14111(TRUE, i14, i29, i59) → Load1328(i14, i29 + -1, i59)
Load1328(i14, i29, i59) → Cond_Load13282(i29 > i59 && i14 <= i59 && i14 > i59, i14, i29, i59)
Cond_Load13282(TRUE, i14, i29, i59) → Load1328(i14, i29 + -1, i59)
Load1411(i14, i29, i59) → Cond_Load14112(i14 > i59, i14, i29, i59)
Cond_Load14112(TRUE, i14, i29, i59) → Load1328(i14 + -1, i29, i59)
Load1328(i14, i29, i59) → Cond_Load13283(i14 > i59, i14, i29, i59)
Cond_Load13283(TRUE, i14, i29, i59) → Load1328(i14 + -1, i29, i59)

The integer pair graph contains the following rules and edges:
(0): LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(i29[0] > i59[0] && i14[0] <= i59[0], i14[0], i29[0], i59[0])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
(4): LOAD1328(i14[4], i29[4], i59[4]) → COND_LOAD13281(i29[4] <= i59[4] && i14[4] <= i59[4] && i14[4] > i59[4], i14[4], i29[4], i59[4])
(5): COND_LOAD13281(TRUE, i14[5], i29[5], i59[5]) → LOAD1328(i14[5], i29[5], i59[5])
(6): LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(i29[6] > i59[6] && i14[6] <= i59[6], i14[6], i29[6], i59[6])
(7): COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], i29[7] + -1, i59[7])
(8): LOAD1328(i14[8], i29[8], i59[8]) → COND_LOAD13282(i29[8] > i59[8] && i14[8] <= i59[8] && i14[8] > i59[8], i14[8], i29[8], i59[8])
(9): COND_LOAD13282(TRUE, i14[9], i29[9], i59[9]) → LOAD1328(i14[9], i29[9] + -1, i59[9])
(10): LOAD1411(i14[10], i29[10], i59[10]) → COND_LOAD14112(i14[10] > i59[10], i14[10], i29[10], i59[10])
(11): COND_LOAD14112(TRUE, i14[11], i29[11], i59[11]) → LOAD1328(i14[11] + -1, i29[11], i59[11])
(12): LOAD1328(i14[12], i29[12], i59[12]) → COND_LOAD13283(i14[12] > i59[12], i14[12], i29[12], i59[12])
(13): COND_LOAD13283(TRUE, i14[13], i29[13], i59[13]) → LOAD1328(i14[13] + -1, i29[13], i59[13])

(0) -> (1), if ((i29[0] →* i29[1])∧(i29[0] > i59[0] && i14[0] <= i59[0] →* TRUE)∧(i59[0] →* i59[1])∧(i14[0] →* i14[1]))


(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(1) -> (6), if ((i14[1] →* i14[6])∧(i59[1] →* i59[6])∧(i29[1] →* i29[6]))


(1) -> (10), if ((i29[1] →* i29[10])∧(i14[1] →* i14[10])∧(i59[1] →* i59[10]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))


(3) -> (0), if ((i59[3] →* i59[0])∧(i29[3] →* i29[0])∧(i14[3] →* i14[0]))


(3) -> (4), if ((i14[3] →* i14[4])∧(i29[3] →* i29[4])∧(i59[3] →* i59[4]))


(3) -> (8), if ((i14[3] →* i14[8])∧(i29[3] →* i29[8])∧(i59[3] →* i59[8]))


(3) -> (12), if ((i29[3] →* i29[12])∧(i14[3] →* i14[12])∧(i59[3] →* i59[12]))


(4) -> (5), if ((i29[4] →* i29[5])∧(i29[4] <= i59[4] && i14[4] <= i59[4] && i14[4] > i59[4] →* TRUE)∧(i59[4] →* i59[5])∧(i14[4] →* i14[5]))


(5) -> (0), if ((i59[5] →* i59[0])∧(i14[5] →* i14[0])∧(i29[5] →* i29[0]))


(5) -> (4), if ((i29[5] →* i29[4])∧(i14[5] →* i14[4])∧(i59[5] →* i59[4]))


(5) -> (8), if ((i14[5] →* i14[8])∧(i29[5] →* i29[8])∧(i59[5] →* i59[8]))


(5) -> (12), if ((i29[5] →* i29[12])∧(i59[5] →* i59[12])∧(i14[5] →* i14[12]))


(6) -> (7), if ((i59[6] →* i59[7])∧(i29[6] > i59[6] && i14[6] <= i59[6] →* TRUE)∧(i29[6] →* i29[7])∧(i14[6] →* i14[7]))


(7) -> (0), if ((i59[7] →* i59[0])∧(i29[7] + -1 →* i29[0])∧(i14[7] →* i14[0]))


(7) -> (4), if ((i59[7] →* i59[4])∧(i29[7] + -1 →* i29[4])∧(i14[7] →* i14[4]))


(7) -> (8), if ((i14[7] →* i14[8])∧(i59[7] →* i59[8])∧(i29[7] + -1 →* i29[8]))


(7) -> (12), if ((i29[7] + -1 →* i29[12])∧(i14[7] →* i14[12])∧(i59[7] →* i59[12]))


(8) -> (9), if ((i29[8] →* i29[9])∧(i14[8] →* i14[9])∧(i29[8] > i59[8] && i14[8] <= i59[8] && i14[8] > i59[8] →* TRUE)∧(i59[8] →* i59[9]))


(9) -> (0), if ((i59[9] →* i59[0])∧(i29[9] + -1 →* i29[0])∧(i14[9] →* i14[0]))


(9) -> (4), if ((i14[9] →* i14[4])∧(i29[9] + -1 →* i29[4])∧(i59[9] →* i59[4]))


(9) -> (8), if ((i29[9] + -1 →* i29[8])∧(i14[9] →* i14[8])∧(i59[9] →* i59[8]))


(9) -> (12), if ((i59[9] →* i59[12])∧(i14[9] →* i14[12])∧(i29[9] + -1 →* i29[12]))


(10) -> (11), if ((i14[10] →* i14[11])∧(i14[10] > i59[10] →* TRUE)∧(i59[10] →* i59[11])∧(i29[10] →* i29[11]))


(11) -> (0), if ((i29[11] →* i29[0])∧(i14[11] + -1 →* i14[0])∧(i59[11] →* i59[0]))


(11) -> (4), if ((i59[11] →* i59[4])∧(i29[11] →* i29[4])∧(i14[11] + -1 →* i14[4]))


(11) -> (8), if ((i29[11] →* i29[8])∧(i14[11] + -1 →* i14[8])∧(i59[11] →* i59[8]))


(11) -> (12), if ((i59[11] →* i59[12])∧(i14[11] + -1 →* i14[12])∧(i29[11] →* i29[12]))


(12) -> (13), if ((i14[12] > i59[12] →* TRUE)∧(i59[12] →* i59[13])∧(i29[12] →* i29[13])∧(i14[12] →* i14[13]))


(13) -> (0), if ((i59[13] →* i59[0])∧(i29[13] →* i29[0])∧(i14[13] + -1 →* i14[0]))


(13) -> (4), if ((i29[13] →* i29[4])∧(i59[13] →* i59[4])∧(i14[13] + -1 →* i14[4]))


(13) -> (8), if ((i14[13] + -1 →* i14[8])∧(i29[13] →* i29[8])∧(i59[13] →* i59[8]))


(13) -> (12), if ((i59[13] →* i59[12])∧(i14[13] + -1 →* i14[12])∧(i29[13] →* i29[12]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(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): LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(i29[0] > i59[0] && i14[0] <= i59[0], i14[0], i29[0], i59[0])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
(4): LOAD1328(i14[4], i29[4], i59[4]) → COND_LOAD13281(i29[4] <= i59[4] && i14[4] <= i59[4] && i14[4] > i59[4], i14[4], i29[4], i59[4])
(5): COND_LOAD13281(TRUE, i14[5], i29[5], i59[5]) → LOAD1328(i14[5], i29[5], i59[5])
(6): LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(i29[6] > i59[6] && i14[6] <= i59[6], i14[6], i29[6], i59[6])
(7): COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], i29[7] + -1, i59[7])
(8): LOAD1328(i14[8], i29[8], i59[8]) → COND_LOAD13282(i29[8] > i59[8] && i14[8] <= i59[8] && i14[8] > i59[8], i14[8], i29[8], i59[8])
(9): COND_LOAD13282(TRUE, i14[9], i29[9], i59[9]) → LOAD1328(i14[9], i29[9] + -1, i59[9])
(10): LOAD1411(i14[10], i29[10], i59[10]) → COND_LOAD14112(i14[10] > i59[10], i14[10], i29[10], i59[10])
(11): COND_LOAD14112(TRUE, i14[11], i29[11], i59[11]) → LOAD1328(i14[11] + -1, i29[11], i59[11])
(12): LOAD1328(i14[12], i29[12], i59[12]) → COND_LOAD13283(i14[12] > i59[12], i14[12], i29[12], i59[12])
(13): COND_LOAD13283(TRUE, i14[13], i29[13], i59[13]) → LOAD1328(i14[13] + -1, i29[13], i59[13])

(0) -> (1), if ((i29[0] →* i29[1])∧(i29[0] > i59[0] && i14[0] <= i59[0] →* TRUE)∧(i59[0] →* i59[1])∧(i14[0] →* i14[1]))


(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(1) -> (6), if ((i14[1] →* i14[6])∧(i59[1] →* i59[6])∧(i29[1] →* i29[6]))


(1) -> (10), if ((i29[1] →* i29[10])∧(i14[1] →* i14[10])∧(i59[1] →* i59[10]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))


(3) -> (0), if ((i59[3] →* i59[0])∧(i29[3] →* i29[0])∧(i14[3] →* i14[0]))


(3) -> (4), if ((i14[3] →* i14[4])∧(i29[3] →* i29[4])∧(i59[3] →* i59[4]))


(3) -> (8), if ((i14[3] →* i14[8])∧(i29[3] →* i29[8])∧(i59[3] →* i59[8]))


(3) -> (12), if ((i29[3] →* i29[12])∧(i14[3] →* i14[12])∧(i59[3] →* i59[12]))


(4) -> (5), if ((i29[4] →* i29[5])∧(i29[4] <= i59[4] && i14[4] <= i59[4] && i14[4] > i59[4] →* TRUE)∧(i59[4] →* i59[5])∧(i14[4] →* i14[5]))


(5) -> (0), if ((i59[5] →* i59[0])∧(i14[5] →* i14[0])∧(i29[5] →* i29[0]))


(5) -> (4), if ((i29[5] →* i29[4])∧(i14[5] →* i14[4])∧(i59[5] →* i59[4]))


(5) -> (8), if ((i14[5] →* i14[8])∧(i29[5] →* i29[8])∧(i59[5] →* i59[8]))


(5) -> (12), if ((i29[5] →* i29[12])∧(i59[5] →* i59[12])∧(i14[5] →* i14[12]))


(6) -> (7), if ((i59[6] →* i59[7])∧(i29[6] > i59[6] && i14[6] <= i59[6] →* TRUE)∧(i29[6] →* i29[7])∧(i14[6] →* i14[7]))


(7) -> (0), if ((i59[7] →* i59[0])∧(i29[7] + -1 →* i29[0])∧(i14[7] →* i14[0]))


(7) -> (4), if ((i59[7] →* i59[4])∧(i29[7] + -1 →* i29[4])∧(i14[7] →* i14[4]))


(7) -> (8), if ((i14[7] →* i14[8])∧(i59[7] →* i59[8])∧(i29[7] + -1 →* i29[8]))


(7) -> (12), if ((i29[7] + -1 →* i29[12])∧(i14[7] →* i14[12])∧(i59[7] →* i59[12]))


(8) -> (9), if ((i29[8] →* i29[9])∧(i14[8] →* i14[9])∧(i29[8] > i59[8] && i14[8] <= i59[8] && i14[8] > i59[8] →* TRUE)∧(i59[8] →* i59[9]))


(9) -> (0), if ((i59[9] →* i59[0])∧(i29[9] + -1 →* i29[0])∧(i14[9] →* i14[0]))


(9) -> (4), if ((i14[9] →* i14[4])∧(i29[9] + -1 →* i29[4])∧(i59[9] →* i59[4]))


(9) -> (8), if ((i29[9] + -1 →* i29[8])∧(i14[9] →* i14[8])∧(i59[9] →* i59[8]))


(9) -> (12), if ((i59[9] →* i59[12])∧(i14[9] →* i14[12])∧(i29[9] + -1 →* i29[12]))


(10) -> (11), if ((i14[10] →* i14[11])∧(i14[10] > i59[10] →* TRUE)∧(i59[10] →* i59[11])∧(i29[10] →* i29[11]))


(11) -> (0), if ((i29[11] →* i29[0])∧(i14[11] + -1 →* i14[0])∧(i59[11] →* i59[0]))


(11) -> (4), if ((i59[11] →* i59[4])∧(i29[11] →* i29[4])∧(i14[11] + -1 →* i14[4]))


(11) -> (8), if ((i29[11] →* i29[8])∧(i14[11] + -1 →* i14[8])∧(i59[11] →* i59[8]))


(11) -> (12), if ((i59[11] →* i59[12])∧(i14[11] + -1 →* i14[12])∧(i29[11] →* i29[12]))


(12) -> (13), if ((i14[12] > i59[12] →* TRUE)∧(i59[12] →* i59[13])∧(i29[12] →* i29[13])∧(i14[12] →* i14[13]))


(13) -> (0), if ((i59[13] →* i59[0])∧(i29[13] →* i29[0])∧(i14[13] + -1 →* i14[0]))


(13) -> (4), if ((i29[13] →* i29[4])∧(i59[13] →* i59[4])∧(i14[13] + -1 →* i14[4]))


(13) -> (8), if ((i14[13] + -1 →* i14[8])∧(i29[13] →* i29[8])∧(i59[13] →* i59[8]))


(13) -> (12), if ((i59[13] →* i59[12])∧(i14[13] + -1 →* i14[12])∧(i29[13] →* i29[12]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(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 LOAD1328(i14, i29, i59) → COND_LOAD1328(&&(>(i29, i59), <=(i14, i59)), i14, i29, i59) the following chains were created:
  • We consider the chain LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]), COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]) which results in the following constraint:

    (1)    (i29[0]=i29[1]∧&&(>(i29[0], i59[0]), <=(i14[0], i59[0]))=TRUE∧i59[0]=i59[1]∧i14[0]=i14[1] ⇒ LOAD1328(i14[0], i29[0], i59[0])≥NonInfC∧LOAD1328(i14[0], i29[0], i59[0])≥COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])∧(UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥))



    We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (2)    (>(i29[0], i59[0])=TRUE∧<=(i14[0], i59[0])=TRUE ⇒ LOAD1328(i14[0], i29[0], i59[0])≥NonInfC∧LOAD1328(i14[0], i29[0], i59[0])≥COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])∧(UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥))



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

    (3)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i59[0] + [bni_49]i14[0] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (4)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i59[0] + [bni_49]i14[0] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (5)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i59[0] + [bni_49]i14[0] ≥ 0∧[(-1)bso_50] ≥ 0)



    We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (6)    (i29[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i59[0] + [bni_49]i14[0] ≥ 0∧[(-1)bso_50] ≥ 0)



    We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (7)    (i29[0] ≥ 0∧i59[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i59[0] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (8)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i59[0] ≥ 0∧[(-1)bso_50] ≥ 0)


    (9)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i59[0] ≥ 0∧[(-1)bso_50] ≥ 0)







For Pair COND_LOAD1328(TRUE, i14, i29, i59) → LOAD1411(i14, i29, i59) the following chains were created:
  • We consider the chain COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]), LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]) which results in the following constraint:

    (10)    (i59[1]=i59[2]∧i14[1]=i14[2]∧i29[1]=i29[2] ⇒ COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



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

    (11)    (COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



    We simplified constraint (11) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (12)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_52] ≥ 0)



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

    (13)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_52] ≥ 0)



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

    (14)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_52] ≥ 0)



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

    (15)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_52] ≥ 0)



  • We consider the chain COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]), LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6]) which results in the following constraint:

    (16)    (i14[1]=i14[6]∧i59[1]=i59[6]∧i29[1]=i29[6] ⇒ COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



    We simplified constraint (16) using rule (IV) which results in the following new constraint:

    (17)    (COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



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

    (18)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_52] ≥ 0)



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

    (19)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_52] ≥ 0)



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

    (20)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_52] ≥ 0)



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

    (21)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_52] ≥ 0)



  • We consider the chain COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]), LOAD1411(i14[10], i29[10], i59[10]) → COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10]) which results in the following constraint:

    (22)    (i29[1]=i29[10]∧i14[1]=i14[10]∧i59[1]=i59[10] ⇒ COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



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

    (23)    (COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



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

    (24)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_52] ≥ 0)



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

    (25)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_52] ≥ 0)



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

    (26)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_52] ≥ 0)



    We simplified constraint (26) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (27)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_52] ≥ 0)







For Pair LOAD1411(i14, i29, i59) → COND_LOAD1411(&&(<=(i29, i59), <=(i14, i59)), i14, i29, i59) the following chains were created:
  • We consider the chain LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]), COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]) which results in the following constraint:

    (28)    (i14[2]=i14[3]∧i59[2]=i59[3]∧&&(<=(i29[2], i59[2]), <=(i14[2], i59[2]))=TRUE∧i29[2]=i29[3] ⇒ LOAD1411(i14[2], i29[2], i59[2])≥NonInfC∧LOAD1411(i14[2], i29[2], i59[2])≥COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])∧(UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥))



    We simplified constraint (28) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (29)    (<=(i29[2], i59[2])=TRUE∧<=(i14[2], i59[2])=TRUE ⇒ LOAD1411(i14[2], i29[2], i59[2])≥NonInfC∧LOAD1411(i14[2], i29[2], i59[2])≥COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])∧(UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥))



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

    (30)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]i59[2] + [bni_53]i14[2] ≥ 0∧[(-1)bso_54] ≥ 0)



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

    (31)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]i59[2] + [bni_53]i14[2] ≥ 0∧[(-1)bso_54] ≥ 0)



    We simplified constraint (31) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (32)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]i59[2] + [bni_53]i14[2] ≥ 0∧[(-1)bso_54] ≥ 0)



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

    (33)    (i59[2] ≥ 0∧i29[2] + i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]i29[2] + [(-1)bni_53]i59[2] + [bni_53]i14[2] ≥ 0∧[(-1)bso_54] ≥ 0)



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

    (34)    (i59[2] ≥ 0∧i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]i14[2] ≥ 0∧[(-1)bso_54] ≥ 0)



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

    (35)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]i14[2] ≥ 0∧[(-1)bso_54] ≥ 0)


    (36)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]i14[2] ≥ 0∧[(-1)bso_54] ≥ 0)







For Pair COND_LOAD1411(TRUE, i14, i29, i59) → LOAD1328(i14, i29, i59) the following chains were created:
  • We consider the chain COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]), LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]) which results in the following constraint:

    (37)    (i59[3]=i59[0]∧i29[3]=i29[0]∧i14[3]=i14[0] ⇒ COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (38)    (COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (39)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_56] ≥ 0)



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

    (40)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_56] ≥ 0)



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

    (41)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_56] ≥ 0)



    We simplified constraint (41) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (42)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_56] ≥ 0)



  • We consider the chain COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]), LOAD1328(i14[4], i29[4], i59[4]) → COND_LOAD13281(&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4])), i14[4], i29[4], i59[4]) which results in the following constraint:

    (43)    (i14[3]=i14[4]∧i29[3]=i29[4]∧i59[3]=i59[4] ⇒ COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (44)    (COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (45)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_56] ≥ 0)



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

    (46)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_56] ≥ 0)



    We simplified constraint (46) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (47)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_56] ≥ 0)



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

    (48)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_56] ≥ 0)



  • We consider the chain COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]), LOAD1328(i14[8], i29[8], i59[8]) → COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8]) which results in the following constraint:

    (49)    (i14[3]=i14[8]∧i29[3]=i29[8]∧i59[3]=i59[8] ⇒ COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (50)    (COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (51)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_56] ≥ 0)



    We simplified constraint (51) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (52)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_56] ≥ 0)



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

    (53)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_56] ≥ 0)



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

    (54)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_56] ≥ 0)



  • We consider the chain COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]), LOAD1328(i14[12], i29[12], i59[12]) → COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12]) which results in the following constraint:

    (55)    (i29[3]=i29[12]∧i14[3]=i14[12]∧i59[3]=i59[12] ⇒ COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (56)    (COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (57)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_56] ≥ 0)



    We simplified constraint (57) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (58)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_56] ≥ 0)



    We simplified constraint (58) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (59)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_56] ≥ 0)



    We simplified constraint (59) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (60)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_56] ≥ 0)







For Pair LOAD1328(i14, i29, i59) → COND_LOAD13281(&&(&&(<=(i29, i59), <=(i14, i59)), >(i14, i59)), i14, i29, i59) the following chains were created:
  • We consider the chain LOAD1328(i14[4], i29[4], i59[4]) → COND_LOAD13281(&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4])), i14[4], i29[4], i59[4]), COND_LOAD13281(TRUE, i14[5], i29[5], i59[5]) → LOAD1328(i14[5], i29[5], i59[5]) which results in the following constraint:

    (61)    (i29[4]=i29[5]∧&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4]))=TRUE∧i59[4]=i59[5]∧i14[4]=i14[5] ⇒ LOAD1328(i14[4], i29[4], i59[4])≥NonInfC∧LOAD1328(i14[4], i29[4], i59[4])≥COND_LOAD13281(&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4])), i14[4], i29[4], i59[4])∧(UIncreasing(COND_LOAD13281(&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4])), i14[4], i29[4], i59[4])), ≥))



    We simplified constraint (61) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (62)    (>(i14[4], i59[4])=TRUE∧<=(i29[4], i59[4])=TRUE∧<=(i14[4], i59[4])=TRUE ⇒ LOAD1328(i14[4], i29[4], i59[4])≥NonInfC∧LOAD1328(i14[4], i29[4], i59[4])≥COND_LOAD13281(&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4])), i14[4], i29[4], i59[4])∧(UIncreasing(COND_LOAD13281(&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4])), i14[4], i29[4], i59[4])), ≥))



    We simplified constraint (62) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (63)    (i14[4] + [-1] + [-1]i59[4] ≥ 0∧i59[4] + [-1]i29[4] ≥ 0∧i59[4] + [-1]i14[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD13281(&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4])), i14[4], i29[4], i59[4])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] + [(-1)bni_57]i59[4] + [bni_57]i14[4] ≥ 0∧[-3 + (-1)bso_58] ≥ 0)



    We simplified constraint (63) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (64)    (i14[4] + [-1] + [-1]i59[4] ≥ 0∧i59[4] + [-1]i29[4] ≥ 0∧i59[4] + [-1]i14[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD13281(&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4])), i14[4], i29[4], i59[4])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] + [(-1)bni_57]i59[4] + [bni_57]i14[4] ≥ 0∧[-3 + (-1)bso_58] ≥ 0)



    We simplified constraint (64) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (65)    (i14[4] + [-1] + [-1]i59[4] ≥ 0∧i59[4] + [-1]i29[4] ≥ 0∧i59[4] + [-1]i14[4] ≥ 0 ⇒ (UIncreasing(COND_LOAD13281(&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4])), i14[4], i29[4], i59[4])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] + [(-1)bni_57]i59[4] + [bni_57]i14[4] ≥ 0∧[-3 + (-1)bso_58] ≥ 0)



    We solved constraint (65) using rule (IDP_SMT_SPLIT).




For Pair COND_LOAD13281(TRUE, i14, i29, i59) → LOAD1328(i14, i29, i59) the following chains were created:
  • We consider the chain COND_LOAD13281(TRUE, i14[5], i29[5], i59[5]) → LOAD1328(i14[5], i29[5], i59[5]), LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]) which results in the following constraint:

    (66)    (i59[5]=i59[0]∧i14[5]=i14[0]∧i29[5]=i29[0] ⇒ COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥NonInfC∧COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥LOAD1328(i14[5], i29[5], i59[5])∧(UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥))



    We simplified constraint (66) using rule (IV) which results in the following new constraint:

    (67)    (COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥NonInfC∧COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥LOAD1328(i14[5], i29[5], i59[5])∧(UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥))



    We simplified constraint (67) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (68)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧[2 + (-1)bso_60] ≥ 0)



    We simplified constraint (68) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (69)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧[2 + (-1)bso_60] ≥ 0)



    We simplified constraint (69) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (70)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧[2 + (-1)bso_60] ≥ 0)



    We simplified constraint (70) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (71)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_60] ≥ 0)



  • We consider the chain COND_LOAD13281(TRUE, i14[5], i29[5], i59[5]) → LOAD1328(i14[5], i29[5], i59[5]), LOAD1328(i14[4], i29[4], i59[4]) → COND_LOAD13281(&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4])), i14[4], i29[4], i59[4]) which results in the following constraint:

    (72)    (i29[5]=i29[4]∧i14[5]=i14[4]∧i59[5]=i59[4] ⇒ COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥NonInfC∧COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥LOAD1328(i14[5], i29[5], i59[5])∧(UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥))



    We simplified constraint (72) using rule (IV) which results in the following new constraint:

    (73)    (COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥NonInfC∧COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥LOAD1328(i14[5], i29[5], i59[5])∧(UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥))



    We simplified constraint (73) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (74)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧[2 + (-1)bso_60] ≥ 0)



    We simplified constraint (74) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (75)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧[2 + (-1)bso_60] ≥ 0)



    We simplified constraint (75) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (76)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧[2 + (-1)bso_60] ≥ 0)



    We simplified constraint (76) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (77)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_60] ≥ 0)



  • We consider the chain COND_LOAD13281(TRUE, i14[5], i29[5], i59[5]) → LOAD1328(i14[5], i29[5], i59[5]), LOAD1328(i14[8], i29[8], i59[8]) → COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8]) which results in the following constraint:

    (78)    (i14[5]=i14[8]∧i29[5]=i29[8]∧i59[5]=i59[8] ⇒ COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥NonInfC∧COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥LOAD1328(i14[5], i29[5], i59[5])∧(UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥))



    We simplified constraint (78) using rule (IV) which results in the following new constraint:

    (79)    (COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥NonInfC∧COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥LOAD1328(i14[5], i29[5], i59[5])∧(UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥))



    We simplified constraint (79) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (80)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧[2 + (-1)bso_60] ≥ 0)



    We simplified constraint (80) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (81)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧[2 + (-1)bso_60] ≥ 0)



    We simplified constraint (81) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (82)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧[2 + (-1)bso_60] ≥ 0)



    We simplified constraint (82) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (83)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_60] ≥ 0)



  • We consider the chain COND_LOAD13281(TRUE, i14[5], i29[5], i59[5]) → LOAD1328(i14[5], i29[5], i59[5]), LOAD1328(i14[12], i29[12], i59[12]) → COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12]) which results in the following constraint:

    (84)    (i29[5]=i29[12]∧i59[5]=i59[12]∧i14[5]=i14[12] ⇒ COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥NonInfC∧COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥LOAD1328(i14[5], i29[5], i59[5])∧(UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥))



    We simplified constraint (84) using rule (IV) which results in the following new constraint:

    (85)    (COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥NonInfC∧COND_LOAD13281(TRUE, i14[5], i29[5], i59[5])≥LOAD1328(i14[5], i29[5], i59[5])∧(UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥))



    We simplified constraint (85) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (86)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧[2 + (-1)bso_60] ≥ 0)



    We simplified constraint (86) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (87)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧[2 + (-1)bso_60] ≥ 0)



    We simplified constraint (87) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (88)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧[2 + (-1)bso_60] ≥ 0)



    We simplified constraint (88) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (89)    ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_60] ≥ 0)







For Pair LOAD1411(i14, i29, i59) → COND_LOAD14111(&&(>(i29, i59), <=(i14, i59)), i14, i29, i59) the following chains were created:
  • We consider the chain LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6]), COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7]) which results in the following constraint:

    (90)    (i59[6]=i59[7]∧&&(>(i29[6], i59[6]), <=(i14[6], i59[6]))=TRUE∧i29[6]=i29[7]∧i14[6]=i14[7] ⇒ LOAD1411(i14[6], i29[6], i59[6])≥NonInfC∧LOAD1411(i14[6], i29[6], i59[6])≥COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])∧(UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥))



    We simplified constraint (90) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (91)    (>(i29[6], i59[6])=TRUE∧<=(i14[6], i59[6])=TRUE ⇒ LOAD1411(i14[6], i29[6], i59[6])≥NonInfC∧LOAD1411(i14[6], i29[6], i59[6])≥COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])∧(UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥))



    We simplified constraint (91) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (92)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [(-1)bni_61]i59[6] + [bni_61]i14[6] ≥ 0∧[(-1)bso_62] ≥ 0)



    We simplified constraint (92) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (93)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [(-1)bni_61]i59[6] + [bni_61]i14[6] ≥ 0∧[(-1)bso_62] ≥ 0)



    We simplified constraint (93) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (94)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [(-1)bni_61]i59[6] + [bni_61]i14[6] ≥ 0∧[(-1)bso_62] ≥ 0)



    We simplified constraint (94) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (95)    (i29[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [(-1)bni_61]i59[6] + [bni_61]i14[6] ≥ 0∧[(-1)bso_62] ≥ 0)



    We simplified constraint (95) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (96)    (i29[6] ≥ 0∧i59[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [(-1)bni_61]i59[6] ≥ 0∧[(-1)bso_62] ≥ 0)



    We simplified constraint (96) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (97)    (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [(-1)bni_61]i59[6] ≥ 0∧[(-1)bso_62] ≥ 0)


    (98)    (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [(-1)bni_61]i59[6] ≥ 0∧[(-1)bso_62] ≥ 0)







For Pair COND_LOAD14111(TRUE, i14, i29, i59) → LOAD1328(i14, +(i29, -1), i59) the following chains were created:
  • We consider the chain LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6]), COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7]) which results in the following constraint:

    (99)    (i59[6]=i59[7]∧&&(>(i29[6], i59[6]), <=(i14[6], i59[6]))=TRUE∧i29[6]=i29[7]∧i14[6]=i14[7] ⇒ COND_LOAD14111(TRUE, i14[7], i29[7], i59[7])≥NonInfC∧COND_LOAD14111(TRUE, i14[7], i29[7], i59[7])≥LOAD1328(i14[7], +(i29[7], -1), i59[7])∧(UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥))



    We simplified constraint (99) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:

    (100)    (>(i29[6], i59[6])=TRUE∧<=(i14[6], i59[6])=TRUE ⇒ COND_LOAD14111(TRUE, i14[6], i29[6], i59[6])≥NonInfC∧COND_LOAD14111(TRUE, i14[6], i29[6], i59[6])≥LOAD1328(i14[6], +(i29[6], -1), i59[6])∧(UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥))



    We simplified constraint (100) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (101)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i59[6] + [bni_63]i14[6] ≥ 0∧[(-1)bso_64] ≥ 0)



    We simplified constraint (101) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (102)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i59[6] + [bni_63]i14[6] ≥ 0∧[(-1)bso_64] ≥ 0)



    We simplified constraint (102) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (103)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i59[6] + [bni_63]i14[6] ≥ 0∧[(-1)bso_64] ≥ 0)



    We simplified constraint (103) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (104)    (i29[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i59[6] + [bni_63]i14[6] ≥ 0∧[(-1)bso_64] ≥ 0)



    We simplified constraint (104) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (105)    (i29[6] ≥ 0∧i59[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i59[6] ≥ 0∧[(-1)bso_64] ≥ 0)



    We simplified constraint (105) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (106)    (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i59[6] ≥ 0∧[(-1)bso_64] ≥ 0)


    (107)    (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i59[6] ≥ 0∧[(-1)bso_64] ≥ 0)







For Pair LOAD1328(i14, i29, i59) → COND_LOAD13282(&&(&&(>(i29, i59), <=(i14, i59)), >(i14, i59)), i14, i29, i59) the following chains were created:
  • We consider the chain LOAD1328(i14[8], i29[8], i59[8]) → COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8]), COND_LOAD13282(TRUE, i14[9], i29[9], i59[9]) → LOAD1328(i14[9], +(i29[9], -1), i59[9]) which results in the following constraint:

    (108)    (i29[8]=i29[9]∧i14[8]=i14[9]∧&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8]))=TRUE∧i59[8]=i59[9] ⇒ LOAD1328(i14[8], i29[8], i59[8])≥NonInfC∧LOAD1328(i14[8], i29[8], i59[8])≥COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8])∧(UIncreasing(COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8])), ≥))



    We simplified constraint (108) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (109)    (>(i14[8], i59[8])=TRUE∧>(i29[8], i59[8])=TRUE∧<=(i14[8], i59[8])=TRUE ⇒ LOAD1328(i14[8], i29[8], i59[8])≥NonInfC∧LOAD1328(i14[8], i29[8], i59[8])≥COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8])∧(UIncreasing(COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8])), ≥))



    We simplified constraint (109) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (110)    (i14[8] + [-1] + [-1]i59[8] ≥ 0∧i29[8] + [-1] + [-1]i59[8] ≥ 0∧i59[8] + [-1]i14[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [(-1)bni_65]i59[8] + [bni_65]i14[8] ≥ 0∧[-1 + (-1)bso_66] + i29[8] + [2]i14[8] ≥ 0)



    We simplified constraint (110) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (111)    (i14[8] + [-1] + [-1]i59[8] ≥ 0∧i29[8] + [-1] + [-1]i59[8] ≥ 0∧i59[8] + [-1]i14[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [(-1)bni_65]i59[8] + [bni_65]i14[8] ≥ 0∧[-1 + (-1)bso_66] + i29[8] + [2]i14[8] ≥ 0)



    We simplified constraint (111) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (112)    (i14[8] + [-1] + [-1]i59[8] ≥ 0∧i29[8] + [-1] + [-1]i59[8] ≥ 0∧i59[8] + [-1]i14[8] ≥ 0 ⇒ (UIncreasing(COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [(-1)bni_65]i59[8] + [bni_65]i14[8] ≥ 0∧[-1 + (-1)bso_66] + i29[8] + [2]i14[8] ≥ 0)



    We solved constraint (112) using rule (IDP_SMT_SPLIT).




For Pair COND_LOAD13282(TRUE, i14, i29, i59) → LOAD1328(i14, +(i29, -1), i59) the following chains were created:
  • We consider the chain LOAD1328(i14[8], i29[8], i59[8]) → COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8]), COND_LOAD13282(TRUE, i14[9], i29[9], i59[9]) → LOAD1328(i14[9], +(i29[9], -1), i59[9]) which results in the following constraint:

    (113)    (i29[8]=i29[9]∧i14[8]=i14[9]∧&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8]))=TRUE∧i59[8]=i59[9] ⇒ COND_LOAD13282(TRUE, i14[9], i29[9], i59[9])≥NonInfC∧COND_LOAD13282(TRUE, i14[9], i29[9], i59[9])≥LOAD1328(i14[9], +(i29[9], -1), i59[9])∧(UIncreasing(LOAD1328(i14[9], +(i29[9], -1), i59[9])), ≥))



    We simplified constraint (113) using rules (III), (IDP_BOOLEAN) which results in the following new constraint:

    (114)    (>(i14[8], i59[8])=TRUE∧>(i29[8], i59[8])=TRUE∧<=(i14[8], i59[8])=TRUE ⇒ COND_LOAD13282(TRUE, i14[8], i29[8], i59[8])≥NonInfC∧COND_LOAD13282(TRUE, i14[8], i29[8], i59[8])≥LOAD1328(i14[8], +(i29[8], -1), i59[8])∧(UIncreasing(LOAD1328(i14[9], +(i29[9], -1), i59[9])), ≥))



    We simplified constraint (114) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (115)    (i14[8] + [-1] + [-1]i59[8] ≥ 0∧i29[8] + [-1] + [-1]i59[8] ≥ 0∧i59[8] + [-1]i14[8] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[9], +(i29[9], -1), i59[9])), ≥)∧[(-1)bni_67 + (-1)Bound*bni_67] + [(-1)bni_67]i59[8] + [(-1)bni_67]i29[8] + [(-1)bni_67]i14[8] ≥ 0∧[(-1)bso_68] + [-1]i29[8] + [-2]i14[8] ≥ 0)



    We simplified constraint (115) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (116)    (i14[8] + [-1] + [-1]i59[8] ≥ 0∧i29[8] + [-1] + [-1]i59[8] ≥ 0∧i59[8] + [-1]i14[8] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[9], +(i29[9], -1), i59[9])), ≥)∧[(-1)bni_67 + (-1)Bound*bni_67] + [(-1)bni_67]i59[8] + [(-1)bni_67]i29[8] + [(-1)bni_67]i14[8] ≥ 0∧[(-1)bso_68] + [-1]i29[8] + [-2]i14[8] ≥ 0)



    We simplified constraint (116) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (117)    (i14[8] + [-1] + [-1]i59[8] ≥ 0∧i29[8] + [-1] + [-1]i59[8] ≥ 0∧i59[8] + [-1]i14[8] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[9], +(i29[9], -1), i59[9])), ≥)∧[(-1)bni_67 + (-1)Bound*bni_67] + [(-1)bni_67]i59[8] + [(-1)bni_67]i29[8] + [(-1)bni_67]i14[8] ≥ 0∧[(-1)bso_68] + [-1]i29[8] + [-2]i14[8] ≥ 0)



    We solved constraint (117) using rule (IDP_SMT_SPLIT).




For Pair LOAD1411(i14, i29, i59) → COND_LOAD14112(>(i14, i59), i14, i29, i59) the following chains were created:
  • We consider the chain LOAD1411(i14[10], i29[10], i59[10]) → COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10]), COND_LOAD14112(TRUE, i14[11], i29[11], i59[11]) → LOAD1328(+(i14[11], -1), i29[11], i59[11]) which results in the following constraint:

    (118)    (i14[10]=i14[11]∧>(i14[10], i59[10])=TRUE∧i59[10]=i59[11]∧i29[10]=i29[11] ⇒ LOAD1411(i14[10], i29[10], i59[10])≥NonInfC∧LOAD1411(i14[10], i29[10], i59[10])≥COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])∧(UIncreasing(COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])), ≥))



    We simplified constraint (118) using rule (IV) which results in the following new constraint:

    (119)    (>(i14[10], i59[10])=TRUE ⇒ LOAD1411(i14[10], i29[10], i59[10])≥NonInfC∧LOAD1411(i14[10], i29[10], i59[10])≥COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])∧(UIncreasing(COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])), ≥))



    We simplified constraint (119) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (120)    (i14[10] + [-1] + [-1]i59[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [(-1)bni_69]i59[10] + [bni_69]i14[10] ≥ 0∧[(-1)bso_70] ≥ 0)



    We simplified constraint (120) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (121)    (i14[10] + [-1] + [-1]i59[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [(-1)bni_69]i59[10] + [bni_69]i14[10] ≥ 0∧[(-1)bso_70] ≥ 0)



    We simplified constraint (121) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (122)    (i14[10] + [-1] + [-1]i59[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [(-1)bni_69]i59[10] + [bni_69]i14[10] ≥ 0∧[(-1)bso_70] ≥ 0)



    We simplified constraint (122) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (123)    (i14[10] + [-1] + [-1]i59[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])), ≥)∧0 = 0∧[(-1)bni_69 + (-1)Bound*bni_69] + [(-1)bni_69]i59[10] + [bni_69]i14[10] ≥ 0∧0 = 0∧[(-1)bso_70] ≥ 0)



    We simplified constraint (123) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (124)    (i14[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])), ≥)∧0 = 0∧[(-1)Bound*bni_69] + [bni_69]i14[10] ≥ 0∧0 = 0∧[(-1)bso_70] ≥ 0)



    We simplified constraint (124) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (125)    (i14[10] ≥ 0∧i59[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])), ≥)∧0 = 0∧[(-1)Bound*bni_69] + [bni_69]i14[10] ≥ 0∧0 = 0∧[(-1)bso_70] ≥ 0)


    (126)    (i14[10] ≥ 0∧i59[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])), ≥)∧0 = 0∧[(-1)Bound*bni_69] + [bni_69]i14[10] ≥ 0∧0 = 0∧[(-1)bso_70] ≥ 0)







For Pair COND_LOAD14112(TRUE, i14, i29, i59) → LOAD1328(+(i14, -1), i29, i59) the following chains were created:
  • We consider the chain LOAD1411(i14[10], i29[10], i59[10]) → COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10]), COND_LOAD14112(TRUE, i14[11], i29[11], i59[11]) → LOAD1328(+(i14[11], -1), i29[11], i59[11]) which results in the following constraint:

    (127)    (i14[10]=i14[11]∧>(i14[10], i59[10])=TRUE∧i59[10]=i59[11]∧i29[10]=i29[11] ⇒ COND_LOAD14112(TRUE, i14[11], i29[11], i59[11])≥NonInfC∧COND_LOAD14112(TRUE, i14[11], i29[11], i59[11])≥LOAD1328(+(i14[11], -1), i29[11], i59[11])∧(UIncreasing(LOAD1328(+(i14[11], -1), i29[11], i59[11])), ≥))



    We simplified constraint (127) using rule (III) which results in the following new constraint:

    (128)    (>(i14[10], i59[10])=TRUE ⇒ COND_LOAD14112(TRUE, i14[10], i29[10], i59[10])≥NonInfC∧COND_LOAD14112(TRUE, i14[10], i29[10], i59[10])≥LOAD1328(+(i14[10], -1), i29[10], i59[10])∧(UIncreasing(LOAD1328(+(i14[11], -1), i29[11], i59[11])), ≥))



    We simplified constraint (128) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (129)    (i14[10] + [-1] + [-1]i59[10] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[11], -1), i29[11], i59[11])), ≥)∧[(-1)bni_71 + (-1)Bound*bni_71] + [(-1)bni_71]i59[10] + [bni_71]i14[10] ≥ 0∧[1 + (-1)bso_72] ≥ 0)



    We simplified constraint (129) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (130)    (i14[10] + [-1] + [-1]i59[10] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[11], -1), i29[11], i59[11])), ≥)∧[(-1)bni_71 + (-1)Bound*bni_71] + [(-1)bni_71]i59[10] + [bni_71]i14[10] ≥ 0∧[1 + (-1)bso_72] ≥ 0)



    We simplified constraint (130) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (131)    (i14[10] + [-1] + [-1]i59[10] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[11], -1), i29[11], i59[11])), ≥)∧[(-1)bni_71 + (-1)Bound*bni_71] + [(-1)bni_71]i59[10] + [bni_71]i14[10] ≥ 0∧[1 + (-1)bso_72] ≥ 0)



    We simplified constraint (131) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (132)    (i14[10] + [-1] + [-1]i59[10] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[11], -1), i29[11], i59[11])), ≥)∧0 = 0∧[(-1)bni_71 + (-1)Bound*bni_71] + [(-1)bni_71]i59[10] + [bni_71]i14[10] ≥ 0∧0 = 0∧[1 + (-1)bso_72] ≥ 0)



    We simplified constraint (132) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (133)    (i14[10] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[11], -1), i29[11], i59[11])), ≥)∧0 = 0∧[(-1)Bound*bni_71] + [bni_71]i14[10] ≥ 0∧0 = 0∧[1 + (-1)bso_72] ≥ 0)



    We simplified constraint (133) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (134)    (i14[10] ≥ 0∧i59[10] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[11], -1), i29[11], i59[11])), ≥)∧0 = 0∧[(-1)Bound*bni_71] + [bni_71]i14[10] ≥ 0∧0 = 0∧[1 + (-1)bso_72] ≥ 0)


    (135)    (i14[10] ≥ 0∧i59[10] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[11], -1), i29[11], i59[11])), ≥)∧0 = 0∧[(-1)Bound*bni_71] + [bni_71]i14[10] ≥ 0∧0 = 0∧[1 + (-1)bso_72] ≥ 0)







For Pair LOAD1328(i14, i29, i59) → COND_LOAD13283(>(i14, i59), i14, i29, i59) the following chains were created:
  • We consider the chain LOAD1328(i14[12], i29[12], i59[12]) → COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12]), COND_LOAD13283(TRUE, i14[13], i29[13], i59[13]) → LOAD1328(+(i14[13], -1), i29[13], i59[13]) which results in the following constraint:

    (136)    (>(i14[12], i59[12])=TRUE∧i59[12]=i59[13]∧i29[12]=i29[13]∧i14[12]=i14[13] ⇒ LOAD1328(i14[12], i29[12], i59[12])≥NonInfC∧LOAD1328(i14[12], i29[12], i59[12])≥COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])∧(UIncreasing(COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])), ≥))



    We simplified constraint (136) using rule (IV) which results in the following new constraint:

    (137)    (>(i14[12], i59[12])=TRUE ⇒ LOAD1328(i14[12], i29[12], i59[12])≥NonInfC∧LOAD1328(i14[12], i29[12], i59[12])≥COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])∧(UIncreasing(COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])), ≥))



    We simplified constraint (137) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (138)    (i14[12] + [-1] + [-1]i59[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])), ≥)∧[(-1)bni_73 + (-1)Bound*bni_73] + [(-1)bni_73]i59[12] + [bni_73]i14[12] ≥ 0∧[(-1)bso_74] ≥ 0)



    We simplified constraint (138) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (139)    (i14[12] + [-1] + [-1]i59[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])), ≥)∧[(-1)bni_73 + (-1)Bound*bni_73] + [(-1)bni_73]i59[12] + [bni_73]i14[12] ≥ 0∧[(-1)bso_74] ≥ 0)



    We simplified constraint (139) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (140)    (i14[12] + [-1] + [-1]i59[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])), ≥)∧[(-1)bni_73 + (-1)Bound*bni_73] + [(-1)bni_73]i59[12] + [bni_73]i14[12] ≥ 0∧[(-1)bso_74] ≥ 0)



    We simplified constraint (140) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (141)    (i14[12] + [-1] + [-1]i59[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])), ≥)∧0 = 0∧[(-1)bni_73 + (-1)Bound*bni_73] + [(-1)bni_73]i59[12] + [bni_73]i14[12] ≥ 0∧0 = 0∧[(-1)bso_74] ≥ 0)



    We simplified constraint (141) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (142)    (i14[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])), ≥)∧0 = 0∧[(-1)Bound*bni_73] + [bni_73]i14[12] ≥ 0∧0 = 0∧[(-1)bso_74] ≥ 0)



    We simplified constraint (142) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (143)    (i14[12] ≥ 0∧i59[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])), ≥)∧0 = 0∧[(-1)Bound*bni_73] + [bni_73]i14[12] ≥ 0∧0 = 0∧[(-1)bso_74] ≥ 0)


    (144)    (i14[12] ≥ 0∧i59[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])), ≥)∧0 = 0∧[(-1)Bound*bni_73] + [bni_73]i14[12] ≥ 0∧0 = 0∧[(-1)bso_74] ≥ 0)







For Pair COND_LOAD13283(TRUE, i14, i29, i59) → LOAD1328(+(i14, -1), i29, i59) the following chains were created:
  • We consider the chain LOAD1328(i14[12], i29[12], i59[12]) → COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12]), COND_LOAD13283(TRUE, i14[13], i29[13], i59[13]) → LOAD1328(+(i14[13], -1), i29[13], i59[13]) which results in the following constraint:

    (145)    (>(i14[12], i59[12])=TRUE∧i59[12]=i59[13]∧i29[12]=i29[13]∧i14[12]=i14[13] ⇒ COND_LOAD13283(TRUE, i14[13], i29[13], i59[13])≥NonInfC∧COND_LOAD13283(TRUE, i14[13], i29[13], i59[13])≥LOAD1328(+(i14[13], -1), i29[13], i59[13])∧(UIncreasing(LOAD1328(+(i14[13], -1), i29[13], i59[13])), ≥))



    We simplified constraint (145) using rule (III) which results in the following new constraint:

    (146)    (>(i14[12], i59[12])=TRUE ⇒ COND_LOAD13283(TRUE, i14[12], i29[12], i59[12])≥NonInfC∧COND_LOAD13283(TRUE, i14[12], i29[12], i59[12])≥LOAD1328(+(i14[12], -1), i29[12], i59[12])∧(UIncreasing(LOAD1328(+(i14[13], -1), i29[13], i59[13])), ≥))



    We simplified constraint (146) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (147)    (i14[12] + [-1] + [-1]i59[12] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[13], -1), i29[13], i59[13])), ≥)∧[(-1)bni_75 + (-1)Bound*bni_75] + [(-1)bni_75]i59[12] + [bni_75]i14[12] ≥ 0∧[1 + (-1)bso_76] ≥ 0)



    We simplified constraint (147) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (148)    (i14[12] + [-1] + [-1]i59[12] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[13], -1), i29[13], i59[13])), ≥)∧[(-1)bni_75 + (-1)Bound*bni_75] + [(-1)bni_75]i59[12] + [bni_75]i14[12] ≥ 0∧[1 + (-1)bso_76] ≥ 0)



    We simplified constraint (148) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (149)    (i14[12] + [-1] + [-1]i59[12] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[13], -1), i29[13], i59[13])), ≥)∧[(-1)bni_75 + (-1)Bound*bni_75] + [(-1)bni_75]i59[12] + [bni_75]i14[12] ≥ 0∧[1 + (-1)bso_76] ≥ 0)



    We simplified constraint (149) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (150)    (i14[12] + [-1] + [-1]i59[12] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[13], -1), i29[13], i59[13])), ≥)∧0 = 0∧[(-1)bni_75 + (-1)Bound*bni_75] + [(-1)bni_75]i59[12] + [bni_75]i14[12] ≥ 0∧0 = 0∧[1 + (-1)bso_76] ≥ 0)



    We simplified constraint (150) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (151)    (i14[12] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[13], -1), i29[13], i59[13])), ≥)∧0 = 0∧[(-1)Bound*bni_75] + [bni_75]i14[12] ≥ 0∧0 = 0∧[1 + (-1)bso_76] ≥ 0)



    We simplified constraint (151) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (152)    (i14[12] ≥ 0∧i59[12] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[13], -1), i29[13], i59[13])), ≥)∧0 = 0∧[(-1)Bound*bni_75] + [bni_75]i14[12] ≥ 0∧0 = 0∧[1 + (-1)bso_76] ≥ 0)


    (153)    (i14[12] ≥ 0∧i59[12] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[13], -1), i29[13], i59[13])), ≥)∧0 = 0∧[(-1)Bound*bni_75] + [bni_75]i14[12] ≥ 0∧0 = 0∧[1 + (-1)bso_76] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD1328(i14, i29, i59) → COND_LOAD1328(&&(>(i29, i59), <=(i14, i59)), i14, i29, i59)
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i59[0] ≥ 0∧[(-1)bso_50] ≥ 0)
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]i59[0] ≥ 0∧[(-1)bso_50] ≥ 0)

  • COND_LOAD1328(TRUE, i14, i29, i59) → LOAD1411(i14, i29, i59)
    • ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_52] ≥ 0)
    • ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_52] ≥ 0)
    • ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_52] ≥ 0)

  • LOAD1411(i14, i29, i59) → COND_LOAD1411(&&(<=(i29, i59), <=(i14, i59)), i14, i29, i59)
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]i14[2] ≥ 0∧[(-1)bso_54] ≥ 0)
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]i14[2] ≥ 0∧[(-1)bso_54] ≥ 0)

  • COND_LOAD1411(TRUE, i14, i29, i59) → LOAD1328(i14, i29, i59)
    • ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_56] ≥ 0)
    • ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_56] ≥ 0)
    • ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_56] ≥ 0)
    • ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_56] ≥ 0)

  • LOAD1328(i14, i29, i59) → COND_LOAD13281(&&(&&(<=(i29, i59), <=(i14, i59)), >(i14, i59)), i14, i29, i59)

  • COND_LOAD13281(TRUE, i14, i29, i59) → LOAD1328(i14, i29, i59)
    • ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_60] ≥ 0)
    • ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_60] ≥ 0)
    • ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_60] ≥ 0)
    • ((UIncreasing(LOAD1328(i14[5], i29[5], i59[5])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[2 + (-1)bso_60] ≥ 0)

  • LOAD1411(i14, i29, i59) → COND_LOAD14111(&&(>(i29, i59), <=(i14, i59)), i14, i29, i59)
    • (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [(-1)bni_61]i59[6] ≥ 0∧[(-1)bso_62] ≥ 0)
    • (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] + [(-1)bni_61]i59[6] ≥ 0∧[(-1)bso_62] ≥ 0)

  • COND_LOAD14111(TRUE, i14, i29, i59) → LOAD1328(i14, +(i29, -1), i59)
    • (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i59[6] ≥ 0∧[(-1)bso_64] ≥ 0)
    • (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [(-1)bni_63]i59[6] ≥ 0∧[(-1)bso_64] ≥ 0)

  • LOAD1328(i14, i29, i59) → COND_LOAD13282(&&(&&(>(i29, i59), <=(i14, i59)), >(i14, i59)), i14, i29, i59)

  • COND_LOAD13282(TRUE, i14, i29, i59) → LOAD1328(i14, +(i29, -1), i59)

  • LOAD1411(i14, i29, i59) → COND_LOAD14112(>(i14, i59), i14, i29, i59)
    • (i14[10] ≥ 0∧i59[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])), ≥)∧0 = 0∧[(-1)Bound*bni_69] + [bni_69]i14[10] ≥ 0∧0 = 0∧[(-1)bso_70] ≥ 0)
    • (i14[10] ≥ 0∧i59[10] ≥ 0 ⇒ (UIncreasing(COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])), ≥)∧0 = 0∧[(-1)Bound*bni_69] + [bni_69]i14[10] ≥ 0∧0 = 0∧[(-1)bso_70] ≥ 0)

  • COND_LOAD14112(TRUE, i14, i29, i59) → LOAD1328(+(i14, -1), i29, i59)
    • (i14[10] ≥ 0∧i59[10] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[11], -1), i29[11], i59[11])), ≥)∧0 = 0∧[(-1)Bound*bni_71] + [bni_71]i14[10] ≥ 0∧0 = 0∧[1 + (-1)bso_72] ≥ 0)
    • (i14[10] ≥ 0∧i59[10] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[11], -1), i29[11], i59[11])), ≥)∧0 = 0∧[(-1)Bound*bni_71] + [bni_71]i14[10] ≥ 0∧0 = 0∧[1 + (-1)bso_72] ≥ 0)

  • LOAD1328(i14, i29, i59) → COND_LOAD13283(>(i14, i59), i14, i29, i59)
    • (i14[12] ≥ 0∧i59[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])), ≥)∧0 = 0∧[(-1)Bound*bni_73] + [bni_73]i14[12] ≥ 0∧0 = 0∧[(-1)bso_74] ≥ 0)
    • (i14[12] ≥ 0∧i59[12] ≥ 0 ⇒ (UIncreasing(COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])), ≥)∧0 = 0∧[(-1)Bound*bni_73] + [bni_73]i14[12] ≥ 0∧0 = 0∧[(-1)bso_74] ≥ 0)

  • COND_LOAD13283(TRUE, i14, i29, i59) → LOAD1328(+(i14, -1), i29, i59)
    • (i14[12] ≥ 0∧i59[12] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[13], -1), i29[13], i59[13])), ≥)∧0 = 0∧[(-1)Bound*bni_75] + [bni_75]i14[12] ≥ 0∧0 = 0∧[1 + (-1)bso_76] ≥ 0)
    • (i14[12] ≥ 0∧i59[12] ≥ 0 ⇒ (UIncreasing(LOAD1328(+(i14[13], -1), i29[13], i59[13])), ≥)∧0 = 0∧[(-1)Bound*bni_75] + [bni_75]i14[12] ≥ 0∧0 = 0∧[1 + (-1)bso_76] ≥ 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) = [3]   
POL(LOAD1328(x1, x2, x3)) = [-1] + [-1]x3 + x1   
POL(COND_LOAD1328(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2   
POL(&&(x1, x2)) = [-1]   
POL(>(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(LOAD1411(x1, x2, x3)) = [-1] + [-1]x3 + x1   
POL(COND_LOAD1411(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2   
POL(COND_LOAD13281(x1, x2, x3, x4)) = [1] + [-1]x4 + x2 + [-1]x1   
POL(COND_LOAD14111(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2   
POL(+(x1, x2)) = x1 + x2   
POL(-1) = [-1]   
POL(COND_LOAD13282(x1, x2, x3, x4)) = [-1] + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1   
POL(COND_LOAD14112(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2   
POL(COND_LOAD13283(x1, x2, x3, x4)) = [-1] + [-1]x4 + x2   

The following pairs are in P>:

LOAD1328(i14[4], i29[4], i59[4]) → COND_LOAD13281(&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4])), i14[4], i29[4], i59[4])
COND_LOAD13281(TRUE, i14[5], i29[5], i59[5]) → LOAD1328(i14[5], i29[5], i59[5])
LOAD1328(i14[8], i29[8], i59[8]) → COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8])
COND_LOAD13282(TRUE, i14[9], i29[9], i59[9]) → LOAD1328(i14[9], +(i29[9], -1), i59[9])
COND_LOAD14112(TRUE, i14[11], i29[11], i59[11]) → LOAD1328(+(i14[11], -1), i29[11], i59[11])
COND_LOAD13283(TRUE, i14[13], i29[13], i59[13]) → LOAD1328(+(i14[13], -1), i29[13], i59[13])

The following pairs are in Pbound:

LOAD1328(i14[4], i29[4], i59[4]) → COND_LOAD13281(&&(&&(<=(i29[4], i59[4]), <=(i14[4], i59[4])), >(i14[4], i59[4])), i14[4], i29[4], i59[4])
LOAD1328(i14[8], i29[8], i59[8]) → COND_LOAD13282(&&(&&(>(i29[8], i59[8]), <=(i14[8], i59[8])), >(i14[8], i59[8])), i14[8], i29[8], i59[8])
COND_LOAD13282(TRUE, i14[9], i29[9], i59[9]) → LOAD1328(i14[9], +(i29[9], -1), i59[9])
LOAD1411(i14[10], i29[10], i59[10]) → COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])
COND_LOAD14112(TRUE, i14[11], i29[11], i59[11]) → LOAD1328(+(i14[11], -1), i29[11], i59[11])
LOAD1328(i14[12], i29[12], i59[12]) → COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])
COND_LOAD13283(TRUE, i14[13], i29[13], i59[13]) → LOAD1328(+(i14[13], -1), i29[13], i59[13])

The following pairs are in P≥:

LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])
COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])
COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])
COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7])
LOAD1411(i14[10], i29[10], i59[10]) → COND_LOAD14112(>(i14[10], i59[10]), i14[10], i29[10], i59[10])
LOAD1328(i14[12], i29[12], i59[12]) → COND_LOAD13283(>(i14[12], i59[12]), i14[12], i29[12], i59[12])

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

TRUE1 → &&(TRUE, TRUE)1
FALSE1 → &&(TRUE, FALSE)1
FALSE1 → &&(FALSE, TRUE)1
FALSE1 → &&(FALSE, FALSE)1

(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): LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(i29[0] > i59[0] && i14[0] <= i59[0], i14[0], i29[0], i59[0])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
(6): LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(i29[6] > i59[6] && i14[6] <= i59[6], i14[6], i29[6], i59[6])
(7): COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], i29[7] + -1, i59[7])
(10): LOAD1411(i14[10], i29[10], i59[10]) → COND_LOAD14112(i14[10] > i59[10], i14[10], i29[10], i59[10])
(12): LOAD1328(i14[12], i29[12], i59[12]) → COND_LOAD13283(i14[12] > i59[12], i14[12], i29[12], i59[12])

(3) -> (0), if ((i59[3] →* i59[0])∧(i29[3] →* i29[0])∧(i14[3] →* i14[0]))


(7) -> (0), if ((i59[7] →* i59[0])∧(i29[7] + -1 →* i29[0])∧(i14[7] →* i14[0]))


(0) -> (1), if ((i29[0] →* i29[1])∧(i29[0] > i59[0] && i14[0] <= i59[0] →* TRUE)∧(i59[0] →* i59[1])∧(i14[0] →* i14[1]))


(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))


(1) -> (6), if ((i14[1] →* i14[6])∧(i59[1] →* i59[6])∧(i29[1] →* i29[6]))


(6) -> (7), if ((i59[6] →* i59[7])∧(i29[6] > i59[6] && i14[6] <= i59[6] →* TRUE)∧(i29[6] →* i29[7])∧(i14[6] →* i14[7]))


(1) -> (10), if ((i29[1] →* i29[10])∧(i14[1] →* i14[10])∧(i59[1] →* i59[10]))


(3) -> (12), if ((i29[3] →* i29[12])∧(i14[3] →* i14[12])∧(i59[3] →* i59[12]))


(7) -> (12), if ((i29[7] + -1 →* i29[12])∧(i14[7] →* i14[12])∧(i59[7] →* i59[12]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(12) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.

(13) 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


R is empty.

The integer pair graph contains the following rules and edges:
(7): COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], i29[7] + -1, i59[7])
(6): LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(i29[6] > i59[6] && i14[6] <= i59[6], i14[6], i29[6], i59[6])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(0): LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(i29[0] > i59[0] && i14[0] <= i59[0], i14[0], i29[0], i59[0])

(3) -> (0), if ((i59[3] →* i59[0])∧(i29[3] →* i29[0])∧(i14[3] →* i14[0]))


(7) -> (0), if ((i59[7] →* i59[0])∧(i29[7] + -1 →* i29[0])∧(i14[7] →* i14[0]))


(0) -> (1), if ((i29[0] →* i29[1])∧(i29[0] > i59[0] && i14[0] <= i59[0] →* TRUE)∧(i59[0] →* i59[1])∧(i14[0] →* i14[1]))


(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))


(1) -> (6), if ((i14[1] →* i14[6])∧(i59[1] →* i59[6])∧(i29[1] →* i29[6]))


(6) -> (7), if ((i59[6] →* i59[7])∧(i29[6] > i59[6] && i14[6] <= i59[6] →* TRUE)∧(i29[6] →* i29[7])∧(i14[6] →* i14[7]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(14) 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_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7]) the following chains were created:
  • We consider the chain LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6]), COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7]), LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]) which results in the following constraint:

    (1)    (i59[6]=i59[7]∧&&(>(i29[6], i59[6]), <=(i14[6], i59[6]))=TRUE∧i29[6]=i29[7]∧i14[6]=i14[7]∧i59[7]=i59[0]∧+(i29[7], -1)=i29[0]∧i14[7]=i14[0] ⇒ COND_LOAD14111(TRUE, i14[7], i29[7], i59[7])≥NonInfC∧COND_LOAD14111(TRUE, i14[7], i29[7], i59[7])≥LOAD1328(i14[7], +(i29[7], -1), i59[7])∧(UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥))



    We simplified constraint (1) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (2)    (>(i29[6], i59[6])=TRUE∧<=(i14[6], i59[6])=TRUE ⇒ COND_LOAD14111(TRUE, i14[6], i29[6], i59[6])≥NonInfC∧COND_LOAD14111(TRUE, i14[6], i29[6], i59[6])≥LOAD1328(i14[6], +(i29[6], -1), i59[6])∧(UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥))



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

    (3)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i59[6] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)



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

    (4)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i59[6] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)



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

    (5)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i59[6] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)



    We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (6)    (i29[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)



    We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (7)    (i29[6] ≥ 0∧i59[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)



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

    (8)    (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)


    (9)    (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)







For Pair LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6]) the following chains were created:
  • We consider the chain LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6]), COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7]) which results in the following constraint:

    (10)    (i59[6]=i59[7]∧&&(>(i29[6], i59[6]), <=(i14[6], i59[6]))=TRUE∧i29[6]=i29[7]∧i14[6]=i14[7] ⇒ LOAD1411(i14[6], i29[6], i59[6])≥NonInfC∧LOAD1411(i14[6], i29[6], i59[6])≥COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])∧(UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥))



    We simplified constraint (10) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (11)    (>(i29[6], i59[6])=TRUE∧<=(i14[6], i59[6])=TRUE ⇒ LOAD1411(i14[6], i29[6], i59[6])≥NonInfC∧LOAD1411(i14[6], i29[6], i59[6])≥COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])∧(UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥))



    We simplified constraint (11) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (12)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i59[6] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (13)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i59[6] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (14)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i59[6] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (15)    (i29[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (16)    (i29[6] ≥ 0∧i59[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)



    We simplified constraint (16) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (17)    (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)


    (18)    (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)







For Pair COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]) the following chains were created:
  • We consider the chain COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]), LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]) which results in the following constraint:

    (19)    (i59[3]=i59[0]∧i29[3]=i29[0]∧i14[3]=i14[0] ⇒ COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (20)    (COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (21)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_34] ≥ 0)



    We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (22)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_34] ≥ 0)



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

    (23)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_34] ≥ 0)



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

    (24)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)







For Pair LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]) the following chains were created:
  • We consider the chain LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]), COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]) which results in the following constraint:

    (25)    (i14[2]=i14[3]∧i59[2]=i59[3]∧&&(<=(i29[2], i59[2]), <=(i14[2], i59[2]))=TRUE∧i29[2]=i29[3] ⇒ LOAD1411(i14[2], i29[2], i59[2])≥NonInfC∧LOAD1411(i14[2], i29[2], i59[2])≥COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])∧(UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥))



    We simplified constraint (25) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (26)    (<=(i29[2], i59[2])=TRUE∧<=(i14[2], i59[2])=TRUE ⇒ LOAD1411(i14[2], i29[2], i59[2])≥NonInfC∧LOAD1411(i14[2], i29[2], i59[2])≥COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])∧(UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥))



    We simplified constraint (26) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (27)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] + [bni_35]i29[2] ≥ 0∧[(-1)bso_36] ≥ 0)



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

    (28)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] + [bni_35]i29[2] ≥ 0∧[(-1)bso_36] ≥ 0)



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

    (29)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] + [bni_35]i29[2] ≥ 0∧[(-1)bso_36] ≥ 0)



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

    (30)    (i59[2] ≥ 0∧i29[2] + i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] ≥ 0∧[(-1)bso_36] ≥ 0)



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

    (31)    (i59[2] ≥ 0∧i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] ≥ 0∧[(-1)bso_36] ≥ 0)



    We simplified constraint (31) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (32)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] ≥ 0∧[(-1)bso_36] ≥ 0)


    (33)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] ≥ 0∧[(-1)bso_36] ≥ 0)







For Pair COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]) the following chains were created:
  • We consider the chain COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]), LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]) which results in the following constraint:

    (34)    (i59[1]=i59[2]∧i14[1]=i14[2]∧i29[1]=i29[2] ⇒ COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



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

    (35)    (COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



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

    (36)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_38] ≥ 0)



    We simplified constraint (36) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (37)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_38] ≥ 0)



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

    (38)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_38] ≥ 0)



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

    (39)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_38] ≥ 0)



  • We consider the chain COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]), LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6]) which results in the following constraint:

    (40)    (i14[1]=i14[6]∧i59[1]=i59[6]∧i29[1]=i29[6] ⇒ COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



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

    (41)    (COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



    We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (42)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_38] ≥ 0)



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

    (43)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_38] ≥ 0)



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

    (44)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_38] ≥ 0)



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

    (45)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_38] ≥ 0)







For Pair LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]) the following chains were created:
  • We consider the chain LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]), COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]) which results in the following constraint:

    (46)    (i29[0]=i29[1]∧&&(>(i29[0], i59[0]), <=(i14[0], i59[0]))=TRUE∧i59[0]=i59[1]∧i14[0]=i14[1] ⇒ LOAD1328(i14[0], i29[0], i59[0])≥NonInfC∧LOAD1328(i14[0], i29[0], i59[0])≥COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])∧(UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥))



    We simplified constraint (46) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (47)    (>(i29[0], i59[0])=TRUE∧<=(i14[0], i59[0])=TRUE ⇒ LOAD1328(i14[0], i29[0], i59[0])≥NonInfC∧LOAD1328(i14[0], i29[0], i59[0])≥COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])∧(UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥))



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

    (48)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i59[0] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)



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

    (49)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i59[0] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)



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

    (50)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i59[0] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)



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

    (51)    (i29[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)



    We simplified constraint (51) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (52)    (i29[0] ≥ 0∧i59[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)



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

    (53)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)


    (54)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7])
    • (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)
    • (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

  • LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])
    • (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)
    • (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)

  • COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
    • ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)

  • LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] ≥ 0∧[(-1)bso_36] ≥ 0)
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] ≥ 0∧[(-1)bso_36] ≥ 0)

  • COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
    • ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_38] ≥ 0)
    • ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_38] ≥ 0)

  • LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 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) = [1]   
POL(COND_LOAD14111(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   
POL(LOAD1328(x1, x2, x3)) = [-1] + [-1]x3 + x2   
POL(+(x1, x2)) = x1 + x2   
POL(-1) = [-1]   
POL(LOAD1411(x1, x2, x3)) = [-1] + [-1]x3 + x2   
POL(&&(x1, x2)) = [-1]   
POL(>(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(COND_LOAD1411(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   
POL(COND_LOAD1328(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   

The following pairs are in P>:

COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7])

The following pairs are in Pbound:

COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7])
LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])
LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])

The following pairs are in P≥:

LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])
COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])
COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])

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

TRUE1 → &&(TRUE, TRUE)1
FALSE1 → &&(TRUE, FALSE)1
FALSE1 → &&(FALSE, TRUE)1
FALSE1 → &&(FALSE, FALSE)1

(15) Complex Obligation (AND)

(16) 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:
(6): LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(i29[6] > i59[6] && i14[6] <= i59[6], i14[6], i29[6], i59[6])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(0): LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(i29[0] > i59[0] && i14[0] <= i59[0], i14[0], i29[0], i59[0])

(3) -> (0), if ((i59[3] →* i59[0])∧(i29[3] →* i29[0])∧(i14[3] →* i14[0]))


(0) -> (1), if ((i29[0] →* i29[1])∧(i29[0] > i59[0] && i14[0] <= i59[0] →* TRUE)∧(i59[0] →* i59[1])∧(i14[0] →* i14[1]))


(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))


(1) -> (6), if ((i14[1] →* i14[6])∧(i59[1] →* i59[6])∧(i29[1] →* i29[6]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(17) IDependencyGraphProof (EQUIVALENT transformation)

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

(18) 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:
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(0): LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(i29[0] > i59[0] && i14[0] <= i59[0], i14[0], i29[0], i59[0])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])

(3) -> (0), if ((i59[3] →* i59[0])∧(i29[3] →* i29[0])∧(i14[3] →* i14[0]))


(0) -> (1), if ((i29[0] →* i29[1])∧(i29[0] > i59[0] && i14[0] <= i59[0] →* TRUE)∧(i59[0] →* i59[1])∧(i14[0] →* i14[1]))


(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(19) 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 LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]) the following chains were created:
  • We consider the chain COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]), LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]), COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]) which results in the following constraint:

    (1)    (i59[1]=i59[2]∧i14[1]=i14[2]∧i29[1]=i29[2]∧i14[2]=i14[3]∧i59[2]=i59[3]∧&&(<=(i29[2], i59[2]), <=(i14[2], i59[2]))=TRUE∧i29[2]=i29[3] ⇒ LOAD1411(i14[2], i29[2], i59[2])≥NonInfC∧LOAD1411(i14[2], i29[2], i59[2])≥COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])∧(UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥))



    We simplified constraint (1) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (2)    (<=(i29[2], i59[2])=TRUE∧<=(i14[2], i59[2])=TRUE ⇒ LOAD1411(i14[2], i29[2], i59[2])≥NonInfC∧LOAD1411(i14[2], i29[2], i59[2])≥COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])∧(UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥))



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

    (3)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)Bound*bni_24] + [(2)bni_24]i59[2] + [(-1)bni_24]i29[2] + [(-1)bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] + [-2]i29[2] ≥ 0)



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

    (4)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)Bound*bni_24] + [(2)bni_24]i59[2] + [(-1)bni_24]i29[2] + [(-1)bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] + [-2]i29[2] ≥ 0)



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

    (5)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)Bound*bni_24] + [(2)bni_24]i59[2] + [(-1)bni_24]i29[2] + [(-1)bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] + [-2]i29[2] ≥ 0)



    We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (6)    (i59[2] ≥ 0∧i29[2] + i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)Bound*bni_24] + [bni_24]i29[2] + [(2)bni_24]i59[2] + [(-1)bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] ≥ 0)



    We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (7)    (i59[2] ≥ 0∧i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)Bound*bni_24] + [bni_24]i59[2] + [bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] ≥ 0)



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

    (8)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)Bound*bni_24] + [bni_24]i59[2] + [bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] ≥ 0)


    (9)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)Bound*bni_24] + [bni_24]i59[2] + [bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] ≥ 0)







For Pair COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]) the following chains were created:
  • We consider the chain LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]), COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]), LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]) which results in the following constraint:

    (10)    (i29[0]=i29[1]∧&&(>(i29[0], i59[0]), <=(i14[0], i59[0]))=TRUE∧i59[0]=i59[1]∧i14[0]=i14[1]∧i59[1]=i59[2]∧i14[1]=i14[2]∧i29[1]=i29[2] ⇒ COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



    We simplified constraint (10) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (11)    (>(i29[0], i59[0])=TRUE∧<=(i14[0], i59[0])=TRUE ⇒ COND_LOAD1328(TRUE, i14[0], i29[0], i59[0])≥NonInfC∧COND_LOAD1328(TRUE, i14[0], i29[0], i59[0])≥LOAD1411(i14[0], i29[0], i59[0])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



    We simplified constraint (11) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (12)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(2)bni_26 + (-1)Bound*bni_26] + [(2)bni_26]i59[0] + [(-1)bni_26]i29[0] + [(-1)bni_26]i14[0] ≥ 0∧[2 + (-1)bso_27] ≥ 0)



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

    (13)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(2)bni_26 + (-1)Bound*bni_26] + [(2)bni_26]i59[0] + [(-1)bni_26]i29[0] + [(-1)bni_26]i14[0] ≥ 0∧[2 + (-1)bso_27] ≥ 0)



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

    (14)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(2)bni_26 + (-1)Bound*bni_26] + [(2)bni_26]i59[0] + [(-1)bni_26]i29[0] + [(-1)bni_26]i14[0] ≥ 0∧[2 + (-1)bso_27] ≥ 0)



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

    (15)    (i29[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[bni_26 + (-1)Bound*bni_26] + [bni_26]i59[0] + [(-1)bni_26]i29[0] + [(-1)bni_26]i14[0] ≥ 0∧[2 + (-1)bso_27] ≥ 0)



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

    (16)    (i29[0] ≥ 0∧i59[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[bni_26 + (-1)Bound*bni_26] + [bni_26]i59[0] + [(-1)bni_26]i29[0] ≥ 0∧[2 + (-1)bso_27] ≥ 0)



    We simplified constraint (16) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (17)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[bni_26 + (-1)Bound*bni_26] + [bni_26]i59[0] + [(-1)bni_26]i29[0] ≥ 0∧[2 + (-1)bso_27] ≥ 0)


    (18)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[bni_26 + (-1)Bound*bni_26] + [bni_26]i59[0] + [(-1)bni_26]i29[0] ≥ 0∧[2 + (-1)bso_27] ≥ 0)







For Pair LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]) the following chains were created:
  • We consider the chain COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]), LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]), COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]) which results in the following constraint:

    (19)    (i59[3]=i59[0]∧i29[3]=i29[0]∧i14[3]=i14[0]∧i29[0]=i29[1]∧&&(>(i29[0], i59[0]), <=(i14[0], i59[0]))=TRUE∧i59[0]=i59[1]∧i14[0]=i14[1] ⇒ LOAD1328(i14[0], i29[0], i59[0])≥NonInfC∧LOAD1328(i14[0], i29[0], i59[0])≥COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])∧(UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥))



    We simplified constraint (19) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (20)    (>(i29[0], i59[0])=TRUE∧<=(i14[0], i59[0])=TRUE ⇒ LOAD1328(i14[0], i29[0], i59[0])≥NonInfC∧LOAD1328(i14[0], i29[0], i59[0])≥COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])∧(UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥))



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

    (21)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]i59[0] + [(2)bni_28]i29[0] + [(-1)bni_28]i14[0] ≥ 0∧[-3 + (-1)bso_29] + [-3]i59[0] + [3]i29[0] ≥ 0)



    We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (22)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]i59[0] + [(2)bni_28]i29[0] + [(-1)bni_28]i14[0] ≥ 0∧[-3 + (-1)bso_29] + [-3]i59[0] + [3]i29[0] ≥ 0)



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

    (23)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]i59[0] + [(2)bni_28]i29[0] + [(-1)bni_28]i14[0] ≥ 0∧[-3 + (-1)bso_29] + [-3]i59[0] + [3]i29[0] ≥ 0)



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

    (24)    (i29[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]i59[0] + [(2)bni_28]i29[0] + [(-1)bni_28]i14[0] ≥ 0∧[(-1)bso_29] + [3]i29[0] ≥ 0)



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

    (25)    (i29[0] ≥ 0∧i59[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]i59[0] + [(2)bni_28]i29[0] ≥ 0∧[(-1)bso_29] + [3]i29[0] ≥ 0)



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

    (26)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]i59[0] + [(2)bni_28]i29[0] ≥ 0∧[(-1)bso_29] + [3]i29[0] ≥ 0)


    (27)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]i59[0] + [(2)bni_28]i29[0] ≥ 0∧[(-1)bso_29] + [3]i29[0] ≥ 0)







For Pair COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]) the following chains were created:
  • We consider the chain LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]), COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]), LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]) which results in the following constraint:

    (28)    (i14[2]=i14[3]∧i59[2]=i59[3]∧&&(<=(i29[2], i59[2]), <=(i14[2], i59[2]))=TRUE∧i29[2]=i29[3]∧i59[3]=i59[0]∧i29[3]=i29[0]∧i14[3]=i14[0] ⇒ COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



    We simplified constraint (28) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (29)    (<=(i29[2], i59[2])=TRUE∧<=(i14[2], i59[2])=TRUE ⇒ COND_LOAD1411(TRUE, i14[2], i29[2], i59[2])≥NonInfC∧COND_LOAD1411(TRUE, i14[2], i29[2], i59[2])≥LOAD1328(i14[2], i29[2], i59[2])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (30)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i29[2] + [(-1)bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] + [-1]i29[2] ≥ 0)



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

    (31)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i29[2] + [(-1)bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] + [-1]i29[2] ≥ 0)



    We simplified constraint (31) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (32)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i29[2] + [(-1)bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] + [-1]i29[2] ≥ 0)



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

    (33)    (i59[2] ≥ 0∧i29[2] + i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i29[2] + [(-1)bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] ≥ 0)



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

    (34)    (i59[2] ≥ 0∧i14[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]i59[2] + [bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] ≥ 0)



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

    (35)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]i59[2] + [bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] ≥ 0)


    (36)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]i59[2] + [bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)Bound*bni_24] + [bni_24]i59[2] + [bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] ≥ 0)
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)Bound*bni_24] + [bni_24]i59[2] + [bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] ≥ 0)

  • COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[bni_26 + (-1)Bound*bni_26] + [bni_26]i59[0] + [(-1)bni_26]i29[0] ≥ 0∧[2 + (-1)bso_27] ≥ 0)
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[bni_26 + (-1)Bound*bni_26] + [bni_26]i59[0] + [(-1)bni_26]i29[0] ≥ 0∧[2 + (-1)bso_27] ≥ 0)

  • LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]i59[0] + [(2)bni_28]i29[0] ≥ 0∧[(-1)bso_29] + [3]i29[0] ≥ 0)
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]i59[0] + [(2)bni_28]i29[0] ≥ 0∧[(-1)bso_29] + [3]i29[0] ≥ 0)

  • COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]i59[2] + [bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] ≥ 0)
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]i59[2] + [bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] ≥ 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) = [1]   
POL(LOAD1411(x1, x2, x3)) = [2]x3 + [-1]x2 + [-1]x1   
POL(COND_LOAD1411(x1, x2, x3, x4)) = [-1] + x3 + [-1]x2 + [-1]x1   
POL(&&(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(COND_LOAD1328(x1, x2, x3, x4)) = [2] + [2]x4 + [-1]x3 + [-1]x2   
POL(LOAD1328(x1, x2, x3)) = [-1] + [-1]x3 + [2]x2 + [-1]x1   
POL(>(x1, x2)) = [-1]   

The following pairs are in P>:

COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])

The following pairs are in Pbound:

LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])
LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])

The following pairs are in P≥:

LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])
LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])
COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])

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

TRUE1 → &&(TRUE, TRUE)1
FALSE1 → &&(TRUE, FALSE)1
FALSE1 → &&(FALSE, TRUE)1
FALSE1 → &&(FALSE, FALSE)1

(20) Complex Obligation (AND)

(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:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(0): LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(i29[0] > i59[0] && i14[0] <= i59[0], i14[0], i29[0], i59[0])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])

(3) -> (0), if ((i59[3] →* i59[0])∧(i29[3] →* i29[0])∧(i14[3] →* i14[0]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(22) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(23) TRUE

(24) 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 contains the following rules and edges:
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])


The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(25) IDependencyGraphProof (EQUIVALENT transformation)

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

(26) TRUE

(27) 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:
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])

(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(28) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(29) TRUE

(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:

Boolean, Integer


R is empty.

The integer pair graph contains the following rules and edges:
(0): LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(i29[0] > i59[0] && i14[0] <= i59[0], i14[0], i29[0], i59[0])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
(5): COND_LOAD13281(TRUE, i14[5], i29[5], i59[5]) → LOAD1328(i14[5], i29[5], i59[5])
(6): LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(i29[6] > i59[6] && i14[6] <= i59[6], i14[6], i29[6], i59[6])
(7): COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], i29[7] + -1, i59[7])

(3) -> (0), if ((i59[3] →* i59[0])∧(i29[3] →* i29[0])∧(i14[3] →* i14[0]))


(5) -> (0), if ((i59[5] →* i59[0])∧(i14[5] →* i14[0])∧(i29[5] →* i29[0]))


(7) -> (0), if ((i59[7] →* i59[0])∧(i29[7] + -1 →* i29[0])∧(i14[7] →* i14[0]))


(0) -> (1), if ((i29[0] →* i29[1])∧(i29[0] > i59[0] && i14[0] <= i59[0] →* TRUE)∧(i59[0] →* i59[1])∧(i14[0] →* i14[1]))


(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))


(1) -> (6), if ((i14[1] →* i14[6])∧(i59[1] →* i59[6])∧(i29[1] →* i29[6]))


(6) -> (7), if ((i59[6] →* i59[7])∧(i29[6] > i59[6] && i14[6] <= i59[6] →* TRUE)∧(i29[6] →* i29[7])∧(i14[6] →* i14[7]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(31) IDependencyGraphProof (EQUIVALENT transformation)

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

(32) 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


R is empty.

The integer pair graph contains the following rules and edges:
(7): COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], i29[7] + -1, i59[7])
(6): LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(i29[6] > i59[6] && i14[6] <= i59[6], i14[6], i29[6], i59[6])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(0): LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(i29[0] > i59[0] && i14[0] <= i59[0], i14[0], i29[0], i59[0])

(3) -> (0), if ((i59[3] →* i59[0])∧(i29[3] →* i29[0])∧(i14[3] →* i14[0]))


(7) -> (0), if ((i59[7] →* i59[0])∧(i29[7] + -1 →* i29[0])∧(i14[7] →* i14[0]))


(0) -> (1), if ((i29[0] →* i29[1])∧(i29[0] > i59[0] && i14[0] <= i59[0] →* TRUE)∧(i59[0] →* i59[1])∧(i14[0] →* i14[1]))


(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))


(1) -> (6), if ((i14[1] →* i14[6])∧(i59[1] →* i59[6])∧(i29[1] →* i29[6]))


(6) -> (7), if ((i59[6] →* i59[7])∧(i29[6] > i59[6] && i14[6] <= i59[6] →* TRUE)∧(i29[6] →* i29[7])∧(i14[6] →* i14[7]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(33) 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_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7]) the following chains were created:
  • We consider the chain LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6]), COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7]), LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]) which results in the following constraint:

    (1)    (i59[6]=i59[7]∧&&(>(i29[6], i59[6]), <=(i14[6], i59[6]))=TRUE∧i29[6]=i29[7]∧i14[6]=i14[7]∧i59[7]=i59[0]∧+(i29[7], -1)=i29[0]∧i14[7]=i14[0] ⇒ COND_LOAD14111(TRUE, i14[7], i29[7], i59[7])≥NonInfC∧COND_LOAD14111(TRUE, i14[7], i29[7], i59[7])≥LOAD1328(i14[7], +(i29[7], -1), i59[7])∧(UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥))



    We simplified constraint (1) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (2)    (>(i29[6], i59[6])=TRUE∧<=(i14[6], i59[6])=TRUE ⇒ COND_LOAD14111(TRUE, i14[6], i29[6], i59[6])≥NonInfC∧COND_LOAD14111(TRUE, i14[6], i29[6], i59[6])≥LOAD1328(i14[6], +(i29[6], -1), i59[6])∧(UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥))



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

    (3)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i59[6] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)



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

    (4)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i59[6] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)



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

    (5)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]i59[6] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)



    We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (6)    (i29[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)



    We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (7)    (i29[6] ≥ 0∧i59[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)



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

    (8)    (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)


    (9)    (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)







For Pair LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6]) the following chains were created:
  • We consider the chain LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6]), COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7]) which results in the following constraint:

    (10)    (i59[6]=i59[7]∧&&(>(i29[6], i59[6]), <=(i14[6], i59[6]))=TRUE∧i29[6]=i29[7]∧i14[6]=i14[7] ⇒ LOAD1411(i14[6], i29[6], i59[6])≥NonInfC∧LOAD1411(i14[6], i29[6], i59[6])≥COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])∧(UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥))



    We simplified constraint (10) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (11)    (>(i29[6], i59[6])=TRUE∧<=(i14[6], i59[6])=TRUE ⇒ LOAD1411(i14[6], i29[6], i59[6])≥NonInfC∧LOAD1411(i14[6], i29[6], i59[6])≥COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])∧(UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥))



    We simplified constraint (11) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (12)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i59[6] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (13)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i59[6] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (14)    (i29[6] + [-1] + [-1]i59[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]i59[6] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (15)    (i29[6] ≥ 0∧i59[6] + [-1]i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)



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

    (16)    (i29[6] ≥ 0∧i59[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)



    We simplified constraint (16) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (17)    (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)


    (18)    (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)







For Pair COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]) the following chains were created:
  • We consider the chain COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]), LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]) which results in the following constraint:

    (19)    (i59[3]=i59[0]∧i29[3]=i29[0]∧i14[3]=i14[0] ⇒ COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (20)    (COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (21)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_34] ≥ 0)



    We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (22)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_34] ≥ 0)



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

    (23)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bso_34] ≥ 0)



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

    (24)    ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)







For Pair LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]) the following chains were created:
  • We consider the chain LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]), COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]) which results in the following constraint:

    (25)    (i14[2]=i14[3]∧i59[2]=i59[3]∧&&(<=(i29[2], i59[2]), <=(i14[2], i59[2]))=TRUE∧i29[2]=i29[3] ⇒ LOAD1411(i14[2], i29[2], i59[2])≥NonInfC∧LOAD1411(i14[2], i29[2], i59[2])≥COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])∧(UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥))



    We simplified constraint (25) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (26)    (<=(i29[2], i59[2])=TRUE∧<=(i14[2], i59[2])=TRUE ⇒ LOAD1411(i14[2], i29[2], i59[2])≥NonInfC∧LOAD1411(i14[2], i29[2], i59[2])≥COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])∧(UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥))



    We simplified constraint (26) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (27)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] + [bni_35]i29[2] ≥ 0∧[(-1)bso_36] ≥ 0)



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

    (28)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] + [bni_35]i29[2] ≥ 0∧[(-1)bso_36] ≥ 0)



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

    (29)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] + [bni_35]i29[2] ≥ 0∧[(-1)bso_36] ≥ 0)



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

    (30)    (i59[2] ≥ 0∧i29[2] + i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] ≥ 0∧[(-1)bso_36] ≥ 0)



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

    (31)    (i59[2] ≥ 0∧i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] ≥ 0∧[(-1)bso_36] ≥ 0)



    We simplified constraint (31) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (32)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] ≥ 0∧[(-1)bso_36] ≥ 0)


    (33)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] ≥ 0∧[(-1)bso_36] ≥ 0)







For Pair COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]) the following chains were created:
  • We consider the chain COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]), LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]) which results in the following constraint:

    (34)    (i59[1]=i59[2]∧i14[1]=i14[2]∧i29[1]=i29[2] ⇒ COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



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

    (35)    (COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



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

    (36)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_38] ≥ 0)



    We simplified constraint (36) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (37)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_38] ≥ 0)



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

    (38)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_38] ≥ 0)



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

    (39)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_38] ≥ 0)



  • We consider the chain COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]), LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6]) which results in the following constraint:

    (40)    (i14[1]=i14[6]∧i59[1]=i59[6]∧i29[1]=i29[6] ⇒ COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



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

    (41)    (COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



    We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (42)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_38] ≥ 0)



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

    (43)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_38] ≥ 0)



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

    (44)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bso_38] ≥ 0)



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

    (45)    ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_38] ≥ 0)







For Pair LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]) the following chains were created:
  • We consider the chain LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]), COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]) which results in the following constraint:

    (46)    (i29[0]=i29[1]∧&&(>(i29[0], i59[0]), <=(i14[0], i59[0]))=TRUE∧i59[0]=i59[1]∧i14[0]=i14[1] ⇒ LOAD1328(i14[0], i29[0], i59[0])≥NonInfC∧LOAD1328(i14[0], i29[0], i59[0])≥COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])∧(UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥))



    We simplified constraint (46) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (47)    (>(i29[0], i59[0])=TRUE∧<=(i14[0], i59[0])=TRUE ⇒ LOAD1328(i14[0], i29[0], i59[0])≥NonInfC∧LOAD1328(i14[0], i29[0], i59[0])≥COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])∧(UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥))



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

    (48)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i59[0] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)



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

    (49)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i59[0] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)



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

    (50)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]i59[0] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)



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

    (51)    (i29[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)



    We simplified constraint (51) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (52)    (i29[0] ≥ 0∧i59[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)



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

    (53)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)


    (54)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7])
    • (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)
    • (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[7], +(i29[7], -1), i59[7])), ≥)∧[(-1)Bound*bni_29] + [bni_29]i29[6] ≥ 0∧[1 + (-1)bso_30] ≥ 0)

  • LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])
    • (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)
    • (i29[6] ≥ 0∧i59[6] ≥ 0∧i14[6] ≥ 0 ⇒ (UIncreasing(COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])), ≥)∧[(-1)Bound*bni_31] + [bni_31]i29[6] ≥ 0∧[(-1)bso_32] ≥ 0)

  • COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
    • ((UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_34] ≥ 0)

  • LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] ≥ 0∧[(-1)bso_36] ≥ 0)
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]i59[2] ≥ 0∧[(-1)bso_36] ≥ 0)

  • COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
    • ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_38] ≥ 0)
    • ((UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_38] ≥ 0)

  • LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 0)
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)Bound*bni_39] + [bni_39]i29[0] ≥ 0∧[(-1)bso_40] ≥ 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(COND_LOAD14111(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   
POL(LOAD1328(x1, x2, x3)) = [-1] + [-1]x3 + x2   
POL(+(x1, x2)) = x1 + x2   
POL(-1) = [-1]   
POL(LOAD1411(x1, x2, x3)) = [-1] + [-1]x3 + x2   
POL(&&(x1, x2)) = [-1]   
POL(>(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(COND_LOAD1411(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   
POL(COND_LOAD1328(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   

The following pairs are in P>:

COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7])

The following pairs are in Pbound:

COND_LOAD14111(TRUE, i14[7], i29[7], i59[7]) → LOAD1328(i14[7], +(i29[7], -1), i59[7])
LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])
LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])

The following pairs are in P≥:

LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(&&(>(i29[6], i59[6]), <=(i14[6], i59[6])), i14[6], i29[6], i59[6])
COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])
COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])

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

FALSE1 → &&(TRUE, FALSE)1
FALSE1 → &&(FALSE, TRUE)1
FALSE1 → &&(FALSE, FALSE)1

(34) Complex Obligation (AND)

(35) 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:
(6): LOAD1411(i14[6], i29[6], i59[6]) → COND_LOAD14111(i29[6] > i59[6] && i14[6] <= i59[6], i14[6], i29[6], i59[6])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(0): LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(i29[0] > i59[0] && i14[0] <= i59[0], i14[0], i29[0], i59[0])

(3) -> (0), if ((i59[3] →* i59[0])∧(i29[3] →* i29[0])∧(i14[3] →* i14[0]))


(0) -> (1), if ((i29[0] →* i29[1])∧(i29[0] > i59[0] && i14[0] <= i59[0] →* TRUE)∧(i59[0] →* i59[1])∧(i14[0] →* i14[1]))


(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))


(1) -> (6), if ((i14[1] →* i14[6])∧(i59[1] →* i59[6])∧(i29[1] →* i29[6]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(36) IDependencyGraphProof (EQUIVALENT transformation)

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

(37) 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:
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(0): LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(i29[0] > i59[0] && i14[0] <= i59[0], i14[0], i29[0], i59[0])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])

(3) -> (0), if ((i59[3] →* i59[0])∧(i29[3] →* i29[0])∧(i14[3] →* i14[0]))


(0) -> (1), if ((i29[0] →* i29[1])∧(i29[0] > i59[0] && i14[0] <= i59[0] →* TRUE)∧(i59[0] →* i59[1])∧(i14[0] →* i14[1]))


(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(38) 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 LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]) the following chains were created:
  • We consider the chain COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]), LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]), COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]) which results in the following constraint:

    (1)    (i59[1]=i59[2]∧i14[1]=i14[2]∧i29[1]=i29[2]∧i14[2]=i14[3]∧i59[2]=i59[3]∧&&(<=(i29[2], i59[2]), <=(i14[2], i59[2]))=TRUE∧i29[2]=i29[3] ⇒ LOAD1411(i14[2], i29[2], i59[2])≥NonInfC∧LOAD1411(i14[2], i29[2], i59[2])≥COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])∧(UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥))



    We simplified constraint (1) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (2)    (<=(i29[2], i59[2])=TRUE∧<=(i14[2], i59[2])=TRUE ⇒ LOAD1411(i14[2], i29[2], i59[2])≥NonInfC∧LOAD1411(i14[2], i29[2], i59[2])≥COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])∧(UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥))



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

    (3)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [(2)bni_24]i59[2] + [(-1)bni_24]i29[2] + [(-1)bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] + [-2]i29[2] ≥ 0)



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

    (4)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [(2)bni_24]i59[2] + [(-1)bni_24]i29[2] + [(-1)bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] + [-2]i29[2] ≥ 0)



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

    (5)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [(2)bni_24]i59[2] + [(-1)bni_24]i29[2] + [(-1)bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] + [-2]i29[2] ≥ 0)



    We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (6)    (i59[2] ≥ 0∧i29[2] + i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i29[2] + [(2)bni_24]i59[2] + [(-1)bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] ≥ 0)



    We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (7)    (i59[2] ≥ 0∧i14[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i59[2] + [bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] ≥ 0)



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

    (8)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i59[2] + [bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] ≥ 0)


    (9)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i59[2] + [bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] ≥ 0)







For Pair COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]) the following chains were created:
  • We consider the chain LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]), COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]), LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]) which results in the following constraint:

    (10)    (i29[0]=i29[1]∧&&(>(i29[0], i59[0]), <=(i14[0], i59[0]))=TRUE∧i59[0]=i59[1]∧i14[0]=i14[1]∧i59[1]=i59[2]∧i14[1]=i14[2]∧i29[1]=i29[2] ⇒ COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥NonInfC∧COND_LOAD1328(TRUE, i14[1], i29[1], i59[1])≥LOAD1411(i14[1], i29[1], i59[1])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



    We simplified constraint (10) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (11)    (>(i29[0], i59[0])=TRUE∧<=(i14[0], i59[0])=TRUE ⇒ COND_LOAD1328(TRUE, i14[0], i29[0], i59[0])≥NonInfC∧COND_LOAD1328(TRUE, i14[0], i29[0], i59[0])≥LOAD1411(i14[0], i29[0], i59[0])∧(UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥))



    We simplified constraint (11) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (12)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(2)bni_26]i59[0] + [(-1)bni_26]i29[0] + [(-1)bni_26]i14[0] ≥ 0∧[(-1)bso_27] ≥ 0)



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

    (13)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(2)bni_26]i59[0] + [(-1)bni_26]i29[0] + [(-1)bni_26]i14[0] ≥ 0∧[(-1)bso_27] ≥ 0)



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

    (14)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(2)bni_26]i59[0] + [(-1)bni_26]i29[0] + [(-1)bni_26]i14[0] ≥ 0∧[(-1)bso_27] ≥ 0)



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

    (15)    (i29[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-2)bni_26 + (-1)Bound*bni_26] + [bni_26]i59[0] + [(-1)bni_26]i29[0] + [(-1)bni_26]i14[0] ≥ 0∧[(-1)bso_27] ≥ 0)



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

    (16)    (i29[0] ≥ 0∧i59[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-2)bni_26 + (-1)Bound*bni_26] + [bni_26]i59[0] + [(-1)bni_26]i29[0] ≥ 0∧[(-1)bso_27] ≥ 0)



    We simplified constraint (16) using rule (IDP_SMT_SPLIT) which results in the following new constraints:

    (17)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-2)bni_26 + (-1)Bound*bni_26] + [bni_26]i59[0] + [(-1)bni_26]i29[0] ≥ 0∧[(-1)bso_27] ≥ 0)


    (18)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-2)bni_26 + (-1)Bound*bni_26] + [bni_26]i59[0] + [(-1)bni_26]i29[0] ≥ 0∧[(-1)bso_27] ≥ 0)







For Pair LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]) the following chains were created:
  • We consider the chain COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]), LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]), COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1]) which results in the following constraint:

    (19)    (i59[3]=i59[0]∧i29[3]=i29[0]∧i14[3]=i14[0]∧i29[0]=i29[1]∧&&(>(i29[0], i59[0]), <=(i14[0], i59[0]))=TRUE∧i59[0]=i59[1]∧i14[0]=i14[1] ⇒ LOAD1328(i14[0], i29[0], i59[0])≥NonInfC∧LOAD1328(i14[0], i29[0], i59[0])≥COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])∧(UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥))



    We simplified constraint (19) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (20)    (>(i29[0], i59[0])=TRUE∧<=(i14[0], i59[0])=TRUE ⇒ LOAD1328(i14[0], i29[0], i59[0])≥NonInfC∧LOAD1328(i14[0], i29[0], i59[0])≥COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])∧(UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥))



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

    (21)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]i59[0] + [(2)bni_28]i29[0] + [(-1)bni_28]i14[0] ≥ 0∧[-1 + (-1)bso_29] + [-3]i59[0] + [3]i29[0] ≥ 0)



    We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (22)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]i59[0] + [(2)bni_28]i29[0] + [(-1)bni_28]i14[0] ≥ 0∧[-1 + (-1)bso_29] + [-3]i59[0] + [3]i29[0] ≥ 0)



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

    (23)    (i29[0] + [-1] + [-1]i59[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[(-1)bni_28 + (-1)Bound*bni_28] + [(-1)bni_28]i59[0] + [(2)bni_28]i29[0] + [(-1)bni_28]i14[0] ≥ 0∧[-1 + (-1)bso_29] + [-3]i59[0] + [3]i29[0] ≥ 0)



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

    (24)    (i29[0] ≥ 0∧i59[0] + [-1]i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]i59[0] + [(2)bni_28]i29[0] + [(-1)bni_28]i14[0] ≥ 0∧[2 + (-1)bso_29] + [3]i29[0] ≥ 0)



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

    (25)    (i29[0] ≥ 0∧i59[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]i59[0] + [(2)bni_28]i29[0] ≥ 0∧[2 + (-1)bso_29] + [3]i29[0] ≥ 0)



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

    (26)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]i59[0] + [(2)bni_28]i29[0] ≥ 0∧[2 + (-1)bso_29] + [3]i29[0] ≥ 0)


    (27)    (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]i59[0] + [(2)bni_28]i29[0] ≥ 0∧[2 + (-1)bso_29] + [3]i29[0] ≥ 0)







For Pair COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]) the following chains were created:
  • We consider the chain LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2]), COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3]), LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0]) which results in the following constraint:

    (28)    (i14[2]=i14[3]∧i59[2]=i59[3]∧&&(<=(i29[2], i59[2]), <=(i14[2], i59[2]))=TRUE∧i29[2]=i29[3]∧i59[3]=i59[0]∧i29[3]=i29[0]∧i14[3]=i14[0] ⇒ COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥NonInfC∧COND_LOAD1411(TRUE, i14[3], i29[3], i59[3])≥LOAD1328(i14[3], i29[3], i59[3])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



    We simplified constraint (28) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (29)    (<=(i29[2], i59[2])=TRUE∧<=(i14[2], i59[2])=TRUE ⇒ COND_LOAD1411(TRUE, i14[2], i29[2], i59[2])≥NonInfC∧COND_LOAD1411(TRUE, i14[2], i29[2], i59[2])≥LOAD1328(i14[2], i29[2], i59[2])∧(UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥))



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

    (30)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i29[2] + [(-1)bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] + [-1]i29[2] ≥ 0)



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

    (31)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i29[2] + [(-1)bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] + [-1]i29[2] ≥ 0)



    We simplified constraint (31) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (32)    (i59[2] + [-1]i29[2] ≥ 0∧i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i29[2] + [(-1)bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] + [-1]i29[2] ≥ 0)



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

    (33)    (i59[2] ≥ 0∧i29[2] + i59[2] + [-1]i14[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [bni_30]i29[2] + [(-1)bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] ≥ 0)



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

    (34)    (i59[2] ≥ 0∧i14[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]i59[2] + [bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] ≥ 0)



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

    (35)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]i59[2] + [bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] ≥ 0)


    (36)    (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]i59[2] + [bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i59[2] + [bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] ≥ 0)
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [bni_24]i59[2] + [bni_24]i14[2] ≥ 0∧[(-1)bso_25] + [2]i59[2] ≥ 0)

  • COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-2)bni_26 + (-1)Bound*bni_26] + [bni_26]i59[0] + [(-1)bni_26]i29[0] ≥ 0∧[(-1)bso_27] ≥ 0)
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(LOAD1411(i14[1], i29[1], i59[1])), ≥)∧[(-2)bni_26 + (-1)Bound*bni_26] + [bni_26]i59[0] + [(-1)bni_26]i29[0] ≥ 0∧[(-1)bso_27] ≥ 0)

  • LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]i59[0] + [(2)bni_28]i29[0] ≥ 0∧[2 + (-1)bso_29] + [3]i29[0] ≥ 0)
    • (i29[0] ≥ 0∧i59[0] ≥ 0∧i14[0] ≥ 0 ⇒ (UIncreasing(COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])), ≥)∧[bni_28 + (-1)Bound*bni_28] + [bni_28]i59[0] + [(2)bni_28]i29[0] ≥ 0∧[2 + (-1)bso_29] + [3]i29[0] ≥ 0)

  • COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]i59[2] + [bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] ≥ 0)
    • (i59[2] ≥ 0∧i14[2] ≥ 0∧i29[2] ≥ 0 ⇒ (UIncreasing(LOAD1328(i14[3], i29[3], i59[3])), ≥)∧[(-1)bni_30 + (-1)Bound*bni_30] + [(-1)bni_30]i59[2] + [bni_30]i14[2] ≥ 0∧[(-1)bso_31] + i59[2] ≥ 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(LOAD1411(x1, x2, x3)) = [-1] + [2]x3 + [-1]x2 + [-1]x1   
POL(COND_LOAD1411(x1, x2, x3, x4)) = [-1] + x3 + [-1]x2   
POL(&&(x1, x2)) = [-1]   
POL(<=(x1, x2)) = [-1]   
POL(COND_LOAD1328(x1, x2, x3, x4)) = [-1] + [2]x4 + [-1]x3 + [-1]x2 + [-1]x1   
POL(LOAD1328(x1, x2, x3)) = [-1] + [-1]x3 + [2]x2 + [-1]x1   
POL(>(x1, x2)) = [-1]   

The following pairs are in P>:

LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])

The following pairs are in Pbound:

LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])
LOAD1328(i14[0], i29[0], i59[0]) → COND_LOAD1328(&&(>(i29[0], i59[0]), <=(i14[0], i59[0])), i14[0], i29[0], i59[0])

The following pairs are in P≥:

LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(&&(<=(i29[2], i59[2]), <=(i14[2], i59[2])), i14[2], i29[2], i59[2])
COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])

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

TRUE1 → &&(TRUE, TRUE)1
FALSE1 → &&(TRUE, FALSE)1
FALSE1 → &&(FALSE, TRUE)1
FALSE1 → &&(FALSE, FALSE)1

(39) Complex Obligation (AND)

(40) 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:
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])

(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(41) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(42) TRUE

(43) 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 contains the following rules and edges:
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])


The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(44) IDependencyGraphProof (EQUIVALENT transformation)

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

(45) TRUE

(46) 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:
(3): COND_LOAD1411(TRUE, i14[3], i29[3], i59[3]) → LOAD1328(i14[3], i29[3], i59[3])
(2): LOAD1411(i14[2], i29[2], i59[2]) → COND_LOAD1411(i29[2] <= i59[2] && i14[2] <= i59[2], i14[2], i29[2], i59[2])
(1): COND_LOAD1328(TRUE, i14[1], i29[1], i59[1]) → LOAD1411(i14[1], i29[1], i59[1])

(1) -> (2), if ((i59[1] →* i59[2])∧(i14[1] →* i14[2])∧(i29[1] →* i29[2]))


(2) -> (3), if ((i14[2] →* i14[3])∧(i59[2] →* i59[3])∧(i29[2] <= i59[2] && i14[2] <= i59[2] →* TRUE)∧(i29[2] →* i29[3]))



The set Q consists of the following terms:
Load1328(x0, x1, x2)
Cond_Load1328(TRUE, x0, x1, x2)
Load1411(x0, x1, x2)
Cond_Load1411(TRUE, x0, x1, x2)
Cond_Load13281(TRUE, x0, x1, x2)
Cond_Load14111(TRUE, x0, x1, x2)
Cond_Load13282(TRUE, x0, x1, x2)
Cond_Load14112(TRUE, x0, x1, x2)
Cond_Load13283(TRUE, x0, x1, x2)

(47) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 3 less nodes.

(48) TRUE