Termination proof of /tmp/tmpNNjYkS/Parts.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBCToGraph (⇒, 440 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToSCCProof (⇒, 0 ms)

↳4 AND

    ↳5 JBCTerminationSCC

        ↳6 SCCToIDPv1Proof (⇒, 470 ms)

        ↳7 IDP

        ↳8 IDPNonInfProof (⇒, 930 ms)

        ↳9 IDP

        ↳10 IDPNonInfProof (⇒, 540 ms)

        ↳11 IDP

        ↳12 IDPNonInfProof (⇒, 1430 ms)

        ↳13 IDP

        ↳14 IDPNonInfProof (⇒, 3420 ms)

        ↳15 AND

            ↳16 IDP

                ↳17 IDependencyGraphProof (⇔, 0 ms)

                ↳18 TRUE

            ↳19 IDP

                ↳20 IDependencyGraphProof (⇔, 0 ms)

                ↳21 TRUE

    ↳22 JBCTerminationSCC

        ↳23 SCCToIDPv1Proof (⇒, 1210 ms)

        ↳24 IDP

        ↳25 IDPNonInfProof (⇒, 1440 ms)

        ↳26 AND

            ↳27 IDP

                ↳28 IDependencyGraphProof (⇔, 0 ms)

                ↳29 IDP

                ↳30 IDPNonInfProof (⇒, 830 ms)

                ↳31 AND

                    ↳32 IDP

                        ↳33 IDependencyGraphProof (⇔, 0 ms)

                        ↳34 TRUE

                    ↳35 IDP

                        ↳36 IDependencyGraphProof (⇔, 0 ms)

                        ↳37 TRUE

            ↳38 IDP

                ↳39 IDependencyGraphProof (⇔, 0 ms)

                ↳40 IDP

                ↳41 IDPNonInfProof (⇒, 730 ms)

                ↳42 IDP

                ↳43 IDependencyGraphProof (⇔, 0 ms)

                ↳44 IDP

                ↳45 IDPNonInfProof (⇒, 400 ms)

                ↳46 AND

                    ↳47 IDP

                        ↳48 IDependencyGraphProof (⇔, 0 ms)

                        ↳49 TRUE

                    ↳50 IDP

                        ↳51 IDependencyGraphProof (⇔, 0 ms)

                        ↳52 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:
674_0_parts_GT(EOS(STATIC_674), i74, i70, i74) → 678_0_parts_GT(EOS(STATIC_678), i74, i70, i74)
678_0_parts_GT(EOS(STATIC_678), i74, i70, i74) → 682_0_parts_Load(EOS(STATIC_682), i74, i70) | >(i74, 0)
682_0_parts_Load(EOS(STATIC_682), i74, i70) → 687_0_parts_GT(EOS(STATIC_687), i74, i70, i70)
687_0_parts_GT(EOS(STATIC_687), i74, i76, i76) → 693_0_parts_GT(EOS(STATIC_693), i74, i76, i76)
693_0_parts_GT(EOS(STATIC_693), i74, i76, i76) → 703_0_parts_Load(EOS(STATIC_703), i74, i76) | >(i76, 0)
703_0_parts_Load(EOS(STATIC_703), i74, i76) → 708_0_parts_Load(EOS(STATIC_708), i74, i76, i76)
708_0_parts_Load(EOS(STATIC_708), i74, i76, i76) → 715_0_parts_LE(EOS(STATIC_715), i74, i76, i76, i74)
715_0_parts_LE(EOS(STATIC_715), i74, i76, i76, i74) → 725_0_parts_LE(EOS(STATIC_725), i74, i76, i76, i74)
715_0_parts_LE(EOS(STATIC_715), i74, i76, i76, i74) → 726_0_parts_LE(EOS(STATIC_726), i74, i76, i76, i74)
725_0_parts_LE(EOS(STATIC_725), i74, i76, i76, i74) → 731_0_parts_Load(EOS(STATIC_731), i74, i76) | <=(i76, i74)
731_0_parts_Load(EOS(STATIC_731), i74, i76) → 747_0_parts_Load(EOS(STATIC_747), i74, i76, i74)
747_0_parts_Load(EOS(STATIC_747), i74, i76, i74) → 753_0_parts_IntArithmetic(EOS(STATIC_753), i74, i76, i74, i76)
753_0_parts_IntArithmetic(EOS(STATIC_753), i74, i76, i74, i76) → 758_0_parts_Load(EOS(STATIC_758), i74, i76, -(i74, i76)) | &&(>(i74, 0), >(i76, 0))
758_0_parts_Load(EOS(STATIC_758), i74, i76, i86) → 763_0_parts_InvokeMethod(EOS(STATIC_763), i74, i76, i86, i76)
763_0_parts_InvokeMethod(EOS(STATIC_763), i74, i76, i86, i76) → 769_1_parts_InvokeMethod(769_0_parts_Load(EOS(STATIC_769), i86, i76), i74, i76, i86, i76)
769_0_parts_Load(EOS(STATIC_769), i86, i76) → 775_0_parts_Load(EOS(STATIC_775), i86, i76)
769_1_parts_InvokeMethod(684_0_parts_Return(EOS(STATIC_684), i96, i97, matching1), i74, i97, i96, i97) → 799_0_parts_Return(EOS(STATIC_799), i74, i97, i96, i97, i96, i97, 1) | =(matching1, 1)
769_1_parts_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), i615, i616, i568), i74, i616, i615, i616) → 1403_0_parts_Return(EOS(STATIC_1403), i74, i616, i615, i616, i615, i616, i568)
769_1_parts_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), i670, i671, i623), i74, i671, i670, i671) → 1440_0_parts_Return(EOS(STATIC_1440), i74, i671, i670, i671, i670, i671, i623)
769_1_parts_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), i727), i74, i735, i734, i735) → 1506_0_parts_Return(EOS(STATIC_1506), i74, i735, i734, i735, i727)
775_0_parts_Load(EOS(STATIC_775), i86, i76) → 671_0_parts_Load(EOS(STATIC_671), i86, i76)
671_0_parts_Load(EOS(STATIC_671), i69, i70) → 674_0_parts_GT(EOS(STATIC_674), i69, i70, i69)
799_0_parts_Return(EOS(STATIC_799), i74, i97, i96, i97, i96, i97, matching1) → 804_0_parts_Load(EOS(STATIC_804), i74, i97, 1) | =(matching1, 1)
804_0_parts_Load(EOS(STATIC_804), i74, i97, matching1) → 885_0_parts_Load(EOS(STATIC_885), i74, i97, 1) | =(matching1, 1)
885_0_parts_Load(EOS(STATIC_885), i74, i118, matching1) → 926_0_parts_Load(EOS(STATIC_926), i74, i118, 1) | =(matching1, 1)
926_0_parts_Load(EOS(STATIC_926), i74, i132, matching1) → 1069_0_parts_Load(EOS(STATIC_1069), i74, i132, 1) | =(matching1, 1)
1069_0_parts_Load(EOS(STATIC_1069), i74, i211, i212) → 1120_0_parts_Load(EOS(STATIC_1120), i74, i211, i212)
1120_0_parts_Load(EOS(STATIC_1120), i74, i282, i284) → 1226_0_parts_Load(EOS(STATIC_1226), i74, i282, i284)
1226_0_parts_Load(EOS(STATIC_1226), i74, i397, i398) → 1268_0_parts_Load(EOS(STATIC_1268), i74, i397, i398)
1268_0_parts_Load(EOS(STATIC_1268), i74, i469, i471) → 1372_0_parts_Load(EOS(STATIC_1372), i74, i469, i471)
1372_0_parts_Load(EOS(STATIC_1372), i74, i577, i578) → 1419_0_parts_Load(EOS(STATIC_1419), i74, i577, i578)
1419_0_parts_Load(EOS(STATIC_1419), i74, i633, i635) → 1424_0_parts_Load(EOS(STATIC_1424), i633, i635, i74)
1424_0_parts_Load(EOS(STATIC_1424), i633, i635, i74) → 1435_0_parts_ConstantStackPush(EOS(STATIC_1435), i635, i74, i633)
1435_0_parts_ConstantStackPush(EOS(STATIC_1435), i635, i74, i633) → 1444_0_parts_IntArithmetic(EOS(STATIC_1444), i635, i74, i633, 1)
1444_0_parts_IntArithmetic(EOS(STATIC_1444), i635, i74, i633, matching1) → 1448_0_parts_InvokeMethod(EOS(STATIC_1448), i635, i74, -(i633, 1)) | &&(>(i633, 0), =(matching1, 1))
1448_0_parts_InvokeMethod(EOS(STATIC_1448), i635, i74, i685) → 1449_1_parts_InvokeMethod(1449_0_parts_Load(EOS(STATIC_1449), i74, i685), i635, i74, i685)
1449_0_parts_Load(EOS(STATIC_1449), i74, i685) → 1450_0_parts_Load(EOS(STATIC_1450), i74, i685)
1450_0_parts_Load(EOS(STATIC_1450), i74, i685) → 671_0_parts_Load(EOS(STATIC_671), i74, i685)
1403_0_parts_Return(EOS(STATIC_1403), i74, i616, i615, i616, i615, i616, i568) → 1404_0_parts_Return(EOS(STATIC_1404), i74, i616, i615, i616, i615, i616, i568)
1404_0_parts_Return(EOS(STATIC_1404), i74, i633, i634, i633, i634, i633, i635) → 1419_0_parts_Load(EOS(STATIC_1419), i74, i633, i635)
1440_0_parts_Return(EOS(STATIC_1440), i74, i671, i670, i671, i670, i671, i623) → 1404_0_parts_Return(EOS(STATIC_1404), i74, i671, i670, i671, i670, i671, i623)
1506_0_parts_Return(EOS(STATIC_1506), i74, i735, i734, i735, i727) → 1357_0_parts_Return(EOS(STATIC_1357), i74, i735, i734, i735, i727)
1357_0_parts_Return(EOS(STATIC_1357), i74, i577, i579, i577, i578) → 1372_0_parts_Load(EOS(STATIC_1372), i74, i577, i578)
726_0_parts_LE(EOS(STATIC_726), i74, i76, i76, i74) → 733_0_parts_Load(EOS(STATIC_733), i74, i76) | >(i76, i74)
733_0_parts_Load(EOS(STATIC_733), i74, i76) → 749_0_parts_Load(EOS(STATIC_749), i74, i76, i74)
749_0_parts_Load(EOS(STATIC_749), i74, i76, i74) → 755_0_parts_InvokeMethod(EOS(STATIC_755), i74, i76, i74, i74)
755_0_parts_InvokeMethod(EOS(STATIC_755), i74, i76, i74, i74) → 760_1_parts_InvokeMethod(760_0_parts_Load(EOS(STATIC_760), i74, i74), i74, i76, i74, i74)
760_0_parts_Load(EOS(STATIC_760), i74, i74) → 765_0_parts_Load(EOS(STATIC_765), i74, i74)
765_0_parts_Load(EOS(STATIC_765), i74, i74) → 671_0_parts_Load(EOS(STATIC_671), i74, i74)
R rules:
674_0_parts_GT(EOS(STATIC_674), i73, i70, i73) → 677_0_parts_GT(EOS(STATIC_677), i73, i70, i73)
677_0_parts_GT(EOS(STATIC_677), i73, i70, i73) → 680_0_parts_ConstantStackPush(EOS(STATIC_680), i73, i70) | <=(i73, 0)
680_0_parts_ConstantStackPush(EOS(STATIC_680), i73, i70) → 684_0_parts_Return(EOS(STATIC_684), i73, i70, 1)
687_0_parts_GT(EOS(STATIC_687), i74, matching1, matching2) → 692_0_parts_GT(EOS(STATIC_692), i74, 0, 0) | &&(=(matching1, 0), =(matching2, 0))
692_0_parts_GT(EOS(STATIC_692), i74, matching1, matching2) → 700_0_parts_ConstantStackPush(EOS(STATIC_700), i74, 0) | &&(&&(<=(0, 0), =(matching1, 0)), =(matching2, 0))
700_0_parts_ConstantStackPush(EOS(STATIC_700), i74, matching1) → 706_0_parts_Return(EOS(STATIC_706), i74, 0, 0) | =(matching1, 0)
760_1_parts_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), i613, i613, i568), i613, i76, i613, i613) → 1397_0_parts_Return(EOS(STATIC_1397), i613, i76, i613, i613, i613, i613, i568)
760_1_parts_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), i668, i668, i623), i668, i76, i668, i668) → 1439_0_parts_Return(EOS(STATIC_1439), i668, i76, i668, i668, i668, i668, i623)
760_1_parts_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), i727), i733, i76, i733, i733) → 1504_0_parts_Return(EOS(STATIC_1504), i733, i76, i733, i733, i727)
876_0_parts_Return(EOS(STATIC_876), i116, i76, i116, i116, matching1) → 1044_0_parts_Return(EOS(STATIC_1044), i116, i76, i116, i116, 1) | =(matching1, 1)
877_0_parts_Return(EOS(STATIC_877), i74, i118, i117, i118, matching1) → 1051_0_parts_Return(EOS(STATIC_1051), i74, i118, i117, i118, 1) | =(matching1, 1)
912_0_parts_Return(EOS(STATIC_912), i129, i76, i129, i129, i129, i129, matching1) → 1096_0_parts_Return(EOS(STATIC_1096), i129, i76, i129, i129, i129, i129, 1) | =(matching1, 1)
913_0_parts_Return(EOS(STATIC_913), i74, i132, i131, i132, i131, i132, matching1) → 1104_0_parts_Return(EOS(STATIC_1104), i74, i132, i131, i132, i131, i132, 1) | =(matching1, 1)
1044_0_parts_Return(EOS(STATIC_1044), i199, i76, i199, i199, i200) → 1207_0_parts_Return(EOS(STATIC_1207), i199, i76, i199, i199, i200)
1051_0_parts_Return(EOS(STATIC_1051), i74, i211, i213, i211, i212) → 1212_0_parts_Return(EOS(STATIC_1212), i74, i211, i213, i211, i212)
1096_0_parts_Return(EOS(STATIC_1096), i271, i76, i271, i271, i271, i271, i272) → 1248_0_parts_Return(EOS(STATIC_1248), i271, i76, i271, i271, i271, i271, i272)
1104_0_parts_Return(EOS(STATIC_1104), i74, i282, i283, i282, i283, i282, i284) → 1254_0_parts_Return(EOS(STATIC_1254), i74, i282, i283, i282, i283, i282, i284)
1207_0_parts_Return(EOS(STATIC_1207), i385, i76, i385, i385, i386) → 1349_0_parts_Return(EOS(STATIC_1349), i385, i76, i385, i385, i386)
1212_0_parts_Return(EOS(STATIC_1212), i74, i397, i399, i397, i398) → 1357_0_parts_Return(EOS(STATIC_1357), i74, i397, i399, i397, i398)
1248_0_parts_Return(EOS(STATIC_1248), i458, i76, i458, i458, i458, i458, i459) → 1398_0_parts_Return(EOS(STATIC_1398), i458, i76, i458, i458, i458, i458, i459)
1254_0_parts_Return(EOS(STATIC_1254), i74, i469, i470, i469, i470, i469, i471) → 1404_0_parts_Return(EOS(STATIC_1404), i74, i469, i470, i469, i470, i469, i471)
1349_0_parts_Return(EOS(STATIC_1349), i567, i76, i567, i567, i568) → 1370_0_parts_Return(EOS(STATIC_1370), i567, i76, i568)
1370_0_parts_Return(EOS(STATIC_1370), i567, i76, i568) → 1416_0_parts_Return(EOS(STATIC_1416), i567, i76, i568)
1397_0_parts_Return(EOS(STATIC_1397), i613, i76, i613, i613, i613, i613, i568) → 1398_0_parts_Return(EOS(STATIC_1398), i613, i76, i613, i613, i613, i613, i568)
1398_0_parts_Return(EOS(STATIC_1398), i622, i76, i622, i622, i622, i622, i623) → 1416_0_parts_Return(EOS(STATIC_1416), i622, i76, i623)
1439_0_parts_Return(EOS(STATIC_1439), i668, i76, i668, i668, i668, i668, i623) → 1398_0_parts_Return(EOS(STATIC_1398), i668, i76, i668, i668, i668, i668, i623)
1449_1_parts_InvokeMethod(706_0_parts_Return(EOS(STATIC_706), i689, matching1, matching2), i635, i689, matching3) → 1460_0_parts_Return(EOS(STATIC_1460), i635, i689, 0, i689, 0, 0) | &&(&&(=(matching1, 0), =(matching2, 0)), =(matching3, 0))
1449_1_parts_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), i690, i691, i568), i635, i690, i691) → 1461_0_parts_Return(EOS(STATIC_1461), i635, i690, i691, i690, i691, i568)
1449_1_parts_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), i692, i693, i623), i635, i692, i693) → 1464_0_parts_Return(EOS(STATIC_1464), i635, i692, i693, i692, i693, i623)
1449_1_parts_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), i727), i635, i739, i740) → 1510_0_parts_Return(EOS(STATIC_1510), i635, i739, i740, i727)
1460_0_parts_Return(EOS(STATIC_1460), i635, i689, matching1, i689, matching2, matching3) → 1465_0_parts_IntArithmetic(EOS(STATIC_1465), i635, 0) | &&(&&(=(matching1, 0), =(matching2, 0)), =(matching3, 0))
1461_0_parts_Return(EOS(STATIC_1461), i635, i690, i691, i690, i691, i568) → 1467_0_parts_IntArithmetic(EOS(STATIC_1467), i635, i568)
1464_0_parts_Return(EOS(STATIC_1464), i635, i692, i693, i692, i693, i623) → 1461_0_parts_Return(EOS(STATIC_1461), i635, i692, i693, i692, i693, i623)
1465_0_parts_IntArithmetic(EOS(STATIC_1465), i635, matching1) → 1467_0_parts_IntArithmetic(EOS(STATIC_1467), i635, 0) | =(matching1, 0)
1467_0_parts_IntArithmetic(EOS(STATIC_1467), i635, i568) → 1490_0_parts_IntArithmetic(EOS(STATIC_1490), i635, i568)
1487_0_parts_Return(EOS(STATIC_1487), i635, i715, i716, i703) → 1490_0_parts_IntArithmetic(EOS(STATIC_1490), i635, i703)
1490_0_parts_IntArithmetic(EOS(STATIC_1490), i635, i703) → 1492_0_parts_Return(EOS(STATIC_1492), +(i635, i703))
1504_0_parts_Return(EOS(STATIC_1504), i733, i76, i733, i733, i727) → 1349_0_parts_Return(EOS(STATIC_1349), i733, i76, i733, i733, i727)
1510_0_parts_Return(EOS(STATIC_1510), i635, i739, i740, i727) → 1487_0_parts_Return(EOS(STATIC_1487), i635, i739, i740, i727)

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

P rules:
674_0_parts_GT(EOS(STATIC_674), x0, x1, x0) → 769_1_parts_InvokeMethod(674_0_parts_GT(EOS(STATIC_674), -(x0, x1), x1, -(x0, x1)), x0, x1, -(x0, x1), x1) | &&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0))
769_1_parts_InvokeMethod(684_0_parts_Return(EOS(STATIC_684), x0, x1, 1), x3, x1, x0, x1) → 1449_1_parts_InvokeMethod(674_0_parts_GT(EOS(STATIC_674), x3, -(x1, 1), x3), 1, x3, -(x1, 1)) | >(x1, 0)
769_1_parts_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), x0, x1, x2), x3, x1, x0, x1) → 1449_1_parts_InvokeMethod(674_0_parts_GT(EOS(STATIC_674), x3, -(x1, 1), x3), x2, x3, -(x1, 1)) | >(x1, 0)
769_1_parts_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), x0, x1, x2), x3, x1, x0, x1) → 1449_1_parts_InvokeMethod(674_0_parts_GT(EOS(STATIC_674), x3, -(x1, 1), x3), x2, x3, -(x1, 1)) | >(x1, 0)
769_1_parts_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), x0), x1, x2, x3, x2) → 1449_1_parts_InvokeMethod(674_0_parts_GT(EOS(STATIC_674), x1, -(x2, 1), x1), x0, x1, -(x2, 1)) | >(x2, 0)
674_0_parts_GT(EOS(STATIC_674), x0, x1, x0) → 760_1_parts_InvokeMethod(674_0_parts_GT(EOS(STATIC_674), x0, x0, x0), x0, x1, x0, x0) | &&(&&(>(x1, x0), >(x1, 0)), >(x0, 0))
R rules:
674_0_parts_GT(EOS(STATIC_674), x0, x1, x0) → 684_0_parts_Return(EOS(STATIC_684), x0, x1, 1) | <=(x0, 0)
760_1_parts_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), x0, x0, x1), x0, x2, x0, x0) → 1416_0_parts_Return(EOS(STATIC_1416), x0, x2, x1)
760_1_parts_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), x0, x0, x1), x0, x2, x0, x0) → 1416_0_parts_Return(EOS(STATIC_1416), x0, x2, x1)
760_1_parts_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), x0), x1, x2, x1, x1) → 1416_0_parts_Return(EOS(STATIC_1416), x1, x2, x0)
1449_1_parts_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), x0, x1, x2), x3, x0, x1) → 1492_0_parts_Return(EOS(STATIC_1492), +(x3, x2))
1449_1_parts_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), x0, x1, x2), x3, x0, x1) → 1492_0_parts_Return(EOS(STATIC_1492), +(x3, x2))
1449_1_parts_InvokeMethod(706_0_parts_Return(EOS(STATIC_706), x0, 0, 0), arith[1], x0, 0) → 1492_0_parts_Return(EOS(STATIC_1492), arith[1])
1449_1_parts_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), x0), x1, x2, x3) → 1492_0_parts_Return(EOS(STATIC_1492), +(x1, x0))

Filtered ground terms:

674_0_parts_GT(x1, x2, x3, x4) → 674_0_parts_GT(x2, x3, x4)
Cond_674_0_parts_GT1(x1, x2, x3, x4, x5) → Cond_674_0_parts_GT1(x1, x3, x4, x5)
1492_0_parts_Return(x1, x2) → 1492_0_parts_Return(x2)
1416_0_parts_Return(x1, x2, x3, x4) → 1416_0_parts_Return(x2, x3, x4)
1370_0_parts_Return(x1, x2, x3, x4) → 1370_0_parts_Return(x2, x3, x4)
684_0_parts_Return(x1, x2, x3, x4) → 684_0_parts_Return(x2, x3)
Cond_674_0_parts_GT(x1, x2, x3, x4, x5) → Cond_674_0_parts_GT(x1, x3, x4, x5)
706_0_parts_Return(x1, x2, x3, x4) → 706_0_parts_Return(x2)

Filtered duplicate args:

674_0_parts_GT(x1, x2, x3) → 674_0_parts_GT(x2, x3)
Cond_674_0_parts_GT(x1, x2, x3, x4) → Cond_674_0_parts_GT(x1, x3, x4)
769_1_parts_InvokeMethod(x1, x2, x3, x4, x5) → 769_1_parts_InvokeMethod(x1, x2, x4, x5)
Cond_769_1_parts_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_769_1_parts_InvokeMethod(x1, x2, x3)
Cond_769_1_parts_InvokeMethod1(x1, x2, x3, x4, x5, x6) → Cond_769_1_parts_InvokeMethod1(x1, x2, x3)
Cond_769_1_parts_InvokeMethod2(x1, x2, x3, x4, x5, x6) → Cond_769_1_parts_InvokeMethod2(x1, x2, x3)
Cond_769_1_parts_InvokeMethod3(x1, x2, x3, x4, x5, x6) → Cond_769_1_parts_InvokeMethod3(x1, x2, x3, x5, x6)
Cond_674_0_parts_GT1(x1, x2, x3, x4) → Cond_674_0_parts_GT1(x1, x3, x4)
760_1_parts_InvokeMethod(x1, x2, x3, x4, x5) → 760_1_parts_InvokeMethod(x1, x3, x5)

Filtered unneeded arguments:

1449_1_parts_InvokeMethod(x1, x2, x3, x4) → 1449_1_parts_InvokeMethod(x1, x3, x4)
Cond_769_1_parts_InvokeMethod3(x1, x2, x3, x4, x5) → Cond_769_1_parts_InvokeMethod3(x1, x3, x5)
1370_0_parts_Return(x1, x2, x3) → 1370_0_parts_Return(x1, x2)
1416_0_parts_Return(x1, x2, x3) → 1416_0_parts_Return(x1, x2)
684_0_parts_Return(x1, x2) → 684_0_parts_Return(x2)

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

P rules:
674_0_parts_GT(x1, x0) → 769_1_parts_InvokeMethod(674_0_parts_GT(x1, -(x0, x1)), x0, -(x0, x1), x1) | &&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0))
769_1_parts_InvokeMethod(684_0_parts_Return(x1), x3, x0, x1) → 1449_1_parts_InvokeMethod(674_0_parts_GT(-(x1, 1), x3), x3, -(x1, 1)) | >(x1, 0)
769_1_parts_InvokeMethod(1370_0_parts_Return(x0, x1), x3, x0, x1) → 1449_1_parts_InvokeMethod(674_0_parts_GT(-(x1, 1), x3), x3, -(x1, 1)) | >(x1, 0)
769_1_parts_InvokeMethod(1416_0_parts_Return(x0, x1), x3, x0, x1) → 1449_1_parts_InvokeMethod(674_0_parts_GT(-(x1, 1), x3), x3, -(x1, 1)) | >(x1, 0)
769_1_parts_InvokeMethod(1492_0_parts_Return(x0), x1, x3, x2) → 1449_1_parts_InvokeMethod(674_0_parts_GT(-(x2, 1), x1), x1, -(x2, 1)) | >(x2, 0)
674_0_parts_GT(x1, x0) → 760_1_parts_InvokeMethod(674_0_parts_GT(x0, x0), x1, x0) | &&(&&(>(x1, x0), >(x1, 0)), >(x0, 0))
R rules:
674_0_parts_GT(x1, x0) → 684_0_parts_Return(x1) | <=(x0, 0)
760_1_parts_InvokeMethod(1370_0_parts_Return(x0, x0), x2, x0) → 1416_0_parts_Return(x0, x2)
760_1_parts_InvokeMethod(1416_0_parts_Return(x0, x0), x2, x0) → 1416_0_parts_Return(x0, x2)
760_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x1) → 1416_0_parts_Return(x1, x2)
1449_1_parts_InvokeMethod(1370_0_parts_Return(x0, x1), x0, x1) → 1492_0_parts_Return(+(x3, x2))
1449_1_parts_InvokeMethod(1416_0_parts_Return(x0, x1), x0, x1) → 1492_0_parts_Return(+(x3, x2))
1449_1_parts_InvokeMethod(706_0_parts_Return(x0), x0, 0) → 1492_0_parts_Return(arith[1])
1449_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x3) → 1492_0_parts_Return(+(x1, x0))

Performed bisimulation on rules. Used the following equivalence classes: {[1370_0_parts_Return_2, 1416_0_parts_Return_2]=1370_0_parts_Return_2, [684_0_parts_Return_1, 706_0_parts_Return_1]=684_0_parts_Return_1, [Cond_769_1_parts_InvokeMethod1_5, Cond_769_1_parts_InvokeMethod2_5]=Cond_769_1_parts_InvokeMethod1_5}

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

P rules:
674_0_PARTS_GT(x1, x0) → COND_674_0_PARTS_GT(&&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0)), x1, x0)
COND_674_0_PARTS_GT(TRUE, x1, x0) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1, -(x0, x1)), x0, -(x0, x1), x1)
COND_674_0_PARTS_GT(TRUE, x1, x0) → 674_0_PARTS_GT(x1, -(x0, x1))
769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1), x3, x0, x1) → COND_769_1_PARTS_INVOKEMETHOD(>(x1, 0), 684_0_parts_Return(x1), x3, x0, x1)
COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1), x3, x0, x1) → 674_0_PARTS_GT(-(x1, 1), x3)
769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0, x1), x3, x0, x1) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1, 0), 1370_0_parts_Return(x0, x1), x3, x0, x1)
COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0, x1), x3, x0, x1) → 674_0_PARTS_GT(-(x1, 1), x3)
769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0), x1, x3, x2) → COND_769_1_PARTS_INVOKEMETHOD3(>(x2, 0), 1492_0_parts_Return(x0), x1, x3, x2)
COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0), x1, x3, x2) → 674_0_PARTS_GT(-(x2, 1), x1)
674_0_PARTS_GT(x1, x0) → COND_674_0_PARTS_GT1(&&(&&(>(x1, x0), >(x1, 0)), >(x0, 0)), x1, x0)
COND_674_0_PARTS_GT1(TRUE, x1, x0) → 674_0_PARTS_GT(x0, x0)
R rules:
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT(<=(x0, 0), x1, x0)
Cond_674_0_parts_GT(TRUE, x1, x0) → 684_0_parts_Return(x1)
760_1_parts_InvokeMethod(1370_0_parts_Return(x0, x0), x2, x0) → 1370_0_parts_Return(x0, x2)
760_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x1) → 1370_0_parts_Return(x1, x2)
1449_1_parts_InvokeMethod(1370_0_parts_Return(x0, x1), x0, x1) → 1492_0_parts_Return(+(x3, x2))
1449_1_parts_InvokeMethod(684_0_parts_Return(x0), x0, 0) → 1492_0_parts_Return(arith[1])
1449_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x3) → 1492_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:
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT(x0 <= 0, x1, x0)
Cond_674_0_parts_GT(TRUE, x1, x0) → 684_0_parts_Return(x1)
760_1_parts_InvokeMethod(1370_0_parts_Return(x0, x0), x2, x0) → 1370_0_parts_Return(x0, x2)
760_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x1) → 1370_0_parts_Return(x1, x2)
1449_1_parts_InvokeMethod(1370_0_parts_Return(x0, x1), x0, x1) → 1492_0_parts_Return(x3 + x2)
1449_1_parts_InvokeMethod(684_0_parts_Return(x0), x0, 0) → 1492_0_parts_Return(arith[1])
1449_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x3) → 1492_0_parts_Return(x1 + x0)

The integer pair graph contains the following rules and edges:
(0): 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0, x1[0], x0[0])
(1): COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], x0[1] - x1[1]), x0[1], x0[1] - x1[1], x1[1])
(2): COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], x0[2] - x1[2])
(3): 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(x1[3] > 0, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
(4): COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(x1[4] - 1, x3[4])
(5): 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(x1[5] > 0, 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])
(6): COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(x1[6] - 1, x3[6])
(7): 769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_769_1_PARTS_INVOKEMETHOD3(x2[7] > 0, 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])
(8): COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 674_0_PARTS_GT(x2[8] - 1, x1[8])
(9): 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(x1[9] > x0[9] && x1[9] > 0 && x0[9] > 0, x1[9], x0[9])
(10): COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_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 (674_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 684_0_parts_Return(x1[3])∧x0[1] →^* x3[3]∧x0[1] - x1[1] →^* x0[3]∧x1[1] →^* x1[3])

(1) -> (5), if (674_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 1370_0_parts_Return(x0[5], x1[5])∧x0[1] →^* x3[5]∧x0[1] - x1[1] →^* x0[5]∧x1[1] →^* x1[5])

(1) -> (7), if (674_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 1492_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 ∧684_0_parts_Return(x1[3]) →^* 684_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 ∧1370_0_parts_Return(x0[5], x1[5]) →^* 1370_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 ∧1492_0_parts_Return(x0[7]) →^* 1492_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:
674_0_parts_GT(x0, x1)
Cond_674_0_parts_GT(TRUE, x0, x1)
760_1_parts_InvokeMethod(1370_0_parts_Return(x0, x0), x1, x0)
760_1_parts_InvokeMethod(1492_0_parts_Return(x0), x1, x2)
1449_1_parts_InvokeMethod(1370_0_parts_Return(x0, x1), x0, x1)
1449_1_parts_InvokeMethod(684_0_parts_Return(x0), x0, 0)
1449_1_parts_InvokeMethod(1492_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@23c6e30f 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 674_0_PARTS_GT(x1, x0) → COND_674_0_PARTS_GT(&&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0)), x1, x0) the following chains were created:

We consider the chain 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_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] ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_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 ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_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_674_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_674_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_674_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_674_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 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_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] ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_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 ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_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_674_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_674_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_674_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_674_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_674_0_PARTS_GT(TRUE, x1, x0) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1, -(x0, x1)), x0, -(x0, x1), x1) the following chains were created:

We consider the chain 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]), 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_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]∧674_0_parts_GT(x1[1], -(x0[1], x1[1]))=684_0_parts_Return(x1[3])∧x0[1]=x3[3]∧-(x0[1], x1[1])=x0[3]∧x1[1]=x1[3] ⇒ COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_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_674_0_parts_GT(<=(-(x0[0], x1[0]), 0), x1[0], -(x0[0], x1[0]))=684_0_parts_Return(x1[0]) ⇒ COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[0], -(x0[0], x1[0])), x0[0], -(x0[0], x1[0]), x1[0])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]), 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_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]∧674_0_parts_GT(x1[1], -(x0[1], x1[1]))=1370_0_parts_Return(x0[5], x1[5])∧x0[1]=x3[5]∧-(x0[1], x1[1])=x0[5]∧x1[1]=x1[5] ⇒ COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_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_674_0_parts_GT(<=(-(x0[0], x1[0]), 0), x1[0], -(x0[0], x1[0]))=1370_0_parts_Return(-(x0[0], x1[0]), x1[0]) ⇒ COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[0], -(x0[0], x1[0])), x0[0], -(x0[0], x1[0]), x1[0])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]), 769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_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]∧674_0_parts_GT(x1[1], -(x0[1], x1[1]))=1492_0_parts_Return(x0[7])∧x0[1]=x1[7]∧-(x0[1], x1[1])=x3[7]∧x1[1]=x2[7] ⇒ COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_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_674_0_parts_GT(<=(-(x0[0], x1[0]), 0), x1[0], -(x0[0], x1[0]))=1492_0_parts_Return(x0[7]) ⇒ COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[0], -(x0[0], x1[0])), x0[0], -(x0[0], x1[0]), x1[0])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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_674_0_PARTS_GT(TRUE, x1, x0) → 674_0_PARTS_GT(x1, -(x0, x1)) the following chains were created:

We consider the chain 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2])), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_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_674_0_PARTS_GT(TRUE, x1[2], x0[2])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[2], x0[2])≥674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))∧(U^Increasing(674_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_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥674_0_PARTS_GT(x1[0], -(x0[0], x1[0]))∧(U^Increasing(674_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(674_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(674_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(674_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(674_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 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2])), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_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_674_0_PARTS_GT(TRUE, x1[2], x0[2])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[2], x0[2])≥674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))∧(U^Increasing(674_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_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥674_0_PARTS_GT(x1[0], -(x0[0], x1[0]))∧(U^Increasing(674_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(674_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(674_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(674_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(674_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 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1), x3, x0, x1) → COND_769_1_PARTS_INVOKEMETHOD(>(x1, 0), 684_0_parts_Return(x1), x3, x0, x1) the following chains were created:

We consider the chain 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]) which results in the following constraint:
(43)    (>(x1[3], 0)=TRUE∧684_0_parts_Return(x1[3])=684_0_parts_Return(x1[4])∧x3[3]=x3[4]∧x0[3]=x0[4]∧x1[3]=x1[4] ⇒ 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_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 ⇒ 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_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_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_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] ≥ 0)

We simplified constraint (45) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(46)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_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] ≥ 0)

We simplified constraint (46) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(47)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_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] ≥ 0)

We simplified constraint (47) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(48)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_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∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_64] ≥ 0)

For Pair COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1), x3, x0, x1) → 674_0_PARTS_GT(-(x1, 1), x3) the following chains were created:

We consider the chain 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_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∧684_0_parts_Return(x1[3])=684_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_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥674_0_PARTS_GT(-(x1[4], 1), x3[4])∧(U^Increasing(674_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_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥674_0_PARTS_GT(-(x1[3], 1), x3[3])∧(U^Increasing(674_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(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [bni_65]x0[3] ≥ 0∧[(-1)bso_66] + x0[3] ≥ 0)

We simplified constraint (51) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(52)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [bni_65]x0[3] ≥ 0∧[(-1)bso_66] + x0[3] ≥ 0)

We simplified constraint (52) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(53)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [bni_65]x0[3] ≥ 0∧[(-1)bso_66] + x0[3] ≥ 0)

We simplified constraint (53) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(54)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 ≥ 0∧[bni_65] ≥ 0∧0 ≥ 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_66] ≥ 0)
We consider the chain 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_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∧684_0_parts_Return(x1[3])=684_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_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥674_0_PARTS_GT(-(x1[4], 1), x3[4])∧(U^Increasing(674_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_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥674_0_PARTS_GT(-(x1[3], 1), x3[3])∧(U^Increasing(674_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(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [bni_65]x0[3] ≥ 0∧[(-1)bso_66] + x0[3] ≥ 0)

We simplified constraint (57) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(58)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [bni_65]x0[3] ≥ 0∧[(-1)bso_66] + x0[3] ≥ 0)

We simplified constraint (58) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(59)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] + [bni_65]x0[3] ≥ 0∧[(-1)bso_66] + x0[3] ≥ 0)

We simplified constraint (59) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(60)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 ≥ 0∧[bni_65] ≥ 0∧0 ≥ 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_66] ≥ 0)

For Pair 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0, x1), x3, x0, x1) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1, 0), 1370_0_parts_Return(x0, x1), x3, x0, x1) the following chains were created:

We consider the chain 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]), COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(-(x1[6], 1), x3[6]) which results in the following constraint:
(61)    (>(x1[5], 0)=TRUE∧1370_0_parts_Return(x0[5], x1[5])=1370_0_parts_Return(x0[6], x1[6])∧x3[5]=x3[6]∧x0[5]=x0[6]∧x1[5]=x1[6] ⇒ 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_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 ⇒ 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_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_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧[(-1)bni_67 + (-1)Bound*bni_67] + [bni_67]x0[5] ≥ 0∧[(-1)bso_68] ≥ 0)

We simplified constraint (63) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(64)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧[(-1)bni_67 + (-1)Bound*bni_67] + [bni_67]x0[5] ≥ 0∧[(-1)bso_68] ≥ 0)

We simplified constraint (64) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(65)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧[(-1)bni_67 + (-1)Bound*bni_67] + [bni_67]x0[5] ≥ 0∧[(-1)bso_68] ≥ 0)

We simplified constraint (65) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(66)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧0 ≥ 0∧[bni_67] ≥ 0∧0 ≥ 0∧[(-1)bni_67 + (-1)Bound*bni_67] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_68] ≥ 0)

For Pair COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0, x1), x3, x0, x1) → 674_0_PARTS_GT(-(x1, 1), x3) the following chains were created:

We consider the chain 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]), COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(-(x1[6], 1), x3[6]), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_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∧1370_0_parts_Return(x0[5], x1[5])=1370_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_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6])≥674_0_PARTS_GT(-(x1[6], 1), x3[6])∧(U^Increasing(674_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_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥674_0_PARTS_GT(-(x1[5], 1), x3[5])∧(U^Increasing(674_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(674_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(674_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(674_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(674_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 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]), COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(-(x1[6], 1), x3[6]), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_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∧1370_0_parts_Return(x0[5], x1[5])=1370_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_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6])≥674_0_PARTS_GT(-(x1[6], 1), x3[6])∧(U^Increasing(674_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_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥674_0_PARTS_GT(-(x1[5], 1), x3[5])∧(U^Increasing(674_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(674_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(674_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(674_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(674_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 769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0), x1, x3, x2) → COND_769_1_PARTS_INVOKEMETHOD3(>(x2, 0), 1492_0_parts_Return(x0), x1, x3, x2) the following chains were created:

We consider the chain 769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]), COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 674_0_PARTS_GT(-(x2[8], 1), x1[8]) which results in the following constraint:
(79)    (>(x2[7], 0)=TRUE∧1492_0_parts_Return(x0[7])=1492_0_parts_Return(x0[8])∧x1[7]=x1[8]∧x3[7]=x3[8]∧x2[7]=x2[8] ⇒ 769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_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 ⇒ 769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_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_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])), ≥)∧[bni_71 + (-1)Bound*bni_71] + [bni_71]x3[7] ≥ 0∧[1 + (-1)bso_72] ≥ 0)

We simplified constraint (81) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(82)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])), ≥)∧[bni_71 + (-1)Bound*bni_71] + [bni_71]x3[7] ≥ 0∧[1 + (-1)bso_72] ≥ 0)

We simplified constraint (82) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(83)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])), ≥)∧[bni_71 + (-1)Bound*bni_71] + [bni_71]x3[7] ≥ 0∧[1 + (-1)bso_72] ≥ 0)

We simplified constraint (83) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(84)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])), ≥)∧0 ≥ 0∧[bni_71] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[bni_71 + (-1)Bound*bni_71] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_72] ≥ 0)

For Pair COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0), x1, x3, x2) → 674_0_PARTS_GT(-(x2, 1), x1) the following chains were created:

We consider the chain 769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]), COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 674_0_PARTS_GT(-(x2[8], 1), x1[8]), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_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∧1492_0_parts_Return(x0[7])=1492_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_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[8]), x1[8], x3[8], x2[8])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[8]), x1[8], x3[8], x2[8])≥674_0_PARTS_GT(-(x2[8], 1), x1[8])∧(U^Increasing(674_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_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥674_0_PARTS_GT(-(x2[7], 1), x1[7])∧(U^Increasing(674_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(674_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[(-1)Bound*bni_73] + [bni_73]x3[7] ≥ 0∧[1 + (-1)bso_74] + x3[7] ≥ 0)

We simplified constraint (87) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(88)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[(-1)Bound*bni_73] + [bni_73]x3[7] ≥ 0∧[1 + (-1)bso_74] + x3[7] ≥ 0)

We simplified constraint (88) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(89)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[(-1)Bound*bni_73] + [bni_73]x3[7] ≥ 0∧[1 + (-1)bso_74] + x3[7] ≥ 0)

We simplified constraint (89) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(90)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧0 ≥ 0∧[bni_73] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)Bound*bni_73] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_74] ≥ 0)
We consider the chain 769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]), COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 674_0_PARTS_GT(-(x2[8], 1), x1[8]), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_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∧1492_0_parts_Return(x0[7])=1492_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_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[8]), x1[8], x3[8], x2[8])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[8]), x1[8], x3[8], x2[8])≥674_0_PARTS_GT(-(x2[8], 1), x1[8])∧(U^Increasing(674_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_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])≥674_0_PARTS_GT(-(x2[7], 1), x1[7])∧(U^Increasing(674_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(674_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[(-1)Bound*bni_73] + [bni_73]x3[7] ≥ 0∧[1 + (-1)bso_74] + x3[7] ≥ 0)

We simplified constraint (93) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(94)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[(-1)Bound*bni_73] + [bni_73]x3[7] ≥ 0∧[1 + (-1)bso_74] + x3[7] ≥ 0)

We simplified constraint (94) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(95)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧[(-1)Bound*bni_73] + [bni_73]x3[7] ≥ 0∧[1 + (-1)bso_74] + x3[7] ≥ 0)

We simplified constraint (95) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(96)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧0 ≥ 0∧[bni_73] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)Bound*bni_73] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_74] ≥ 0)

For Pair 674_0_PARTS_GT(x1, x0) → COND_674_0_PARTS_GT1(&&(&&(>(x1, x0), >(x1, 0)), >(x0, 0)), x1, x0) the following chains were created:

We consider the chain 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]), COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_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] ⇒ 674_0_PARTS_GT(x1[9], x0[9])≥NonInfC∧674_0_PARTS_GT(x1[9], x0[9])≥COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])∧(U^Increasing(COND_674_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 ⇒ 674_0_PARTS_GT(x1[9], x0[9])≥NonInfC∧674_0_PARTS_GT(x1[9], x0[9])≥COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])∧(U^Increasing(COND_674_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_674_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_674_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_674_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_674_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_674_0_PARTS_GT1(TRUE, x1, x0) → 674_0_PARTS_GT(x0, x0) the following chains were created:

We consider the chain COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_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_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (103) using rule (IV) which results in the following new constraint:
(104)    (COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_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(674_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(674_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(674_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(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_77] = 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_78] ≥ 0)
We consider the chain COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_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_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (109) using rule (IV) which results in the following new constraint:
(110)    (COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_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(674_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(674_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(674_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(674_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.

674_0_PARTS_GT(x1, x0) → COND_674_0_PARTS_GT(&&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0)), x1, x0)
- (0 ≥ 0 ⇒ (U^Increasing(COND_674_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_674_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_674_0_PARTS_GT(TRUE, x1, x0) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1, -(x0, x1)), x0, -(x0, x1), x1)
- (0 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_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_674_0_PARTS_GT(TRUE, x1, x0) → 674_0_PARTS_GT(x1, -(x0, x1))
- (0 ≥ 0 ⇒ (U^Increasing(674_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(674_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)
769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1), x3, x0, x1) → COND_769_1_PARTS_INVOKEMETHOD(>(x1, 0), 684_0_parts_Return(x1), x3, x0, x1)
- (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_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∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_64] ≥ 0)
COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1), x3, x0, x1) → 674_0_PARTS_GT(-(x1, 1), x3)
- (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 ≥ 0∧[bni_65] ≥ 0∧0 ≥ 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_66] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 ≥ 0∧[bni_65] ≥ 0∧0 ≥ 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_66] ≥ 0)
769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0, x1), x3, x0, x1) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1, 0), 1370_0_parts_Return(x0, x1), x3, x0, x1)
- (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧0 ≥ 0∧[bni_67] ≥ 0∧0 ≥ 0∧[(-1)bni_67 + (-1)Bound*bni_67] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_68] ≥ 0)
COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0, x1), x3, x0, x1) → 674_0_PARTS_GT(-(x1, 1), x3)
- (0 ≥ 0 ⇒ (U^Increasing(674_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(674_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)
769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0), x1, x3, x2) → COND_769_1_PARTS_INVOKEMETHOD3(>(x2, 0), 1492_0_parts_Return(x0), x1, x3, x2)
- (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])), ≥)∧0 ≥ 0∧[bni_71] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[bni_71 + (-1)Bound*bni_71] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_72] ≥ 0)
COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0), x1, x3, x2) → 674_0_PARTS_GT(-(x2, 1), x1)
- (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧0 ≥ 0∧[bni_73] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)Bound*bni_73] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_74] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x2[8], 1), x1[8])), ≥)∧0 ≥ 0∧[bni_73] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)Bound*bni_73] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_74] ≥ 0)
674_0_PARTS_GT(x1, x0) → COND_674_0_PARTS_GT1(&&(&&(>(x1, x0), >(x1, 0)), >(x0, 0)), x1, x0)
- (0 ≥ 0 ⇒ (U^Increasing(COND_674_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_674_0_PARTS_GT1(TRUE, x1, x0) → 674_0_PARTS_GT(x0, x0)
- ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_77] = 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_78] ≥ 0)
- ((U^Increasing(674_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(674_0_parts_GT(x₁, x₂)) = [2]x₂
POL(Cond_674_0_parts_GT(x₁, x₂, x₃)) = x₃
POL(<=(x₁, x₂)) = 0
POL(0) = 0
POL(684_0_parts_Return(x₁)) = 0
POL(760_1_parts_InvokeMethod(x₁, x₂, x₃)) = 0
POL(1370_0_parts_Return(x₁, x₂)) = 0
POL(1492_0_parts_Return(x₁)) = [1]
POL(1449_1_parts_InvokeMethod(x₁, x₂, x₃)) = 0
POL(+(x₁, x₂)) = 0
POL(674_0_PARTS_GT(x₁, x₂)) = [-1]
POL(COND_674_0_PARTS_GT(x₁, x₂, x₃)) = [-1] + [-1]x₁
POL(&&(x₁, x₂)) = 0
POL(>(x₁, x₂)) = 0
POL(769_1_PARTS_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + x₃ + [2]x₁
POL(-(x₁, x₂)) = 0
POL(COND_769_1_PARTS_INVOKEMETHOD(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₄ + [-1]x₂
POL(1) = 0
POL(COND_769_1_PARTS_INVOKEMETHOD1(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₄ + [-1]x₂
POL(COND_769_1_PARTS_INVOKEMETHOD3(x₁, x₂, x₃, x₄, x₅)) = [1] + x₄ + [-1]x₂
POL(COND_674_0_PARTS_GT1(x₁, x₂, x₃)) = [-1]

The following pairs are in P_>:

769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])
COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 674_0_PARTS_GT(-(x2[8], 1), x1[8])

The following pairs are in P_bound:

674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4])
769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])
COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(-(x1[6], 1), x3[6])
769_1_PARTS_INVOKEMETHOD(1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7]) → COND_769_1_PARTS_INVOKEMETHOD3(>(x2[7], 0), 1492_0_parts_Return(x0[7]), x1[7], x3[7], x2[7])
COND_769_1_PARTS_INVOKEMETHOD3(TRUE, 1492_0_parts_Return(x0[8]), x1[8], x3[8], x2[8]) → 674_0_PARTS_GT(-(x2[8], 1), x1[8])
674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])

The following pairs are in P_≥:

674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4])
769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])
COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(-(x1[6], 1), x3[6])
674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])
COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10])

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
674_0_parts_GT(x1, x0)¹ → Cond_674_0_parts_GT(<=(x0, 0), x1, x0)¹
Cond_674_0_parts_GT(TRUE, x1, x0)¹ → 684_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:
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT(x0 <= 0, x1, x0)
Cond_674_0_parts_GT(TRUE, x1, x0) → 684_0_parts_Return(x1)
760_1_parts_InvokeMethod(1370_0_parts_Return(x0, x0), x2, x0) → 1370_0_parts_Return(x0, x2)
760_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x1) → 1370_0_parts_Return(x1, x2)
1449_1_parts_InvokeMethod(1370_0_parts_Return(x0, x1), x0, x1) → 1492_0_parts_Return(x3 + x2)
1449_1_parts_InvokeMethod(684_0_parts_Return(x0), x0, 0) → 1492_0_parts_Return(arith[1])
1449_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x3) → 1492_0_parts_Return(x1 + x0)

The integer pair graph contains the following rules and edges:
(0): 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0, x1[0], x0[0])
(1): COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], x0[1] - x1[1]), x0[1], x0[1] - x1[1], x1[1])
(2): COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], x0[2] - x1[2])
(3): 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(x1[3] > 0, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
(4): COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(x1[4] - 1, x3[4])
(5): 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(x1[5] > 0, 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])
(6): COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(x1[6] - 1, x3[6])
(9): 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(x1[9] > x0[9] && x1[9] > 0 && x0[9] > 0, x1[9], x0[9])
(10): COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_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])

(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 (674_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 684_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 ∧684_0_parts_Return(x1[3]) →^* 684_0_parts_Return(x1[4])∧x3[3] →^* x3[4]∧x0[3] →^* x0[4]∧x1[3] →^* x1[4])

(1) -> (5), if (674_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 1370_0_parts_Return(x0[5], x1[5])∧x0[1] →^* x3[5]∧x0[1] - x1[1] →^* x0[5]∧x1[1] →^* x1[5])

(5) -> (6), if (x1[5] > 0 ∧1370_0_parts_Return(x0[5], x1[5]) →^* 1370_0_parts_Return(x0[6], x1[6])∧x3[5] →^* x3[6]∧x0[5] →^* x0[6]∧x1[5] →^* x1[6])

(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])

(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) 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@23c6e30f 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 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_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 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_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] ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_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 ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_51 + (-1)Bound*bni_51] ≥ 0∧[(-1)bso_52] ≥ 0)

We simplified constraint (3) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(4)    (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_51 + (-1)Bound*bni_51] ≥ 0∧[(-1)bso_52] ≥ 0)

We simplified constraint (4) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(5)    (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_51 + (-1)Bound*bni_51] ≥ 0∧[(-1)bso_52] ≥ 0)

We simplified constraint (5) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(6)    (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_51 + (-1)Bound*bni_51] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_52] ≥ 0)
We consider the chain 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_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] ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_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 ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_51 + (-1)Bound*bni_51] ≥ 0∧[(-1)bso_52] ≥ 0)

We simplified constraint (9) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(10)    (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_51 + (-1)Bound*bni_51] ≥ 0∧[(-1)bso_52] ≥ 0)

We simplified constraint (10) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(11)    (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)bni_51 + (-1)Bound*bni_51] ≥ 0∧[(-1)bso_52] ≥ 0)

We simplified constraint (11) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(12)    (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_51 + (-1)Bound*bni_51] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_52] ≥ 0)

For Pair COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_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 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]), 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_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]∧674_0_parts_GT(x1[1], -(x0[1], x1[1]))=684_0_parts_Return(x1[3])∧x0[1]=x3[3]∧-(x0[1], x1[1])=x0[3]∧x1[1]=x1[3] ⇒ COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_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_674_0_parts_GT(<=(-(x0[0], x1[0]), 0), x1[0], -(x0[0], x1[0]))=684_0_parts_Return(x1[0]) ⇒ COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[0], -(x0[0], x1[0])), x0[0], -(x0[0], x1[0]), x1[0])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] ≥ 0∧[(-1)bso_54] ≥ 0)

We simplified constraint (15) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(16)    (0 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] ≥ 0∧[(-1)bso_54] ≥ 0)

We simplified constraint (16) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(17)    (0 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] ≥ 0∧[(-1)bso_54] ≥ 0)

We simplified constraint (17) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(18)    (0 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_53 + (-1)Bound*bni_53] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_54] ≥ 0)
We consider the chain 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]), 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_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]∧674_0_parts_GT(x1[1], -(x0[1], x1[1]))=1370_0_parts_Return(x0[5], x1[5])∧x0[1]=x3[5]∧-(x0[1], x1[1])=x0[5]∧x1[1]=x1[5] ⇒ COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_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_674_0_parts_GT(<=(-(x0[0], x1[0]), 0), x1[0], -(x0[0], x1[0]))=1370_0_parts_Return(-(x0[0], x1[0]), x1[0]) ⇒ COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[0], -(x0[0], x1[0])), x0[0], -(x0[0], x1[0]), x1[0])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] ≥ 0∧[(-1)bso_54] ≥ 0)

We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(22)    (0 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] ≥ 0∧[(-1)bso_54] ≥ 0)

We simplified constraint (22) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(23)    (0 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)bni_53 + (-1)Bound*bni_53] ≥ 0∧[(-1)bso_54] ≥ 0)

We simplified constraint (23) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(24)    (0 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_53 + (-1)Bound*bni_53] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_54] ≥ 0)

For Pair COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2])) the following chains were created:

We consider the chain 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2])), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(25)    (&&(&&(>(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_674_0_PARTS_GT(TRUE, x1[2], x0[2])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[2], x0[2])≥674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))∧(U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (25) using rules (III), (IV) which results in the following new constraint:
(26)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE ⇒ COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥674_0_PARTS_GT(x1[0], -(x0[0], x1[0]))∧(U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (26) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(27)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] ≥ 0∧[(-1)bso_56] ≥ 0)

We simplified constraint (27) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(28)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] ≥ 0∧[(-1)bso_56] ≥ 0)

We simplified constraint (28) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(29)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] ≥ 0∧[(-1)bso_56] ≥ 0)

We simplified constraint (29) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(30)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_55 + (-1)Bound*bni_55] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_56] ≥ 0)
We consider the chain 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2])), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) 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[9]∧-(x0[2], x1[2])=x0[9] ⇒ COND_674_0_PARTS_GT(TRUE, x1[2], x0[2])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[2], x0[2])≥674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))∧(U^Increasing(674_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_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥674_0_PARTS_GT(x1[0], -(x0[0], x1[0]))∧(U^Increasing(674_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(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] ≥ 0∧[(-1)bso_56] ≥ 0)

We simplified constraint (33) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(34)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] ≥ 0∧[(-1)bso_56] ≥ 0)

We simplified constraint (34) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(35)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(-1)bni_55 + (-1)Bound*bni_55] ≥ 0∧[(-1)bso_56] ≥ 0)

We simplified constraint (35) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(36)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_55 + (-1)Bound*bni_55] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_56] ≥ 0)

For Pair 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) the following chains were created:

We consider the chain 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]) which results in the following constraint:
(37)    (>(x1[3], 0)=TRUE∧684_0_parts_Return(x1[3])=684_0_parts_Return(x1[4])∧x3[3]=x3[4]∧x0[3]=x0[4]∧x1[3]=x1[4] ⇒ 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥))

We simplified constraint (37) using rules (I), (II), (IV) which results in the following new constraint:
(38)    (>(x1[3], 0)=TRUE ⇒ 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥))

We simplified constraint (38) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(39)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] + [bni_57]x0[3] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (39) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(40)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] + [bni_57]x0[3] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(41)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[(-1)bni_57 + (-1)Bound*bni_57] + [bni_57]x0[3] ≥ 0∧[(-1)bso_58] ≥ 0)

We simplified constraint (41) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(42)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 ≥ 0∧[bni_57] ≥ 0∧0 ≥ 0∧[(-1)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_58] ≥ 0)

For Pair COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]) the following chains were created:

We consider the chain 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(43)    (>(x1[3], 0)=TRUE∧684_0_parts_Return(x1[3])=684_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_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥674_0_PARTS_GT(-(x1[4], 1), x3[4])∧(U^Increasing(674_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_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥674_0_PARTS_GT(-(x1[3], 1), x3[3])∧(U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (44) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(45)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [bni_59]x0[3] ≥ 0∧[(-1)bso_60] + x0[3] ≥ 0)

We simplified constraint (45) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(46)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [bni_59]x0[3] ≥ 0∧[(-1)bso_60] + 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(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [bni_59]x0[3] ≥ 0∧[(-1)bso_60] + x0[3] ≥ 0)

We simplified constraint (47) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(48)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 ≥ 0∧[bni_59] ≥ 0∧0 ≥ 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_60] ≥ 0)
We consider the chain 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(49)    (>(x1[3], 0)=TRUE∧684_0_parts_Return(x1[3])=684_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_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥674_0_PARTS_GT(-(x1[4], 1), x3[4])∧(U^Increasing(674_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_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥674_0_PARTS_GT(-(x1[3], 1), x3[3])∧(U^Increasing(674_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(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [bni_59]x0[3] ≥ 0∧[(-1)bso_60] + x0[3] ≥ 0)

We simplified constraint (51) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(52)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [bni_59]x0[3] ≥ 0∧[(-1)bso_60] + x0[3] ≥ 0)

We simplified constraint (52) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(53)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)bni_59 + (-1)Bound*bni_59] + [bni_59]x0[3] ≥ 0∧[(-1)bso_60] + x0[3] ≥ 0)

We simplified constraint (53) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(54)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 ≥ 0∧[bni_59] ≥ 0∧0 ≥ 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_60] ≥ 0)

For Pair 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) the following chains were created:

We consider the chain 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]), COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(-(x1[6], 1), x3[6]) which results in the following constraint:
(55)    (>(x1[5], 0)=TRUE∧1370_0_parts_Return(x0[5], x1[5])=1370_0_parts_Return(x0[6], x1[6])∧x3[5]=x3[6]∧x0[5]=x0[6]∧x1[5]=x1[6] ⇒ 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥))

We simplified constraint (55) using rules (I), (II), (IV) which results in the following new constraint:
(56)    (>(x1[5], 0)=TRUE ⇒ 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥))

We simplified constraint (56) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(57)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧[bni_61 + (-1)Bound*bni_61] + [(2)bni_61]x0[5] ≥ 0∧[1 + (-1)bso_62] ≥ 0)

We simplified constraint (57) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(58)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧[bni_61 + (-1)Bound*bni_61] + [(2)bni_61]x0[5] ≥ 0∧[1 + (-1)bso_62] ≥ 0)

We simplified constraint (58) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(59)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧[bni_61 + (-1)Bound*bni_61] + [(2)bni_61]x0[5] ≥ 0∧[1 + (-1)bso_62] ≥ 0)

We simplified constraint (59) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(60)    (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧0 ≥ 0∧[(2)bni_61] ≥ 0∧0 ≥ 0∧[bni_61 + (-1)Bound*bni_61] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_62] ≥ 0)

For Pair COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(-(x1[6], 1), x3[6]) the following chains were created:

We consider the chain 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]), COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(-(x1[6], 1), x3[6]), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(61)    (>(x1[5], 0)=TRUE∧1370_0_parts_Return(x0[5], x1[5])=1370_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_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6])≥674_0_PARTS_GT(-(x1[6], 1), x3[6])∧(U^Increasing(674_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥))

We simplified constraint (61) using rules (I), (II), (III), (IV) which results in the following new constraint:
(62)    (>(x1[5], 0)=TRUE ⇒ COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥674_0_PARTS_GT(-(x1[5], 1), x3[5])∧(U^Increasing(674_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥))

We simplified constraint (62) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(63)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧[(-1)Bound*bni_63] + [(2)bni_63]x0[5] ≥ 0∧[1 + (-1)bso_64] + [2]x0[5] ≥ 0)

We simplified constraint (63) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(64)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧[(-1)Bound*bni_63] + [(2)bni_63]x0[5] ≥ 0∧[1 + (-1)bso_64] + [2]x0[5] ≥ 0)

We simplified constraint (64) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(65)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧[(-1)Bound*bni_63] + [(2)bni_63]x0[5] ≥ 0∧[1 + (-1)bso_64] + [2]x0[5] ≥ 0)

We simplified constraint (65) using rules (IDP_UNRESTRICTED_VARS), (IDP_POLY_GCD) which results in the following new constraint:
(66)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧0 ≥ 0∧[(2)bni_63] ≥ 0∧0 ≥ 0∧[(-1)Bound*bni_63] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_64] ≥ 0∧[1] ≥ 0)
We consider the chain 769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]), COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(-(x1[6], 1), x3[6]), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(67)    (>(x1[5], 0)=TRUE∧1370_0_parts_Return(x0[5], x1[5])=1370_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_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6])≥674_0_PARTS_GT(-(x1[6], 1), x3[6])∧(U^Increasing(674_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_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])≥674_0_PARTS_GT(-(x1[5], 1), x3[5])∧(U^Increasing(674_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(674_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧[(-1)Bound*bni_63] + [(2)bni_63]x0[5] ≥ 0∧[1 + (-1)bso_64] + [2]x0[5] ≥ 0)

We simplified constraint (69) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(70)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧[(-1)Bound*bni_63] + [(2)bni_63]x0[5] ≥ 0∧[1 + (-1)bso_64] + [2]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(674_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧[(-1)Bound*bni_63] + [(2)bni_63]x0[5] ≥ 0∧[1 + (-1)bso_64] + [2]x0[5] ≥ 0)

We simplified constraint (71) using rules (IDP_UNRESTRICTED_VARS), (IDP_POLY_GCD) which results in the following new constraint:
(72)    (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧0 ≥ 0∧[(2)bni_63] ≥ 0∧0 ≥ 0∧[(-1)Bound*bni_63] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_64] ≥ 0∧[1] ≥ 0)

For Pair 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_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 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]), COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]) which results in the following constraint:
(73)    (&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0))=TRUE∧x1[9]=x1[10]∧x0[9]=x0[10] ⇒ 674_0_PARTS_GT(x1[9], x0[9])≥NonInfC∧674_0_PARTS_GT(x1[9], x0[9])≥COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])∧(U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥))

We simplified constraint (73) using rule (IV) which results in the following new constraint:
(74)    (&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0))=TRUE ⇒ 674_0_PARTS_GT(x1[9], x0[9])≥NonInfC∧674_0_PARTS_GT(x1[9], x0[9])≥COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])∧(U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥))

We simplified constraint (74) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(75)    (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (75) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(76)    (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (76) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(77)    (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧[(-1)bso_66] ≥ 0)

We simplified constraint (77) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(78)    (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_66] ≥ 0)

For Pair COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]) the following chains were created:

We consider the chain COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(79)    (x0[10]=x1[0]∧x0[10]=x0[0] ⇒ COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (79) using rule (IV) which results in the following new constraint:
(80)    (COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (80) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(81)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_67] = 0∧[(-1)bso_68] ≥ 0)

We simplified constraint (81) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(82)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_67] = 0∧[(-1)bso_68] ≥ 0)

We simplified constraint (82) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(83)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_67] = 0∧[(-1)bso_68] ≥ 0)

We simplified constraint (83) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(84)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_67] = 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_68] ≥ 0)
We consider the chain COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(85)    (x0[10]=x1[9]∧x0[10]=x0[9] ⇒ COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (85) using rule (IV) which results in the following new constraint:
(86)    (COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (86) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(87)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_67] = 0∧[(-1)bso_68] ≥ 0)

We simplified constraint (87) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(88)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_67] = 0∧[(-1)bso_68] ≥ 0)

We simplified constraint (88) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(89)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_67] = 0∧[(-1)bso_68] ≥ 0)

We simplified constraint (89) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(90)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_67] = 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_68] ≥ 0)

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

674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
- (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_51 + (-1)Bound*bni_51] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_52] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_51 + (-1)Bound*bni_51] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_52] ≥ 0)
COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
- (0 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_53 + (-1)Bound*bni_53] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_54] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_53 + (-1)Bound*bni_53] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_54] ≥ 0)
COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
- (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_55 + (-1)Bound*bni_55] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_56] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_55 + (-1)Bound*bni_55] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_56] ≥ 0)
769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
- (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 ≥ 0∧[bni_57] ≥ 0∧0 ≥ 0∧[(-1)bni_57 + (-1)Bound*bni_57] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_58] ≥ 0)
COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4])
- (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 ≥ 0∧[bni_59] ≥ 0∧0 ≥ 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_60] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 ≥ 0∧[bni_59] ≥ 0∧0 ≥ 0∧[(-1)bni_59 + (-1)Bound*bni_59] ≥ 0∧0 ≥ 0∧[1] ≥ 0∧0 ≥ 0∧[(-1)bso_60] ≥ 0)
769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])
- (0 ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])), ≥)∧0 ≥ 0∧[(2)bni_61] ≥ 0∧0 ≥ 0∧[bni_61 + (-1)Bound*bni_61] ≥ 0∧0 ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_62] ≥ 0)
COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(-(x1[6], 1), x3[6])
- (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧0 ≥ 0∧[(2)bni_63] ≥ 0∧0 ≥ 0∧[(-1)Bound*bni_63] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_64] ≥ 0∧[1] ≥ 0)
- (0 ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[6], 1), x3[6])), ≥)∧0 ≥ 0∧[(2)bni_63] ≥ 0∧0 ≥ 0∧[(-1)Bound*bni_63] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[1 + (-1)bso_64] ≥ 0∧[1] ≥ 0)
674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])
- (0 ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧0 ≥ 0∧0 ≥ 0∧[(-1)bni_65 + (-1)Bound*bni_65] ≥ 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_66] ≥ 0)
COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10])
- ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_67] = 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_68] ≥ 0)
- ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_67] = 0∧0 ≥ 0∧0 ≥ 0∧[(-1)bso_68] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(674_0_parts_GT(x₁, x₂)) = 0
POL(Cond_674_0_parts_GT(x₁, x₂, x₃)) = 0
POL(<=(x₁, x₂)) = 0
POL(0) = 0
POL(684_0_parts_Return(x₁)) = 0
POL(760_1_parts_InvokeMethod(x₁, x₂, x₃)) = 0
POL(1370_0_parts_Return(x₁, x₂)) = [2] + x₁
POL(1492_0_parts_Return(x₁)) = 0
POL(1449_1_parts_InvokeMethod(x₁, x₂, x₃)) = 0
POL(+(x₁, x₂)) = 0
POL(674_0_PARTS_GT(x₁, x₂)) = [-1]
POL(COND_674_0_PARTS_GT(x₁, x₂, x₃)) = [-1] + x₁
POL(&&(x₁, x₂)) = 0
POL(>(x₁, x₂)) = 0
POL(769_1_PARTS_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + x₃ + x₁
POL(-(x₁, x₂)) = 0
POL(COND_769_1_PARTS_INVOKEMETHOD(x₁, x₂, x₃, x₄, x₅)) = [-1] + x₄ + [-1]x₂
POL(1) = 0
POL(COND_769_1_PARTS_INVOKEMETHOD1(x₁, x₂, x₃, x₄, x₅)) = [2]x₄
POL(COND_674_0_PARTS_GT1(x₁, x₂, x₃)) = [-1] + [2]x₁

The following pairs are in P_>:

769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])
COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(-(x1[6], 1), x3[6])

The following pairs are in P_bound:

674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4])
769_1_PARTS_INVOKEMETHOD(1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5]) → COND_769_1_PARTS_INVOKEMETHOD1(>(x1[5], 0), 1370_0_parts_Return(x0[5], x1[5]), x3[5], x0[5], x1[5])
COND_769_1_PARTS_INVOKEMETHOD1(TRUE, 1370_0_parts_Return(x0[6], x1[6]), x3[6], x0[6], x1[6]) → 674_0_PARTS_GT(-(x1[6], 1), x3[6])
674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])

The following pairs are in P_≥:

674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4])
674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])
COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10])

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
674_0_parts_GT(x1, x0)¹ ↔ Cond_674_0_parts_GT(<=(x0, 0), x1, x0)¹
Cond_674_0_parts_GT(TRUE, x1, x0)¹ ↔ 684_0_parts_Return(x1)¹

(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:
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT(x0 <= 0, x1, x0)
Cond_674_0_parts_GT(TRUE, x1, x0) → 684_0_parts_Return(x1)
760_1_parts_InvokeMethod(1370_0_parts_Return(x0, x0), x2, x0) → 1370_0_parts_Return(x0, x2)
760_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x1) → 1370_0_parts_Return(x1, x2)
1449_1_parts_InvokeMethod(1370_0_parts_Return(x0, x1), x0, x1) → 1492_0_parts_Return(x3 + x2)
1449_1_parts_InvokeMethod(684_0_parts_Return(x0), x0, 0) → 1492_0_parts_Return(arith[1])
1449_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x3) → 1492_0_parts_Return(x1 + x0)

The integer pair graph contains the following rules and edges:
(0): 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(x1[0] > 0 && x1[0] <= x0[0] && x0[0] > 0, x1[0], x0[0])
(1): COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], x0[1] - x1[1]), x0[1], x0[1] - x1[1], x1[1])
(2): COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], x0[2] - x1[2])
(3): 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(x1[3] > 0, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
(4): COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(x1[4] - 1, x3[4])
(9): 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(x1[9] > x0[9] && x1[9] > 0 && x0[9] > 0, x1[9], x0[9])
(10): COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_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])

(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 (674_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 684_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 ∧684_0_parts_Return(x1[3]) →^* 684_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) 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@56650022 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 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_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 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_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] ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_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 ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[bni_50 + (-1)Bound*bni_50] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[bni_50 + (-1)Bound*bni_50] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[bni_50 + (-1)Bound*bni_50] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(2)bni_50 + (-1)Bound*bni_50] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(2)bni_50 + (-1)Bound*bni_50] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(2)bni_50 + (-1)Bound*bni_50] + [bni_50]x1[0] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 0)
We consider the chain 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2])) 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] ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥))

We simplified constraint (9) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(10)    (>(x0[0], 0)=TRUE∧>(x1[0], 0)=TRUE∧<=(x1[0], x0[0])=TRUE ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥))

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(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[bni_50 + (-1)Bound*bni_50] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 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(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[bni_50 + (-1)Bound*bni_50] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 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(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[bni_50 + (-1)Bound*bni_50] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 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(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(2)bni_50 + (-1)Bound*bni_50] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 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(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(2)bni_50 + (-1)Bound*bni_50] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 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(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(2)bni_50 + (-1)Bound*bni_50] + [bni_50]x1[0] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 0)

For Pair COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_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 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]), 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) which results in the following constraint:
(17)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[1]∧x0[0]=x0[1]∧674_0_parts_GT(x1[1], -(x0[1], x1[1]))=684_0_parts_Return(x1[3])∧x0[1]=x3[3]∧-(x0[1], x1[1])=x0[3]∧x1[1]=x1[3] ⇒ COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (17) using rules (III), (IV), (VII), (IDP_BOOLEAN), (REWRITING) which results in the following new constraint:
(18)    (<=(-(x0[0], x1[0]), 0)=x0∧-(x0[0], x1[0])=x1∧Cond_674_0_parts_GT(x0, x1[0], x1)=684_0_parts_Return(x1[0])∧>(x0[0], 0)=TRUE∧>(x1[0], 0)=TRUE∧<=(x1[0], x0[0])=TRUE ⇒ COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[0], -(x0[0], x1[0])), x0[0], -(x0[0], x1[0]), x1[0])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (18) using rule (V) (with possible (I) afterwards) using induction on Cond_674_0_parts_GT(x0, x1[0], x1)=684_0_parts_Return(x1[0]) which results in the following new constraint:
(19)    (684_0_parts_Return(x3)=684_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_674_0_PARTS_GT(TRUE, x3, x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x3, x0[0])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x3, -(x0[0], x3)), x0[0], -(x0[0], x3), x3)∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (19) using rules (I), (II), (IV), (DELETE_TRIVIAL_REDUCESTO) which results in the following new constraint:
(20)    (<=(-(x0[0], x3), 0)=TRUE∧>(x0[0], 0)=TRUE∧>(x3, 0)=TRUE∧<=(x3, x0[0])=TRUE ⇒ COND_674_0_PARTS_GT(TRUE, x3, x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x3, x0[0])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x3, -(x0[0], x3)), x0[0], -(x0[0], x3), x3)∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_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)    ([-1]x0[0] + x3 ≥ 0∧x0[0] + [-1] ≥ 0∧x3 + [-1] ≥ 0∧x0[0] + [-1]x3 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[bni_52 + (-1)Bound*bni_52] + [bni_52]x0[0] ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(22)    ([-1]x0[0] + x3 ≥ 0∧x0[0] + [-1] ≥ 0∧x3 + [-1] ≥ 0∧x0[0] + [-1]x3 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[bni_52 + (-1)Bound*bni_52] + [bni_52]x0[0] ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (22) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(23)    ([-1]x0[0] + x3 ≥ 0∧x0[0] + [-1] ≥ 0∧x3 + [-1] ≥ 0∧x0[0] + [-1]x3 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[bni_52 + (-1)Bound*bni_52] + [bni_52]x0[0] ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (23) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(24)    ([-1] + [-1]x0[0] + x3 ≥ 0∧x0[0] ≥ 0∧x3 + [-1] ≥ 0∧[1] + x0[0] + [-1]x3 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(2)bni_52 + (-1)Bound*bni_52] + [bni_52]x0[0] ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (24) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(25)    (x3 ≥ 0∧x0[0] ≥ 0∧x0[0] + x3 ≥ 0∧[-1]x3 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(2)bni_52 + (-1)Bound*bni_52] + [bni_52]x0[0] ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (25) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(26)    (0 ≥ 0∧x0[0] ≥ 0∧x0[0] ≥ 0∧0 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(2)bni_52 + (-1)Bound*bni_52] + [bni_52]x0[0] ≥ 0∧[(-1)bso_53] ≥ 0)

For Pair COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2])) the following chains were created:

We consider the chain 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2])), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(27)    (&&(&&(>(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_674_0_PARTS_GT(TRUE, x1[2], x0[2])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[2], x0[2])≥674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))∧(U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (27) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(28)    (>(x0[0], 0)=TRUE∧>(x1[0], 0)=TRUE∧<=(x1[0], x0[0])=TRUE ⇒ COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥674_0_PARTS_GT(x1[0], -(x0[0], x1[0]))∧(U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (28) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(29)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[bni_54 + (-1)Bound*bni_54] + [bni_54]x0[0] ≥ 0∧[(-1)bso_55] + x1[0] ≥ 0)

We simplified constraint (29) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(30)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[bni_54 + (-1)Bound*bni_54] + [bni_54]x0[0] ≥ 0∧[(-1)bso_55] + x1[0] ≥ 0)

We simplified constraint (30) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(31)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[bni_54 + (-1)Bound*bni_54] + [bni_54]x0[0] ≥ 0∧[(-1)bso_55] + x1[0] ≥ 0)

We simplified constraint (31) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(32)    (x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧[1] + x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(2)bni_54 + (-1)Bound*bni_54] + [bni_54]x0[0] ≥ 0∧[(-1)bso_55] + x1[0] ≥ 0)

We simplified constraint (32) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(33)    (x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(2)bni_54 + (-1)Bound*bni_54] + [bni_54]x0[0] ≥ 0∧[1 + (-1)bso_55] + x1[0] ≥ 0)

We simplified constraint (33) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(34)    (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(2)bni_54 + (-1)Bound*bni_54] + [bni_54]x1[0] + [bni_54]x0[0] ≥ 0∧[1 + (-1)bso_55] + x1[0] ≥ 0)
We consider the chain 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2])), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(35)    (&&(&&(>(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_674_0_PARTS_GT(TRUE, x1[2], x0[2])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[2], x0[2])≥674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))∧(U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (35) using rules (III), (IV), (IDP_BOOLEAN) which results in the following new constraint:
(36)    (>(x0[0], 0)=TRUE∧>(x1[0], 0)=TRUE∧<=(x1[0], x0[0])=TRUE ⇒ COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥674_0_PARTS_GT(x1[0], -(x0[0], x1[0]))∧(U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥))

We simplified constraint (36) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(37)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[bni_54 + (-1)Bound*bni_54] + [bni_54]x0[0] ≥ 0∧[(-1)bso_55] + x1[0] ≥ 0)

We simplified constraint (37) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(38)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[bni_54 + (-1)Bound*bni_54] + [bni_54]x0[0] ≥ 0∧[(-1)bso_55] + x1[0] ≥ 0)

We simplified constraint (38) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(39)    (x0[0] + [-1] ≥ 0∧x1[0] + [-1] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[bni_54 + (-1)Bound*bni_54] + [bni_54]x0[0] ≥ 0∧[(-1)bso_55] + x1[0] ≥ 0)

We simplified constraint (39) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(40)    (x0[0] ≥ 0∧x1[0] + [-1] ≥ 0∧[1] + x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(2)bni_54 + (-1)Bound*bni_54] + [bni_54]x0[0] ≥ 0∧[(-1)bso_55] + x1[0] ≥ 0)

We simplified constraint (40) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(41)    (x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] + [-1]x1[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(2)bni_54 + (-1)Bound*bni_54] + [bni_54]x0[0] ≥ 0∧[1 + (-1)bso_55] + x1[0] ≥ 0)

We simplified constraint (41) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(42)    (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(2)bni_54 + (-1)Bound*bni_54] + [bni_54]x1[0] + [bni_54]x0[0] ≥ 0∧[1 + (-1)bso_55] + x1[0] ≥ 0)

We consider the chain 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]) which results in the following constraint:
(43)    (>(x1[3], 0)=TRUE∧684_0_parts_Return(x1[3])=684_0_parts_Return(x1[4])∧x3[3]=x3[4]∧x0[3]=x0[4]∧x1[3]=x1[4] ⇒ 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_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 ⇒ 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_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)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[bni_56 + (-1)Bound*bni_56] + [bni_56]x3[3] ≥ 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (45) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(46)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[bni_56 + (-1)Bound*bni_56] + [bni_56]x3[3] ≥ 0∧[(-1)bso_57] ≥ 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(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[bni_56 + (-1)Bound*bni_56] + [bni_56]x3[3] ≥ 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (47) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(48)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 = 0∧[bni_56] = 0∧[bni_56 + (-1)Bound*bni_56] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

We simplified constraint (48) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(49)    (x1[3] ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 = 0∧[bni_56] = 0∧[bni_56 + (-1)Bound*bni_56] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)

For Pair COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]) the following chains were created:

We consider the chain 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(50)    (>(x1[3], 0)=TRUE∧684_0_parts_Return(x1[3])=684_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_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥674_0_PARTS_GT(-(x1[4], 1), x3[4])∧(U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (50) using rules (I), (II), (III), (IV) which results in the following new constraint:
(51)    (>(x1[3], 0)=TRUE ⇒ COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥674_0_PARTS_GT(-(x1[3], 1), x3[3])∧(U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (51) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(52)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[bni_58 + (-1)Bound*bni_58] + [bni_58]x3[3] ≥ 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (52) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(53)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[bni_58 + (-1)Bound*bni_58] + [bni_58]x3[3] ≥ 0∧[(-1)bso_59] ≥ 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(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[bni_58 + (-1)Bound*bni_58] + [bni_58]x3[3] ≥ 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (54) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(55)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧[bni_58] = 0∧[bni_58 + (-1)Bound*bni_58] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (55) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(56)    (x1[3] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧[bni_58] = 0∧[bni_58 + (-1)Bound*bni_58] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_59] ≥ 0)
We consider the chain 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(57)    (>(x1[3], 0)=TRUE∧684_0_parts_Return(x1[3])=684_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_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥674_0_PARTS_GT(-(x1[4], 1), x3[4])∧(U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (57) using rules (I), (II), (III), (IV) which results in the following new constraint:
(58)    (>(x1[3], 0)=TRUE ⇒ COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥674_0_PARTS_GT(-(x1[3], 1), x3[3])∧(U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (58) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(59)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[bni_58 + (-1)Bound*bni_58] + [bni_58]x3[3] ≥ 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (59) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(60)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[bni_58 + (-1)Bound*bni_58] + [bni_58]x3[3] ≥ 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (60) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(61)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[bni_58 + (-1)Bound*bni_58] + [bni_58]x3[3] ≥ 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (61) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(62)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧[bni_58] = 0∧[bni_58 + (-1)Bound*bni_58] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_59] ≥ 0)

We simplified constraint (62) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(63)    (x1[3] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧[bni_58] = 0∧[bni_58 + (-1)Bound*bni_58] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_59] ≥ 0)

For Pair 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_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 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]), COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]) which results in the following constraint:
(64)    (&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0))=TRUE∧x1[9]=x1[10]∧x0[9]=x0[10] ⇒ 674_0_PARTS_GT(x1[9], x0[9])≥NonInfC∧674_0_PARTS_GT(x1[9], x0[9])≥COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])∧(U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥))

We simplified constraint (64) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(65)    (>(x0[9], 0)=TRUE∧>(x1[9], x0[9])=TRUE∧>(x1[9], 0)=TRUE ⇒ 674_0_PARTS_GT(x1[9], x0[9])≥NonInfC∧674_0_PARTS_GT(x1[9], x0[9])≥COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])∧(U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥))

We simplified constraint (65) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(66)    (x0[9] + [-1] ≥ 0∧x1[9] + [-1] + [-1]x0[9] ≥ 0∧x1[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[bni_60 + (-1)Bound*bni_60] + [bni_60]x0[9] ≥ 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (66) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(67)    (x0[9] + [-1] ≥ 0∧x1[9] + [-1] + [-1]x0[9] ≥ 0∧x1[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[bni_60 + (-1)Bound*bni_60] + [bni_60]x0[9] ≥ 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (67) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(68)    (x0[9] + [-1] ≥ 0∧x1[9] + [-1] + [-1]x0[9] ≥ 0∧x1[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[bni_60 + (-1)Bound*bni_60] + [bni_60]x0[9] ≥ 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (68) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(69)    (x0[9] ≥ 0∧x1[9] + [-2] + [-1]x0[9] ≥ 0∧x1[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(2)bni_60 + (-1)Bound*bni_60] + [bni_60]x0[9] ≥ 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (69) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(70)    (x0[9] ≥ 0∧x1[9] ≥ 0∧[1] + x0[9] + x1[9] ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(2)bni_60 + (-1)Bound*bni_60] + [bni_60]x0[9] ≥ 0∧[(-1)bso_61] ≥ 0)

For Pair COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]) the following chains were created:

We consider the chain COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(71)    (x0[10]=x1[0]∧x0[10]=x0[0] ⇒ COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (71) using rule (IV) which results in the following new constraint:
(72)    (COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (72) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(73)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_62] = 0∧[(-1)bso_63] ≥ 0)

We simplified constraint (73) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(74)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_62] = 0∧[(-1)bso_63] ≥ 0)

We simplified constraint (74) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(75)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_62] = 0∧[(-1)bso_63] ≥ 0)

We simplified constraint (75) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(76)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_62] = 0∧0 = 0∧0 = 0∧[(-1)bso_63] ≥ 0)
We consider the chain COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(77)    (x0[10]=x1[9]∧x0[10]=x0[9] ⇒ COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (77) using rule (IV) which results in the following new constraint:
(78)    (COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (78) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(79)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_62] = 0∧[(-1)bso_63] ≥ 0)

We simplified constraint (79) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(80)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_62] = 0∧[(-1)bso_63] ≥ 0)

We simplified constraint (80) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(81)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_62] = 0∧[(-1)bso_63] ≥ 0)

We simplified constraint (81) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(82)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_62] = 0∧0 = 0∧0 = 0∧[(-1)bso_63] ≥ 0)

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

674_0_PARTS_GT(x1[0], x0[0]) → COND_674_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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(2)bni_50 + (-1)Bound*bni_50] + [bni_50]x1[0] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 0)
- (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(2)bni_50 + (-1)Bound*bni_50] + [bni_50]x1[0] + [bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 0)
COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(2)bni_52 + (-1)Bound*bni_52] + [bni_52]x0[0] ≥ 0∧[(-1)bso_53] ≥ 0)
COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
- (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(2)bni_54 + (-1)Bound*bni_54] + [bni_54]x1[0] + [bni_54]x0[0] ≥ 0∧[1 + (-1)bso_55] + x1[0] ≥ 0)
- (x1[0] + x0[0] ≥ 0∧x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))), ≥)∧[(2)bni_54 + (-1)Bound*bni_54] + [bni_54]x1[0] + [bni_54]x0[0] ≥ 0∧[1 + (-1)bso_55] + x1[0] ≥ 0)
769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
- (x1[3] ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 = 0∧[bni_56] = 0∧[bni_56 + (-1)Bound*bni_56] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_57] ≥ 0)
COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4])
- (x1[3] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧[bni_58] = 0∧[bni_58 + (-1)Bound*bni_58] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_59] ≥ 0)
- (x1[3] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧[bni_58] = 0∧[bni_58 + (-1)Bound*bni_58] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_59] ≥ 0)
674_0_PARTS_GT(x1[9], x0[9]) → COND_674_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_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(2)bni_60 + (-1)Bound*bni_60] + [bni_60]x0[9] ≥ 0∧[(-1)bso_61] ≥ 0)
COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10])
- ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_62] = 0∧0 = 0∧0 = 0∧[(-1)bso_63] ≥ 0)
- ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_62] = 0∧0 = 0∧0 = 0∧[(-1)bso_63] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = [3]
POL(674_0_parts_GT(x₁, x₂)) = [1] + [-1]x₁
POL(Cond_674_0_parts_GT(x₁, x₂, x₃)) = [1] + [-1]x₂
POL(<=(x₁, x₂)) = [-1]
POL(0) = 0
POL(684_0_parts_Return(x₁)) = [1] + [-1]x₁
POL(760_1_parts_InvokeMethod(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(1370_0_parts_Return(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(1492_0_parts_Return(x₁)) = [-1] + [-1]x₁
POL(1449_1_parts_InvokeMethod(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(+(x₁, x₂)) = x₁ + x₂
POL(674_0_PARTS_GT(x₁, x₂)) = [1] + x₂
POL(COND_674_0_PARTS_GT(x₁, x₂, x₃)) = [1] + x₃
POL(&&(x₁, x₂)) = 0
POL(>(x₁, x₂)) = [-1]
POL(769_1_PARTS_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [2] + [-1]x₄ + x₂ + [-1]x₁
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(COND_769_1_PARTS_INVOKEMETHOD(x₁, x₂, x₃, x₄, x₅)) = [2] + [-1]x₅ + x₃ + [-1]x₂
POL(1) = [1]
POL(COND_674_0_PARTS_GT1(x₁, x₂, x₃)) = [1] + x₃ + [-1]x₁

The following pairs are in P_>:

COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))

The following pairs are in P_bound:

674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
COND_674_0_PARTS_GT(TRUE, x1[2], x0[2]) → 674_0_PARTS_GT(x1[2], -(x0[2], x1[2]))
674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])

The following pairs are in P_≥:

674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4])
674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])
COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10])

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

TRUE¹ → &&(TRUE, TRUE)¹
FALSE¹ → &&(TRUE, FALSE)¹
FALSE¹ → &&(FALSE, TRUE)¹
FALSE¹ → &&(FALSE, FALSE)¹
674_0_parts_GT(x1, x0)¹ ↔ Cond_674_0_parts_GT(<=(x0, 0), x1, x0)¹
Cond_674_0_parts_GT(TRUE, x1, x0)¹ ↔ 684_0_parts_Return(x1)¹

(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

(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])

(1) -> (3), if (674_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 684_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 ∧684_0_parts_Return(x1[3]) →^* 684_0_parts_Return(x1[4])∧x3[3] →^* x3[4]∧x0[3] →^* x0[4]∧x1[3] →^* x1[4])

(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)

We consider the chain 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_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] ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_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 ⇒ 674_0_PARTS_GT(x1[0], x0[0])≥NonInfC∧674_0_PARTS_GT(x1[0], x0[0])≥COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])∧(U^Increasing(COND_674_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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]x0[0] + [bni_50]x1[0] ≥ 0∧[(-1)bso_51] ≥ 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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]x0[0] + [bni_50]x1[0] ≥ 0∧[(-1)bso_51] ≥ 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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]x0[0] + [bni_50]x1[0] ≥ 0∧[(-1)bso_51] ≥ 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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_50 + (-1)bni_50] + [(-1)bni_50]x0[0] + [bni_50]x1[0] ≥ 0∧[(-1)bso_51] ≥ 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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]x0[0] + [bni_50]x1[0] ≥ 0∧[(-1)bso_51] ≥ 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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 0)

For Pair COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_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 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]), COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1]), 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) which results in the following constraint:
(9)    (&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0))=TRUE∧x1[0]=x1[1]∧x0[0]=x0[1]∧674_0_parts_GT(x1[1], -(x0[1], x1[1]))=684_0_parts_Return(x1[3])∧x0[1]=x3[3]∧-(x0[1], x1[1])=x0[3]∧x1[1]=x1[3] ⇒ COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[1], x0[1])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (9) using rules (III), (IV), (VII), (IDP_BOOLEAN), (REWRITING) which results in the following new constraint:
(10)    (<=(-(x0[0], x1[0]), 0)=x0∧-(x0[0], x1[0])=x1∧Cond_674_0_parts_GT(x0, x1[0], x1)=684_0_parts_Return(x1[0])∧>(x0[0], 0)=TRUE∧>(x1[0], 0)=TRUE∧<=(x1[0], x0[0])=TRUE ⇒ COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x1[0], x0[0])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[0], -(x0[0], x1[0])), x0[0], -(x0[0], x1[0]), x1[0])∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (10) using rule (V) (with possible (I) afterwards) using induction on Cond_674_0_parts_GT(x0, x1[0], x1)=684_0_parts_Return(x1[0]) which results in the following new constraint:
(11)    (684_0_parts_Return(x3)=684_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_674_0_PARTS_GT(TRUE, x3, x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x3, x0[0])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x3, -(x0[0], x3)), x0[0], -(x0[0], x3), x3)∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (11) using rules (I), (II), (IV), (DELETE_TRIVIAL_REDUCESTO) which results in the following new constraint:
(12)    (<=(-(x0[0], x3), 0)=TRUE∧>(x0[0], 0)=TRUE∧>(x3, 0)=TRUE∧<=(x3, x0[0])=TRUE ⇒ COND_674_0_PARTS_GT(TRUE, x3, x0[0])≥NonInfC∧COND_674_0_PARTS_GT(TRUE, x3, x0[0])≥769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x3, -(x0[0], x3)), x0[0], -(x0[0], x3), x3)∧(U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥))

We simplified constraint (12) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(13)    ([-1]x0[0] + x3 ≥ 0∧x0[0] + [-1] ≥ 0∧x3 + [-1] ≥ 0∧x0[0] + [-1]x3 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)Bound*bni_52] + [(-1)bni_52]x0[0] + [bni_52]x3 ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (13) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(14)    ([-1]x0[0] + x3 ≥ 0∧x0[0] + [-1] ≥ 0∧x3 + [-1] ≥ 0∧x0[0] + [-1]x3 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)Bound*bni_52] + [(-1)bni_52]x0[0] + [bni_52]x3 ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (14) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(15)    ([-1]x0[0] + x3 ≥ 0∧x0[0] + [-1] ≥ 0∧x3 + [-1] ≥ 0∧x0[0] + [-1]x3 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)Bound*bni_52] + [(-1)bni_52]x0[0] + [bni_52]x3 ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (15) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(16)    ([-1] + [-1]x0[0] + x3 ≥ 0∧x0[0] ≥ 0∧x3 + [-1] ≥ 0∧[1] + x0[0] + [-1]x3 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)Bound*bni_52 + (-1)bni_52] + [(-1)bni_52]x0[0] + [bni_52]x3 ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (16) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(17)    (x3 ≥ 0∧x0[0] ≥ 0∧x0[0] + x3 ≥ 0∧[-1]x3 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)Bound*bni_52] + [bni_52]x3 ≥ 0∧[(-1)bso_53] ≥ 0)

We simplified constraint (17) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(18)    (0 ≥ 0∧x0[0] ≥ 0∧x0[0] ≥ 0∧0 ≥ 0 ⇒ (U^Increasing(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)Bound*bni_52] ≥ 0∧[(-1)bso_53] ≥ 0)

We consider the chain 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]) which results in the following constraint:
(19)    (>(x1[3], 0)=TRUE∧684_0_parts_Return(x1[3])=684_0_parts_Return(x1[4])∧x3[3]=x3[4]∧x0[3]=x0[4]∧x1[3]=x1[4] ⇒ 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥))

We simplified constraint (19) using rules (I), (II), (IV) which results in the following new constraint:
(20)    (>(x1[3], 0)=TRUE ⇒ 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])∧(U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥))

We simplified constraint (20) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(21)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[(-1)Bound*bni_54] + [bni_54]x1[3] + [(-1)bni_54]x3[3] ≥ 0∧[(-1)bso_55] ≥ 0)

We simplified constraint (21) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(22)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[(-1)Bound*bni_54] + [bni_54]x1[3] + [(-1)bni_54]x3[3] ≥ 0∧[(-1)bso_55] ≥ 0)

We simplified constraint (22) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(23)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧[(-1)Bound*bni_54] + [bni_54]x1[3] + [(-1)bni_54]x3[3] ≥ 0∧[(-1)bso_55] ≥ 0)

We simplified constraint (23) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(24)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 = 0∧[(-1)bni_54] = 0∧[(-1)Bound*bni_54] + [bni_54]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_55] ≥ 0)

We simplified constraint (24) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(25)    (x1[3] ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 = 0∧[(-1)bni_54] = 0∧[(-1)Bound*bni_54 + bni_54] + [bni_54]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_55] ≥ 0)

For Pair COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]) the following chains were created:

We consider the chain 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(26)    (>(x1[3], 0)=TRUE∧684_0_parts_Return(x1[3])=684_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_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥674_0_PARTS_GT(-(x1[4], 1), x3[4])∧(U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (26) using rules (I), (II), (III), (IV) which results in the following new constraint:
(27)    (>(x1[3], 0)=TRUE ⇒ COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥674_0_PARTS_GT(-(x1[3], 1), x3[3])∧(U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (27) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(28)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)Bound*bni_56] + [bni_56]x1[3] + [(-1)bni_56]x3[3] ≥ 0∧[1 + (-1)bso_57] ≥ 0)

We simplified constraint (28) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(29)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)Bound*bni_56] + [bni_56]x1[3] + [(-1)bni_56]x3[3] ≥ 0∧[1 + (-1)bso_57] ≥ 0)

We simplified constraint (29) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(30)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)Bound*bni_56] + [bni_56]x1[3] + [(-1)bni_56]x3[3] ≥ 0∧[1 + (-1)bso_57] ≥ 0)

We simplified constraint (30) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(31)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧[(-1)bni_56] = 0∧[(-1)Bound*bni_56] + [bni_56]x1[3] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_57] ≥ 0)

We simplified constraint (31) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(32)    (x1[3] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧[(-1)bni_56] = 0∧[(-1)Bound*bni_56 + bni_56] + [bni_56]x1[3] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_57] ≥ 0)
We consider the chain 769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]), COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4]), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(33)    (>(x1[3], 0)=TRUE∧684_0_parts_Return(x1[3])=684_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_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4])≥674_0_PARTS_GT(-(x1[4], 1), x3[4])∧(U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (33) using rules (I), (II), (III), (IV) which results in the following new constraint:
(34)    (>(x1[3], 0)=TRUE ⇒ COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥NonInfC∧COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])≥674_0_PARTS_GT(-(x1[3], 1), x3[3])∧(U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥))

We simplified constraint (34) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(35)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)Bound*bni_56] + [bni_56]x1[3] + [(-1)bni_56]x3[3] ≥ 0∧[1 + (-1)bso_57] ≥ 0)

We simplified constraint (35) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(36)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)Bound*bni_56] + [bni_56]x1[3] + [(-1)bni_56]x3[3] ≥ 0∧[1 + (-1)bso_57] ≥ 0)

We simplified constraint (36) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(37)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧[(-1)Bound*bni_56] + [bni_56]x1[3] + [(-1)bni_56]x3[3] ≥ 0∧[1 + (-1)bso_57] ≥ 0)

We simplified constraint (37) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(38)    (x1[3] + [-1] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧[(-1)bni_56] = 0∧[(-1)Bound*bni_56] + [bni_56]x1[3] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_57] ≥ 0)

We simplified constraint (38) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(39)    (x1[3] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧[(-1)bni_56] = 0∧[(-1)Bound*bni_56 + bni_56] + [bni_56]x1[3] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_57] ≥ 0)

For Pair 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_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 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]), COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]) which results in the following constraint:
(40)    (&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0))=TRUE∧x1[9]=x1[10]∧x0[9]=x0[10] ⇒ 674_0_PARTS_GT(x1[9], x0[9])≥NonInfC∧674_0_PARTS_GT(x1[9], x0[9])≥COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])∧(U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥))

We simplified constraint (40) using rules (IV), (IDP_BOOLEAN) which results in the following new constraint:
(41)    (>(x0[9], 0)=TRUE∧>(x1[9], x0[9])=TRUE∧>(x1[9], 0)=TRUE ⇒ 674_0_PARTS_GT(x1[9], x0[9])≥NonInfC∧674_0_PARTS_GT(x1[9], x0[9])≥COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])∧(U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥))

We simplified constraint (41) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(42)    (x0[9] + [-1] ≥ 0∧x1[9] + [-1] + [-1]x0[9] ≥ 0∧x1[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]x0[9] + [bni_58]x1[9] ≥ 0∧[(-1)bso_59] + [-1]x0[9] + x1[9] ≥ 0)

We simplified constraint (42) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(43)    (x0[9] + [-1] ≥ 0∧x1[9] + [-1] + [-1]x0[9] ≥ 0∧x1[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]x0[9] + [bni_58]x1[9] ≥ 0∧[(-1)bso_59] + [-1]x0[9] + x1[9] ≥ 0)

We simplified constraint (43) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(44)    (x0[9] + [-1] ≥ 0∧x1[9] + [-1] + [-1]x0[9] ≥ 0∧x1[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)Bound*bni_58] + [(-1)bni_58]x0[9] + [bni_58]x1[9] ≥ 0∧[(-1)bso_59] + [-1]x0[9] + x1[9] ≥ 0)

We simplified constraint (44) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(45)    (x0[9] ≥ 0∧x1[9] + [-2] + [-1]x0[9] ≥ 0∧x1[9] + [-1] ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)Bound*bni_58 + (-1)bni_58] + [(-1)bni_58]x0[9] + [bni_58]x1[9] ≥ 0∧[-1 + (-1)bso_59] + [-1]x0[9] + x1[9] ≥ 0)

We simplified constraint (45) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(46)    (x0[9] ≥ 0∧x1[9] ≥ 0∧[1] + x0[9] + x1[9] ≥ 0 ⇒ (U^Increasing(COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)Bound*bni_58 + bni_58] + [bni_58]x1[9] ≥ 0∧[1 + (-1)bso_59] + x1[9] ≥ 0)

For Pair COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]) the following chains were created:

We consider the chain COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]), 674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0]) which results in the following constraint:
(47)    (x0[10]=x1[0]∧x0[10]=x0[0] ⇒ COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (47) using rule (IV) which results in the following new constraint:
(48)    (COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (48) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(49)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_60] = 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (49) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(50)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_60] = 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (50) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(51)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_60] = 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (51) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(52)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_60] = 0∧0 = 0∧0 = 0∧[(-1)bso_61] ≥ 0)
We consider the chain COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10]), 674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9]) which results in the following constraint:
(53)    (x0[10]=x1[9]∧x0[10]=x0[9] ⇒ COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (53) using rule (IV) which results in the following new constraint:
(54)    (COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥NonInfC∧COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10])≥674_0_PARTS_GT(x0[10], x0[10])∧(U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥))

We simplified constraint (54) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(55)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_60] = 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (55) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(56)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_60] = 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (56) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(57)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_60] = 0∧[(-1)bso_61] ≥ 0)

We simplified constraint (57) using rule (IDP_UNRESTRICTED_VARS) which results in the following new constraint:
(58)    ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_60] = 0∧0 = 0∧0 = 0∧[(-1)bso_61] ≥ 0)

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

674_0_PARTS_GT(x1[0], x0[0]) → COND_674_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_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])), ≥)∧[(-1)Bound*bni_50] + [(-1)bni_50]x0[0] ≥ 0∧[(-1)bso_51] ≥ 0)
COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_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(769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])), ≥)∧[(-1)Bound*bni_52] ≥ 0∧[(-1)bso_53] ≥ 0)
769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
- (x1[3] ≥ 0 ⇒ (U^Increasing(COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])), ≥)∧0 = 0∧[(-1)bni_54] = 0∧[(-1)Bound*bni_54 + bni_54] + [bni_54]x1[3] ≥ 0∧0 = 0∧0 = 0∧[(-1)bso_55] ≥ 0)
COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4])
- (x1[3] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧[(-1)bni_56] = 0∧[(-1)Bound*bni_56 + bni_56] + [bni_56]x1[3] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_57] ≥ 0)
- (x1[3] ≥ 0 ⇒ (U^Increasing(674_0_PARTS_GT(-(x1[4], 1), x3[4])), ≥)∧0 = 0∧[(-1)bni_56] = 0∧[(-1)Bound*bni_56 + bni_56] + [bni_56]x1[3] ≥ 0∧0 = 0∧0 = 0∧[1 + (-1)bso_57] ≥ 0)
674_0_PARTS_GT(x1[9], x0[9]) → COND_674_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_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])), ≥)∧[(-1)Bound*bni_58 + bni_58] + [bni_58]x1[9] ≥ 0∧[1 + (-1)bso_59] + x1[9] ≥ 0)
COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10])
- ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_60] = 0∧0 = 0∧0 = 0∧[(-1)bso_61] ≥ 0)
- ((U^Increasing(674_0_PARTS_GT(x0[10], x0[10])), ≥)∧[bni_60] = 0∧0 = 0∧0 = 0∧[(-1)bso_61] ≥ 0)

POL(TRUE) = 0
POL(FALSE) = 0
POL(674_0_parts_GT(x₁, x₂)) = [-1] + [-1]x₁
POL(Cond_674_0_parts_GT(x₁, x₂, x₃)) = [-1] + [-1]x₂
POL(<=(x₁, x₂)) = [-1]
POL(0) = 0
POL(684_0_parts_Return(x₁)) = [-1] + [-1]x₁
POL(760_1_parts_InvokeMethod(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(1370_0_parts_Return(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(1492_0_parts_Return(x₁)) = [-1] + [-1]x₁
POL(1449_1_parts_InvokeMethod(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(+(x₁, x₂)) = x₁ + x₂
POL(674_0_PARTS_GT(x₁, x₂)) = [-1]x₂ + x₁
POL(COND_674_0_PARTS_GT(x₁, x₂, x₃)) = [-1]x₃ + x₂ + [-1]x₁
POL(&&(x₁, x₂)) = 0
POL(>(x₁, x₂)) = [-1]
POL(769_1_PARTS_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₂ + [-1]x₁
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(COND_769_1_PARTS_INVOKEMETHOD(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₃ + [-1]x₂
POL(1) = [1]
POL(COND_674_0_PARTS_GT1(x₁, x₂, x₃)) = 0

The following pairs are in P_>:

COND_769_1_PARTS_INVOKEMETHOD(TRUE, 684_0_parts_Return(x1[4]), x3[4], x0[4], x1[4]) → 674_0_PARTS_GT(-(x1[4], 1), x3[4])
674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])

The following pairs are in P_bound:

COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
674_0_PARTS_GT(x1[9], x0[9]) → COND_674_0_PARTS_GT1(&&(&&(>(x1[9], x0[9]), >(x1[9], 0)), >(x0[9], 0)), x1[9], x0[9])

The following pairs are in P_≥:

674_0_PARTS_GT(x1[0], x0[0]) → COND_674_0_PARTS_GT(&&(&&(>(x1[0], 0), <=(x1[0], x0[0])), >(x0[0], 0)), x1[0], x0[0])
COND_674_0_PARTS_GT(TRUE, x1[1], x0[1]) → 769_1_PARTS_INVOKEMETHOD(674_0_parts_GT(x1[1], -(x0[1], x1[1])), x0[1], -(x0[1], x1[1]), x1[1])
769_1_PARTS_INVOKEMETHOD(684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3]) → COND_769_1_PARTS_INVOKEMETHOD(>(x1[3], 0), 684_0_parts_Return(x1[3]), x3[3], x0[3], x1[3])
COND_674_0_PARTS_GT1(TRUE, x1[10], x0[10]) → 674_0_PARTS_GT(x0[10], x0[10])

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
Cond_674_0_parts_GT(<=(x0, 0), x1, x0)¹ → 674_0_parts_GT(x1, x0)¹
Cond_674_0_parts_GT(TRUE, x1, x0)¹ ↔ 684_0_parts_Return(x1)¹

(15) Complex Obligation (AND)

(16) Obligation:

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

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

The following domains are used:

Integer, Boolean

(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])

(1) -> (3), if (674_0_parts_GT(x1[1], x0[1] - x1[1]) →^* 684_0_parts_Return(x1[3])∧x0[1] →^* x3[3]∧x0[1] - x1[1] →^* x0[3]∧x1[1] →^* x1[3])

(17) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 4 less nodes.

(18) TRUE

(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:

Integer, Boolean

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

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

(3) -> (4), if (x1[3] > 0 ∧684_0_parts_Return(x1[3]) →^* 684_0_parts_Return(x1[4])∧x3[3] →^* x3[4]∧x0[3] →^* x0[4]∧x1[3] →^* x1[4])

(20) IDependencyGraphProof (EQUIVALENT transformation)

The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 4 less nodes.

(21) TRUE

(22) 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

(23) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 51 rules for P and 90 rules for R.

P rules:
439_0_main_Load(EOS(STATIC_439), java.lang.Object(ARRAY(i1)), i29, i29) → 441_0_main_ArrayLength(EOS(STATIC_441), java.lang.Object(ARRAY(i1)), i29, i29, java.lang.Object(ARRAY(i1)))
441_0_main_ArrayLength(EOS(STATIC_441), java.lang.Object(ARRAY(i1)), i29, i29, java.lang.Object(ARRAY(i1))) → 443_0_main_GT(EOS(STATIC_443), java.lang.Object(ARRAY(i1)), i29, i29, i1) | >=(i1, 0)
443_0_main_GT(EOS(STATIC_443), java.lang.Object(ARRAY(i1)), i29, i29, i1) → 446_0_main_GT(EOS(STATIC_446), java.lang.Object(ARRAY(i1)), i29, i29, i1)
446_0_main_GT(EOS(STATIC_446), java.lang.Object(ARRAY(i1)), i29, i29, i1) → 450_0_main_ConstantStackPush(EOS(STATIC_450), java.lang.Object(ARRAY(i1)), i29) | <=(i29, i1)
450_0_main_ConstantStackPush(EOS(STATIC_450), java.lang.Object(ARRAY(i1)), i29) → 454_0_main_Store(EOS(STATIC_454), java.lang.Object(ARRAY(i1)), i29, 0)
454_0_main_Store(EOS(STATIC_454), java.lang.Object(ARRAY(i1)), i29, matching1) → 456_0_main_Load(EOS(STATIC_456), java.lang.Object(ARRAY(i1)), i29, 0) | =(matching1, 0)
456_0_main_Load(EOS(STATIC_456), java.lang.Object(ARRAY(i1)), i29, matching1) → 523_0_main_Load(EOS(STATIC_523), java.lang.Object(ARRAY(i1)), i29, 0) | =(matching1, 0)
523_0_main_Load(EOS(STATIC_523), java.lang.Object(ARRAY(i1)), i39, i40) → 614_0_main_Load(EOS(STATIC_614), java.lang.Object(ARRAY(i1)), i39, i40)
614_0_main_Load(EOS(STATIC_614), java.lang.Object(ARRAY(i1)), i56, i57) → 744_0_main_Load(EOS(STATIC_744), java.lang.Object(ARRAY(i1)), i56, i57)
744_0_main_Load(EOS(STATIC_744), java.lang.Object(ARRAY(i1)), i81, i82) → 752_0_main_Load(EOS(STATIC_752), java.lang.Object(ARRAY(i1)), i81, i82, i82)
752_0_main_Load(EOS(STATIC_752), java.lang.Object(ARRAY(i1)), i81, i82, i82) → 757_0_main_ArrayLength(EOS(STATIC_757), java.lang.Object(ARRAY(i1)), i81, i82, i82, java.lang.Object(ARRAY(i1)))
757_0_main_ArrayLength(EOS(STATIC_757), java.lang.Object(ARRAY(i1)), i81, i82, i82, java.lang.Object(ARRAY(i1))) → 762_0_main_GT(EOS(STATIC_762), java.lang.Object(ARRAY(i1)), i81, i82, i82, i1) | >=(i1, 0)
762_0_main_GT(EOS(STATIC_762), java.lang.Object(ARRAY(i1)), i81, i82, i82, i1) → 767_0_main_GT(EOS(STATIC_767), java.lang.Object(ARRAY(i1)), i81, i82, i82, i1)
762_0_main_GT(EOS(STATIC_762), java.lang.Object(ARRAY(i1)), i81, i82, i82, i1) → 768_0_main_GT(EOS(STATIC_768), java.lang.Object(ARRAY(i1)), i81, i82, i82, i1)
767_0_main_GT(EOS(STATIC_767), java.lang.Object(ARRAY(i1)), i81, i82, i82, i1) → 771_0_main_Inc(EOS(STATIC_771), java.lang.Object(ARRAY(i1)), i81) | >(i82, i1)
771_0_main_Inc(EOS(STATIC_771), java.lang.Object(ARRAY(i1)), i81) → 780_0_main_JMP(EOS(STATIC_780), java.lang.Object(ARRAY(i1)), +(i81, 1))
780_0_main_JMP(EOS(STATIC_780), java.lang.Object(ARRAY(i1)), i92) → 788_0_main_Load(EOS(STATIC_788), java.lang.Object(ARRAY(i1)), i92)
788_0_main_Load(EOS(STATIC_788), java.lang.Object(ARRAY(i1)), i92) → 436_0_main_Load(EOS(STATIC_436), java.lang.Object(ARRAY(i1)), i92)
436_0_main_Load(EOS(STATIC_436), java.lang.Object(ARRAY(i1)), i29) → 439_0_main_Load(EOS(STATIC_439), java.lang.Object(ARRAY(i1)), i29, i29)
768_0_main_GT(EOS(STATIC_768), java.lang.Object(ARRAY(i1)), i81, i82, i82, i1) → 773_0_main_Load(EOS(STATIC_773), java.lang.Object(ARRAY(i1)), i81, i82) | <=(i82, i1)
773_0_main_Load(EOS(STATIC_773), java.lang.Object(ARRAY(i1)), i81, i82) → 782_0_main_Load(EOS(STATIC_782), java.lang.Object(ARRAY(i1)), i81, i82, i81)
782_0_main_Load(EOS(STATIC_782), java.lang.Object(ARRAY(i1)), i81, i82, i81) → 790_0_main_InvokeMethod(EOS(STATIC_790), java.lang.Object(ARRAY(i1)), i81, i82, i81, i82)
790_0_main_InvokeMethod(EOS(STATIC_790), java.lang.Object(ARRAY(i1)), i81, i82, i81, i82) → 798_1_main_InvokeMethod(798_0_parts_Load(EOS(STATIC_798), i81, i82), java.lang.Object(ARRAY(i1)), i81, i82, i81, i82)
798_1_main_InvokeMethod(684_0_parts_Return(EOS(STATIC_684), i102, i103, matching1), java.lang.Object(ARRAY(i1)), i102, i103, i102, i103) → 818_0_parts_Return(EOS(STATIC_818), java.lang.Object(ARRAY(i1)), i102, i103, i102, i103, i102, i103, 1) | =(matching1, 1)
798_1_main_InvokeMethod(706_0_parts_Return(EOS(STATIC_706), i104, matching1, matching2), java.lang.Object(ARRAY(i1)), i104, matching3, i104, matching4) → 819_0_parts_Return(EOS(STATIC_819), java.lang.Object(ARRAY(i1)), i104, 0, i104, 0, i104, 0, 0) | &&(&&(&&(=(matching1, 0), =(matching2, 0)), =(matching3, 0)), =(matching4, 0))
798_1_main_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), i617, i618, i568), java.lang.Object(ARRAY(i1)), i617, i618, i617, i618) → 1409_0_parts_Return(EOS(STATIC_1409), java.lang.Object(ARRAY(i1)), i617, i618, i617, i618, i617, i618, i568)
798_1_main_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), i672, i673, i623), java.lang.Object(ARRAY(i1)), i672, i673, i672, i673) → 1443_0_parts_Return(EOS(STATIC_1443), java.lang.Object(ARRAY(i1)), i672, i673, i672, i673, i672, i673, i623)
798_1_main_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), i727), java.lang.Object(ARRAY(i1)), i736, i737, i736, i737) → 1508_0_parts_Return(EOS(STATIC_1508), java.lang.Object(ARRAY(i1)), i736, i737, i736, i737, i727)
818_0_parts_Return(EOS(STATIC_818), java.lang.Object(ARRAY(i1)), i102, i103, i102, i103, i102, i103, matching1) → 823_0_main_StackPop(EOS(STATIC_823), java.lang.Object(ARRAY(i1)), i102, i103, 1) | =(matching1, 1)
823_0_main_StackPop(EOS(STATIC_823), java.lang.Object(ARRAY(i1)), i102, i103, matching1) → 829_0_main_Inc(EOS(STATIC_829), java.lang.Object(ARRAY(i1)), i102, i103) | =(matching1, 1)
829_0_main_Inc(EOS(STATIC_829), java.lang.Object(ARRAY(i1)), i102, i103) → 835_0_main_JMP(EOS(STATIC_835), java.lang.Object(ARRAY(i1)), i102, +(i103, 1)) | >=(i103, 0)
835_0_main_JMP(EOS(STATIC_835), java.lang.Object(ARRAY(i1)), i102, i106) → 843_0_main_Load(EOS(STATIC_843), java.lang.Object(ARRAY(i1)), i102, i106)
843_0_main_Load(EOS(STATIC_843), java.lang.Object(ARRAY(i1)), i102, i106) → 744_0_main_Load(EOS(STATIC_744), java.lang.Object(ARRAY(i1)), i102, i106)
819_0_parts_Return(EOS(STATIC_819), java.lang.Object(ARRAY(i1)), i104, matching1, i104, matching2, i104, matching3, matching4) → 826_0_main_StackPop(EOS(STATIC_826), java.lang.Object(ARRAY(i1)), i104, 0, 0) | &&(&&(&&(=(matching1, 0), =(matching2, 0)), =(matching3, 0)), =(matching4, 0))
826_0_main_StackPop(EOS(STATIC_826), java.lang.Object(ARRAY(i1)), i104, matching1, matching2) → 832_0_main_Inc(EOS(STATIC_832), java.lang.Object(ARRAY(i1)), i104, 0) | &&(=(matching1, 0), =(matching2, 0))
832_0_main_Inc(EOS(STATIC_832), java.lang.Object(ARRAY(i1)), i104, matching1) → 838_0_main_JMP(EOS(STATIC_838), java.lang.Object(ARRAY(i1)), i104, 1) | =(matching1, 0)
838_0_main_JMP(EOS(STATIC_838), java.lang.Object(ARRAY(i1)), i104, matching1) → 846_0_main_Load(EOS(STATIC_846), java.lang.Object(ARRAY(i1)), i104, 1) | =(matching1, 1)
846_0_main_Load(EOS(STATIC_846), java.lang.Object(ARRAY(i1)), i104, matching1) → 744_0_main_Load(EOS(STATIC_744), java.lang.Object(ARRAY(i1)), i104, 1) | =(matching1, 1)
1409_0_parts_Return(EOS(STATIC_1409), java.lang.Object(ARRAY(i1)), i617, i618, i617, i618, i617, i618, i568) → 1410_0_parts_Return(EOS(STATIC_1410), java.lang.Object(ARRAY(i1)), i617, i618, i617, i618, i617, i618, i568)
1410_0_parts_Return(EOS(STATIC_1410), java.lang.Object(ARRAY(i1)), i648, i649, i648, i649, i648, i649, i650) → 1421_0_main_StackPop(EOS(STATIC_1421), java.lang.Object(ARRAY(i1)), i648, i649, i650)
1421_0_main_StackPop(EOS(STATIC_1421), java.lang.Object(ARRAY(i1)), i648, i649, i650) → 1426_0_main_Inc(EOS(STATIC_1426), java.lang.Object(ARRAY(i1)), i648, i649)
1426_0_main_Inc(EOS(STATIC_1426), java.lang.Object(ARRAY(i1)), i648, i649) → 1437_0_main_JMP(EOS(STATIC_1437), java.lang.Object(ARRAY(i1)), i648, +(i649, 1)) | >(i649, 0)
1437_0_main_JMP(EOS(STATIC_1437), java.lang.Object(ARRAY(i1)), i648, i674) → 1446_0_main_Load(EOS(STATIC_1446), java.lang.Object(ARRAY(i1)), i648, i674)
1446_0_main_Load(EOS(STATIC_1446), java.lang.Object(ARRAY(i1)), i648, i674) → 744_0_main_Load(EOS(STATIC_744), java.lang.Object(ARRAY(i1)), i648, i674)
1443_0_parts_Return(EOS(STATIC_1443), java.lang.Object(ARRAY(i1)), i672, i673, i672, i673, i672, i673, i623) → 1410_0_parts_Return(EOS(STATIC_1410), java.lang.Object(ARRAY(i1)), i672, i673, i672, i673, i672, i673, i623)
1508_0_parts_Return(EOS(STATIC_1508), java.lang.Object(ARRAY(i1)), i736, i737, i736, i737, i727) → 1365_0_parts_Return(EOS(STATIC_1365), java.lang.Object(ARRAY(i1)), i736, i737, i736, i737, i727)
1365_0_parts_Return(EOS(STATIC_1365), java.lang.Object(ARRAY(i1)), i590, i591, i590, i591, i589) → 1376_0_main_StackPop(EOS(STATIC_1376), java.lang.Object(ARRAY(i1)), i590, i591, i589)
1376_0_main_StackPop(EOS(STATIC_1376), java.lang.Object(ARRAY(i1)), i590, i591, i589) → 1381_0_main_Inc(EOS(STATIC_1381), java.lang.Object(ARRAY(i1)), i590, i591)
1381_0_main_Inc(EOS(STATIC_1381), java.lang.Object(ARRAY(i1)), i590, i591) → 1393_0_main_JMP(EOS(STATIC_1393), java.lang.Object(ARRAY(i1)), i590, +(i591, 1)) | >(i591, 0)
1393_0_main_JMP(EOS(STATIC_1393), java.lang.Object(ARRAY(i1)), i590, i619) → 1413_0_main_Load(EOS(STATIC_1413), java.lang.Object(ARRAY(i1)), i590, i619)
1413_0_main_Load(EOS(STATIC_1413), java.lang.Object(ARRAY(i1)), i590, i619) → 744_0_main_Load(EOS(STATIC_744), java.lang.Object(ARRAY(i1)), i590, i619)
R rules:
798_0_parts_Load(EOS(STATIC_798), i81, i82) → 802_0_parts_Load(EOS(STATIC_802), i81, i82)
802_0_parts_Load(EOS(STATIC_802), i81, i82) → 671_0_parts_Load(EOS(STATIC_671), i81, i82)
765_0_parts_Load(EOS(STATIC_765), i74, i74) → 671_0_parts_Load(EOS(STATIC_671), i74, i74)
775_0_parts_Load(EOS(STATIC_775), i76) → 671_0_parts_Load(EOS(STATIC_671), i86, i76)
1450_0_parts_Load(EOS(STATIC_1450), i74) → 671_0_parts_Load(EOS(STATIC_671), i74, i685)
671_0_parts_Load(EOS(STATIC_671), i69, i70) → 674_0_parts_GT(EOS(STATIC_674), i69, i70, i69)
674_0_parts_GT(EOS(STATIC_674), i73, i70, i73) → 677_0_parts_GT(EOS(STATIC_677), i73, i70, i73)
674_0_parts_GT(EOS(STATIC_674), i74, i70, i74) → 678_0_parts_GT(EOS(STATIC_678), i74, i70, i74)
677_0_parts_GT(EOS(STATIC_677), i73, i70, i73) → 680_0_parts_ConstantStackPush(EOS(STATIC_680), i73, i70) | <=(i73, 0)
678_0_parts_GT(EOS(STATIC_678), i74, i70, i74) → 682_0_parts_Load(EOS(STATIC_682), i74, i70) | >(i74, 0)
680_0_parts_ConstantStackPush(EOS(STATIC_680), i73, i70) → 684_0_parts_Return(EOS(STATIC_684), i73, i70, 1)
682_0_parts_Load(EOS(STATIC_682), i74, i70) → 687_0_parts_GT(EOS(STATIC_687), i74, i70, i70)
687_0_parts_GT(EOS(STATIC_687), i74, matching1, matching2) → 692_0_parts_GT(EOS(STATIC_692), i74, 0, 0) | &&(=(matching1, 0), =(matching2, 0))
687_0_parts_GT(EOS(STATIC_687), i74, i76, i76) → 693_0_parts_GT(EOS(STATIC_693), i74, i76, i76)
692_0_parts_GT(EOS(STATIC_692), i74, matching1, matching2) → 700_0_parts_ConstantStackPush(EOS(STATIC_700), i74, 0) | &&(&&(<=(0, 0), =(matching1, 0)), =(matching2, 0))
693_0_parts_GT(EOS(STATIC_693), i74, i76, i76) → 703_0_parts_Load(EOS(STATIC_703), i74, i76) | >(i76, 0)
700_0_parts_ConstantStackPush(EOS(STATIC_700), i74, matching1) → 706_0_parts_Return(EOS(STATIC_706), i74, 0, 0) | =(matching1, 0)
703_0_parts_Load(EOS(STATIC_703), i74, i76) → 708_0_parts_Load(EOS(STATIC_708), i74, i76, i76)
708_0_parts_Load(EOS(STATIC_708), i74, i76, i76) → 715_0_parts_LE(EOS(STATIC_715), i74, i76, i76, i74)
715_0_parts_LE(EOS(STATIC_715), i74, i76, i76, i74) → 725_0_parts_LE(EOS(STATIC_725), i74, i76, i76, i74)
715_0_parts_LE(EOS(STATIC_715), i74, i76, i76, i74) → 726_0_parts_LE(EOS(STATIC_726), i74, i76, i76, i74)
725_0_parts_LE(EOS(STATIC_725), i74, i76, i76, i74) → 731_0_parts_Load(EOS(STATIC_731), i74, i76) | <=(i76, i74)
726_0_parts_LE(EOS(STATIC_726), i74, i76, i76, i74) → 733_0_parts_Load(EOS(STATIC_733), i74, i76) | >(i76, i74)
731_0_parts_Load(EOS(STATIC_731), i74, i76) → 747_0_parts_Load(EOS(STATIC_747), i74, i76, i74)
733_0_parts_Load(EOS(STATIC_733), i74, i76) → 749_0_parts_Load(EOS(STATIC_749), i74, i76, i74)
747_0_parts_Load(EOS(STATIC_747), i74, i76, i74) → 753_0_parts_IntArithmetic(EOS(STATIC_753), i74, i76, i74, i76)
749_0_parts_Load(EOS(STATIC_749), i74, i76, i74) → 755_0_parts_InvokeMethod(EOS(STATIC_755), i74, i76, i74, i74)
753_0_parts_IntArithmetic(EOS(STATIC_753), i74, i76, i74, i76) → 758_0_parts_Load(EOS(STATIC_758), i74, i76) | &&(>(i74, 0), >(i76, 0))
755_0_parts_InvokeMethod(EOS(STATIC_755), i74, i76, i74, i74) → 760_1_parts_InvokeMethod(760_0_parts_Load(EOS(STATIC_760), i74, i74), i74, i76, i74, i74)
758_0_parts_Load(EOS(STATIC_758), i74, i76) → 763_0_parts_InvokeMethod(EOS(STATIC_763), i74, i76, i76)
760_0_parts_Load(EOS(STATIC_760), i74, i74) → 765_0_parts_Load(EOS(STATIC_765), i74, i74)
760_1_parts_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), i613, i613, i568), i613, i76, i613, i613) → 1397_0_parts_Return(EOS(STATIC_1397), i613, i76, i613, i613, i613, i613, i568)
760_1_parts_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), i668, i668, i623), i668, i76, i668, i668) → 1439_0_parts_Return(EOS(STATIC_1439), i668, i76, i668, i668, i668, i668, i623)
760_1_parts_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), i727), i733, i76, i733, i733) → 1504_0_parts_Return(EOS(STATIC_1504), i733, i76, i733, i733, i727)
763_0_parts_InvokeMethod(EOS(STATIC_763), i74, i76, i76) → 769_1_parts_InvokeMethod(769_0_parts_Load(EOS(STATIC_769), i76), i74, i76, i76)
769_0_parts_Load(EOS(STATIC_769), i76) → 775_0_parts_Load(EOS(STATIC_775), i76)
769_1_parts_InvokeMethod(684_0_parts_Return(EOS(STATIC_684), i96, i97, matching1), i74, i97, i97) → 799_0_parts_Return(EOS(STATIC_799), i74, i97, i97, i97, 1) | =(matching1, 1)
769_1_parts_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), i615, i616, i568), i74, i616, i616) → 1403_0_parts_Return(EOS(STATIC_1403), i74, i616, i616, i616, i568)
769_1_parts_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), i670, i671, i623), i74, i671, i671) → 1440_0_parts_Return(EOS(STATIC_1440), i74, i671, i671, i671, i623)
769_1_parts_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), i727), i74, i735, i735) → 1506_0_parts_Return(EOS(STATIC_1506), i74, i735, i735, i727)
799_0_parts_Return(EOS(STATIC_799), i74, i97, i97, i97, matching1) → 804_0_parts_Load(EOS(STATIC_804), i74, i97, 1) | =(matching1, 1)
804_0_parts_Load(EOS(STATIC_804), i74, i97, matching1) → 885_0_parts_Load(EOS(STATIC_885), i74, i97, 1) | =(matching1, 1)
876_0_parts_Return(EOS(STATIC_876), i116, i76, i116, i116, matching1) → 1044_0_parts_Return(EOS(STATIC_1044), i116, i76, i116, i116, 1) | =(matching1, 1)
877_0_parts_Return(EOS(STATIC_877), i74, i118, i118, matching1) → 1051_0_parts_Return(EOS(STATIC_1051), i74, i118, i118, 1) | =(matching1, 1)
885_0_parts_Load(EOS(STATIC_885), i74, i118, matching1) → 926_0_parts_Load(EOS(STATIC_926), i74, i118, 1) | =(matching1, 1)
912_0_parts_Return(EOS(STATIC_912), i129, i76, i129, i129, i129, i129, matching1) → 1096_0_parts_Return(EOS(STATIC_1096), i129, i76, i129, i129, i129, i129, 1) | =(matching1, 1)
913_0_parts_Return(EOS(STATIC_913), i74, i132, i132, i132, matching1) → 1104_0_parts_Return(EOS(STATIC_1104), i74, i132, i132, i132, 1) | =(matching1, 1)
926_0_parts_Load(EOS(STATIC_926), i74, i132, matching1) → 1069_0_parts_Load(EOS(STATIC_1069), i74, i132, 1) | =(matching1, 1)
1044_0_parts_Return(EOS(STATIC_1044), i199, i76, i199, i199, i200) → 1207_0_parts_Return(EOS(STATIC_1207), i199, i76, i199, i199, i200)
1051_0_parts_Return(EOS(STATIC_1051), i74, i211, i211, i212) → 1212_0_parts_Return(EOS(STATIC_1212), i74, i211, i211, i212)
1069_0_parts_Load(EOS(STATIC_1069), i74, i211, i212) → 1120_0_parts_Load(EOS(STATIC_1120), i74, i211, i212)
1096_0_parts_Return(EOS(STATIC_1096), i271, i76, i271, i271, i271, i271, i272) → 1248_0_parts_Return(EOS(STATIC_1248), i271, i76, i271, i271, i271, i271, i272)
1104_0_parts_Return(EOS(STATIC_1104), i74, i282, i282, i282, i284) → 1254_0_parts_Return(EOS(STATIC_1254), i74, i282, i282, i282, i284)
1120_0_parts_Load(EOS(STATIC_1120), i74, i282, i284) → 1226_0_parts_Load(EOS(STATIC_1226), i74, i282, i284)
1207_0_parts_Return(EOS(STATIC_1207), i385, i76, i385, i385, i386) → 1349_0_parts_Return(EOS(STATIC_1349), i385, i76, i385, i385, i386)
1212_0_parts_Return(EOS(STATIC_1212), i74, i397, i397, i398) → 1357_0_parts_Return(EOS(STATIC_1357), i74, i397, i397, i398)
1226_0_parts_Load(EOS(STATIC_1226), i74, i397, i398) → 1268_0_parts_Load(EOS(STATIC_1268), i74, i397, i398)
1248_0_parts_Return(EOS(STATIC_1248), i458, i76, i458, i458, i458, i458, i459) → 1398_0_parts_Return(EOS(STATIC_1398), i458, i76, i458, i458, i458, i458, i459)
1254_0_parts_Return(EOS(STATIC_1254), i74, i469, i469, i469, i471) → 1404_0_parts_Return(EOS(STATIC_1404), i74, i469, i469, i469, i471)
1268_0_parts_Load(EOS(STATIC_1268), i74, i469, i471) → 1372_0_parts_Load(EOS(STATIC_1372), i74, i469, i471)
1349_0_parts_Return(EOS(STATIC_1349), i567, i76, i567, i567, i568) → 1370_0_parts_Return(EOS(STATIC_1370), i567, i76, i568)
1357_0_parts_Return(EOS(STATIC_1357), i74, i577, i577, i578) → 1372_0_parts_Load(EOS(STATIC_1372), i74, i577, i578)
1370_0_parts_Return(EOS(STATIC_1370), i567, i76, i568) → 1416_0_parts_Return(EOS(STATIC_1416), i567, i76, i568)
1372_0_parts_Load(EOS(STATIC_1372), i74, i577, i578) → 1419_0_parts_Load(EOS(STATIC_1419), i74, i577, i578)
1397_0_parts_Return(EOS(STATIC_1397), i613, i76, i613, i613, i613, i613, i568) → 1398_0_parts_Return(EOS(STATIC_1398), i613, i76, i613, i613, i613, i613, i568)
1398_0_parts_Return(EOS(STATIC_1398), i622, i76, i622, i622, i622, i622, i623) → 1416_0_parts_Return(EOS(STATIC_1416), i622, i76, i623)
1403_0_parts_Return(EOS(STATIC_1403), i74, i616, i616, i616, i568) → 1404_0_parts_Return(EOS(STATIC_1404), i74, i616, i616, i616, i568)
1404_0_parts_Return(EOS(STATIC_1404), i74, i633, i633, i633, i635) → 1419_0_parts_Load(EOS(STATIC_1419), i74, i633, i635)
1419_0_parts_Load(EOS(STATIC_1419), i74, i633, i635) → 1424_0_parts_Load(EOS(STATIC_1424), i633, i635, i74)
1424_0_parts_Load(EOS(STATIC_1424), i633, i635, i74) → 1435_0_parts_ConstantStackPush(EOS(STATIC_1435), i635, i74, i633)
1435_0_parts_ConstantStackPush(EOS(STATIC_1435), i635, i74, i633) → 1444_0_parts_IntArithmetic(EOS(STATIC_1444), i635, i74, i633)
1439_0_parts_Return(EOS(STATIC_1439), i668, i76, i668, i668, i668, i668, i623) → 1398_0_parts_Return(EOS(STATIC_1398), i668, i76, i668, i668, i668, i668, i623)
1440_0_parts_Return(EOS(STATIC_1440), i74, i671, i671, i671, i623) → 1404_0_parts_Return(EOS(STATIC_1404), i74, i671, i671, i671, i623)
1444_0_parts_IntArithmetic(EOS(STATIC_1444), i635, i74, i633) → 1448_0_parts_InvokeMethod(EOS(STATIC_1448), i635, i74) | >(i633, 0)
1448_0_parts_InvokeMethod(EOS(STATIC_1448), i635, i74) → 1449_1_parts_InvokeMethod(1449_0_parts_Load(EOS(STATIC_1449), i74), i635, i74)
1449_0_parts_Load(EOS(STATIC_1449), i74) → 1450_0_parts_Load(EOS(STATIC_1450), i74)
1449_1_parts_InvokeMethod(706_0_parts_Return(EOS(STATIC_706), i689, matching1, matching2), i635, i689) → 1460_0_parts_Return(EOS(STATIC_1460), i635, i689, 0, i689, 0, 0) | &&(=(matching1, 0), =(matching2, 0))
1449_1_parts_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), i690, i691, i568), i635, i690) → 1461_0_parts_Return(EOS(STATIC_1461), i635, i690, i690, i568)
1449_1_parts_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), i692, i693, i623), i635, i692) → 1464_0_parts_Return(EOS(STATIC_1464), i635, i692, i692, i623)
1449_1_parts_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), i727), i635, i739) → 1510_0_parts_Return(EOS(STATIC_1510), i635, i739, i727)
1460_0_parts_Return(EOS(STATIC_1460), i635, i689, matching1, i689, matching2, matching3) → 1465_0_parts_IntArithmetic(EOS(STATIC_1465), i635, 0) | &&(&&(=(matching1, 0), =(matching2, 0)), =(matching3, 0))
1461_0_parts_Return(EOS(STATIC_1461), i635, i690, i690, i568) → 1467_0_parts_IntArithmetic(EOS(STATIC_1467), i635, i568)
1464_0_parts_Return(EOS(STATIC_1464), i635, i692, i692, i623) → 1461_0_parts_Return(EOS(STATIC_1461), i635, i692, i692, i623)
1465_0_parts_IntArithmetic(EOS(STATIC_1465), i635, matching1) → 1467_0_parts_IntArithmetic(EOS(STATIC_1467), i635, 0) | =(matching1, 0)
1467_0_parts_IntArithmetic(EOS(STATIC_1467), i635, i568) → 1490_0_parts_IntArithmetic(EOS(STATIC_1490), i635, i568)
1487_0_parts_Return(EOS(STATIC_1487), i635, i715, i703) → 1490_0_parts_IntArithmetic(EOS(STATIC_1490), i635, i703)
1490_0_parts_IntArithmetic(EOS(STATIC_1490), i635, i703) → 1492_0_parts_Return(EOS(STATIC_1492), +(i635, i703))
1504_0_parts_Return(EOS(STATIC_1504), i733, i76, i733, i733, i727) → 1349_0_parts_Return(EOS(STATIC_1349), i733, i76, i733, i733, i727)
1506_0_parts_Return(EOS(STATIC_1506), i74, i735, i735, i727) → 1357_0_parts_Return(EOS(STATIC_1357), i74, i735, i735, i727)
1510_0_parts_Return(EOS(STATIC_1510), i635, i739, i727) → 1487_0_parts_Return(EOS(STATIC_1487), i635, i739, i727)

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

P rules:
762_0_main_GT(EOS(STATIC_762), java.lang.Object(ARRAY(x0)), x1, x2, x2, x0) → 762_0_main_GT(EOS(STATIC_762), java.lang.Object(ARRAY(x0)), +(x1, 1), 0, 0, x0) | &&(&&(>(x2, x0), >(+(x0, 1), 0)), >=(x0, +(x1, 1)))
762_0_main_GT(EOS(STATIC_762), java.lang.Object(ARRAY(x0)), x1, x2, x2, x0) → 798_1_main_InvokeMethod(798_0_parts_Load(EOS(STATIC_798), x1, x2), java.lang.Object(ARRAY(x0)), x1, x2, x1, x2) | <=(x2, x0)
798_1_main_InvokeMethod(684_0_parts_Return(EOS(STATIC_684), x0, x1, 1), java.lang.Object(ARRAY(x3)), x0, x1, x0, x1) → 762_0_main_GT(EOS(STATIC_762), java.lang.Object(ARRAY(x3)), x0, +(x1, 1), +(x1, 1), x3) | &&(>(+(x3, 1), 0), >(+(x1, 1), 0))
798_1_main_InvokeMethod(706_0_parts_Return(EOS(STATIC_706), x0, 0, 0), java.lang.Object(ARRAY(x3)), x0, 0, x0, 0) → 762_0_main_GT(EOS(STATIC_762), java.lang.Object(ARRAY(x3)), x0, 1, 1, x3) | >(+(x3, 1), 0)
798_1_main_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), x0, x1, x2), java.lang.Object(ARRAY(x3)), x0, x1, x0, x1) → 762_0_main_GT(EOS(STATIC_762), java.lang.Object(ARRAY(x3)), x0, +(x1, 1), +(x1, 1), x3) | &&(>(+(x3, 1), 0), >(x1, 0))
798_1_main_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), x0, x1, x2), java.lang.Object(ARRAY(x3)), x0, x1, x0, x1) → 762_0_main_GT(EOS(STATIC_762), java.lang.Object(ARRAY(x3)), x0, +(x1, 1), +(x1, 1), x3) | &&(>(+(x3, 1), 0), >(x1, 0))
798_1_main_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), x0), java.lang.Object(ARRAY(x1)), x2, x3, x2, x3) → 762_0_main_GT(EOS(STATIC_762), java.lang.Object(ARRAY(x1)), x2, +(x3, 1), +(x3, 1), x1) | &&(>(x3, 0), >(+(x1, 1), 0))
R rules:
798_0_parts_Load(EOS(STATIC_798), x0, x1) → 674_0_parts_GT(EOS(STATIC_674), x0, x1, x0)
674_0_parts_GT(EOS(STATIC_674), x0, x1, x0) → 684_0_parts_Return(EOS(STATIC_684), x0, x1, 1) | <=(x0, 0)
674_0_parts_GT(EOS(STATIC_674), x0, 0, x0) → 706_0_parts_Return(EOS(STATIC_706), x0, 0, 0) | >(x0, 0)
674_0_parts_GT(EOS(STATIC_674), x0, x1, x0) → 760_1_parts_InvokeMethod(674_0_parts_GT(EOS(STATIC_674), x0, x0, x0), x0, x1, x0, x0) | &&(&&(>(x1, x0), >(x1, 0)), >(x0, 0))
674_0_parts_GT(EOS(STATIC_674), x0, x1, x0) → 769_1_parts_InvokeMethod(674_0_parts_GT(EOS(STATIC_674), x2, x1, x2), x0, x1, x1) | &&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0))
760_1_parts_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), x0, x0, x1), x0, x2, x0, x0) → 1416_0_parts_Return(EOS(STATIC_1416), x0, x2, x1)
760_1_parts_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), x0, x0, x1), x0, x2, x0, x0) → 1416_0_parts_Return(EOS(STATIC_1416), x0, x2, x1)
760_1_parts_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), x0), x1, x2, x1, x1) → 1416_0_parts_Return(EOS(STATIC_1416), x1, x2, x0)
769_1_parts_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), x0, x1, x2), x3, x1, x1) → 1449_1_parts_InvokeMethod(674_0_parts_GT(EOS(STATIC_674), x3, x4, x3), x2, x3) | >(x1, 0)
769_1_parts_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), x0, x1, x2), x3, x1, x1) → 1449_1_parts_InvokeMethod(674_0_parts_GT(EOS(STATIC_674), x3, x4, x3), x2, x3) | >(x1, 0)
769_1_parts_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), x0), x1, x2, x2) → 1449_1_parts_InvokeMethod(674_0_parts_GT(EOS(STATIC_674), x1, x3, x1), x0, x1) | >(x2, 0)
769_1_parts_InvokeMethod(684_0_parts_Return(EOS(STATIC_684), x0, x1, 1), x3, x1, x1) → 1449_1_parts_InvokeMethod(674_0_parts_GT(EOS(STATIC_674), x3, x4, x3), 1, x3) | >(x1, 0)
1449_1_parts_InvokeMethod(1370_0_parts_Return(EOS(STATIC_1370), x0, x1, x2), x3, x0) → 1492_0_parts_Return(EOS(STATIC_1492), +(x3, x2))
1449_1_parts_InvokeMethod(1416_0_parts_Return(EOS(STATIC_1416), x0, x1, x2), x3, x0) → 1492_0_parts_Return(EOS(STATIC_1492), +(x3, x2))
1449_1_parts_InvokeMethod(706_0_parts_Return(EOS(STATIC_706), x0, 0, 0), arith[1], x0) → 1492_0_parts_Return(EOS(STATIC_1492), arith[1])
1449_1_parts_InvokeMethod(1492_0_parts_Return(EOS(STATIC_1492), x0), x1, x2) → 1492_0_parts_Return(EOS(STATIC_1492), +(x1, x0))

Filtered ground terms:

762_0_main_GT(x1, x2, x3, x4, x5, x6) → 762_0_main_GT(x2, x3, x4, x5, x6)
1492_0_parts_Return(x1, x2) → 1492_0_parts_Return(x2)
1416_0_parts_Return(x1, x2, x3, x4) → 1416_0_parts_Return(x2, x3, x4)
1370_0_parts_Return(x1, x2, x3, x4) → 1370_0_parts_Return(x2, x3, x4)
Cond_798_1_main_InvokeMethod1(x1, x2, x3, x4, x5, x6, x7) → Cond_798_1_main_InvokeMethod1(x1, x2, x3, x4, x6)
706_0_parts_Return(x1, x2, x3, x4) → 706_0_parts_Return(x2)
684_0_parts_Return(x1, x2, x3, x4) → 684_0_parts_Return(x2, x3)
798_0_parts_Load(x1, x2, x3) → 798_0_parts_Load(x2, x3)
Cond_762_0_main_GT1(x1, x2, x3, x4, x5, x6, x7) → Cond_762_0_main_GT1(x1, x3, x4, x5, x6, x7)
Cond_762_0_main_GT(x1, x2, x3, x4, x5, x6, x7) → Cond_762_0_main_GT(x1, x3, x4, x5, x6, x7)
674_0_parts_GT(x1, x2, x3, x4) → 674_0_parts_GT(x2, x3, x4)
Cond_674_0_parts_GT3(x1, x2, x3, x4, x5, x6) → Cond_674_0_parts_GT3(x1, x3, x4, x5, x6)
Cond_674_0_parts_GT2(x1, x2, x3, x4, x5) → Cond_674_0_parts_GT2(x1, x3, x4, x5)
Cond_674_0_parts_GT1(x1, x2, x3, x4, x5) → Cond_674_0_parts_GT1(x1, x3, x5)
Cond_674_0_parts_GT(x1, x2, x3, x4, x5) → Cond_674_0_parts_GT(x1, x3, x4, x5)

Filtered duplicate args:

762_0_main_GT(x1, x2, x3, x4, x5) → 762_0_main_GT(x1, x2, x4)
Cond_762_0_main_GT(x1, x2, x3, x4, x5, x6) → Cond_762_0_main_GT(x1, x2, x3, x5)
Cond_762_0_main_GT1(x1, x2, x3, x4, x5, x6) → Cond_762_0_main_GT1(x1, x2, x3, x5)
798_1_main_InvokeMethod(x1, x2, x3, x4, x5, x6) → 798_1_main_InvokeMethod(x1, x2, x5, x6)
Cond_798_1_main_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → Cond_798_1_main_InvokeMethod(x1, x2, x3)
Cond_798_1_main_InvokeMethod1(x1, x2, x3, x4, x5) → Cond_798_1_main_InvokeMethod1(x1, x2, x3)
Cond_798_1_main_InvokeMethod2(x1, x2, x3, x4, x5, x6, x7) → Cond_798_1_main_InvokeMethod2(x1, x2, x3)
Cond_798_1_main_InvokeMethod3(x1, x2, x3, x4, x5, x6, x7) → Cond_798_1_main_InvokeMethod3(x1, x2, x3)
Cond_798_1_main_InvokeMethod4(x1, x2, x3, x4, x5, x6, x7) → Cond_798_1_main_InvokeMethod4(x1, x2, x3, x6, x7)
674_0_parts_GT(x1, x2, x3) → 674_0_parts_GT(x2, x3)
Cond_674_0_parts_GT(x1, x2, x3, x4) → Cond_674_0_parts_GT(x1, x3, x4)
Cond_674_0_parts_GT1(x1, x2, x3) → Cond_674_0_parts_GT1(x1, x3)
Cond_674_0_parts_GT2(x1, x2, x3, x4) → Cond_674_0_parts_GT2(x1, x3, x4)
760_1_parts_InvokeMethod(x1, x2, x3, x4, x5) → 760_1_parts_InvokeMethod(x1, x3, x5)
Cond_674_0_parts_GT3(x1, x2, x3, x4, x5) → Cond_674_0_parts_GT3(x1, x3, x4, x5)
769_1_parts_InvokeMethod(x1, x2, x3, x4) → 769_1_parts_InvokeMethod(x1, x2, x4)
Cond_769_1_parts_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_769_1_parts_InvokeMethod(x1, x2, x3, x6)
Cond_769_1_parts_InvokeMethod1(x1, x2, x3, x4, x5, x6) → Cond_769_1_parts_InvokeMethod1(x1, x2, x3, x6)
Cond_769_1_parts_InvokeMethod2(x1, x2, x3, x4, x5, x6) → Cond_769_1_parts_InvokeMethod2(x1, x2, x3, x5, x6)
Cond_769_1_parts_InvokeMethod3(x1, x2, x3, x4, x5, x6) → Cond_769_1_parts_InvokeMethod3(x1, x2, x3, x6)

Filtered unneeded arguments:

Cond_762_0_main_GT(x1, x2, x3, x4) → Cond_762_0_main_GT(x1, x2, x3)
Cond_798_1_main_InvokeMethod4(x1, x2, x3, x4, x5) → Cond_798_1_main_InvokeMethod4(x1, x3, x4, x5)
1370_0_parts_Return(x1, x2, x3) → 1370_0_parts_Return(x1, x2)
1416_0_parts_Return(x1, x2, x3) → 1416_0_parts_Return(x1, x2)
Cond_769_1_parts_InvokeMethod(x1, x2, x3, x4) → Cond_769_1_parts_InvokeMethod(x1, x3, x4)
1449_1_parts_InvokeMethod(x1, x2, x3) → 1449_1_parts_InvokeMethod(x1, x3)
Cond_769_1_parts_InvokeMethod1(x1, x2, x3, x4) → Cond_769_1_parts_InvokeMethod1(x1, x3, x4)
Cond_769_1_parts_InvokeMethod2(x1, x2, x3, x4, x5) → Cond_769_1_parts_InvokeMethod2(x1, x3, x5)
Cond_769_1_parts_InvokeMethod3(x1, x2, x3, x4) → Cond_769_1_parts_InvokeMethod3(x1, x3, x4)

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

P rules:
762_0_main_GT(java.lang.Object(ARRAY(x0)), x1, x2) → 762_0_main_GT(java.lang.Object(ARRAY(x0)), +(x1, 1), 0) | &&(&&(>(x2, x0), >=(x0, +(x1, 1))), >(x0, -1))
762_0_main_GT(java.lang.Object(ARRAY(x0)), x1, x2) → 798_1_main_InvokeMethod(798_0_parts_Load(x1, x2), java.lang.Object(ARRAY(x0)), x1, x2) | <=(x2, x0)
798_1_main_InvokeMethod(684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 762_0_main_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1)) | &&(>(x3, -1), >(x1, -1))
798_1_main_InvokeMethod(706_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → 762_0_main_GT(java.lang.Object(ARRAY(x3)), x0, 1) | >(x3, -1)
798_1_main_InvokeMethod(1370_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 762_0_main_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1)) | &&(>(x3, -1), >(x1, 0))
798_1_main_InvokeMethod(1416_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 762_0_main_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1)) | &&(>(x3, -1), >(x1, 0))
798_1_main_InvokeMethod(1492_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → 762_0_main_GT(java.lang.Object(ARRAY(x1)), x2, +(x3, 1)) | &&(>(x3, 0), >(x1, -1))
R rules:
798_0_parts_Load(x0, x1) → 674_0_parts_GT(x1, x0)
674_0_parts_GT(x1, x0) → 684_0_parts_Return(x0, x1) | <=(x0, 0)
674_0_parts_GT(0, x0) → 706_0_parts_Return(x0) | >(x0, 0)
674_0_parts_GT(x1, x0) → 760_1_parts_InvokeMethod(674_0_parts_GT(x0, x0), x1, x0) | &&(&&(>(x1, x0), >(x1, 0)), >(x0, 0))
674_0_parts_GT(x1, x0) → 769_1_parts_InvokeMethod(674_0_parts_GT(x1, x2), x0, x1) | &&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0))
760_1_parts_InvokeMethod(1370_0_parts_Return(x0, x0), x2, x0) → 1416_0_parts_Return(x0, x2)
760_1_parts_InvokeMethod(1416_0_parts_Return(x0, x0), x2, x0) → 1416_0_parts_Return(x0, x2)
760_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x1) → 1416_0_parts_Return(x1, x2)
769_1_parts_InvokeMethod(1370_0_parts_Return(x0, x1), x3, x1) → 1449_1_parts_InvokeMethod(674_0_parts_GT(x4, x3), x3) | >(x1, 0)
769_1_parts_InvokeMethod(1416_0_parts_Return(x0, x1), x3, x1) → 1449_1_parts_InvokeMethod(674_0_parts_GT(x4, x3), x3) | >(x1, 0)
769_1_parts_InvokeMethod(1492_0_parts_Return(x0), x1, x2) → 1449_1_parts_InvokeMethod(674_0_parts_GT(x3, x1), x1) | >(x2, 0)
769_1_parts_InvokeMethod(684_0_parts_Return(x0, x1), x3, x1) → 1449_1_parts_InvokeMethod(674_0_parts_GT(x4, x3), x3) | >(x1, 0)
1449_1_parts_InvokeMethod(1370_0_parts_Return(x0, x1), x0) → 1492_0_parts_Return(+(x3, x2))
1449_1_parts_InvokeMethod(1416_0_parts_Return(x0, x1), x0) → 1492_0_parts_Return(+(x3, x2))
1449_1_parts_InvokeMethod(706_0_parts_Return(x0), x0) → 1492_0_parts_Return(arith[1])
1449_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2) → 1492_0_parts_Return(+(x1, x0))

Performed bisimulation on rules. Used the following equivalence classes: {[684_0_parts_Return_2, 1370_0_parts_Return_2, 1416_0_parts_Return_2]=684_0_parts_Return_2, [Cond_798_1_main_InvokeMethod2_5, Cond_798_1_main_InvokeMethod3_5]=Cond_798_1_main_InvokeMethod2_5, [Cond_769_1_parts_InvokeMethod_5, Cond_769_1_parts_InvokeMethod1_5, Cond_769_1_parts_InvokeMethod3_5]=Cond_769_1_parts_InvokeMethod_5}

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

P rules:
762_0_MAIN_GT(java.lang.Object(ARRAY(x0)), x1, x2) → COND_762_0_MAIN_GT(&&(&&(>(x2, x0), >=(x0, +(x1, 1))), >(x0, -1)), java.lang.Object(ARRAY(x0)), x1, x2)
COND_762_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0)), x1, x2) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x0)), +(x1, 1), 0)
762_0_MAIN_GT(java.lang.Object(ARRAY(x0)), x1, x2) → COND_762_0_MAIN_GT1(<=(x2, x0), java.lang.Object(ARRAY(x0)), x1, x2)
COND_762_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0)), x1, x2) → 798_1_MAIN_INVOKEMETHOD(798_0_parts_Load(x1, x2), java.lang.Object(ARRAY(x0)), x1, x2)
798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → COND_798_1_MAIN_INVOKEMETHOD(&&(>(x3, -1), >(x1, -1)), 684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1)
COND_798_1_MAIN_INVOKEMETHOD(TRUE, 684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1))
798_1_MAIN_INVOKEMETHOD(706_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → COND_798_1_MAIN_INVOKEMETHOD1(>(x3, -1), 706_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0)
COND_798_1_MAIN_INVOKEMETHOD1(TRUE, 706_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, 1)
798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → COND_798_1_MAIN_INVOKEMETHOD2(&&(>(x3, -1), >(x1, 0)), 684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1)
COND_798_1_MAIN_INVOKEMETHOD2(TRUE, 684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1))
798_1_MAIN_INVOKEMETHOD(1492_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → COND_798_1_MAIN_INVOKEMETHOD4(&&(>(x3, 0), >(x1, -1)), 1492_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3)
COND_798_1_MAIN_INVOKEMETHOD4(TRUE, 1492_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x1)), x2, +(x3, 1))
R rules:
798_0_parts_Load(x0, x1) → 674_0_parts_GT(x1, x0)
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT(<=(x0, 0), x1, x0)
Cond_674_0_parts_GT(TRUE, x1, x0) → 684_0_parts_Return(x0, x1)
674_0_parts_GT(0, x0) → Cond_674_0_parts_GT1(>(x0, 0), 0, x0)
Cond_674_0_parts_GT1(TRUE, 0, x0) → 706_0_parts_Return(x0)
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT2(&&(&&(>(x1, x0), >(x1, 0)), >(x0, 0)), x1, x0)
Cond_674_0_parts_GT2(TRUE, x1, x0) → 760_1_parts_InvokeMethod(674_0_parts_GT(x0, x0), x1, x0)
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT3(&&(&&(>(x1, 0), <=(x1, x0)), >(x0, 0)), x1, x0, x2)
Cond_674_0_parts_GT3(TRUE, x1, x0, x2) → 769_1_parts_InvokeMethod(674_0_parts_GT(x1, x2), x0, x1)
760_1_parts_InvokeMethod(684_0_parts_Return(x0, x0), x2, x0) → 684_0_parts_Return(x0, x2)
760_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x1) → 684_0_parts_Return(x1, x2)
769_1_parts_InvokeMethod(684_0_parts_Return(x0, x1), x3, x1) → Cond_769_1_parts_InvokeMethod(>(x1, 0), 684_0_parts_Return(x0, x1), x3, x1, x4)
Cond_769_1_parts_InvokeMethod(TRUE, 684_0_parts_Return(x0, x1), x3, x1, x4) → 1449_1_parts_InvokeMethod(674_0_parts_GT(x4, x3), x3)
769_1_parts_InvokeMethod(1492_0_parts_Return(x0), x1, x2) → Cond_769_1_parts_InvokeMethod2(>(x2, 0), 1492_0_parts_Return(x0), x1, x2, x3)
Cond_769_1_parts_InvokeMethod2(TRUE, 1492_0_parts_Return(x0), x1, x2, x3) → 1449_1_parts_InvokeMethod(674_0_parts_GT(x3, x1), x1)
1449_1_parts_InvokeMethod(684_0_parts_Return(x0, x1), x0) → 1492_0_parts_Return(+(x3, x2))
1449_1_parts_InvokeMethod(706_0_parts_Return(x0), x0) → 1492_0_parts_Return(arith[1])
1449_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2) → 1492_0_parts_Return(+(x1, x0))

(24) Obligation:

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

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

The following domains are used:

Integer, Boolean

The ITRS R consists of the following rules:
798_0_parts_Load(x0, x1) → 674_0_parts_GT(x1, x0)
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT(x0 <= 0, x1, x0)
Cond_674_0_parts_GT(TRUE, x1, x0) → 684_0_parts_Return(x0, x1)
674_0_parts_GT(0, x0) → Cond_674_0_parts_GT1(x0 > 0, 0, x0)
Cond_674_0_parts_GT1(TRUE, 0, x0) → 706_0_parts_Return(x0)
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT2(x1 > x0 && x1 > 0 && x0 > 0, x1, x0)
Cond_674_0_parts_GT2(TRUE, x1, x0) → 760_1_parts_InvokeMethod(674_0_parts_GT(x0, x0), x1, x0)
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT3(x1 > 0 && x1 <= x0 && x0 > 0, x1, x0, x2)
Cond_674_0_parts_GT3(TRUE, x1, x0, x2) → 769_1_parts_InvokeMethod(674_0_parts_GT(x1, x2), x0, x1)
760_1_parts_InvokeMethod(684_0_parts_Return(x0, x0), x2, x0) → 684_0_parts_Return(x0, x2)
760_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x1) → 684_0_parts_Return(x1, x2)
769_1_parts_InvokeMethod(684_0_parts_Return(x0, x1), x3, x1) → Cond_769_1_parts_InvokeMethod(x1 > 0, 684_0_parts_Return(x0, x1), x3, x1, x4)
Cond_769_1_parts_InvokeMethod(TRUE, 684_0_parts_Return(x0, x1), x3, x1, x4) → 1449_1_parts_InvokeMethod(674_0_parts_GT(x4, x3), x3)
769_1_parts_InvokeMethod(1492_0_parts_Return(x0), x1, x2) → Cond_769_1_parts_InvokeMethod2(x2 > 0, 1492_0_parts_Return(x0), x1, x2, x3)
Cond_769_1_parts_InvokeMethod2(TRUE, 1492_0_parts_Return(x0), x1, x2, x3) → 1449_1_parts_InvokeMethod(674_0_parts_GT(x3, x1), x1)
1449_1_parts_InvokeMethod(684_0_parts_Return(x0, x1), x0) → 1492_0_parts_Return(x3 + x2)
1449_1_parts_InvokeMethod(706_0_parts_Return(x0), x0) → 1492_0_parts_Return(arith[1])
1449_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2) → 1492_0_parts_Return(x1 + x0)

The integer pair graph contains the following rules and edges:
(0): 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0]) → COND_762_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_762_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0[1])), x1[1], x2[1]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), x1[1] + 1, 0)
(2): 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2]) → COND_762_0_MAIN_GT1(x2[2] <= x0[2], java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])
(3): COND_762_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3]) → 798_1_MAIN_INVOKEMETHOD(798_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])
(4): 798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4]) → COND_798_1_MAIN_INVOKEMETHOD(x3[4] > -1 && x1[4] > -1, 684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])
(5): COND_798_1_MAIN_INVOKEMETHOD(TRUE, 684_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], x1[5] + 1)
(6): 798_1_MAIN_INVOKEMETHOD(706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0) → COND_798_1_MAIN_INVOKEMETHOD1(x3[6] > -1, 706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)
(7): COND_798_1_MAIN_INVOKEMETHOD1(TRUE, 706_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)
(8): 798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8]) → COND_798_1_MAIN_INVOKEMETHOD2(x3[8] > -1 && x1[8] > 0, 684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])
(9): COND_798_1_MAIN_INVOKEMETHOD2(TRUE, 684_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], x1[9] + 1)
(10): 798_1_MAIN_INVOKEMETHOD(1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10]) → COND_798_1_MAIN_INVOKEMETHOD4(x3[10] > 0 && x1[10] > -1, 1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])
(11): COND_798_1_MAIN_INVOKEMETHOD4(TRUE, 1492_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11]) → 762_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 (798_0_parts_Load(x1[3], x2[3]) →^* 684_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 (798_0_parts_Load(x1[3], x2[3]) →^* 706_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 (798_0_parts_Load(x1[3], x2[3]) →^* 684_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 (798_0_parts_Load(x1[3], x2[3]) →^* 1492_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 ∧684_0_parts_Return(x0[4], x1[4]) →^* 684_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 ∧706_0_parts_Return(x0[6]) →^* 706_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 ∧684_0_parts_Return(x0[8], x1[8]) →^* 684_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 ∧1492_0_parts_Return(x0[10]) →^* 1492_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:
798_0_parts_Load(x0, x1)
674_0_parts_GT(x0, x1)
Cond_674_0_parts_GT(TRUE, x0, x1)
Cond_674_0_parts_GT1(TRUE, 0, x0)
Cond_674_0_parts_GT2(TRUE, x0, x1)
Cond_674_0_parts_GT3(TRUE, x0, x1, x2)
760_1_parts_InvokeMethod(684_0_parts_Return(x0, x0), x1, x0)
760_1_parts_InvokeMethod(1492_0_parts_Return(x0), x1, x2)
769_1_parts_InvokeMethod(684_0_parts_Return(x0, x1), x2, x1)
Cond_769_1_parts_InvokeMethod(TRUE, 684_0_parts_Return(x0, x1), x2, x1, x3)
769_1_parts_InvokeMethod(1492_0_parts_Return(x0), x1, x2)
Cond_769_1_parts_InvokeMethod2(TRUE, 1492_0_parts_Return(x0), x1, x2, x3)
1449_1_parts_InvokeMethod(684_0_parts_Return(x0, x1), x0)
1449_1_parts_InvokeMethod(706_0_parts_Return(x0), x0)
1449_1_parts_InvokeMethod(1492_0_parts_Return(x0), x1)

(25) 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@44ea2ca9 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 762_0_MAIN_GT(java.lang.Object(ARRAY(x0)), x1, x2) → COND_762_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 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0]) → COND_762_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_762_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0[1])), x1[1], x2[1]) → 762_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] ⇒ 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])≥NonInfC∧762_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])≥COND_762_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_762_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 ⇒ 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])≥NonInfC∧762_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0])≥COND_762_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_762_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_762_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_762_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_762_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_762_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_762_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_762_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_762_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_762_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0)), x1, x2) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x0)), +(x1, 1), 0) the following chains were created:

We consider the chain COND_762_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0[1])), x1[1], x2[1]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0) which results in the following constraint:
(10)    (COND_762_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0[1])), x1[1], x2[1])≥NonInfC∧COND_762_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0[1])), x1[1], x2[1])≥762_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0)∧(U^Increasing(762_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(762_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(762_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(762_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(762_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 762_0_MAIN_GT(java.lang.Object(ARRAY(x0)), x1, x2) → COND_762_0_MAIN_GT1(<=(x2, x0), java.lang.Object(ARRAY(x0)), x1, x2) the following chains were created:

We consider the chain 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2]) → COND_762_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2]), COND_762_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3]) → 798_1_MAIN_INVOKEMETHOD(798_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] ⇒ 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])≥NonInfC∧762_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])≥COND_762_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])∧(U^Increasing(COND_762_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 ⇒ 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])≥NonInfC∧762_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])≥COND_762_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])∧(U^Increasing(COND_762_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_762_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_762_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_762_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_762_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_762_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_762_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_762_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_762_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0)), x1, x2) → 798_1_MAIN_INVOKEMETHOD(798_0_parts_Load(x1, x2), java.lang.Object(ARRAY(x0)), x1, x2) the following chains were created:

We consider the chain COND_762_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3]) → 798_1_MAIN_INVOKEMETHOD(798_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_762_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])≥NonInfC∧COND_762_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])≥798_1_MAIN_INVOKEMETHOD(798_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])∧(U^Increasing(798_1_MAIN_INVOKEMETHOD(798_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(798_1_MAIN_INVOKEMETHOD(798_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(798_1_MAIN_INVOKEMETHOD(798_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(798_1_MAIN_INVOKEMETHOD(798_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(798_1_MAIN_INVOKEMETHOD(798_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 798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → COND_798_1_MAIN_INVOKEMETHOD(&&(>(x3, -1), >(x1, -1)), 684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) the following chains were created:

We consider the chain 798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4]) → COND_798_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4]), COND_798_1_MAIN_INVOKEMETHOD(TRUE, 684_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5]) → 762_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∧684_0_parts_Return(x0[4], x1[4])=684_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] ⇒ 798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])≥NonInfC∧798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])≥COND_798_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])∧(U^Increasing(COND_798_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 684_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 ⇒ 798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])≥NonInfC∧798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])≥COND_798_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])∧(U^Increasing(COND_798_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 684_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_798_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 684_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_798_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 684_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_798_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 684_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_798_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 684_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_798_1_MAIN_INVOKEMETHOD(TRUE, 684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1)) the following chains were created:

We consider the chain COND_798_1_MAIN_INVOKEMETHOD(TRUE, 684_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1)) which results in the following constraint:
(35)    (COND_798_1_MAIN_INVOKEMETHOD(TRUE, 684_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5])≥NonInfC∧COND_798_1_MAIN_INVOKEMETHOD(TRUE, 684_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5])≥762_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1))∧(U^Increasing(762_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(762_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(762_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(762_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(762_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 798_1_MAIN_INVOKEMETHOD(706_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → COND_798_1_MAIN_INVOKEMETHOD1(>(x3, -1), 706_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) the following chains were created:

We consider the chain 798_1_MAIN_INVOKEMETHOD(706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0) → COND_798_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0), COND_798_1_MAIN_INVOKEMETHOD1(TRUE, 706_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1) which results in the following constraint:
(40)    (>(x3[6], -1)=TRUE∧706_0_parts_Return(x0[6])=706_0_parts_Return(x0[7])∧java.lang.Object(ARRAY(x3[6]))=java.lang.Object(ARRAY(x3[7]))∧x0[6]=x0[7] ⇒ 798_1_MAIN_INVOKEMETHOD(706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)≥NonInfC∧798_1_MAIN_INVOKEMETHOD(706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)≥COND_798_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)∧(U^Increasing(COND_798_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 706_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 ⇒ 798_1_MAIN_INVOKEMETHOD(706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)≥NonInfC∧798_1_MAIN_INVOKEMETHOD(706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)≥COND_798_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)∧(U^Increasing(COND_798_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 706_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_798_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 706_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_798_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 706_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_798_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 706_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_798_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 706_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_798_1_MAIN_INVOKEMETHOD1(TRUE, 706_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, 1) the following chains were created:

We consider the chain COND_798_1_MAIN_INVOKEMETHOD1(TRUE, 706_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1) which results in the following constraint:
(46)    (COND_798_1_MAIN_INVOKEMETHOD1(TRUE, 706_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0)≥NonInfC∧COND_798_1_MAIN_INVOKEMETHOD1(TRUE, 706_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0)≥762_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)∧(U^Increasing(762_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(762_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(762_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(762_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(762_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 798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → COND_798_1_MAIN_INVOKEMETHOD2(&&(>(x3, -1), >(x1, 0)), 684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) the following chains were created:

We consider the chain 798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8]) → COND_798_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8]), COND_798_1_MAIN_INVOKEMETHOD2(TRUE, 684_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9]) → 762_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∧684_0_parts_Return(x0[8], x1[8])=684_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] ⇒ 798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])≥NonInfC∧798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])≥COND_798_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])∧(U^Increasing(COND_798_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 684_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 ⇒ 798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])≥NonInfC∧798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])≥COND_798_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])∧(U^Increasing(COND_798_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 684_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_798_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 684_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_798_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 684_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_798_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 684_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_798_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 684_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_798_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 684_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_798_1_MAIN_INVOKEMETHOD2(TRUE, 684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1)) the following chains were created:

We consider the chain COND_798_1_MAIN_INVOKEMETHOD2(TRUE, 684_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1)) which results in the following constraint:
(58)    (COND_798_1_MAIN_INVOKEMETHOD2(TRUE, 684_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9])≥NonInfC∧COND_798_1_MAIN_INVOKEMETHOD2(TRUE, 684_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9])≥762_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1))∧(U^Increasing(762_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(762_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(762_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(762_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(762_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 798_1_MAIN_INVOKEMETHOD(1492_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → COND_798_1_MAIN_INVOKEMETHOD4(&&(>(x3, 0), >(x1, -1)), 1492_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) the following chains were created:

We consider the chain 798_1_MAIN_INVOKEMETHOD(1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10]) → COND_798_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10]), COND_798_1_MAIN_INVOKEMETHOD4(TRUE, 1492_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11]) → 762_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∧1492_0_parts_Return(x0[10])=1492_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] ⇒ 798_1_MAIN_INVOKEMETHOD(1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])≥NonInfC∧798_1_MAIN_INVOKEMETHOD(1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])≥COND_798_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])∧(U^Increasing(COND_798_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 1492_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 ⇒ 798_1_MAIN_INVOKEMETHOD(1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])≥NonInfC∧798_1_MAIN_INVOKEMETHOD(1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])≥COND_798_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])∧(U^Increasing(COND_798_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 1492_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_798_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 1492_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_798_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 1492_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_798_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 1492_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_798_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 1492_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_798_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 1492_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_798_1_MAIN_INVOKEMETHOD4(TRUE, 1492_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x1)), x2, +(x3, 1)) the following chains were created:

We consider the chain COND_798_1_MAIN_INVOKEMETHOD4(TRUE, 1492_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], +(x3[11], 1)) which results in the following constraint:
(70)    (COND_798_1_MAIN_INVOKEMETHOD4(TRUE, 1492_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11])≥NonInfC∧COND_798_1_MAIN_INVOKEMETHOD4(TRUE, 1492_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11])≥762_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], +(x3[11], 1))∧(U^Increasing(762_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(762_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(762_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(762_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(762_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.

762_0_MAIN_GT(java.lang.Object(ARRAY(x0)), x1, x2) → COND_762_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_762_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_762_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_762_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0)), x1, x2) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x0)), +(x1, 1), 0)
- ((U^Increasing(762_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)
762_0_MAIN_GT(java.lang.Object(ARRAY(x0)), x1, x2) → COND_762_0_MAIN_GT1(<=(x2, x0), java.lang.Object(ARRAY(x0)), x1, x2)
- (x0[2] ≥ 0∧x2[2] ≥ 0 ⇒ (U^Increasing(COND_762_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_762_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_762_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0)), x1, x2) → 798_1_MAIN_INVOKEMETHOD(798_0_parts_Load(x1, x2), java.lang.Object(ARRAY(x0)), x1, x2)
- ((U^Increasing(798_1_MAIN_INVOKEMETHOD(798_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)
798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → COND_798_1_MAIN_INVOKEMETHOD(&&(>(x3, -1), >(x1, -1)), 684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1)
- (x3[4] ≥ 0∧x1[4] ≥ 0 ⇒ (U^Increasing(COND_798_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 684_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_798_1_MAIN_INVOKEMETHOD(TRUE, 684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1))
- ((U^Increasing(762_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)
798_1_MAIN_INVOKEMETHOD(706_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → COND_798_1_MAIN_INVOKEMETHOD1(>(x3, -1), 706_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0)
- (x3[6] ≥ 0 ⇒ (U^Increasing(COND_798_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 706_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_798_1_MAIN_INVOKEMETHOD1(TRUE, 706_0_parts_Return(x0), java.lang.Object(ARRAY(x3)), x0, 0) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, 1)
- ((U^Increasing(762_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)), ≥)∧[bni_52] = 0∧0 = 0∧0 = 0∧[(-1)bso_53] ≥ 0)
798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → COND_798_1_MAIN_INVOKEMETHOD2(&&(>(x3, -1), >(x1, 0)), 684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1)
- (x3[8] ≥ 0∧x1[8] ≥ 0 ⇒ (U^Increasing(COND_798_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 684_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_798_1_MAIN_INVOKEMETHOD2(TRUE, 684_0_parts_Return(x0, x1), java.lang.Object(ARRAY(x3)), x0, x1) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3)), x0, +(x1, 1))
- ((U^Increasing(762_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)
798_1_MAIN_INVOKEMETHOD(1492_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → COND_798_1_MAIN_INVOKEMETHOD4(&&(>(x3, 0), >(x1, -1)), 1492_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3)
- (x3[10] ≥ 0∧x1[10] ≥ 0 ⇒ (U^Increasing(COND_798_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 1492_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_798_1_MAIN_INVOKEMETHOD4(TRUE, 1492_0_parts_Return(x0), java.lang.Object(ARRAY(x1)), x2, x3) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x1)), x2, +(x3, 1))
- ((U^Increasing(762_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(798_0_parts_Load(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(674_0_parts_GT(x₁, x₂)) = [-1] + [-1]x₁ + [-1]x₂
POL(Cond_674_0_parts_GT(x₁, x₂, x₃)) = [-1]x₃ + [-1]x₂
POL(<=(x₁, x₂)) = [-1]
POL(0) = 0
POL(684_0_parts_Return(x₁, x₂)) = [-1] + [-1]x₁ + [-1]x₂
POL(Cond_674_0_parts_GT1(x₁, x₂, x₃)) = [1] + [-1]x₃
POL(>(x₁, x₂)) = [-1]
POL(706_0_parts_Return(x₁)) = x₁
POL(Cond_674_0_parts_GT2(x₁, x₂, x₃)) = [-1]x₃ + [-1]x₂
POL(&&(x₁, x₂)) = [-1]
POL(760_1_parts_InvokeMethod(x₁, x₂, x₃)) = [-1] + [-1]x₁ + [-1]x₃ + [-1]x₂
POL(Cond_674_0_parts_GT3(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₃ + [-1]x₂
POL(769_1_parts_InvokeMethod(x₁, x₂, x₃)) = [1] + [-1]x₂ + [-1]x₃
POL(1492_0_parts_Return(x₁)) = x₁
POL(Cond_769_1_parts_InvokeMethod(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₄ + [-1]x₃
POL(1449_1_parts_InvokeMethod(x₁, x₂)) = [-1] + [-1]x₁ + [-1]x₂
POL(Cond_769_1_parts_InvokeMethod2(x₁, x₂, x₃, x₄, x₅)) = [-1]x₄ + [-1]x₃
POL(+(x₁, x₂)) = x₁ + x₂
POL(762_0_MAIN_GT(x₁, x₂, x₃)) = [-1] + [-1]x₂ + [2]x₁
POL(java.lang.Object(x₁)) = x₁
POL(ARRAY(x₁)) = x₁
POL(COND_762_0_MAIN_GT(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₃ + [2]x₂
POL(>=(x₁, x₂)) = [-1]
POL(1) = [1]
POL(-1) = [-1]
POL(COND_762_0_MAIN_GT1(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₃ + [2]x₂
POL(798_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₃ + [2]x₂
POL(COND_798_1_MAIN_INVOKEMETHOD(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₄ + [2]x₃
POL(COND_798_1_MAIN_INVOKEMETHOD1(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₄ + [2]x₃
POL(COND_798_1_MAIN_INVOKEMETHOD2(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₄ + [2]x₃
POL(COND_798_1_MAIN_INVOKEMETHOD4(x₁, x₂, x₃, x₄, x₅)) = [-1] + [-1]x₄ + [2]x₃

The following pairs are in P_>:

COND_762_0_MAIN_GT(TRUE, java.lang.Object(ARRAY(x0[1])), x1[1], x2[1]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[1])), +(x1[1], 1), 0)

The following pairs are in P_bound:

762_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0]) → COND_762_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_≥:

762_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0]) → COND_762_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])
762_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2]) → COND_762_0_MAIN_GT1(<=(x2[2], x0[2]), java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])
COND_762_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3]) → 798_1_MAIN_INVOKEMETHOD(798_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])
798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4]) → COND_798_1_MAIN_INVOKEMETHOD(&&(>(x3[4], -1), >(x1[4], -1)), 684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])
COND_798_1_MAIN_INVOKEMETHOD(TRUE, 684_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], +(x1[5], 1))
798_1_MAIN_INVOKEMETHOD(706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0) → COND_798_1_MAIN_INVOKEMETHOD1(>(x3[6], -1), 706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)
COND_798_1_MAIN_INVOKEMETHOD1(TRUE, 706_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)
798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8]) → COND_798_1_MAIN_INVOKEMETHOD2(&&(>(x3[8], -1), >(x1[8], 0)), 684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])
COND_798_1_MAIN_INVOKEMETHOD2(TRUE, 684_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], +(x1[9], 1))
798_1_MAIN_INVOKEMETHOD(1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10]) → COND_798_1_MAIN_INVOKEMETHOD4(&&(>(x3[10], 0), >(x1[10], -1)), 1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])
COND_798_1_MAIN_INVOKEMETHOD4(TRUE, 1492_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11]) → 762_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:

798_0_parts_Load(x0, x1)¹ ↔ 674_0_parts_GT(x1, x0)¹
Cond_674_0_parts_GT(<=(x0, 0), x1, x0)¹ → 674_0_parts_GT(x1, x0)¹
769_1_parts_InvokeMethod(1492_0_parts_Return(x0), x1, x2)¹ → Cond_769_1_parts_InvokeMethod2(>(x2, 0), 1492_0_parts_Return(x0), x1, x2, x3)¹

(26) Complex Obligation (AND)

(27) Obligation:

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

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

The following domains are used:

Integer, Boolean

The ITRS R consists of the following rules:
798_0_parts_Load(x0, x1) → 674_0_parts_GT(x1, x0)
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT(x0 <= 0, x1, x0)
Cond_674_0_parts_GT(TRUE, x1, x0) → 684_0_parts_Return(x0, x1)
674_0_parts_GT(0, x0) → Cond_674_0_parts_GT1(x0 > 0, 0, x0)
Cond_674_0_parts_GT1(TRUE, 0, x0) → 706_0_parts_Return(x0)
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT2(x1 > x0 && x1 > 0 && x0 > 0, x1, x0)
Cond_674_0_parts_GT2(TRUE, x1, x0) → 760_1_parts_InvokeMethod(674_0_parts_GT(x0, x0), x1, x0)
674_0_parts_GT(x1, x0) → Cond_674_0_parts_GT3(x1 > 0 && x1 <= x0 && x0 > 0, x1, x0, x2)
Cond_674_0_parts_GT3(TRUE, x1, x0, x2) → 769_1_parts_InvokeMethod(674_0_parts_GT(x1, x2), x0, x1)
760_1_parts_InvokeMethod(684_0_parts_Return(x0, x0), x2, x0) → 684_0_parts_Return(x0, x2)
760_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2, x1) → 684_0_parts_Return(x1, x2)
769_1_parts_InvokeMethod(684_0_parts_Return(x0, x1), x3, x1) → Cond_769_1_parts_InvokeMethod(x1 > 0, 684_0_parts_Return(x0, x1), x3, x1, x4)
Cond_769_1_parts_InvokeMethod(TRUE, 684_0_parts_Return(x0, x1), x3, x1, x4) → 1449_1_parts_InvokeMethod(674_0_parts_GT(x4, x3), x3)
769_1_parts_InvokeMethod(1492_0_parts_Return(x0), x1, x2) → Cond_769_1_parts_InvokeMethod2(x2 > 0, 1492_0_parts_Return(x0), x1, x2, x3)
Cond_769_1_parts_InvokeMethod2(TRUE, 1492_0_parts_Return(x0), x1, x2, x3) → 1449_1_parts_InvokeMethod(674_0_parts_GT(x3, x1), x1)
1449_1_parts_InvokeMethod(684_0_parts_Return(x0, x1), x0) → 1492_0_parts_Return(x3 + x2)
1449_1_parts_InvokeMethod(706_0_parts_Return(x0), x0) → 1492_0_parts_Return(arith[1])
1449_1_parts_InvokeMethod(1492_0_parts_Return(x0), x2) → 1492_0_parts_Return(x1 + x0)

The integer pair graph contains the following rules and edges:
(0): 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[0])), x1[0], x2[0]) → COND_762_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): 762_0_MAIN_GT(java.lang.Object(ARRAY(x0[2])), x1[2], x2[2]) → COND_762_0_MAIN_GT1(x2[2] <= x0[2], java.lang.Object(ARRAY(x0[2])), x1[2], x2[2])
(3): COND_762_0_MAIN_GT1(TRUE, java.lang.Object(ARRAY(x0[3])), x1[3], x2[3]) → 798_1_MAIN_INVOKEMETHOD(798_0_parts_Load(x1[3], x2[3]), java.lang.Object(ARRAY(x0[3])), x1[3], x2[3])
(4): 798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4]) → COND_798_1_MAIN_INVOKEMETHOD(x3[4] > -1 && x1[4] > -1, 684_0_parts_Return(x0[4], x1[4]), java.lang.Object(ARRAY(x3[4])), x0[4], x1[4])
(5): COND_798_1_MAIN_INVOKEMETHOD(TRUE, 684_0_parts_Return(x0[5], x1[5]), java.lang.Object(ARRAY(x3[5])), x0[5], x1[5]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[5])), x0[5], x1[5] + 1)
(6): 798_1_MAIN_INVOKEMETHOD(706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0) → COND_798_1_MAIN_INVOKEMETHOD1(x3[6] > -1, 706_0_parts_Return(x0[6]), java.lang.Object(ARRAY(x3[6])), x0[6], 0)
(7): COND_798_1_MAIN_INVOKEMETHOD1(TRUE, 706_0_parts_Return(x0[7]), java.lang.Object(ARRAY(x3[7])), x0[7], 0) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[7])), x0[7], 1)
(8): 798_1_MAIN_INVOKEMETHOD(684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8]) → COND_798_1_MAIN_INVOKEMETHOD2(x3[8] > -1 && x1[8] > 0, 684_0_parts_Return(x0[8], x1[8]), java.lang.Object(ARRAY(x3[8])), x0[8], x1[8])
(9): COND_798_1_MAIN_INVOKEMETHOD2(TRUE, 684_0_parts_Return(x0[9], x1[9]), java.lang.Object(ARRAY(x3[9])), x0[9], x1[9]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x3[9])), x0[9], x1[9] + 1)
(10): 798_1_MAIN_INVOKEMETHOD(1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10]) → COND_798_1_MAIN_INVOKEMETHOD4(x3[10] > 0 && x1[10] > -1, 1492_0_parts_Return(x0[10]), java.lang.Object(ARRAY(x1[10])), x2[10], x3[10])
(11): COND_798_1_MAIN_INVOKEMETHOD4(TRUE, 1492_0_parts_Return(x0[11]), java.lang.Object(ARRAY(x1[11])), x2[11], x3[11]) → 762_0_MAIN_GT(java.lang.Object(ARRAY(x1[11])), x2[11], x3[11] + 1)