Termination proof of /tmp/tmpfrmERp/Parts.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBCToGraph (⇒, 2410 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToSCCProof (⇒, 0 ms)

↳4 AND

    ↳5 JBCTerminationSCC

        ↳6 SCCToIDPv1Proof (⇒, 460 ms)

        ↳7 IDP

        ↳8 IDPNonInfProof (⇒, 830 ms)

        ↳9 IDP

        ↳10 IDependencyGraphProof (⇔, 0 ms)

        ↳11 IDP

        ↳12 UsableRulesProof (⇔, 0 ms)

        ↳13 IDP

        ↳14 IDPNonInfProof (⇒, 1110 ms)

        ↳15 IDP

        ↳16 IDependencyGraphProof (⇔, 0 ms)

        ↳17 IDP

        ↳18 UsableRulesProof (⇔, 0 ms)

        ↳19 IDP

        ↳20 IDPNonInfProof (⇒, 180 ms)

        ↳21 IDP

        ↳22 IDependencyGraphProof (⇔, 0 ms)

        ↳23 TRUE

    ↳24 JBCTerminationSCC

        ↳25 SCCToIDPv1Proof (⇒, 1090 ms)

        ↳26 IDP

        ↳27 IDPNonInfProof (⇒, 1170 ms)

        ↳28 AND

            ↳29 IDP

                ↳30 IDependencyGraphProof (⇔, 0 ms)

                ↳31 IDP

                ↳32 IDPNonInfProof (⇒, 590 ms)

                ↳33 AND

                    ↳34 IDP

                        ↳35 IDependencyGraphProof (⇔, 0 ms)

                        ↳36 TRUE

                    ↳37 IDP

                        ↳38 IDependencyGraphProof (⇔, 0 ms)

                        ↳39 TRUE

            ↳40 IDP

                ↳41 IDependencyGraphProof (⇔, 0 ms)

                ↳42 IDP

                ↳43 IDPNonInfProof (⇒, 580 ms)

                ↳44 IDP

                ↳45 IDependencyGraphProof (⇔, 0 ms)

                ↳46 IDP

                ↳47 IDPNonInfProof (⇒, 470 ms)

                ↳48 AND

                    ↳49 IDP

                        ↳50 IDependencyGraphProof (⇔, 0 ms)

                        ↳51 TRUE

                    ↳52 IDP

                        ↳53 IDependencyGraphProof (⇔, 0 ms)

                        ↳54 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_24 (Apple Inc.) Main-Class: Parts

public class Parts {

    public static int parts(int p, int q) {
	if (p <= 0) return 1;
	else if (q <= 0) return 0;
	else if (q > p) return parts(p, p);
	else return parts(p-q, q) + parts(p, q-1);
    }

    public static void main(String args[]) {
	for (int p = 0; p <= args.length; p++)
	    for (int q = 0; q <= args.length; q++)
		parts(p, q);
    }
}

(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
Parts.main([Ljava/lang/String;)V: Graph of 84 nodes with 1 SCC.

Parts.parts(II)I: Graph of 82 nodes with 0 SCCs.

(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 2 SCCss.

(4) Complex Obligation (AND)

(5) Obligation:

SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: Parts.parts(II)I
SCC calls the following helper methods: Parts.parts(II)I
Performed SCC analyses: UsedFieldsAnalysis

(6) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 49 rules for P and 39 rules for R.

P rules:
997_0_parts_GT(EOS(STATIC_997), i164, i160, i164) → 1000_0_parts_GT(EOS(STATIC_1000), i164, i160, i164)
1000_0_parts_GT(EOS(STATIC_1000), i164, i160, i164) → 1003_0_parts_Load(EOS(STATIC_1003), i164, i160) | >(i164, 0)
1003_0_parts_Load(EOS(STATIC_1003), i164, i160) → 1006_0_parts_GT(EOS(STATIC_1006), i164, i160, i160)
1006_0_parts_GT(EOS(STATIC_1006), i164, i166, i166) → 1010_0_parts_GT(EOS(STATIC_1010), i164, i166, i166)
1010_0_parts_GT(EOS(STATIC_1010), i164, i166, i166) → 1016_0_parts_Load(EOS(STATIC_1016), i164, i166) | >(i166, 0)
1016_0_parts_Load(EOS(STATIC_1016), i164, i166) → 1020_0_parts_Load(EOS(STATIC_1020), i164, i166, i166)
1020_0_parts_Load(EOS(STATIC_1020), i164, i166, i166) → 1025_0_parts_LE(EOS(STATIC_1025), i164, i166, i166, i164)
1025_0_parts_LE(EOS(STATIC_1025), i164, i166, i166, i164) → 1029_0_parts_LE(EOS(STATIC_1029), i164, i166, i166, i164)
1025_0_parts_LE(EOS(STATIC_1025), i164, i166, i166, i164) → 1030_0_parts_LE(EOS(STATIC_1030), i164, i166, i166, i164)
1029_0_parts_LE(EOS(STATIC_1029), i164, i166, i166, i164) → 1034_0_parts_Load(EOS(STATIC_1034), i164, i166) | <=(i166, i164)
1034_0_parts_Load(EOS(STATIC_1034), i164, i166) → 1044_0_parts_Load(EOS(STATIC_1044), i164, i166, i164)
1044_0_parts_Load(EOS(STATIC_1044), i164, i166, i164) → 1048_0_parts_IntArithmetic(EOS(STATIC_1048), i164, i166, i164, i166)
1048_0_parts_IntArithmetic(EOS(STATIC_1048), i164, i166, i164, i166) → 1053_0_parts_Load(EOS(STATIC_1053), i164, i166, -(i164, i166)) | &&(>(i164, 0), >(i166, 0))
1053_0_parts_Load(EOS(STATIC_1053), i164, i166, i176) → 1058_0_parts_InvokeMethod(EOS(STATIC_1058), i164, i166, i176, i166)
1058_0_parts_InvokeMethod(EOS(STATIC_1058), i164, i166, i176, i166) → 1063_1_parts_InvokeMethod(1063_0_parts_Load(EOS(STATIC_1063), i176, i166), i164, i166, i176, i166)
1063_0_parts_Load(EOS(STATIC_1063), i176, i166) → 1068_0_parts_Load(EOS(STATIC_1068), i176, i166)
1063_1_parts_InvokeMethod(1004_0_parts_Return(EOS(STATIC_1004), i185, i186, matching1), i164, i186, i185, i186) → 1165_0_parts_Return(EOS(STATIC_1165), i164, i186, i185, i186, i185, i186, 1) | =(matching1, 1)
1063_1_parts_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), i770, i771, i723), i164, i771, i770, i771) → 1736_0_parts_Return(EOS(STATIC_1736), i164, i771, i770, i771, i770, i771, i723)
1063_1_parts_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), i825, i826, i778), i164, i826, i825, i826) → 1775_0_parts_Return(EOS(STATIC_1775), i164, i826, i825, i826, i825, i826, i778)
1063_1_parts_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), i946), i164, i954, i953, i954) → 3778_0_parts_Return(EOS(STATIC_3778), i164, i954, i953, i954, i946)
1068_0_parts_Load(EOS(STATIC_1068), i176, i166) → 996_0_parts_Load(EOS(STATIC_996), i176, i166)
996_0_parts_Load(EOS(STATIC_996), i159, i160) → 997_0_parts_GT(EOS(STATIC_997), i159, i160, i159)
1165_0_parts_Return(EOS(STATIC_1165), i164, i186, i185, i186, i185, i186, matching1) → 1168_0_parts_Load(EOS(STATIC_1168), i164, i186, 1) | =(matching1, 1)
1168_0_parts_Load(EOS(STATIC_1168), i164, i186, matching1) → 1228_0_parts_Load(EOS(STATIC_1228), i164, i186, 1) | =(matching1, 1)
1228_0_parts_Load(EOS(STATIC_1228), i164, i265, matching1) → 1255_0_parts_Load(EOS(STATIC_1255), i164, i265, 1) | =(matching1, 1)
1255_0_parts_Load(EOS(STATIC_1255), i164, i279, matching1) → 1367_0_parts_Load(EOS(STATIC_1367), i164, i279, 1) | =(matching1, 1)
1367_0_parts_Load(EOS(STATIC_1367), i164, i357, i358) → 1411_0_parts_Load(EOS(STATIC_1411), i164, i357, i358)
1411_0_parts_Load(EOS(STATIC_1411), i164, i429, i431) → 1529_0_parts_Load(EOS(STATIC_1529), i164, i429, i431)
1529_0_parts_Load(EOS(STATIC_1529), i164, i543, i544) → 1582_0_parts_Load(EOS(STATIC_1582), i164, i543, i544)
1582_0_parts_Load(EOS(STATIC_1582), i164, i624, i626) → 1692_0_parts_Load(EOS(STATIC_1692), i164, i624, i626)
1692_0_parts_Load(EOS(STATIC_1692), i164, i732, i733) → 1752_0_parts_Load(EOS(STATIC_1752), i164, i732, i733)
1752_0_parts_Load(EOS(STATIC_1752), i164, i788, i790) → 1757_0_parts_Load(EOS(STATIC_1757), i788, i790, i164)
1757_0_parts_Load(EOS(STATIC_1757), i788, i790, i164) → 1767_0_parts_ConstantStackPush(EOS(STATIC_1767), i790, i164, i788)
1767_0_parts_ConstantStackPush(EOS(STATIC_1767), i790, i164, i788) → 1779_0_parts_IntArithmetic(EOS(STATIC_1779), i790, i164, i788, 1)
1779_0_parts_IntArithmetic(EOS(STATIC_1779), i790, i164, i788, matching1) → 1784_0_parts_InvokeMethod(EOS(STATIC_1784), i790, i164, -(i788, 1)) | &&(>(i788, 0), =(matching1, 1))
1784_0_parts_InvokeMethod(EOS(STATIC_1784), i790, i164, i840) → 1786_1_parts_InvokeMethod(1786_0_parts_Load(EOS(STATIC_1786), i164, i840), i790, i164, i840)
1786_0_parts_Load(EOS(STATIC_1786), i164, i840) → 1788_0_parts_Load(EOS(STATIC_1788), i164, i840)
1788_0_parts_Load(EOS(STATIC_1788), i164, i840) → 996_0_parts_Load(EOS(STATIC_996), i164, i840)
1736_0_parts_Return(EOS(STATIC_1736), i164, i771, i770, i771, i770, i771, i723) → 1737_0_parts_Return(EOS(STATIC_1737), i164, i771, i770, i771, i770, i771, i723)
1737_0_parts_Return(EOS(STATIC_1737), i164, i788, i789, i788, i789, i788, i790) → 1752_0_parts_Load(EOS(STATIC_1752), i164, i788, i790)
1775_0_parts_Return(EOS(STATIC_1775), i164, i826, i825, i826, i825, i826, i778) → 1737_0_parts_Return(EOS(STATIC_1737), i164, i826, i825, i826, i825, i826, i778)
3778_0_parts_Return(EOS(STATIC_3778), i164, i954, i953, i954, i946) → 1675_0_parts_Return(EOS(STATIC_1675), i164, i954, i953, i954, i946)
1675_0_parts_Return(EOS(STATIC_1675), i164, i732, i734, i732, i733) → 1692_0_parts_Load(EOS(STATIC_1692), i164, i732, i733)
1030_0_parts_LE(EOS(STATIC_1030), i164, i166, i166, i164) → 1036_0_parts_Load(EOS(STATIC_1036), i164, i166) | >(i166, i164)
1036_0_parts_Load(EOS(STATIC_1036), i164, i166) → 1045_0_parts_Load(EOS(STATIC_1045), i164, i166, i164)
1045_0_parts_Load(EOS(STATIC_1045), i164, i166, i164) → 1050_0_parts_InvokeMethod(EOS(STATIC_1050), i164, i166, i164, i164)
1050_0_parts_InvokeMethod(EOS(STATIC_1050), i164, i166, i164, i164) → 1055_1_parts_InvokeMethod(1055_0_parts_Load(EOS(STATIC_1055), i164, i164), i164, i166, i164, i164)
1055_0_parts_Load(EOS(STATIC_1055), i164, i164) → 1059_0_parts_Load(EOS(STATIC_1059), i164, i164)
1059_0_parts_Load(EOS(STATIC_1059), i164, i164) → 996_0_parts_Load(EOS(STATIC_996), i164, i164)
R rules:
997_0_parts_GT(EOS(STATIC_997), i163, i160, i163) → 999_0_parts_GT(EOS(STATIC_999), i163, i160, i163)
999_0_parts_GT(EOS(STATIC_999), i163, i160, i163) → 1002_0_parts_ConstantStackPush(EOS(STATIC_1002), i163, i160) | <=(i163, 0)
1002_0_parts_ConstantStackPush(EOS(STATIC_1002), i163, i160) → 1004_0_parts_Return(EOS(STATIC_1004), i163, i160, 1)
1006_0_parts_GT(EOS(STATIC_1006), i164, matching1, matching2) → 1009_0_parts_GT(EOS(STATIC_1009), i164, 0, 0) | &&(=(matching1, 0), =(matching2, 0))
1009_0_parts_GT(EOS(STATIC_1009), i164, matching1, matching2) → 1014_0_parts_ConstantStackPush(EOS(STATIC_1014), i164, 0) | &&(&&(<=(0, 0), =(matching1, 0)), =(matching2, 0))
1014_0_parts_ConstantStackPush(EOS(STATIC_1014), i164, matching1) → 1018_0_parts_Return(EOS(STATIC_1018), i164, 0, 0) | =(matching1, 0)
1055_1_parts_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), i768, i768, i723), i768, i166, i768, i768) → 1730_0_parts_Return(EOS(STATIC_1730), i768, i166, i768, i768, i768, i768, i723)
1055_1_parts_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), i823, i823, i778), i823, i166, i823, i823) → 1772_0_parts_Return(EOS(STATIC_1772), i823, i166, i823, i823, i823, i823, i778)
1055_1_parts_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), i946), i952, i166, i952, i952) → 3777_0_parts_Return(EOS(STATIC_3777), i952, i166, i952, i952, i946)
1221_0_parts_Return(EOS(STATIC_1221), i263, i166, i263, i263, matching1) → 1334_0_parts_Return(EOS(STATIC_1334), i263, i166, i263, i263, 1) | =(matching1, 1)
1222_0_parts_Return(EOS(STATIC_1222), i164, i265, i264, i265, matching1) → 1340_0_parts_Return(EOS(STATIC_1340), i164, i265, i264, i265, 1) | =(matching1, 1)
1244_0_parts_Return(EOS(STATIC_1244), i276, i166, i276, i276, i276, i276, matching1) → 1391_0_parts_Return(EOS(STATIC_1391), i276, i166, i276, i276, i276, i276, 1) | =(matching1, 1)
1246_0_parts_Return(EOS(STATIC_1246), i164, i279, i278, i279, i278, i279, matching1) → 1396_0_parts_Return(EOS(STATIC_1396), i164, i279, i278, i279, i278, i279, 1) | =(matching1, 1)
1334_0_parts_Return(EOS(STATIC_1334), i345, i166, i345, i345, i346) → 1489_0_parts_Return(EOS(STATIC_1489), i345, i166, i345, i345, i346)
1340_0_parts_Return(EOS(STATIC_1340), i164, i357, i359, i357, i358) → 1495_0_parts_Return(EOS(STATIC_1495), i164, i357, i359, i357, i358)
1391_0_parts_Return(EOS(STATIC_1391), i418, i166, i418, i418, i418, i418, i419) → 1558_0_parts_Return(EOS(STATIC_1558), i418, i166, i418, i418, i418, i418, i419)
1396_0_parts_Return(EOS(STATIC_1396), i164, i429, i430, i429, i430, i429, i431) → 1565_0_parts_Return(EOS(STATIC_1565), i164, i429, i430, i429, i430, i429, i431)
1489_0_parts_Return(EOS(STATIC_1489), i531, i166, i531, i531, i532) → 1668_0_parts_Return(EOS(STATIC_1668), i531, i166, i531, i531, i532)
1495_0_parts_Return(EOS(STATIC_1495), i164, i543, i545, i543, i544) → 1675_0_parts_Return(EOS(STATIC_1675), i164, i543, i545, i543, i544)
1558_0_parts_Return(EOS(STATIC_1558), i613, i166, i613, i613, i613, i613, i614) → 1731_0_parts_Return(EOS(STATIC_1731), i613, i166, i613, i613, i613, i613, i614)
1565_0_parts_Return(EOS(STATIC_1565), i164, i624, i625, i624, i625, i624, i626) → 1737_0_parts_Return(EOS(STATIC_1737), i164, i624, i625, i624, i625, i624, i626)
1668_0_parts_Return(EOS(STATIC_1668), i722, i166, i722, i722, i723) → 1689_0_parts_Return(EOS(STATIC_1689), i722, i166, i723)
1689_0_parts_Return(EOS(STATIC_1689), i722, i166, i723) → 1749_0_parts_Return(EOS(STATIC_1749), i722, i166, i723)
1730_0_parts_Return(EOS(STATIC_1730), i768, i166, i768, i768, i768, i768, i723) → 1731_0_parts_Return(EOS(STATIC_1731), i768, i166, i768, i768, i768, i768, i723)
1731_0_parts_Return(EOS(STATIC_1731), i777, i166, i777, i777, i777, i777, i778) → 1749_0_parts_Return(EOS(STATIC_1749), i777, i166, i778)
1772_0_parts_Return(EOS(STATIC_1772), i823, i166, i823, i823, i823, i823, i778) → 1731_0_parts_Return(EOS(STATIC_1731), i823, i166, i823, i823, i823, i823, i778)
1786_1_parts_InvokeMethod(1018_0_parts_Return(EOS(STATIC_1018), i844, matching1, matching2), i790, i844, matching3) → 1800_0_parts_Return(EOS(STATIC_1800), i790, i844, 0, i844, 0, 0) | &&(&&(=(matching1, 0), =(matching2, 0)), =(matching3, 0))
1786_1_parts_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), i845, i846, i723), i790, i845, i846) → 1801_0_parts_Return(EOS(STATIC_1801), i790, i845, i846, i845, i846, i723)
1786_1_parts_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), i847, i848, i778), i790, i847, i848) → 1804_0_parts_Return(EOS(STATIC_1804), i790, i847, i848, i847, i848, i778)
1786_1_parts_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), i946), i790, i958, i959) → 3781_0_parts_Return(EOS(STATIC_3781), i790, i958, i959, i946)
1800_0_parts_Return(EOS(STATIC_1800), i790, i844, matching1, i844, matching2, matching3) → 1805_0_parts_IntArithmetic(EOS(STATIC_1805), i790, 0) | &&(&&(=(matching1, 0), =(matching2, 0)), =(matching3, 0))
1801_0_parts_Return(EOS(STATIC_1801), i790, i845, i846, i845, i846, i723) → 1807_0_parts_IntArithmetic(EOS(STATIC_1807), i790, i723)
1804_0_parts_Return(EOS(STATIC_1804), i790, i847, i848, i847, i848, i778) → 1801_0_parts_Return(EOS(STATIC_1801), i790, i847, i848, i847, i848, i778)
1805_0_parts_IntArithmetic(EOS(STATIC_1805), i790, matching1) → 1807_0_parts_IntArithmetic(EOS(STATIC_1807), i790, 0) | =(matching1, 0)
1807_0_parts_IntArithmetic(EOS(STATIC_1807), i790, i723) → 3771_0_parts_IntArithmetic(EOS(STATIC_3771), i790, i723)
1832_0_parts_Return(EOS(STATIC_1832), i790, i870, i871, i858) → 3771_0_parts_IntArithmetic(EOS(STATIC_3771), i790, i858)
3771_0_parts_IntArithmetic(EOS(STATIC_3771), i790, i858) → 3772_0_parts_Return(EOS(STATIC_3772), +(i790, i858))
3777_0_parts_Return(EOS(STATIC_3777), i952, i166, i952, i952, i946) → 1668_0_parts_Return(EOS(STATIC_1668), i952, i166, i952, i952, i946)
3781_0_parts_Return(EOS(STATIC_3781), i790, i958, i959, i946) → 1832_0_parts_Return(EOS(STATIC_1832), i790, i958, i959, i946)

Combined rules. Obtained 6 conditional rules for P and 8 conditional rules for R.

P rules:
997_0_parts_GT(EOS(STATIC_997), x0, x1, x0) → 1063_1_parts_InvokeMethod(997_0_parts_GT(EOS(STATIC_997), -(x0, x1), x1, -(x0, x1)), x0, x1, -(x0, x1), x1) | &&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0))
1063_1_parts_InvokeMethod(1004_0_parts_Return(EOS(STATIC_1004), x0, x1, 1), x3, x1, x0, x1) → 1786_1_parts_InvokeMethod(997_0_parts_GT(EOS(STATIC_997), x3, -(x1, 1), x3), 1, x3, -(x1, 1)) | >(x1, 0)
1063_1_parts_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), x0, x1, x2), x3, x1, x0, x1) → 1786_1_parts_InvokeMethod(997_0_parts_GT(EOS(STATIC_997), x3, -(x1, 1), x3), x2, x3, -(x1, 1)) | >(x1, 0)
1063_1_parts_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), x0, x1, x2), x3, x1, x0, x1) → 1786_1_parts_InvokeMethod(997_0_parts_GT(EOS(STATIC_997), x3, -(x1, 1), x3), x2, x3, -(x1, 1)) | >(x1, 0)
1063_1_parts_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), x0), x1, x2, x3, x2) → 1786_1_parts_InvokeMethod(997_0_parts_GT(EOS(STATIC_997), x1, -(x2, 1), x1), x0, x1, -(x2, 1)) | >(x2, 0)
997_0_parts_GT(EOS(STATIC_997), x0, x1, x0) → 1055_1_parts_InvokeMethod(997_0_parts_GT(EOS(STATIC_997), x0, x0, x0), x0, x1, x0, x0) | &&(&&(>(x1, x0), >(x1, 0)), >(x0, 0))
R rules:
997_0_parts_GT(EOS(STATIC_997), x0, x1, x0) → 1004_0_parts_Return(EOS(STATIC_1004), x0, x1, 1) | <=(x0, 0)
1055_1_parts_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), x0, x0, x1), x0, x2, x0, x0) → 1749_0_parts_Return(EOS(STATIC_1749), x0, x2, x1)
1055_1_parts_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), x0, x0, x1), x0, x2, x0, x0) → 1749_0_parts_Return(EOS(STATIC_1749), x0, x2, x1)
1055_1_parts_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), x0), x1, x2, x1, x1) → 1749_0_parts_Return(EOS(STATIC_1749), x1, x2, x0)
1786_1_parts_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), x0, x1, x2), x3, x0, x1) → 3772_0_parts_Return(EOS(STATIC_3772), +(x3, x2))
1786_1_parts_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), x0, x1, x2), x3, x0, x1) → 3772_0_parts_Return(EOS(STATIC_3772), +(x3, x2))
1786_1_parts_InvokeMethod(1018_0_parts_Return(EOS(STATIC_1018), x0, 0, 0), arith[1], x0, 0) → 3772_0_parts_Return(EOS(STATIC_3772), arith[1])
1786_1_parts_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), x0), x1, x2, x3) → 3772_0_parts_Return(EOS(STATIC_3772), +(x1, x0))

Filtered ground terms:

997_0_parts_GT(x1, x2, x3, x4) → 997_0_parts_GT(x2, x3, x4)
Cond_997_0_parts_GT1(x1, x2, x3, x4, x5) → Cond_997_0_parts_GT1(x1, x3, x4, x5)
3772_0_parts_Return(x1, x2) → 3772_0_parts_Return(x2)
1749_0_parts_Return(x1, x2, x3, x4) → 1749_0_parts_Return(x2, x3, x4)
1689_0_parts_Return(x1, x2, x3, x4) → 1689_0_parts_Return(x2, x3, x4)
1004_0_parts_Return(x1, x2, x3, x4) → 1004_0_parts_Return(x2, x3)
Cond_997_0_parts_GT(x1, x2, x3, x4, x5) → Cond_997_0_parts_GT(x1, x3, x4, x5)
1018_0_parts_Return(x1, x2, x3, x4) → 1018_0_parts_Return(x2)

Filtered duplicate args:

997_0_parts_GT(x1, x2, x3) → 997_0_parts_GT(x2, x3)
Cond_997_0_parts_GT(x1, x2, x3, x4) → Cond_997_0_parts_GT(x1, x3, x4)
1063_1_parts_InvokeMethod(x1, x2, x3, x4, x5) → 1063_1_parts_InvokeMethod(x1, x2, x4, x5)
Cond_1063_1_parts_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_1063_1_parts_InvokeMethod(x1, x2, x3)
Cond_1063_1_parts_InvokeMethod1(x1, x2, x3, x4, x5, x6) → Cond_1063_1_parts_InvokeMethod1(x1, x2, x3)
Cond_1063_1_parts_InvokeMethod2(x1, x2, x3, x4, x5, x6) → Cond_1063_1_parts_InvokeMethod2(x1, x2, x3)
Cond_1063_1_parts_InvokeMethod3(x1, x2, x3, x4, x5, x6) → Cond_1063_1_parts_InvokeMethod3(x1, x2, x3, x5, x6)
Cond_997_0_parts_GT1(x1, x2, x3, x4) → Cond_997_0_parts_GT1(x1, x3, x4)
1055_1_parts_InvokeMethod(x1, x2, x3, x4, x5) → 1055_1_parts_InvokeMethod(x1, x3, x5)

Filtered unneeded arguments:

1786_1_parts_InvokeMethod(x1, x2, x3, x4) → 1786_1_parts_InvokeMethod(x1, x3, x4)
Cond_1063_1_parts_InvokeMethod3(x1, x2, x3, x4, x5) → Cond_1063_1_parts_InvokeMethod3(x1, x3, x5)
1689_0_parts_Return(x1, x2, x3) → 1689_0_parts_Return(x1, x2)
1749_0_parts_Return(x1, x2, x3) → 1749_0_parts_Return(x1, x2)
1004_0_parts_Return(x1, x2) → 1004_0_parts_Return(x2)

Combined rules. Obtained 6 conditional rules for P and 8 conditional rules for R.

P rules:
997_0_parts_GT(x1, x0) → 1063_1_parts_InvokeMethod(997_0_parts_GT(x1, -(x0, x1)), x0, -(x0, x1), x1) | &&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0))
1063_1_parts_InvokeMethod(1004_0_parts_Return(x1), x3, x0, x1) → 1786_1_parts_InvokeMethod(997_0_parts_GT(-(x1, 1), x3), x3, -(x1, 1)) | >(x1, 0)
1063_1_parts_InvokeMethod(1689_0_parts_Return(x0, x1), x3, x0, x1) → 1786_1_parts_InvokeMethod(997_0_parts_GT(-(x1, 1), x3), x3, -(x1, 1)) | >(x1, 0)
1063_1_parts_InvokeMethod(1749_0_parts_Return(x0, x1), x3, x0, x1) → 1786_1_parts_InvokeMethod(997_0_parts_GT(-(x1, 1), x3), x3, -(x1, 1)) | >(x1, 0)
1063_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1, x3, x2) → 1786_1_parts_InvokeMethod(997_0_parts_GT(-(x2, 1), x1), x1, -(x2, 1)) | >(x2, 0)
997_0_parts_GT(x1, x0) → 1055_1_parts_InvokeMethod(997_0_parts_GT(x0, x0), x1, x0) | &&(&&(>(x1, x0), >(x1, 0)), >(x0, 0))
R rules:
997_0_parts_GT(x1, x0) → 1004_0_parts_Return(x1) | <=(x0, 0)
1055_1_parts_InvokeMethod(1689_0_parts_Return(x0, x0), x2, x0) → 1749_0_parts_Return(x0, x2)
1055_1_parts_InvokeMethod(1749_0_parts_Return(x0, x0), x2, x0) → 1749_0_parts_Return(x0, x2)
1055_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x1) → 1749_0_parts_Return(x1, x2)
1786_1_parts_InvokeMethod(1689_0_parts_Return(x0, x1), x0, x1) → 3772_0_parts_Return(+(x3, x2))
1786_1_parts_InvokeMethod(1749_0_parts_Return(x0, x1), x0, x1) → 3772_0_parts_Return(+(x3, x2))
1786_1_parts_InvokeMethod(1018_0_parts_Return(x0), x0, 0) → 3772_0_parts_Return(arith[1])
1786_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x3) → 3772_0_parts_Return(+(x1, x0))

Performed bisimulation on rules. Used the following equivalence classes: {[1689_0_parts_Return_2, 1749_0_parts_Return_2]=1689_0_parts_Return_2, [1004_0_parts_Return_1, 1018_0_parts_Return_1]=1004_0_parts_Return_1, [Cond_1063_1_parts_InvokeMethod1_5, Cond_1063_1_parts_InvokeMethod2_5]=Cond_1063_1_parts_InvokeMethod1_5}

Finished conversion. Obtained 11 rules for P and 7 rules for R. System has predefined symbols.

P rules:
997_0_PARTS_GT(x1, x0) → COND_997_0_PARTS_GT(&&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0)), x1, x0)
COND_997_0_PARTS_GT(TRUE, x1, x0) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1, -(x0, x1)), x0, -(x0, x1), x1)
COND_997_0_PARTS_GT(TRUE, x1, x0) → 997_0_PARTS_GT(x1, -(x0, x1))
1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1), x3, x0, x1) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1, 0), 1004_0_parts_Return(x1), x3, x0, x1)
COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1), x3, x0, x1) → 997_0_PARTS_GT(-(x1, 1), x3)
1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0, x1), x3, x0, x1) → COND_1063_1_PARTS_INVOKEMETHOD1(>(x1, 0), 1689_0_parts_Return(x0, x1), x3, x0, x1)
COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0, x1), x3, x0, x1) → 997_0_PARTS_GT(-(x1, 1), x3)
1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0), x1, x3, x2) → COND_1063_1_PARTS_INVOKEMETHOD3(>(x2, 0), 3772_0_parts_Return(x0), x1, x3, x2)
COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0), x1, x3, x2) → 997_0_PARTS_GT(-(x2, 1), x1)
997_0_PARTS_GT(x1, x0) → COND_997_0_PARTS_GT1(&&(&&(>(x1, x0), >(x1, 0)), >(x0, 0)), x1, x0)
COND_997_0_PARTS_GT1(TRUE, x1, x0) → 997_0_PARTS_GT(x0, x0)
R rules:
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT(<=(x0, 0), x1, x0)
Cond_997_0_parts_GT(TRUE, x1, x0) → 1004_0_parts_Return(x1)
1055_1_parts_InvokeMethod(1689_0_parts_Return(x0, x0), x2, x0) → 1689_0_parts_Return(x0, x2)
1055_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x1) → 1689_0_parts_Return(x1, x2)
1786_1_parts_InvokeMethod(1689_0_parts_Return(x0, x1), x0, x1) → 3772_0_parts_Return(+(x3, x2))
1786_1_parts_InvokeMethod(1004_0_parts_Return(x0), x0, 0) → 3772_0_parts_Return(arith[1])
1786_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x3) → 3772_0_parts_Return(+(x1, x0))

(7) 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

The ITRS R consists of the following rules:
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT(x0 <= 0, x1, x0)
Cond_997_0_parts_GT(TRUE, x1, x0) → 1004_0_parts_Return(x1)
1055_1_parts_InvokeMethod(1689_0_parts_Return(x0, x0), x2, x0) → 1689_0_parts_Return(x0, x2)
1055_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x1) → 1689_0_parts_Return(x1, x2)
1786_1_parts_InvokeMethod(1689_0_parts_Return(x0, x1), x0, x1) → 3772_0_parts_Return(x3 + x2)
1786_1_parts_InvokeMethod(1004_0_parts_Return(x0), x0, 0) → 3772_0_parts_Return(arith[1])
1786_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x3) → 3772_0_parts_Return(x1 + x0)

The integer pair graph contains the following rules and edges:
(0): 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0, x1[0], x0[0])
(1): COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], x0[1] - x1[1]), x0[1], x0[1] - x1[1], x1[1])
(2): COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], x0[2] - x1[2])
(3): 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(x1[3] > 0, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
(4): COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(x1[4] - 1, x3[4])
(5): 1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_1063_1_PARTS_INVOKEMETHOD1(x1[5] > 0, 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])
(6): COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 997_0_PARTS_GT(x1[6] - 1, x3[6])
(7): 1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_1063_1_PARTS_INVOKEMETHOD3(x2[7] > 0, 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])
(8): COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 997_0_PARTS_GT(x2[8] - 1, x1[8])
(9): 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(x1[9] > x0[9] && x1[9] > 0 && x0[9] > 0, x1[9], x0[9])
(10): COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10])

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

(0) -> (2), if (x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0 ∧x1[0] →^* x1[2]∧x0[0] →^* x0[2])

(1) -> (3), if (997_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 1004_0_parts_Return(x1[3])∧x0[1] →^* x3[3]∧x0[1] - x1[1] →^* x0[3]∧x1[1] →^* x1[3])

(1) -> (5), if (997_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 1689_0_parts_Return(x0[5], x1[5])∧x0[1] →^* x3[5]∧x0[1] - x1[1] →^* x0[5]∧x1[1] →^* x1[5])

(1) -> (7), if (997_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 3772_0_parts_Return(x0[7])∧x0[1] →^* x1[7]∧x0[1] - x1[1] →^* x3[7]∧x1[1] →^* x2[7])

(2) -> (0), if (x1[2] →^* x1[0]∧x0[2] - x1[2] →^* x0[0])

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

(3) -> (4), if (x1[3] > 0 ∧1004_0_parts_Return(x1[3]) →^* 1004_0_parts_Return(x1[4])∧x3[3] →^* x3[4]∧x0[3] →^* x0[4]∧x1[3] →^* x1[4])

(4) -> (0), if (x1[4] - 1 →^* x1[0]∧x3[4] →^* x0[0])

(4) -> (9), if (x1[4] - 1 →^* x1[9]∧x3[4] →^* x0[9])

(5) -> (6), if (x1[5] > 0 ∧1689_0_parts_Return(x0[5], x1[5]) →^* 1689_0_parts_Return(x0[6], x1[6])∧x3[5] →^* x3[6]∧x0[5] →^* x0[6]∧x1[5] →^* x1[6])

(6) -> (0), if (x1[6] - 1 →^* x1[0]∧x3[6] →^* x0[0])

(6) -> (9), if (x1[6] - 1 →^* x1[9]∧x3[6] →^* x0[9])

(7) -> (8), if (x2[7] > 0 ∧3772_0_parts_Return(x0[7]) →^* 3772_0_parts_Return(x0[8])∧x1[7] →^* x1[8]∧x3[7] →^* x3[8]∧x2[7] →^* x2[8])

(8) -> (0), if (x2[8] - 1 →^* x1[0]∧x1[8] →^* x0[0])

(8) -> (9), if (x2[8] - 1 →^* x1[9]∧x1[8] →^* x0[9])

(9) -> (10), if (x1[9] > x0[9] && x1[9] > 0 && x0[9] > 0 ∧x1[9] →^* x1[10]∧x0[9] →^* x0[10])

(10) -> (0), if (x0[10] →^* x1[0]∧x0[10] →^* x0[0])

(10) -> (9), if (x0[10] →^* x1[9]∧x0[10] →^* x0[9])

The set Q consists of the following terms:
997_0_parts_GT(x0, x1)
Cond_997_0_parts_GT(TRUE, x0, x1)
1055_1_parts_InvokeMethod(1689_0_parts_Return(x0, x0), x1, x0)
1055_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1, x2)
1786_1_parts_InvokeMethod(1689_0_parts_Return(x0, x1), x0, x1)
1786_1_parts_InvokeMethod(1004_0_parts_Return(x0), x0, 0)
1786_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1, x2)

(8) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: true Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@4ab50848 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 997_0_PARTS_GT(x1, x0) → COND_997_0_PARTS_GT(&&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0)), x1, x0) the following chains were created:

We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]) which results in the following constraint:
(1)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[1]∧x0[0]=x0[1] ⇒ 997_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧997_0_PARTS_GT(x1[0], x0[0])≥COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥))

We simplified constraint (1) using rule (IV) which results in the following new constraint:
(2)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE ⇒ 997_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧997_0_PARTS_GT(x1[0], x0[0])≥COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_58] ≥ 0)
We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2])) which results in the following constraint:
(7)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[2]∧x0[0]=x0[2] ⇒ 997_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧997_0_PARTS_GT(x1[0], x0[0])≥COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥))

We simplified constraint (7) using rule (IV) which results in the following new constraint:
(8)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE ⇒ 997_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧997_0_PARTS_GT(x1[0], x0[0])≥COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥))

We simplified constraint (8) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(9)    (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (9) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(10)    (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (10) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(11)    (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (11) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(12)    (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_58] ≥ 0)

For Pair COND_997_0_PARTS_GT(TRUE, x1, x0) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1, -(x0, x1)), x0, -(x0, x1), x1) the following chains were created:

We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]), 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) which results in the following constraint:
(13)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[1]∧x0[0]=x0[1]∧997_0_parts_GT(x1[1], -(x0[1], x1[1]))=1004_0_parts_Return(x1[3])∧x0[1]=x3[3]∧-(x0[1], x1[1])=x0[3]∧x1[1]=x1[3] ⇒ COND_997_0_PARTS_GT(TRUE, x1[1], x0[1])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[1], x0[1])≥1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])∧(U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (13) using rules (III), (IV), (REWRITING) which results in the following new constraint:
(14)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧Cond_997_0_parts_GT(<=(-(x0[0], x1[0]), 0), x1[0], -(x0[0], x1[0]))=1004_0_parts_Return(x1[0]) ⇒ COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[0], -(x0[0], x1[0])), x0[0], -(x0[0], x1[0]), x1[0])∧(U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (14) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(15)    (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (15) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(16)    (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (16) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(17)    (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (17) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(18)    (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_60] ≥ 0)
We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]), 1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) which results in the following constraint:
(19)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[1]∧x0[0]=x0[1]∧997_0_parts_GT(x1[1], -(x0[1], x1[1]))=1689_0_parts_Return(x0[5], x1[5])∧x0[1]=x3[5]∧-(x0[1], x1[1])=x0[5]∧x1[1]=x1[5] ⇒ COND_997_0_PARTS_GT(TRUE, x1[1], x0[1])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[1], x0[1])≥1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])∧(U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (19) using rules (III), (IV), (REWRITING) which results in the following new constraint:
(20)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧Cond_997_0_parts_GT(<=(-(x0[0], x1[0]), 0), x1[0], -(x0[0], x1[0]))=1689_0_parts_Return(-(x0[0], x1[0]), x1[0]) ⇒ COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[0], -(x0[0], x1[0])), x0[0], -(x0[0], x1[0]), x1[0])∧(U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (20) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(21)    (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(22)    (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (22) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(23)    (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (23) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(24)    (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_60] ≥ 0)
We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]), 1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) which results in the following constraint:
(25)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[1]∧x0[0]=x0[1]∧997_0_parts_GT(x1[1], -(x0[1], x1[1]))=3772_0_parts_Return(x0[7])∧x0[1]=x1[7]∧-(x0[1], x1[1])=x3[7]∧x1[1]=x2[7] ⇒ COND_997_0_PARTS_GT(TRUE, x1[1], x0[1])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[1], x0[1])≥1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])∧(U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (25) using rules (III), (IV), (REWRITING) which results in the following new constraint:
(26)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧Cond_997_0_parts_GT(<=(-(x0[0], x1[0]), 0), x1[0], -(x0[0], x1[0]))=3772_0_parts_Return(x0[7]) ⇒ COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[0], -(x0[0], x1[0])), x0[0], -(x0[0], x1[0]), x1[0])∧(U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (26) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(27)    (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (27) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(28)    (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (28) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(29)    (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧[(-1)bso_60] ≥ 0)

We simplified constraint (29) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(30)    (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_60] ≥ 0)

For Pair COND_997_0_PARTS_GT(TRUE, x1, x0) → 997_0_PARTS_GT(x1, -(x0, x1)) the following chains were created:

We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2])), 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(31)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[2]∧x0[0]=x0[2]∧x1[2]=x1[0]1∧-(x0[2], x1[2])=x0[0]1 ⇒ COND_997_0_PARTS_GT(TRUE, x1[2], x0[2])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[2], x0[2])≥997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))∧(U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (31) using rules (III), (IV) which results in the following new constraint:
(32)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE ⇒ COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥997_0_PARTS_GT(x1[0], -(x0[0], x1[0]))∧(U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (32) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(33)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧[(-1)bso_62] ≥ 0)

We simplified constraint (33) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(34)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧[(-1)bso_62] ≥ 0)

We simplified constraint (34) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(35)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧[(-1)bso_62] ≥ 0)

We simplified constraint (35) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(36)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_62] ≥ 0)
We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2])), 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(37)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[2]∧x0[0]=x0[2]∧x1[2]=x1[9]∧-(x0[2], x1[2])=x0[9] ⇒ COND_997_0_PARTS_GT(TRUE, x1[2], x0[2])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[2], x0[2])≥997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))∧(U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (37) using rules (III), (IV) which results in the following new constraint:
(38)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE ⇒ COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥997_0_PARTS_GT(x1[0], -(x0[0], x1[0]))∧(U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (38) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(39)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧[(-1)bso_62] ≥ 0)

We simplified constraint (39) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(40)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧[(-1)bso_62] ≥ 0)

We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(41)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧[(-1)bso_62] ≥ 0)

We simplified constraint (41) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(42)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_62] ≥ 0)

For Pair 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1), x3, x0, x1) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1, 0), 1004_0_parts_Return(x1), x3, x0, x1) the following chains were created:

We consider the chain 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(-(x1[4], 1), x3[4]) which results in the following constraint:
(43)    (>(x1[3], 0)=TRUE∧1004_0_parts_Return(x1[3])=1004_0_parts_Return(x1[4])∧x3[3]=x3[4]∧x0[3]=x0[4]∧x1[3]=x1[4] ⇒ 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])∧(U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥))

We simplified constraint (43) using rules (I), (II), (IV) which results in the following new constraint:
(44)    (>(x1[3], 0)=TRUE ⇒ 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])∧(U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥))

We simplified constraint (44) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(45)    (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [bni_63]x0[3] ≥ 0∧[(-1)bso_64] + x0[3] ≥ 0)

We simplified constraint (45) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(46)    (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [bni_63]x0[3] ≥ 0∧[(-1)bso_64] + x0[3] ≥ 0)

We simplified constraint (46) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(47)    (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[(-1)bni_63 + (-1)Bound*bni_63] + [bni_63]x0[3] ≥ 0∧[(-1)bso_64] + x0[3] ≥ 0)

We simplified constraint (47) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(48)    (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 ≥ 0∧[bni_63] ≥ 0∧0 ≥ 0∧[(-1)bni_63 + (-1)Bound*bni_63] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_64] ≥ 0)

For Pair COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1), x3, x0, x1) → 997_0_PARTS_GT(-(x1, 1), x3) the following chains were created:

We consider the chain 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(-(x1[4], 1), x3[4]), 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(49)    (>(x1[3], 0)=TRUE∧1004_0_parts_Return(x1[3])=1004_0_parts_Return(x1[4])∧x3[3]=x3[4]∧x0[3]=x0[4]∧x1[3]=x1[4]∧-(x1[4], 1)=x1[0]∧x3[4]=x0[0] ⇒ COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥997_0_PARTS_GT(-(x1[4], 1), x3[4])∧(U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (49) using rules (I), (II), (III), (IV) which results in the following new constraint:
(50)    (>(x1[3], 0)=TRUE ⇒ COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥997_0_PARTS_GT(-(x1[3], 1), x3[3])∧(U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (50) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(51)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (51) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(52)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (52) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(53)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (53) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(54)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_66] ≥ 0)
We consider the chain 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(-(x1[4], 1), x3[4]), 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(55)    (>(x1[3], 0)=TRUE∧1004_0_parts_Return(x1[3])=1004_0_parts_Return(x1[4])∧x3[3]=x3[4]∧x0[3]=x0[4]∧x1[3]=x1[4]∧-(x1[4], 1)=x1[9]∧x3[4]=x0[9] ⇒ COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥997_0_PARTS_GT(-(x1[4], 1), x3[4])∧(U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (55) using rules (I), (II), (III), (IV) which results in the following new constraint:
(56)    (>(x1[3], 0)=TRUE ⇒ COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥997_0_PARTS_GT(-(x1[3], 1), x3[3])∧(U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (56) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(57)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (57) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(58)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (58) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(59)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (59) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(60)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_66] ≥ 0)

For Pair 1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0, x1), x3, x0, x1) → COND_1063_1_PARTS_INVOKEMETHOD1(>(x1, 0), 1689_0_parts_Return(x0, x1), x3, x0, x1) the following chains were created:

We consider the chain 1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]), COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 997_0_PARTS_GT(-(x1[6], 1), x3[6]) which results in the following constraint:
(61)    (>(x1[5], 0)=TRUE∧1689_0_parts_Return(x0[5], x1[5])=1689_0_parts_Return(x0[6], x1[6])∧x3[5]=x3[6]∧x0[5]=x0[6]∧x1[5]=x1[6] ⇒ 1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥NonInfC∧1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])∧(U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥))

We simplified constraint (61) using rules (I), (II), (IV) which results in the following new constraint:
(62)    (>(x1[5], 0)=TRUE ⇒ 1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥NonInfC∧1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])∧(U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥))

We simplified constraint (62) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(63)    (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧[(2)bni_67 + (-1)Bound*bni_67] + [bni_67]x1[5] + [bni_67]x0[5] ≥ 0∧[3 + (-1)bso_68] + x1[5] ≥ 0)

We simplified constraint (63) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(64)    (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧[(2)bni_67 + (-1)Bound*bni_67] + [bni_67]x1[5] + [bni_67]x0[5] ≥ 0∧[3 + (-1)bso_68] + x1[5] ≥ 0)

We simplified constraint (64) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(65)    (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧[(2)bni_67 + (-1)Bound*bni_67] + [bni_67]x1[5] + [bni_67]x0[5] ≥ 0∧[3 + (-1)bso_68] + x1[5] ≥ 0)

We simplified constraint (65) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(66)    (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧[bni_67] ≥ 0∧[bni_67] ≥ 0∧0 ≥ 0∧[(2)bni_67 + (-1)Bound*bni_67] ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[3 + (-1)bso_68] ≥ 0)

For Pair COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0, x1), x3, x0, x1) → 997_0_PARTS_GT(-(x1, 1), x3) the following chains were created:

We consider the chain 1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]), COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 997_0_PARTS_GT(-(x1[6], 1), x3[6]), 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(67)    (>(x1[5], 0)=TRUE∧1689_0_parts_Return(x0[5], x1[5])=1689_0_parts_Return(x0[6], x1[6])∧x3[5]=x3[6]∧x0[5]=x0[6]∧x1[5]=x1[6]∧-(x1[6], 1)=x1[0]∧x3[6]=x0[0] ⇒ COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6])≥997_0_PARTS_GT(-(x1[6], 1), x3[6])∧(U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥))

We simplified constraint (67) using rules (I), (II), (III), (IV) which results in the following new constraint:
(68)    (>(x1[5], 0)=TRUE ⇒ COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥997_0_PARTS_GT(-(x1[5], 1), x3[5])∧(U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥))

We simplified constraint (68) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(69)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [bni_69]x0[5] ≥ 0∧[(-1)bso_70] + x0[5] ≥ 0)

We simplified constraint (69) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(70)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [bni_69]x0[5] ≥ 0∧[(-1)bso_70] + x0[5] ≥ 0)

We simplified constraint (70) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(71)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [bni_69]x0[5] ≥ 0∧[(-1)bso_70] + x0[5] ≥ 0)

We simplified constraint (71) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(72)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧0 ≥ 0∧[bni_69] ≥ 0∧0 ≥ 0∧[(-1)bni_69 + (-1)Bound*bni_69] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_70] ≥ 0)
We consider the chain 1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]), COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 997_0_PARTS_GT(-(x1[6], 1), x3[6]), 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(73)    (>(x1[5], 0)=TRUE∧1689_0_parts_Return(x0[5], x1[5])=1689_0_parts_Return(x0[6], x1[6])∧x3[5]=x3[6]∧x0[5]=x0[6]∧x1[5]=x1[6]∧-(x1[6], 1)=x1[9]∧x3[6]=x0[9] ⇒ COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6])≥997_0_PARTS_GT(-(x1[6], 1), x3[6])∧(U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥))

We simplified constraint (73) using rules (I), (II), (III), (IV) which results in the following new constraint:
(74)    (>(x1[5], 0)=TRUE ⇒ COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥997_0_PARTS_GT(-(x1[5], 1), x3[5])∧(U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥))

We simplified constraint (74) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(75)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [bni_69]x0[5] ≥ 0∧[(-1)bso_70] + x0[5] ≥ 0)

We simplified constraint (75) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(76)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [bni_69]x0[5] ≥ 0∧[(-1)bso_70] + x0[5] ≥ 0)

We simplified constraint (76) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(77)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧[(-1)bni_69 + (-1)Bound*bni_69] + [bni_69]x0[5] ≥ 0∧[(-1)bso_70] + x0[5] ≥ 0)

We simplified constraint (77) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(78)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧0 ≥ 0∧[bni_69] ≥ 0∧0 ≥ 0∧[(-1)bni_69 + (-1)Bound*bni_69] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_70] ≥ 0)

For Pair 1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0), x1, x3, x2) → COND_1063_1_PARTS_INVOKEMETHOD3(>(x2, 0), 3772_0_parts_Return(x0), x1, x3, x2) the following chains were created:

We consider the chain 1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]), COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 997_0_PARTS_GT(-(x2[8], 1), x1[8]) which results in the following constraint:
(79)    (>(x2[7], 0)=TRUE∧3772_0_parts_Return(x0[7])=3772_0_parts_Return(x0[8])∧x1[7]=x1[8]∧x3[7]=x3[8]∧x2[7]=x2[8] ⇒ 1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥NonInfC∧1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])∧(U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])), ≥))

We simplified constraint (79) using rules (I), (II), (IV) which results in the following new constraint:
(80)    (>(x2[7], 0)=TRUE ⇒ 1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥NonInfC∧1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])∧(U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])), ≥))

We simplified constraint (80) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(81)    (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])), ≥)∧[(2)bni_71 + (-1)Bound*bni_71] + [bni_71]x2[7] + [bni_71]x3[7] ≥ 0∧[3 + (-1)bso_72] + x3[7] ≥ 0)

We simplified constraint (81) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(82)    (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])), ≥)∧[(2)bni_71 + (-1)Bound*bni_71] + [bni_71]x2[7] + [bni_71]x3[7] ≥ 0∧[3 + (-1)bso_72] + x3[7] ≥ 0)

We simplified constraint (82) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(83)    (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])), ≥)∧[(2)bni_71 + (-1)Bound*bni_71] + [bni_71]x2[7] + [bni_71]x3[7] ≥ 0∧[3 + (-1)bso_72] + x3[7] ≥ 0)

We simplified constraint (83) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(84)    (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])), ≥)∧[bni_71] ≥ 0∧[bni_71] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(2)bni_71 + (-1)Bound*bni_71] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[3 + (-1)bso_72] ≥ 0)

For Pair COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0), x1, x3, x2) → 997_0_PARTS_GT(-(x2, 1), x1) the following chains were created:

We consider the chain 1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]), COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 997_0_PARTS_GT(-(x2[8], 1), x1[8]), 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(85)    (>(x2[7], 0)=TRUE∧3772_0_parts_Return(x0[7])=3772_0_parts_Return(x0[8])∧x1[7]=x1[8]∧x3[7]=x3[8]∧x2[7]=x2[8]∧-(x2[8], 1)=x1[0]∧x1[8]=x0[0] ⇒ COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[8]), x1[8], x3[8], x2[8])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[8]), x1[8], x3[8], x2[8])≥997_0_PARTS_GT(-(x2[8], 1), x1[8])∧(U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥))

We simplified constraint (85) using rules (I), (II), (III), (IV) which results in the following new constraint:
(86)    (>(x2[7], 0)=TRUE ⇒ COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥997_0_PARTS_GT(-(x2[7], 1), x1[7])∧(U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥))

We simplified constraint (86) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(87)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[(-1)bni_73 + (-1)Bound*bni_73] + [bni_73]x2[7] ≥ 0∧[(-1)bso_74] + x2[7] ≥ 0)

We simplified constraint (87) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(88)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[(-1)bni_73 + (-1)Bound*bni_73] + [bni_73]x2[7] ≥ 0∧[(-1)bso_74] + x2[7] ≥ 0)

We simplified constraint (88) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(89)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[(-1)bni_73 + (-1)Bound*bni_73] + [bni_73]x2[7] ≥ 0∧[(-1)bso_74] + x2[7] ≥ 0)

We simplified constraint (89) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(90)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[bni_73] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_73 + (-1)Bound*bni_73] ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_74] ≥ 0)
We consider the chain 1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]), COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 997_0_PARTS_GT(-(x2[8], 1), x1[8]), 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(91)    (>(x2[7], 0)=TRUE∧3772_0_parts_Return(x0[7])=3772_0_parts_Return(x0[8])∧x1[7]=x1[8]∧x3[7]=x3[8]∧x2[7]=x2[8]∧-(x2[8], 1)=x1[9]∧x1[8]=x0[9] ⇒ COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[8]), x1[8], x3[8], x2[8])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[8]), x1[8], x3[8], x2[8])≥997_0_PARTS_GT(-(x2[8], 1), x1[8])∧(U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥))

We simplified constraint (91) using rules (I), (II), (III), (IV) which results in the following new constraint:
(92)    (>(x2[7], 0)=TRUE ⇒ COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥997_0_PARTS_GT(-(x2[7], 1), x1[7])∧(U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥))

We simplified constraint (92) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(93)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[(-1)bni_73 + (-1)Bound*bni_73] + [bni_73]x2[7] ≥ 0∧[(-1)bso_74] + x2[7] ≥ 0)

We simplified constraint (93) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(94)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[(-1)bni_73 + (-1)Bound*bni_73] + [bni_73]x2[7] ≥ 0∧[(-1)bso_74] + x2[7] ≥ 0)

We simplified constraint (94) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(95)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[(-1)bni_73 + (-1)Bound*bni_73] + [bni_73]x2[7] ≥ 0∧[(-1)bso_74] + x2[7] ≥ 0)

We simplified constraint (95) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(96)    (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[bni_73] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_73 + (-1)Bound*bni_73] ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_74] ≥ 0)

For Pair 997_0_PARTS_GT(x1, x0) → COND_997_0_PARTS_GT1(&&(&&(>(x1, x0), >(x1, 0)), >(x0, 0)), x1, x0) the following chains were created:

We consider the chain 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]), COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10]) which results in the following constraint:
(97)    (&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0))=TRUE∧x1[9]=x1[10]∧x0[9]=x0[10] ⇒ 997_0_PARTS_GT(x1[9], x0[9])≥NonInfC∧997_0_PARTS_GT(x1[9], x0[9])≥COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])∧(U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥))

We simplified constraint (97) using rule (IV) which results in the following new constraint:
(98)    (&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0))=TRUE ⇒ 997_0_PARTS_GT(x1[9], x0[9])≥NonInfC∧997_0_PARTS_GT(x1[9], x0[9])≥COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])∧(U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥))

We simplified constraint (98) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(99)    (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)bni_75 + (-1)Bound*bni_75] ≥ 0∧[(-1)bso_76] ≥ 0)

We simplified constraint (99) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(100)    (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)bni_75 + (-1)Bound*bni_75] ≥ 0∧[(-1)bso_76] ≥ 0)

We simplified constraint (100) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(101)    (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)bni_75 + (-1)Bound*bni_75] ≥ 0∧[(-1)bso_76] ≥ 0)

We simplified constraint (101) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(102)    (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_75 + (-1)Bound*bni_75] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_76] ≥ 0)

For Pair COND_997_0_PARTS_GT1(TRUE, x1, x0) → 997_0_PARTS_GT(x0, x0) the following chains were created:

We consider the chain COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10]), 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(103)    (x0[10]=x1[0]∧x0[10]=x0[0] ⇒ COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥997_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (103) using rule (IV) which results in the following new constraint:
(104)    (COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥997_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (104) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(105)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_77] = 0∧[(-1)bso_78] ≥ 0)

We simplified constraint (105) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(106)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_77] = 0∧[(-1)bso_78] ≥ 0)

We simplified constraint (106) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(107)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_77] = 0∧[(-1)bso_78] ≥ 0)

We simplified constraint (107) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(108)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_77] = 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_78] ≥ 0)
We consider the chain COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10]), 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(109)    (x0[10]=x1[9]∧x0[10]=x0[9] ⇒ COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥997_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (109) using rule (IV) which results in the following new constraint:
(110)    (COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥997_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (110) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(111)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_77] = 0∧[(-1)bso_78] ≥ 0)

We simplified constraint (111) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(112)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_77] = 0∧[(-1)bso_78] ≥ 0)

We simplified constraint (112) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(113)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_77] = 0∧[(-1)bso_78] ≥ 0)

We simplified constraint (113) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(114)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_77] = 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_78] ≥ 0)

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

997_0_PARTS_GT(x1, x0) → COND_997_0_PARTS_GT(&&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0)), x1, x0)
- (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_58] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_58] ≥ 0)
COND_997_0_PARTS_GT(TRUE, x1, x0) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1, -(x0, x1)), x0, -(x0, x1), x1)
- (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_60] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_60] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_60] ≥ 0)
COND_997_0_PARTS_GT(TRUE, x1, x0) → 997_0_PARTS_GT(x1, -(x0, x1))
- (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_62] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_61 + (-1)Bound*bni_61] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_62] ≥ 0)
1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1), x3, x0, x1) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1, 0), 1004_0_parts_Return(x1), x3, x0, x1)
- (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 ≥ 0∧[bni_63] ≥ 0∧0 ≥ 0∧[(-1)bni_63 + (-1)Bound*bni_63] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_64] ≥ 0)
COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1), x3, x0, x1) → 997_0_PARTS_GT(-(x1, 1), x3)
- (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_66] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_66] ≥ 0)
1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0, x1), x3, x0, x1) → COND_1063_1_PARTS_INVOKEMETHOD1(>(x1, 0), 1689_0_parts_Return(x0, x1), x3, x0, x1)
- (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧[bni_67] ≥ 0∧[bni_67] ≥ 0∧0 ≥ 0∧[(2)bni_67 + (-1)Bound*bni_67] ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[3 + (-1)bso_68] ≥ 0)
COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0, x1), x3, x0, x1) → 997_0_PARTS_GT(-(x1, 1), x3)
- (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧0 ≥ 0∧[bni_69] ≥ 0∧0 ≥ 0∧[(-1)bni_69 + (-1)Bound*bni_69] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_70] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧0 ≥ 0∧[bni_69] ≥ 0∧0 ≥ 0∧[(-1)bni_69 + (-1)Bound*bni_69] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_70] ≥ 0)
1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0), x1, x3, x2) → COND_1063_1_PARTS_INVOKEMETHOD3(>(x2, 0), 3772_0_parts_Return(x0), x1, x3, x2)
- (0 ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])), ≥)∧[bni_71] ≥ 0∧[bni_71] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(2)bni_71 + (-1)Bound*bni_71] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[3 + (-1)bso_72] ≥ 0)
COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0), x1, x3, x2) → 997_0_PARTS_GT(-(x2, 1), x1)
- (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[bni_73] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_73 + (-1)Bound*bni_73] ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_74] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[bni_73] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_73 + (-1)Bound*bni_73] ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_74] ≥ 0)
997_0_PARTS_GT(x1, x0) → COND_997_0_PARTS_GT1(&&(&&(>(x1, x0), >(x1, 0)), >(x0, 0)), x1, x0)
- (0 ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_75 + (-1)Bound*bni_75] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_76] ≥ 0)
COND_997_0_PARTS_GT1(TRUE, x1, x0) → 997_0_PARTS_GT(x0, x0)
- ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_77] = 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_78] ≥ 0)
- ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_77] = 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_78] ≥ 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 with natural coefficients for non-tuple symbols [NONINF][POLO]:

POL(TRUE) = 0
POL(FALSE) = 0
POL(997_0_parts_GT(x₁, x₂)) = [3] + x₁
POL(Cond_997_0_parts_GT(x₁, x₂, x₃)) = [3] + x₂
POL(<=(x₁, x₂)) = 0
POL(0) = 0
POL(1004_0_parts_Return(x₁)) = [3] + x₁
POL(1055_1_parts_InvokeMethod(x₁, x₂, x₃)) = 0
POL(1689_0_parts_Return(x₁, x₂)) = 0
POL(3772_0_parts_Return(x₁)) = 0
POL(1786_1_parts_InvokeMethod(x₁, x₂, x₃)) = 0
POL(+(x₁, x₂)) = 0
POL(997_0_PARTS_GT(x₁, x₂)) = [-1]
POL(COND_997_0_PARTS_GT(x₁, x₂, x₃)) = [-1]
POL(&&(x₁, x₂)) = 0
POL(>(x₁, x₂)) = 0
POL(1063_1_PARTS_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [2] + x₄ + x₃ + [-1]x₁
POL(-(x₁, x₂)) = 0
POL(COND_1063_1_PARTS_INVOKEMETHOD(x₁, x₂, x₃, x₄, x₅)) = [-1]
POL(1) = 0
POL(COND_1063_1_PARTS_INVOKEMETHOD1(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₄ + [-1]x₂
POL(COND_1063_1_PARTS_INVOKEMETHOD3(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₅ + [-1]x₂
POL(COND_997_0_PARTS_GT1(x₁, x₂, x₃)) = [-1]

The following pairs are in P_>:

1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])
1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])

The following pairs are in P_bound:

997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(-(x1[4], 1), x3[4])
1063_1_PARTS_INVOKEMETHOD(1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_1063_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1689_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])
COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 997_0_PARTS_GT(-(x1[6], 1), x3[6])
1063_1_PARTS_INVOKEMETHOD(3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_1063_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 3772_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])
COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 997_0_PARTS_GT(-(x2[8], 1), x1[8])
997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])

The following pairs are in P_≥:

997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(-(x1[4], 1), x3[4])
COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 997_0_PARTS_GT(-(x1[6], 1), x3[6])
COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 997_0_PARTS_GT(-(x2[8], 1), x1[8])
997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])
COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10])

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

997_0_parts_GT(x1, x0)¹ ↔ Cond_997_0_parts_GT(<=(x0, 0), x1, x0)¹
Cond_997_0_parts_GT(TRUE, x1, x0)¹ ↔ 1004_0_parts_Return(x1)¹

(9) 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

The ITRS R consists of the following rules:
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT(x0 <= 0, x1, x0)
Cond_997_0_parts_GT(TRUE, x1, x0) → 1004_0_parts_Return(x1)
1055_1_parts_InvokeMethod(1689_0_parts_Return(x0, x0), x2, x0) → 1689_0_parts_Return(x0, x2)
1055_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x1) → 1689_0_parts_Return(x1, x2)
1786_1_parts_InvokeMethod(1689_0_parts_Return(x0, x1), x0, x1) → 3772_0_parts_Return(x3 + x2)
1786_1_parts_InvokeMethod(1004_0_parts_Return(x0), x0, 0) → 3772_0_parts_Return(arith[1])
1786_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x3) → 3772_0_parts_Return(x1 + x0)

The integer pair graph contains the following rules and edges:
(0): 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0, x1[0], x0[0])
(1): COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], x0[1] - x1[1]), x0[1], x0[1] - x1[1], x1[1])
(2): COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], x0[2] - x1[2])
(3): 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(x1[3] > 0, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
(4): COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(x1[4] - 1, x3[4])
(6): COND_1063_1_PARTS_INVOKEMETHOD1(TRUE, 1689_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 997_0_PARTS_GT(x1[6] - 1, x3[6])
(8): COND_1063_1_PARTS_INVOKEMETHOD3(TRUE, 3772_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 997_0_PARTS_GT(x2[8] - 1, x1[8])
(9): 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(x1[9] > x0[9] && x1[9] > 0 && x0[9] > 0, x1[9], x0[9])
(10): COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10])

(2) -> (0), if (x1[2] →^* x1[0]∧x0[2] - x1[2] →^* x0[0])

(4) -> (0), if (x1[4] - 1 →^* x1[0]∧x3[4] →^* x0[0])

(6) -> (0), if (x1[6] - 1 →^* x1[0]∧x3[6] →^* x0[0])

(8) -> (0), if (x2[8] - 1 →^* x1[0]∧x1[8] →^* x0[0])

(10) -> (0), if (x0[10] →^* x1[0]∧x0[10] →^* x0[0])

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

(0) -> (2), if (x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0 ∧x1[0] →^* x1[2]∧x0[0] →^* x0[2])

(1) -> (3), if (997_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 1004_0_parts_Return(x1[3])∧x0[1] →^* x3[3]∧x0[1] - x1[1] →^* x0[3]∧x1[1] →^* x1[3])

(3) -> (4), if (x1[3] > 0 ∧1004_0_parts_Return(x1[3]) →^* 1004_0_parts_Return(x1[4])∧x3[3] →^* x3[4]∧x0[3] →^* x0[4]∧x1[3] →^* x1[4])

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

(4) -> (9), if (x1[4] - 1 →^* x1[9]∧x3[4] →^* x0[9])

(6) -> (9), if (x1[6] - 1 →^* x1[9]∧x3[6] →^* x0[9])

(8) -> (9), if (x2[8] - 1 →^* x1[9]∧x1[8] →^* x0[9])

(10) -> (9), if (x0[10] →^* x1[9]∧x0[10] →^* x0[9])

(9) -> (10), if (x1[9] > x0[9] && x1[9] > 0 && x0[9] > 0 ∧x1[9] →^* x1[10]∧x0[9] →^* x0[10])

(10) IDependencyGraphProof (EQUIVALENT transformation)

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

(11) Obligation:

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

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

The following domains are used:

Integer, Boolean

The ITRS R consists of the following rules:
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT(x0 <= 0, x1, x0)
Cond_997_0_parts_GT(TRUE, x1, x0) → 1004_0_parts_Return(x1)
1055_1_parts_InvokeMethod(1689_0_parts_Return(x0, x0), x2, x0) → 1689_0_parts_Return(x0, x2)
1055_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x1) → 1689_0_parts_Return(x1, x2)
1786_1_parts_InvokeMethod(1689_0_parts_Return(x0, x1), x0, x1) → 3772_0_parts_Return(x3 + x2)
1786_1_parts_InvokeMethod(1004_0_parts_Return(x0), x0, 0) → 3772_0_parts_Return(arith[1])
1786_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x3) → 3772_0_parts_Return(x1 + x0)

The integer pair graph contains the following rules and edges:
(2): COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], x0[2] - x1[2])
(10): COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10])
(9): 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(x1[9] > x0[9] && x1[9] > 0 && x0[9] > 0, x1[9], x0[9])
(4): COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(x1[4] - 1, x3[4])
(3): 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(x1[3] > 0, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
(1): COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], x0[1] - x1[1]), x0[1], x0[1] - x1[1], x1[1])
(0): 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0, x1[0], x0[0])

(2) -> (0), if (x1[2] →^* x1[0]∧x0[2] - x1[2] →^* x0[0])

(4) -> (0), if (x1[4] - 1 →^* x1[0]∧x3[4] →^* x0[0])

(10) -> (0), if (x0[10] →^* x1[0]∧x0[10] →^* x0[0])

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

(0) -> (2), if (x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0 ∧x1[0] →^* x1[2]∧x0[0] →^* x0[2])

(1) -> (3), if (997_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 1004_0_parts_Return(x1[3])∧x0[1] →^* x3[3]∧x0[1] - x1[1] →^* x0[3]∧x1[1] →^* x1[3])

(3) -> (4), if (x1[3] > 0 ∧1004_0_parts_Return(x1[3]) →^* 1004_0_parts_Return(x1[4])∧x3[3] →^* x3[4]∧x0[3] →^* x0[4]∧x1[3] →^* x1[4])

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

(4) -> (9), if (x1[4] - 1 →^* x1[9]∧x3[4] →^* x0[9])

(10) -> (9), if (x0[10] →^* x1[9]∧x0[10] →^* x0[9])

(9) -> (10), if (x1[9] > x0[9] && x1[9] > 0 && x0[9] > 0 ∧x1[9] →^* x1[10]∧x0[9] →^* x0[10])

(12) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(13) Obligation:

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

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

The following domains are used:

Integer, Boolean

The ITRS R consists of the following rules:
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT(x0 <= 0, x1, x0)
Cond_997_0_parts_GT(TRUE, x1, x0) → 1004_0_parts_Return(x1)

The integer pair graph contains the following rules and edges:
(2): COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], x0[2] - x1[2])
(10): COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10])
(9): 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(x1[9] > x0[9] && x1[9] > 0 && x0[9] > 0, x1[9], x0[9])
(4): COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(x1[4] - 1, x3[4])
(3): 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(x1[3] > 0, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
(1): COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], x0[1] - x1[1]), x0[1], x0[1] - x1[1], x1[1])
(0): 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0, x1[0], x0[0])

(2) -> (0), if (x1[2] →^* x1[0]∧x0[2] - x1[2] →^* x0[0])

(4) -> (0), if (x1[4] - 1 →^* x1[0]∧x3[4] →^* x0[0])

(10) -> (0), if (x0[10] →^* x1[0]∧x0[10] →^* x0[0])

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

(0) -> (2), if (x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0 ∧x1[0] →^* x1[2]∧x0[0] →^* x0[2])

(1) -> (3), if (997_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 1004_0_parts_Return(x1[3])∧x0[1] →^* x3[3]∧x0[1] - x1[1] →^* x0[3]∧x1[1] →^* x1[3])

(3) -> (4), if (x1[3] > 0 ∧1004_0_parts_Return(x1[3]) →^* 1004_0_parts_Return(x1[4])∧x3[3] →^* x3[4]∧x0[3] →^* x0[4]∧x1[3] →^* x1[4])

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

(4) -> (9), if (x1[4] - 1 →^* x1[9]∧x3[4] →^* x0[9])

(10) -> (9), if (x0[10] →^* x1[9]∧x0[10] →^* x0[9])

(9) -> (10), if (x1[9] > x0[9] && x1[9] > 0 && x0[9] > 0 ∧x1[9] →^* x1[10]∧x0[9] →^* x0[10])

(14) 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@48080eb6 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_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2])) the following chains were created:

We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2])), 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(1)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[2]∧x0[0]=x0[2]∧x1[2]=x1[0]1∧-(x0[2], x1[2])=x0[0]1 ⇒ COND_997_0_PARTS_GT(TRUE, x1[2], x0[2])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[2], x0[2])≥997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))∧(U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (1) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>(x0[0], 0)=TRUE∧>(x1[0], 0)=TRUE∧<=(x1[0], x0[0])=TRUE ⇒ COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥997_0_PARTS_GT(x1[0], -(x0[0], x1[0]))∧(U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧[1] + x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(8)    (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)
We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2])), 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(9)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[2]∧x0[0]=x0[2]∧x1[2]=x1[9]∧-(x0[2], x1[2])=x0[9] ⇒ COND_997_0_PARTS_GT(TRUE, x1[2], x0[2])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[2], x0[2])≥997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))∧(U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (9) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(10)    (>(x0[0], 0)=TRUE∧>(x1[0], 0)=TRUE∧<=(x1[0], x0[0])=TRUE ⇒ COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥997_0_PARTS_GT(x1[0], -(x0[0], x1[0]))∧(U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (10) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(11)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (11) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(12)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (12) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(13)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    (x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧[1] + x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_37 + (-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (14) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(15)    (x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)

We simplified constraint (15) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(16)    (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)

For Pair COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10]) the following chains were created:

We consider the chain COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10]), 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(17)    (x0[10]=x1[0]∧x0[10]=x0[0] ⇒ COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥997_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (17) using rule (IV) which results in the following new constraint:
(18)    (COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥997_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (18) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(19)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_39] = 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (19) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(20)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_39] = 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (20) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(21)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_39] = 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (21) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(22)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_39] = 0∧0 = 0∧0 = 0∧[(-1)bso_40] ≥ 0)
We consider the chain COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10]), 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(23)    (x0[10]=x1[9]∧x0[10]=x0[9] ⇒ COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥997_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (23) using rule (IV) which results in the following new constraint:
(24)    (COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10])≥997_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (24) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(25)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_39] = 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (25) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(26)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_39] = 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (26) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(27)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_39] = 0∧[(-1)bso_40] ≥ 0)

We simplified constraint (27) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(28)    ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_39] = 0∧0 = 0∧0 = 0∧[(-1)bso_40] ≥ 0)

For Pair 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) the following chains were created:

We consider the chain 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]), COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10]) which results in the following constraint:
(29)    (&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0))=TRUE∧x1[9]=x1[10]∧x0[9]=x0[10] ⇒ 997_0_PARTS_GT(x1[9], x0[9])≥NonInfC∧997_0_PARTS_GT(x1[9], x0[9])≥COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])∧(U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥))

We simplified constraint (29) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(30)    (>(x0[9], 0)=TRUE∧>(x1[9], x0[9])=TRUE∧>(x1[9], 0)=TRUE ⇒ 997_0_PARTS_GT(x1[9], x0[9])≥NonInfC∧997_0_PARTS_GT(x1[9], x0[9])≥COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])∧(U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥))

We simplified constraint (30) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(31)    (x0[9] + [-1] ≥ 0∧x1[9] + [-1] + [-1]x0[9] ≥ 0∧x1[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [bni_41]x1[9] ≥ 0∧[(-1)bso_42] + [-1]x0[9] + x1[9] ≥ 0)

We simplified constraint (31) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(32)    (x0[9] + [-1] ≥ 0∧x1[9] + [-1] + [-1]x0[9] ≥ 0∧x1[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [bni_41]x1[9] ≥ 0∧[(-1)bso_42] + [-1]x0[9] + x1[9] ≥ 0)

We simplified constraint (32) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(33)    (x0[9] + [-1] ≥ 0∧x1[9] + [-1] + [-1]x0[9] ≥ 0∧x1[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [bni_41]x1[9] ≥ 0∧[(-1)bso_42] + [-1]x0[9] + x1[9] ≥ 0)

We simplified constraint (33) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(34)    (x0[9] ≥ 0∧x1[9] + [-2] + [-1]x0[9] ≥ 0∧x1[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)bni_41 + (-1)Bound*bni_41] + [bni_41]x1[9] ≥ 0∧[-1 + (-1)bso_42] + [-1]x0[9] + x1[9] ≥ 0)

We simplified constraint (34) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(35)    (x0[9] ≥ 0∧x1[9] ≥ 0∧[1] + x0[9] + x1[9] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[bni_41 + (-1)Bound*bni_41] + [bni_41]x0[9] + [bni_41]x1[9] ≥ 0∧[1 + (-1)bso_42] + x1[9] ≥ 0)

For Pair COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(-(x1[4], 1), x3[4]) the following chains were created:

We consider the chain 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(-(x1[4], 1), x3[4]), 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(36)    (>(x1[3], 0)=TRUE∧1004_0_parts_Return(x1[3])=1004_0_parts_Return(x1[4])∧x3[3]=x3[4]∧x0[3]=x0[4]∧x1[3]=x1[4]∧-(x1[4], 1)=x1[0]∧x3[4]=x0[0] ⇒ COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥997_0_PARTS_GT(-(x1[4], 1), x3[4])∧(U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (36) using rules (I), (II), (III), (IV) which results in the following new constraint:
(37)    (>(x1[3], 0)=TRUE ⇒ COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥997_0_PARTS_GT(-(x1[3], 1), x3[3])∧(U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (37) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(38)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-2)bni_43 + (-1)Bound*bni_43] + [bni_43]x1[3] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (38) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(39)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-2)bni_43 + (-1)Bound*bni_43] + [bni_43]x1[3] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (39) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(40)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-2)bni_43 + (-1)Bound*bni_43] + [bni_43]x1[3] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (40) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(41)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧0 = 0∧[(-2)bni_43 + (-1)Bound*bni_43] + [bni_43]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (41) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(42)    (x1[3] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_43 + (-1)Bound*bni_43] + [bni_43]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)
We consider the chain 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(-(x1[4], 1), x3[4]), 997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(43)    (>(x1[3], 0)=TRUE∧1004_0_parts_Return(x1[3])=1004_0_parts_Return(x1[4])∧x3[3]=x3[4]∧x0[3]=x0[4]∧x1[3]=x1[4]∧-(x1[4], 1)=x1[9]∧x3[4]=x0[9] ⇒ COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥997_0_PARTS_GT(-(x1[4], 1), x3[4])∧(U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (43) using rules (I), (II), (III), (IV) which results in the following new constraint:
(44)    (>(x1[3], 0)=TRUE ⇒ COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥997_0_PARTS_GT(-(x1[3], 1), x3[3])∧(U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (44) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(45)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-2)bni_43 + (-1)Bound*bni_43] + [bni_43]x1[3] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (45) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(46)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-2)bni_43 + (-1)Bound*bni_43] + [bni_43]x1[3] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (46) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(47)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-2)bni_43 + (-1)Bound*bni_43] + [bni_43]x1[3] ≥ 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (47) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(48)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧0 = 0∧[(-2)bni_43 + (-1)Bound*bni_43] + [bni_43]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)

We simplified constraint (48) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(49)    (x1[3] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_43 + (-1)Bound*bni_43] + [bni_43]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)

For Pair 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) the following chains were created:

We consider the chain 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(-(x1[4], 1), x3[4]) which results in the following constraint:
(50)    (>(x1[3], 0)=TRUE∧1004_0_parts_Return(x1[3])=1004_0_parts_Return(x1[4])∧x3[3]=x3[4]∧x0[3]=x0[4]∧x1[3]=x1[4] ⇒ 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])∧(U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥))

We simplified constraint (50) using rules (I), (II), (IV) which results in the following new constraint:
(51)    (>(x1[3], 0)=TRUE ⇒ 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])∧(U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥))

We simplified constraint (51) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(52)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[(-2)bni_45 + (-1)Bound*bni_45] + [bni_45]x1[3] ≥ 0∧[(-1)bso_46] ≥ 0)

We simplified constraint (52) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(53)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[(-2)bni_45 + (-1)Bound*bni_45] + [bni_45]x1[3] ≥ 0∧[(-1)bso_46] ≥ 0)

We simplified constraint (53) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(54)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[(-2)bni_45 + (-1)Bound*bni_45] + [bni_45]x1[3] ≥ 0∧[(-1)bso_46] ≥ 0)

We simplified constraint (54) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(55)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 = 0∧0 = 0∧[(-2)bni_45 + (-1)Bound*bni_45] + [bni_45]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_46] ≥ 0)

We simplified constraint (55) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(56)    (x1[3] ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_45 + (-1)Bound*bni_45] + [bni_45]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_46] ≥ 0)

For Pair COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]) the following chains were created:

We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]), 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) which results in the following constraint:
(57)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[1]∧x0[0]=x0[1]∧997_0_parts_GT(x1[1], -(x0[1], x1[1]))=1004_0_parts_Return(x1[3])∧x0[1]=x3[3]∧-(x0[1], x1[1])=x0[3]∧x1[1]=x1[3] ⇒ COND_997_0_PARTS_GT(TRUE, x1[1], x0[1])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[1], x0[1])≥1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])∧(U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (57) using rules (III), (IV), (VII), (IDP_BOOLEAN), (REWRITING) which results in the following new constraint:
(58)    (<=(-(x0[0], x1[0]), 0)=x0∧-(x0[0], x1[0])=x1∧Cond_997_0_parts_GT(x0, x1[0], x1)=1004_0_parts_Return(x1[0])∧>(x0[0], 0)=TRUE∧>(x1[0], 0)=TRUE∧<=(x1[0], x0[0])=TRUE ⇒ COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[0], -(x0[0], x1[0])), x0[0], -(x0[0], x1[0]), x1[0])∧(U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (58) using rule (V) (with possible (I) afterwards) using induction on Cond_997_0_parts_GT(x0, x1[0], x1)=1004_0_parts_Return(x1[0]) which results in the following new constraint:
(59)    (1004_0_parts_Return(x3)=1004_0_parts_Return(x3)∧<=(-(x0[0], x3), 0)=TRUE∧-(x0[0], x3)=x2∧>(x0[0], 0)=TRUE∧>(x3, 0)=TRUE∧<=(x3, x0[0])=TRUE ⇒ COND_997_0_PARTS_GT(TRUE, x3, x0[0])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x3, x0[0])≥1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x3, -(x0[0], x3)), x0[0], -(x0[0], x3), x3)∧(U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (59) using rules (I), (II), (IV), (DELETE_TRIVIAL_REDUCESTO) which results in the following new constraint:
(60)    (<=(-(x0[0], x3), 0)=TRUE∧>(x0[0], 0)=TRUE∧>(x3, 0)=TRUE∧<=(x3, x0[0])=TRUE ⇒ COND_997_0_PARTS_GT(TRUE, x3, x0[0])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x3, x0[0])≥1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x3, -(x0[0], x3)), x0[0], -(x0[0], x3), x3)∧(U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (60) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(61)    ([-1]x0[0] + x3 ≥ 0∧x0[0] + [-1] ≥ 0∧x3 + [-1] ≥ 0∧x0[0] + [-1]x3 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_47 + (-1)Bound*bni_47] + [bni_47]x3 ≥ 0∧[1 + (-1)bso_48] ≥ 0)

We simplified constraint (61) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(62)    ([-1]x0[0] + x3 ≥ 0∧x0[0] + [-1] ≥ 0∧x3 + [-1] ≥ 0∧x0[0] + [-1]x3 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_47 + (-1)Bound*bni_47] + [bni_47]x3 ≥ 0∧[1 + (-1)bso_48] ≥ 0)

We simplified constraint (62) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(63)    ([-1]x0[0] + x3 ≥ 0∧x0[0] + [-1] ≥ 0∧x3 + [-1] ≥ 0∧x0[0] + [-1]x3 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_47 + (-1)Bound*bni_47] + [bni_47]x3 ≥ 0∧[1 + (-1)bso_48] ≥ 0)

We simplified constraint (63) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(64)    ([-1] + [-1]x0[0] + x3 ≥ 0∧x0[0] ≥ 0∧x3 + [-1] ≥ 0∧[1] + x0[0] + [-1]x3 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_47 + (-1)Bound*bni_47] + [bni_47]x3 ≥ 0∧[1 + (-1)bso_48] ≥ 0)

We simplified constraint (64) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(65)    (x3 ≥ 0∧x0[0] ≥ 0∧x0[0] + x3 ≥ 0∧[-1]x3 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)Bound*bni_47] + [bni_47]x0[0] + [bni_47]x3 ≥ 0∧[1 + (-1)bso_48] ≥ 0)

We simplified constraint (65) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(66)    (0 ≥ 0∧x0[0] ≥ 0∧x0[0] ≥ 0∧0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)Bound*bni_47] + [bni_47]x0[0] ≥ 0∧[1 + (-1)bso_48] ≥ 0)

For Pair 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) the following chains were created:

We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]) which results in the following constraint:
(67)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[1]∧x0[0]=x0[1] ⇒ 997_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧997_0_PARTS_GT(x1[0], x0[0])≥COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥))

We simplified constraint (67) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(68)    (>(x0[0], 0)=TRUE∧>(x1[0], 0)=TRUE∧<=(x1[0], x0[0])=TRUE ⇒ 997_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧997_0_PARTS_GT(x1[0], x0[0])≥COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥))

We simplified constraint (68) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(69)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (69) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(70)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (70) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(71)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (71) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(72)    (x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧[1] + x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (72) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(73)    (x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (73) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(74)    (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)
We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2])) which results in the following constraint:
(75)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[2]∧x0[0]=x0[2] ⇒ 997_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧997_0_PARTS_GT(x1[0], x0[0])≥COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥))

We simplified constraint (75) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(76)    (>(x0[0], 0)=TRUE∧>(x1[0], 0)=TRUE∧<=(x1[0], x0[0])=TRUE ⇒ 997_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧997_0_PARTS_GT(x1[0], x0[0])≥COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥))

We simplified constraint (76) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(77)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (77) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(78)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (78) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(79)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (79) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(80)    (x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧[1] + x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_49 + (-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (80) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(81)    (x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)

We simplified constraint (81) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(82)    (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)

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

COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
- (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)
- (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)Bound*bni_37] + [bni_37]x1[0] ≥ 0∧[(-1)bso_38] ≥ 0)
COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10])
- ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_39] = 0∧0 = 0∧0 = 0∧[(-1)bso_40] ≥ 0)
- ((U^Increasing(997_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_39] = 0∧0 = 0∧0 = 0∧[(-1)bso_40] ≥ 0)
997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])
- (x0[9] ≥ 0∧x1[9] ≥ 0∧[1] + x0[9] + x1[9] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[bni_41 + (-1)Bound*bni_41] + [bni_41]x0[9] + [bni_41]x1[9] ≥ 0∧[1 + (-1)bso_42] + x1[9] ≥ 0)
COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(-(x1[4], 1), x3[4])
- (x1[3] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_43 + (-1)Bound*bni_43] + [bni_43]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)
- (x1[3] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_43 + (-1)Bound*bni_43] + [bni_43]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_44] ≥ 0)
1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
- (x1[3] ≥ 0 ⇒ (U^Increasing(COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 = 0∧0 = 0∧[(-1)bni_45 + (-1)Bound*bni_45] + [bni_45]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_46] ≥ 0)
COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
- (0 ≥ 0∧x0[0] ≥ 0∧x0[0] ≥ 0∧0 ≥ 0 ⇒ (U^Increasing(1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)Bound*bni_47] + [bni_47]x0[0] ≥ 0∧[1 + (-1)bso_48] ≥ 0)
997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
- (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)
- (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_49] + [bni_49]x1[0] ≥ 0∧[(-1)bso_50] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(997_0_parts_GT(x₁, x₂)) = [1] + [-1]x₁
POL(Cond_997_0_parts_GT(x₁, x₂, x₃)) = [1] + [-1]x₂
POL(<=(x₁, x₂)) = [-1]
POL(0) = 0
POL(1004_0_parts_Return(x₁)) = [1] + [-1]x₁
POL(COND_997_0_PARTS_GT(x₁, x₂, x₃)) = [-1] + x₂ + [-1]x₁
POL(997_0_PARTS_GT(x₁, x₂)) = [-1] + x₁
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(COND_997_0_PARTS_GT1(x₁, x₂, x₃)) = [-1] + x₃ + [-1]x₁
POL(&&(x₁, x₂)) = 0
POL(>(x₁, x₂)) = [-1]
POL(COND_1063_1_PARTS_INVOKEMETHOD(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₂
POL(1) = [1]
POL(1063_1_PARTS_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₁

The following pairs are in P_>:

997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])
COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])

The following pairs are in P_bound:

COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
997_0_PARTS_GT(x1[9], x0[9]) → COND_997_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])
COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(-(x1[4], 1), x3[4])
1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
COND_997_0_PARTS_GT(TRUE, x1[1], x0[1]) → 1063_1_PARTS_INVOKEMETHOD(997_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])

The following pairs are in P_≥:

COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10])
COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(-(x1[4], 1), x3[4])
1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])

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
997_0_parts_GT(x1, x0)¹ ↔ Cond_997_0_parts_GT(<=(x0, 0), x1, x0)¹
Cond_997_0_parts_GT(TRUE, x1, x0)¹ ↔ 1004_0_parts_Return(x1)¹

(15) 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

The ITRS R consists of the following rules:
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT(x0 <= 0, x1, x0)
Cond_997_0_parts_GT(TRUE, x1, x0) → 1004_0_parts_Return(x1)

The integer pair graph contains the following rules and edges:
(2): COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], x0[2] - x1[2])
(10): COND_997_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 997_0_PARTS_GT(x0[10], x0[10])
(4): COND_1063_1_PARTS_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 997_0_PARTS_GT(x1[4] - 1, x3[4])
(3): 1063_1_PARTS_INVOKEMETHOD(1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_1063_1_PARTS_INVOKEMETHOD(x1[3] > 0, 1004_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
(0): 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0, x1[0], x0[0])

(2) -> (0), if (x1[2] →^* x1[0]∧x0[2] - x1[2] →^* x0[0])

(4) -> (0), if (x1[4] - 1 →^* x1[0]∧x3[4] →^* x0[0])

(10) -> (0), if (x0[10] →^* x1[0]∧x0[10] →^* x0[0])

(0) -> (2), if (x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0 ∧x1[0] →^* x1[2]∧x0[0] →^* x0[2])

(3) -> (4), if (x1[3] > 0 ∧1004_0_parts_Return(x1[3]) →^* 1004_0_parts_Return(x1[4])∧x3[3] →^* x3[4]∧x0[3] →^* x0[4]∧x1[3] →^* x1[4])

(16) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.

(17) 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

(2) -> (0), if (x1[2] →^* x1[0]∧x0[2] - x1[2] →^* x0[0])

(0) -> (2), if (x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0 ∧x1[0] →^* x1[2]∧x0[0] →^* x0[2])

(18) UsableRulesProof (EQUIVALENT transformation)

As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R.

(19) 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

(2) -> (0), if (x1[2] →^* x1[0]∧x0[2] - x1[2] →^* x0[0])

(0) -> (2), if (x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0 ∧x1[0] →^* x1[2]∧x0[0] →^* x0[2])

(20) 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@48080eb6 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 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) the following chains were created:

We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2])) which results in the following constraint:
(1)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[2]∧x0[0]=x0[2] ⇒ 997_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧997_0_PARTS_GT(x1[0], x0[0])≥COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥))

We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>(x0[0], 0)=TRUE∧>(x1[0], 0)=TRUE∧<=(x1[0], x0[0])=TRUE ⇒ 997_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧997_0_PARTS_GT(x1[0], x0[0])≥COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]x0[0] + [(-1)bni_13]x1[0] ≥ 0∧[(-1)bso_14] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]x0[0] + [(-1)bni_13]x1[0] ≥ 0∧[(-1)bso_14] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_13 + (-1)Bound*bni_13] + [bni_13]x0[0] + [(-1)bni_13]x1[0] ≥ 0∧[(-1)bso_14] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧[1] + x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_13] + [bni_13]x0[0] + [(-1)bni_13]x1[0] ≥ 0∧[(-1)bso_14] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(7)    (x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_13 + (-1)bni_13] + [bni_13]x0[0] + [(-1)bni_13]x1[0] ≥ 0∧[(-1)bso_14] ≥ 0)

We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(8)    (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_13 + (-1)bni_13] + [bni_13]x0[0] ≥ 0∧[(-1)bso_14] ≥ 0)

For Pair COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2])) the following chains were created:

We consider the chain 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2])), 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(9)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[2]∧x0[0]=x0[2]∧x1[2]=x1[0]1∧-(x0[2], x1[2])=x0[0]1 ⇒ COND_997_0_PARTS_GT(TRUE, x1[2], x0[2])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[2], x0[2])≥997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))∧(U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (9) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(10)    (>(x0[0], 0)=TRUE∧>(x1[0], 0)=TRUE∧<=(x1[0], x0[0])=TRUE ⇒ COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_997_0_PARTS_GT(TRUE, x1[0], x0[0])≥997_0_PARTS_GT(x1[0], -(x0[0], x1[0]))∧(U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (10) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(11)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]x0[0] + [(-1)bni_15]x1[0] ≥ 0∧[(-1)bso_16] + x1[0] ≥ 0)

We simplified constraint (11) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(12)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]x0[0] + [(-1)bni_15]x1[0] ≥ 0∧[(-1)bso_16] + x1[0] ≥ 0)

We simplified constraint (12) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(13)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_15 + (-1)Bound*bni_15] + [bni_15]x0[0] + [(-1)bni_15]x1[0] ≥ 0∧[(-1)bso_16] + x1[0] ≥ 0)

We simplified constraint (13) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    (x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧[1] + x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)Bound*bni_15] + [bni_15]x0[0] + [(-1)bni_15]x1[0] ≥ 0∧[(-1)bso_16] + x1[0] ≥ 0)

We simplified constraint (14) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(15)    (x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)Bound*bni_15 + (-1)bni_15] + [bni_15]x0[0] + [(-1)bni_15]x1[0] ≥ 0∧[1 + (-1)bso_16] + x1[0] ≥ 0)

We simplified constraint (15) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(16)    (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)Bound*bni_15 + (-1)bni_15] + [bni_15]x0[0] ≥ 0∧[1 + (-1)bso_16] + x1[0] ≥ 0)

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

997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
- (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_13 + (-1)bni_13] + [bni_13]x0[0] ≥ 0∧[(-1)bso_14] ≥ 0)
COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
- (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)Bound*bni_15 + (-1)bni_15] + [bni_15]x0[0] ≥ 0∧[1 + (-1)bso_16] + x1[0] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = [1]
POL(997_0_PARTS_GT(x₁, x₂)) = [-1] + x₂ + [-1]x₁
POL(COND_997_0_PARTS_GT(x₁, x₂, x₃)) = [-1] + x₃ + [-1]x₂ + [-1]x₁
POL(&&(x₁, x₂)) = 0
POL(>(x₁, x₂)) = [-1]
POL(0) = 0
POL(<=(x₁, x₂)) = [-1]
POL(-(x₁, x₂)) = x₁ + [-1]x₂

The following pairs are in P_>:

COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))

The following pairs are in P_bound:

997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
COND_997_0_PARTS_GT(TRUE, x1[2], x0[2]) → 997_0_PARTS_GT(x1[2], -(x0[2], x1[2]))

The following pairs are in P_≥:

997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])

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

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

(21) Obligation:

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

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

The following domains are used:

Boolean, Integer

R is empty.

The integer pair graph contains the following rules and edges:
(0): 997_0_PARTS_GT(x1[0], x0[0]) → COND_997_0_PARTS_GT(x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0, x1[0], x0[0])

The set Q consists of the following terms:
997_0_parts_GT(x0, x1)
Cond_997_0_parts_GT(TRUE, x0, x1)
1055_1_parts_InvokeMethod(1689_0_parts_Return(x0, x0), x1, x0)
1055_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1, x2)
1786_1_parts_InvokeMethod(1689_0_parts_Return(x0, x1), x0, x1)
1786_1_parts_InvokeMethod(1004_0_parts_Return(x0), x0, 0)
1786_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1, x2)

(22) IDependencyGraphProof (EQUIVALENT transformation)

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

(23) TRUE

(24) Obligation:

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

(25) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 51 rules for P and 90 rules for R.

P rules:
435_0_main_Load(EOS(STATIC_435), java.lang.Object(ARRAY(i1)), i29, i29) → 437_0_main_ArrayLength(EOS(STATIC_437), java.lang.Object(ARRAY(i1)), i29, i29, java.lang.Object(ARRAY(i1)))
437_0_main_ArrayLength(EOS(STATIC_437), java.lang.Object(ARRAY(i1)), i29, i29, java.lang.Object(ARRAY(i1))) → 439_0_main_GT(EOS(STATIC_439), java.lang.Object(ARRAY(i1)), i29, i29, i1) | >=(i1, 0)
439_0_main_GT(EOS(STATIC_439), java.lang.Object(ARRAY(i1)), i29, i29, i1) → 443_0_main_GT(EOS(STATIC_443), java.lang.Object(ARRAY(i1)), i29, i29, i1)
443_0_main_GT(EOS(STATIC_443), java.lang.Object(ARRAY(i1)), i29, i29, i1) → 447_0_main_ConstantStackPush(EOS(STATIC_447), java.lang.Object(ARRAY(i1)), i29) | <=(i29, i1)
447_0_main_ConstantStackPush(EOS(STATIC_447), java.lang.Object(ARRAY(i1)), i29) → 451_0_main_Store(EOS(STATIC_451), java.lang.Object(ARRAY(i1)), i29, 0)
451_0_main_Store(EOS(STATIC_451), java.lang.Object(ARRAY(i1)), i29, matching1) → 452_0_main_Load(EOS(STATIC_452), java.lang.Object(ARRAY(i1)), i29, 0) | =(matching1, 0)
452_0_main_Load(EOS(STATIC_452), java.lang.Object(ARRAY(i1)), i29, matching1) → 522_0_main_Load(EOS(STATIC_522), java.lang.Object(ARRAY(i1)), i29, 0) | =(matching1, 0)
522_0_main_Load(EOS(STATIC_522), java.lang.Object(ARRAY(i1)), i39, i40) → 860_0_main_Load(EOS(STATIC_860), java.lang.Object(ARRAY(i1)), i39, i40)
860_0_main_Load(EOS(STATIC_860), java.lang.Object(ARRAY(i1)), i98, i99) → 1041_0_main_Load(EOS(STATIC_1041), java.lang.Object(ARRAY(i1)), i98, i99)
1041_0_main_Load(EOS(STATIC_1041), java.lang.Object(ARRAY(i1)), i171, i172) → 1047_0_main_Load(EOS(STATIC_1047), java.lang.Object(ARRAY(i1)), i171, i172, i172)
1047_0_main_Load(EOS(STATIC_1047), java.lang.Object(ARRAY(i1)), i171, i172, i172) → 1051_0_main_ArrayLength(EOS(STATIC_1051), java.lang.Object(ARRAY(i1)), i171, i172, i172, java.lang.Object(ARRAY(i1)))
1051_0_main_ArrayLength(EOS(STATIC_1051), java.lang.Object(ARRAY(i1)), i171, i172, i172, java.lang.Object(ARRAY(i1))) → 1056_0_main_GT(EOS(STATIC_1056), java.lang.Object(ARRAY(i1)), i171, i172, i172, i1) | >=(i1, 0)
1056_0_main_GT(EOS(STATIC_1056), java.lang.Object(ARRAY(i1)), i171, i172, i172, i1) → 1061_0_main_GT(EOS(STATIC_1061), java.lang.Object(ARRAY(i1)), i171, i172, i172, i1)
1056_0_main_GT(EOS(STATIC_1056), java.lang.Object(ARRAY(i1)), i171, i172, i172, i1) → 1062_0_main_GT(EOS(STATIC_1062), java.lang.Object(ARRAY(i1)), i171, i172, i172, i1)
1061_0_main_GT(EOS(STATIC_1061), java.lang.Object(ARRAY(i1)), i171, i172, i172, i1) → 1065_0_main_Inc(EOS(STATIC_1065), java.lang.Object(ARRAY(i1)), i171) | >(i172, i1)
1065_0_main_Inc(EOS(STATIC_1065), java.lang.Object(ARRAY(i1)), i171) → 1072_0_main_JMP(EOS(STATIC_1072), java.lang.Object(ARRAY(i1)), +(i171, 1))
1072_0_main_JMP(EOS(STATIC_1072), java.lang.Object(ARRAY(i1)), i181) → 1078_0_main_Load(EOS(STATIC_1078), java.lang.Object(ARRAY(i1)), i181)
1078_0_main_Load(EOS(STATIC_1078), java.lang.Object(ARRAY(i1)), i181) → 432_0_main_Load(EOS(STATIC_432), java.lang.Object(ARRAY(i1)), i181)
432_0_main_Load(EOS(STATIC_432), java.lang.Object(ARRAY(i1)), i29) → 435_0_main_Load(EOS(STATIC_435), java.lang.Object(ARRAY(i1)), i29, i29)
1062_0_main_GT(EOS(STATIC_1062), java.lang.Object(ARRAY(i1)), i171, i172, i172, i1) → 1067_0_main_Load(EOS(STATIC_1067), java.lang.Object(ARRAY(i1)), i171, i172) | <=(i172, i1)
1067_0_main_Load(EOS(STATIC_1067), java.lang.Object(ARRAY(i1)), i171, i172) → 1073_0_main_Load(EOS(STATIC_1073), java.lang.Object(ARRAY(i1)), i171, i172, i171)
1073_0_main_Load(EOS(STATIC_1073), java.lang.Object(ARRAY(i1)), i171, i172, i171) → 1080_0_main_InvokeMethod(EOS(STATIC_1080), java.lang.Object(ARRAY(i1)), i171, i172, i171, i172)
1080_0_main_InvokeMethod(EOS(STATIC_1080), java.lang.Object(ARRAY(i1)), i171, i172, i171, i172) → 1163_1_main_InvokeMethod(1163_0_parts_Load(EOS(STATIC_1163), i171, i172), java.lang.Object(ARRAY(i1)), i171, i172, i171, i172)
1163_1_main_InvokeMethod(1004_0_parts_Return(EOS(STATIC_1004), i249, i250, matching1), java.lang.Object(ARRAY(i1)), i249, i250, i249, i250) → 1178_0_parts_Return(EOS(STATIC_1178), java.lang.Object(ARRAY(i1)), i249, i250, i249, i250, i249, i250, 1) | =(matching1, 1)
1163_1_main_InvokeMethod(1018_0_parts_Return(EOS(STATIC_1018), i251, matching1, matching2), java.lang.Object(ARRAY(i1)), i251, matching3, i251, matching4) → 1179_0_parts_Return(EOS(STATIC_1179), java.lang.Object(ARRAY(i1)), i251, 0, i251, 0, i251, 0, 0) | &&(&&(&&(=(matching1, 0), =(matching2, 0)), =(matching3, 0)), =(matching4, 0))
1163_1_main_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), i772, i773, i723), java.lang.Object(ARRAY(i1)), i772, i773, i772, i773) → 1742_0_parts_Return(EOS(STATIC_1742), java.lang.Object(ARRAY(i1)), i772, i773, i772, i773, i772, i773, i723)
1163_1_main_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), i827, i828, i778), java.lang.Object(ARRAY(i1)), i827, i828, i827, i828) → 1778_0_parts_Return(EOS(STATIC_1778), java.lang.Object(ARRAY(i1)), i827, i828, i827, i828, i827, i828, i778)
1163_1_main_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), i946), java.lang.Object(ARRAY(i1)), i955, i956, i955, i956) → 3779_0_parts_Return(EOS(STATIC_3779), java.lang.Object(ARRAY(i1)), i955, i956, i955, i956, i946)
1178_0_parts_Return(EOS(STATIC_1178), java.lang.Object(ARRAY(i1)), i249, i250, i249, i250, i249, i250, matching1) → 1181_0_main_StackPop(EOS(STATIC_1181), java.lang.Object(ARRAY(i1)), i249, i250, 1) | =(matching1, 1)
1181_0_main_StackPop(EOS(STATIC_1181), java.lang.Object(ARRAY(i1)), i249, i250, matching1) → 1186_0_main_Inc(EOS(STATIC_1186), java.lang.Object(ARRAY(i1)), i249, i250) | =(matching1, 1)
1186_0_main_Inc(EOS(STATIC_1186), java.lang.Object(ARRAY(i1)), i249, i250) → 1190_0_main_JMP(EOS(STATIC_1190), java.lang.Object(ARRAY(i1)), i249, +(i250, 1)) | >=(i250, 0)
1190_0_main_JMP(EOS(STATIC_1190), java.lang.Object(ARRAY(i1)), i249, i253) → 1197_0_main_Load(EOS(STATIC_1197), java.lang.Object(ARRAY(i1)), i249, i253)
1197_0_main_Load(EOS(STATIC_1197), java.lang.Object(ARRAY(i1)), i249, i253) → 1041_0_main_Load(EOS(STATIC_1041), java.lang.Object(ARRAY(i1)), i249, i253)
1179_0_parts_Return(EOS(STATIC_1179), java.lang.Object(ARRAY(i1)), i251, matching1, i251, matching2, i251, matching3, matching4) → 1183_0_main_StackPop(EOS(STATIC_1183), java.lang.Object(ARRAY(i1)), i251, 0, 0) | &&(&&(&&(=(matching1, 0), =(matching2, 0)), =(matching3, 0)), =(matching4, 0))
1183_0_main_StackPop(EOS(STATIC_1183), java.lang.Object(ARRAY(i1)), i251, matching1, matching2) → 1188_0_main_Inc(EOS(STATIC_1188), java.lang.Object(ARRAY(i1)), i251, 0) | &&(=(matching1, 0), =(matching2, 0))
1188_0_main_Inc(EOS(STATIC_1188), java.lang.Object(ARRAY(i1)), i251, matching1) → 1192_0_main_JMP(EOS(STATIC_1192), java.lang.Object(ARRAY(i1)), i251, 1) | =(matching1, 0)
1192_0_main_JMP(EOS(STATIC_1192), java.lang.Object(ARRAY(i1)), i251, matching1) → 1200_0_main_Load(EOS(STATIC_1200), java.lang.Object(ARRAY(i1)), i251, 1) | =(matching1, 1)
1200_0_main_Load(EOS(STATIC_1200), java.lang.Object(ARRAY(i1)), i251, matching1) → 1041_0_main_Load(EOS(STATIC_1041), java.lang.Object(ARRAY(i1)), i251, 1) | =(matching1, 1)
1742_0_parts_Return(EOS(STATIC_1742), java.lang.Object(ARRAY(i1)), i772, i773, i772, i773, i772, i773, i723) → 1743_0_parts_Return(EOS(STATIC_1743), java.lang.Object(ARRAY(i1)), i772, i773, i772, i773, i772, i773, i723)
1743_0_parts_Return(EOS(STATIC_1743), java.lang.Object(ARRAY(i1)), i803, i804, i803, i804, i803, i804, i805) → 1754_0_main_StackPop(EOS(STATIC_1754), java.lang.Object(ARRAY(i1)), i803, i804, i805)
1754_0_main_StackPop(EOS(STATIC_1754), java.lang.Object(ARRAY(i1)), i803, i804, i805) → 1759_0_main_Inc(EOS(STATIC_1759), java.lang.Object(ARRAY(i1)), i803, i804)
1759_0_main_Inc(EOS(STATIC_1759), java.lang.Object(ARRAY(i1)), i803, i804) → 1770_0_main_JMP(EOS(STATIC_1770), java.lang.Object(ARRAY(i1)), i803, +(i804, 1)) | >(i804, 0)
1770_0_main_JMP(EOS(STATIC_1770), java.lang.Object(ARRAY(i1)), i803, i829) → 1783_0_main_Load(EOS(STATIC_1783), java.lang.Object(ARRAY(i1)), i803, i829)
1783_0_main_Load(EOS(STATIC_1783), java.lang.Object(ARRAY(i1)), i803, i829) → 1041_0_main_Load(EOS(STATIC_1041), java.lang.Object(ARRAY(i1)), i803, i829)
1778_0_parts_Return(EOS(STATIC_1778), java.lang.Object(ARRAY(i1)), i827, i828, i827, i828, i827, i828, i778) → 1743_0_parts_Return(EOS(STATIC_1743), java.lang.Object(ARRAY(i1)), i827, i828, i827, i828, i827, i828, i778)
3779_0_parts_Return(EOS(STATIC_3779), java.lang.Object(ARRAY(i1)), i955, i956, i955, i956, i946) → 1682_0_parts_Return(EOS(STATIC_1682), java.lang.Object(ARRAY(i1)), i955, i956, i955, i956, i946)
1682_0_parts_Return(EOS(STATIC_1682), java.lang.Object(ARRAY(i1)), i745, i746, i745, i746, i744) → 1698_0_main_StackPop(EOS(STATIC_1698), java.lang.Object(ARRAY(i1)), i745, i746, i744)
1698_0_main_StackPop(EOS(STATIC_1698), java.lang.Object(ARRAY(i1)), i745, i746, i744) → 1706_0_main_Inc(EOS(STATIC_1706), java.lang.Object(ARRAY(i1)), i745, i746)
1706_0_main_Inc(EOS(STATIC_1706), java.lang.Object(ARRAY(i1)), i745, i746) → 1726_0_main_JMP(EOS(STATIC_1726), java.lang.Object(ARRAY(i1)), i745, +(i746, 1)) | >(i746, 0)
1726_0_main_JMP(EOS(STATIC_1726), java.lang.Object(ARRAY(i1)), i745, i774) → 1747_0_main_Load(EOS(STATIC_1747), java.lang.Object(ARRAY(i1)), i745, i774)
1747_0_main_Load(EOS(STATIC_1747), java.lang.Object(ARRAY(i1)), i745, i774) → 1041_0_main_Load(EOS(STATIC_1041), java.lang.Object(ARRAY(i1)), i745, i774)
R rules:
1163_0_parts_Load(EOS(STATIC_1163), i171, i172) → 1167_0_parts_Load(EOS(STATIC_1167), i171, i172)
1167_0_parts_Load(EOS(STATIC_1167), i171, i172) → 996_0_parts_Load(EOS(STATIC_996), i171, i172)
1059_0_parts_Load(EOS(STATIC_1059), i164, i164) → 996_0_parts_Load(EOS(STATIC_996), i164, i164)
1068_0_parts_Load(EOS(STATIC_1068), i166) → 996_0_parts_Load(EOS(STATIC_996), i176, i166)
1788_0_parts_Load(EOS(STATIC_1788), i164) → 996_0_parts_Load(EOS(STATIC_996), i164, i840)
996_0_parts_Load(EOS(STATIC_996), i159, i160) → 997_0_parts_GT(EOS(STATIC_997), i159, i160, i159)
997_0_parts_GT(EOS(STATIC_997), i163, i160, i163) → 999_0_parts_GT(EOS(STATIC_999), i163, i160, i163)
997_0_parts_GT(EOS(STATIC_997), i164, i160, i164) → 1000_0_parts_GT(EOS(STATIC_1000), i164, i160, i164)
999_0_parts_GT(EOS(STATIC_999), i163, i160, i163) → 1002_0_parts_ConstantStackPush(EOS(STATIC_1002), i163, i160) | <=(i163, 0)
1000_0_parts_GT(EOS(STATIC_1000), i164, i160, i164) → 1003_0_parts_Load(EOS(STATIC_1003), i164, i160) | >(i164, 0)
1002_0_parts_ConstantStackPush(EOS(STATIC_1002), i163, i160) → 1004_0_parts_Return(EOS(STATIC_1004), i163, i160, 1)
1003_0_parts_Load(EOS(STATIC_1003), i164, i160) → 1006_0_parts_GT(EOS(STATIC_1006), i164, i160, i160)
1006_0_parts_GT(EOS(STATIC_1006), i164, matching1, matching2) → 1009_0_parts_GT(EOS(STATIC_1009), i164, 0, 0) | &&(=(matching1, 0), =(matching2, 0))
1006_0_parts_GT(EOS(STATIC_1006), i164, i166, i166) → 1010_0_parts_GT(EOS(STATIC_1010), i164, i166, i166)
1009_0_parts_GT(EOS(STATIC_1009), i164, matching1, matching2) → 1014_0_parts_ConstantStackPush(EOS(STATIC_1014), i164, 0) | &&(&&(<=(0, 0), =(matching1, 0)), =(matching2, 0))
1010_0_parts_GT(EOS(STATIC_1010), i164, i166, i166) → 1016_0_parts_Load(EOS(STATIC_1016), i164, i166) | >(i166, 0)
1014_0_parts_ConstantStackPush(EOS(STATIC_1014), i164, matching1) → 1018_0_parts_Return(EOS(STATIC_1018), i164, 0, 0) | =(matching1, 0)
1016_0_parts_Load(EOS(STATIC_1016), i164, i166) → 1020_0_parts_Load(EOS(STATIC_1020), i164, i166, i166)
1020_0_parts_Load(EOS(STATIC_1020), i164, i166, i166) → 1025_0_parts_LE(EOS(STATIC_1025), i164, i166, i166, i164)
1025_0_parts_LE(EOS(STATIC_1025), i164, i166, i166, i164) → 1029_0_parts_LE(EOS(STATIC_1029), i164, i166, i166, i164)
1025_0_parts_LE(EOS(STATIC_1025), i164, i166, i166, i164) → 1030_0_parts_LE(EOS(STATIC_1030), i164, i166, i166, i164)
1029_0_parts_LE(EOS(STATIC_1029), i164, i166, i166, i164) → 1034_0_parts_Load(EOS(STATIC_1034), i164, i166) | <=(i166, i164)
1030_0_parts_LE(EOS(STATIC_1030), i164, i166, i166, i164) → 1036_0_parts_Load(EOS(STATIC_1036), i164, i166) | >(i166, i164)
1034_0_parts_Load(EOS(STATIC_1034), i164, i166) → 1044_0_parts_Load(EOS(STATIC_1044), i164, i166, i164)
1036_0_parts_Load(EOS(STATIC_1036), i164, i166) → 1045_0_parts_Load(EOS(STATIC_1045), i164, i166, i164)
1044_0_parts_Load(EOS(STATIC_1044), i164, i166, i164) → 1048_0_parts_IntArithmetic(EOS(STATIC_1048), i164, i166, i164, i166)
1045_0_parts_Load(EOS(STATIC_1045), i164, i166, i164) → 1050_0_parts_InvokeMethod(EOS(STATIC_1050), i164, i166, i164, i164)
1048_0_parts_IntArithmetic(EOS(STATIC_1048), i164, i166, i164, i166) → 1053_0_parts_Load(EOS(STATIC_1053), i164, i166) | &&(>(i164, 0), >(i166, 0))
1050_0_parts_InvokeMethod(EOS(STATIC_1050), i164, i166, i164, i164) → 1055_1_parts_InvokeMethod(1055_0_parts_Load(EOS(STATIC_1055), i164, i164), i164, i166, i164, i164)
1053_0_parts_Load(EOS(STATIC_1053), i164, i166) → 1058_0_parts_InvokeMethod(EOS(STATIC_1058), i164, i166, i166)
1055_0_parts_Load(EOS(STATIC_1055), i164, i164) → 1059_0_parts_Load(EOS(STATIC_1059), i164, i164)
1055_1_parts_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), i768, i768, i723), i768, i166, i768, i768) → 1730_0_parts_Return(EOS(STATIC_1730), i768, i166, i768, i768, i768, i768, i723)
1055_1_parts_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), i823, i823, i778), i823, i166, i823, i823) → 1772_0_parts_Return(EOS(STATIC_1772), i823, i166, i823, i823, i823, i823, i778)
1055_1_parts_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), i946), i952, i166, i952, i952) → 3777_0_parts_Return(EOS(STATIC_3777), i952, i166, i952, i952, i946)
1058_0_parts_InvokeMethod(EOS(STATIC_1058), i164, i166, i166) → 1063_1_parts_InvokeMethod(1063_0_parts_Load(EOS(STATIC_1063), i166), i164, i166, i166)
1063_0_parts_Load(EOS(STATIC_1063), i166) → 1068_0_parts_Load(EOS(STATIC_1068), i166)
1063_1_parts_InvokeMethod(1004_0_parts_Return(EOS(STATIC_1004), i185, i186, matching1), i164, i186, i186) → 1165_0_parts_Return(EOS(STATIC_1165), i164, i186, i186, i186, 1) | =(matching1, 1)
1063_1_parts_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), i770, i771, i723), i164, i771, i771) → 1736_0_parts_Return(EOS(STATIC_1736), i164, i771, i771, i771, i723)
1063_1_parts_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), i825, i826, i778), i164, i826, i826) → 1775_0_parts_Return(EOS(STATIC_1775), i164, i826, i826, i826, i778)
1063_1_parts_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), i946), i164, i954, i954) → 3778_0_parts_Return(EOS(STATIC_3778), i164, i954, i954, i946)
1165_0_parts_Return(EOS(STATIC_1165), i164, i186, i186, i186, matching1) → 1168_0_parts_Load(EOS(STATIC_1168), i164, i186, 1) | =(matching1, 1)
1168_0_parts_Load(EOS(STATIC_1168), i164, i186, matching1) → 1228_0_parts_Load(EOS(STATIC_1228), i164, i186, 1) | =(matching1, 1)
1221_0_parts_Return(EOS(STATIC_1221), i263, i166, i263, i263, matching1) → 1334_0_parts_Return(EOS(STATIC_1334), i263, i166, i263, i263, 1) | =(matching1, 1)
1222_0_parts_Return(EOS(STATIC_1222), i164, i265, i265, matching1) → 1340_0_parts_Return(EOS(STATIC_1340), i164, i265, i265, 1) | =(matching1, 1)
1228_0_parts_Load(EOS(STATIC_1228), i164, i265, matching1) → 1255_0_parts_Load(EOS(STATIC_1255), i164, i265, 1) | =(matching1, 1)
1244_0_parts_Return(EOS(STATIC_1244), i276, i166, i276, i276, i276, i276, matching1) → 1391_0_parts_Return(EOS(STATIC_1391), i276, i166, i276, i276, i276, i276, 1) | =(matching1, 1)
1246_0_parts_Return(EOS(STATIC_1246), i164, i279, i279, i279, matching1) → 1396_0_parts_Return(EOS(STATIC_1396), i164, i279, i279, i279, 1) | =(matching1, 1)
1255_0_parts_Load(EOS(STATIC_1255), i164, i279, matching1) → 1367_0_parts_Load(EOS(STATIC_1367), i164, i279, 1) | =(matching1, 1)
1334_0_parts_Return(EOS(STATIC_1334), i345, i166, i345, i345, i346) → 1489_0_parts_Return(EOS(STATIC_1489), i345, i166, i345, i345, i346)
1340_0_parts_Return(EOS(STATIC_1340), i164, i357, i357, i358) → 1495_0_parts_Return(EOS(STATIC_1495), i164, i357, i357, i358)
1367_0_parts_Load(EOS(STATIC_1367), i164, i357, i358) → 1411_0_parts_Load(EOS(STATIC_1411), i164, i357, i358)
1391_0_parts_Return(EOS(STATIC_1391), i418, i166, i418, i418, i418, i418, i419) → 1558_0_parts_Return(EOS(STATIC_1558), i418, i166, i418, i418, i418, i418, i419)
1396_0_parts_Return(EOS(STATIC_1396), i164, i429, i429, i429, i431) → 1565_0_parts_Return(EOS(STATIC_1565), i164, i429, i429, i429, i431)
1411_0_parts_Load(EOS(STATIC_1411), i164, i429, i431) → 1529_0_parts_Load(EOS(STATIC_1529), i164, i429, i431)
1489_0_parts_Return(EOS(STATIC_1489), i531, i166, i531, i531, i532) → 1668_0_parts_Return(EOS(STATIC_1668), i531, i166, i531, i531, i532)
1495_0_parts_Return(EOS(STATIC_1495), i164, i543, i543, i544) → 1675_0_parts_Return(EOS(STATIC_1675), i164, i543, i543, i544)
1529_0_parts_Load(EOS(STATIC_1529), i164, i543, i544) → 1582_0_parts_Load(EOS(STATIC_1582), i164, i543, i544)
1558_0_parts_Return(EOS(STATIC_1558), i613, i166, i613, i613, i613, i613, i614) → 1731_0_parts_Return(EOS(STATIC_1731), i613, i166, i613, i613, i613, i613, i614)
1565_0_parts_Return(EOS(STATIC_1565), i164, i624, i624, i624, i626) → 1737_0_parts_Return(EOS(STATIC_1737), i164, i624, i624, i624, i626)
1582_0_parts_Load(EOS(STATIC_1582), i164, i624, i626) → 1692_0_parts_Load(EOS(STATIC_1692), i164, i624, i626)
1668_0_parts_Return(EOS(STATIC_1668), i722, i166, i722, i722, i723) → 1689_0_parts_Return(EOS(STATIC_1689), i722, i166, i723)
1675_0_parts_Return(EOS(STATIC_1675), i164, i732, i732, i733) → 1692_0_parts_Load(EOS(STATIC_1692), i164, i732, i733)
1689_0_parts_Return(EOS(STATIC_1689), i722, i166, i723) → 1749_0_parts_Return(EOS(STATIC_1749), i722, i166, i723)
1692_0_parts_Load(EOS(STATIC_1692), i164, i732, i733) → 1752_0_parts_Load(EOS(STATIC_1752), i164, i732, i733)
1730_0_parts_Return(EOS(STATIC_1730), i768, i166, i768, i768, i768, i768, i723) → 1731_0_parts_Return(EOS(STATIC_1731), i768, i166, i768, i768, i768, i768, i723)
1731_0_parts_Return(EOS(STATIC_1731), i777, i166, i777, i777, i777, i777, i778) → 1749_0_parts_Return(EOS(STATIC_1749), i777, i166, i778)
1736_0_parts_Return(EOS(STATIC_1736), i164, i771, i771, i771, i723) → 1737_0_parts_Return(EOS(STATIC_1737), i164, i771, i771, i771, i723)
1737_0_parts_Return(EOS(STATIC_1737), i164, i788, i788, i788, i790) → 1752_0_parts_Load(EOS(STATIC_1752), i164, i788, i790)
1752_0_parts_Load(EOS(STATIC_1752), i164, i788, i790) → 1757_0_parts_Load(EOS(STATIC_1757), i788, i790, i164)
1757_0_parts_Load(EOS(STATIC_1757), i788, i790, i164) → 1767_0_parts_ConstantStackPush(EOS(STATIC_1767), i790, i164, i788)
1767_0_parts_ConstantStackPush(EOS(STATIC_1767), i790, i164, i788) → 1779_0_parts_IntArithmetic(EOS(STATIC_1779), i790, i164, i788)
1772_0_parts_Return(EOS(STATIC_1772), i823, i166, i823, i823, i823, i823, i778) → 1731_0_parts_Return(EOS(STATIC_1731), i823, i166, i823, i823, i823, i823, i778)
1775_0_parts_Return(EOS(STATIC_1775), i164, i826, i826, i826, i778) → 1737_0_parts_Return(EOS(STATIC_1737), i164, i826, i826, i826, i778)
1779_0_parts_IntArithmetic(EOS(STATIC_1779), i790, i164, i788) → 1784_0_parts_InvokeMethod(EOS(STATIC_1784), i790, i164) | >(i788, 0)
1784_0_parts_InvokeMethod(EOS(STATIC_1784), i790, i164) → 1786_1_parts_InvokeMethod(1786_0_parts_Load(EOS(STATIC_1786), i164), i790, i164)
1786_0_parts_Load(EOS(STATIC_1786), i164) → 1788_0_parts_Load(EOS(STATIC_1788), i164)
1786_1_parts_InvokeMethod(1018_0_parts_Return(EOS(STATIC_1018), i844, matching1, matching2), i790, i844) → 1800_0_parts_Return(EOS(STATIC_1800), i790, i844, 0, i844, 0, 0) | &&(=(matching1, 0), =(matching2, 0))
1786_1_parts_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), i845, i846, i723), i790, i845) → 1801_0_parts_Return(EOS(STATIC_1801), i790, i845, i845, i723)
1786_1_parts_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), i847, i848, i778), i790, i847) → 1804_0_parts_Return(EOS(STATIC_1804), i790, i847, i847, i778)
1786_1_parts_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), i946), i790, i958) → 3781_0_parts_Return(EOS(STATIC_3781), i790, i958, i946)
1800_0_parts_Return(EOS(STATIC_1800), i790, i844, matching1, i844, matching2, matching3) → 1805_0_parts_IntArithmetic(EOS(STATIC_1805), i790, 0) | &&(&&(=(matching1, 0), =(matching2, 0)), =(matching3, 0))
1801_0_parts_Return(EOS(STATIC_1801), i790, i845, i845, i723) → 1807_0_parts_IntArithmetic(EOS(STATIC_1807), i790, i723)
1804_0_parts_Return(EOS(STATIC_1804), i790, i847, i847, i778) → 1801_0_parts_Return(EOS(STATIC_1801), i790, i847, i847, i778)
1805_0_parts_IntArithmetic(EOS(STATIC_1805), i790, matching1) → 1807_0_parts_IntArithmetic(EOS(STATIC_1807), i790, 0) | =(matching1, 0)
1807_0_parts_IntArithmetic(EOS(STATIC_1807), i790, i723) → 3771_0_parts_IntArithmetic(EOS(STATIC_3771), i790, i723)
1832_0_parts_Return(EOS(STATIC_1832), i790, i870, i858) → 3771_0_parts_IntArithmetic(EOS(STATIC_3771), i790, i858)
3771_0_parts_IntArithmetic(EOS(STATIC_3771), i790, i858) → 3772_0_parts_Return(EOS(STATIC_3772), +(i790, i858))
3777_0_parts_Return(EOS(STATIC_3777), i952, i166, i952, i952, i946) → 1668_0_parts_Return(EOS(STATIC_1668), i952, i166, i952, i952, i946)
3778_0_parts_Return(EOS(STATIC_3778), i164, i954, i954, i946) → 1675_0_parts_Return(EOS(STATIC_1675), i164, i954, i954, i946)
3781_0_parts_Return(EOS(STATIC_3781), i790, i958, i946) → 1832_0_parts_Return(EOS(STATIC_1832), i790, i958, i946)

Combined rules. Obtained 7 conditional rules for P and 16 conditional rules for R.

P rules:
1056_0_main_GT(EOS(STATIC_1056), java.lang.Object(ARRAY(x0)), x1, x2, x2, x0) → 1056_0_main_GT(EOS(STATIC_1056), java.lang.Object(ARRAY(x0)), +(x1, 1), 0, 0, x0) | &&(&&(>(x2, x0), >(+(x0, 1), 0)), >=(x0, +(x1, 1)))
1056_0_main_GT(EOS(STATIC_1056), java.lang.Object(ARRAY(x0)), x1, x2, x2, x0) → 1163_1_main_InvokeMethod(1163_0_parts_Load(EOS(STATIC_1163), x1, x2), java.lang.Object(ARRAY(x0)), x1, x2, x1, x2) | <=(x2, x0)
1163_1_main_InvokeMethod(1004_0_parts_Return(EOS(STATIC_1004), x0, x1, 1), java.lang.Object(ARRAY(x3)), x0, x1, x0, x1) → 1056_0_main_GT(EOS(STATIC_1056), java.lang.Object(ARRAY(x3)), x0, +(x1, 1), +(x1, 1), x3) | &&(>(+(x3, 1), 0), >(+(x1, 1), 0))
1163_1_main_InvokeMethod(1018_0_parts_Return(EOS(STATIC_1018), x0, 0, 0), java.lang.Object(ARRAY(x3)), x0, 0, x0, 0) → 1056_0_main_GT(EOS(STATIC_1056), java.lang.Object(ARRAY(x3)), x0, 1, 1, x3) | >(+(x3, 1), 0)
1163_1_main_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), x0, x1, x2), java.lang.Object(ARRAY(x3)), x0, x1, x0, x1) → 1056_0_main_GT(EOS(STATIC_1056), java.lang.Object(ARRAY(x3)), x0, +(x1, 1), +(x1, 1), x3) | &&(>(+(x3, 1), 0), >(x1, 0))
1163_1_main_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), x0, x1, x2), java.lang.Object(ARRAY(x3)), x0, x1, x0, x1) → 1056_0_main_GT(EOS(STATIC_1056), java.lang.Object(ARRAY(x3)), x0, +(x1, 1), +(x1, 1), x3) | &&(>(+(x3, 1), 0), >(x1, 0))
1163_1_main_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), x0), java.lang.Object(ARRAY(x1)), x2, x3, x2, x3) → 1056_0_main_GT(EOS(STATIC_1056), java.lang.Object(ARRAY(x1)), x2, +(x3, 1), +(x3, 1), x1) | &&(>(x3, 0), >(+(x1, 1), 0))
R rules:
1163_0_parts_Load(EOS(STATIC_1163), x0, x1) → 997_0_parts_GT(EOS(STATIC_997), x0, x1, x0)
997_0_parts_GT(EOS(STATIC_997), x0, x1, x0) → 1004_0_parts_Return(EOS(STATIC_1004), x0, x1, 1) | <=(x0, 0)
997_0_parts_GT(EOS(STATIC_997), x0, 0, x0) → 1018_0_parts_Return(EOS(STATIC_1018), x0, 0, 0) | >(x0, 0)
997_0_parts_GT(EOS(STATIC_997), x0, x1, x0) → 1055_1_parts_InvokeMethod(997_0_parts_GT(EOS(STATIC_997), x0, x0, x0), x0, x1, x0, x0) | &&(&&(>(x1, x0), >(x1, 0)), >(x0, 0))
997_0_parts_GT(EOS(STATIC_997), x0, x1, x0) → 1063_1_parts_InvokeMethod(997_0_parts_GT(EOS(STATIC_997), x2, x1, x2), x0, x1, x1) | &&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0))
1055_1_parts_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), x0, x0, x1), x0, x2, x0, x0) → 1749_0_parts_Return(EOS(STATIC_1749), x0, x2, x1)
1055_1_parts_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), x0, x0, x1), x0, x2, x0, x0) → 1749_0_parts_Return(EOS(STATIC_1749), x0, x2, x1)
1055_1_parts_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), x0), x1, x2, x1, x1) → 1749_0_parts_Return(EOS(STATIC_1749), x1, x2, x0)
1063_1_parts_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), x0, x1, x2), x3, x1, x1) → 1786_1_parts_InvokeMethod(997_0_parts_GT(EOS(STATIC_997), x3, x4, x3), x2, x3) | >(x1, 0)
1063_1_parts_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), x0, x1, x2), x3, x1, x1) → 1786_1_parts_InvokeMethod(997_0_parts_GT(EOS(STATIC_997), x3, x4, x3), x2, x3) | >(x1, 0)
1063_1_parts_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), x0), x1, x2, x2) → 1786_1_parts_InvokeMethod(997_0_parts_GT(EOS(STATIC_997), x1, x3, x1), x0, x1) | >(x2, 0)
1063_1_parts_InvokeMethod(1004_0_parts_Return(EOS(STATIC_1004), x0, x1, 1), x3, x1, x1) → 1786_1_parts_InvokeMethod(997_0_parts_GT(EOS(STATIC_997), x3, x4, x3), 1, x3) | >(x1, 0)
1786_1_parts_InvokeMethod(1689_0_parts_Return(EOS(STATIC_1689), x0, x1, x2), x3, x0) → 3772_0_parts_Return(EOS(STATIC_3772), +(x3, x2))
1786_1_parts_InvokeMethod(1749_0_parts_Return(EOS(STATIC_1749), x0, x1, x2), x3, x0) → 3772_0_parts_Return(EOS(STATIC_3772), +(x3, x2))
1786_1_parts_InvokeMethod(1018_0_parts_Return(EOS(STATIC_1018), x0, 0, 0), arith[1], x0) → 3772_0_parts_Return(EOS(STATIC_3772), arith[1])
1786_1_parts_InvokeMethod(3772_0_parts_Return(EOS(STATIC_3772), x0), x1, x2) → 3772_0_parts_Return(EOS(STATIC_3772), +(x1, x0))

Filtered ground terms:

1056_0_main_GT(x1, x2, x3, x4, x5, x6) → 1056_0_main_GT(x2, x3, x4, x5, x6)
3772_0_parts_Return(x1, x2) → 3772_0_parts_Return(x2)
1749_0_parts_Return(x1, x2, x3, x4) → 1749_0_parts_Return(x2, x3, x4)
1689_0_parts_Return(x1, x2, x3, x4) → 1689_0_parts_Return(x2, x3, x4)
Cond_1163_1_main_InvokeMethod1(x1, x2, x3, x4, x5, x6, x7) → Cond_1163_1_main_InvokeMethod1(x1, x2, x3, x4, x6)
1018_0_parts_Return(x1, x2, x3, x4) → 1018_0_parts_Return(x2)
1004_0_parts_Return(x1, x2, x3, x4) → 1004_0_parts_Return(x2, x3)
1163_0_parts_Load(x1, x2, x3) → 1163_0_parts_Load(x2, x3)
Cond_1056_0_main_GT1(x1, x2, x3, x4, x5, x6, x7) → Cond_1056_0_main_GT1(x1, x3, x4, x5, x6, x7)
Cond_1056_0_main_GT(x1, x2, x3, x4, x5, x6, x7) → Cond_1056_0_main_GT(x1, x3, x4, x5, x6, x7)
997_0_parts_GT(x1, x2, x3, x4) → 997_0_parts_GT(x2, x3, x4)
Cond_997_0_parts_GT3(x1, x2, x3, x4, x5, x6) → Cond_997_0_parts_GT3(x1, x3, x4, x5, x6)
Cond_997_0_parts_GT2(x1, x2, x3, x4, x5) → Cond_997_0_parts_GT2(x1, x3, x4, x5)
Cond_997_0_parts_GT1(x1, x2, x3, x4, x5) → Cond_997_0_parts_GT1(x1, x3, x5)
Cond_997_0_parts_GT(x1, x2, x3, x4, x5) → Cond_997_0_parts_GT(x1, x3, x4, x5)

Filtered duplicate args:

1056_0_main_GT(x1, x2, x3, x4, x5) → 1056_0_main_GT(x1, x2, x4)
Cond_1056_0_main_GT(x1, x2, x3, x4, x5, x6) → Cond_1056_0_main_GT(x1, x2, x3, x5)
Cond_1056_0_main_GT1(x1, x2, x3, x4, x5, x6) → Cond_1056_0_main_GT1(x1, x2, x3, x5)
1163_1_main_InvokeMethod(x1, x2, x3, x4, x5, x6) → 1163_1_main_InvokeMethod(x1, x2, x5, x6)
Cond_1163_1_main_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → Cond_1163_1_main_InvokeMethod(x1, x2, x3)
Cond_1163_1_main_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_1163_1_main_InvokeMethod1(x1, x2, x3)
Cond_1163_1_main_InvokeMethod2(x1, x2, x3, x4, x5, x6, x7) → Cond_1163_1_main_InvokeMethod2(x1, x2, x3)
Cond_1163_1_main_InvokeMethod3(x1, x2, x3, x4, x5, x6, x7) → Cond_1163_1_main_InvokeMethod3(x1, x2, x3)
Cond_1163_1_main_InvokeMethod4(x1, x2, x3, x4, x5, x6, x7) → Cond_1163_1_main_InvokeMethod4(x1, x2, x3, x6, x7)
997_0_parts_GT(x1, x2, x3) → 997_0_parts_GT(x2, x3)
Cond_997_0_parts_GT(x1, x2, x3, x4) → Cond_997_0_parts_GT(x1, x3, x4)
Cond_997_0_parts_GT1(x1, x2, x3) → Cond_997_0_parts_GT1(x1, x3)
Cond_997_0_parts_GT2(x1, x2, x3, x4) → Cond_997_0_parts_GT2(x1, x3, x4)
1055_1_parts_InvokeMethod(x1, x2, x3, x4, x5) → 1055_1_parts_InvokeMethod(x1, x3, x5)
Cond_997_0_parts_GT3(x1, x2, x3, x4, x5) → Cond_997_0_parts_GT3(x1, x3, x4, x5)
1063_1_parts_InvokeMethod(x1, x2, x3, x4) → 1063_1_parts_InvokeMethod(x1, x2, x4)
Cond_1063_1_parts_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_1063_1_parts_InvokeMethod(x1, x2, x3, x6)
Cond_1063_1_parts_InvokeMethod1(x1, x2, x3, x4, x5, x6) → Cond_1063_1_parts_InvokeMethod1(x1, x2, x3, x6)
Cond_1063_1_parts_InvokeMethod2(x1, x2, x3, x4, x5, x6) → Cond_1063_1_parts_InvokeMethod2(x1, x2, x3, x5, x6)
Cond_1063_1_parts_InvokeMethod3(x1, x2, x3, x4, x5, x6) → Cond_1063_1_parts_InvokeMethod3(x1, x2, x3, x6)

Filtered unneeded arguments:

Cond_1056_0_main_GT(x1, x2, x3, x4) → Cond_1056_0_main_GT(x1, x2, x3)
Cond_1163_1_main_InvokeMethod4(x1, x2, x3, x4, x5) → Cond_1163_1_main_InvokeMethod4(x1, x3, x4, x5)
1689_0_parts_Return(x1, x2, x3) → 1689_0_parts_Return(x1, x2)
1749_0_parts_Return(x1, x2, x3) → 1749_0_parts_Return(x1, x2)
Cond_1063_1_parts_InvokeMethod(x1, x2, x3, x4) → Cond_1063_1_parts_InvokeMethod(x1, x3, x4)
1786_1_parts_InvokeMethod(x1, x2, x3) → 1786_1_parts_InvokeMethod(x1, x3)
Cond_1063_1_parts_InvokeMethod1(x1, x2, x3, x4) → Cond_1063_1_parts_InvokeMethod1(x1, x3, x4)
Cond_1063_1_parts_InvokeMethod2(x1, x2, x3, x4, x5) → Cond_1063_1_parts_InvokeMethod2(x1, x3, x5)
Cond_1063_1_parts_InvokeMethod3(x1, x2, x3, x4) → Cond_1063_1_parts_InvokeMethod3(x1, x3, x4)

Combined rules. Obtained 7 conditional rules for P and 16 conditional rules for R.

P rules:
1056_0_main_GT(java.lang.Object(ARRAY(x0)), x1, x2) → 1056_0_main_GT(java.lang.Object(ARRAY(x0)), +(x1, 1), 0) | &&(&&(>(x2, x0), >=(x0, +(x1, 1))), >(x0, -1))
1056_0_main_GT(java.lang.Object(ARRAY(x0)), x1, x2) → 1163_1_main_InvokeMethod(1163_0_parts_Load(x1, x2), java.lang.Object(ARRAY(x0)), x1, x2) | <=(x2, x0)
1163_1_main_InvokeMethod(1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 1056_0_main_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1)) | &&(>(x3, -1), >(x1, -1))
1163_1_main_InvokeMethod(1018_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → 1056_0_main_GT(java.lang.Object(ARRAY(x3)), x0, 1) | >(x3, -1)
1163_1_main_InvokeMethod(1689_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 1056_0_main_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1)) | &&(>(x3, -1), >(x1, 0))
1163_1_main_InvokeMethod(1749_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 1056_0_main_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1)) | &&(>(x3, -1), >(x1, 0))
1163_1_main_InvokeMethod(3772_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → 1056_0_main_GT(java.lang.Object(ARRAY(x1)), x2, +(x3, 1)) | &&(>(x3, 0), >(x1, -1))
R rules:
1163_0_parts_Load(x0, x1) → 997_0_parts_GT(x1, x0)
997_0_parts_GT(x1, x0) → 1004_0_parts_Return(x0, x1) | <=(x0, 0)
997_0_parts_GT(0, x0) → 1018_0_parts_Return(x0) | >(x0, 0)
997_0_parts_GT(x1, x0) → 1055_1_parts_InvokeMethod(997_0_parts_GT(x0, x0), x1, x0) | &&(&&(>(x1, x0), >(x1, 0)), >(x0, 0))
997_0_parts_GT(x1, x0) → 1063_1_parts_InvokeMethod(997_0_parts_GT(x1, x2), x0, x1) | &&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0))
1055_1_parts_InvokeMethod(1689_0_parts_Return(x0, x0), x2, x0) → 1749_0_parts_Return(x0, x2)
1055_1_parts_InvokeMethod(1749_0_parts_Return(x0, x0), x2, x0) → 1749_0_parts_Return(x0, x2)
1055_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x1) → 1749_0_parts_Return(x1, x2)
1063_1_parts_InvokeMethod(1689_0_parts_Return(x0, x1), x3, x1) → 1786_1_parts_InvokeMethod(997_0_parts_GT(x4, x3), x3) | >(x1, 0)
1063_1_parts_InvokeMethod(1749_0_parts_Return(x0, x1), x3, x1) → 1786_1_parts_InvokeMethod(997_0_parts_GT(x4, x3), x3) | >(x1, 0)
1063_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1, x2) → 1786_1_parts_InvokeMethod(997_0_parts_GT(x3, x1), x1) | >(x2, 0)
1063_1_parts_InvokeMethod(1004_0_parts_Return(x0, x1), x3, x1) → 1786_1_parts_InvokeMethod(997_0_parts_GT(x4, x3), x3) | >(x1, 0)
1786_1_parts_InvokeMethod(1689_0_parts_Return(x0, x1), x0) → 3772_0_parts_Return(+(x3, x2))
1786_1_parts_InvokeMethod(1749_0_parts_Return(x0, x1), x0) → 3772_0_parts_Return(+(x3, x2))
1786_1_parts_InvokeMethod(1018_0_parts_Return(x0), x0) → 3772_0_parts_Return(arith[1])
1786_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2) → 3772_0_parts_Return(+(x1, x0))

Performed bisimulation on rules. Used the following equivalence classes: {[1004_0_parts_Return_2, 1689_0_parts_Return_2, 1749_0_parts_Return_2]=1004_0_parts_Return_2, [Cond_1163_1_main_InvokeMethod2_5, Cond_1163_1_main_InvokeMethod3_5]=Cond_1163_1_main_InvokeMethod2_5, [Cond_1063_1_parts_InvokeMethod_5, Cond_1063_1_parts_InvokeMethod1_5, Cond_1063_1_parts_InvokeMethod3_5]=Cond_1063_1_parts_InvokeMethod_5}

Finished conversion. Obtained 12 rules for P and 18 rules for R. System has predefined symbols.

P rules:
1056_0_MAIN_GT(java.lang.Object(ARRAY(x0)), x1, x2) → COND_1056_0_MAIN_GT(&&(&&(>(x2, x0), >=(x0, +(x1, 1))), >(x0, -1)), java.lang.Object(ARRAY(x0)), x1, x2)
COND_1056_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0)), x1, x2) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0)), +(x1, 1), 0)
1056_0_MAIN_GT(java.lang.Object(ARRAY(x0)), x1, x2) → COND_1056_0_MAIN_GT1(<=(x2, x0), java.lang.Object(ARRAY(x0)), x1, x2)
COND_1056_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0)), x1, x2) → 1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1, x2), java.lang.Object(ARRAY(x0)), x1, x2)
1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3, -1), >(x1, -1)), 1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1)
COND_1163_1_MAIN_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1))
1163_1_MAIN_INVOKEMETHOD(1018_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → COND_1163_1_MAIN_INVOKEMETHOD1(>(x3, -1), 1018_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0)
COND_1163_1_MAIN_INVOKEMETHOD1(TRUE, 1018_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, 1)
1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3, -1), >(x1, 0)), 1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1)
COND_1163_1_MAIN_INVOKEMETHOD2(TRUE, 1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1))
1163_1_MAIN_INVOKEMETHOD(3772_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3, 0), >(x1, -1)), 3772_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3)
COND_1163_1_MAIN_INVOKEMETHOD4(TRUE, 3772_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x1)), x2, +(x3, 1))
R rules:
1163_0_parts_Load(x0, x1) → 997_0_parts_GT(x1, x0)
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT(<=(x0, 0), x1, x0)
Cond_997_0_parts_GT(TRUE, x1, x0) → 1004_0_parts_Return(x0, x1)
997_0_parts_GT(0, x0) → Cond_997_0_parts_GT1(>(x0, 0), 0, x0)
Cond_997_0_parts_GT1(TRUE, 0, x0) → 1018_0_parts_Return(x0)
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT2(&&(&&(>(x1, x0), >(x1, 0)), >(x0, 0)), x1, x0)
Cond_997_0_parts_GT2(TRUE, x1, x0) → 1055_1_parts_InvokeMethod(997_0_parts_GT(x0, x0), x1, x0)
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT3(&&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0)), x1, x0, x2)
Cond_997_0_parts_GT3(TRUE, x1, x0, x2) → 1063_1_parts_InvokeMethod(997_0_parts_GT(x1, x2), x0, x1)
1055_1_parts_InvokeMethod(1004_0_parts_Return(x0, x0), x2, x0) → 1004_0_parts_Return(x0, x2)
1055_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x1) → 1004_0_parts_Return(x1, x2)
1063_1_parts_InvokeMethod(1004_0_parts_Return(x0, x1), x3, x1) → Cond_1063_1_parts_InvokeMethod(>(x1, 0), 1004_0_parts_Return(x0, x1), x3, x1, x4)
Cond_1063_1_parts_InvokeMethod(TRUE, 1004_0_parts_Return(x0, x1), x3, x1, x4) → 1786_1_parts_InvokeMethod(997_0_parts_GT(x4, x3), x3)
1063_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1, x2) → Cond_1063_1_parts_InvokeMethod2(>(x2, 0), 3772_0_parts_Return(x0), x1, x2, x3)
Cond_1063_1_parts_InvokeMethod2(TRUE, 3772_0_parts_Return(x0), x1, x2, x3) → 1786_1_parts_InvokeMethod(997_0_parts_GT(x3, x1), x1)
1786_1_parts_InvokeMethod(1004_0_parts_Return(x0, x1), x0) → 3772_0_parts_Return(+(x3, x2))
1786_1_parts_InvokeMethod(1018_0_parts_Return(x0), x0) → 3772_0_parts_Return(arith[1])
1786_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2) → 3772_0_parts_Return(+(x1, x0))

(26) 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

The ITRS R consists of the following rules:
1163_0_parts_Load(x0, x1) → 997_0_parts_GT(x1, x0)
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT(x0 <= 0, x1, x0)
Cond_997_0_parts_GT(TRUE, x1, x0) → 1004_0_parts_Return(x0, x1)
997_0_parts_GT(0, x0) → Cond_997_0_parts_GT1(x0 > 0, 0, x0)
Cond_997_0_parts_GT1(TRUE, 0, x0) → 1018_0_parts_Return(x0)
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT2(x1 > x0 && x1 > 0 && x0 > 0, x1, x0)
Cond_997_0_parts_GT2(TRUE, x1, x0) → 1055_1_parts_InvokeMethod(997_0_parts_GT(x0, x0), x1, x0)
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT3(x1 > 0 && x1 <= x0 && x0 > 0, x1, x0, x2)
Cond_997_0_parts_GT3(TRUE, x1, x0, x2) → 1063_1_parts_InvokeMethod(997_0_parts_GT(x1, x2), x0, x1)
1055_1_parts_InvokeMethod(1004_0_parts_Return(x0, x0), x2, x0) → 1004_0_parts_Return(x0, x2)
1055_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x1) → 1004_0_parts_Return(x1, x2)
1063_1_parts_InvokeMethod(1004_0_parts_Return(x0, x1), x3, x1) → Cond_1063_1_parts_InvokeMethod(x1 > 0, 1004_0_parts_Return(x0, x1), x3, x1, x4)
Cond_1063_1_parts_InvokeMethod(TRUE, 1004_0_parts_Return(x0, x1), x3, x1, x4) → 1786_1_parts_InvokeMethod(997_0_parts_GT(x4, x3), x3)
1063_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1, x2) → Cond_1063_1_parts_InvokeMethod2(x2 > 0, 3772_0_parts_Return(x0), x1, x2, x3)
Cond_1063_1_parts_InvokeMethod2(TRUE, 3772_0_parts_Return(x0), x1, x2, x3) → 1786_1_parts_InvokeMethod(997_0_parts_GT(x3, x1), x1)
1786_1_parts_InvokeMethod(1004_0_parts_Return(x0, x1), x0) → 3772_0_parts_Return(x3 + x2)
1786_1_parts_InvokeMethod(1018_0_parts_Return(x0), x0) → 3772_0_parts_Return(arith[1])
1786_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2) → 3772_0_parts_Return(x1 + x0)

The integer pair graph contains the following rules and edges:
(0): 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0]) → COND_1056_0_MAIN_GT(x2[0] > x0[0] && x0[0] >= x1[0] + 1 && x0[0] > -1, java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])
(1): COND_1056_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0[1])), x1[1], x2[1]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), x1[1] + 1, 0)
(2): 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2]) → COND_1056_0_MAIN_GT1(x2[2] <= x0[2], java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])
(3): COND_1056_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3]) → 1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])
(4): 1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4]) → COND_1163_1_MAIN_INVOKEMETHOD(x3[4] > -1 && x1[4] > -1, 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])
(5): COND_1163_1_MAIN_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], x1[5] + 1)
(6): 1163_1_MAIN_INVOKEMETHOD(1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0) → COND_1163_1_MAIN_INVOKEMETHOD1(x3[6] > -1, 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)
(7): COND_1163_1_MAIN_INVOKEMETHOD1(TRUE, 1018_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)
(8): 1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8]) → COND_1163_1_MAIN_INVOKEMETHOD2(x3[8] > -1 && x1[8] > 0, 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])
(9): COND_1163_1_MAIN_INVOKEMETHOD2(TRUE, 1004_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], x1[9] + 1)
(10): 1163_1_MAIN_INVOKEMETHOD(3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10]) → COND_1163_1_MAIN_INVOKEMETHOD4(x3[10] > 0 && x1[10] > -1, 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])
(11): COND_1163_1_MAIN_INVOKEMETHOD4(TRUE, 3772_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], x3[11] + 1)

(0) -> (1), if (x2[0] > x0[0] && x0[0] >= x1[0] + 1 && x0[0] > -1 ∧java.lang.Object(ARRAY(x0[0])) →^* java.lang.Object(ARRAY(x0[1]))∧x1[0] →^* x1[1]∧x2[0] →^* x2[1])

(1) -> (0), if (java.lang.Object(ARRAY(x0[1])) →^* java.lang.Object(ARRAY(x0[0]))∧x1[1] + 1 →^* x1[0]∧0 →^* x2[0])

(1) -> (2), if (java.lang.Object(ARRAY(x0[1])) →^* java.lang.Object(ARRAY(x0[2]))∧x1[1] + 1 →^* x1[2]∧0 →^* x2[2])

(2) -> (3), if (x2[2] <= x0[2] ∧java.lang.Object(ARRAY(x0[2])) →^* java.lang.Object(ARRAY(x0[3]))∧x1[2] →^* x1[3]∧x2[2] →^* x2[3])

(3) -> (4), if (1163_0_parts_Load(x1[3], x2[3]) →^* 1004_0_parts_Return(x0[4], x1[4])∧java.lang.Object(ARRAY(x0[3])) →^* java.lang.Object(ARRAY(x3[4]))∧x1[3] →^* x0[4]∧x2[3] →^* x1[4])

(3) -> (6), if (1163_0_parts_Load(x1[3], x2[3]) →^* 1018_0_parts_Return(x0[6])∧java.lang.Object(ARRAY(x0[3])) →^* java.lang.Object(ARRAY(x3[6]))∧x1[3] →^* x0[6]∧x2[3] →^* 0)

(3) -> (8), if (1163_0_parts_Load(x1[3], x2[3]) →^* 1004_0_parts_Return(x0[8], x1[8])∧java.lang.Object(ARRAY(x0[3])) →^* java.lang.Object(ARRAY(x3[8]))∧x1[3] →^* x0[8]∧x2[3] →^* x1[8])

(3) -> (10), if (1163_0_parts_Load(x1[3], x2[3]) →^* 3772_0_parts_Return(x0[10])∧java.lang.Object(ARRAY(x0[3])) →^* java.lang.Object(ARRAY(x1[10]))∧x1[3] →^* x2[10]∧x2[3] →^* x3[10])

(4) -> (5), if (x3[4] > -1 && x1[4] > -1 ∧1004_0_parts_Return(x0[4], x1[4]) →^* 1004_0_parts_Return(x0[5], x1[5])∧java.lang.Object(ARRAY(x3[4])) →^* java.lang.Object(ARRAY(x3[5]))∧x0[4] →^* x0[5]∧x1[4] →^* x1[5])

(5) -> (0), if (java.lang.Object(ARRAY(x3[5])) →^* java.lang.Object(ARRAY(x0[0]))∧x0[5] →^* x1[0]∧x1[5] + 1 →^* x2[0])

(5) -> (2), if (java.lang.Object(ARRAY(x3[5])) →^* java.lang.Object(ARRAY(x0[2]))∧x0[5] →^* x1[2]∧x1[5] + 1 →^* x2[2])

(6) -> (7), if (x3[6] > -1 ∧1018_0_parts_Return(x0[6]) →^* 1018_0_parts_Return(x0[7])∧java.lang.Object(ARRAY(x3[6])) →^* java.lang.Object(ARRAY(x3[7]))∧x0[6] →^* x0[7])

(7) -> (0), if (java.lang.Object(ARRAY(x3[7])) →^* java.lang.Object(ARRAY(x0[0]))∧x0[7] →^* x1[0]∧1 →^* x2[0])

(7) -> (2), if (java.lang.Object(ARRAY(x3[7])) →^* java.lang.Object(ARRAY(x0[2]))∧x0[7] →^* x1[2]∧1 →^* x2[2])

(8) -> (9), if (x3[8] > -1 && x1[8] > 0 ∧1004_0_parts_Return(x0[8], x1[8]) →^* 1004_0_parts_Return(x0[9], x1[9])∧java.lang.Object(ARRAY(x3[8])) →^* java.lang.Object(ARRAY(x3[9]))∧x0[8] →^* x0[9]∧x1[8] →^* x1[9])

(9) -> (0), if (java.lang.Object(ARRAY(x3[9])) →^* java.lang.Object(ARRAY(x0[0]))∧x0[9] →^* x1[0]∧x1[9] + 1 →^* x2[0])

(9) -> (2), if (java.lang.Object(ARRAY(x3[9])) →^* java.lang.Object(ARRAY(x0[2]))∧x0[9] →^* x1[2]∧x1[9] + 1 →^* x2[2])

(10) -> (11), if (x3[10] > 0 && x1[10] > -1 ∧3772_0_parts_Return(x0[10]) →^* 3772_0_parts_Return(x0[11])∧java.lang.Object(ARRAY(x1[10])) →^* java.lang.Object(ARRAY(x1[11]))∧x2[10] →^* x2[11]∧x3[10] →^* x3[11])

(11) -> (0), if (java.lang.Object(ARRAY(x1[11])) →^* java.lang.Object(ARRAY(x0[0]))∧x2[11] →^* x1[0]∧x3[11] + 1 →^* x2[0])

(11) -> (2), if (java.lang.Object(ARRAY(x1[11])) →^* java.lang.Object(ARRAY(x0[2]))∧x2[11] →^* x1[2]∧x3[11] + 1 →^* x2[2])

The set Q consists of the following terms:
1163_0_parts_Load(x0, x1)
997_0_parts_GT(x0, x1)
Cond_997_0_parts_GT(TRUE, x0, x1)
Cond_997_0_parts_GT1(TRUE, 0, x0)
Cond_997_0_parts_GT2(TRUE, x0, x1)
Cond_997_0_parts_GT3(TRUE, x0, x1, x2)
1055_1_parts_InvokeMethod(1004_0_parts_Return(x0, x0), x1, x0)
1055_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1, x2)
1063_1_parts_InvokeMethod(1004_0_parts_Return(x0, x1), x2, x1)
Cond_1063_1_parts_InvokeMethod(TRUE, 1004_0_parts_Return(x0, x1), x2, x1, x3)
1063_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1, x2)
Cond_1063_1_parts_InvokeMethod2(TRUE, 3772_0_parts_Return(x0), x1, x2, x3)
1786_1_parts_InvokeMethod(1004_0_parts_Return(x0, x1), x0)
1786_1_parts_InvokeMethod(1018_0_parts_Return(x0), x0)
1786_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1)

(27) 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.IdpCand1ShapeHeuristic@5575b290 Constraint Generator: NonInfConstraintGenerator: PathGenerator: MetricPathGenerator: Max Left Steps: 0 Max Right Steps: 0

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 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0)), x1, x2) → COND_1056_0_MAIN_GT(&&(&&(>(x2, x0), >=(x0, +(x1, 1))), >(x0, -1)), java.lang.Object(ARRAY(x0)), x1, x2) the following chains were created:

We consider the chain 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0]) → COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0]), COND_1056_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0[1])), x1[1], x2[1]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0) which results in the following constraint:
(1)    (&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1))=TRUE∧java.lang.Object(ARRAY(x0[0]))=java.lang.Object(ARRAY(x0[1]))∧x1[0]=x1[1]∧x2[0]=x2[1] ⇒ 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])≥NonInfC∧1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])≥COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])∧(U^Increasing(COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])), ≥))

We simplified constraint (1) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(2)    (>(x0[0], -1)=TRUE∧>(x2[0], x0[0])=TRUE∧>=(x0[0], +(x1[0], 1))=TRUE ⇒ 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])≥NonInfC∧1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])≥COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])∧(U^Increasing(COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(3)    (x0[0] ≥ 0∧x2[0] + [-1] + [-1]x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(-1)bni_38]x1[0] + [(2)bni_38]x0[0] ≥ 0∧[(-1)bso_39] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (x0[0] ≥ 0∧x2[0] + [-1] + [-1]x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(-1)bni_38]x1[0] + [(2)bni_38]x0[0] ≥ 0∧[(-1)bso_39] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (x0[0] ≥ 0∧x2[0] + [-1] + [-1]x0[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(-1)bni_38]x1[0] + [(2)bni_38]x0[0] ≥ 0∧[(-1)bso_39] ≥ 0)

We simplified constraint (5) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(6)    (x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(2)bni_38]x0[0] + [(-1)bni_38]x1[0] ≥ 0∧[(-1)bso_39] ≥ 0)

We simplified constraint (6) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(7)    (x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1] + [-1]x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(2)bni_38]x0[0] + [(-1)bni_38]x1[0] ≥ 0∧[(-1)bso_39] ≥ 0)

(8)    (x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1] + x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(2)bni_38]x0[0] + [bni_38]x1[0] ≥ 0∧[(-1)bso_39] ≥ 0)

We simplified constraint (7) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(9)    ([1] + x1[0] + x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])), ≥)∧[bni_38 + (-1)Bound*bni_38] + [bni_38]x1[0] + [(2)bni_38]x0[0] ≥ 0∧[(-1)bso_39] ≥ 0)

For Pair COND_1056_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0)), x1, x2) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0)), +(x1, 1), 0) the following chains were created:

We consider the chain COND_1056_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0[1])), x1[1], x2[1]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0) which results in the following constraint:
(10)    (COND_1056_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0[1])), x1[1], x2[1])≥NonInfC∧COND_1056_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0[1])), x1[1], x2[1])≥1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0)∧(U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0)), ≥))

We simplified constraint (10) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(11)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0)), ≥)∧[bni_40] = 0∧[1 + (-1)bso_41] ≥ 0)

We simplified constraint (11) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(12)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0)), ≥)∧[bni_40] = 0∧[1 + (-1)bso_41] ≥ 0)

We simplified constraint (12) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(13)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0)), ≥)∧[bni_40] = 0∧[1 + (-1)bso_41] ≥ 0)

We simplified constraint (13) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(14)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0)), ≥)∧[bni_40] = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_41] ≥ 0)

For Pair 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0)), x1, x2) → COND_1056_0_MAIN_GT1(<=(x2, x0), java.lang.Object(ARRAY(x0)), x1, x2) the following chains were created:

We consider the chain 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2]) → COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2]), COND_1056_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3]) → 1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3]) which results in the following constraint:
(15)    (<=(x2[2], x0[2])=TRUE∧java.lang.Object(ARRAY(x0[2]))=java.lang.Object(ARRAY(x0[3]))∧x1[2]=x1[3]∧x2[2]=x2[3] ⇒ 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])≥NonInfC∧1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])≥COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])∧(U^Increasing(COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])), ≥))

We simplified constraint (15) using rules (I), (II), (IV) which results in the following new constraint:
(16)    (<=(x2[2], x0[2])=TRUE ⇒ 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])≥NonInfC∧1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])≥COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])∧(U^Increasing(COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])), ≥))

We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(17)    (x0[2] + [-1]x2[2] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [(-1)bni_42]x1[2] + [(2)bni_42]x0[2] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (17) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(18)    (x0[2] + [-1]x2[2] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [(-1)bni_42]x1[2] + [(2)bni_42]x0[2] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (18) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(19)    (x0[2] + [-1]x2[2] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])), ≥)∧[(-1)bni_42 + (-1)Bound*bni_42] + [(-1)bni_42]x1[2] + [(2)bni_42]x0[2] ≥ 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (19) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(20)    (x0[2] + [-1]x2[2] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])), ≥)∧[(-1)bni_42] = 0∧[(-1)bni_42 + (-1)Bound*bni_42] + [(2)bni_42]x0[2] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (20) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(21)    (x0[2] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])), ≥)∧[(-1)bni_42] = 0∧[(-1)bni_42 + (-1)Bound*bni_42] + [(2)bni_42]x2[2] + [(2)bni_42]x0[2] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)

We simplified constraint (21) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(22)    (x0[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])), ≥)∧[(-1)bni_42] = 0∧[(-1)bni_42 + (-1)Bound*bni_42] + [(2)bni_42]x2[2] + [(2)bni_42]x0[2] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)

(23)    (x0[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])), ≥)∧[(-1)bni_42] = 0∧[(-1)bni_42 + (-1)Bound*bni_42] + [(-2)bni_42]x2[2] + [(2)bni_42]x0[2] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)

For Pair COND_1056_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0)), x1, x2) → 1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1, x2), java.lang.Object(ARRAY(x0)), x1, x2) the following chains were created:

We consider the chain COND_1056_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3]) → 1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3]) which results in the following constraint:
(24)    (COND_1056_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])≥NonInfC∧COND_1056_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])≥1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])∧(U^Increasing(1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])), ≥))

We simplified constraint (24) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(25)    ((U^Increasing(1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])), ≥)∧[bni_44] = 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (25) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(26)    ((U^Increasing(1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])), ≥)∧[bni_44] = 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (26) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(27)    ((U^Increasing(1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])), ≥)∧[bni_44] = 0∧[(-1)bso_45] ≥ 0)

We simplified constraint (27) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(28)    ((U^Increasing(1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])), ≥)∧[bni_44] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)

For Pair 1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3, -1), >(x1, -1)), 1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) the following chains were created:

We consider the chain 1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4]) → COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4]), COND_1163_1_MAIN_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1)) which results in the following constraint:
(29)    (&&(>(x3[4], -1), >(x1[4], -1))=TRUE∧1004_0_parts_Return(x0[4], x1[4])=1004_0_parts_Return(x0[5], x1[5])∧java.lang.Object(ARRAY(x3[4]))=java.lang.Object(ARRAY(x3[5]))∧x0[4]=x0[5]∧x1[4]=x1[5] ⇒ 1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])≥NonInfC∧1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])≥COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])∧(U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])), ≥))

We simplified constraint (29) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(30)    (>(x3[4], -1)=TRUE∧>(x1[4], -1)=TRUE ⇒ 1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])≥NonInfC∧1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])≥COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])∧(U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])), ≥))

We simplified constraint (30) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(31)    (x3[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])), ≥)∧[(-1)bni_46 + (-1)Bound*bni_46] + [(-1)bni_46]x0[4] + [(2)bni_46]x3[4] ≥ 0∧[(-1)bso_47] ≥ 0)

We simplified constraint (31) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(32)    (x3[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])), ≥)∧[(-1)bni_46 + (-1)Bound*bni_46] + [(-1)bni_46]x0[4] + [(2)bni_46]x3[4] ≥ 0∧[(-1)bso_47] ≥ 0)

We simplified constraint (32) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(33)    (x3[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])), ≥)∧[(-1)bni_46 + (-1)Bound*bni_46] + [(-1)bni_46]x0[4] + [(2)bni_46]x3[4] ≥ 0∧[(-1)bso_47] ≥ 0)

We simplified constraint (33) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(34)    (x3[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])), ≥)∧[(-1)bni_46] = 0∧[(-1)bni_46 + (-1)Bound*bni_46] + [(2)bni_46]x3[4] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)

For Pair COND_1163_1_MAIN_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1)) the following chains were created:

We consider the chain COND_1163_1_MAIN_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1)) which results in the following constraint:
(35)    (COND_1163_1_MAIN_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5])≥NonInfC∧COND_1163_1_MAIN_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5])≥1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1))∧(U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1))), ≥))

We simplified constraint (35) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(36)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1))), ≥)∧[bni_48] = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (36) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(37)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1))), ≥)∧[bni_48] = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (37) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(38)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1))), ≥)∧[bni_48] = 0∧[(-1)bso_49] ≥ 0)

We simplified constraint (38) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(39)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1))), ≥)∧[bni_48] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_49] ≥ 0)

For Pair 1163_1_MAIN_INVOKEMETHOD(1018_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → COND_1163_1_MAIN_INVOKEMETHOD1(>(x3, -1), 1018_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) the following chains were created:

We consider the chain 1163_1_MAIN_INVOKEMETHOD(1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0) → COND_1163_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0), COND_1163_1_MAIN_INVOKEMETHOD1(TRUE, 1018_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1) which results in the following constraint:
(40)    (>(x3[6], -1)=TRUE∧1018_0_parts_Return(x0[6])=1018_0_parts_Return(x0[7])∧java.lang.Object(ARRAY(x3[6]))=java.lang.Object(ARRAY(x3[7]))∧x0[6]=x0[7] ⇒ 1163_1_MAIN_INVOKEMETHOD(1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)≥NonInfC∧1163_1_MAIN_INVOKEMETHOD(1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)≥COND_1163_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)∧(U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)), ≥))

We simplified constraint (40) using rules (I), (II), (IV) which results in the following new constraint:
(41)    (>(x3[6], -1)=TRUE ⇒ 1163_1_MAIN_INVOKEMETHOD(1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)≥NonInfC∧1163_1_MAIN_INVOKEMETHOD(1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)≥COND_1163_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)∧(U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)), ≥))

We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(42)    (x3[6] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]x0[6] + [(2)bni_50]x3[6] ≥ 0∧[(-1)bso_51] ≥ 0)

We simplified constraint (42) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(43)    (x3[6] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]x0[6] + [(2)bni_50]x3[6] ≥ 0∧[(-1)bso_51] ≥ 0)

We simplified constraint (43) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(44)    (x3[6] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)), ≥)∧[(-1)bni_50 + (-1)Bound*bni_50] + [(-1)bni_50]x0[6] + [(2)bni_50]x3[6] ≥ 0∧[(-1)bso_51] ≥ 0)

We simplified constraint (44) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(45)    (x3[6] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)), ≥)∧[(-1)bni_50] = 0∧[(-1)bni_50 + (-1)Bound*bni_50] + [(2)bni_50]x3[6] ≥ 0∧0 = 0∧[(-1)bso_51] ≥ 0)

For Pair COND_1163_1_MAIN_INVOKEMETHOD1(TRUE, 1018_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, 1) the following chains were created:

We consider the chain COND_1163_1_MAIN_INVOKEMETHOD1(TRUE, 1018_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1) which results in the following constraint:
(46)    (COND_1163_1_MAIN_INVOKEMETHOD1(TRUE, 1018_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0)≥NonInfC∧COND_1163_1_MAIN_INVOKEMETHOD1(TRUE, 1018_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0)≥1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)∧(U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)), ≥))

We simplified constraint (46) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(47)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)), ≥)∧[bni_52] = 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (47) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(48)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)), ≥)∧[bni_52] = 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (48) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(49)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)), ≥)∧[bni_52] = 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (49) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(50)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)), ≥)∧[bni_52] = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)

For Pair 1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3, -1), >(x1, 0)), 1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) the following chains were created:

We consider the chain 1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8]) → COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8]), COND_1163_1_MAIN_INVOKEMETHOD2(TRUE, 1004_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1)) which results in the following constraint:
(51)    (&&(>(x3[8], -1), >(x1[8], 0))=TRUE∧1004_0_parts_Return(x0[8], x1[8])=1004_0_parts_Return(x0[9], x1[9])∧java.lang.Object(ARRAY(x3[8]))=java.lang.Object(ARRAY(x3[9]))∧x0[8]=x0[9]∧x1[8]=x1[9] ⇒ 1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])≥NonInfC∧1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])≥COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])∧(U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])), ≥))

We simplified constraint (51) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(52)    (>(x3[8], -1)=TRUE∧>(x1[8], 0)=TRUE ⇒ 1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])≥NonInfC∧1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])≥COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])∧(U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])), ≥))

We simplified constraint (52) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(53)    (x3[8] ≥ 0∧x1[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]x0[8] + [(2)bni_54]x3[8] ≥ 0∧[(-1)bso_55] ≥ 0)

We simplified constraint (53) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(54)    (x3[8] ≥ 0∧x1[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]x0[8] + [(2)bni_54]x3[8] ≥ 0∧[(-1)bso_55] ≥ 0)

We simplified constraint (54) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(55)    (x3[8] ≥ 0∧x1[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])), ≥)∧[(-1)bni_54 + (-1)Bound*bni_54] + [(-1)bni_54]x0[8] + [(2)bni_54]x3[8] ≥ 0∧[(-1)bso_55] ≥ 0)

We simplified constraint (55) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(56)    (x3[8] ≥ 0∧x1[8] + [-1] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])), ≥)∧[(-1)bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(2)bni_54]x3[8] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)

We simplified constraint (56) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(57)    (x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])), ≥)∧[(-1)bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(2)bni_54]x3[8] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)

For Pair COND_1163_1_MAIN_INVOKEMETHOD2(TRUE, 1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1)) the following chains were created:

We consider the chain COND_1163_1_MAIN_INVOKEMETHOD2(TRUE, 1004_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1)) which results in the following constraint:
(58)    (COND_1163_1_MAIN_INVOKEMETHOD2(TRUE, 1004_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9])≥NonInfC∧COND_1163_1_MAIN_INVOKEMETHOD2(TRUE, 1004_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9])≥1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1))∧(U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1))), ≥))

We simplified constraint (58) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(59)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1))), ≥)∧[bni_56] = 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (59) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(60)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1))), ≥)∧[bni_56] = 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (60) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(61)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1))), ≥)∧[bni_56] = 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (61) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(62)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1))), ≥)∧[bni_56] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

For Pair 1163_1_MAIN_INVOKEMETHOD(3772_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3, 0), >(x1, -1)), 3772_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) the following chains were created:

We consider the chain 1163_1_MAIN_INVOKEMETHOD(3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10]) → COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10]), COND_1163_1_MAIN_INVOKEMETHOD4(TRUE, 3772_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], +(x3[11], 1)) which results in the following constraint:
(63)    (&&(>(x3[10], 0), >(x1[10], -1))=TRUE∧3772_0_parts_Return(x0[10])=3772_0_parts_Return(x0[11])∧java.lang.Object(ARRAY(x1[10]))=java.lang.Object(ARRAY(x1[11]))∧x2[10]=x2[11]∧x3[10]=x3[11] ⇒ 1163_1_MAIN_INVOKEMETHOD(3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])≥NonInfC∧1163_1_MAIN_INVOKEMETHOD(3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])≥COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])∧(U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])), ≥))

We simplified constraint (63) using rules (I), (II), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(64)    (>(x3[10], 0)=TRUE∧>(x1[10], -1)=TRUE ⇒ 1163_1_MAIN_INVOKEMETHOD(3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])≥NonInfC∧1163_1_MAIN_INVOKEMETHOD(3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])≥COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])∧(U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])), ≥))

We simplified constraint (64) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(65)    (x3[10] + [-1] ≥ 0∧x1[10] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]x2[10] + [(2)bni_58]x1[10] ≥ 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (65) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(66)    (x3[10] + [-1] ≥ 0∧x1[10] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]x2[10] + [(2)bni_58]x1[10] ≥ 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (66) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(67)    (x3[10] + [-1] ≥ 0∧x1[10] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])), ≥)∧[(-1)bni_58 + (-1)Bound*bni_58] + [(-1)bni_58]x2[10] + [(2)bni_58]x1[10] ≥ 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (67) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(68)    (x3[10] + [-1] ≥ 0∧x1[10] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])), ≥)∧0 = 0∧[(-1)bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(2)bni_58]x1[10] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (68) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(69)    (x3[10] ≥ 0∧x1[10] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])), ≥)∧0 = 0∧[(-1)bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(2)bni_58]x1[10] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_59] ≥ 0)

For Pair COND_1163_1_MAIN_INVOKEMETHOD4(TRUE, 3772_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x1)), x2, +(x3, 1)) the following chains were created:

We consider the chain COND_1163_1_MAIN_INVOKEMETHOD4(TRUE, 3772_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], +(x3[11], 1)) which results in the following constraint:
(70)    (COND_1163_1_MAIN_INVOKEMETHOD4(TRUE, 3772_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11])≥NonInfC∧COND_1163_1_MAIN_INVOKEMETHOD4(TRUE, 3772_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11])≥1056_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], +(x3[11], 1))∧(U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], +(x3[11], 1))), ≥))

We simplified constraint (70) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(71)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], +(x3[11], 1))), ≥)∧[bni_60] = 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (71) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(72)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], +(x3[11], 1))), ≥)∧[bni_60] = 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (72) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(73)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], +(x3[11], 1))), ≥)∧[bni_60] = 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (73) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(74)    ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], +(x3[11], 1))), ≥)∧[bni_60] = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_61] ≥ 0)

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

1056_0_MAIN_GT(java.lang.Object(ARRAY(x0)), x1, x2) → COND_1056_0_MAIN_GT(&&(&&(>(x2, x0), >=(x0, +(x1, 1))), >(x0, -1)), java.lang.Object(ARRAY(x0)), x1, x2)
- (x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] + [-1] + x1[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])), ≥)∧[(-1)bni_38 + (-1)Bound*bni_38] + [(2)bni_38]x0[0] + [bni_38]x1[0] ≥ 0∧[(-1)bso_39] ≥ 0)
- ([1] + x1[0] + x0[0] ≥ 0∧x2[0] ≥ 0∧x0[0] ≥ 0∧x1[0] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])), ≥)∧[bni_38 + (-1)Bound*bni_38] + [bni_38]x1[0] + [(2)bni_38]x0[0] ≥ 0∧[(-1)bso_39] ≥ 0)
COND_1056_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0)), x1, x2) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0)), +(x1, 1), 0)
- ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0)), ≥)∧[bni_40] = 0∧0 = 0∧0 = 0∧0 = 0∧[1 + (-1)bso_41] ≥ 0)
1056_0_MAIN_GT(java.lang.Object(ARRAY(x0)), x1, x2) → COND_1056_0_MAIN_GT1(<=(x2, x0), java.lang.Object(ARRAY(x0)), x1, x2)
- (x0[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])), ≥)∧[(-1)bni_42] = 0∧[(-1)bni_42 + (-1)Bound*bni_42] + [(2)bni_42]x2[2] + [(2)bni_42]x0[2] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)
- (x0[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])), ≥)∧[(-1)bni_42] = 0∧[(-1)bni_42 + (-1)Bound*bni_42] + [(-2)bni_42]x2[2] + [(2)bni_42]x0[2] ≥ 0∧0 = 0∧[(-1)bso_43] ≥ 0)
COND_1056_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0)), x1, x2) → 1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1, x2), java.lang.Object(ARRAY(x0)), x1, x2)
- ((U^Increasing(1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])), ≥)∧[bni_44] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_45] ≥ 0)
1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3, -1), >(x1, -1)), 1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1)
- (x3[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])), ≥)∧[(-1)bni_46] = 0∧[(-1)bni_46 + (-1)Bound*bni_46] + [(2)bni_46]x3[4] ≥ 0∧0 = 0∧[(-1)bso_47] ≥ 0)
COND_1163_1_MAIN_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1))
- ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1))), ≥)∧[bni_48] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_49] ≥ 0)
1163_1_MAIN_INVOKEMETHOD(1018_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → COND_1163_1_MAIN_INVOKEMETHOD1(>(x3, -1), 1018_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0)
- (x3[6] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)), ≥)∧[(-1)bni_50] = 0∧[(-1)bni_50 + (-1)Bound*bni_50] + [(2)bni_50]x3[6] ≥ 0∧0 = 0∧[(-1)bso_51] ≥ 0)
COND_1163_1_MAIN_INVOKEMETHOD1(TRUE, 1018_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, 1)
- ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)), ≥)∧[bni_52] = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)
1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3, -1), >(x1, 0)), 1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1)
- (x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])), ≥)∧[(-1)bni_54] = 0∧[(-1)bni_54 + (-1)Bound*bni_54] + [(2)bni_54]x3[8] ≥ 0∧0 = 0∧[(-1)bso_55] ≥ 0)
COND_1163_1_MAIN_INVOKEMETHOD2(TRUE, 1004_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1))
- ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1))), ≥)∧[bni_56] = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)
1163_1_MAIN_INVOKEMETHOD(3772_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3, 0), >(x1, -1)), 3772_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3)
- (x3[10] ≥ 0∧x1[10] ≥ 0 ⇒ (U^Increasing(COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])), ≥)∧0 = 0∧[(-1)bni_58] = 0∧[(-1)bni_58 + (-1)Bound*bni_58] + [(2)bni_58]x1[10] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_59] ≥ 0)
COND_1163_1_MAIN_INVOKEMETHOD4(TRUE, 3772_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x1)), x2, +(x3, 1))
- ((U^Increasing(1056_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], +(x3[11], 1))), ≥)∧[bni_60] = 0∧0 = 0∧0 = 0∧0 = 0∧0 = 0∧[(-1)bso_61] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(1163_0_parts_Load(x₁, x₂)) = [-1] + x₂ + [-1]x₁
POL(997_0_parts_GT(x₁, x₂)) = [-1] + [-1]x₁ + [-1]x₂
POL(Cond_997_0_parts_GT(x₁, x₂, x₃)) = [-1]x₃ + x₂
POL(<=(x₁, x₂)) = [-1]
POL(0) = 0
POL(1004_0_parts_Return(x₁, x₂)) = [-1] + [-1]x₁ + x₂
POL(Cond_997_0_parts_GT1(x₁, x₂, x₃)) = [-1]
POL(>(x₁, x₂)) = [-1]
POL(1018_0_parts_Return(x₁)) = x₁
POL(Cond_997_0_parts_GT2(x₁, x₂, x₃)) = [2] + [-1]x₃ + x₂
POL(&&(x₁, x₂)) = [-1]
POL(1055_1_parts_InvokeMethod(x₁, x₂, x₃)) = [-1] + [-1]x₁ + [-1]x₃ + x₂
POL(Cond_997_0_parts_GT3(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₃ + x₂
POL(1063_1_parts_InvokeMethod(x₁, x₂, x₃)) = [1] + [-1]x₁ + [-1]x₂ + x₃
POL(3772_0_parts_Return(x₁)) = x₁
POL(Cond_1063_1_parts_InvokeMethod(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₄ + [-1]x₃ + [-1]x₂
POL(1786_1_parts_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₁ + [-1]x₂
POL(Cond_1063_1_parts_InvokeMethod2(x₁, x₂, x₃, x₄, x₅)) = [1] + x₄ + [-1]x₃ + [-1]x₂
POL(+(x₁, x₂)) = x₁ + x₂
POL(1056_0_MAIN_GT(x₁, x₂, x₃)) = [-1] + [-1]x₂ + [2]x₁
POL(java.lang.Object(x₁)) = x₁
POL(ARRAY(x₁)) = x₁
POL(COND_1056_0_MAIN_GT(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₃ + [2]x₂
POL(>=(x₁, x₂)) = [-1]
POL(1) = [1]
POL(-1) = [-1]
POL(COND_1056_0_MAIN_GT1(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₃ + [2]x₂
POL(1163_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₃ + [2]x₂
POL(COND_1163_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₄ + [2]x₃
POL(COND_1163_1_MAIN_INVOKEMETHOD1(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₄ + [2]x₃
POL(COND_1163_1_MAIN_INVOKEMETHOD2(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₄ + [2]x₃
POL(COND_1163_1_MAIN_INVOKEMETHOD4(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₄ + [2]x₃

The following pairs are in P_>:

COND_1056_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0[1])), x1[1], x2[1]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0)

The following pairs are in P_bound:

1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0]) → COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])

The following pairs are in P_≥:

1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0]) → COND_1056_0_MAIN_GT(&&(&&(>(x2[0], x0[0]), >=(x0[0], +(x1[0], 1))), >(x0[0], -1)), java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])
1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2]) → COND_1056_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])
COND_1056_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3]) → 1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])
1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4]) → COND_1163_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])
COND_1163_1_MAIN_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1))
1163_1_MAIN_INVOKEMETHOD(1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0) → COND_1163_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)
COND_1163_1_MAIN_INVOKEMETHOD1(TRUE, 1018_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)
1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8]) → COND_1163_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])
COND_1163_1_MAIN_INVOKEMETHOD2(TRUE, 1004_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1))
1163_1_MAIN_INVOKEMETHOD(3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10]) → COND_1163_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])
COND_1163_1_MAIN_INVOKEMETHOD4(TRUE, 3772_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], +(x3[11], 1))

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

1063_1_parts_InvokeMethod(1004_0_parts_Return(x0, x1), x3, x1)¹ → Cond_1063_1_parts_InvokeMethod(>(x1, 0), 1004_0_parts_Return(x0, x1), x3, x1, x4)¹
1063_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1, x2)¹ ↔ Cond_1063_1_parts_InvokeMethod2(>(x2, 0), 3772_0_parts_Return(x0), x1, x2, x3)¹

(28) Complex Obligation (AND)

(29) 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

The ITRS R consists of the following rules:
1163_0_parts_Load(x0, x1) → 997_0_parts_GT(x1, x0)
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT(x0 <= 0, x1, x0)
Cond_997_0_parts_GT(TRUE, x1, x0) → 1004_0_parts_Return(x0, x1)
997_0_parts_GT(0, x0) → Cond_997_0_parts_GT1(x0 > 0, 0, x0)
Cond_997_0_parts_GT1(TRUE, 0, x0) → 1018_0_parts_Return(x0)
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT2(x1 > x0 && x1 > 0 && x0 > 0, x1, x0)
Cond_997_0_parts_GT2(TRUE, x1, x0) → 1055_1_parts_InvokeMethod(997_0_parts_GT(x0, x0), x1, x0)
997_0_parts_GT(x1, x0) → Cond_997_0_parts_GT3(x1 > 0 && x1 <= x0 && x0 > 0, x1, x0, x2)
Cond_997_0_parts_GT3(TRUE, x1, x0, x2) → 1063_1_parts_InvokeMethod(997_0_parts_GT(x1, x2), x0, x1)
1055_1_parts_InvokeMethod(1004_0_parts_Return(x0, x0), x2, x0) → 1004_0_parts_Return(x0, x2)
1055_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2, x1) → 1004_0_parts_Return(x1, x2)
1063_1_parts_InvokeMethod(1004_0_parts_Return(x0, x1), x3, x1) → Cond_1063_1_parts_InvokeMethod(x1 > 0, 1004_0_parts_Return(x0, x1), x3, x1, x4)
Cond_1063_1_parts_InvokeMethod(TRUE, 1004_0_parts_Return(x0, x1), x3, x1, x4) → 1786_1_parts_InvokeMethod(997_0_parts_GT(x4, x3), x3)
1063_1_parts_InvokeMethod(3772_0_parts_Return(x0), x1, x2) → Cond_1063_1_parts_InvokeMethod2(x2 > 0, 3772_0_parts_Return(x0), x1, x2, x3)
Cond_1063_1_parts_InvokeMethod2(TRUE, 3772_0_parts_Return(x0), x1, x2, x3) → 1786_1_parts_InvokeMethod(997_0_parts_GT(x3, x1), x1)
1786_1_parts_InvokeMethod(1004_0_parts_Return(x0, x1), x0) → 3772_0_parts_Return(x3 + x2)
1786_1_parts_InvokeMethod(1018_0_parts_Return(x0), x0) → 3772_0_parts_Return(arith[1])
1786_1_parts_InvokeMethod(3772_0_parts_Return(x0), x2) → 3772_0_parts_Return(x1 + x0)

The integer pair graph contains the following rules and edges:
(0): 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0]) → COND_1056_0_MAIN_GT(x2[0] > x0[0] && x0[0] >= x1[0] + 1 && x0[0] > -1, java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])
(2): 1056_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2]) → COND_1056_0_MAIN_GT1(x2[2] <= x0[2], java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])
(3): COND_1056_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3]) → 1163_1_MAIN_INVOKEMETHOD(1163_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])
(4): 1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4]) → COND_1163_1_MAIN_INVOKEMETHOD(x3[4] > -1 && x1[4] > -1, 1004_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])
(5): COND_1163_1_MAIN_INVOKEMETHOD(TRUE, 1004_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], x1[5] + 1)
(6): 1163_1_MAIN_INVOKEMETHOD(1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0) → COND_1163_1_MAIN_INVOKEMETHOD1(x3[6] > -1, 1018_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)
(7): COND_1163_1_MAIN_INVOKEMETHOD1(TRUE, 1018_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)
(8): 1163_1_MAIN_INVOKEMETHOD(1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8]) → COND_1163_1_MAIN_INVOKEMETHOD2(x3[8] > -1 && x1[8] > 0, 1004_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])
(9): COND_1163_1_MAIN_INVOKEMETHOD2(TRUE, 1004_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], x1[9] + 1)
(10): 1163_1_MAIN_INVOKEMETHOD(3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10]) → COND_1163_1_MAIN_INVOKEMETHOD4(x3[10] > 0 && x1[10] > -1, 3772_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])
(11): COND_1163_1_MAIN_INVOKEMETHOD4(TRUE, 3772_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11]) → 1056_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], x3[11] + 1)