Termination proof of /tmp/tmpt_696C/AProVEMathRecursive.jar

Termination of the given JBC could be proven:

0 JBC

↳1 JBCToGraph (⇒, 200 ms)

↳2 JBCTerminationGraph

↳3 TerminationGraphToSCCProof (⇒, 0 ms)

↳4 JBCTerminationSCC

↳5 SCCToIDPv1Proof (⇒, 750 ms)

↳6 IDP

↳7 IDPNonInfProof (⇒, 2920 ms)

↳8 IDP

↳9 IDependencyGraphProof (⇔, 0 ms)

↳10 TRUE

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_14 (Sun Microsystems Inc.) Main-Class: AProVEMathRecursive

public class AProVEMathRecursive {
  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    power(x, y);
  }

  public static int power(int base, int exponent) {           
    if (exponent <= 0) {
      return 1;
    } else if (exponent == 1) {
      return base;
    } else if (base == 2) {
      return base << (exponent-1);
    } else if (exponent % 2 == 1) {
      return base * power(base, exponent-1);
    } else {
      int halfPower = power(base, exponent/2);
      return halfPower * halfPower;
    }
  }
}


public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
    if (args.length <= index) {
      return 0;
    }
    String string = args[index];
    index++;
    if (string == null) {
      return 0;
    }
    return string.length();
  }
}

(1) JBCToGraph (SOUND transformation)

Constructed TerminationGraph.

(2) Obligation:

Termination Graph based on JBC Program:
AProVEMathRecursive.main([Ljava/lang/String;)V: Graph of 149 nodes with 0 SCCs.

AProVEMathRecursive.power(II)I: Graph of 125 nodes with 0 SCCs.

(3) TerminationGraphToSCCProof (SOUND transformation)

Splitted TerminationGraph to 1 SCCs.

(4) Obligation:

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

(5) SCCToIDPv1Proof (SOUND transformation)

Transformed FIGraph SCCs to IDPs. Log:

Generated 59 rules for P and 70 rules for R.

P rules:
382_0_power_GT(EOS(STATIC_382), i60, i65, i65) → 385_0_power_GT(EOS(STATIC_385), i60, i65, i65)
385_0_power_GT(EOS(STATIC_385), i60, i65, i65) → 387_0_power_Load(EOS(STATIC_387), i60, i65) | >(i65, 0)
387_0_power_Load(EOS(STATIC_387), i60, i65) → 389_0_power_ConstantStackPush(EOS(STATIC_389), i60, i65, i65)
389_0_power_ConstantStackPush(EOS(STATIC_389), i60, i65, i65) → 391_0_power_NE(EOS(STATIC_391), i60, i65, i65, 1)
391_0_power_NE(EOS(STATIC_391), i60, i73, i73, matching1) → 412_0_power_NE(EOS(STATIC_412), i60, i73, i73, 1) | =(matching1, 1)
412_0_power_NE(EOS(STATIC_412), i60, i73, i73, matching1) → 424_0_power_Load(EOS(STATIC_424), i60, i73) | &&(!(=(i73, 1)), =(matching1, 1))
424_0_power_Load(EOS(STATIC_424), i60, i73) → 431_0_power_ConstantStackPush(EOS(STATIC_431), i60, i73, i60)
431_0_power_ConstantStackPush(EOS(STATIC_431), i60, i73, i60) → 438_0_power_NE(EOS(STATIC_438), i60, i73, i60, 2)
438_0_power_NE(EOS(STATIC_438), i86, i73, i86, matching1) → 452_0_power_NE(EOS(STATIC_452), i86, i73, i86, 2) | =(matching1, 2)
438_0_power_NE(EOS(STATIC_438), i87, i73, i87, matching1) → 455_0_power_NE(EOS(STATIC_455), i87, i73, i87, 2) | =(matching1, 2)
452_0_power_NE(EOS(STATIC_452), i86, i73, i86, matching1) → 461_0_power_Load(EOS(STATIC_461), i86, i73) | &&(!(=(i86, 2)), =(matching1, 2))
461_0_power_Load(EOS(STATIC_461), i86, i73) → 472_0_power_ConstantStackPush(EOS(STATIC_472), i86, i73, i73)
472_0_power_ConstantStackPush(EOS(STATIC_472), i86, i73, i73) → 481_0_power_IntArithmetic(EOS(STATIC_481), i86, i73, i73, 2)
481_0_power_IntArithmetic(EOS(STATIC_481), i86, i73, i73, matching1) → 490_0_power_ConstantStackPush(EOS(STATIC_490), i86, i73, %(i73, 2)) | =(matching1, 2)
490_0_power_ConstantStackPush(EOS(STATIC_490), i86, i73, i90) → 497_0_power_NE(EOS(STATIC_497), i86, i73, i90, 1)
497_0_power_NE(EOS(STATIC_497), i86, i73, matching1, matching2) → 505_0_power_NE(EOS(STATIC_505), i86, i73, 0, 1) | &&(=(matching1, 0), =(matching2, 1))
497_0_power_NE(EOS(STATIC_497), i86, i73, matching1, matching2) → 506_0_power_NE(EOS(STATIC_506), i86, i73, 1, 1) | &&(=(matching1, 1), =(matching2, 1))
505_0_power_NE(EOS(STATIC_505), i86, i73, matching1, matching2) → 514_0_power_Load(EOS(STATIC_514), i86, i73) | &&(=(matching1, 0), =(matching2, 1))
514_0_power_Load(EOS(STATIC_514), i86, i73) → 525_0_power_Load(EOS(STATIC_525), i73, i86)
525_0_power_Load(EOS(STATIC_525), i73, i86) → 542_0_power_ConstantStackPush(EOS(STATIC_542), i86, i73)
542_0_power_ConstantStackPush(EOS(STATIC_542), i86, i73) → 554_0_power_IntArithmetic(EOS(STATIC_554), i86, i73, 2)
554_0_power_IntArithmetic(EOS(STATIC_554), i86, i73, matching1) → 568_0_power_InvokeMethod(EOS(STATIC_568), i86, /(i73, 2)) | &&(>(i73, 1), =(matching1, 2))
568_0_power_InvokeMethod(EOS(STATIC_568), i86, i104) → 579_1_power_InvokeMethod(579_0_power_Load(EOS(STATIC_579), i86, i104), i86, i104)
579_0_power_Load(EOS(STATIC_579), i86, i104) → 589_0_power_Load(EOS(STATIC_589), i86, i104)
589_0_power_Load(EOS(STATIC_589), i86, i104) → 379_0_power_Load(EOS(STATIC_379), i86, i104)
379_0_power_Load(EOS(STATIC_379), i60, i61) → 382_0_power_GT(EOS(STATIC_382), i60, i61, i61)
506_0_power_NE(EOS(STATIC_506), i86, i73, matching1, matching2) → 516_0_power_Load(EOS(STATIC_516), i86, i73) | &&(=(matching1, 1), =(matching2, 1))
516_0_power_Load(EOS(STATIC_516), i86, i73) → 526_0_power_Load(EOS(STATIC_526), i86, i73, i86)
526_0_power_Load(EOS(STATIC_526), i86, i73, i86) → 544_0_power_Load(EOS(STATIC_544), i86, i73, i86, i86)
544_0_power_Load(EOS(STATIC_544), i86, i73, i86, i86) → 556_0_power_ConstantStackPush(EOS(STATIC_556), i86, i73, i86, i86, i73)
556_0_power_ConstantStackPush(EOS(STATIC_556), i86, i73, i86, i86, i73) → 570_0_power_IntArithmetic(EOS(STATIC_570), i86, i73, i86, i86, i73, 1)
570_0_power_IntArithmetic(EOS(STATIC_570), i86, i73, i86, i86, i73, matching1) → 581_0_power_InvokeMethod(EOS(STATIC_581), i86, i73, i86, i86, -(i73, 1)) | &&(>(i73, 0), =(matching1, 1))
581_0_power_InvokeMethod(EOS(STATIC_581), i86, i73, i86, i86, i106) → 590_1_power_InvokeMethod(590_0_power_Load(EOS(STATIC_590), i86, i106), i86, i73, i86, i86, i106)
590_0_power_Load(EOS(STATIC_590), i86, i106) → 598_0_power_Load(EOS(STATIC_598), i86, i106)
598_0_power_Load(EOS(STATIC_598), i86, i106) → 379_0_power_Load(EOS(STATIC_379), i86, i106)
455_0_power_NE(EOS(STATIC_455), i87, i73, i87, matching1) → 465_0_power_Load(EOS(STATIC_465), i87, i73) | &&(!(=(i87, 2)), =(matching1, 2))
465_0_power_Load(EOS(STATIC_465), i87, i73) → 476_0_power_ConstantStackPush(EOS(STATIC_476), i87, i73, i73)
476_0_power_ConstantStackPush(EOS(STATIC_476), i87, i73, i73) → 486_0_power_IntArithmetic(EOS(STATIC_486), i87, i73, i73, 2)
486_0_power_IntArithmetic(EOS(STATIC_486), i87, i73, i73, matching1) → 494_0_power_ConstantStackPush(EOS(STATIC_494), i87, i73, %(i73, 2)) | =(matching1, 2)
494_0_power_ConstantStackPush(EOS(STATIC_494), i87, i73, i91) → 503_0_power_NE(EOS(STATIC_503), i87, i73, i91, 1)
503_0_power_NE(EOS(STATIC_503), i87, i73, matching1, matching2) → 511_0_power_NE(EOS(STATIC_511), i87, i73, 0, 1) | &&(=(matching1, 0), =(matching2, 1))
503_0_power_NE(EOS(STATIC_503), i87, i73, matching1, matching2) → 512_0_power_NE(EOS(STATIC_512), i87, i73, 1, 1) | &&(=(matching1, 1), =(matching2, 1))
511_0_power_NE(EOS(STATIC_511), i87, i73, matching1, matching2) → 520_0_power_Load(EOS(STATIC_520), i87, i73) | &&(=(matching1, 0), =(matching2, 1))
520_0_power_Load(EOS(STATIC_520), i87, i73) → 538_0_power_Load(EOS(STATIC_538), i73, i87)
538_0_power_Load(EOS(STATIC_538), i73, i87) → 550_0_power_ConstantStackPush(EOS(STATIC_550), i87, i73)
550_0_power_ConstantStackPush(EOS(STATIC_550), i87, i73) → 564_0_power_IntArithmetic(EOS(STATIC_564), i87, i73, 2)
564_0_power_IntArithmetic(EOS(STATIC_564), i87, i73, matching1) → 575_0_power_InvokeMethod(EOS(STATIC_575), i87, /(i73, 2)) | &&(>(i73, 1), =(matching1, 2))
575_0_power_InvokeMethod(EOS(STATIC_575), i87, i105) → 584_1_power_InvokeMethod(584_0_power_Load(EOS(STATIC_584), i87, i105), i87, i105)
584_0_power_Load(EOS(STATIC_584), i87, i105) → 593_0_power_Load(EOS(STATIC_593), i87, i105)
593_0_power_Load(EOS(STATIC_593), i87, i105) → 379_0_power_Load(EOS(STATIC_379), i87, i105)
512_0_power_NE(EOS(STATIC_512), i87, i73, matching1, matching2) → 523_0_power_Load(EOS(STATIC_523), i87, i73) | &&(=(matching1, 1), =(matching2, 1))
523_0_power_Load(EOS(STATIC_523), i87, i73) → 540_0_power_Load(EOS(STATIC_540), i87, i73, i87)
540_0_power_Load(EOS(STATIC_540), i87, i73, i87) → 552_0_power_Load(EOS(STATIC_552), i87, i73, i87, i87)
552_0_power_Load(EOS(STATIC_552), i87, i73, i87, i87) → 566_0_power_ConstantStackPush(EOS(STATIC_566), i87, i73, i87, i87, i73)
566_0_power_ConstantStackPush(EOS(STATIC_566), i87, i73, i87, i87, i73) → 577_0_power_IntArithmetic(EOS(STATIC_577), i87, i73, i87, i87, i73, 1)
577_0_power_IntArithmetic(EOS(STATIC_577), i87, i73, i87, i87, i73, matching1) → 587_0_power_InvokeMethod(EOS(STATIC_587), i87, i73, i87, i87, -(i73, 1)) | &&(>(i73, 0), =(matching1, 1))
587_0_power_InvokeMethod(EOS(STATIC_587), i87, i73, i87, i87, i107) → 595_1_power_InvokeMethod(595_0_power_Load(EOS(STATIC_595), i87, i107), i87, i73, i87, i87, i107)
595_0_power_Load(EOS(STATIC_595), i87, i107) → 600_0_power_Load(EOS(STATIC_600), i87, i107)
600_0_power_Load(EOS(STATIC_600), i87, i107) → 379_0_power_Load(EOS(STATIC_379), i87, i107)
R rules:
382_0_power_GT(EOS(STATIC_382), i60, matching1, matching2) → 384_0_power_GT(EOS(STATIC_384), i60, 0, 0) | &&(=(matching1, 0), =(matching2, 0))
384_0_power_GT(EOS(STATIC_384), i60, matching1, matching2) → 386_0_power_ConstantStackPush(EOS(STATIC_386), i60, 0) | &&(&&(<=(0, 0), =(matching1, 0)), =(matching2, 0))
386_0_power_ConstantStackPush(EOS(STATIC_386), i60, matching1) → 388_0_power_Return(EOS(STATIC_388), i60, 0) | =(matching1, 0)
391_0_power_NE(EOS(STATIC_391), i60, matching1, matching2, matching3) → 410_0_power_NE(EOS(STATIC_410), i60, 1, 1, 1) | &&(&&(=(matching1, 1), =(matching2, 1)), =(matching3, 1))
410_0_power_NE(EOS(STATIC_410), i60, matching1, matching2, matching3) → 422_0_power_Load(EOS(STATIC_422), i60, 1) | &&(&&(=(matching1, 1), =(matching2, 1)), =(matching3, 1))
422_0_power_Load(EOS(STATIC_422), i60, matching1) → 429_0_power_Return(EOS(STATIC_429), i60, 1, i60) | =(matching1, 1)
438_0_power_NE(EOS(STATIC_438), matching1, i73, matching2, matching3) → 453_0_power_NE(EOS(STATIC_453), 2, i73, 2, 2) | &&(&&(=(matching1, 2), =(matching2, 2)), =(matching3, 2))
453_0_power_NE(EOS(STATIC_453), matching1, i73, matching2, matching3) → 463_0_power_Load(EOS(STATIC_463), 2, i73) | &&(&&(=(matching1, 2), =(matching2, 2)), =(matching3, 2))
463_0_power_Load(EOS(STATIC_463), matching1, i73) → 474_0_power_Load(EOS(STATIC_474), 2, i73, 2) | =(matching1, 2)
474_0_power_Load(EOS(STATIC_474), matching1, i73, matching2) → 483_0_power_ConstantStackPush(EOS(STATIC_483), 2, i73, 2, i73) | &&(=(matching1, 2), =(matching2, 2))
483_0_power_ConstantStackPush(EOS(STATIC_483), matching1, i73, matching2, i73) → 492_0_power_IntArithmetic(EOS(STATIC_492), 2, i73, 2, i73) | &&(=(matching1, 2), =(matching2, 2))
492_0_power_IntArithmetic(EOS(STATIC_492), matching1, i73, matching2, i73) → 499_0_power_IntArithmetic(EOS(STATIC_499), 2, i73, 2) | &&(&&(>(i73, 0), =(matching1, 2)), =(matching2, 2))
499_0_power_IntArithmetic(EOS(STATIC_499), matching1, i73, matching2) → 508_0_power_Return(EOS(STATIC_508), 2, i73) | &&(=(matching1, 2), =(matching2, 2))
579_1_power_InvokeMethod(429_0_power_Return(EOS(STATIC_429), i118, matching1, i118), i118, matching2) → 623_0_power_Return(EOS(STATIC_623), i118, 1, i118, 1, i118) | &&(=(matching1, 1), =(matching2, 1))
579_1_power_InvokeMethod(896_0_power_Return(EOS(STATIC_896), i337, i338, i320), i337, i338) → 978_0_power_Return(EOS(STATIC_978), i337, i338, i337, i338, i320)
579_1_power_InvokeMethod(968_0_power_Return(EOS(STATIC_968), i370), i415, i416) → 1050_0_power_Return(EOS(STATIC_1050), i415, i416, i370)
584_1_power_InvokeMethod(429_0_power_Return(EOS(STATIC_429), i134, matching1, i134), i134, matching2) → 636_0_power_Return(EOS(STATIC_636), i134, 1, i134, 1, i134) | &&(=(matching1, 1), =(matching2, 1))
584_1_power_InvokeMethod(676_0_power_Return(EOS(STATIC_676), i200, i201), i200, i201) → 760_0_power_Return(EOS(STATIC_760), i200, i201, i200, i201)
584_1_power_InvokeMethod(710_0_power_Return(EOS(STATIC_710)), i250, i251) → 849_0_power_Return(EOS(STATIC_849), i250, i251)
584_1_power_InvokeMethod(907_0_power_Return(EOS(STATIC_907), i359, i360), i359, i360) → 998_0_power_Return(EOS(STATIC_998), i359, i360, i359, i360)
584_1_power_InvokeMethod(988_0_power_Return(EOS(STATIC_988)), i434, i435) → 1067_0_power_Return(EOS(STATIC_1067), i434, i435)
590_1_power_InvokeMethod(429_0_power_Return(EOS(STATIC_429), i147, matching1, i147), i147, i73, i147, i147, matching2) → 652_0_power_Return(EOS(STATIC_652), i147, i73, i147, i147, 1, i147, 1, i147) | &&(=(matching1, 1), =(matching2, 1))
590_1_power_InvokeMethod(896_0_power_Return(EOS(STATIC_896), i343, i344, i320), i343, i73, i343, i343, i344) → 983_0_power_Return(EOS(STATIC_983), i343, i73, i343, i343, i344, i343, i344, i320)
590_1_power_InvokeMethod(968_0_power_Return(EOS(STATIC_968), i370), i422, i73, i422, i422, i423) → 1054_0_power_Return(EOS(STATIC_1054), i422, i73, i422, i422, i423, i370)
595_1_power_InvokeMethod(429_0_power_Return(EOS(STATIC_429), i160, matching1, i160), i160, i73, i160, i160, matching2) → 658_0_power_Return(EOS(STATIC_658), i160, i73, i160, i160, 1, i160, 1, i160) | &&(=(matching1, 1), =(matching2, 1))
595_1_power_InvokeMethod(676_0_power_Return(EOS(STATIC_676), i209, i210), i209, i73, i209, i209, i210) → 763_0_power_Return(EOS(STATIC_763), i209, i73, i209, i209, i210, i209, i210)
595_1_power_InvokeMethod(710_0_power_Return(EOS(STATIC_710)), i258, i73, i258, i258, i259) → 853_0_power_Return(EOS(STATIC_853), i258, i73, i258, i258, i259)
595_1_power_InvokeMethod(907_0_power_Return(EOS(STATIC_907), i366, i367), i366, i73, i366, i366, i367) → 1003_0_power_Return(EOS(STATIC_1003), i366, i73, i366, i366, i367, i366, i367)
595_1_power_InvokeMethod(988_0_power_Return(EOS(STATIC_988)), i440, i73, i440, i440, i441) → 1072_0_power_Return(EOS(STATIC_1072), i440, i73, i440, i440, i441)
623_0_power_Return(EOS(STATIC_623), i118, matching1, i118, matching2, i118) → 650_0_power_Store(EOS(STATIC_650), i118) | &&(=(matching1, 1), =(matching2, 1))
636_0_power_Return(EOS(STATIC_636), i134, matching1, i134, matching2, i134) → 656_0_power_Store(EOS(STATIC_656), i134) | &&(=(matching1, 1), =(matching2, 1))
650_0_power_Store(EOS(STATIC_650), i118) → 790_0_power_Store(EOS(STATIC_790), i118)
652_0_power_Return(EOS(STATIC_652), i147, i73, i147, i147, matching1, i147, matching2, i147) → 664_0_power_IntArithmetic(EOS(STATIC_664), i147, i73, i147, i147) | &&(=(matching1, 1), =(matching2, 1))
656_0_power_Store(EOS(STATIC_656), i134) → 666_0_power_Load(EOS(STATIC_666), i134)
658_0_power_Return(EOS(STATIC_658), i160, i73, i160, i160, matching1, i160, matching2, i160) → 668_0_power_IntArithmetic(EOS(STATIC_668), i160, i73, i160, i160) | &&(=(matching1, 1), =(matching2, 1))
664_0_power_IntArithmetic(EOS(STATIC_664), i147, i73, i147, i147) → 794_0_power_IntArithmetic(EOS(STATIC_794), i147, i73, i147, i147)
666_0_power_Load(EOS(STATIC_666), i134) → 674_0_power_Load(EOS(STATIC_674), i134, i134)
668_0_power_IntArithmetic(EOS(STATIC_668), i160, i73, i160, i160) → 676_0_power_Return(EOS(STATIC_676), i160, i73) | &&(>(i160, 1), >(i160, 1))
674_0_power_Load(EOS(STATIC_674), i134, i134) → 682_0_power_IntArithmetic(EOS(STATIC_682), i134, i134)
682_0_power_IntArithmetic(EOS(STATIC_682), i134, i134) → 710_0_power_Return(EOS(STATIC_710)) | &&(>(i134, 1), >(i134, 1))
739_0_power_Return(EOS(STATIC_739), i176, i177, i176, i177, i166) → 790_0_power_Store(EOS(STATIC_790), i166)
741_0_power_Return(EOS(STATIC_741), i182, i73, i182, i182, i183, i182, i183, i166) → 794_0_power_IntArithmetic(EOS(STATIC_794), i182, i73, i182, i166)
760_0_power_Return(EOS(STATIC_760), i200, i201, i200, i201) → 822_0_power_Store(EOS(STATIC_822))
763_0_power_Return(EOS(STATIC_763), i209, i73, i209, i209, i210, i209, i210) → 825_0_power_IntArithmetic(EOS(STATIC_825), i209, i73, i209)
790_0_power_Store(EOS(STATIC_790), i166) → 870_0_power_Store(EOS(STATIC_870), i166)
794_0_power_IntArithmetic(EOS(STATIC_794), i182, i73, i182, i166) → 875_0_power_IntArithmetic(EOS(STATIC_875), i182, i73, i182, i166)
822_0_power_Store(EOS(STATIC_822)) → 885_0_power_Store(EOS(STATIC_885))
825_0_power_IntArithmetic(EOS(STATIC_825), i209, i73, i209) → 891_0_power_IntArithmetic(EOS(STATIC_891), i209, i73, i209)
831_0_power_Return(EOS(STATIC_831), i224, i225, i169) → 870_0_power_Store(EOS(STATIC_870), i169)
833_0_power_Return(EOS(STATIC_833), i230, i73, i230, i230, i231, i169) → 875_0_power_IntArithmetic(EOS(STATIC_875), i230, i73, i230, i169)
849_0_power_Return(EOS(STATIC_849), i250, i251) → 885_0_power_Store(EOS(STATIC_885))
853_0_power_Return(EOS(STATIC_853), i258, i73, i258, i258, i259) → 891_0_power_IntArithmetic(EOS(STATIC_891), i258, i73, i258)
870_0_power_Store(EOS(STATIC_870), i169) → 894_0_power_Load(EOS(STATIC_894), i169)
875_0_power_IntArithmetic(EOS(STATIC_875), i230, i73, i230, i169) → 896_0_power_Return(EOS(STATIC_896), i230, i73, *(i230, i169)) | &&(<=(i230, 1), <=(i169, 1))
885_0_power_Store(EOS(STATIC_885)) → 904_0_power_Load(EOS(STATIC_904))
891_0_power_IntArithmetic(EOS(STATIC_891), i258, i73, i258) → 907_0_power_Return(EOS(STATIC_907), i258, i73) | >(i258, 1)
894_0_power_Load(EOS(STATIC_894), i169) → 909_0_power_Load(EOS(STATIC_909), i169, i169)
904_0_power_Load(EOS(STATIC_904)) → 915_0_power_Load(EOS(STATIC_915))
909_0_power_Load(EOS(STATIC_909), i169, i169) → 919_0_power_IntArithmetic(EOS(STATIC_919), i169, i169)
915_0_power_Load(EOS(STATIC_915)) → 944_0_power_IntArithmetic(EOS(STATIC_944))
919_0_power_IntArithmetic(EOS(STATIC_919), i169, i169) → 968_0_power_Return(EOS(STATIC_968), *(i169, i169)) | &&(<=(i169, 1), <=(i169, 1))
944_0_power_IntArithmetic(EOS(STATIC_944)) → 988_0_power_Return(EOS(STATIC_988))
978_0_power_Return(EOS(STATIC_978), i337, i338, i337, i338, i320) → 739_0_power_Return(EOS(STATIC_739), i337, i338, i337, i338, i320)
983_0_power_Return(EOS(STATIC_983), i343, i73, i343, i343, i344, i343, i344, i320) → 741_0_power_Return(EOS(STATIC_741), i343, i73, i343, i343, i344, i343, i344, i320)
998_0_power_Return(EOS(STATIC_998), i359, i360, i359, i360) → 760_0_power_Return(EOS(STATIC_760), i359, i360, i359, i360)
1003_0_power_Return(EOS(STATIC_1003), i366, i73, i366, i366, i367, i366, i367) → 763_0_power_Return(EOS(STATIC_763), i366, i73, i366, i366, i367, i366, i367)
1050_0_power_Return(EOS(STATIC_1050), i415, i416, i370) → 831_0_power_Return(EOS(STATIC_831), i415, i416, i370)
1054_0_power_Return(EOS(STATIC_1054), i422, i73, i422, i422, i423, i370) → 833_0_power_Return(EOS(STATIC_833), i422, i73, i422, i422, i423, i370)
1067_0_power_Return(EOS(STATIC_1067), i434, i435) → 849_0_power_Return(EOS(STATIC_849), i434, i435)
1072_0_power_Return(EOS(STATIC_1072), i440, i73, i440, i440, i441) → 853_0_power_Return(EOS(STATIC_853), i440, i73, i440, i440, i441)

Combined rules. Obtained 4 conditional rules for P and 17 conditional rules for R.

P rules:
382_0_power_GT(EOS(STATIC_382), x0, x1, x1) → 579_1_power_InvokeMethod(382_0_power_GT(EOS(STATIC_382), x0, /(x1, 2), /(x1, 2)), x0, /(x1, 2)) | &&(&&(>(x1, 1), !(=(x0, 2))), =(0, %(x1, 2)))
382_0_power_GT(EOS(STATIC_382), x0, x1, x1) → 590_1_power_InvokeMethod(382_0_power_GT(EOS(STATIC_382), x0, -(x1, 1), -(x1, 1)), x0, x1, x0, x0, -(x1, 1)) | &&(&&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2))), =(1, %(x1, 2)))
382_0_power_GT(EOS(STATIC_382), x0, x1, x1) → 584_1_power_InvokeMethod(382_0_power_GT(EOS(STATIC_382), x0, /(x1, 2), /(x1, 2)), x0, /(x1, 2)) | &&(&&(>(x1, 1), !(=(x0, 2))), =(0, %(x1, 2)))
382_0_power_GT(EOS(STATIC_382), x0, x1, x1) → 595_1_power_InvokeMethod(382_0_power_GT(EOS(STATIC_382), x0, -(x1, 1), -(x1, 1)), x0, x1, x0, x0, -(x1, 1)) | &&(&&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2))), =(1, %(x1, 2)))
R rules:
382_0_power_GT(EOS(STATIC_382), x0, 0, 0) → 388_0_power_Return(EOS(STATIC_388), x0, 0)
595_1_power_InvokeMethod(429_0_power_Return(EOS(STATIC_429), x0, 1, x0), x0, x2, x0, x0, 1) → 676_0_power_Return(EOS(STATIC_676), x0, x2) | >(x0, 1)
584_1_power_InvokeMethod(429_0_power_Return(EOS(STATIC_429), x0, 1, x0), x0, 1) → 710_0_power_Return(EOS(STATIC_710)) | >(x0, 1)
590_1_power_InvokeMethod(429_0_power_Return(EOS(STATIC_429), x0, 1, x0), x0, x2, x0, x0, 1) → 896_0_power_Return(EOS(STATIC_896), x0, x2, *(x0, x0)) | <=(x0, 1)
595_1_power_InvokeMethod(710_0_power_Return(EOS(STATIC_710)), x0, x1, x0, x0, x2) → 907_0_power_Return(EOS(STATIC_907), x0, x1) | >(x0, 1)
595_1_power_InvokeMethod(988_0_power_Return(EOS(STATIC_988)), x0, x1, x0, x0, x2) → 907_0_power_Return(EOS(STATIC_907), x0, x1) | >(x0, 1)
595_1_power_InvokeMethod(676_0_power_Return(EOS(STATIC_676), x0, x1), x0, x2, x0, x0, x1) → 907_0_power_Return(EOS(STATIC_907), x0, x2) | >(x0, 1)
595_1_power_InvokeMethod(907_0_power_Return(EOS(STATIC_907), x0, x1), x0, x2, x0, x0, x1) → 907_0_power_Return(EOS(STATIC_907), x0, x2) | >(x0, 1)
579_1_power_InvokeMethod(429_0_power_Return(EOS(STATIC_429), x0, 1, x0), x0, 1) → 968_0_power_Return(EOS(STATIC_968), *(x0, x0)) | <=(x0, 1)
584_1_power_InvokeMethod(710_0_power_Return(EOS(STATIC_710)), x0, x1) → 988_0_power_Return(EOS(STATIC_988))
584_1_power_InvokeMethod(988_0_power_Return(EOS(STATIC_988)), x0, x1) → 988_0_power_Return(EOS(STATIC_988))
584_1_power_InvokeMethod(676_0_power_Return(EOS(STATIC_676), x0, x1), x0, x1) → 988_0_power_Return(EOS(STATIC_988))
584_1_power_InvokeMethod(907_0_power_Return(EOS(STATIC_907), x0, x1), x0, x1) → 988_0_power_Return(EOS(STATIC_988))
579_1_power_InvokeMethod(896_0_power_Return(EOS(STATIC_896), x0, x1, x2), x0, x1) → 968_0_power_Return(EOS(STATIC_968), *(x2, x2)) | <=(x2, 1)
590_1_power_InvokeMethod(896_0_power_Return(EOS(STATIC_896), x0, x1, x2), x0, x3, x0, x0, x1) → 896_0_power_Return(EOS(STATIC_896), x0, x3, *(x0, x2)) | &&(<=(x2, 1), <=(x0, 1))
579_1_power_InvokeMethod(968_0_power_Return(EOS(STATIC_968), x0), x1, x2) → 968_0_power_Return(EOS(STATIC_968), *(x0, x0)) | <=(x0, 1)
590_1_power_InvokeMethod(968_0_power_Return(EOS(STATIC_968), x0), x1, x2, x1, x1, x3) → 896_0_power_Return(EOS(STATIC_896), x1, x2, *(x1, x0)) | &&(<=(x1, 1), <=(x0, 1))

Filtered ground terms:

382_0_power_GT(x1, x2, x3, x4) → 382_0_power_GT(x2, x3, x4)
Cond_382_0_power_GT3(x1, x2, x3, x4, x5) → Cond_382_0_power_GT3(x1, x3, x4, x5)
Cond_382_0_power_GT2(x1, x2, x3, x4, x5) → Cond_382_0_power_GT2(x1, x3, x4, x5)
Cond_382_0_power_GT1(x1, x2, x3, x4, x5) → Cond_382_0_power_GT1(x1, x3, x4, x5)
Cond_382_0_power_GT(x1, x2, x3, x4, x5) → Cond_382_0_power_GT(x1, x3, x4, x5)
896_0_power_Return(x1, x2, x3, x4) → 896_0_power_Return(x2, x3, x4)
968_0_power_Return(x1, x2) → 968_0_power_Return(x2)
988_0_power_Return(x1) → 988_0_power_Return
907_0_power_Return(x1, x2, x3) → 907_0_power_Return(x2, x3)
676_0_power_Return(x1, x2, x3) → 676_0_power_Return(x2, x3)
710_0_power_Return(x1) → 710_0_power_Return
Cond_579_1_power_InvokeMethod(x1, x2, x3, x4) → Cond_579_1_power_InvokeMethod(x1, x2, x3)
429_0_power_Return(x1, x2, x3, x4) → 429_0_power_Return(x2, x4)
Cond_595_1_power_InvokeMethod2(x1, x2, x3, x4, x5, x6, x7) → Cond_595_1_power_InvokeMethod2(x1, x3, x4, x5, x6, x7)
Cond_595_1_power_InvokeMethod1(x1, x2, x3, x4, x5, x6, x7) → Cond_595_1_power_InvokeMethod1(x1, x3, x4, x5, x6, x7)
Cond_590_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → Cond_590_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6)
Cond_584_1_power_InvokeMethod(x1, x2, x3, x4) → Cond_584_1_power_InvokeMethod(x1, x2, x3)
Cond_595_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6, x7) → Cond_595_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6)
388_0_power_Return(x1, x2, x3) → 388_0_power_Return(x2)

Filtered duplicate args:

382_0_power_GT(x1, x2, x3) → 382_0_power_GT(x1, x3)
Cond_382_0_power_GT(x1, x2, x3, x4) → Cond_382_0_power_GT(x1, x2, x4)
Cond_382_0_power_GT1(x1, x2, x3, x4) → Cond_382_0_power_GT1(x1, x2, x4)
590_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6) → 590_1_power_InvokeMethod(x1, x3, x5, x6)
Cond_382_0_power_GT2(x1, x2, x3, x4) → Cond_382_0_power_GT2(x1, x2, x4)
Cond_382_0_power_GT3(x1, x2, x3, x4) → Cond_382_0_power_GT3(x1, x2, x4)
595_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6) → 595_1_power_InvokeMethod(x1, x3, x5, x6)
429_0_power_Return(x1, x2) → 429_0_power_Return(x2)
Cond_595_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_595_1_power_InvokeMethod(x1, x2, x4)
Cond_584_1_power_InvokeMethod(x1, x2, x3) → Cond_584_1_power_InvokeMethod(x1, x2)
Cond_590_1_power_InvokeMethod(x1, x2, x3, x4, x5, x6) → Cond_590_1_power_InvokeMethod(x1, x2, x4)
Cond_595_1_power_InvokeMethod1(x1, x2, x3, x4, x5, x6) → Cond_595_1_power_InvokeMethod1(x1, x3, x5, x6)
Cond_595_1_power_InvokeMethod2(x1, x2, x3, x4, x5, x6) → Cond_595_1_power_InvokeMethod2(x1, x3, x5, x6)
Cond_595_1_power_InvokeMethod3(x1, x2, x3, x4, x5, x6, x7) → Cond_595_1_power_InvokeMethod3(x1, x2, x4)
Cond_595_1_power_InvokeMethod4(x1, x2, x3, x4, x5, x6, x7) → Cond_595_1_power_InvokeMethod4(x1, x2, x4)
Cond_579_1_power_InvokeMethod(x1, x2, x3) → Cond_579_1_power_InvokeMethod(x1, x2)
Cond_579_1_power_InvokeMethod1(x1, x2, x3, x4) → Cond_579_1_power_InvokeMethod1(x1, x2)
Cond_590_1_power_InvokeMethod1(x1, x2, x3, x4, x5, x6, x7) → Cond_590_1_power_InvokeMethod1(x1, x2, x4)
Cond_590_1_power_InvokeMethod2(x1, x2, x3, x4, x5, x6, x7) → Cond_590_1_power_InvokeMethod2(x1, x2, x4, x6, x7)

Filtered unneeded arguments:

590_1_power_InvokeMethod(x1, x2, x3, x4) → 590_1_power_InvokeMethod(x1, x3, x4)
595_1_power_InvokeMethod(x1, x2, x3, x4) → 595_1_power_InvokeMethod(x1, x3, x4)
Cond_595_1_power_InvokeMethod(x1, x2, x3) → Cond_595_1_power_InvokeMethod(x1, x2)
Cond_584_1_power_InvokeMethod(x1, x2) → Cond_584_1_power_InvokeMethod(x1)
Cond_590_1_power_InvokeMethod(x1, x2, x3) → Cond_590_1_power_InvokeMethod(x1, x2)
Cond_595_1_power_InvokeMethod1(x1, x2, x3, x4) → Cond_595_1_power_InvokeMethod1(x1, x3)
Cond_595_1_power_InvokeMethod2(x1, x2, x3, x4) → Cond_595_1_power_InvokeMethod2(x1, x3)
Cond_595_1_power_InvokeMethod3(x1, x2, x3) → Cond_595_1_power_InvokeMethod3(x1, x2)
Cond_595_1_power_InvokeMethod4(x1, x2, x3) → Cond_595_1_power_InvokeMethod4(x1, x2)
Cond_590_1_power_InvokeMethod1(x1, x2, x3) → Cond_590_1_power_InvokeMethod1(x1, x2)
Cond_579_1_power_InvokeMethod2(x1, x2, x3, x4) → Cond_579_1_power_InvokeMethod2(x1, x2)
Cond_590_1_power_InvokeMethod2(x1, x2, x3, x4, x5) → Cond_590_1_power_InvokeMethod2(x1, x2, x4)
676_0_power_Return(x1, x2) → 676_0_power_Return(x1)
907_0_power_Return(x1, x2) → 907_0_power_Return(x1)
896_0_power_Return(x1, x2, x3) → 896_0_power_Return(x1, x3)

Filtered modulo operations.

Combined rules. Obtained 4 conditional rules for P and 17 conditional rules for R.

P rules:
382_0_power_GT(x0, x1) → 579_1_power_InvokeMethod(382_0_power_GT(x0, /(x1, 2)), x0, /(x1, 2)) | &&(>(x1, 1), !(=(x0, 2)))
382_0_power_GT(x0, x1) → 590_1_power_InvokeMethod(382_0_power_GT(x0, -(x1, 1)), x0, -(x1, 1)) | &&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2)))
382_0_power_GT(x0, x1) → 584_1_power_InvokeMethod(382_0_power_GT(x0, /(x1, 2)), x0, /(x1, 2)) | &&(>(x1, 1), !(=(x0, 2)))
382_0_power_GT(x0, x1) → 595_1_power_InvokeMethod(382_0_power_GT(x0, -(x1, 1)), x0, -(x1, 1)) | &&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2)))
R rules:
382_0_power_GT(x0, 0) → 388_0_power_Return(x0)
595_1_power_InvokeMethod(429_0_power_Return(x0), x0, 1) → 676_0_power_Return(x0) | >(x0, 1)
584_1_power_InvokeMethod(429_0_power_Return(x0), x0, 1) → 710_0_power_Return | >(x0, 1)
590_1_power_InvokeMethod(429_0_power_Return(x0), x0, 1) → 896_0_power_Return(x0, *(x0, x0)) | <=(x0, 1)
595_1_power_InvokeMethod(710_0_power_Return, x0, x2) → 907_0_power_Return(x0) | >(x0, 1)
595_1_power_InvokeMethod(988_0_power_Return, x0, x2) → 907_0_power_Return(x0) | >(x0, 1)
595_1_power_InvokeMethod(676_0_power_Return(x0), x0, x1) → 907_0_power_Return(x0) | >(x0, 1)
595_1_power_InvokeMethod(907_0_power_Return(x0), x0, x1) → 907_0_power_Return(x0) | >(x0, 1)
579_1_power_InvokeMethod(429_0_power_Return(x0), x0, 1) → 968_0_power_Return(*(x0, x0)) | <=(x0, 1)
584_1_power_InvokeMethod(710_0_power_Return, x0, x1) → 988_0_power_Return
584_1_power_InvokeMethod(988_0_power_Return, x0, x1) → 988_0_power_Return
584_1_power_InvokeMethod(676_0_power_Return(x0), x0, x1) → 988_0_power_Return
584_1_power_InvokeMethod(907_0_power_Return(x0), x0, x1) → 988_0_power_Return
579_1_power_InvokeMethod(896_0_power_Return(x0, x2), x0, x1) → 968_0_power_Return(*(x2, x2)) | <=(x2, 1)
590_1_power_InvokeMethod(896_0_power_Return(x0, x2), x0, x1) → 896_0_power_Return(x0, *(x0, x2)) | &&(<=(x2, 1), <=(x0, 1))
579_1_power_InvokeMethod(968_0_power_Return(x0), x1, x2) → 968_0_power_Return(*(x0, x0)) | <=(x0, 1)
590_1_power_InvokeMethod(968_0_power_Return(x0), x1, x3) → 896_0_power_Return(x1, *(x1, x0)) | &&(<=(x1, 1), <=(x0, 1))

Performed bisimulation on rules. Used the following equivalence classes: {[388_0_power_Return_1, 429_0_power_Return_1, 676_0_power_Return_1, 907_0_power_Return_1]=388_0_power_Return_1, [Cond_595_1_power_InvokeMethod3_4, Cond_595_1_power_InvokeMethod4_4]=Cond_595_1_power_InvokeMethod3_4, [Cond_595_1_power_InvokeMethod1_4, Cond_595_1_power_InvokeMethod2_4]=Cond_595_1_power_InvokeMethod1_4, [710_0_power_Return, 988_0_power_Return]=710_0_power_Return}

Finished conversion. Obtained 8 rules for P and 23 rules for R. System has predefined symbols.

P rules:
382_0_POWER_GT(x0, x1) → COND_382_0_POWER_GT(&&(>(x1, 1), !(=(x0, 2))), x0, x1)
COND_382_0_POWER_GT(TRUE, x0, x1) → 382_0_POWER_GT(x0, /(x1, 2))
382_0_POWER_GT(x0, x1) → COND_382_0_POWER_GT1(&&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2))), x0, x1)
COND_382_0_POWER_GT1(TRUE, x0, x1) → 382_0_POWER_GT(x0, -(x1, 1))
382_0_POWER_GT(x0, x1) → COND_382_0_POWER_GT2(&&(>(x1, 1), !(=(x0, 2))), x0, x1)
COND_382_0_POWER_GT2(TRUE, x0, x1) → 382_0_POWER_GT(x0, /(x1, 2))
382_0_POWER_GT(x0, x1) → COND_382_0_POWER_GT3(&&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2))), x0, x1)
COND_382_0_POWER_GT3(TRUE, x0, x1) → 382_0_POWER_GT(x0, -(x1, 1))
R rules:
382_0_power_GT(x0, 0) → 388_0_power_Return(x0)
595_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1) → Cond_595_1_power_InvokeMethod(>(x0, 1), 388_0_power_Return(x0), x0, 1)
Cond_595_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1) → 388_0_power_Return(x0)
584_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1) → Cond_584_1_power_InvokeMethod(>(x0, 1), 388_0_power_Return(x0), x0, 1)
Cond_584_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1) → 710_0_power_Return
590_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1) → Cond_590_1_power_InvokeMethod(<=(x0, 1), 388_0_power_Return(x0), x0, 1)
Cond_590_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1) → 896_0_power_Return(x0, *(x0, x0))
595_1_power_InvokeMethod(710_0_power_Return, x0, x2) → Cond_595_1_power_InvokeMethod1(>(x0, 1), 710_0_power_Return, x0, x2)
Cond_595_1_power_InvokeMethod1(TRUE, 710_0_power_Return, x0, x2) → 388_0_power_Return(x0)
595_1_power_InvokeMethod(388_0_power_Return(x0), x0, x1) → Cond_595_1_power_InvokeMethod3(>(x0, 1), 388_0_power_Return(x0), x0, x1)
Cond_595_1_power_InvokeMethod3(TRUE, 388_0_power_Return(x0), x0, x1) → 388_0_power_Return(x0)
579_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1) → Cond_579_1_power_InvokeMethod(<=(x0, 1), 388_0_power_Return(x0), x0, 1)
Cond_579_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1) → 968_0_power_Return(*(x0, x0))
584_1_power_InvokeMethod(710_0_power_Return, x0, x1) → 710_0_power_Return
584_1_power_InvokeMethod(388_0_power_Return(x0), x0, x1) → 710_0_power_Return
579_1_power_InvokeMethod(896_0_power_Return(x0, x2), x0, x1) → Cond_579_1_power_InvokeMethod1(<=(x2, 1), 896_0_power_Return(x0, x2), x0, x1)
Cond_579_1_power_InvokeMethod1(TRUE, 896_0_power_Return(x0, x2), x0, x1) → 968_0_power_Return(*(x2, x2))
590_1_power_InvokeMethod(896_0_power_Return(x0, x2), x0, x1) → Cond_590_1_power_InvokeMethod1(&&(<=(x2, 1), <=(x0, 1)), 896_0_power_Return(x0, x2), x0, x1)
Cond_590_1_power_InvokeMethod1(TRUE, 896_0_power_Return(x0, x2), x0, x1) → 896_0_power_Return(x0, *(x0, x2))
579_1_power_InvokeMethod(968_0_power_Return(x0), x1, x2) → Cond_579_1_power_InvokeMethod2(<=(x0, 1), 968_0_power_Return(x0), x1, x2)
Cond_579_1_power_InvokeMethod2(TRUE, 968_0_power_Return(x0), x1, x2) → 968_0_power_Return(*(x0, x0))
590_1_power_InvokeMethod(968_0_power_Return(x0), x1, x3) → Cond_590_1_power_InvokeMethod2(&&(<=(x1, 1), <=(x0, 1)), 968_0_power_Return(x0), x1, x3)
Cond_590_1_power_InvokeMethod2(TRUE, 968_0_power_Return(x0), x1, x3) → 896_0_power_Return(x1, *(x1, x0))

(6) Obligation:

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

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

The following domains are used:

Integer, Boolean

The ITRS R consists of the following rules:
382_0_power_GT(x0, 0) → 388_0_power_Return(x0)
595_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1) → Cond_595_1_power_InvokeMethod(x0 > 1, 388_0_power_Return(x0), x0, 1)
Cond_595_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1) → 388_0_power_Return(x0)
584_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1) → Cond_584_1_power_InvokeMethod(x0 > 1, 388_0_power_Return(x0), x0, 1)
Cond_584_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1) → 710_0_power_Return
590_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1) → Cond_590_1_power_InvokeMethod(x0 <= 1, 388_0_power_Return(x0), x0, 1)
Cond_590_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1) → 896_0_power_Return(x0, x0 * x0)
595_1_power_InvokeMethod(710_0_power_Return, x0, x2) → Cond_595_1_power_InvokeMethod1(x0 > 1, 710_0_power_Return, x0, x2)
Cond_595_1_power_InvokeMethod1(TRUE, 710_0_power_Return, x0, x2) → 388_0_power_Return(x0)
595_1_power_InvokeMethod(388_0_power_Return(x0), x0, x1) → Cond_595_1_power_InvokeMethod3(x0 > 1, 388_0_power_Return(x0), x0, x1)
Cond_595_1_power_InvokeMethod3(TRUE, 388_0_power_Return(x0), x0, x1) → 388_0_power_Return(x0)
579_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1) → Cond_579_1_power_InvokeMethod(x0 <= 1, 388_0_power_Return(x0), x0, 1)
Cond_579_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1) → 968_0_power_Return(x0 * x0)
584_1_power_InvokeMethod(710_0_power_Return, x0, x1) → 710_0_power_Return
584_1_power_InvokeMethod(388_0_power_Return(x0), x0, x1) → 710_0_power_Return
579_1_power_InvokeMethod(896_0_power_Return(x0, x2), x0, x1) → Cond_579_1_power_InvokeMethod1(x2 <= 1, 896_0_power_Return(x0, x2), x0, x1)
Cond_579_1_power_InvokeMethod1(TRUE, 896_0_power_Return(x0, x2), x0, x1) → 968_0_power_Return(x2 * x2)
590_1_power_InvokeMethod(896_0_power_Return(x0, x2), x0, x1) → Cond_590_1_power_InvokeMethod1(x2 <= 1 && x0 <= 1, 896_0_power_Return(x0, x2), x0, x1)
Cond_590_1_power_InvokeMethod1(TRUE, 896_0_power_Return(x0, x2), x0, x1) → 896_0_power_Return(x0, x0 * x2)
579_1_power_InvokeMethod(968_0_power_Return(x0), x1, x2) → Cond_579_1_power_InvokeMethod2(x0 <= 1, 968_0_power_Return(x0), x1, x2)
Cond_579_1_power_InvokeMethod2(TRUE, 968_0_power_Return(x0), x1, x2) → 968_0_power_Return(x0 * x0)
590_1_power_InvokeMethod(968_0_power_Return(x0), x1, x3) → Cond_590_1_power_InvokeMethod2(x1 <= 1 && x0 <= 1, 968_0_power_Return(x0), x1, x3)
Cond_590_1_power_InvokeMethod2(TRUE, 968_0_power_Return(x0), x1, x3) → 896_0_power_Return(x1, x1 * x0)

The integer pair graph contains the following rules and edges:
(0): 382_0_POWER_GT(x0[0], x1[0]) → COND_382_0_POWER_GT(x1[0] > 1 && !(x0[0] = 2), x0[0], x1[0])
(1): COND_382_0_POWER_GT(TRUE, x0[1], x1[1]) → 382_0_POWER_GT(x0[1], x1[1] / 2)
(2): 382_0_POWER_GT(x0[2], x1[2]) → COND_382_0_POWER_GT1(x1[2] > 0 && !(x1[2] = 1) && !(x0[2] = 2), x0[2], x1[2])
(3): COND_382_0_POWER_GT1(TRUE, x0[3], x1[3]) → 382_0_POWER_GT(x0[3], x1[3] - 1)
(4): 382_0_POWER_GT(x0[4], x1[4]) → COND_382_0_POWER_GT2(x1[4] > 1 && !(x0[4] = 2), x0[4], x1[4])
(5): COND_382_0_POWER_GT2(TRUE, x0[5], x1[5]) → 382_0_POWER_GT(x0[5], x1[5] / 2)
(6): 382_0_POWER_GT(x0[6], x1[6]) → COND_382_0_POWER_GT3(x1[6] > 0 && !(x1[6] = 1) && !(x0[6] = 2), x0[6], x1[6])
(7): COND_382_0_POWER_GT3(TRUE, x0[7], x1[7]) → 382_0_POWER_GT(x0[7], x1[7] - 1)

(0) -> (1), if (x1[0] > 1 && !(x0[0] = 2) ∧x0[0] →^* x0[1]∧x1[0] →^* x1[1])

(1) -> (0), if (x0[1] →^* x0[0]∧x1[1] / 2 →^* x1[0])

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

(1) -> (4), if (x0[1] →^* x0[4]∧x1[1] / 2 →^* x1[4])

(1) -> (6), if (x0[1] →^* x0[6]∧x1[1] / 2 →^* x1[6])

(2) -> (3), if (x1[2] > 0 && !(x1[2] = 1) && !(x0[2] = 2) ∧x0[2] →^* x0[3]∧x1[2] →^* x1[3])

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

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

(3) -> (4), if (x0[3] →^* x0[4]∧x1[3] - 1 →^* x1[4])

(3) -> (6), if (x0[3] →^* x0[6]∧x1[3] - 1 →^* x1[6])

(4) -> (5), if (x1[4] > 1 && !(x0[4] = 2) ∧x0[4] →^* x0[5]∧x1[4] →^* x1[5])

(5) -> (0), if (x0[5] →^* x0[0]∧x1[5] / 2 →^* x1[0])

(5) -> (2), if (x0[5] →^* x0[2]∧x1[5] / 2 →^* x1[2])

(5) -> (4), if (x0[5] →^* x0[4]∧x1[5] / 2 →^* x1[4])

(5) -> (6), if (x0[5] →^* x0[6]∧x1[5] / 2 →^* x1[6])

(6) -> (7), if (x1[6] > 0 && !(x1[6] = 1) && !(x0[6] = 2) ∧x0[6] →^* x0[7]∧x1[6] →^* x1[7])

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

(7) -> (2), if (x0[7] →^* x0[2]∧x1[7] - 1 →^* x1[2])

(7) -> (4), if (x0[7] →^* x0[4]∧x1[7] - 1 →^* x1[4])

(7) -> (6), if (x0[7] →^* x0[6]∧x1[7] - 1 →^* x1[6])

The set Q consists of the following terms:
382_0_power_GT(x0, 0)
Cond_595_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1)
Cond_584_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1)
590_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1)
Cond_590_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1)
595_1_power_InvokeMethod(710_0_power_Return, x0, x1)
Cond_595_1_power_InvokeMethod1(TRUE, 710_0_power_Return, x0, x1)
595_1_power_InvokeMethod(388_0_power_Return(x0), x0, x1)
Cond_595_1_power_InvokeMethod3(TRUE, 388_0_power_Return(x0), x0, x1)
579_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1)
Cond_579_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1)
584_1_power_InvokeMethod(710_0_power_Return, x0, x1)
584_1_power_InvokeMethod(388_0_power_Return(x0), x0, x1)
579_1_power_InvokeMethod(896_0_power_Return(x0, x1), x0, x2)
Cond_579_1_power_InvokeMethod1(TRUE, 896_0_power_Return(x0, x1), x0, x2)
590_1_power_InvokeMethod(896_0_power_Return(x0, x1), x0, x2)
Cond_590_1_power_InvokeMethod1(TRUE, 896_0_power_Return(x0, x1), x0, x2)
579_1_power_InvokeMethod(968_0_power_Return(x0), x1, x2)
Cond_579_1_power_InvokeMethod2(TRUE, 968_0_power_Return(x0), x1, x2)
590_1_power_InvokeMethod(968_0_power_Return(x0), x1, x2)
Cond_590_1_power_InvokeMethod2(TRUE, 968_0_power_Return(x0), x1, x2)

(7) IDPNonInfProof (SOUND transformation)

Used the following options for this NonInfProof:
IDPGPoloSolver: Range: [(-1,2)] IsNat: false Interpretation Shape Heuristic: aprove.DPFramework.IDPProblem.Processors.nonInf.poly.IdpDefaultShapeHeuristic@713a902c 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 382_0_POWER_GT(x0, x1) → COND_382_0_POWER_GT(&&(>(x1, 1), !(=(x0, 2))), x0, x1) the following chains were created:

We consider the chain 382_0_POWER_GT(x0[0], x1[0]) → COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0]), COND_382_0_POWER_GT(TRUE, x0[1], x1[1]) → 382_0_POWER_GT(x0[1], /(x1[1], 2)) which results in the following constraint:
(1)    (&&(>(x1[0], 1), !(=(x0[0], 2)))=TRUE∧x0[0]=x0[1]∧x1[0]=x1[1] ⇒ 382_0_POWER_GT(x0[0], x1[0])≥NonInfC∧382_0_POWER_GT(x0[0], x1[0])≥COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])∧(U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥))

We simplified constraint (1) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:
(2)    (>(x1[0], 1)=TRUE∧<(x0[0], 2)=TRUE ⇒ 382_0_POWER_GT(x0[0], x1[0])≥NonInfC∧382_0_POWER_GT(x0[0], x1[0])≥COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])∧(U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥))

(3)    (>(x1[0], 1)=TRUE∧>(x0[0], 2)=TRUE ⇒ 382_0_POWER_GT(x0[0], x1[0])≥NonInfC∧382_0_POWER_GT(x0[0], x1[0])≥COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])∧(U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥))

We simplified constraint (2) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(4)    (x1[0] + [-2] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[(-1)bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)

We simplified constraint (3) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(5)    (x1[0] + [-2] ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[(-1)bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)

We simplified constraint (4) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(6)    (x1[0] + [-2] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[(-1)bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)

We simplified constraint (5) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(7)    (x1[0] + [-2] ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[(-1)bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)

We simplified constraint (6) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(8)    (x1[0] + [-2] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[(-1)bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)

We simplified constraint (7) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(9)    (x1[0] + [-2] ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[(-1)bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)

We simplified constraint (8) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(10)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)

We simplified constraint (9) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(11)    (x1[0] ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)

We simplified constraint (10) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(12)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)

(13)    (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)

We simplified constraint (11) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(14)    (x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)

For Pair COND_382_0_POWER_GT(TRUE, x0, x1) → 382_0_POWER_GT(x0, /(x1, 2)) the following chains were created:

We consider the chain 382_0_POWER_GT(x0[0], x1[0]) → COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0]), COND_382_0_POWER_GT(TRUE, x0[1], x1[1]) → 382_0_POWER_GT(x0[1], /(x1[1], 2)) which results in the following constraint:
(15)    (&&(>(x1[0], 1), !(=(x0[0], 2)))=TRUE∧x0[0]=x0[1]∧x1[0]=x1[1] ⇒ COND_382_0_POWER_GT(TRUE, x0[1], x1[1])≥NonInfC∧COND_382_0_POWER_GT(TRUE, x0[1], x1[1])≥382_0_POWER_GT(x0[1], /(x1[1], 2))∧(U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

We simplified constraint (15) using rules (III), (IDP_BOOLEAN) which results in the following new constraints:
(16)    (>(x1[0], 1)=TRUE∧<(x0[0], 2)=TRUE ⇒ COND_382_0_POWER_GT(TRUE, x0[0], x1[0])≥NonInfC∧COND_382_0_POWER_GT(TRUE, x0[0], x1[0])≥382_0_POWER_GT(x0[0], /(x1[0], 2))∧(U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

(17)    (>(x1[0], 1)=TRUE∧>(x0[0], 2)=TRUE ⇒ COND_382_0_POWER_GT(TRUE, x0[0], x1[0])≥NonInfC∧COND_382_0_POWER_GT(TRUE, x0[0], x1[0])≥382_0_POWER_GT(x0[0], /(x1[0], 2))∧(U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥))

We simplified constraint (16) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(18)    (x1[0] + [-2] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] + x1[0] + [-1]max{x1[0], [-1]x1[0]} ≥ 0)

We simplified constraint (17) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(19)    (x1[0] + [-2] ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] + x1[0] + [-1]max{x1[0], [-1]x1[0]} ≥ 0)

We simplified constraint (18) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(20)    (x1[0] + [-2] ≥ 0∧[1] + [-1]x0[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] + x1[0] + [-1]max{x1[0], [-1]x1[0]} ≥ 0)

We simplified constraint (19) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(21)    (x1[0] + [-2] ≥ 0∧x0[0] + [-3] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] + x1[0] + [-1]max{x1[0], [-1]x1[0]} ≥ 0)

We simplified constraint (20) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(22)    (x1[0] + [-2] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)

We simplified constraint (21) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(23)    (x1[0] + [-2] ≥ 0∧x0[0] + [-3] ≥ 0∧[2]x1[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[(-1)bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)

We simplified constraint (22) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(24)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] + [2]x1[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)

We simplified constraint (23) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(25)    (x1[0] ≥ 0∧x0[0] + [-3] ≥ 0∧[4] + [2]x1[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)

We simplified constraint (24) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(26)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧[4] + [2]x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)

(27)    (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧[4] + [2]x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)

We simplified constraint (26) using rule (IDP_POLY_GCD) which results in the following new constraint:
(28)    (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)

We simplified constraint (27) using rule (IDP_POLY_GCD) which results in the following new constraint:
(29)    (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)

We simplified constraint (25) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(30)    (x1[0] ≥ 0∧x0[0] ≥ 0∧[4] + [2]x1[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)

We simplified constraint (30) using rule (IDP_POLY_GCD) which results in the following new constraint:
(31)    (x1[0] ≥ 0∧x0[0] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)

For Pair 382_0_POWER_GT(x0, x1) → COND_382_0_POWER_GT1(&&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2))), x0, x1) the following chains were created:

We consider the chain 382_0_POWER_GT(x0[2], x1[2]) → COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2]), COND_382_0_POWER_GT1(TRUE, x0[3], x1[3]) → 382_0_POWER_GT(x0[3], -(x1[3], 1)) which results in the following constraint:
(32)    (&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2)))=TRUE∧x0[2]=x0[3]∧x1[2]=x1[3] ⇒ 382_0_POWER_GT(x0[2], x1[2])≥NonInfC∧382_0_POWER_GT(x0[2], x1[2])≥COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])∧(U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥))

We simplified constraint (32) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:
(33)    (>(x1[2], 0)=TRUE∧<(x0[2], 2)=TRUE∧<(x1[2], 1)=TRUE ⇒ 382_0_POWER_GT(x0[2], x1[2])≥NonInfC∧382_0_POWER_GT(x0[2], x1[2])≥COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])∧(U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥))

(34)    (>(x1[2], 0)=TRUE∧<(x0[2], 2)=TRUE∧>(x1[2], 1)=TRUE ⇒ 382_0_POWER_GT(x0[2], x1[2])≥NonInfC∧382_0_POWER_GT(x0[2], x1[2])≥COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])∧(U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥))

We simplified constraint (33) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(35)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (34) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(36)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (35) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(37)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (36) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(38)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (39) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(40)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (41) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(42)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (37) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(43)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (38) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(44)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (40) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(45)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (42) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(46)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[(-1)bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We solved constraint (43) using rule (IDP_SMT_SPLIT).We simplified constraint (44) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(47)    (x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1] + x1[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We solved constraint (45) using rule (IDP_SMT_SPLIT).We simplified constraint (46) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(48)    (x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1] + x1[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[(-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (47) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(49)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (49) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(50)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

(51)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (48) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(52)    ([1] + x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

We simplified constraint (52) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(53)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)

For Pair COND_382_0_POWER_GT1(TRUE, x0, x1) → 382_0_POWER_GT(x0, -(x1, 1)) the following chains were created:

We consider the chain 382_0_POWER_GT(x0[2], x1[2]) → COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2]), COND_382_0_POWER_GT1(TRUE, x0[3], x1[3]) → 382_0_POWER_GT(x0[3], -(x1[3], 1)) which results in the following constraint:
(54)    (&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2)))=TRUE∧x0[2]=x0[3]∧x1[2]=x1[3] ⇒ COND_382_0_POWER_GT1(TRUE, x0[3], x1[3])≥NonInfC∧COND_382_0_POWER_GT1(TRUE, x0[3], x1[3])≥382_0_POWER_GT(x0[3], -(x1[3], 1))∧(U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

We simplified constraint (54) using rules (III), (IDP_BOOLEAN) which results in the following new constraints:
(55)    (>(x1[2], 0)=TRUE∧<(x0[2], 2)=TRUE∧<(x1[2], 1)=TRUE ⇒ COND_382_0_POWER_GT1(TRUE, x0[2], x1[2])≥NonInfC∧COND_382_0_POWER_GT1(TRUE, x0[2], x1[2])≥382_0_POWER_GT(x0[2], -(x1[2], 1))∧(U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

(56)    (>(x1[2], 0)=TRUE∧<(x0[2], 2)=TRUE∧>(x1[2], 1)=TRUE ⇒ COND_382_0_POWER_GT1(TRUE, x0[2], x1[2])≥NonInfC∧COND_382_0_POWER_GT1(TRUE, x0[2], x1[2])≥382_0_POWER_GT(x0[2], -(x1[2], 1))∧(U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥))

We simplified constraint (55) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(57)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (56) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(58)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (57) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(59)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (58) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(60)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (61) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(62)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (63) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(64)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (59) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(65)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (60) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(66)    (x1[2] + [-1] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (62) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(67)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1]x1[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (64) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(68)    (x1[2] + [-1] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] + [-2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We solved constraint (65) using rule (IDP_SMT_SPLIT).We simplified constraint (66) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(69)    (x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧[-1] + x1[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We solved constraint (67) using rule (IDP_SMT_SPLIT).We simplified constraint (68) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(70)    (x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧[-1] + x1[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[(-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (69) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(71)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (71) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(72)    ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

(73)    ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (70) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(74)    ([1] + x1[2] ≥ 0∧x0[2] + [-3] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

We simplified constraint (74) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(75)    ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)

For Pair 382_0_POWER_GT(x0, x1) → COND_382_0_POWER_GT2(&&(>(x1, 1), !(=(x0, 2))), x0, x1) the following chains were created:

We consider the chain 382_0_POWER_GT(x0[4], x1[4]) → COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4]), COND_382_0_POWER_GT2(TRUE, x0[5], x1[5]) → 382_0_POWER_GT(x0[5], /(x1[5], 2)) which results in the following constraint:
(76)    (&&(>(x1[4], 1), !(=(x0[4], 2)))=TRUE∧x0[4]=x0[5]∧x1[4]=x1[5] ⇒ 382_0_POWER_GT(x0[4], x1[4])≥NonInfC∧382_0_POWER_GT(x0[4], x1[4])≥COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])∧(U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥))

We simplified constraint (76) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:
(77)    (>(x1[4], 1)=TRUE∧<(x0[4], 2)=TRUE ⇒ 382_0_POWER_GT(x0[4], x1[4])≥NonInfC∧382_0_POWER_GT(x0[4], x1[4])≥COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])∧(U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥))

(78)    (>(x1[4], 1)=TRUE∧>(x0[4], 2)=TRUE ⇒ 382_0_POWER_GT(x0[4], x1[4])≥NonInfC∧382_0_POWER_GT(x0[4], x1[4])≥COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])∧(U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥))

We simplified constraint (77) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(79)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[(-1)bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (78) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(80)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[(-1)bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (79) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(81)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[(-1)bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (80) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(82)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[(-1)bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (81) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(83)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[(-1)bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (82) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(84)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[(-1)bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (83) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(85)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (84) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(86)    (x1[4] ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (85) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(87)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)

(88)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)

We simplified constraint (86) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(89)    (x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)

For Pair COND_382_0_POWER_GT2(TRUE, x0, x1) → 382_0_POWER_GT(x0, /(x1, 2)) the following chains were created:

We consider the chain 382_0_POWER_GT(x0[4], x1[4]) → COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4]), COND_382_0_POWER_GT2(TRUE, x0[5], x1[5]) → 382_0_POWER_GT(x0[5], /(x1[5], 2)) which results in the following constraint:
(90)    (&&(>(x1[4], 1), !(=(x0[4], 2)))=TRUE∧x0[4]=x0[5]∧x1[4]=x1[5] ⇒ COND_382_0_POWER_GT2(TRUE, x0[5], x1[5])≥NonInfC∧COND_382_0_POWER_GT2(TRUE, x0[5], x1[5])≥382_0_POWER_GT(x0[5], /(x1[5], 2))∧(U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥))

We simplified constraint (90) using rules (III), (IDP_BOOLEAN) which results in the following new constraints:
(91)    (>(x1[4], 1)=TRUE∧<(x0[4], 2)=TRUE ⇒ COND_382_0_POWER_GT2(TRUE, x0[4], x1[4])≥NonInfC∧COND_382_0_POWER_GT2(TRUE, x0[4], x1[4])≥382_0_POWER_GT(x0[4], /(x1[4], 2))∧(U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥))

(92)    (>(x1[4], 1)=TRUE∧>(x0[4], 2)=TRUE ⇒ COND_382_0_POWER_GT2(TRUE, x0[4], x1[4])≥NonInfC∧COND_382_0_POWER_GT2(TRUE, x0[4], x1[4])≥382_0_POWER_GT(x0[4], /(x1[4], 2))∧(U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥))

We simplified constraint (91) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(93)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[(-1)bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (92) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(94)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[(-1)bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (93) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(95)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[(-1)bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (94) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(96)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[(-1)bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] + x1[4] + [-1]max{x1[4], [-1]x1[4]} ≥ 0)

We simplified constraint (95) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(97)    (x1[4] + [-2] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[(-1)bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)

We simplified constraint (96) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(98)    (x1[4] + [-2] ≥ 0∧x0[4] + [-3] ≥ 0∧[2]x1[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[(-1)bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)

We simplified constraint (97) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(99)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)

We simplified constraint (98) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(100)    (x1[4] ≥ 0∧x0[4] + [-3] ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)

We simplified constraint (99) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(101)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧[4] + [2]x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)

(102)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧[4] + [2]x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)

We simplified constraint (101) using rule (IDP_POLY_GCD) which results in the following new constraint:
(103)    (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧x0[4] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)

We simplified constraint (102) using rule (IDP_POLY_GCD) which results in the following new constraint:
(104)    (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)

We simplified constraint (100) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(105)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[4] + [2]x1[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)

We simplified constraint (105) using rule (IDP_POLY_GCD) which results in the following new constraint:
(106)    (x1[4] ≥ 0∧x0[4] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)

For Pair 382_0_POWER_GT(x0, x1) → COND_382_0_POWER_GT3(&&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2))), x0, x1) the following chains were created:

We consider the chain 382_0_POWER_GT(x0[6], x1[6]) → COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6]), COND_382_0_POWER_GT3(TRUE, x0[7], x1[7]) → 382_0_POWER_GT(x0[7], -(x1[7], 1)) which results in the following constraint:
(107)    (&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2)))=TRUE∧x0[6]=x0[7]∧x1[6]=x1[7] ⇒ 382_0_POWER_GT(x0[6], x1[6])≥NonInfC∧382_0_POWER_GT(x0[6], x1[6])≥COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])∧(U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥))

We simplified constraint (107) using rules (IV), (IDP_BOOLEAN) which results in the following new constraints:
(108)    (>(x1[6], 0)=TRUE∧<(x0[6], 2)=TRUE∧<(x1[6], 1)=TRUE ⇒ 382_0_POWER_GT(x0[6], x1[6])≥NonInfC∧382_0_POWER_GT(x0[6], x1[6])≥COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])∧(U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥))

(109)    (>(x1[6], 0)=TRUE∧<(x0[6], 2)=TRUE∧>(x1[6], 1)=TRUE ⇒ 382_0_POWER_GT(x0[6], x1[6])≥NonInfC∧382_0_POWER_GT(x0[6], x1[6])≥COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])∧(U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥))

We simplified constraint (108) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(110)    (x1[6] + [-1] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧[-1]x1[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[(-1)bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (109) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(111)    (x1[6] + [-1] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧x1[6] + [-2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[(-1)bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (110) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(112)    (x1[6] + [-1] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧[-1]x1[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[(-1)bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (111) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(113)    (x1[6] + [-1] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧x1[6] + [-2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[(-1)bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (114) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(115)    (x1[6] + [-1] ≥ 0∧x0[6] + [-3] ≥ 0∧[-1]x1[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[(-1)bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (116) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(117)    (x1[6] + [-1] ≥ 0∧x0[6] + [-3] ≥ 0∧x1[6] + [-2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[(-1)bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (112) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(118)    (x1[6] + [-1] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧[-1]x1[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[(-1)bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (113) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(119)    (x1[6] + [-1] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧x1[6] + [-2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[(-1)bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (115) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(120)    (x1[6] + [-1] ≥ 0∧x0[6] + [-3] ≥ 0∧[-1]x1[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[(-1)bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (117) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(121)    (x1[6] + [-1] ≥ 0∧x0[6] + [-3] ≥ 0∧x1[6] + [-2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[(-1)bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We solved constraint (118) using rule (IDP_SMT_SPLIT).We simplified constraint (119) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(122)    (x1[6] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧[-1] + x1[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[(-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We solved constraint (120) using rule (IDP_SMT_SPLIT).We simplified constraint (121) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(123)    (x1[6] ≥ 0∧x0[6] + [-3] ≥ 0∧[-1] + x1[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[(-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (122) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(124)    ([1] + x1[6] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (124) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(125)    ([1] + x1[6] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧x1[6] ≥ 0∧x0[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

(126)    ([1] + x1[6] ≥ 0∧[1] + x0[6] ≥ 0∧x1[6] ≥ 0∧x0[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (123) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(127)    ([1] + x1[6] ≥ 0∧x0[6] + [-3] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

We simplified constraint (127) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(128)    ([1] + x1[6] ≥ 0∧x0[6] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)

For Pair COND_382_0_POWER_GT3(TRUE, x0, x1) → 382_0_POWER_GT(x0, -(x1, 1)) the following chains were created:

We consider the chain 382_0_POWER_GT(x0[6], x1[6]) → COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6]), COND_382_0_POWER_GT3(TRUE, x0[7], x1[7]) → 382_0_POWER_GT(x0[7], -(x1[7], 1)) which results in the following constraint:
(129)    (&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2)))=TRUE∧x0[6]=x0[7]∧x1[6]=x1[7] ⇒ COND_382_0_POWER_GT3(TRUE, x0[7], x1[7])≥NonInfC∧COND_382_0_POWER_GT3(TRUE, x0[7], x1[7])≥382_0_POWER_GT(x0[7], -(x1[7], 1))∧(U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥))

We simplified constraint (129) using rules (III), (IDP_BOOLEAN) which results in the following new constraints:
(130)    (>(x1[6], 0)=TRUE∧<(x0[6], 2)=TRUE∧<(x1[6], 1)=TRUE ⇒ COND_382_0_POWER_GT3(TRUE, x0[6], x1[6])≥NonInfC∧COND_382_0_POWER_GT3(TRUE, x0[6], x1[6])≥382_0_POWER_GT(x0[6], -(x1[6], 1))∧(U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥))

(131)    (>(x1[6], 0)=TRUE∧<(x0[6], 2)=TRUE∧>(x1[6], 1)=TRUE ⇒ COND_382_0_POWER_GT3(TRUE, x0[6], x1[6])≥NonInfC∧COND_382_0_POWER_GT3(TRUE, x0[6], x1[6])≥382_0_POWER_GT(x0[6], -(x1[6], 1))∧(U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥))

We simplified constraint (130) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(132)    (x1[6] + [-1] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧[-1]x1[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[(-1)bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (131) using rule (POLY_CONSTRAINTS) which results in the following new constraint:
(133)    (x1[6] + [-1] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧x1[6] + [-2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[(-1)bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (132) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(134)    (x1[6] + [-1] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧[-1]x1[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[(-1)bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (133) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(135)    (x1[6] + [-1] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧x1[6] + [-2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[(-1)bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (136) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(137)    (x1[6] + [-1] ≥ 0∧x0[6] + [-3] ≥ 0∧[-1]x1[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[(-1)bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (138) using rule (IDP_POLY_SIMPLIFY) which results in the following new constraint:
(139)    (x1[6] + [-1] ≥ 0∧x0[6] + [-3] ≥ 0∧x1[6] + [-2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[(-1)bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (134) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(140)    (x1[6] + [-1] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧[-1]x1[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[(-1)bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (135) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(141)    (x1[6] + [-1] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧x1[6] + [-2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[(-1)bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (137) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(142)    (x1[6] + [-1] ≥ 0∧x0[6] + [-3] ≥ 0∧[-1]x1[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[(-1)bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (139) using rule (POLY_REMOVE_MIN_MAX) which results in the following new constraint:
(143)    (x1[6] + [-1] ≥ 0∧x0[6] + [-3] ≥ 0∧x1[6] + [-2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[(-1)bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We solved constraint (140) using rule (IDP_SMT_SPLIT).We simplified constraint (141) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(144)    (x1[6] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧[-1] + x1[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[(-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We solved constraint (142) using rule (IDP_SMT_SPLIT).We simplified constraint (143) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(145)    (x1[6] ≥ 0∧x0[6] + [-3] ≥ 0∧[-1] + x1[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[(-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (144) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(146)    ([1] + x1[6] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (146) using rule (IDP_SMT_SPLIT) which results in the following new constraints:
(147)    ([1] + x1[6] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧x1[6] ≥ 0∧x0[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

(148)    ([1] + x1[6] ≥ 0∧[1] + x0[6] ≥ 0∧x1[6] ≥ 0∧x0[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (145) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(149)    ([1] + x1[6] ≥ 0∧x0[6] + [-3] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

We simplified constraint (149) using rule (IDP_SMT_SPLIT) which results in the following new constraint:
(150)    ([1] + x1[6] ≥ 0∧x0[6] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

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

382_0_POWER_GT(x0, x1) → COND_382_0_POWER_GT(&&(>(x1, 1), !(=(x0, 2))), x0, x1)
- (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)
- (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)
- (x1[0] ≥ 0∧x0[0] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])), ≥)∧[bni_104 + (-1)Bound*bni_104] + [bni_104]x1[0] ≥ 0∧[(-1)bso_105] ≥ 0)
COND_382_0_POWER_GT(TRUE, x0, x1) → 382_0_POWER_GT(x0, /(x1, 2))
- (x1[0] ≥ 0∧[1] + [-1]x0[0] ≥ 0∧x0[0] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)
- (x1[0] ≥ 0∧[1] + x0[0] ≥ 0∧x0[0] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)
- (x1[0] ≥ 0∧x0[0] ≥ 0∧[2] + x1[0] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[1], /(x1[1], 2))), ≥)∧[bni_106 + (-1)Bound*bni_106] + [bni_106]x1[0] ≥ 0∧[1 + (-1)bso_110] ≥ 0)
382_0_POWER_GT(x0, x1) → COND_382_0_POWER_GT1(&&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2))), x0, x1)
- ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)
- ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)
- ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])), ≥)∧[bni_111 + (-1)Bound*bni_111] + [bni_111]x1[2] ≥ 0∧[(-1)bso_112] ≥ 0)
COND_382_0_POWER_GT1(TRUE, x0, x1) → 382_0_POWER_GT(x0, -(x1, 1))
- ([1] + x1[2] ≥ 0∧[1] + [-1]x0[2] ≥ 0∧x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)
- ([1] + x1[2] ≥ 0∧[1] + x0[2] ≥ 0∧x1[2] ≥ 0∧x0[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)
- ([1] + x1[2] ≥ 0∧x0[2] ≥ 0∧x1[2] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[3], -(x1[3], 1))), ≥)∧[bni_113 + (-1)Bound*bni_113] + [bni_113]x1[2] ≥ 0∧[1 + (-1)bso_114] ≥ 0)
382_0_POWER_GT(x0, x1) → COND_382_0_POWER_GT2(&&(>(x1, 1), !(=(x0, 2))), x0, x1)
- (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)
- (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)
- (x1[4] ≥ 0∧x0[4] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])), ≥)∧[bni_115 + (-1)Bound*bni_115] + [bni_115]x1[4] ≥ 0∧[(-1)bso_116] ≥ 0)
COND_382_0_POWER_GT2(TRUE, x0, x1) → 382_0_POWER_GT(x0, /(x1, 2))
- (x1[4] ≥ 0∧[1] + [-1]x0[4] ≥ 0∧x0[4] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)
- (x1[4] ≥ 0∧[1] + x0[4] ≥ 0∧x0[4] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)
- (x1[4] ≥ 0∧x0[4] ≥ 0∧[2] + x1[4] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[5], /(x1[5], 2))), ≥)∧[bni_117 + (-1)Bound*bni_117] + [bni_117]x1[4] ≥ 0∧[1 + (-1)bso_118] ≥ 0)
382_0_POWER_GT(x0, x1) → COND_382_0_POWER_GT3(&&(&&(>(x1, 0), !(=(x1, 1))), !(=(x0, 2))), x0, x1)
- ([1] + x1[6] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧x1[6] ≥ 0∧x0[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)
- ([1] + x1[6] ≥ 0∧[1] + x0[6] ≥ 0∧x1[6] ≥ 0∧x0[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)
- ([1] + x1[6] ≥ 0∧x0[6] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])), ≥)∧[bni_119 + (-1)Bound*bni_119] + [bni_119]x1[6] ≥ 0∧[(-1)bso_120] ≥ 0)
COND_382_0_POWER_GT3(TRUE, x0, x1) → 382_0_POWER_GT(x0, -(x1, 1))
- ([1] + x1[6] ≥ 0∧[1] + [-1]x0[6] ≥ 0∧x1[6] ≥ 0∧x0[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)
- ([1] + x1[6] ≥ 0∧[1] + x0[6] ≥ 0∧x1[6] ≥ 0∧x0[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)
- ([1] + x1[6] ≥ 0∧x0[6] ≥ 0∧x1[6] ≥ 0 ⇒ (U^Increasing(382_0_POWER_GT(x0[7], -(x1[7], 1))), ≥)∧[bni_121 + (-1)Bound*bni_121] + [bni_121]x1[6] ≥ 0∧[1 + (-1)bso_122] ≥ 0)

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

POL(TRUE) = 0
POL(FALSE) = 0
POL(382_0_power_GT(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(0) = 0
POL(388_0_power_Return(x₁)) = [-1] + [-1]x₁
POL(595_1_power_InvokeMethod(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(1) = [1]
POL(Cond_595_1_power_InvokeMethod(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(>(x₁, x₂)) = [-1]
POL(584_1_power_InvokeMethod(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(Cond_584_1_power_InvokeMethod(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(710_0_power_Return) = [-1]
POL(590_1_power_InvokeMethod(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(Cond_590_1_power_InvokeMethod(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(<=(x₁, x₂)) = [-1]
POL(896_0_power_Return(x₁, x₂)) = [-1] + [-1]x₂ + [-1]x₁
POL(*(x₁, x₂)) = x₁·x₂
POL(Cond_595_1_power_InvokeMethod1(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(Cond_595_1_power_InvokeMethod3(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(579_1_power_InvokeMethod(x₁, x₂, x₃)) = [-1] + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(Cond_579_1_power_InvokeMethod(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(968_0_power_Return(x₁)) = [-1] + [-1]x₁
POL(Cond_579_1_power_InvokeMethod1(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(Cond_590_1_power_InvokeMethod1(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(&&(x₁, x₂)) = [-1]
POL(Cond_579_1_power_InvokeMethod2(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(Cond_590_1_power_InvokeMethod2(x₁, x₂, x₃, x₄)) = [-1] + [-1]x₄ + [-1]x₃ + [-1]x₂ + [-1]x₁
POL(382_0_POWER_GT(x₁, x₂)) = [-1] + x₂
POL(COND_382_0_POWER_GT(x₁, x₂, x₃)) = [-1] + x₃
POL(!(x₁)) = [-1]
POL(=(x₁, x₂)) = [-1]
POL(2) = [2]
POL(COND_382_0_POWER_GT1(x₁, x₂, x₃)) = [-1] + x₃
POL(-(x₁, x₂)) = x₁ + [-1]x₂
POL(COND_382_0_POWER_GT2(x₁, x₂, x₃)) = [-1] + x₃
POL(COND_382_0_POWER_GT3(x₁, x₂, x₃)) = [-1] + x₃

Polynomial Interpretations with Context Sensitive Arithemetic Replacement
POL(Term^CSAR-Mode @ Context)

POL(/(x₁, 2)¹ @ {382_0_POWER_GT_2/1}) = max{x₁, [-1]x₁} + [-1]

The following pairs are in P_>:

COND_382_0_POWER_GT(TRUE, x0[1], x1[1]) → 382_0_POWER_GT(x0[1], /(x1[1], 2))
COND_382_0_POWER_GT1(TRUE, x0[3], x1[3]) → 382_0_POWER_GT(x0[3], -(x1[3], 1))
COND_382_0_POWER_GT2(TRUE, x0[5], x1[5]) → 382_0_POWER_GT(x0[5], /(x1[5], 2))
COND_382_0_POWER_GT3(TRUE, x0[7], x1[7]) → 382_0_POWER_GT(x0[7], -(x1[7], 1))

The following pairs are in P_bound:

382_0_POWER_GT(x0[0], x1[0]) → COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])
COND_382_0_POWER_GT(TRUE, x0[1], x1[1]) → 382_0_POWER_GT(x0[1], /(x1[1], 2))
382_0_POWER_GT(x0[2], x1[2]) → COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])
COND_382_0_POWER_GT1(TRUE, x0[3], x1[3]) → 382_0_POWER_GT(x0[3], -(x1[3], 1))
382_0_POWER_GT(x0[4], x1[4]) → COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])
COND_382_0_POWER_GT2(TRUE, x0[5], x1[5]) → 382_0_POWER_GT(x0[5], /(x1[5], 2))
382_0_POWER_GT(x0[6], x1[6]) → COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])
COND_382_0_POWER_GT3(TRUE, x0[7], x1[7]) → 382_0_POWER_GT(x0[7], -(x1[7], 1))

The following pairs are in P_≥:

382_0_POWER_GT(x0[0], x1[0]) → COND_382_0_POWER_GT(&&(>(x1[0], 1), !(=(x0[0], 2))), x0[0], x1[0])
382_0_POWER_GT(x0[2], x1[2]) → COND_382_0_POWER_GT1(&&(&&(>(x1[2], 0), !(=(x1[2], 1))), !(=(x0[2], 2))), x0[2], x1[2])
382_0_POWER_GT(x0[4], x1[4]) → COND_382_0_POWER_GT2(&&(>(x1[4], 1), !(=(x0[4], 2))), x0[4], x1[4])
382_0_POWER_GT(x0[6], x1[6]) → COND_382_0_POWER_GT3(&&(&&(>(x1[6], 0), !(=(x1[6], 1))), !(=(x0[6], 2))), x0[6], x1[6])

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

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

(8) Obligation:

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

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

The following domains are used:

Integer, Boolean

The ITRS R consists of the following rules:
382_0_power_GT(x0, 0) → 388_0_power_Return(x0)
595_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1) → Cond_595_1_power_InvokeMethod(x0 > 1, 388_0_power_Return(x0), x0, 1)
Cond_595_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1) → 388_0_power_Return(x0)
584_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1) → Cond_584_1_power_InvokeMethod(x0 > 1, 388_0_power_Return(x0), x0, 1)
Cond_584_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1) → 710_0_power_Return
590_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1) → Cond_590_1_power_InvokeMethod(x0 <= 1, 388_0_power_Return(x0), x0, 1)
Cond_590_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1) → 896_0_power_Return(x0, x0 * x0)
595_1_power_InvokeMethod(710_0_power_Return, x0, x2) → Cond_595_1_power_InvokeMethod1(x0 > 1, 710_0_power_Return, x0, x2)
Cond_595_1_power_InvokeMethod1(TRUE, 710_0_power_Return, x0, x2) → 388_0_power_Return(x0)
595_1_power_InvokeMethod(388_0_power_Return(x0), x0, x1) → Cond_595_1_power_InvokeMethod3(x0 > 1, 388_0_power_Return(x0), x0, x1)
Cond_595_1_power_InvokeMethod3(TRUE, 388_0_power_Return(x0), x0, x1) → 388_0_power_Return(x0)
579_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1) → Cond_579_1_power_InvokeMethod(x0 <= 1, 388_0_power_Return(x0), x0, 1)
Cond_579_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1) → 968_0_power_Return(x0 * x0)
584_1_power_InvokeMethod(710_0_power_Return, x0, x1) → 710_0_power_Return
584_1_power_InvokeMethod(388_0_power_Return(x0), x0, x1) → 710_0_power_Return
579_1_power_InvokeMethod(896_0_power_Return(x0, x2), x0, x1) → Cond_579_1_power_InvokeMethod1(x2 <= 1, 896_0_power_Return(x0, x2), x0, x1)
Cond_579_1_power_InvokeMethod1(TRUE, 896_0_power_Return(x0, x2), x0, x1) → 968_0_power_Return(x2 * x2)
590_1_power_InvokeMethod(896_0_power_Return(x0, x2), x0, x1) → Cond_590_1_power_InvokeMethod1(x2 <= 1 && x0 <= 1, 896_0_power_Return(x0, x2), x0, x1)
Cond_590_1_power_InvokeMethod1(TRUE, 896_0_power_Return(x0, x2), x0, x1) → 896_0_power_Return(x0, x0 * x2)
579_1_power_InvokeMethod(968_0_power_Return(x0), x1, x2) → Cond_579_1_power_InvokeMethod2(x0 <= 1, 968_0_power_Return(x0), x1, x2)
Cond_579_1_power_InvokeMethod2(TRUE, 968_0_power_Return(x0), x1, x2) → 968_0_power_Return(x0 * x0)
590_1_power_InvokeMethod(968_0_power_Return(x0), x1, x3) → Cond_590_1_power_InvokeMethod2(x1 <= 1 && x0 <= 1, 968_0_power_Return(x0), x1, x3)
Cond_590_1_power_InvokeMethod2(TRUE, 968_0_power_Return(x0), x1, x3) → 896_0_power_Return(x1, x1 * x0)

The integer pair graph contains the following rules and edges:
(0): 382_0_POWER_GT(x0[0], x1[0]) → COND_382_0_POWER_GT(x1[0] > 1 && !(x0[0] = 2), x0[0], x1[0])
(2): 382_0_POWER_GT(x0[2], x1[2]) → COND_382_0_POWER_GT1(x1[2] > 0 && !(x1[2] = 1) && !(x0[2] = 2), x0[2], x1[2])
(4): 382_0_POWER_GT(x0[4], x1[4]) → COND_382_0_POWER_GT2(x1[4] > 1 && !(x0[4] = 2), x0[4], x1[4])
(6): 382_0_POWER_GT(x0[6], x1[6]) → COND_382_0_POWER_GT3(x1[6] > 0 && !(x1[6] = 1) && !(x0[6] = 2), x0[6], x1[6])

The set Q consists of the following terms:
382_0_power_GT(x0, 0)
Cond_595_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1)
Cond_584_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1)
590_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1)
Cond_590_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1)
595_1_power_InvokeMethod(710_0_power_Return, x0, x1)
Cond_595_1_power_InvokeMethod1(TRUE, 710_0_power_Return, x0, x1)
595_1_power_InvokeMethod(388_0_power_Return(x0), x0, x1)
Cond_595_1_power_InvokeMethod3(TRUE, 388_0_power_Return(x0), x0, x1)
579_1_power_InvokeMethod(388_0_power_Return(x0), x0, 1)
Cond_579_1_power_InvokeMethod(TRUE, 388_0_power_Return(x0), x0, 1)
584_1_power_InvokeMethod(710_0_power_Return, x0, x1)
584_1_power_InvokeMethod(388_0_power_Return(x0), x0, x1)
579_1_power_InvokeMethod(896_0_power_Return(x0, x1), x0, x2)
Cond_579_1_power_InvokeMethod1(TRUE, 896_0_power_Return(x0, x1), x0, x2)
590_1_power_InvokeMethod(896_0_power_Return(x0, x1), x0, x2)
Cond_590_1_power_InvokeMethod1(TRUE, 896_0_power_Return(x0, x1), x0, x2)
579_1_power_InvokeMethod(968_0_power_Return(x0), x1, x2)
Cond_579_1_power_InvokeMethod2(TRUE, 968_0_power_Return(x0), x1, x2)
590_1_power_InvokeMethod(968_0_power_Return(x0), x1, x2)
Cond_590_1_power_InvokeMethod2(TRUE, 968_0_power_Return(x0), x1, x2)

(9) IDependencyGraphProof (EQUIVALENT transformation)

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

(0) Obligation:

(1) JBCToGraph (SOUND transformation)

(2) Obligation:

(3) TerminationGraphToSCCProof (SOUND transformation)

(4) Obligation:

(5) SCCToIDPv1Proof (SOUND transformation)

(6) Obligation:

(7) IDPNonInfProof (SOUND transformation)

(8) Obligation:

(9) IDependencyGraphProof (EQUIVALENT transformation)

(10) TRUE