Termination proof of /tmp/tmpIZjDml/PastaC3.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBCToGraph (⇒, 150 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToSCCProof (⇒, 0 ms)

↳4 JBCTerminationSCC

↳5 SCCToIDPv1Proof (⇒, 60 ms)

↳6 IDP

↳7 IDPNonInfProof (⇒, 920 ms)

↳8 IDP

↳9 IDependencyGraphProof (⇔, 0 ms)

↳10 IDP

↳11 IDPNonInfProof (⇒, 80 ms)

↳12 IDP

↳13 IDependencyGraphProof (⇔, 0 ms)

↳14 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_16 (Sun Microsystems Inc.) Main-Class: PastaC3

/**
 * 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 PastaC3 {
    public static void main(String[] args) {
        Random.args = args;
        int x = Random.random();
        int y = Random.random();
        int z = Random.random();

        while (x < y) {
            if (x < z) {
                x++;
            } else {
                z++;
            }
        }
    }
}


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:
PastaC3.main([Ljava/lang/String;)V: Graph of 249 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: PastaC3.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 16 rules for P and 0 rules for R.

P rules:
538_0_main_Load(EOS(STATIC_538), i18, i47, i91, i18) → 545_0_main_GE(EOS(STATIC_545), i18, i47, i91, i18, i47)
545_0_main_GE(EOS(STATIC_545), i18, i47, i91, i18, i47) → 560_0_main_GE(EOS(STATIC_560), i18, i47, i91, i18, i47)
560_0_main_GE(EOS(STATIC_560), i18, i47, i91, i18, i47) → 571_0_main_Load(EOS(STATIC_571), i18, i47, i91) | <(i18, i47)
571_0_main_Load(EOS(STATIC_571), i18, i47, i91) → 579_0_main_Load(EOS(STATIC_579), i18, i47, i91, i18)
579_0_main_Load(EOS(STATIC_579), i18, i47, i91, i18) → 590_0_main_GE(EOS(STATIC_590), i18, i47, i91, i18, i91)
590_0_main_GE(EOS(STATIC_590), i18, i47, i91, i18, i91) → 601_0_main_GE(EOS(STATIC_601), i18, i47, i91, i18, i91)
590_0_main_GE(EOS(STATIC_590), i18, i47, i91, i18, i91) → 602_0_main_GE(EOS(STATIC_602), i18, i47, i91, i18, i91)
601_0_main_GE(EOS(STATIC_601), i18, i47, i91, i18, i91) → 613_0_main_Inc(EOS(STATIC_613), i18, i47, i91) | >=(i18, i91)
613_0_main_Inc(EOS(STATIC_613), i18, i47, i91) → 623_0_main_JMP(EOS(STATIC_623), i18, i47, +(i91, 1)) | >=(i91, 0)
623_0_main_JMP(EOS(STATIC_623), i18, i47, i101) → 643_0_main_Load(EOS(STATIC_643), i18, i47, i101)
643_0_main_Load(EOS(STATIC_643), i18, i47, i101) → 530_0_main_Load(EOS(STATIC_530), i18, i47, i101)
530_0_main_Load(EOS(STATIC_530), i18, i47, i91) → 538_0_main_Load(EOS(STATIC_538), i18, i47, i91, i18)
602_0_main_GE(EOS(STATIC_602), i18, i47, i91, i18, i91) → 615_0_main_Inc(EOS(STATIC_615), i18, i47, i91) | <(i18, i91)
615_0_main_Inc(EOS(STATIC_615), i18, i47, i91) → 625_0_main_JMP(EOS(STATIC_625), +(i18, 1), i47, i91) | >=(i18, 0)
625_0_main_JMP(EOS(STATIC_625), i102, i47, i91) → 647_0_main_Load(EOS(STATIC_647), i102, i47, i91)
647_0_main_Load(EOS(STATIC_647), i102, i47, i91) → 530_0_main_Load(EOS(STATIC_530), i102, i47, i91)
R rules:

Combined rules. Obtained 2 conditional rules for P and 0 conditional rules for R.

P rules:
538_0_main_Load(EOS(STATIC_538), x0, x1, x2, x0) → 538_0_main_Load(EOS(STATIC_538), x0, x1, +(x2, 1), x0) | &&(&&(>(+(x2, 1), 0), <=(x2, x0)), >(x1, x0))
538_0_main_Load(EOS(STATIC_538), x0, x1, x2, x0) → 538_0_main_Load(EOS(STATIC_538), +(x0, 1), x1, x2, +(x0, 1)) | &&(&&(>(x2, x0), >(x1, x0)), >(+(x0, 1), 0))
R rules:

Filtered ground terms:

538_0_main_Load(x1, x2, x3, x4, x5) → 538_0_main_Load(x2, x3, x4, x5)
EOS(x1) → EOS
Cond_538_0_main_Load1(x1, x2, x3, x4, x5, x6) → Cond_538_0_main_Load1(x1, x3, x4, x5, x6)
Cond_538_0_main_Load(x1, x2, x3, x4, x5, x6) → Cond_538_0_main_Load(x1, x3, x4, x5, x6)

Filtered duplicate args:

538_0_main_Load(x1, x2, x3, x4) → 538_0_main_Load(x2, x3, x4)
Cond_538_0_main_Load(x1, x2, x3, x4, x5) → Cond_538_0_main_Load(x1, x3, x4, x5)
Cond_538_0_main_Load1(x1, x2, x3, x4, x5) → Cond_538_0_main_Load1(x1, x3, x4, x5)

Combined rules. Obtained 2 conditional rules for P and 0 conditional rules for R.

P rules:
538_0_main_Load(x1, x2, x0) → 538_0_main_Load(x1, +(x2, 1), x0) | &&(&&(>(x2, -1), <=(x2, x0)), >(x1, x0))
538_0_main_Load(x1, x2, x0) → 538_0_main_Load(x1, x2, +(x0, 1)) | &&(&&(>(x2, x0), >(x1, x0)), >(x0, -1))
R rules:

Finished conversion. Obtained 4 rules for P and 0 rules for R. System has predefined symbols.

P rules:
538_0_MAIN_LOAD(x1, x2, x0) → COND_538_0_MAIN_LOAD(&&(&&(>(x2, -1), <=(x2, x0)), >(x1, x0)), x1, x2, x0)
COND_538_0_MAIN_LOAD(TRUE, x1, x2, x0) → 538_0_MAIN_LOAD(x1, +(x2, 1), x0)
538_0_MAIN_LOAD(x1, x2, x0) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2, x0), >(x1, x0)), >(x0, -1)), x1, x2, x0)
COND_538_0_MAIN_LOAD1(TRUE, x1, x2, x0) → 538_0_MAIN_LOAD(x1, x2, +(x0, 1))
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:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 538_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_538_0_MAIN_LOAD(x2[0] > -1 && x2[0] <= x0[0] && x1[0] > x0[0], x1[0], x2[0], x0[0])
(1): COND_538_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 538_0_MAIN_LOAD(x1[1], x2[1] + 1, x0[1])
(2): 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(x2[2] > x0[2] && x1[2] > x0[2] && x0[2] > -1, x1[2], x2[2], x0[2])
(3): COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], x0[3] + 1)

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

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

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

(2) -> (3), if (x2[2] > x0[2] && x1[2] > x0[2] && x0[2] > -1 ∧x1[2] →^* x1[3]∧x2[2] →^* x2[3]∧x0[2] →^* x0[3])

(3) -> (0), if (x1[3] →^* x1[0]∧x2[3] →^* x2[0]∧x0[3] + 1 →^* x0[0])

(3) -> (2), if (x1[3] →^* x1[2]∧x2[3] →^* x2[2]∧x0[3] + 1 →^* x0[2])

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@2303f1ff 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 538_0_MAIN_LOAD(x1, x2, x0) → COND_538_0_MAIN_LOAD(&&(&&(>(x2, -1), <=(x2, x0)), >(x1, x0)), x1, x2, x0) the following chains were created:

We consider the chain 538_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0]), COND_538_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1]) which results in the following constraint:
(1)    (&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0]))=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1] ⇒ 538_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥NonInfC∧538_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0])∧(U^Increasing(COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥))

We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>(x1[0], x0[0])=TRUE∧>(x2[0], -1)=TRUE∧<=(x2[0], x0[0])=TRUE ⇒ 538_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥NonInfC∧538_0_MAIN_LOAD(x1[0], x2[0], x0[0])≥COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0])∧(U^Increasing(COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[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)    (x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [(-1)bni_20]x2[0] + [bni_20]x1[0] ≥ 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [(-1)bni_20]x2[0] + [bni_20]x1[0] ≥ 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥)∧[(-1)bni_20 + (-1)Bound*bni_20] + [(-1)bni_20]x2[0] + [bni_20]x1[0] ≥ 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x1[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_20] + [bni_20]x0[0] + [(-1)bni_20]x2[0] + [bni_20]x1[0] ≥ 0∧[(-1)bso_21] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x1[0] ≥ 0∧x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_20] + [bni_20]x0[0] + [bni_20]x1[0] ≥ 0∧[(-1)bso_21] ≥ 0)

For Pair COND_538_0_MAIN_LOAD(TRUE, x1, x2, x0) → 538_0_MAIN_LOAD(x1, +(x2, 1), x0) the following chains were created:

We consider the chain 538_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0]), COND_538_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1]), 538_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0]) which results in the following constraint:
(8)    (&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0]))=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1]∧x1[1]=x1[0]1∧+(x2[1], 1)=x2[0]1∧x0[1]=x0[0]1 ⇒ COND_538_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_538_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])∧(U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥))

We simplified constraint (8) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(9)    (>(x1[0], x0[0])=TRUE∧>(x2[0], -1)=TRUE∧<=(x2[0], x0[0])=TRUE ⇒ COND_538_0_MAIN_LOAD(TRUE, x1[0], x2[0], x0[0])≥NonInfC∧COND_538_0_MAIN_LOAD(TRUE, x1[0], x2[0], x0[0])≥538_0_MAIN_LOAD(x1[0], +(x2[0], 1), x0[0])∧(U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥))

We simplified constraint (9) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(10)    (x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [(-1)bni_22]x2[0] + [bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (10) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(11)    (x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [(-1)bni_22]x2[0] + [bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (11) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(12)    (x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [(-1)bni_22]x2[0] + [bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(13)    (x1[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥)∧[(-1)Bound*bni_22] + [bni_22]x0[0] + [(-1)bni_22]x2[0] + [bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    (x1[0] ≥ 0∧x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥)∧[(-1)Bound*bni_22] + [bni_22]x0[0] + [bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] ≥ 0)
We consider the chain 538_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0]), COND_538_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1]), 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2]) which results in the following constraint:
(15)    (&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0]))=TRUE∧x1[0]=x1[1]∧x2[0]=x2[1]∧x0[0]=x0[1]∧x1[1]=x1[2]∧+(x2[1], 1)=x2[2]∧x0[1]=x0[2] ⇒ COND_538_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥NonInfC∧COND_538_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1])≥538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])∧(U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥))

We simplified constraint (15) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(16)    (>(x1[0], x0[0])=TRUE∧>(x2[0], -1)=TRUE∧<=(x2[0], x0[0])=TRUE ⇒ COND_538_0_MAIN_LOAD(TRUE, x1[0], x2[0], x0[0])≥NonInfC∧COND_538_0_MAIN_LOAD(TRUE, x1[0], x2[0], x0[0])≥538_0_MAIN_LOAD(x1[0], +(x2[0], 1), x0[0])∧(U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥))

We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(17)    (x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [(-1)bni_22]x2[0] + [bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (17) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(18)    (x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [(-1)bni_22]x2[0] + [bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (18) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(19)    (x1[0] + [-1] + [-1]x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥)∧[(-1)bni_22 + (-1)Bound*bni_22] + [(-1)bni_22]x2[0] + [bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (19) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(20)    (x1[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1]x2[0] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥)∧[(-1)Bound*bni_22] + [bni_22]x0[0] + [(-1)bni_22]x2[0] + [bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

We simplified constraint (20) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(21)    (x1[0] ≥ 0∧x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥)∧[(-1)Bound*bni_22] + [bni_22]x0[0] + [bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] ≥ 0)

For Pair 538_0_MAIN_LOAD(x1, x2, x0) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2, x0), >(x1, x0)), >(x0, -1)), x1, x2, x0) the following chains were created:

We consider the chain 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2]), COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1)) which results in the following constraint:
(22)    (&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1))=TRUE∧x1[2]=x1[3]∧x2[2]=x2[3]∧x0[2]=x0[3] ⇒ 538_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥NonInfC∧538_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])∧(U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥))

We simplified constraint (22) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(23)    (>(x0[2], -1)=TRUE∧>(x2[2], x0[2])=TRUE∧>(x1[2], x0[2])=TRUE ⇒ 538_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥NonInfC∧538_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])∧(U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥))

We simplified constraint (23) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(24)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x2[2] + [bni_24]x1[2] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (24) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(25)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x2[2] + [bni_24]x1[2] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (25) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(26)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x2[2] + [bni_24]x1[2] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (26) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(27)    (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥)∧[(-2)bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x0[2] + [(-1)bni_24]x2[2] + [bni_24]x1[2] ≥ 0∧[(-1)bso_25] ≥ 0)

We simplified constraint (27) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(28)    (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x2[2] + [bni_24]x1[2] ≥ 0∧[(-1)bso_25] ≥ 0)

For Pair COND_538_0_MAIN_LOAD1(TRUE, x1, x2, x0) → 538_0_MAIN_LOAD(x1, x2, +(x0, 1)) the following chains were created:

We consider the chain 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2]), COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1)), 538_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0]) which results in the following constraint:
(29)    (&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1))=TRUE∧x1[2]=x1[3]∧x2[2]=x2[3]∧x0[2]=x0[3]∧x1[3]=x1[0]∧x2[3]=x2[0]∧+(x0[3], 1)=x0[0] ⇒ COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3])≥NonInfC∧COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3])≥538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))∧(U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥))

We simplified constraint (29) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(30)    (>(x0[2], -1)=TRUE∧>(x2[2], x0[2])=TRUE∧>(x1[2], x0[2])=TRUE ⇒ COND_538_0_MAIN_LOAD1(TRUE, x1[2], x2[2], x0[2])≥NonInfC∧COND_538_0_MAIN_LOAD1(TRUE, x1[2], x2[2], x0[2])≥538_0_MAIN_LOAD(x1[2], x2[2], +(x0[2], 1))∧(U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥))

We simplified constraint (30) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(31)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x2[2] + [bni_26]x1[2] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (31) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(32)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x2[2] + [bni_26]x1[2] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (32) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(33)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x2[2] + [bni_26]x1[2] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (33) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(34)    (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-2)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x0[2] + [(-1)bni_26]x2[2] + [bni_26]x1[2] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(35)    (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x2[2] + [bni_26]x1[2] ≥ 0∧[(-1)bso_27] ≥ 0)
We consider the chain 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2]), COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1)), 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2]) which results in the following constraint:
(36)    (&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1))=TRUE∧x1[2]=x1[3]∧x2[2]=x2[3]∧x0[2]=x0[3]∧x1[3]=x1[2]1∧x2[3]=x2[2]1∧+(x0[3], 1)=x0[2]1 ⇒ COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3])≥NonInfC∧COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3])≥538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))∧(U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥))

We simplified constraint (36) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(37)    (>(x0[2], -1)=TRUE∧>(x2[2], x0[2])=TRUE∧>(x1[2], x0[2])=TRUE ⇒ COND_538_0_MAIN_LOAD1(TRUE, x1[2], x2[2], x0[2])≥NonInfC∧COND_538_0_MAIN_LOAD1(TRUE, x1[2], x2[2], x0[2])≥538_0_MAIN_LOAD(x1[2], x2[2], +(x0[2], 1))∧(U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥))

We simplified constraint (37) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(38)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x2[2] + [bni_26]x1[2] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (38) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(39)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x2[2] + [bni_26]x1[2] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (39) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(40)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x2[2] + [bni_26]x1[2] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (40) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(41)    (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-2)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x0[2] + [(-1)bni_26]x2[2] + [bni_26]x1[2] ≥ 0∧[(-1)bso_27] ≥ 0)

We simplified constraint (41) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(42)    (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x2[2] + [bni_26]x1[2] ≥ 0∧[(-1)bso_27] ≥ 0)

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

538_0_MAIN_LOAD(x1, x2, x0) → COND_538_0_MAIN_LOAD(&&(&&(>(x2, -1), <=(x2, x0)), >(x1, x0)), x1, x2, x0)
- (x1[0] ≥ 0∧x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0])), ≥)∧[(-1)Bound*bni_20] + [bni_20]x0[0] + [bni_20]x1[0] ≥ 0∧[(-1)bso_21] ≥ 0)
COND_538_0_MAIN_LOAD(TRUE, x1, x2, x0) → 538_0_MAIN_LOAD(x1, +(x2, 1), x0)
- (x1[0] ≥ 0∧x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥)∧[(-1)Bound*bni_22] + [bni_22]x0[0] + [bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] ≥ 0)
- (x1[0] ≥ 0∧x2[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])), ≥)∧[(-1)Bound*bni_22] + [bni_22]x0[0] + [bni_22]x1[0] ≥ 0∧[1 + (-1)bso_23] ≥ 0)
538_0_MAIN_LOAD(x1, x2, x0) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2, x0), >(x1, x0)), >(x0, -1)), x1, x2, x0)
- (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥)∧[(-1)bni_24 + (-1)Bound*bni_24] + [(-1)bni_24]x2[2] + [bni_24]x1[2] ≥ 0∧[(-1)bso_25] ≥ 0)
COND_538_0_MAIN_LOAD1(TRUE, x1, x2, x0) → 538_0_MAIN_LOAD(x1, x2, +(x0, 1))
- (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x2[2] + [bni_26]x1[2] ≥ 0∧[(-1)bso_27] ≥ 0)
- (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_26 + (-1)Bound*bni_26] + [(-1)bni_26]x2[2] + [bni_26]x1[2] ≥ 0∧[(-1)bso_27] ≥ 0)

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

POL(TRUE) = 0
POL(FALSE) = [3]
POL(538_0_MAIN_LOAD(x₁, x₂, x₃)) = [-1] + [-1]x₂ + x₁
POL(COND_538_0_MAIN_LOAD(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₃ + x₂
POL(&&(x₁, x₂)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(-1) = [-1]
POL(<=(x₁, x₂)) = [-1]
POL(+(x₁, x₂)) = x₁ + x₂
POL(1) = [1]
POL(COND_538_0_MAIN_LOAD1(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₃ + x₂

The following pairs are in P_>:

COND_538_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])

The following pairs are in P_bound:

538_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0])
COND_538_0_MAIN_LOAD(TRUE, x1[1], x2[1], x0[1]) → 538_0_MAIN_LOAD(x1[1], +(x2[1], 1), x0[1])

The following pairs are in P_≥:

538_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_538_0_MAIN_LOAD(&&(&&(>(x2[0], -1), <=(x2[0], x0[0])), >(x1[0], x0[0])), x1[0], x2[0], x0[0])
538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])
COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))

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

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

(8) Obligation:

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

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 538_0_MAIN_LOAD(x1[0], x2[0], x0[0]) → COND_538_0_MAIN_LOAD(x2[0] > -1 && x2[0] <= x0[0] && x1[0] > x0[0], x1[0], x2[0], x0[0])
(2): 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(x2[2] > x0[2] && x1[2] > x0[2] && x0[2] > -1, x1[2], x2[2], x0[2])
(3): COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], x0[3] + 1)

(3) -> (0), if (x1[3] →^* x1[0]∧x2[3] →^* x2[0]∧x0[3] + 1 →^* x0[0])

(3) -> (2), if (x1[3] →^* x1[2]∧x2[3] →^* x2[2]∧x0[3] + 1 →^* x0[2])

(2) -> (3), if (x2[2] > x0[2] && x1[2] > x0[2] && x0[2] > -1 ∧x1[2] →^* x1[3]∧x2[2] →^* x2[3]∧x0[2] →^* x0[3])

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:
(3): COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], x0[3] + 1)
(2): 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(x2[2] > x0[2] && x1[2] > x0[2] && x0[2] > -1, x1[2], x2[2], x0[2])

(3) -> (2), if (x1[3] →^* x1[2]∧x2[3] →^* x2[2]∧x0[3] + 1 →^* x0[2])

(2) -> (3), if (x2[2] > x0[2] && x1[2] > x0[2] && x0[2] > -1 ∧x1[2] →^* x1[3]∧x2[2] →^* x2[3]∧x0[2] →^* x0[3])

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@2303f1ff 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_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1)) the following chains were created:

We consider the chain 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2]), COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1)), 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2]) which results in the following constraint:
(1)    (&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1))=TRUE∧x1[2]=x1[3]∧x2[2]=x2[3]∧x0[2]=x0[3]∧x1[3]=x1[2]1∧x2[3]=x2[2]1∧+(x0[3], 1)=x0[2]1 ⇒ COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3])≥NonInfC∧COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3])≥538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))∧(U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥))

We simplified constraint (1) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>(x0[2], -1)=TRUE∧>(x2[2], x0[2])=TRUE∧>(x1[2], x0[2])=TRUE ⇒ COND_538_0_MAIN_LOAD1(TRUE, x1[2], x2[2], x0[2])≥NonInfC∧COND_538_0_MAIN_LOAD1(TRUE, x1[2], x2[2], x0[2])≥538_0_MAIN_LOAD(x1[2], x2[2], +(x0[2], 1))∧(U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_14 + (-1)Bound*bni_14] + [(-1)bni_14]x0[2] + [bni_14]x2[2] ≥ 0∧[1 + (-1)bso_15] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_14 + (-1)Bound*bni_14] + [(-1)bni_14]x0[2] + [bni_14]x2[2] ≥ 0∧[1 + (-1)bso_15] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)bni_14 + (-1)Bound*bni_14] + [(-1)bni_14]x0[2] + [bni_14]x2[2] ≥ 0∧[1 + (-1)bso_15] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)Bound*bni_14] + [bni_14]x2[2] ≥ 0∧[1 + (-1)bso_15] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)Bound*bni_14] + [bni_14]x2[2] ≥ 0∧[1 + (-1)bso_15] ≥ 0)

For Pair 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2]) the following chains were created:

We consider the chain 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2]), COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1)) which results in the following constraint:
(8)    (&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1))=TRUE∧x1[2]=x1[3]∧x2[2]=x2[3]∧x0[2]=x0[3] ⇒ 538_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥NonInfC∧538_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])∧(U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥))

We simplified constraint (8) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(9)    (>(x0[2], -1)=TRUE∧>(x2[2], x0[2])=TRUE∧>(x1[2], x0[2])=TRUE ⇒ 538_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥NonInfC∧538_0_MAIN_LOAD(x1[2], x2[2], x0[2])≥COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])∧(U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥))

We simplified constraint (9) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(10)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥)∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]x0[2] + [bni_16]x2[2] ≥ 0∧[(-1)bso_17] ≥ 0)

We simplified constraint (10) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(11)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥)∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]x0[2] + [bni_16]x2[2] ≥ 0∧[(-1)bso_17] ≥ 0)

We simplified constraint (11) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(12)    (x0[2] ≥ 0∧x2[2] + [-1] + [-1]x0[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥)∧[(-1)bni_16 + (-1)Bound*bni_16] + [(-1)bni_16]x0[2] + [bni_16]x2[2] ≥ 0∧[(-1)bso_17] ≥ 0)

We simplified constraint (12) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(13)    (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] + [-1] + [-1]x0[2] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥)∧[(-1)Bound*bni_16] + [bni_16]x2[2] ≥ 0∧[(-1)bso_17] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥)∧[(-1)Bound*bni_16] + [bni_16]x2[2] ≥ 0∧[(-1)bso_17] ≥ 0)

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

COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))
- (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))), ≥)∧[(-1)Bound*bni_14] + [bni_14]x2[2] ≥ 0∧[1 + (-1)bso_15] ≥ 0)
538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])
- (x0[2] ≥ 0∧x2[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])), ≥)∧[(-1)Bound*bni_16] + [bni_16]x2[2] ≥ 0∧[(-1)bso_17] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(COND_538_0_MAIN_LOAD1(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + x₃ + [-1]x₁
POL(538_0_MAIN_LOAD(x₁, x₂, x₃)) = [-1] + [-1]x₃ + x₂
POL(+(x₁, x₂)) = x₁ + x₂
POL(1) = [1]
POL(&&(x₁, x₂)) = 0
POL(>(x₁, x₂)) = [-1]
POL(-1) = [-1]

The following pairs are in P_>:

COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))

The following pairs are in P_bound:

COND_538_0_MAIN_LOAD1(TRUE, x1[3], x2[3], x0[3]) → 538_0_MAIN_LOAD(x1[3], x2[3], +(x0[3], 1))
538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])

The following pairs are in P_≥:

538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(&&(&&(>(x2[2], x0[2]), >(x1[2], x0[2])), >(x0[2], -1)), x1[2], x2[2], x0[2])

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

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

(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:
(2): 538_0_MAIN_LOAD(x1[2], x2[2], x0[2]) → COND_538_0_MAIN_LOAD1(x2[2] > x0[2] && x1[2] > x0[2] && x0[2] > -1, x1[2], x2[2], x0[2])

The set Q is empty.

(13) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 1 less node.

(0) Obligation:

(1) JBCToGraph (SOUND transformation)

(2) Obligation:

(3) TerminationGraphToSCCProof (SOUND transformation)

(4) Obligation:

(5) SCCToIDPv1Proof (SOUND transformation)

(6) Obligation:

(7) IDPNonInfProof (SOUND transformation)

(8) Obligation:

(9) IDependencyGraphProof (EQUIVALENT transformation)

(10) Obligation:

(11) IDPNonInfProof (SOUND transformation)

(12) Obligation:

(13) IDependencyGraphProof (EQUIVALENT transformation)

(14) TRUE