Termination of the given JBC could be proven:

0 JBC
↳1 JBCToGraph (⇒, 1980 ms)
↳2 JBCTerminationGraph
↳3 TerminationGraphToSCCProof (⇒, 0 ms)
↳4 JBCTerminationSCC
↳5 SCCToIDPv1Proof (⇒, 60 ms)
↳6 IDP
↳7 IDPNonInfProof (⇒, 1000 ms)
↳8 IDP
↳9 IDependencyGraphProof (⇔, 0 ms)
↳10 IDP
↳11 IDPNonInfProof (⇒, 620 ms)
↳12 IDP
↳13 IDPNonInfProof (⇒, 400 ms)
↳14 IDP
↳15 IDependencyGraphProof (⇔, 0 ms)
↳16 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: 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) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
PastaB13.main([Ljava/lang/String;)V: Graph of 269 nodes with 1 SCC.


(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 1 SCCs.

(4) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: PastaB13.main([Ljava/lang/String;)V
SCC calls the following helper methods:
Performed SCC analyses: UsedFieldsAnalysis

(5) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 30 rules for P and 0 rules for R.


P rules:
3648_0_main_Load(EOS(STATIC_3648), i113, i1801, i88, i113) → 3650_0_main_GT(EOS(STATIC_3650), i113, i1801, i88, i113, i88)
3650_0_main_GT(EOS(STATIC_3650), i113, i1801, i88, i113, i88) → 3651_0_main_GT(EOS(STATIC_3651), i113, i1801, i88, i113, i88)
3650_0_main_GT(EOS(STATIC_3650), i113, i1801, i88, i113, i88) → 3652_0_main_GT(EOS(STATIC_3652), i113, i1801, i88, i113, i88)
3651_0_main_GT(EOS(STATIC_3651), i113, i1801, i88, i113, i88) → 3654_0_main_Load(EOS(STATIC_3654), i113, i1801, i88) | >(i113, i88)
3654_0_main_Load(EOS(STATIC_3654), i113, i1801, i88) → 3671_0_main_Load(EOS(STATIC_3671), i113, i1801, i88)
3671_0_main_Load(EOS(STATIC_3671), i113, i1801, i88) → 3674_0_main_Load(EOS(STATIC_3674), i113, i1801, i88, i113)
3674_0_main_Load(EOS(STATIC_3674), i113, i1801, i88, i113) → 3675_0_main_LE(EOS(STATIC_3675), i113, i1801, i88, i113, i88)
3675_0_main_LE(EOS(STATIC_3675), i113, i1801, i88, i113, i88) → 3677_0_main_LE(EOS(STATIC_3677), i113, i1801, i88, i113, i88)
3675_0_main_LE(EOS(STATIC_3675), i113, i1801, i88, i113, i88) → 3678_0_main_LE(EOS(STATIC_3678), i113, i1801, i88, i113, i88)
3677_0_main_LE(EOS(STATIC_3677), i113, i1801, i88, i113, i88) → 3679_0_main_Load(EOS(STATIC_3679), i113, i1801, i88) | <=(i113, i88)
3679_0_main_Load(EOS(STATIC_3679), i113, i1801, i88) → 3682_0_main_Load(EOS(STATIC_3682), i113, i1801, i88, i1801)
3682_0_main_Load(EOS(STATIC_3682), i113, i1801, i88, i1801) → 3685_0_main_LE(EOS(STATIC_3685), i113, i1801, i88, i1801, i88)
3685_0_main_LE(EOS(STATIC_3685), i113, i1801, i88, i1801, i88) → 3688_0_main_LE(EOS(STATIC_3688), i113, i1801, i88, i1801, i88)
3685_0_main_LE(EOS(STATIC_3685), i113, i1801, i88, i1801, i88) → 3689_0_main_LE(EOS(STATIC_3689), i113, i1801, i88, i1801, i88)
3688_0_main_LE(EOS(STATIC_3688), i113, i1801, i88, i1801, i88) → 3842_0_main_Load(EOS(STATIC_3842), i113, i1801, i88) | <=(i1801, i88)
3842_0_main_Load(EOS(STATIC_3842), i113, i1801, i88) → 3647_0_main_Load(EOS(STATIC_3647), i113, i1801, i88)
3647_0_main_Load(EOS(STATIC_3647), i113, i1801, i88) → 3648_0_main_Load(EOS(STATIC_3648), i113, i1801, i88, i113)
3689_0_main_LE(EOS(STATIC_3689), i113, i1801, i88, i1801, i88) → 3843_0_main_Inc(EOS(STATIC_3843), i113, i1801, i88) | >(i1801, i88)
3843_0_main_Inc(EOS(STATIC_3843), i113, i1801, i88) → 4012_0_main_JMP(EOS(STATIC_4012), i113, +(i1801, -1), i88)
4012_0_main_JMP(EOS(STATIC_4012), i113, i2274, i88) → 4014_0_main_Load(EOS(STATIC_4014), i113, i2274, i88)
4014_0_main_Load(EOS(STATIC_4014), i113, i2274, i88) → 3647_0_main_Load(EOS(STATIC_3647), i113, i2274, i88)
3678_0_main_LE(EOS(STATIC_3678), i113, i1801, i88, i113, i88) → 3680_0_main_Inc(EOS(STATIC_3680), i113, i1801, i88) | >(i113, i88)
3680_0_main_Inc(EOS(STATIC_3680), i113, i1801, i88) → 3683_0_main_JMP(EOS(STATIC_3683), +(i113, -1), i1801, i88)
3683_0_main_JMP(EOS(STATIC_3683), i1803, i1801, i88) → 3687_0_main_Load(EOS(STATIC_3687), i1803, i1801, i88)
3687_0_main_Load(EOS(STATIC_3687), i1803, i1801, i88) → 3647_0_main_Load(EOS(STATIC_3647), i1803, i1801, i88)
3652_0_main_GT(EOS(STATIC_3652), i113, i1801, i88, i113, i88) → 3655_0_main_Load(EOS(STATIC_3655), i113, i1801, i88) | <=(i113, i88)
3655_0_main_Load(EOS(STATIC_3655), i113, i1801, i88) → 3657_0_main_Load(EOS(STATIC_3657), i113, i1801, i88, i1801)
3657_0_main_Load(EOS(STATIC_3657), i113, i1801, i88, i1801) → 3660_0_main_LE(EOS(STATIC_3660), i113, i1801, i88, i1801, i88)
3660_0_main_LE(EOS(STATIC_3660), i113, i1801, i88, i1801, i88) → 3665_0_main_LE(EOS(STATIC_3665), i113, i1801, i88, i1801, i88)
3665_0_main_LE(EOS(STATIC_3665), i113, i1801, i88, i1801, i88) → 3671_0_main_Load(EOS(STATIC_3671), i113, i1801, i88) | >(i1801, i88)
R rules:

Combined rules. Obtained 5 conditional rules for P and 0 conditional rules for R.


P rules:
3648_0_main_Load(EOS(STATIC_3648), x0, x1, x2, x0) → 3675_0_main_LE(EOS(STATIC_3675), x0, x1, x2, x0, x2) | <(x2, x0)
3675_0_main_LE(EOS(STATIC_3675), x0, x1, x2, x0, x2) → 3648_0_main_Load(EOS(STATIC_3648), x0, x1, x2, x0) | &&(>=(x2, x1), >=(x2, x0))
3675_0_main_LE(EOS(STATIC_3675), x0, x1, x2, x0, x2) → 3648_0_main_Load(EOS(STATIC_3648), x0, +(x1, -1), x2, x0) | &&(>=(x2, x0), <(x2, x1))
3675_0_main_LE(EOS(STATIC_3675), x0, x1, x2, x0, x2) → 3648_0_main_Load(EOS(STATIC_3648), +(x0, -1), x1, x2, +(x0, -1)) | <(x2, x0)
3648_0_main_Load(EOS(STATIC_3648), x0, x1, x2, x0) → 3675_0_main_LE(EOS(STATIC_3675), x0, x1, x2, x0, x2) | &&(>=(x2, x0), <(x2, x1))
R rules:

Filtered ground terms:



3675_0_main_LE(x1, x2, x3, x4, x5, x6) → 3675_0_main_LE(x2, x3, x4, x5, x6)
Cond_3648_0_main_Load1(x1, x2, x3, x4, x5, x6) → Cond_3648_0_main_Load1(x1, x3, x4, x5, x6)
3648_0_main_Load(x1, x2, x3, x4, x5) → 3648_0_main_Load(x2, x3, x4, x5)
Cond_3675_0_main_LE2(x1, x2, x3, x4, x5, x6, x7) → Cond_3675_0_main_LE2(x1, x3, x4, x5, x6, x7)
Cond_3675_0_main_LE1(x1, x2, x3, x4, x5, x6, x7) → Cond_3675_0_main_LE1(x1, x3, x4, x5, x6, x7)
Cond_3675_0_main_LE(x1, x2, x3, x4, x5, x6, x7) → Cond_3675_0_main_LE(x1, x3, x4, x5, x6, x7)
Cond_3648_0_main_Load(x1, x2, x3, x4, x5, x6) → Cond_3648_0_main_Load(x1, x3, x4, x5, x6)

Filtered duplicate args:



3648_0_main_Load(x1, x2, x3, x4) → 3648_0_main_Load(x2, x3, x4)
Cond_3648_0_main_Load(x1, x2, x3, x4, x5) → Cond_3648_0_main_Load(x1, x3, x4, x5)
3675_0_main_LE(x1, x2, x3, x4, x5) → 3675_0_main_LE(x2, x4, x5)
Cond_3675_0_main_LE(x1, x2, x3, x4, x5, x6) → Cond_3675_0_main_LE(x1, x3, x5, x6)
Cond_3675_0_main_LE1(x1, x2, x3, x4, x5, x6) → Cond_3675_0_main_LE1(x1, x3, x5, x6)
Cond_3675_0_main_LE2(x1, x2, x3, x4, x5, x6) → Cond_3675_0_main_LE2(x1, x3, x5, x6)
Cond_3648_0_main_Load1(x1, x2, x3, x4, x5) → Cond_3648_0_main_Load1(x1, x3, x4, x5)

Combined rules. Obtained 5 conditional rules for P and 0 conditional rules for R.


P rules:
3648_0_main_Load(x1, x2, x0) → 3675_0_main_LE(x1, x0, x2) | <(x2, x0)
3675_0_main_LE(x1, x0, x2) → 3648_0_main_Load(x1, x2, x0) | &&(>=(x2, x1), >=(x2, x0))
3675_0_main_LE(x1, x0, x2) → 3648_0_main_Load(+(x1, -1), x2, x0) | &&(>=(x2, x0), <(x2, x1))
3675_0_main_LE(x1, x0, x2) → 3648_0_main_Load(x1, x2, +(x0, -1)) | <(x2, x0)
3648_0_main_Load(x1, x2, x0) → 3675_0_main_LE(x1, x0, x2) | &&(>=(x2, x0), <(x2, x1))
R rules:

Finished conversion. Obtained 10 rules for P and 0 rules for R. System has predefined symbols.


P rules:
3648_0_MAIN_LOAD(x1, x2, x0) → COND_3648_0_MAIN_LOAD(<(x2, x0), x1, x2, x0)
COND_3648_0_MAIN_LOAD(TRUE, x1, x2, x0) → 3675_0_MAIN_LE(x1, x0, x2)
3675_0_MAIN_LE(x1, x0, x2) → COND_3675_0_MAIN_LE(&&(>=(x2, x1), >=(x2, x0)), x1, x0, x2)
COND_3675_0_MAIN_LE(TRUE, x1, x0, x2) → 3648_0_MAIN_LOAD(x1, x2, x0)
3675_0_MAIN_LE(x1, x0, x2) → COND_3675_0_MAIN_LE1(&&(>=(x2, x0), <(x2, x1)), x1, x0, x2)
COND_3675_0_MAIN_LE1(TRUE, x1, x0, x2) → 3648_0_MAIN_LOAD(+(x1, -1), x2, x0)
3675_0_MAIN_LE(x1, x0, x2) → COND_3675_0_MAIN_LE2(<(x2, x0), x1, x0, x2)
COND_3675_0_MAIN_LE2(TRUE, x1, x0, x2) → 3648_0_MAIN_LOAD(x1, x2, +(x0, -1))
3648_0_MAIN_LOAD(x1, x2, x0) → COND_3648_0_MAIN_LOAD1(&&(>=(x2, x0), <(x2, x1)), x1, x2, x0)
COND_3648_0_MAIN_LOAD1(TRUE, x1, x2, x0) → 3675_0_MAIN_LE(x1, x0, x2)
R rules:

(6) Obligation:

IDP problem:
The following function symbols are pre-defined:
!=~Neq: (Integer, Integer) -> Boolean
*~Mul: (Integer, Integer) -> Integer
>=~Ge: (Integer, Integer) -> Boolean
-1~UnaryMinus: (Integer) -> Integer
|~Bwor: (Integer, Integer) -> Integer
/~Div: (Integer, Integer) -> Integer
=~Eq: (Integer, Integer) -> Boolean
~Bwxor: (Integer, Integer) -> Integer
||~Lor: (Boolean, Boolean) -> Boolean
!~Lnot: (Boolean) -> Boolean
<~Lt: (Integer, Integer) -> Boolean
-~Sub: (Integer, Integer) -> Integer
<=~Le: (Integer, Integer) -> Boolean
>~Gt: (Integer, Integer) -> Boolean
~~Bwnot: (Integer) -> Integer
%~Mod: (Integer, Integer) -> Integer
&~Bwand: (Integer, Integer) -> Integer
+~Add: (Integer, Integer) -> Integer
&&~Land: (Boolean, Boolean) -> Boolean


The following domains are used:

Integer, Boolean


R is empty.

The integer pair graph contains the following rules and edges:
(0): 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(x2[0] < x0[0], x1[0], x2[0], x0[0])
(1): COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1])
(2): 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(x2[2] >= x1[2] && x2[2] >= x0[2], x1[2], x0[2], x2[2])
(3): COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])
(4): 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(x2[4] >= x0[4] && x2[4] < x1[4], x1[4], x0[4], x2[4])
(5): COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(x1[5] + -1, x2[5], x0[5])
(6): 3675_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_3675_0_MAIN_LE2(x2[6] < x0[6], x1[6], x0[6], x2[6])
(7): COND_3675_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 3648_0_MAIN_LOAD(x1[7], x2[7], x0[7] + -1)
(8): 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(x2[8] >= x0[8] && x2[8] < x1[8], x1[8], x2[8], x0[8])
(9): COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9])

(0) -> (1), if (x2[0] < x0[0] ∧x1[0] →* x1[1]∧x2[0] →* x2[1]∧x0[0] →* x0[1])


(1) -> (2), if (x1[1] →* x1[2]∧x0[1] →* x0[2]∧x2[1] →* x2[2])


(1) -> (4), if (x1[1] →* x1[4]∧x0[1] →* x0[4]∧x2[1] →* x2[4])


(1) -> (6), if (x1[1] →* x1[6]∧x0[1] →* x0[6]∧x2[1] →* x2[6])


(2) -> (3), if (x2[2] >= x1[2] && x2[2] >= x0[2] ∧x1[2] →* x1[3]∧x0[2] →* x0[3]∧x2[2] →* x2[3])


(3) -> (0), if (x1[3] →* x1[0]∧x2[3] →* x2[0]∧x0[3] →* x0[0])


(3) -> (8), if (x1[3] →* x1[8]∧x2[3] →* x2[8]∧x0[3] →* x0[8])


(4) -> (5), if (x2[4] >= x0[4] && x2[4] < x1[4] ∧x1[4] →* x1[5]∧x0[4] →* x0[5]∧x2[4] →* x2[5])


(5) -> (0), if (x1[5] + -1 →* x1[0]∧x2[5] →* x2[0]∧x0[5] →* x0[0])


(5) -> (8), if (x1[5] + -1 →* x1[8]∧x2[5] →* x2[8]∧x0[5] →* x0[8])


(6) -> (7), if (x2[6] < x0[6] ∧x1[6] →* x1[7]∧x0[6] →* x0[7]∧x2[6] →* x2[7])


(7) -> (0), if (x1[7] →* x1[0]∧x2[7] →* x2[0]∧x0[7] + -1 →* x0[0])


(7) -> (8), if (x1[7] →* x1[8]∧x2[7] →* x2[8]∧x0[7] + -1 →* x0[8])


(8) -> (9), if (x2[8] >= x0[8] && x2[8] < x1[8] ∧x1[8] →* x1[9]∧x2[8] →* x2[9]∧x0[8] →* x0[9])


(9) -> (2), if (x1[9] →* x1[2]∧x0[9] →* x0[2]∧x2[9] →* x2[2])


(9) -> (4), if (x1[9] →* x1[4]∧x0[9] →* x0[4]∧x2[9] →* x2[4])


(9) -> (6), if (x1[9] →* x1[6]∧x0[9] →* x0[6]∧x2[9] →* x2[6])



The set Q is empty.

(7) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@65931a75 Constraint Generator: NonInfConstraintGenerator: PathGenerator: MetricPathGenerator: Max Left Steps: 1 Max Right Steps: 1

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 3648_0_MAIN_LOAD(x1, x2, x0) → COND_3648_0_MAIN_LOAD(<(x2, x0), x1, x2, x0) the following chains were created:
  • We consider the chain 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]), COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]) which results in the following constraint:

    (1)    (<(x2[0], x0[0])=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1] ⇒ 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥NonInfC∧3648_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])∧(UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥))



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

    (2)    (<(x2[0], x0[0])=TRUE ⇒ 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥NonInfC∧3648_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])∧(UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥))



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

    (3)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [bni_39]x0[0] + [(-1)bni_39]x2[0] ≥ 0∧[(-1)bso_40] ≥ 0)



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

    (4)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [bni_39]x0[0] + [(-1)bni_39]x2[0] ≥ 0∧[(-1)bso_40] ≥ 0)



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

    (5)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [bni_39]x0[0] + [(-1)bni_39]x2[0] ≥ 0∧[(-1)bso_40] ≥ 0)



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

    (6)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧0 = 0∧[(-1)bni_39 + (-1)Bound*bni_39] + [bni_39]x0[0] + [(-1)bni_39]x2[0] ≥ 0∧0 = 0∧[(-1)bso_40] ≥ 0)



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

    (7)    (x0[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]x0[0] ≥ 0∧0 = 0∧[(-1)bso_40] ≥ 0)



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

    (8)    (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]x0[0] ≥ 0∧0 = 0∧[(-1)bso_40] ≥ 0)


    (9)    (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]x0[0] ≥ 0∧0 = 0∧[(-1)bso_40] ≥ 0)







For Pair COND_3648_0_MAIN_LOAD(TRUE, x1, x2, x0) → 3675_0_MAIN_LE(x1, x0, x2) the following chains were created:
  • We consider the chain COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]) which results in the following constraint:

    (10)    (x1[1]=x1[2]∧x0[1]=x0[2]∧x2[1]=x2[2] ⇒ COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥3675_0_MAIN_LE(x1[1], x0[1], x2[1])∧(UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))



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

    (11)    (COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥3675_0_MAIN_LE(x1[1], x0[1], x2[1])∧(UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))



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

    (12)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧[(-1)bso_42] ≥ 0)



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

    (13)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧[(-1)bso_42] ≥ 0)



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

    (14)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧[(-1)bso_42] ≥ 0)



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

    (15)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_42] ≥ 0)



  • We consider the chain COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]) which results in the following constraint:

    (16)    (x1[1]=x1[4]∧x0[1]=x0[4]∧x2[1]=x2[4] ⇒ COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥3675_0_MAIN_LE(x1[1], x0[1], x2[1])∧(UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))



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

    (17)    (COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥3675_0_MAIN_LE(x1[1], x0[1], x2[1])∧(UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))



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

    (18)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧[(-1)bso_42] ≥ 0)



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

    (19)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧[(-1)bso_42] ≥ 0)



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

    (20)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧[(-1)bso_42] ≥ 0)



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

    (21)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_42] ≥ 0)



  • We consider the chain COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6]) which results in the following constraint:

    (22)    (x1[1]=x1[6]∧x0[1]=x0[6]∧x2[1]=x2[6] ⇒ COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥3675_0_MAIN_LE(x1[1], x0[1], x2[1])∧(UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))



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

    (23)    (COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥3675_0_MAIN_LE(x1[1], x0[1], x2[1])∧(UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))



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

    (24)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧[(-1)bso_42] ≥ 0)



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

    (25)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧[(-1)bso_42] ≥ 0)



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

    (26)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧[(-1)bso_42] ≥ 0)



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

    (27)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_42] ≥ 0)







For Pair 3675_0_MAIN_LE(x1, x0, x2) → COND_3675_0_MAIN_LE(&&(>=(x2, x1), >=(x2, x0)), x1, x0, x2) the following chains were created:
  • We consider the chain 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]) which results in the following constraint:

    (28)    (&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3] ⇒ 3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥NonInfC∧3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])∧(UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))



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

    (29)    (>=(x2[2], x1[2])=TRUE∧>=(x2[2], x0[2])=TRUE ⇒ 3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥NonInfC∧3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])∧(UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))



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

    (30)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]x2[2] + [bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)



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

    (31)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]x2[2] + [bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)



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

    (32)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]x2[2] + [bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)



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

    (33)    (x2[2] ≥ 0∧x1[2] + x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]x1[2] + [(-1)bni_43]x2[2] + [bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)



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

    (34)    (x2[2] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)



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

    (35)    (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)


    (36)    (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)







For Pair COND_3675_0_MAIN_LE(TRUE, x1, x0, x2) → 3648_0_MAIN_LOAD(x1, x2, x0) the following chains were created:
  • We consider the chain COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) which results in the following constraint:

    (37)    (x1[3]=x1[0]∧x2[3]=x2[0]∧x0[3]=x0[0] ⇒ COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



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

    (38)    (COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



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

    (39)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_45] = 0∧[(-1)bso_46] ≥ 0)



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

    (40)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_45] = 0∧[(-1)bso_46] ≥ 0)



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

    (41)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_45] = 0∧[(-1)bso_46] ≥ 0)



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

    (42)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_45] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_46] ≥ 0)



  • We consider the chain COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]) which results in the following constraint:

    (43)    (x1[3]=x1[8]∧x2[3]=x2[8]∧x0[3]=x0[8] ⇒ COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



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

    (44)    (COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



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

    (45)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_45] = 0∧[(-1)bso_46] ≥ 0)



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

    (46)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_45] = 0∧[(-1)bso_46] ≥ 0)



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

    (47)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_45] = 0∧[(-1)bso_46] ≥ 0)



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

    (48)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_45] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_46] ≥ 0)







For Pair 3675_0_MAIN_LE(x1, x0, x2) → COND_3675_0_MAIN_LE1(&&(>=(x2, x0), <(x2, x1)), x1, x0, x2) the following chains were created:
  • We consider the chain 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]), COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5]) which results in the following constraint:

    (49)    (&&(>=(x2[4], x0[4]), <(x2[4], x1[4]))=TRUE∧x1[4]=x1[5]∧x0[4]=x0[5]∧x2[4]=x2[5] ⇒ 3675_0_MAIN_LE(x1[4], x0[4], x2[4])≥NonInfC∧3675_0_MAIN_LE(x1[4], x0[4], x2[4])≥COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])∧(UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥))



    We simplified constraint (49) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (50)    (>=(x2[4], x0[4])=TRUE∧<(x2[4], x1[4])=TRUE ⇒ 3675_0_MAIN_LE(x1[4], x0[4], x2[4])≥NonInfC∧3675_0_MAIN_LE(x1[4], x0[4], x2[4])≥COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])∧(UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥))



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

    (51)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)bni_47 + (-1)Bound*bni_47] + [(-1)bni_47]x2[4] + [bni_47]x0[4] ≥ 0∧[(-1)bso_48] ≥ 0)



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

    (52)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)bni_47 + (-1)Bound*bni_47] + [(-1)bni_47]x2[4] + [bni_47]x0[4] ≥ 0∧[(-1)bso_48] ≥ 0)



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

    (53)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)bni_47 + (-1)Bound*bni_47] + [(-1)bni_47]x2[4] + [bni_47]x0[4] ≥ 0∧[(-1)bso_48] ≥ 0)



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

    (54)    (x2[4] ≥ 0∧x1[4] + [-1] + [-1]x0[4] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)bni_47 + (-1)Bound*bni_47] + [(-1)bni_47]x2[4] ≥ 0∧[(-1)bso_48] ≥ 0)



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

    (55)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)Bound*bni_47 + (-1)bni_47] + [(-1)bni_47]x2[4] ≥ 0∧[(-1)bso_48] ≥ 0)



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

    (56)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)Bound*bni_47 + (-1)bni_47] + [(-1)bni_47]x2[4] ≥ 0∧[(-1)bso_48] ≥ 0)


    (57)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)Bound*bni_47 + (-1)bni_47] + [(-1)bni_47]x2[4] ≥ 0∧[(-1)bso_48] ≥ 0)







For Pair COND_3675_0_MAIN_LE1(TRUE, x1, x0, x2) → 3648_0_MAIN_LOAD(+(x1, -1), x2, x0) the following chains were created:
  • We consider the chain 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]), COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) which results in the following constraint:

    (58)    (&&(>=(x2[4], x0[4]), <(x2[4], x1[4]))=TRUE∧x1[4]=x1[5]∧x0[4]=x0[5]∧x2[4]=x2[5]∧+(x1[5], -1)=x1[0]∧x2[5]=x2[0]∧x0[5]=x0[0] ⇒ COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5])≥NonInfC∧COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5])≥3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])∧(UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥))



    We simplified constraint (58) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (59)    (>=(x2[4], x0[4])=TRUE∧<(x2[4], x1[4])=TRUE ⇒ COND_3675_0_MAIN_LE1(TRUE, x1[4], x0[4], x2[4])≥NonInfC∧COND_3675_0_MAIN_LE1(TRUE, x1[4], x0[4], x2[4])≥3648_0_MAIN_LOAD(+(x1[4], -1), x2[4], x0[4])∧(UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥))



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

    (60)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]x2[4] + [bni_49]x0[4] ≥ 0∧[(-1)bso_50] ≥ 0)



    We simplified constraint (60) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (61)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]x2[4] + [bni_49]x0[4] ≥ 0∧[(-1)bso_50] ≥ 0)



    We simplified constraint (61) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (62)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]x2[4] + [bni_49]x0[4] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (63)    (x2[4] ≥ 0∧x1[4] + [-1] + [-1]x0[4] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]x2[4] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (64)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_49 + (-1)bni_49] + [(-1)bni_49]x2[4] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (65)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_49 + (-1)bni_49] + [(-1)bni_49]x2[4] ≥ 0∧[(-1)bso_50] ≥ 0)


    (66)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_49 + (-1)bni_49] + [(-1)bni_49]x2[4] ≥ 0∧[(-1)bso_50] ≥ 0)



  • We consider the chain 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]), COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]) which results in the following constraint:

    (67)    (&&(>=(x2[4], x0[4]), <(x2[4], x1[4]))=TRUE∧x1[4]=x1[5]∧x0[4]=x0[5]∧x2[4]=x2[5]∧+(x1[5], -1)=x1[8]∧x2[5]=x2[8]∧x0[5]=x0[8] ⇒ COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5])≥NonInfC∧COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5])≥3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])∧(UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥))



    We simplified constraint (67) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (68)    (>=(x2[4], x0[4])=TRUE∧<(x2[4], x1[4])=TRUE ⇒ COND_3675_0_MAIN_LE1(TRUE, x1[4], x0[4], x2[4])≥NonInfC∧COND_3675_0_MAIN_LE1(TRUE, x1[4], x0[4], x2[4])≥3648_0_MAIN_LOAD(+(x1[4], -1), x2[4], x0[4])∧(UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥))



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

    (69)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]x2[4] + [bni_49]x0[4] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (70)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]x2[4] + [bni_49]x0[4] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (71)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]x2[4] + [bni_49]x0[4] ≥ 0∧[(-1)bso_50] ≥ 0)



    We simplified constraint (71) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (72)    (x2[4] ≥ 0∧x1[4] + [-1] + [-1]x0[4] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [(-1)bni_49]x2[4] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (73)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_49 + (-1)bni_49] + [(-1)bni_49]x2[4] ≥ 0∧[(-1)bso_50] ≥ 0)



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

    (74)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_49 + (-1)bni_49] + [(-1)bni_49]x2[4] ≥ 0∧[(-1)bso_50] ≥ 0)


    (75)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_49 + (-1)bni_49] + [(-1)bni_49]x2[4] ≥ 0∧[(-1)bso_50] ≥ 0)







For Pair 3675_0_MAIN_LE(x1, x0, x2) → COND_3675_0_MAIN_LE2(<(x2, x0), x1, x0, x2) the following chains were created:
  • We consider the chain 3675_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6]), COND_3675_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1)) which results in the following constraint:

    (76)    (<(x2[6], x0[6])=TRUE∧x1[6]=x1[7]∧x0[6]=x0[7]∧x2[6]=x2[7] ⇒ 3675_0_MAIN_LE(x1[6], x0[6], x2[6])≥NonInfC∧3675_0_MAIN_LE(x1[6], x0[6], x2[6])≥COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])∧(UIncreasing(COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥))



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

    (77)    (<(x2[6], x0[6])=TRUE ⇒ 3675_0_MAIN_LE(x1[6], x0[6], x2[6])≥NonInfC∧3675_0_MAIN_LE(x1[6], x0[6], x2[6])≥COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])∧(UIncreasing(COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥))



    We simplified constraint (77) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (78)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[(-1)bni_51 + (-1)Bound*bni_51] + [(-1)bni_51]x2[6] + [bni_51]x0[6] ≥ 0∧[(-1)bso_52] ≥ 0)



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

    (79)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[(-1)bni_51 + (-1)Bound*bni_51] + [(-1)bni_51]x2[6] + [bni_51]x0[6] ≥ 0∧[(-1)bso_52] ≥ 0)



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

    (80)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧[(-1)bni_51 + (-1)Bound*bni_51] + [(-1)bni_51]x2[6] + [bni_51]x0[6] ≥ 0∧[(-1)bso_52] ≥ 0)



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

    (81)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧0 = 0∧[(-1)bni_51 + (-1)Bound*bni_51] + [(-1)bni_51]x2[6] + [bni_51]x0[6] ≥ 0∧0 = 0∧[(-1)bso_52] ≥ 0)



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

    (82)    (x0[6] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧0 = 0∧[(-1)Bound*bni_51] + [bni_51]x0[6] ≥ 0∧0 = 0∧[(-1)bso_52] ≥ 0)



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

    (83)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧0 = 0∧[(-1)Bound*bni_51] + [bni_51]x0[6] ≥ 0∧0 = 0∧[(-1)bso_52] ≥ 0)


    (84)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧0 = 0∧[(-1)Bound*bni_51] + [bni_51]x0[6] ≥ 0∧0 = 0∧[(-1)bso_52] ≥ 0)







For Pair COND_3675_0_MAIN_LE2(TRUE, x1, x0, x2) → 3648_0_MAIN_LOAD(x1, x2, +(x0, -1)) the following chains were created:
  • We consider the chain 3675_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6]), COND_3675_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1)), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) which results in the following constraint:

    (85)    (<(x2[6], x0[6])=TRUE∧x1[6]=x1[7]∧x0[6]=x0[7]∧x2[6]=x2[7]∧x1[7]=x1[0]∧x2[7]=x2[0]∧+(x0[7], -1)=x0[0] ⇒ COND_3675_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7])≥NonInfC∧COND_3675_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7])≥3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))∧(UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥))



    We simplified constraint (85) using rules (III), (IV) which results in the following new constraint:

    (86)    (<(x2[6], x0[6])=TRUE ⇒ COND_3675_0_MAIN_LE2(TRUE, x1[6], x0[6], x2[6])≥NonInfC∧COND_3675_0_MAIN_LE2(TRUE, x1[6], x0[6], x2[6])≥3648_0_MAIN_LOAD(x1[6], x2[6], +(x0[6], -1))∧(UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥))



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

    (87)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]x2[6] + [bni_53]x0[6] ≥ 0∧[1 + (-1)bso_54] ≥ 0)



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

    (88)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]x2[6] + [bni_53]x0[6] ≥ 0∧[1 + (-1)bso_54] ≥ 0)



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

    (89)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]x2[6] + [bni_53]x0[6] ≥ 0∧[1 + (-1)bso_54] ≥ 0)



    We simplified constraint (89) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (90)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]x2[6] + [bni_53]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_54] ≥ 0)



    We simplified constraint (90) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (91)    (x0[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_53] + [bni_53]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_54] ≥ 0)



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

    (92)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_53] + [bni_53]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_54] ≥ 0)


    (93)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_53] + [bni_53]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_54] ≥ 0)



  • We consider the chain 3675_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6]), COND_3675_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1)), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]) which results in the following constraint:

    (94)    (<(x2[6], x0[6])=TRUE∧x1[6]=x1[7]∧x0[6]=x0[7]∧x2[6]=x2[7]∧x1[7]=x1[8]∧x2[7]=x2[8]∧+(x0[7], -1)=x0[8] ⇒ COND_3675_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7])≥NonInfC∧COND_3675_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7])≥3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))∧(UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥))



    We simplified constraint (94) using rules (III), (IV) which results in the following new constraint:

    (95)    (<(x2[6], x0[6])=TRUE ⇒ COND_3675_0_MAIN_LE2(TRUE, x1[6], x0[6], x2[6])≥NonInfC∧COND_3675_0_MAIN_LE2(TRUE, x1[6], x0[6], x2[6])≥3648_0_MAIN_LOAD(x1[6], x2[6], +(x0[6], -1))∧(UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥))



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

    (96)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]x2[6] + [bni_53]x0[6] ≥ 0∧[1 + (-1)bso_54] ≥ 0)



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

    (97)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]x2[6] + [bni_53]x0[6] ≥ 0∧[1 + (-1)bso_54] ≥ 0)



    We simplified constraint (97) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (98)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]x2[6] + [bni_53]x0[6] ≥ 0∧[1 + (-1)bso_54] ≥ 0)



    We simplified constraint (98) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:

    (99)    (x0[6] + [-1] + [-1]x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)bni_53 + (-1)Bound*bni_53] + [(-1)bni_53]x2[6] + [bni_53]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_54] ≥ 0)



    We simplified constraint (99) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (100)    (x0[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_53] + [bni_53]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_54] ≥ 0)



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

    (101)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_53] + [bni_53]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_54] ≥ 0)


    (102)    (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_53] + [bni_53]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_54] ≥ 0)







For Pair 3648_0_MAIN_LOAD(x1, x2, x0) → COND_3648_0_MAIN_LOAD1(&&(>=(x2, x0), <(x2, x1)), x1, x2, x0) the following chains were created:
  • We consider the chain 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]), COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]) which results in the following constraint:

    (103)    (&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUE∧x1[8]=x1[9]∧x2[8]=x2[9]∧x0[8]=x0[9] ⇒ 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥NonInfC∧3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])∧(UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥))



    We simplified constraint (103) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (104)    (>=(x2[8], x0[8])=TRUE∧<(x2[8], x1[8])=TRUE ⇒ 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥NonInfC∧3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])∧(UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥))



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

    (105)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [bni_55]x0[8] + [(-1)bni_55]x2[8] ≥ 0∧[(-1)bso_56] ≥ 0)



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

    (106)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [bni_55]x0[8] + [(-1)bni_55]x2[8] ≥ 0∧[(-1)bso_56] ≥ 0)



    We simplified constraint (106) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:

    (107)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [bni_55]x0[8] + [(-1)bni_55]x2[8] ≥ 0∧[(-1)bso_56] ≥ 0)



    We simplified constraint (107) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (108)    (x2[8] ≥ 0∧x1[8] + [-1] + [-1]x0[8] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]x2[8] ≥ 0∧[(-1)bso_56] ≥ 0)



    We simplified constraint (108) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (109)    (x2[8] ≥ 0∧x0[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]x2[8] ≥ 0∧[(-1)bso_56] ≥ 0)



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

    (110)    (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]x2[8] ≥ 0∧[(-1)bso_56] ≥ 0)


    (111)    (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]x2[8] ≥ 0∧[(-1)bso_56] ≥ 0)







For Pair COND_3648_0_MAIN_LOAD1(TRUE, x1, x2, x0) → 3675_0_MAIN_LE(x1, x0, x2) the following chains were created:
  • We consider the chain COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]) which results in the following constraint:

    (112)    (x1[9]=x1[2]∧x0[9]=x0[2]∧x2[9]=x2[2] ⇒ COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥NonInfC∧COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥3675_0_MAIN_LE(x1[9], x0[9], x2[9])∧(UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥))



    We simplified constraint (112) using rule (IV) which results in the following new constraint:

    (113)    (COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥NonInfC∧COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥3675_0_MAIN_LE(x1[9], x0[9], x2[9])∧(UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥))



    We simplified constraint (113) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (114)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧[(-1)bso_58] ≥ 0)



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

    (115)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧[(-1)bso_58] ≥ 0)



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

    (116)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧[(-1)bso_58] ≥ 0)



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

    (117)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)



  • We consider the chain COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]) which results in the following constraint:

    (118)    (x1[9]=x1[4]∧x0[9]=x0[4]∧x2[9]=x2[4] ⇒ COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥NonInfC∧COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥3675_0_MAIN_LE(x1[9], x0[9], x2[9])∧(UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥))



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

    (119)    (COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥NonInfC∧COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥3675_0_MAIN_LE(x1[9], x0[9], x2[9])∧(UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥))



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

    (120)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧[(-1)bso_58] ≥ 0)



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

    (121)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧[(-1)bso_58] ≥ 0)



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

    (122)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧[(-1)bso_58] ≥ 0)



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

    (123)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)



  • We consider the chain COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6]) which results in the following constraint:

    (124)    (x1[9]=x1[6]∧x0[9]=x0[6]∧x2[9]=x2[6] ⇒ COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥NonInfC∧COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥3675_0_MAIN_LE(x1[9], x0[9], x2[9])∧(UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥))



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

    (125)    (COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥NonInfC∧COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥3675_0_MAIN_LE(x1[9], x0[9], x2[9])∧(UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥))



    We simplified constraint (125) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (126)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧[(-1)bso_58] ≥ 0)



    We simplified constraint (126) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:

    (127)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧[(-1)bso_58] ≥ 0)



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

    (128)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧[(-1)bso_58] ≥ 0)



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

    (129)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • 3648_0_MAIN_LOAD(x1, x2, x0) → COND_3648_0_MAIN_LOAD(<(x2, x0), x1, x2, x0)
    • (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]x0[0] ≥ 0∧0 = 0∧[(-1)bso_40] ≥ 0)
    • (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧0 = 0∧[(-1)Bound*bni_39] + [bni_39]x0[0] ≥ 0∧0 = 0∧[(-1)bso_40] ≥ 0)

  • COND_3648_0_MAIN_LOAD(TRUE, x1, x2, x0) → 3675_0_MAIN_LE(x1, x0, x2)
    • ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_42] ≥ 0)
    • ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_42] ≥ 0)
    • ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_41] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_42] ≥ 0)

  • 3675_0_MAIN_LE(x1, x0, x2) → COND_3675_0_MAIN_LE(&&(>=(x2, x1), >=(x2, x0)), x1, x0, x2)
    • (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)
    • (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_43 + (-1)Bound*bni_43] + [(-1)bni_43]x0[2] ≥ 0∧[(-1)bso_44] ≥ 0)

  • COND_3675_0_MAIN_LE(TRUE, x1, x0, x2) → 3648_0_MAIN_LOAD(x1, x2, x0)
    • ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_45] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_46] ≥ 0)
    • ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_45] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_46] ≥ 0)

  • 3675_0_MAIN_LE(x1, x0, x2) → COND_3675_0_MAIN_LE1(&&(>=(x2, x0), <(x2, x1)), x1, x0, x2)
    • (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)Bound*bni_47 + (-1)bni_47] + [(-1)bni_47]x2[4] ≥ 0∧[(-1)bso_48] ≥ 0)
    • (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(-1)Bound*bni_47 + (-1)bni_47] + [(-1)bni_47]x2[4] ≥ 0∧[(-1)bso_48] ≥ 0)

  • COND_3675_0_MAIN_LE1(TRUE, x1, x0, x2) → 3648_0_MAIN_LOAD(+(x1, -1), x2, x0)
    • (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_49 + (-1)bni_49] + [(-1)bni_49]x2[4] ≥ 0∧[(-1)bso_50] ≥ 0)
    • (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_49 + (-1)bni_49] + [(-1)bni_49]x2[4] ≥ 0∧[(-1)bso_50] ≥ 0)
    • (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_49 + (-1)bni_49] + [(-1)bni_49]x2[4] ≥ 0∧[(-1)bso_50] ≥ 0)
    • (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(-1)Bound*bni_49 + (-1)bni_49] + [(-1)bni_49]x2[4] ≥ 0∧[(-1)bso_50] ≥ 0)

  • 3675_0_MAIN_LE(x1, x0, x2) → COND_3675_0_MAIN_LE2(<(x2, x0), x1, x0, x2)
    • (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧0 = 0∧[(-1)Bound*bni_51] + [bni_51]x0[6] ≥ 0∧0 = 0∧[(-1)bso_52] ≥ 0)
    • (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])), ≥)∧0 = 0∧[(-1)Bound*bni_51] + [bni_51]x0[6] ≥ 0∧0 = 0∧[(-1)bso_52] ≥ 0)

  • COND_3675_0_MAIN_LE2(TRUE, x1, x0, x2) → 3648_0_MAIN_LOAD(x1, x2, +(x0, -1))
    • (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_53] + [bni_53]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_54] ≥ 0)
    • (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_53] + [bni_53]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_54] ≥ 0)
    • (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_53] + [bni_53]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_54] ≥ 0)
    • (x0[6] ≥ 0∧x2[6] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))), ≥)∧0 = 0∧[(-1)Bound*bni_53] + [bni_53]x0[6] ≥ 0∧0 = 0∧[1 + (-1)bso_54] ≥ 0)

  • 3648_0_MAIN_LOAD(x1, x2, x0) → COND_3648_0_MAIN_LOAD1(&&(>=(x2, x0), <(x2, x1)), x1, x2, x0)
    • (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]x2[8] ≥ 0∧[(-1)bso_56] ≥ 0)
    • (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] + [(-1)bni_55]x2[8] ≥ 0∧[(-1)bso_56] ≥ 0)

  • COND_3648_0_MAIN_LOAD1(TRUE, x1, x2, x0) → 3675_0_MAIN_LE(x1, x0, x2)
    • ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)
    • ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 0)
    • ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_57] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_58] ≥ 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(3648_0_MAIN_LOAD(x1, x2, x3)) = [-1] + x3 + [-1]x2   
POL(COND_3648_0_MAIN_LOAD(x1, x2, x3, x4)) = [-1] + x4 + [-1]x3   
POL(<(x1, x2)) = [-1]   
POL(3675_0_MAIN_LE(x1, x2, x3)) = [-1] + [-1]x3 + x2   
POL(COND_3675_0_MAIN_LE(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(COND_3675_0_MAIN_LE1(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   
POL(+(x1, x2)) = x1 + x2   
POL(-1) = [-1]   
POL(COND_3675_0_MAIN_LE2(x1, x2, x3, x4)) = [-1] + [-1]x4 + x3   
POL(COND_3648_0_MAIN_LOAD1(x1, x2, x3, x4)) = [-1] + x4 + [-1]x3   

The following pairs are in P>:

COND_3675_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))

The following pairs are in Pbound:

3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])
3675_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])
COND_3675_0_MAIN_LE2(TRUE, x1[7], x0[7], x2[7]) → 3648_0_MAIN_LOAD(x1[7], x2[7], +(x0[7], -1))

The following pairs are in P≥:

3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])
COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1])
3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])
COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])
3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])
COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])
3675_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_3675_0_MAIN_LE2(<(x2[6], x0[6]), x1[6], x0[6], x2[6])
3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])
COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9])

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

FALSE1 → &&(FALSE, TRUE)1

(8) Obligation:

IDP problem:
The following function symbols are pre-defined:
!=~Neq: (Integer, Integer) -> Boolean
*~Mul: (Integer, Integer) -> Integer
>=~Ge: (Integer, Integer) -> Boolean
-1~UnaryMinus: (Integer) -> Integer
|~Bwor: (Integer, Integer) -> Integer
/~Div: (Integer, Integer) -> Integer
=~Eq: (Integer, Integer) -> Boolean
~Bwxor: (Integer, Integer) -> Integer
||~Lor: (Boolean, Boolean) -> Boolean
!~Lnot: (Boolean) -> Boolean
<~Lt: (Integer, Integer) -> Boolean
-~Sub: (Integer, Integer) -> Integer
<=~Le: (Integer, Integer) -> Boolean
>~Gt: (Integer, Integer) -> Boolean
~~Bwnot: (Integer) -> Integer
%~Mod: (Integer, Integer) -> Integer
&~Bwand: (Integer, Integer) -> Integer
+~Add: (Integer, Integer) -> Integer
&&~Land: (Boolean, Boolean) -> Boolean


The following domains are used:

Integer, Boolean


R is empty.

The integer pair graph contains the following rules and edges:
(0): 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(x2[0] < x0[0], x1[0], x2[0], x0[0])
(1): COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1])
(2): 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(x2[2] >= x1[2] && x2[2] >= x0[2], x1[2], x0[2], x2[2])
(3): COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])
(4): 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(x2[4] >= x0[4] && x2[4] < x1[4], x1[4], x0[4], x2[4])
(5): COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(x1[5] + -1, x2[5], x0[5])
(6): 3675_0_MAIN_LE(x1[6], x0[6], x2[6]) → COND_3675_0_MAIN_LE2(x2[6] < x0[6], x1[6], x0[6], x2[6])
(8): 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(x2[8] >= x0[8] && x2[8] < x1[8], x1[8], x2[8], x0[8])
(9): COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9])

(3) -> (0), if (x1[3] →* x1[0]∧x2[3] →* x2[0]∧x0[3] →* x0[0])


(5) -> (0), if (x1[5] + -1 →* x1[0]∧x2[5] →* x2[0]∧x0[5] →* x0[0])


(0) -> (1), if (x2[0] < x0[0] ∧x1[0] →* x1[1]∧x2[0] →* x2[1]∧x0[0] →* x0[1])


(1) -> (2), if (x1[1] →* x1[2]∧x0[1] →* x0[2]∧x2[1] →* x2[2])


(9) -> (2), if (x1[9] →* x1[2]∧x0[9] →* x0[2]∧x2[9] →* x2[2])


(2) -> (3), if (x2[2] >= x1[2] && x2[2] >= x0[2] ∧x1[2] →* x1[3]∧x0[2] →* x0[3]∧x2[2] →* x2[3])


(1) -> (4), if (x1[1] →* x1[4]∧x0[1] →* x0[4]∧x2[1] →* x2[4])


(9) -> (4), if (x1[9] →* x1[4]∧x0[9] →* x0[4]∧x2[9] →* x2[4])


(4) -> (5), if (x2[4] >= x0[4] && x2[4] < x1[4] ∧x1[4] →* x1[5]∧x0[4] →* x0[5]∧x2[4] →* x2[5])


(1) -> (6), if (x1[1] →* x1[6]∧x0[1] →* x0[6]∧x2[1] →* x2[6])


(9) -> (6), if (x1[9] →* x1[6]∧x0[9] →* x0[6]∧x2[9] →* x2[6])


(3) -> (8), if (x1[3] →* x1[8]∧x2[3] →* x2[8]∧x0[3] →* x0[8])


(5) -> (8), if (x1[5] + -1 →* x1[8]∧x2[5] →* x2[8]∧x0[5] →* x0[8])


(8) -> (9), if (x2[8] >= x0[8] && x2[8] < x1[8] ∧x1[8] →* x1[9]∧x2[8] →* x2[9]∧x0[8] →* x0[9])



The set Q is empty.

(9) IDependencyGraphProof (EQUIVALENT transformation)

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

(10) 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:
(5): COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(x1[5] + -1, x2[5], x0[5])
(4): 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(x2[4] >= x0[4] && x2[4] < x1[4], x1[4], x0[4], x2[4])
(9): COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9])
(8): 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(x2[8] >= x0[8] && x2[8] < x1[8], x1[8], x2[8], x0[8])
(3): COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])
(2): 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(x2[2] >= x1[2] && x2[2] >= x0[2], x1[2], x0[2], x2[2])
(1): COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1])
(0): 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(x2[0] < x0[0], x1[0], x2[0], x0[0])

(3) -> (0), if (x1[3] →* x1[0]∧x2[3] →* x2[0]∧x0[3] →* x0[0])


(5) -> (0), if (x1[5] + -1 →* x1[0]∧x2[5] →* x2[0]∧x0[5] →* x0[0])


(0) -> (1), if (x2[0] < x0[0] ∧x1[0] →* x1[1]∧x2[0] →* x2[1]∧x0[0] →* x0[1])


(1) -> (2), if (x1[1] →* x1[2]∧x0[1] →* x0[2]∧x2[1] →* x2[2])


(9) -> (2), if (x1[9] →* x1[2]∧x0[9] →* x0[2]∧x2[9] →* x2[2])


(2) -> (3), if (x2[2] >= x1[2] && x2[2] >= x0[2] ∧x1[2] →* x1[3]∧x0[2] →* x0[3]∧x2[2] →* x2[3])


(1) -> (4), if (x1[1] →* x1[4]∧x0[1] →* x0[4]∧x2[1] →* x2[4])


(9) -> (4), if (x1[9] →* x1[4]∧x0[9] →* x0[4]∧x2[9] →* x2[4])


(4) -> (5), if (x2[4] >= x0[4] && x2[4] < x1[4] ∧x1[4] →* x1[5]∧x0[4] →* x0[5]∧x2[4] →* x2[5])


(3) -> (8), if (x1[3] →* x1[8]∧x2[3] →* x2[8]∧x0[3] →* x0[8])


(5) -> (8), if (x1[5] + -1 →* x1[8]∧x2[5] →* x2[8]∧x0[5] →* x0[8])


(8) -> (9), if (x2[8] >= x0[8] && x2[8] < x1[8] ∧x1[8] →* x1[9]∧x2[8] →* x2[9]∧x0[8] →* x0[9])



The set Q is empty.

(11) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@65931a75 Constraint Generator: NonInfConstraintGenerator: PathGenerator: MetricPathGenerator: Max Left Steps: 1 Max Right Steps: 1

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_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5]) the following chains were created:
  • We consider the chain 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]), COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) which results in the following constraint:

    (1)    (&&(>=(x2[4], x0[4]), <(x2[4], x1[4]))=TRUE∧x1[4]=x1[5]∧x0[4]=x0[5]∧x2[4]=x2[5]∧+(x1[5], -1)=x1[0]∧x2[5]=x2[0]∧x0[5]=x0[0] ⇒ COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5])≥NonInfC∧COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5])≥3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])∧(UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥))



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

    (2)    (>=(x2[4], x0[4])=TRUE∧<(x2[4], x1[4])=TRUE ⇒ COND_3675_0_MAIN_LE1(TRUE, x1[4], x0[4], x2[4])≥NonInfC∧COND_3675_0_MAIN_LE1(TRUE, x1[4], x0[4], x2[4])≥3648_0_MAIN_LOAD(+(x1[4], -1), x2[4], x0[4])∧(UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥))



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

    (3)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[4] + [(-1)bni_34]x0[4] + [(2)bni_34]x1[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)



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

    (4)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[4] + [(-1)bni_34]x0[4] + [(2)bni_34]x1[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)



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

    (5)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[4] + [(-1)bni_34]x0[4] + [(2)bni_34]x1[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)



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

    (6)    (x2[4] ≥ 0∧x1[4] + [-1] + [-1]x0[4] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[bni_34 + (-1)Bound*bni_34] + [(-2)bni_34]x0[4] + [(-1)bni_34]x2[4] + [(2)bni_34]x1[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)



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

    (7)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [bni_34]x2[4] + [(2)bni_34]x0[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)



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

    (8)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [bni_34]x2[4] + [(2)bni_34]x0[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)


    (9)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [bni_34]x2[4] + [(2)bni_34]x0[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)



  • We consider the chain 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]), COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]) which results in the following constraint:

    (10)    (&&(>=(x2[4], x0[4]), <(x2[4], x1[4]))=TRUE∧x1[4]=x1[5]∧x0[4]=x0[5]∧x2[4]=x2[5]∧+(x1[5], -1)=x1[8]∧x2[5]=x2[8]∧x0[5]=x0[8] ⇒ COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5])≥NonInfC∧COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5])≥3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])∧(UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥))



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

    (11)    (>=(x2[4], x0[4])=TRUE∧<(x2[4], x1[4])=TRUE ⇒ COND_3675_0_MAIN_LE1(TRUE, x1[4], x0[4], x2[4])≥NonInfC∧COND_3675_0_MAIN_LE1(TRUE, x1[4], x0[4], x2[4])≥3648_0_MAIN_LOAD(+(x1[4], -1), x2[4], x0[4])∧(UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥))



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

    (12)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[4] + [(-1)bni_34]x0[4] + [(2)bni_34]x1[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)



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

    (13)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[4] + [(-1)bni_34]x0[4] + [(2)bni_34]x1[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)



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

    (14)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[bni_34 + (-1)Bound*bni_34] + [(-1)bni_34]x2[4] + [(-1)bni_34]x0[4] + [(2)bni_34]x1[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)



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

    (15)    (x2[4] ≥ 0∧x1[4] + [-1] + [-1]x0[4] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[bni_34 + (-1)Bound*bni_34] + [(-2)bni_34]x0[4] + [(-1)bni_34]x2[4] + [(2)bni_34]x1[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)



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

    (16)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [bni_34]x2[4] + [(2)bni_34]x0[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)



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

    (17)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [bni_34]x2[4] + [(2)bni_34]x0[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)


    (18)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [bni_34]x2[4] + [(2)bni_34]x0[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)







For Pair 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]) the following chains were created:
  • We consider the chain 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]), COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5]) which results in the following constraint:

    (19)    (&&(>=(x2[4], x0[4]), <(x2[4], x1[4]))=TRUE∧x1[4]=x1[5]∧x0[4]=x0[5]∧x2[4]=x2[5] ⇒ 3675_0_MAIN_LE(x1[4], x0[4], x2[4])≥NonInfC∧3675_0_MAIN_LE(x1[4], x0[4], x2[4])≥COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])∧(UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥))



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

    (20)    (>=(x2[4], x0[4])=TRUE∧<(x2[4], x1[4])=TRUE ⇒ 3675_0_MAIN_LE(x1[4], x0[4], x2[4])≥NonInfC∧3675_0_MAIN_LE(x1[4], x0[4], x2[4])≥COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])∧(UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥))



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

    (21)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(2)bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]x2[4] + [(-1)bni_36]x0[4] + [(2)bni_36]x1[4] ≥ 0∧[1 + (-1)bso_37] ≥ 0)



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

    (22)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(2)bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]x2[4] + [(-1)bni_36]x0[4] + [(2)bni_36]x1[4] ≥ 0∧[1 + (-1)bso_37] ≥ 0)



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

    (23)    (x2[4] + [-1]x0[4] ≥ 0∧x1[4] + [-1] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(2)bni_36 + (-1)Bound*bni_36] + [(-1)bni_36]x2[4] + [(-1)bni_36]x0[4] + [(2)bni_36]x1[4] ≥ 0∧[1 + (-1)bso_37] ≥ 0)



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

    (24)    (x2[4] ≥ 0∧x1[4] + [-1] + [-1]x0[4] + [-1]x2[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(2)bni_36 + (-1)Bound*bni_36] + [(-2)bni_36]x0[4] + [(-1)bni_36]x2[4] + [(2)bni_36]x1[4] ≥ 0∧[1 + (-1)bso_37] ≥ 0)



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

    (25)    (x2[4] ≥ 0∧x0[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x2[4] + [(2)bni_36]x0[4] ≥ 0∧[1 + (-1)bso_37] ≥ 0)



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

    (26)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x2[4] + [(2)bni_36]x0[4] ≥ 0∧[1 + (-1)bso_37] ≥ 0)


    (27)    (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x2[4] + [(2)bni_36]x0[4] ≥ 0∧[1 + (-1)bso_37] ≥ 0)







For Pair COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]) the following chains were created:
  • We consider the chain COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]) which results in the following constraint:

    (28)    (x1[9]=x1[2]∧x0[9]=x0[2]∧x2[9]=x2[2] ⇒ COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥NonInfC∧COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥3675_0_MAIN_LE(x1[9], x0[9], x2[9])∧(UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥))



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

    (29)    (COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥NonInfC∧COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥3675_0_MAIN_LE(x1[9], x0[9], x2[9])∧(UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥))



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

    (30)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_38] = 0∧[(-1)bso_39] ≥ 0)



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

    (31)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_38] = 0∧[(-1)bso_39] ≥ 0)



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

    (32)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_38] = 0∧[(-1)bso_39] ≥ 0)



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

    (33)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_38] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)



  • We consider the chain COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]) which results in the following constraint:

    (34)    (x1[9]=x1[4]∧x0[9]=x0[4]∧x2[9]=x2[4] ⇒ COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥NonInfC∧COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥3675_0_MAIN_LE(x1[9], x0[9], x2[9])∧(UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥))



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

    (35)    (COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥NonInfC∧COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥3675_0_MAIN_LE(x1[9], x0[9], x2[9])∧(UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥))



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

    (36)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_38] = 0∧[(-1)bso_39] ≥ 0)



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

    (37)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_38] = 0∧[(-1)bso_39] ≥ 0)



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

    (38)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_38] = 0∧[(-1)bso_39] ≥ 0)



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

    (39)    ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_38] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)







For Pair 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]) the following chains were created:
  • We consider the chain 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]), COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]) which results in the following constraint:

    (40)    (&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUE∧x1[8]=x1[9]∧x2[8]=x2[9]∧x0[8]=x0[9] ⇒ 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥NonInfC∧3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])∧(UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥))



    We simplified constraint (40) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (41)    (>=(x2[8], x0[8])=TRUE∧<(x2[8], x1[8])=TRUE ⇒ 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥NonInfC∧3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])∧(UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥))



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

    (42)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(2)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]x0[8] + [(-1)bni_40]x2[8] + [(2)bni_40]x1[8] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (43)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(2)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]x0[8] + [(-1)bni_40]x2[8] + [(2)bni_40]x1[8] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (44)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(2)bni_40 + (-1)Bound*bni_40] + [(-1)bni_40]x0[8] + [(-1)bni_40]x2[8] + [(2)bni_40]x1[8] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (45)    (x2[8] ≥ 0∧x1[8] + [-1] + [-1]x0[8] + [-1]x2[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(2)bni_40 + (-1)Bound*bni_40] + [(-2)bni_40]x0[8] + [(-1)bni_40]x2[8] + [(2)bni_40]x1[8] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (46)    (x2[8] ≥ 0∧x0[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(4)bni_40 + (-1)Bound*bni_40] + [bni_40]x2[8] + [(2)bni_40]x0[8] ≥ 0∧[(-1)bso_41] ≥ 0)



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

    (47)    (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(4)bni_40 + (-1)Bound*bni_40] + [bni_40]x2[8] + [(2)bni_40]x0[8] ≥ 0∧[(-1)bso_41] ≥ 0)


    (48)    (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(4)bni_40 + (-1)Bound*bni_40] + [bni_40]x2[8] + [(2)bni_40]x0[8] ≥ 0∧[(-1)bso_41] ≥ 0)







For Pair COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]) the following chains were created:
  • We consider the chain COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) which results in the following constraint:

    (49)    (x1[3]=x1[0]∧x2[3]=x2[0]∧x0[3]=x0[0] ⇒ COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



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

    (50)    (COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



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

    (51)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_42] = 0∧[(-1)bso_43] ≥ 0)



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

    (52)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_42] = 0∧[(-1)bso_43] ≥ 0)



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

    (53)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_42] = 0∧[(-1)bso_43] ≥ 0)



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

    (54)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_42] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)



  • We consider the chain COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]) which results in the following constraint:

    (55)    (x1[3]=x1[8]∧x2[3]=x2[8]∧x0[3]=x0[8] ⇒ COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



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

    (56)    (COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



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

    (57)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_42] = 0∧[(-1)bso_43] ≥ 0)



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

    (58)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_42] = 0∧[(-1)bso_43] ≥ 0)



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

    (59)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_42] = 0∧[(-1)bso_43] ≥ 0)



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

    (60)    ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_42] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)







For Pair 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]) the following chains were created:
  • We consider the chain 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]) which results in the following constraint:

    (61)    (&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3] ⇒ 3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥NonInfC∧3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])∧(UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))



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

    (62)    (>=(x2[2], x1[2])=TRUE∧>=(x2[2], x0[2])=TRUE ⇒ 3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥NonInfC∧3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])∧(UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))



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

    (63)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(2)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]x2[2] + [(-1)bni_44]x0[2] + [(2)bni_44]x1[2] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (64)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(2)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]x2[2] + [(-1)bni_44]x0[2] + [(2)bni_44]x1[2] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (65)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(2)bni_44 + (-1)Bound*bni_44] + [(-1)bni_44]x2[2] + [(-1)bni_44]x0[2] + [(2)bni_44]x1[2] ≥ 0∧[(-1)bso_45] ≥ 0)



    We simplified constraint (65) using rule (IDP_SMT_SPLIT) which results in the following new constraint:

    (66)    (x2[2] ≥ 0∧x1[2] + x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(2)bni_44 + (-1)Bound*bni_44] + [bni_44]x1[2] + [(-1)bni_44]x2[2] + [(-1)bni_44]x0[2] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (67)    (x2[2] ≥ 0∧x0[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(2)bni_44 + (-1)Bound*bni_44] + [(-2)bni_44]x2[2] + [bni_44]x0[2] ≥ 0∧[(-1)bso_45] ≥ 0)



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

    (68)    (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(2)bni_44 + (-1)Bound*bni_44] + [(-2)bni_44]x2[2] + [bni_44]x0[2] ≥ 0∧[(-1)bso_45] ≥ 0)


    (69)    (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(2)bni_44 + (-1)Bound*bni_44] + [(-2)bni_44]x2[2] + [bni_44]x0[2] ≥ 0∧[(-1)bso_45] ≥ 0)







For Pair COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]) the following chains were created:
  • We consider the chain COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]) which results in the following constraint:

    (70)    (x1[1]=x1[2]∧x0[1]=x0[2]∧x2[1]=x2[2] ⇒ COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥3675_0_MAIN_LE(x1[1], x0[1], x2[1])∧(UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))



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

    (71)    (COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥3675_0_MAIN_LE(x1[1], x0[1], x2[1])∧(UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))



    We simplified constraint (71) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (72)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_46] = 0∧[(-1)bso_47] ≥ 0)



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

    (73)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_46] = 0∧[(-1)bso_47] ≥ 0)



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

    (74)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_46] = 0∧[(-1)bso_47] ≥ 0)



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

    (75)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_46] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)



  • We consider the chain COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4]) which results in the following constraint:

    (76)    (x1[1]=x1[4]∧x0[1]=x0[4]∧x2[1]=x2[4] ⇒ COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥3675_0_MAIN_LE(x1[1], x0[1], x2[1])∧(UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))



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

    (77)    (COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥3675_0_MAIN_LE(x1[1], x0[1], x2[1])∧(UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))



    We simplified constraint (77) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (78)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_46] = 0∧[(-1)bso_47] ≥ 0)



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

    (79)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_46] = 0∧[(-1)bso_47] ≥ 0)



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

    (80)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_46] = 0∧[(-1)bso_47] ≥ 0)



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

    (81)    ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_46] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)







For Pair 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) the following chains were created:
  • We consider the chain 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]), COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]) which results in the following constraint:

    (82)    (<(x2[0], x0[0])=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1] ⇒ 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥NonInfC∧3648_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])∧(UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥))



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

    (83)    (<(x2[0], x0[0])=TRUE ⇒ 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥NonInfC∧3648_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])∧(UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥))



    We simplified constraint (83) using rule (POLY_CONSTRAINTS) which results in the following new constraint:

    (84)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(2)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x0[0] + [(-1)bni_48]x2[0] + [(2)bni_48]x1[0] ≥ 0∧[(-1)bso_49] ≥ 0)



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

    (85)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(2)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x0[0] + [(-1)bni_48]x2[0] + [(2)bni_48]x1[0] ≥ 0∧[(-1)bso_49] ≥ 0)



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

    (86)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(2)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x0[0] + [(-1)bni_48]x2[0] + [(2)bni_48]x1[0] ≥ 0∧[(-1)bso_49] ≥ 0)



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

    (87)    (x0[0] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(2)bni_48] = 0∧[(2)bni_48 + (-1)Bound*bni_48] + [(-1)bni_48]x0[0] + [(-1)bni_48]x2[0] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)



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

    (88)    (x0[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(2)bni_48] = 0∧[bni_48 + (-1)Bound*bni_48] + [(-2)bni_48]x2[0] + [(-1)bni_48]x0[0] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)



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

    (89)    (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(2)bni_48] = 0∧[bni_48 + (-1)Bound*bni_48] + [(-2)bni_48]x2[0] + [(-1)bni_48]x0[0] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)


    (90)    (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(2)bni_48] = 0∧[bni_48 + (-1)Bound*bni_48] + [(2)bni_48]x2[0] + [(-1)bni_48]x0[0] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)







To summarize, we get the following constraints P≥ for the following pairs.
  • COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])
    • (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [bni_34]x2[4] + [(2)bni_34]x0[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)
    • (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [bni_34]x2[4] + [(2)bni_34]x0[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)
    • (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [bni_34]x2[4] + [(2)bni_34]x0[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)
    • (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])), ≥)∧[(3)bni_34 + (-1)Bound*bni_34] + [bni_34]x2[4] + [(2)bni_34]x0[4] ≥ 0∧[1 + (-1)bso_35] ≥ 0)

  • 3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])
    • (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x2[4] + [(2)bni_36]x0[4] ≥ 0∧[1 + (-1)bso_37] ≥ 0)
    • (x2[4] ≥ 0∧x0[4] ≥ 0∧x1[4] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])), ≥)∧[(4)bni_36 + (-1)Bound*bni_36] + [bni_36]x2[4] + [(2)bni_36]x0[4] ≥ 0∧[1 + (-1)bso_37] ≥ 0)

  • COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9])
    • ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_38] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)
    • ((UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[bni_38] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_39] ≥ 0)

  • 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])
    • (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(4)bni_40 + (-1)Bound*bni_40] + [bni_40]x2[8] + [(2)bni_40]x0[8] ≥ 0∧[(-1)bso_41] ≥ 0)
    • (x2[8] ≥ 0∧x0[8] ≥ 0∧x1[8] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(4)bni_40 + (-1)Bound*bni_40] + [bni_40]x2[8] + [(2)bni_40]x0[8] ≥ 0∧[(-1)bso_41] ≥ 0)

  • COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])
    • ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_42] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)
    • ((UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[bni_42] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_43] ≥ 0)

  • 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])
    • (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(2)bni_44 + (-1)Bound*bni_44] + [(-2)bni_44]x2[2] + [bni_44]x0[2] ≥ 0∧[(-1)bso_45] ≥ 0)
    • (x2[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(2)bni_44 + (-1)Bound*bni_44] + [(-2)bni_44]x2[2] + [bni_44]x0[2] ≥ 0∧[(-1)bso_45] ≥ 0)

  • COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1])
    • ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_46] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)
    • ((UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[bni_46] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_47] ≥ 0)

  • 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])
    • (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(2)bni_48] = 0∧[bni_48 + (-1)Bound*bni_48] + [(-2)bni_48]x2[0] + [(-1)bni_48]x0[0] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 0)
    • (x0[0] ≥ 0∧x2[0] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(2)bni_48] = 0∧[bni_48 + (-1)Bound*bni_48] + [(2)bni_48]x2[0] + [(-1)bni_48]x0[0] ≥ 0∧0 = 0∧[(-1)bso_49] ≥ 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_3675_0_MAIN_LE1(x1, x2, x3, x4)) = [1] + [-1]x4 + [-1]x3 + [2]x2   
POL(3648_0_MAIN_LOAD(x1, x2, x3)) = [2] + [-1]x3 + [-1]x2 + [2]x1   
POL(+(x1, x2)) = x1 + x2   
POL(-1) = [-1]   
POL(3675_0_MAIN_LE(x1, x2, x3)) = [2] + [-1]x3 + [-1]x2 + [2]x1   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(<(x1, x2)) = [-1]   
POL(COND_3648_0_MAIN_LOAD1(x1, x2, x3, x4)) = [2] + [-1]x4 + [-1]x3 + [2]x2   
POL(COND_3675_0_MAIN_LE(x1, x2, x3, x4)) = [2] + [-1]x4 + [-1]x3 + [2]x2   
POL(COND_3648_0_MAIN_LOAD(x1, x2, x3, x4)) = [2] + [-1]x4 + [-1]x3 + [2]x2   

The following pairs are in P>:

COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])
3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])

The following pairs are in Pbound:

COND_3675_0_MAIN_LE1(TRUE, x1[5], x0[5], x2[5]) → 3648_0_MAIN_LOAD(+(x1[5], -1), x2[5], x0[5])
3675_0_MAIN_LE(x1[4], x0[4], x2[4]) → COND_3675_0_MAIN_LE1(&&(>=(x2[4], x0[4]), <(x2[4], x1[4])), x1[4], x0[4], x2[4])
3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])

The following pairs are in P≥:

COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9])
3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])
COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])
3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])
COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1])
3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])

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

FALSE1 → &&(FALSE, TRUE)1

(12) 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:
(9): COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9])
(8): 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(x2[8] >= x0[8] && x2[8] < x1[8], x1[8], x2[8], x0[8])
(3): COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])
(2): 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(x2[2] >= x1[2] && x2[2] >= x0[2], x1[2], x0[2], x2[2])
(1): COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1])
(0): 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(x2[0] < x0[0], x1[0], x2[0], x0[0])

(3) -> (0), if (x1[3] →* x1[0]∧x2[3] →* x2[0]∧x0[3] →* x0[0])


(0) -> (1), if (x2[0] < x0[0] ∧x1[0] →* x1[1]∧x2[0] →* x2[1]∧x0[0] →* x0[1])


(1) -> (2), if (x1[1] →* x1[2]∧x0[1] →* x0[2]∧x2[1] →* x2[2])


(9) -> (2), if (x1[9] →* x1[2]∧x0[9] →* x0[2]∧x2[9] →* x2[2])


(2) -> (3), if (x2[2] >= x1[2] && x2[2] >= x0[2] ∧x1[2] →* x1[3]∧x0[2] →* x0[3]∧x2[2] →* x2[3])


(3) -> (8), if (x1[3] →* x1[8]∧x2[3] →* x2[8]∧x0[3] →* x0[8])


(8) -> (9), if (x2[8] >= x0[8] && x2[8] < x1[8] ∧x1[8] →* x1[9]∧x2[8] →* x2[9]∧x0[8] →* x0[9])



The set Q is empty.

(13) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@476a382b Constraint Generator: NonInfConstraintGenerator: PathGenerator: MetricPathGenerator: Max Left Steps: 3 Max Right Steps: 2

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_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]) the following chains were created:
  • We consider the chain 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]), COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]) which results in the following constraint:

    (1)    (&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3]∧x1[3]=x1[8]∧x2[3]=x2[8]∧x0[3]=x0[8]∧&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUE∧x1[8]=x1[9]∧x2[8]=x2[9]∧x0[8]=x0[9]∧x1[9]=x1[2]1∧x0[9]=x0[2]1∧x2[9]=x2[2]1∧&&(>=(x2[2]1, x1[2]1), >=(x2[2]1, x0[2]1))=TRUE∧x1[2]1=x1[3]1∧x0[2]1=x0[3]1∧x2[2]1=x2[3]1 ⇒ COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥NonInfC∧COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9])≥3675_0_MAIN_LE(x1[9], x0[9], x2[9])∧(UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥))



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

    (2)    (>=(x2[2], x1[2])=TRUE∧>=(x2[2], x0[2])=TRUE∧<(x2[2], x1[2])=TRUE ⇒ COND_3648_0_MAIN_LOAD1(TRUE, x1[2], x2[2], x0[2])≥NonInfC∧COND_3648_0_MAIN_LOAD1(TRUE, x1[2], x2[2], x0[2])≥3675_0_MAIN_LE(x1[2], x0[2], x2[2])∧(UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥))



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

    (3)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x2[2] ≥ 0 ⇒ (UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]x0[2] + [(-1)bni_29]x2[2] + [(-1)bni_29]x1[2] ≥ 0∧[(-1)bso_30] ≥ 0)



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

    (4)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x2[2] ≥ 0 ⇒ (UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]x0[2] + [(-1)bni_29]x2[2] + [(-1)bni_29]x1[2] ≥ 0∧[(-1)bso_30] ≥ 0)



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

    (5)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x2[2] ≥ 0 ⇒ (UIncreasing(3675_0_MAIN_LE(x1[9], x0[9], x2[9])), ≥)∧[(-1)bni_29 + (-1)Bound*bni_29] + [(-1)bni_29]x0[2] + [(-1)bni_29]x2[2] + [(-1)bni_29]x1[2] ≥ 0∧[(-1)bso_30] ≥ 0)



    We solved constraint (5) using rule (IDP_SMT_SPLIT).




For Pair 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]) the following chains were created:
  • We consider the chain COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]), COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]) which results in the following constraint:

    (6)    (x1[1]=x1[2]∧x0[1]=x0[2]∧x2[1]=x2[2]∧&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3]∧x1[3]=x1[8]∧x2[3]=x2[8]∧x0[3]=x0[8]∧&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUE∧x1[8]=x1[9]∧x2[8]=x2[9]∧x0[8]=x0[9]∧x1[9]=x1[2]1∧x0[9]=x0[2]1∧x2[9]=x2[2]1 ⇒ 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥NonInfC∧3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])∧(UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥))



    We simplified constraint (6) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (7)    (>=(x2[2], x1[2])=TRUE∧>=(x2[2], x0[2])=TRUE∧<(x2[2], x1[2])=TRUE ⇒ 3648_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥NonInfC∧3648_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥COND_3648_0_MAIN_LOAD1(&&(>=(x2[2], x0[2]), <(x2[2], x1[2])), x1[2], x2[2], x0[2])∧(UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥))



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

    (8)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x2[2] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]x0[2] + [(-1)bni_31]x2[2] + [(-1)bni_31]x1[2] ≥ 0∧[-1 + (-1)bso_32] ≥ 0)



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

    (9)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x2[2] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]x0[2] + [(-1)bni_31]x2[2] + [(-1)bni_31]x1[2] ≥ 0∧[-1 + (-1)bso_32] ≥ 0)



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

    (10)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x2[2] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]x0[2] + [(-1)bni_31]x2[2] + [(-1)bni_31]x1[2] ≥ 0∧[-1 + (-1)bso_32] ≥ 0)



    We solved constraint (10) using rule (IDP_SMT_SPLIT).
  • We consider the chain COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]), COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]) which results in the following constraint:

    (11)    (x1[9]=x1[2]∧x0[9]=x0[2]∧x2[9]=x2[2]∧&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3]∧x1[3]=x1[8]∧x2[3]=x2[8]∧x0[3]=x0[8]∧&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUE∧x1[8]=x1[9]1∧x2[8]=x2[9]1∧x0[8]=x0[9]1∧x1[9]1=x1[2]1∧x0[9]1=x0[2]1∧x2[9]1=x2[2]1 ⇒ 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥NonInfC∧3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])≥COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])∧(UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥))



    We simplified constraint (11) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (12)    (>=(x2[2], x1[2])=TRUE∧>=(x2[2], x0[2])=TRUE∧<(x2[2], x1[2])=TRUE ⇒ 3648_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥NonInfC∧3648_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥COND_3648_0_MAIN_LOAD1(&&(>=(x2[2], x0[2]), <(x2[2], x1[2])), x1[2], x2[2], x0[2])∧(UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥))



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

    (13)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x2[2] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]x0[2] + [(-1)bni_31]x2[2] + [(-1)bni_31]x1[2] ≥ 0∧[-1 + (-1)bso_32] ≥ 0)



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

    (14)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x2[2] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]x0[2] + [(-1)bni_31]x2[2] + [(-1)bni_31]x1[2] ≥ 0∧[-1 + (-1)bso_32] ≥ 0)



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

    (15)    (x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x2[2] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])), ≥)∧[(-1)bni_31 + (-1)Bound*bni_31] + [(-1)bni_31]x0[2] + [(-1)bni_31]x2[2] + [(-1)bni_31]x1[2] ≥ 0∧[-1 + (-1)bso_32] ≥ 0)



    We solved constraint (15) using rule (IDP_SMT_SPLIT).




For Pair COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]) the following chains were created:
  • We consider the chain 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]), COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]), COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]) which results in the following constraint:

    (16)    (<(x2[0], x0[0])=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1]∧x1[1]=x1[2]∧x0[1]=x0[2]∧x2[1]=x2[2]∧&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3]∧x1[3]=x1[0]1∧x2[3]=x2[0]1∧x0[3]=x0[0]1∧<(x2[0]1, x0[0]1)=TRUE∧x1[0]1=x1[1]1∧x2[0]1=x2[1]1∧x0[0]1=x0[1]1 ⇒ COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



    We simplified constraint (16) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (17)    (<(x2[0], x0[0])=TRUE∧>=(x2[0], x1[2])=TRUE∧>=(x2[0], x0[0])=TRUE ⇒ COND_3675_0_MAIN_LE(TRUE, x1[2], x0[0], x2[0])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[2], x0[0], x2[0])≥3648_0_MAIN_LOAD(x1[2], x2[0], x0[0])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



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

    (18)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[0] + [(-1)bni_33]x0[0] + [(-1)bni_33]x1[2] ≥ 0∧[(-1)bso_34] ≥ 0)



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

    (19)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[0] + [(-1)bni_33]x0[0] + [(-1)bni_33]x1[2] ≥ 0∧[(-1)bso_34] ≥ 0)



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

    (20)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[0] + [(-1)bni_33]x0[0] + [(-1)bni_33]x1[2] ≥ 0∧[(-1)bso_34] ≥ 0)



    We solved constraint (20) using rule (IDP_SMT_SPLIT).
  • We consider the chain 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]), COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]), COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]) which results in the following constraint:

    (21)    (<(x2[0], x0[0])=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1]∧x1[1]=x1[2]∧x0[1]=x0[2]∧x2[1]=x2[2]∧&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3]∧x1[3]=x1[8]∧x2[3]=x2[8]∧x0[3]=x0[8]∧&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUE∧x1[8]=x1[9]∧x2[8]=x2[9]∧x0[8]=x0[9] ⇒ COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



    We simplified constraint (21) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (22)    (<(x2[0], x0[0])=TRUE∧>=(x2[0], x1[2])=TRUE∧>=(x2[0], x0[0])=TRUE∧<(x2[0], x1[2])=TRUE ⇒ COND_3675_0_MAIN_LE(TRUE, x1[2], x0[0], x2[0])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[2], x0[0], x2[0])≥3648_0_MAIN_LOAD(x1[2], x2[0], x0[0])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



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

    (23)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0∧x1[2] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[0] + [(-1)bni_33]x0[0] + [(-1)bni_33]x1[2] ≥ 0∧[(-1)bso_34] ≥ 0)



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

    (24)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0∧x1[2] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[0] + [(-1)bni_33]x0[0] + [(-1)bni_33]x1[2] ≥ 0∧[(-1)bso_34] ≥ 0)



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

    (25)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0∧x1[2] + [-1] + [-1]x2[0] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[0] + [(-1)bni_33]x0[0] + [(-1)bni_33]x1[2] ≥ 0∧[(-1)bso_34] ≥ 0)



    We solved constraint (25) using rule (IDP_SMT_SPLIT).
  • We consider the chain 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]), COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]), COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]) which results in the following constraint:

    (26)    (&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUE∧x1[8]=x1[9]∧x2[8]=x2[9]∧x0[8]=x0[9]∧x1[9]=x1[2]∧x0[9]=x0[2]∧x2[9]=x2[2]∧&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3]∧x1[3]=x1[0]∧x2[3]=x2[0]∧x0[3]=x0[0]∧<(x2[0], x0[0])=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1] ⇒ COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



    We simplified constraint (26) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (27)    (<(x2[8], x0[8])=TRUE∧>=(x2[8], x0[8])=TRUE∧<(x2[8], x1[8])=TRUE∧>=(x2[8], x1[8])=TRUE ⇒ COND_3675_0_MAIN_LE(TRUE, x1[8], x0[8], x2[8])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[8], x0[8], x2[8])≥3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



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

    (28)    (x0[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[8] + [(-1)bni_33]x0[8] + [(-1)bni_33]x1[8] ≥ 0∧[(-1)bso_34] ≥ 0)



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

    (29)    (x0[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[8] + [(-1)bni_33]x0[8] + [(-1)bni_33]x1[8] ≥ 0∧[(-1)bso_34] ≥ 0)



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

    (30)    (x0[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[8] + [(-1)bni_33]x0[8] + [(-1)bni_33]x1[8] ≥ 0∧[(-1)bso_34] ≥ 0)



    We solved constraint (30) using rule (IDP_SMT_SPLIT).
  • We consider the chain 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]), COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]), COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]) which results in the following constraint:

    (31)    (&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUE∧x1[8]=x1[9]∧x2[8]=x2[9]∧x0[8]=x0[9]∧x1[9]=x1[2]∧x0[9]=x0[2]∧x2[9]=x2[2]∧&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3]∧x1[3]=x1[8]1∧x2[3]=x2[8]1∧x0[3]=x0[8]1∧&&(>=(x2[8]1, x0[8]1), <(x2[8]1, x1[8]1))=TRUE∧x1[8]1=x1[9]1∧x2[8]1=x2[9]1∧x0[8]1=x0[9]1 ⇒ COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3])≥3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



    We simplified constraint (31) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (32)    (>=(x2[8], x0[8])=TRUE∧<(x2[8], x1[8])=TRUE∧>=(x2[8], x1[8])=TRUE ⇒ COND_3675_0_MAIN_LE(TRUE, x1[8], x0[8], x2[8])≥NonInfC∧COND_3675_0_MAIN_LE(TRUE, x1[8], x0[8], x2[8])≥3648_0_MAIN_LOAD(x1[8], x2[8], x0[8])∧(UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥))



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

    (33)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[8] + [(-1)bni_33]x0[8] + [(-1)bni_33]x1[8] ≥ 0∧[(-1)bso_34] ≥ 0)



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

    (34)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[8] + [(-1)bni_33]x0[8] + [(-1)bni_33]x1[8] ≥ 0∧[(-1)bso_34] ≥ 0)



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

    (35)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])), ≥)∧[(-1)bni_33 + (-1)Bound*bni_33] + [(-1)bni_33]x2[8] + [(-1)bni_33]x0[8] + [(-1)bni_33]x1[8] ≥ 0∧[(-1)bso_34] ≥ 0)



    We solved constraint (35) using rule (IDP_SMT_SPLIT).




For Pair 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]) the following chains were created:
  • We consider the chain COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]), COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) which results in the following constraint:

    (36)    (x1[3]=x1[0]∧x2[3]=x2[0]∧x0[3]=x0[0]∧<(x2[0], x0[0])=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1]∧x1[1]=x1[2]∧x0[1]=x0[2]∧x2[1]=x2[2]∧&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]1∧x0[2]=x0[3]1∧x2[2]=x2[3]1∧x1[3]1=x1[0]1∧x2[3]1=x2[0]1∧x0[3]1=x0[0]1 ⇒ 3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥NonInfC∧3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])∧(UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))



    We simplified constraint (36) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (37)    (<(x2[0], x0[0])=TRUE∧>=(x2[0], x1[2])=TRUE∧>=(x2[0], x0[0])=TRUE ⇒ 3675_0_MAIN_LE(x1[2], x0[0], x2[0])≥NonInfC∧3675_0_MAIN_LE(x1[2], x0[0], x2[0])≥COND_3675_0_MAIN_LE(&&(>=(x2[0], x1[2]), >=(x2[0], x0[0])), x1[2], x0[0], x2[0])∧(UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))



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

    (38)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]x2[0] + [(-1)bni_35]x0[0] + [(-1)bni_35]x1[2] ≥ 0∧[-1 + (-1)bso_36] ≥ 0)



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

    (39)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]x2[0] + [(-1)bni_35]x0[0] + [(-1)bni_35]x1[2] ≥ 0∧[-1 + (-1)bso_36] ≥ 0)



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

    (40)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]x2[0] + [(-1)bni_35]x0[0] + [(-1)bni_35]x1[2] ≥ 0∧[-1 + (-1)bso_36] ≥ 0)



    We solved constraint (40) using rule (IDP_SMT_SPLIT).
  • We consider the chain COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]), COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) which results in the following constraint:

    (41)    (x1[3]=x1[8]∧x2[3]=x2[8]∧x0[3]=x0[8]∧&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUE∧x1[8]=x1[9]∧x2[8]=x2[9]∧x0[8]=x0[9]∧x1[9]=x1[2]∧x0[9]=x0[2]∧x2[9]=x2[2]∧&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]1∧x0[2]=x0[3]1∧x2[2]=x2[3]1∧x1[3]1=x1[0]∧x2[3]1=x2[0]∧x0[3]1=x0[0] ⇒ 3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥NonInfC∧3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])∧(UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))



    We simplified constraint (41) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (42)    (>=(x2[8], x0[8])=TRUE∧<(x2[8], x1[8])=TRUE∧>=(x2[8], x1[8])=TRUE ⇒ 3675_0_MAIN_LE(x1[8], x0[8], x2[8])≥NonInfC∧3675_0_MAIN_LE(x1[8], x0[8], x2[8])≥COND_3675_0_MAIN_LE(&&(>=(x2[8], x1[8]), >=(x2[8], x0[8])), x1[8], x0[8], x2[8])∧(UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))



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

    (43)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]x2[8] + [(-1)bni_35]x0[8] + [(-1)bni_35]x1[8] ≥ 0∧[-1 + (-1)bso_36] ≥ 0)



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

    (44)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]x2[8] + [(-1)bni_35]x0[8] + [(-1)bni_35]x1[8] ≥ 0∧[-1 + (-1)bso_36] ≥ 0)



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

    (45)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]x2[8] + [(-1)bni_35]x0[8] + [(-1)bni_35]x1[8] ≥ 0∧[-1 + (-1)bso_36] ≥ 0)



    We solved constraint (45) using rule (IDP_SMT_SPLIT).
  • We consider the chain COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]), COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]) which results in the following constraint:

    (46)    (x1[3]=x1[0]∧x2[3]=x2[0]∧x0[3]=x0[0]∧<(x2[0], x0[0])=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1]∧x1[1]=x1[2]∧x0[1]=x0[2]∧x2[1]=x2[2]∧&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]1∧x0[2]=x0[3]1∧x2[2]=x2[3]1∧x1[3]1=x1[8]∧x2[3]1=x2[8]∧x0[3]1=x0[8] ⇒ 3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥NonInfC∧3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])∧(UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))



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

    (47)    (<(x2[0], x0[0])=TRUE∧>=(x2[0], x1[2])=TRUE∧>=(x2[0], x0[0])=TRUE ⇒ 3675_0_MAIN_LE(x1[2], x0[0], x2[0])≥NonInfC∧3675_0_MAIN_LE(x1[2], x0[0], x2[0])≥COND_3675_0_MAIN_LE(&&(>=(x2[0], x1[2]), >=(x2[0], x0[0])), x1[2], x0[0], x2[0])∧(UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))



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

    (48)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]x2[0] + [(-1)bni_35]x0[0] + [(-1)bni_35]x1[2] ≥ 0∧[-1 + (-1)bso_36] ≥ 0)



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

    (49)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]x2[0] + [(-1)bni_35]x0[0] + [(-1)bni_35]x1[2] ≥ 0∧[-1 + (-1)bso_36] ≥ 0)



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

    (50)    (x0[0] + [-1] + [-1]x2[0] ≥ 0∧x2[0] + [-1]x1[2] ≥ 0∧x2[0] + [-1]x0[0] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]x2[0] + [(-1)bni_35]x0[0] + [(-1)bni_35]x1[2] ≥ 0∧[-1 + (-1)bso_36] ≥ 0)



    We solved constraint (50) using rule (IDP_SMT_SPLIT).
  • We consider the chain COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]), COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8]) which results in the following constraint:

    (51)    (x1[3]=x1[8]∧x2[3]=x2[8]∧x0[3]=x0[8]∧&&(>=(x2[8], x0[8]), <(x2[8], x1[8]))=TRUE∧x1[8]=x1[9]∧x2[8]=x2[9]∧x0[8]=x0[9]∧x1[9]=x1[2]∧x0[9]=x0[2]∧x2[9]=x2[2]∧&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]1∧x0[2]=x0[3]1∧x2[2]=x2[3]1∧x1[3]1=x1[8]1∧x2[3]1=x2[8]1∧x0[3]1=x0[8]1 ⇒ 3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥NonInfC∧3675_0_MAIN_LE(x1[2], x0[2], x2[2])≥COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])∧(UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))



    We simplified constraint (51) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (52)    (>=(x2[8], x0[8])=TRUE∧<(x2[8], x1[8])=TRUE∧>=(x2[8], x1[8])=TRUE ⇒ 3675_0_MAIN_LE(x1[8], x0[8], x2[8])≥NonInfC∧3675_0_MAIN_LE(x1[8], x0[8], x2[8])≥COND_3675_0_MAIN_LE(&&(>=(x2[8], x1[8]), >=(x2[8], x0[8])), x1[8], x0[8], x2[8])∧(UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥))



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

    (53)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]x2[8] + [(-1)bni_35]x0[8] + [(-1)bni_35]x1[8] ≥ 0∧[-1 + (-1)bso_36] ≥ 0)



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

    (54)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]x2[8] + [(-1)bni_35]x0[8] + [(-1)bni_35]x1[8] ≥ 0∧[-1 + (-1)bso_36] ≥ 0)



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

    (55)    (x2[8] + [-1]x0[8] ≥ 0∧x1[8] + [-1] + [-1]x2[8] ≥ 0∧x2[8] + [-1]x1[8] ≥ 0 ⇒ (UIncreasing(COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])), ≥)∧[(-1)bni_35 + (-1)Bound*bni_35] + [(-1)bni_35]x2[8] + [(-1)bni_35]x0[8] + [(-1)bni_35]x1[8] ≥ 0∧[-1 + (-1)bso_36] ≥ 0)



    We solved constraint (55) using rule (IDP_SMT_SPLIT).




For Pair COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]) the following chains were created:
  • We consider the chain 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]), COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]) which results in the following constraint:

    (56)    (&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3]∧x1[3]=x1[0]∧x2[3]=x2[0]∧x0[3]=x0[0]∧<(x2[0], x0[0])=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1]∧x1[1]=x1[2]1∧x0[1]=x0[2]1∧x2[1]=x2[2]1∧&&(>=(x2[2]1, x1[2]1), >=(x2[2]1, x0[2]1))=TRUE∧x1[2]1=x1[3]1∧x0[2]1=x0[3]1∧x2[2]1=x2[3]1 ⇒ COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥3675_0_MAIN_LE(x1[1], x0[1], x2[1])∧(UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))



    We simplified constraint (56) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (57)    (<(x2[2], x0[2])=TRUE∧>=(x2[2], x1[2])=TRUE∧>=(x2[2], x0[2])=TRUE ⇒ COND_3648_0_MAIN_LOAD(TRUE, x1[2], x2[2], x0[2])≥NonInfC∧COND_3648_0_MAIN_LOAD(TRUE, x1[2], x2[2], x0[2])≥3675_0_MAIN_LE(x1[2], x0[2], x2[2])∧(UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥))



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

    (58)    (x0[2] + [-1] + [-1]x2[2] ≥ 0∧x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]x0[2] + [(-1)bni_37]x2[2] + [(-1)bni_37]x1[2] ≥ 0∧[(-1)bso_38] ≥ 0)



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

    (59)    (x0[2] + [-1] + [-1]x2[2] ≥ 0∧x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]x0[2] + [(-1)bni_37]x2[2] + [(-1)bni_37]x1[2] ≥ 0∧[(-1)bso_38] ≥ 0)



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

    (60)    (x0[2] + [-1] + [-1]x2[2] ≥ 0∧x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(3675_0_MAIN_LE(x1[1], x0[1], x2[1])), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [(-1)bni_37]x0[2] + [(-1)bni_37]x2[2] + [(-1)bni_37]x1[2] ≥ 0∧[(-1)bso_38] ≥ 0)



    We solved constraint (60) using rule (IDP_SMT_SPLIT).




For Pair 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]) the following chains were created:
  • We consider the chain COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]), COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]) which results in the following constraint:

    (61)    (x1[1]=x1[2]∧x0[1]=x0[2]∧x2[1]=x2[2]∧&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3]∧x1[3]=x1[0]∧x2[3]=x2[0]∧x0[3]=x0[0]∧<(x2[0], x0[0])=TRUE∧x1[0]=x1[1]1∧x2[0]=x2[1]1∧x0[0]=x0[1]1∧x1[1]1=x1[2]1∧x0[1]1=x0[2]1∧x2[1]1=x2[2]1 ⇒ 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥NonInfC∧3648_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])∧(UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥))



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

    (62)    (<(x2[2], x0[2])=TRUE∧>=(x2[2], x1[2])=TRUE∧>=(x2[2], x0[2])=TRUE ⇒ 3648_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥NonInfC∧3648_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥COND_3648_0_MAIN_LOAD(<(x2[2], x0[2]), x1[2], x2[2], x0[2])∧(UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥))



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

    (63)    (x0[2] + [-1] + [-1]x2[2] ≥ 0∧x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]x0[2] + [(-1)bni_39]x2[2] + [(-1)bni_39]x1[2] ≥ 0∧[-1 + (-1)bso_40] ≥ 0)



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

    (64)    (x0[2] + [-1] + [-1]x2[2] ≥ 0∧x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]x0[2] + [(-1)bni_39]x2[2] + [(-1)bni_39]x1[2] ≥ 0∧[-1 + (-1)bso_40] ≥ 0)



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

    (65)    (x0[2] + [-1] + [-1]x2[2] ≥ 0∧x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]x0[2] + [(-1)bni_39]x2[2] + [(-1)bni_39]x1[2] ≥ 0∧[-1 + (-1)bso_40] ≥ 0)



    We solved constraint (65) using rule (IDP_SMT_SPLIT).
  • We consider the chain COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]), COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3]), 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0]), COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1]), 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2]) which results in the following constraint:

    (66)    (x1[9]=x1[2]∧x0[9]=x0[2]∧x2[9]=x2[2]∧&&(>=(x2[2], x1[2]), >=(x2[2], x0[2]))=TRUE∧x1[2]=x1[3]∧x0[2]=x0[3]∧x2[2]=x2[3]∧x1[3]=x1[0]∧x2[3]=x2[0]∧x0[3]=x0[0]∧<(x2[0], x0[0])=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1]∧x1[1]=x1[2]1∧x0[1]=x0[2]1∧x2[1]=x2[2]1 ⇒ 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥NonInfC∧3648_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])∧(UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥))



    We simplified constraint (66) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:

    (67)    (<(x2[2], x0[2])=TRUE∧>=(x2[2], x1[2])=TRUE∧>=(x2[2], x0[2])=TRUE ⇒ 3648_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥NonInfC∧3648_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥COND_3648_0_MAIN_LOAD(<(x2[2], x0[2]), x1[2], x2[2], x0[2])∧(UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥))



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

    (68)    (x0[2] + [-1] + [-1]x2[2] ≥ 0∧x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]x0[2] + [(-1)bni_39]x2[2] + [(-1)bni_39]x1[2] ≥ 0∧[-1 + (-1)bso_40] ≥ 0)



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

    (69)    (x0[2] + [-1] + [-1]x2[2] ≥ 0∧x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]x0[2] + [(-1)bni_39]x2[2] + [(-1)bni_39]x1[2] ≥ 0∧[-1 + (-1)bso_40] ≥ 0)



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

    (70)    (x0[2] + [-1] + [-1]x2[2] ≥ 0∧x2[2] + [-1]x1[2] ≥ 0∧x2[2] + [-1]x0[2] ≥ 0 ⇒ (UIncreasing(COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_39 + (-1)Bound*bni_39] + [(-1)bni_39]x0[2] + [(-1)bni_39]x2[2] + [(-1)bni_39]x1[2] ≥ 0∧[-1 + (-1)bso_40] ≥ 0)



    We solved constraint (70) using rule (IDP_SMT_SPLIT).




To summarize, we get the following constraints P≥ for the following pairs.
  • COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9])

  • 3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])

  • COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])

  • 3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])

  • COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1])

  • 3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[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_3648_0_MAIN_LOAD1(x1, x2, x3, x4)) = [-1] + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1   
POL(3675_0_MAIN_LE(x1, x2, x3)) = [-1] + [-1]x3 + [-1]x2 + [-1]x1   
POL(3648_0_MAIN_LOAD(x1, x2, x3)) = [-1] + [-1]x3 + [-1]x2 + [-1]x1   
POL(&&(x1, x2)) = [-1]   
POL(>=(x1, x2)) = [-1]   
POL(<(x1, x2)) = [-1]   
POL(COND_3675_0_MAIN_LE(x1, x2, x3, x4)) = [-1] + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1   
POL(COND_3648_0_MAIN_LOAD(x1, x2, x3, x4)) = [-1] + [-1]x4 + [-1]x3 + [-1]x2 + [-1]x1   

The following pairs are in P>:

COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9])
3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])
COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])
3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])
COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1])
3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])

The following pairs are in Pbound:

COND_3648_0_MAIN_LOAD1(TRUE, x1[9], x2[9], x0[9]) → 3675_0_MAIN_LE(x1[9], x0[9], x2[9])
3648_0_MAIN_LOAD(x1[8], x2[8], x0[8]) → COND_3648_0_MAIN_LOAD1(&&(>=(x2[8], x0[8]), <(x2[8], x1[8])), x1[8], x2[8], x0[8])
COND_3675_0_MAIN_LE(TRUE, x1[3], x0[3], x2[3]) → 3648_0_MAIN_LOAD(x1[3], x2[3], x0[3])
3675_0_MAIN_LE(x1[2], x0[2], x2[2]) → COND_3675_0_MAIN_LE(&&(>=(x2[2], x1[2]), >=(x2[2], x0[2])), x1[2], x0[2], x2[2])
COND_3648_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 3675_0_MAIN_LE(x1[1], x0[1], x2[1])
3648_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_3648_0_MAIN_LOAD(<(x2[0], x0[0]), x1[0], x2[0], x0[0])

The following pairs are in P≥:
none

There are no usable rules.

(14) Obligation:

IDP problem:
The following function symbols are pre-defined:
!=~Neq: (Integer, Integer) -> Boolean
*~Mul: (Integer, Integer) -> Integer
>=~Ge: (Integer, Integer) -> Boolean
-1~UnaryMinus: (Integer) -> Integer
|~Bwor: (Integer, Integer) -> Integer
/~Div: (Integer, Integer) -> Integer
=~Eq: (Integer, Integer) -> Boolean
~Bwxor: (Integer, Integer) -> Integer
||~Lor: (Boolean, Boolean) -> Boolean
!~Lnot: (Boolean) -> Boolean
<~Lt: (Integer, Integer) -> Boolean
-~Sub: (Integer, Integer) -> Integer
<=~Le: (Integer, Integer) -> Boolean
>~Gt: (Integer, Integer) -> Boolean
~~Bwnot: (Integer) -> Integer
%~Mod: (Integer, Integer) -> Integer
&~Bwand: (Integer, Integer) -> Integer
+~Add: (Integer, Integer) -> Integer
&&~Land: (Boolean, Boolean) -> Boolean


The following domains are used:
none


R is empty.

The integer pair graph is empty.

The set Q is empty.

(15) IDependencyGraphProof (EQUIVALENT transformation)

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

(16) TRUE