/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


termination of the given Bare JBC problem could be proven:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 801 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 234 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 182 ms]
(12) AND
    (13) IRSwT
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IRSwT
        (16) TempFilterProof [SOUND, 35 ms]
        (17) IntTRS
        (18) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) IRSwT
        (21) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (22) IRSwT
        (23) TempFilterProof [SOUND, 82 ms]
        (24) IntTRS
        (25) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (26) IntTRS
        (27) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (28) IntTRS
        (29) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (30) YES


----------------------------------------

(0)
Obligation:
need to prove termination of the following program:
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) BareJBCToJBCProof (EQUIVALENT)
initialized classpath
----------------------------------------

(2)
Obligation:
need to prove termination of the following program:
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();
  }
}



----------------------------------------

(3) JBCToGraph (EQUIVALENT)
Constructed TerminationGraph.
----------------------------------------

(4)
Obligation:
Termination Graph based on JBC Program:
AProVEMathRecursive.main([Ljava/lang/String;)V: Graph of 211 nodes with 0 SCCs.



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





----------------------------------------

(5) TerminationGraphToSCCProof (SOUND)
Splitted TerminationGraph to 1 SCCs.
----------------------------------------

(6)
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:
*Used field analysis yielded the following read fields:

*Marker field analysis yielded the following relations that could be markers:

----------------------------------------

(7) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 63 IRulesP rules:
f682_0_power_GT(EOS(STATIC_682), i120, i122, i120, i122, i122) -> f689_0_power_GT(EOS(STATIC_689), i120, i122, i120, i122, i122) :|: TRUE
f689_0_power_GT(EOS(STATIC_689), i120, i122, i120, i122, i122) -> f692_0_power_Load(EOS(STATIC_692), i120, i122, i120, i122) :|: i122 > 0
f692_0_power_Load(EOS(STATIC_692), i120, i122, i120, i122) -> f695_0_power_ConstantStackPush(EOS(STATIC_695), i120, i122, i120, i122, i122) :|: TRUE
f695_0_power_ConstantStackPush(EOS(STATIC_695), i120, i122, i120, i122, i122) -> f698_0_power_NE(EOS(STATIC_698), i120, i122, i120, i122, i122, 1) :|: TRUE
f698_0_power_NE(EOS(STATIC_698), i120, i139, i120, i139, i139, matching1) -> f713_0_power_NE(EOS(STATIC_713), i120, i139, i120, i139, i139, 1) :|: TRUE && matching1 = 1
f713_0_power_NE(EOS(STATIC_713), i120, i139, i120, i139, i139, matching1) -> f719_0_power_Load(EOS(STATIC_719), i120, i139, i120, i139) :|: i139 > 1 && matching1 = 1
f719_0_power_Load(EOS(STATIC_719), i120, i139, i120, i139) -> f722_0_power_ConstantStackPush(EOS(STATIC_722), i120, i139, i120, i139, i120) :|: TRUE
f722_0_power_ConstantStackPush(EOS(STATIC_722), i120, i139, i120, i139, i120) -> f725_0_power_NE(EOS(STATIC_725), i120, i139, i120, i139, i120, 2) :|: TRUE
f725_0_power_NE(EOS(STATIC_725), i158, i139, i158, i139, i158, matching1) -> f727_0_power_NE(EOS(STATIC_727), i158, i139, i158, i139, i158, 2) :|: TRUE && matching1 = 2
f725_0_power_NE(EOS(STATIC_725), i159, i139, i159, i139, i159, matching1) -> f729_0_power_NE(EOS(STATIC_729), i159, i139, i159, i139, i159, 2) :|: TRUE && matching1 = 2
f727_0_power_NE(EOS(STATIC_727), i158, i139, i158, i139, i158, matching1) -> f733_0_power_Load(EOS(STATIC_733), i158, i139, i158, i139) :|: i158 < 2 && matching1 = 2
f733_0_power_Load(EOS(STATIC_733), i158, i139, i158, i139) -> f781_0_power_ConstantStackPush(EOS(STATIC_781), i158, i139, i158, i139, i139) :|: TRUE
f781_0_power_ConstantStackPush(EOS(STATIC_781), i158, i139, i158, i139, i139) -> f789_0_power_IntArithmetic(EOS(STATIC_789), i158, i139, i158, i139, i139, 2) :|: TRUE
f789_0_power_IntArithmetic(EOS(STATIC_789), i158, i139, i158, i139, i139, matching1) -> f799_0_power_ConstantStackPush(EOS(STATIC_799), i158, i139, i158, i139, i139 % 2) :|: TRUE && matching1 = 2
f799_0_power_ConstantStackPush(EOS(STATIC_799), i158, i139, i158, i139, i172) -> f806_0_power_NE(EOS(STATIC_806), i158, i139, i158, i139, i172, 1) :|: TRUE
f806_0_power_NE(EOS(STATIC_806), i158, i139, i158, i139, matching1, matching2) -> f822_0_power_NE(EOS(STATIC_822), i158, i139, i158, i139, 0, 1) :|: i172 = 0 && matching1 = 0 && matching2 = 1
f806_0_power_NE(EOS(STATIC_806), i158, i139, i158, i139, matching1, matching2) -> f823_0_power_NE(EOS(STATIC_823), i158, i139, i158, i139, 1, 1) :|: i172 = 1 && matching1 = 1 && matching2 = 1
f822_0_power_NE(EOS(STATIC_822), i158, i139, i158, i139, matching1, matching2) -> f828_0_power_Load(EOS(STATIC_828), i158, i139, i158, i139) :|: TRUE && matching1 = 0 && matching2 = 1
f828_0_power_Load(EOS(STATIC_828), i158, i139, i158, i139) -> f838_0_power_Load(EOS(STATIC_838), i158, i139, i139, i158) :|: TRUE
f838_0_power_Load(EOS(STATIC_838), i158, i139, i139, i158) -> f858_0_power_ConstantStackPush(EOS(STATIC_858), i158, i139, i158, i139) :|: TRUE
f858_0_power_ConstantStackPush(EOS(STATIC_858), i158, i139, i158, i139) -> f874_0_power_IntArithmetic(EOS(STATIC_874), i158, i139, i158, i139, 2) :|: TRUE
f874_0_power_IntArithmetic(EOS(STATIC_874), i158, i139, i158, i139, matching1) -> f899_0_power_InvokeMethod(EOS(STATIC_899), i158, i139, i158, i201) :|: i201 = i139 / 2 && i139 > 1 && i201 < i139 && matching1 = 2
f899_0_power_InvokeMethod(EOS(STATIC_899), i158, i139, i158, i201) -> f909_0_power_Load(EOS(STATIC_909), i158, i201, i158, i201) :|: i158 <= 1 && i139 > 1 && i201 >= 1
f899_0_power_InvokeMethod(EOS(STATIC_899), i158, i139, i158, i201) -> f909_1_power_Load(EOS(STATIC_909), i158, i139, i158, i201) :|: i158 <= 1 && i139 > 1 && i201 >= 1
f909_0_power_Load(EOS(STATIC_909), i158, i201, i158, i201) -> f914_0_power_Load(EOS(STATIC_914), i158, i201, i158, i201) :|: TRUE
f914_0_power_Load(EOS(STATIC_914), i158, i201, i158, i201) -> f679_0_power_Load(EOS(STATIC_679), i158, i201, i158, i201) :|: TRUE
f679_0_power_Load(EOS(STATIC_679), i120, i121, i120, i121) -> f682_0_power_GT(EOS(STATIC_682), i120, i121, i120, i121, i121) :|: TRUE
f823_0_power_NE(EOS(STATIC_823), i158, i139, i158, i139, matching1, matching2) -> f833_0_power_Load(EOS(STATIC_833), i158, i139, i158, i139) :|: TRUE && matching1 = 1 && matching2 = 1
f833_0_power_Load(EOS(STATIC_833), i158, i139, i158, i139) -> f839_0_power_Load(EOS(STATIC_839), i158, i139, i158, i139, i158) :|: TRUE
f839_0_power_Load(EOS(STATIC_839), i158, i139, i158, i139, i158) -> f861_0_power_Load(EOS(STATIC_861), i158, i139, i139, i158, i158) :|: TRUE
f861_0_power_Load(EOS(STATIC_861), i158, i139, i139, i158, i158) -> f876_0_power_ConstantStackPush(EOS(STATIC_876), i158, i139, i158, i158, i139) :|: TRUE
f876_0_power_ConstantStackPush(EOS(STATIC_876), i158, i139, i158, i158, i139) -> f901_0_power_IntArithmetic(EOS(STATIC_901), i158, i139, i158, i158, i139, 1) :|: TRUE
f901_0_power_IntArithmetic(EOS(STATIC_901), i158, i139, i158, i158, i139, matching1) -> f910_0_power_InvokeMethod(EOS(STATIC_910), i158, i139, i158, i158, i139 - 1) :|: i139 > 0 && matching1 = 1
f910_0_power_InvokeMethod(EOS(STATIC_910), i158, i139, i158, i158, i204) -> f915_0_power_Load(EOS(STATIC_915), i158, i204, i158, i204) :|: i158 <= 1 && i139 > 1 && i204 >= 1 && i204 < i139
f910_0_power_InvokeMethod(EOS(STATIC_910), i158, i139, i158, i158, i204) -> f915_1_power_Load(EOS(STATIC_915), i158, i139, i158, i158, i204) :|: i158 <= 1 && i139 > 1 && i204 >= 1 && i204 < i139
f915_0_power_Load(EOS(STATIC_915), i158, i204, i158, i204) -> f920_0_power_Load(EOS(STATIC_920), i158, i204, i158, i204) :|: TRUE
f920_0_power_Load(EOS(STATIC_920), i158, i204, i158, i204) -> f679_0_power_Load(EOS(STATIC_679), i158, i204, i158, i204) :|: TRUE
f729_0_power_NE(EOS(STATIC_729), i159, i139, i159, i139, i159, matching1) -> f738_0_power_Load(EOS(STATIC_738), i159, i139, i159, i139) :|: i159 > 2 && matching1 = 2
f738_0_power_Load(EOS(STATIC_738), i159, i139, i159, i139) -> f786_0_power_ConstantStackPush(EOS(STATIC_786), i159, i139, i159, i139, i139) :|: TRUE
f786_0_power_ConstantStackPush(EOS(STATIC_786), i159, i139, i159, i139, i139) -> f794_0_power_IntArithmetic(EOS(STATIC_794), i159, i139, i159, i139, i139, 2) :|: TRUE
f794_0_power_IntArithmetic(EOS(STATIC_794), i159, i139, i159, i139, i139, matching1) -> f804_0_power_ConstantStackPush(EOS(STATIC_804), i159, i139, i159, i139, i139 % 2) :|: TRUE && matching1 = 2
f804_0_power_ConstantStackPush(EOS(STATIC_804), i159, i139, i159, i139, i174) -> f819_0_power_NE(EOS(STATIC_819), i159, i139, i159, i139, i174, 1) :|: TRUE
f819_0_power_NE(EOS(STATIC_819), i159, i139, i159, i139, matching1, matching2) -> f826_0_power_NE(EOS(STATIC_826), i159, i139, i159, i139, 0, 1) :|: i174 = 0 && matching1 = 0 && matching2 = 1
f819_0_power_NE(EOS(STATIC_819), i159, i139, i159, i139, matching1, matching2) -> f827_0_power_NE(EOS(STATIC_827), i159, i139, i159, i139, 1, 1) :|: i174 = 1 && matching1 = 1 && matching2 = 1
f826_0_power_NE(EOS(STATIC_826), i159, i139, i159, i139, matching1, matching2) -> f835_0_power_Load(EOS(STATIC_835), i159, i139, i159, i139) :|: TRUE && matching1 = 0 && matching2 = 1
f835_0_power_Load(EOS(STATIC_835), i159, i139, i159, i139) -> f853_0_power_Load(EOS(STATIC_853), i159, i139, i139, i159) :|: TRUE
f853_0_power_Load(EOS(STATIC_853), i159, i139, i139, i159) -> f868_0_power_ConstantStackPush(EOS(STATIC_868), i159, i139, i159, i139) :|: TRUE
f868_0_power_ConstantStackPush(EOS(STATIC_868), i159, i139, i159, i139) -> f893_0_power_IntArithmetic(EOS(STATIC_893), i159, i139, i159, i139, 2) :|: TRUE
f893_0_power_IntArithmetic(EOS(STATIC_893), i159, i139, i159, i139, matching1) -> f907_0_power_InvokeMethod(EOS(STATIC_907), i159, i139, i159, i203) :|: i203 = i139 / 2 && i139 > 1 && i203 < i139 && matching1 = 2
f907_0_power_InvokeMethod(EOS(STATIC_907), i159, i139, i159, i203) -> f912_0_power_Load(EOS(STATIC_912), i159, i203, i159, i203) :|: i159 > 1 && i139 > 1 && i203 >= 1
f907_0_power_InvokeMethod(EOS(STATIC_907), i159, i139, i159, i203) -> f912_1_power_Load(EOS(STATIC_912), i159, i139, i159, i203) :|: i159 > 1 && i139 > 1 && i203 >= 1
f912_0_power_Load(EOS(STATIC_912), i159, i203, i159, i203) -> f916_0_power_Load(EOS(STATIC_916), i159, i203, i159, i203) :|: TRUE
f916_0_power_Load(EOS(STATIC_916), i159, i203, i159, i203) -> f679_0_power_Load(EOS(STATIC_679), i159, i203, i159, i203) :|: TRUE
f827_0_power_NE(EOS(STATIC_827), i159, i139, i159, i139, matching1, matching2) -> f837_0_power_Load(EOS(STATIC_837), i159, i139, i159, i139) :|: TRUE && matching1 = 1 && matching2 = 1
f837_0_power_Load(EOS(STATIC_837), i159, i139, i159, i139) -> f856_0_power_Load(EOS(STATIC_856), i159, i139, i159, i139, i159) :|: TRUE
f856_0_power_Load(EOS(STATIC_856), i159, i139, i159, i139, i159) -> f872_0_power_Load(EOS(STATIC_872), i159, i139, i139, i159, i159) :|: TRUE
f872_0_power_Load(EOS(STATIC_872), i159, i139, i139, i159, i159) -> f896_0_power_ConstantStackPush(EOS(STATIC_896), i159, i139, i159, i159, i139) :|: TRUE
f896_0_power_ConstantStackPush(EOS(STATIC_896), i159, i139, i159, i159, i139) -> f908_0_power_IntArithmetic(EOS(STATIC_908), i159, i139, i159, i159, i139, 1) :|: TRUE
f908_0_power_IntArithmetic(EOS(STATIC_908), i159, i139, i159, i159, i139, matching1) -> f913_0_power_InvokeMethod(EOS(STATIC_913), i159, i139, i159, i159, i139 - 1) :|: i139 > 0 && matching1 = 1
f913_0_power_InvokeMethod(EOS(STATIC_913), i159, i139, i159, i159, i205) -> f918_0_power_Load(EOS(STATIC_918), i159, i205, i159, i205) :|: i159 > 1 && i139 > 1 && i205 >= 1 && i205 < i139
f913_0_power_InvokeMethod(EOS(STATIC_913), i159, i139, i159, i159, i205) -> f918_1_power_Load(EOS(STATIC_918), i159, i139, i159, i159, i205) :|: i159 > 1 && i139 > 1 && i205 >= 1 && i205 < i139
f918_0_power_Load(EOS(STATIC_918), i159, i205, i159, i205) -> f921_0_power_Load(EOS(STATIC_921), i159, i205, i159, i205) :|: TRUE
f921_0_power_Load(EOS(STATIC_921), i159, i205, i159, i205) -> f679_0_power_Load(EOS(STATIC_679), i159, i205, i159, i205) :|: TRUE
Combined rules. Obtained 12 IRulesP rules:
f682_0_power_GT(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) -> f682_0_power_GT'(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) :|: i122:0 > 1 && i120:0 < 2 && i122:0 - 2 * div = 1 && i122:0 - 1 < i122:0
f682_0_power_GT'(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) -> f682_0_power_GT(EOS(STATIC_682), i120:0, i122:0 - 1, i120:0, i122:0 - 1, i122:0 - 1) :|: i122:0 > 1 && i120:0 < 2 && i122:0 - 2 * div = 1 && i122:0 - 1 < i122:0 && i122:0 - 2 * div < 2 && i122:0 - 2 * div > -2
f682_0_power_GT(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) -> f682_0_power_GT'(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) :|: i122:0 > 1 && i120:0 < 2 && i122:0 - 2 * div = 0 && i122:0 > div1 && div1 > 0
f682_0_power_GT'(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) -> f682_0_power_GT(EOS(STATIC_682), i120:0, div1, i120:0, div1, div1) :|: i122:0 > 1 && i120:0 < 2 && i122:0 - 2 * div = 0 && i122:0 > div1 && div1 > 0 && i122:0 - 2 * div > -2 && i122:0 - 2 * div < 2 && i122:0 - 2 * div1 < 2 && i122:0 - 2 * div1 > -2
f682_0_power_GT(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) -> f682_0_power_GT'(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) :|: i122:0 > 1 && i120:0 > 2 && i122:0 - 1 < i122:0 && i122:0 - 2 * div = 1
f682_0_power_GT'(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) -> f682_0_power_GT(EOS(STATIC_682), i120:0, i122:0 - 1, i120:0, i122:0 - 1, i122:0 - 1) :|: i122:0 > 1 && i120:0 > 2 && i122:0 - 2 * div = 1 && i122:0 - 1 < i122:0 && i122:0 - 2 * div < 2 && i122:0 - 2 * div > -2
f682_0_power_GT(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) -> f682_0_power_GT'(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) :|: i122:0 > 1 && i120:0 > 2 && i122:0 - 2 * div = 0 && div1 > 0 && i122:0 > div1
f682_0_power_GT'(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) -> f682_0_power_GT(EOS(STATIC_682), i120:0, div1, i120:0, div1, div1) :|: i122:0 > 1 && i120:0 > 2 && i122:0 - 2 * div = 0 && i122:0 > div1 && div1 > 0 && i122:0 - 2 * div > -2 && i122:0 - 2 * div < 2 && i122:0 - 2 * div1 < 2 && i122:0 - 2 * div1 > -2
Removed following non-SCC rules:
f682_0_power_GT'(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) -> f909_1_power_Load(EOS(STATIC_909), i120:0, i122:0, i120:0, div1) :|: i122:0 > 1 && i120:0 < 2 && i122:0 - 2 * div = 0 && i122:0 > div1 && div1 > 0 && i122:0 - 2 * div > -2 && i122:0 - 2 * div < 2 && i122:0 - 2 * div1 < 2 && i122:0 - 2 * div1 > -2
f682_0_power_GT'(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) -> f918_1_power_Load(EOS(STATIC_918), i120:0, i122:0, i120:0, i120:0, i122:0 - 1) :|: i122:0 > 1 && i120:0 > 2 && i122:0 - 2 * div = 1 && i122:0 - 1 < i122:0 && i122:0 - 2 * div < 2 && i122:0 - 2 * div > -2
f682_0_power_GT'(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) -> f915_1_power_Load(EOS(STATIC_915), i120:0, i122:0, i120:0, i120:0, i122:0 - 1) :|: i122:0 > 1 && i120:0 < 2 && i122:0 - 2 * div = 1 && i122:0 - 1 < i122:0 && i122:0 - 2 * div < 2 && i122:0 - 2 * div > -2
f682_0_power_GT'(EOS(STATIC_682), i120:0, i122:0, i120:0, i122:0, i122:0) -> f912_1_power_Load(EOS(STATIC_912), i120:0, i122:0, i120:0, div1) :|: i122:0 > 1 && i120:0 > 2 && i122:0 - 2 * div = 0 && i122:0 > div1 && div1 > 0 && i122:0 - 2 * div > -2 && i122:0 - 2 * div < 2 && i122:0 - 2 * div1 < 2 && i122:0 - 2 * div1 > -2
Filtered constant ground arguments:
   f682_0_power_GT(x1, x2, x3, x4, x5, x6) -> f682_0_power_GT(x2, x3, x4, x5, x6)
   f682_0_power_GT'(x1, x2, x3, x4, x5, x6) -> f682_0_power_GT'(x2, x3, x4, x5, x6)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f682_0_power_GT(x1, x2, x3, x4, x5) -> f682_0_power_GT(x3, x5)
   f682_0_power_GT'(x1, x2, x3, x4, x5) -> f682_0_power_GT'(x3, x5)
Finished conversion. Obtained 8 rules.P rules:
f682_0_power_GT(i120:0, i122:0) -> f682_0_power_GT'(i120:0, i122:0) :|: i120:0 < 2 && i122:0 > 1 && i122:0 - 1 < i122:0 && i122:0 - 2 * div = 1
f682_0_power_GT'(i120:0, i122:0) -> f682_0_power_GT(i120:0, i122:0 - 1) :|: i120:0 < 2 && i122:0 > 1 && i122:0 - 2 * div = 1 && i122:0 - 1 < i122:0 && i122:0 - 2 * div > -2 && i122:0 - 2 * div < 2
f682_0_power_GT(i120:0, i122:0) -> f682_0_power_GT'(i120:0, i122:0) :|: i120:0 < 2 && i122:0 > 1 && i122:0 - 2 * div = 0 && div1 > 0 && i122:0 > div1
f682_0_power_GT'(i120:0, i122:0) -> f682_0_power_GT(i120:0, div1) :|: i120:0 < 2 && i122:0 > 1 && i122:0 - 2 * div = 0 && i122:0 > div1 && div1 > 0 && i122:0 - 2 * div > -2 && i122:0 - 2 * div < 2 && i122:0 - 2 * div1 > -2 && i122:0 - 2 * div1 < 2
f682_0_power_GT(i120:0, i122:0) -> f682_0_power_GT'(i120:0, i122:0) :|: i120:0 > 2 && i122:0 > 1 && i122:0 - 2 * div = 1 && i122:0 - 1 < i122:0
f682_0_power_GT'(i120:0, i122:0) -> f682_0_power_GT(i120:0, i122:0 - 1) :|: i120:0 > 2 && i122:0 > 1 && i122:0 - 2 * div = 1 && i122:0 - 1 < i122:0 && i122:0 - 2 * div > -2 && i122:0 - 2 * div < 2
f682_0_power_GT(i120:0, i122:0) -> f682_0_power_GT'(i120:0, i122:0) :|: i120:0 > 2 && i122:0 > 1 && i122:0 - 2 * div = 0 && i122:0 > div1 && div1 > 0
f682_0_power_GT'(i120:0, i122:0) -> f682_0_power_GT(i120:0, div1) :|: i120:0 > 2 && i122:0 > 1 && i122:0 - 2 * div = 0 && i122:0 > div1 && div1 > 0 && i122:0 - 2 * div > -2 && i122:0 - 2 * div < 2 && i122:0 - 2 * div1 > -2 && i122:0 - 2 * div1 < 2

----------------------------------------

(8)
Obligation:
Rules:
f682_0_power_GT(x, x1) -> f682_0_power_GT'(x, x1) :|: x < 2 && x1 > 1 && x1 - 1 < x1 && x1 - 2 * x2 = 1
f682_0_power_GT'(x3, x4) -> f682_0_power_GT(x3, x4 - 1) :|: x3 < 2 && x4 > 1 && x4 - 2 * x5 = 1 && x4 - 1 < x4 && x4 - 2 * x5 > -2 && x4 - 2 * x5 < 2
f682_0_power_GT(x6, x7) -> f682_0_power_GT'(x6, x7) :|: x6 < 2 && x7 > 1 && x7 - 2 * x8 = 0 && x9 > 0 && x7 > x9
f682_0_power_GT'(x10, x11) -> f682_0_power_GT(x10, x12) :|: x10 < 2 && x11 > 1 && x11 - 2 * x13 = 0 && x11 > x12 && x12 > 0 && x11 - 2 * x13 > -2 && x11 - 2 * x13 < 2 && x11 - 2 * x12 > -2 && x11 - 2 * x12 < 2
f682_0_power_GT(x14, x15) -> f682_0_power_GT'(x14, x15) :|: x14 > 2 && x15 > 1 && x15 - 2 * x16 = 1 && x15 - 1 < x15
f682_0_power_GT'(x17, x18) -> f682_0_power_GT(x17, x18 - 1) :|: x17 > 2 && x18 > 1 && x18 - 2 * x19 = 1 && x18 - 1 < x18 && x18 - 2 * x19 > -2 && x18 - 2 * x19 < 2
f682_0_power_GT(x20, x21) -> f682_0_power_GT'(x20, x21) :|: x20 > 2 && x21 > 1 && x21 - 2 * x22 = 0 && x21 > x23 && x23 > 0
f682_0_power_GT'(x24, x25) -> f682_0_power_GT(x24, x26) :|: x24 > 2 && x25 > 1 && x25 - 2 * x27 = 0 && x25 > x26 && x26 > 0 && x25 - 2 * x27 > -2 && x25 - 2 * x27 < 2 && x25 - 2 * x26 > -2 && x25 - 2 * x26 < 2

----------------------------------------

(9) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(10)
Obligation:
Rules:
f682_0_power_GT(x, x1) -> f682_0_power_GT'(x, x1) :|: x < 2 && x1 > 1 && x1 - 1 < x1 && x1 - 2 * x2 = 1
f682_0_power_GT'(x3, x4) -> f682_0_power_GT(x3, arith) :|: x3 < 2 && x4 > 1 && x4 - 2 * x5 = 1 && x4 - 1 < x4 && x4 - 2 * x5 > -2 && x4 - 2 * x5 < 2 && arith = x4 - 1
f682_0_power_GT(x6, x7) -> f682_0_power_GT'(x6, x7) :|: x6 < 2 && x7 > 1 && x7 - 2 * x8 = 0 && x9 > 0 && x7 > x9
f682_0_power_GT'(x10, x11) -> f682_0_power_GT(x10, x12) :|: x10 < 2 && x11 > 1 && x11 - 2 * x13 = 0 && x11 > x12 && x12 > 0 && x11 - 2 * x13 > -2 && x11 - 2 * x13 < 2 && x11 - 2 * x12 > -2 && x11 - 2 * x12 < 2
f682_0_power_GT(x14, x15) -> f682_0_power_GT'(x14, x15) :|: x14 > 2 && x15 > 1 && x15 - 2 * x16 = 1 && x15 - 1 < x15
f682_0_power_GT'(x28, x29) -> f682_0_power_GT(x28, x30) :|: x28 > 2 && x29 > 1 && x29 - 2 * x31 = 1 && x29 - 1 < x29 && x29 - 2 * x31 > -2 && x29 - 2 * x31 < 2 && x30 = x29 - 1
f682_0_power_GT(x20, x21) -> f682_0_power_GT'(x20, x21) :|: x20 > 2 && x21 > 1 && x21 - 2 * x22 = 0 && x21 > x23 && x23 > 0
f682_0_power_GT'(x24, x25) -> f682_0_power_GT(x24, x26) :|: x24 > 2 && x25 > 1 && x25 - 2 * x27 = 0 && x25 > x26 && x26 > 0 && x25 - 2 * x27 > -2 && x25 - 2 * x27 < 2 && x25 - 2 * x26 > -2 && x25 - 2 * x26 < 2

----------------------------------------

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f682_0_power_GT(x, x1) -> f682_0_power_GT'(x, x1) :|: x < 2 && x1 > 1 && x1 - 1 < x1 && x1 - 2 * x2 = 1
(2) f682_0_power_GT'(x3, x4) -> f682_0_power_GT(x3, arith) :|: x3 < 2 && x4 > 1 && x4 - 2 * x5 = 1 && x4 - 1 < x4 && x4 - 2 * x5 > -2 && x4 - 2 * x5 < 2 && arith = x4 - 1
(3) f682_0_power_GT(x6, x7) -> f682_0_power_GT'(x6, x7) :|: x6 < 2 && x7 > 1 && x7 - 2 * x8 = 0 && x9 > 0 && x7 > x9
(4) f682_0_power_GT'(x10, x11) -> f682_0_power_GT(x10, x12) :|: x10 < 2 && x11 > 1 && x11 - 2 * x13 = 0 && x11 > x12 && x12 > 0 && x11 - 2 * x13 > -2 && x11 - 2 * x13 < 2 && x11 - 2 * x12 > -2 && x11 - 2 * x12 < 2
(5) f682_0_power_GT(x14, x15) -> f682_0_power_GT'(x14, x15) :|: x14 > 2 && x15 > 1 && x15 - 2 * x16 = 1 && x15 - 1 < x15
(6) f682_0_power_GT'(x28, x29) -> f682_0_power_GT(x28, x30) :|: x28 > 2 && x29 > 1 && x29 - 2 * x31 = 1 && x29 - 1 < x29 && x29 - 2 * x31 > -2 && x29 - 2 * x31 < 2 && x30 = x29 - 1
(7) f682_0_power_GT(x20, x21) -> f682_0_power_GT'(x20, x21) :|: x20 > 2 && x21 > 1 && x21 - 2 * x22 = 0 && x21 > x23 && x23 > 0
(8) f682_0_power_GT'(x24, x25) -> f682_0_power_GT(x24, x26) :|: x24 > 2 && x25 > 1 && x25 - 2 * x27 = 0 && x25 > x26 && x26 > 0 && x25 - 2 * x27 > -2 && x25 - 2 * x27 < 2 && x25 - 2 * x26 > -2 && x25 - 2 * x26 < 2

Arcs:
(1) -> (2)
(2) -> (3)
(3) -> (4)
(4) -> (1), (3)
(5) -> (6)
(6) -> (7)
(7) -> (8)
(8) -> (5), (7)

This digraph is fully evaluated!
----------------------------------------

(12)
Complex Obligation (AND)

----------------------------------------

(13)
Obligation:

Termination digraph:
Nodes:
(1) f682_0_power_GT(x14, x15) -> f682_0_power_GT'(x14, x15) :|: x14 > 2 && x15 > 1 && x15 - 2 * x16 = 1 && x15 - 1 < x15
(2) f682_0_power_GT'(x24, x25) -> f682_0_power_GT(x24, x26) :|: x24 > 2 && x25 > 1 && x25 - 2 * x27 = 0 && x25 > x26 && x26 > 0 && x25 - 2 * x27 > -2 && x25 - 2 * x27 < 2 && x25 - 2 * x26 > -2 && x25 - 2 * x26 < 2
(3) f682_0_power_GT(x20, x21) -> f682_0_power_GT'(x20, x21) :|: x20 > 2 && x21 > 1 && x21 - 2 * x22 = 0 && x21 > x23 && x23 > 0
(4) f682_0_power_GT'(x28, x29) -> f682_0_power_GT(x28, x30) :|: x28 > 2 && x29 > 1 && x29 - 2 * x31 = 1 && x29 - 1 < x29 && x29 - 2 * x31 > -2 && x29 - 2 * x31 < 2 && x30 = x29 - 1

Arcs:
(1) -> (4)
(2) -> (1), (3)
(3) -> (2)
(4) -> (3)

This digraph is fully evaluated!

----------------------------------------

(14) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(15)
Obligation:
Rules:
f682_0_power_GT(x14:0, x15:0) -> f682_0_power_GT'(x14:0, x15:0) :|: x15:0 - 2 * x16:0 = 1 && x15:0 - 1 < x15:0 && x15:0 > 1 && x14:0 > 2
f682_0_power_GT(x20:0, x21:0) -> f682_0_power_GT'(x20:0, x21:0) :|: x23:0 < x21:0 && x23:0 > 0 && x21:0 - 2 * x22:0 = 0 && x21:0 > 1 && x20:0 > 2
f682_0_power_GT'(x28:0, x29:0) -> f682_0_power_GT(x28:0, x29:0 - 1) :|: x29:0 - 2 * x31:0 > -2 && x29:0 - 2 * x31:0 < 2 && x29:0 - 1 < x29:0 && x29:0 - 2 * x31:0 = 1 && x29:0 > 1 && x28:0 > 2
f682_0_power_GT'(x24:0, x25:0) -> f682_0_power_GT(x24:0, x26:0) :|: x25:0 - 2 * x26:0 > -2 && x25:0 - 2 * x26:0 < 2 && x25:0 - 2 * x27:0 < 2 && x25:0 - 2 * x27:0 > -2 && x26:0 > 0 && x26:0 < x25:0 && x25:0 - 2 * x27:0 = 0 && x25:0 > 1 && x24:0 > 2

----------------------------------------

(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f682_0_power_GT(INTEGER, INTEGER)
f682_0_power_GT'(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(17)
Obligation:
Rules:
f682_0_power_GT(x14:0, x15:0) -> f682_0_power_GT'(x14:0, x15:0) :|: x15:0 - 2 * x16:0 = 1 && x15:0 - 1 < x15:0 && x15:0 > 1 && x14:0 > 2
f682_0_power_GT(x20:0, x21:0) -> f682_0_power_GT'(x20:0, x21:0) :|: x23:0 < x21:0 && x23:0 > 0 && x21:0 - 2 * x22:0 = 0 && x21:0 > 1 && x20:0 > 2
f682_0_power_GT'(x28:0, x29:0) -> f682_0_power_GT(x28:0, c) :|: c = x29:0 - 1 && (x29:0 - 2 * x31:0 > -2 && x29:0 - 2 * x31:0 < 2 && x29:0 - 1 < x29:0 && x29:0 - 2 * x31:0 = 1 && x29:0 > 1 && x28:0 > 2)
f682_0_power_GT'(x24:0, x25:0) -> f682_0_power_GT(x24:0, x26:0) :|: x25:0 - 2 * x26:0 > -2 && x25:0 - 2 * x26:0 < 2 && x25:0 - 2 * x27:0 < 2 && x25:0 - 2 * x27:0 > -2 && x26:0 > 0 && x26:0 < x25:0 && x25:0 - 2 * x27:0 = 0 && x25:0 > 1 && x24:0 > 2

----------------------------------------

(18) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f682_0_power_GT ] = 2*f682_0_power_GT_2 + 1
[ f682_0_power_GT' ] = 2*f682_0_power_GT'_2

The following rules are decreasing:
f682_0_power_GT(x14:0, x15:0) -> f682_0_power_GT'(x14:0, x15:0) :|: x15:0 - 2 * x16:0 = 1 && x15:0 - 1 < x15:0 && x15:0 > 1 && x14:0 > 2
f682_0_power_GT(x20:0, x21:0) -> f682_0_power_GT'(x20:0, x21:0) :|: x23:0 < x21:0 && x23:0 > 0 && x21:0 - 2 * x22:0 = 0 && x21:0 > 1 && x20:0 > 2
f682_0_power_GT'(x28:0, x29:0) -> f682_0_power_GT(x28:0, c) :|: c = x29:0 - 1 && (x29:0 - 2 * x31:0 > -2 && x29:0 - 2 * x31:0 < 2 && x29:0 - 1 < x29:0 && x29:0 - 2 * x31:0 = 1 && x29:0 > 1 && x28:0 > 2)
f682_0_power_GT'(x24:0, x25:0) -> f682_0_power_GT(x24:0, x26:0) :|: x25:0 - 2 * x26:0 > -2 && x25:0 - 2 * x26:0 < 2 && x25:0 - 2 * x27:0 < 2 && x25:0 - 2 * x27:0 > -2 && x26:0 > 0 && x26:0 < x25:0 && x25:0 - 2 * x27:0 = 0 && x25:0 > 1 && x24:0 > 2

The following rules are bounded:
f682_0_power_GT(x14:0, x15:0) -> f682_0_power_GT'(x14:0, x15:0) :|: x15:0 - 2 * x16:0 = 1 && x15:0 - 1 < x15:0 && x15:0 > 1 && x14:0 > 2
f682_0_power_GT(x20:0, x21:0) -> f682_0_power_GT'(x20:0, x21:0) :|: x23:0 < x21:0 && x23:0 > 0 && x21:0 - 2 * x22:0 = 0 && x21:0 > 1 && x20:0 > 2
f682_0_power_GT'(x28:0, x29:0) -> f682_0_power_GT(x28:0, c) :|: c = x29:0 - 1 && (x29:0 - 2 * x31:0 > -2 && x29:0 - 2 * x31:0 < 2 && x29:0 - 1 < x29:0 && x29:0 - 2 * x31:0 = 1 && x29:0 > 1 && x28:0 > 2)
f682_0_power_GT'(x24:0, x25:0) -> f682_0_power_GT(x24:0, x26:0) :|: x25:0 - 2 * x26:0 > -2 && x25:0 - 2 * x26:0 < 2 && x25:0 - 2 * x27:0 < 2 && x25:0 - 2 * x27:0 > -2 && x26:0 > 0 && x26:0 < x25:0 && x25:0 - 2 * x27:0 = 0 && x25:0 > 1 && x24:0 > 2


----------------------------------------

(19)
YES

----------------------------------------

(20)
Obligation:

Termination digraph:
Nodes:
(1) f682_0_power_GT(x, x1) -> f682_0_power_GT'(x, x1) :|: x < 2 && x1 > 1 && x1 - 1 < x1 && x1 - 2 * x2 = 1
(2) f682_0_power_GT'(x10, x11) -> f682_0_power_GT(x10, x12) :|: x10 < 2 && x11 > 1 && x11 - 2 * x13 = 0 && x11 > x12 && x12 > 0 && x11 - 2 * x13 > -2 && x11 - 2 * x13 < 2 && x11 - 2 * x12 > -2 && x11 - 2 * x12 < 2
(3) f682_0_power_GT(x6, x7) -> f682_0_power_GT'(x6, x7) :|: x6 < 2 && x7 > 1 && x7 - 2 * x8 = 0 && x9 > 0 && x7 > x9
(4) f682_0_power_GT'(x3, x4) -> f682_0_power_GT(x3, arith) :|: x3 < 2 && x4 > 1 && x4 - 2 * x5 = 1 && x4 - 1 < x4 && x4 - 2 * x5 > -2 && x4 - 2 * x5 < 2 && arith = x4 - 1

Arcs:
(1) -> (4)
(2) -> (1), (3)
(3) -> (2)
(4) -> (3)

This digraph is fully evaluated!

----------------------------------------

(21) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(22)
Obligation:
Rules:
f682_0_power_GT'(x10:0, x11:0) -> f682_0_power_GT(x10:0, x12:0) :|: x11:0 - 2 * x12:0 > -2 && x11:0 - 2 * x12:0 < 2 && x11:0 - 2 * x13:0 < 2 && x11:0 - 2 * x13:0 > -2 && x12:0 > 0 && x12:0 < x11:0 && x11:0 - 2 * x13:0 = 0 && x11:0 > 1 && x10:0 < 2
f682_0_power_GT(x6:0, x7:0) -> f682_0_power_GT'(x6:0, x7:0) :|: x9:0 > 0 && x9:0 < x7:0 && x7:0 - 2 * x8:0 = 0 && x7:0 > 1 && x6:0 < 2
f682_0_power_GT'(x3:0, x4:0) -> f682_0_power_GT(x3:0, x4:0 - 1) :|: x4:0 - 2 * x5:0 > -2 && x4:0 - 2 * x5:0 < 2 && x4:0 - 1 < x4:0 && x4:0 - 2 * x5:0 = 1 && x4:0 > 1 && x3:0 < 2
f682_0_power_GT(x:0, x1:0) -> f682_0_power_GT'(x:0, x1:0) :|: x1:0 - 1 < x1:0 && x1:0 - 2 * x2:0 = 1 && x1:0 > 1 && x:0 < 2

----------------------------------------

(23) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f682_0_power_GT'(INTEGER, INTEGER)
f682_0_power_GT(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(24)
Obligation:
Rules:
f682_0_power_GT'(x10:0, x11:0) -> f682_0_power_GT(x10:0, x12:0) :|: x11:0 - 2 * x12:0 > -2 && x11:0 - 2 * x12:0 < 2 && x11:0 - 2 * x13:0 < 2 && x11:0 - 2 * x13:0 > -2 && x12:0 > 0 && x12:0 < x11:0 && x11:0 - 2 * x13:0 = 0 && x11:0 > 1 && x10:0 < 2
f682_0_power_GT(x6:0, x7:0) -> f682_0_power_GT'(x6:0, x7:0) :|: x9:0 > 0 && x9:0 < x7:0 && x7:0 - 2 * x8:0 = 0 && x7:0 > 1 && x6:0 < 2
f682_0_power_GT'(x3:0, x4:0) -> f682_0_power_GT(x3:0, c) :|: c = x4:0 - 1 && (x4:0 - 2 * x5:0 > -2 && x4:0 - 2 * x5:0 < 2 && x4:0 - 1 < x4:0 && x4:0 - 2 * x5:0 = 1 && x4:0 > 1 && x3:0 < 2)
f682_0_power_GT(x:0, x1:0) -> f682_0_power_GT'(x:0, x1:0) :|: x1:0 - 1 < x1:0 && x1:0 - 2 * x2:0 = 1 && x1:0 > 1 && x:0 < 2

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(25) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f682_0_power_GT'(x, x1)] = x1
[f682_0_power_GT(x2, x3)] = x3

The following rules are decreasing:
f682_0_power_GT'(x3:0, x4:0) -> f682_0_power_GT(x3:0, c) :|: c = x4:0 - 1 && (x4:0 - 2 * x5:0 > -2 && x4:0 - 2 * x5:0 < 2 && x4:0 - 1 < x4:0 && x4:0 - 2 * x5:0 = 1 && x4:0 > 1 && x3:0 < 2)
The following rules are bounded:
f682_0_power_GT'(x10:0, x11:0) -> f682_0_power_GT(x10:0, x12:0) :|: x11:0 - 2 * x12:0 > -2 && x11:0 - 2 * x12:0 < 2 && x11:0 - 2 * x13:0 < 2 && x11:0 - 2 * x13:0 > -2 && x12:0 > 0 && x12:0 < x11:0 && x11:0 - 2 * x13:0 = 0 && x11:0 > 1 && x10:0 < 2
f682_0_power_GT(x6:0, x7:0) -> f682_0_power_GT'(x6:0, x7:0) :|: x9:0 > 0 && x9:0 < x7:0 && x7:0 - 2 * x8:0 = 0 && x7:0 > 1 && x6:0 < 2
f682_0_power_GT'(x3:0, x4:0) -> f682_0_power_GT(x3:0, c) :|: c = x4:0 - 1 && (x4:0 - 2 * x5:0 > -2 && x4:0 - 2 * x5:0 < 2 && x4:0 - 1 < x4:0 && x4:0 - 2 * x5:0 = 1 && x4:0 > 1 && x3:0 < 2)
f682_0_power_GT(x:0, x1:0) -> f682_0_power_GT'(x:0, x1:0) :|: x1:0 - 1 < x1:0 && x1:0 - 2 * x2:0 = 1 && x1:0 > 1 && x:0 < 2

----------------------------------------

(26)
Obligation:
Rules:
f682_0_power_GT'(x10:0, x11:0) -> f682_0_power_GT(x10:0, x12:0) :|: x11:0 - 2 * x12:0 > -2 && x11:0 - 2 * x12:0 < 2 && x11:0 - 2 * x13:0 < 2 && x11:0 - 2 * x13:0 > -2 && x12:0 > 0 && x12:0 < x11:0 && x11:0 - 2 * x13:0 = 0 && x11:0 > 1 && x10:0 < 2
f682_0_power_GT(x6:0, x7:0) -> f682_0_power_GT'(x6:0, x7:0) :|: x9:0 > 0 && x9:0 < x7:0 && x7:0 - 2 * x8:0 = 0 && x7:0 > 1 && x6:0 < 2
f682_0_power_GT(x:0, x1:0) -> f682_0_power_GT'(x:0, x1:0) :|: x1:0 - 1 < x1:0 && x1:0 - 2 * x2:0 = 1 && x1:0 > 1 && x:0 < 2

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(27) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f682_0_power_GT'(x, x1)] = 2 + x1
[f682_0_power_GT(x2, x3)] = 2*x3

The following rules are decreasing:
f682_0_power_GT'(x10:0, x11:0) -> f682_0_power_GT(x10:0, x12:0) :|: x11:0 - 2 * x12:0 > -2 && x11:0 - 2 * x12:0 < 2 && x11:0 - 2 * x13:0 < 2 && x11:0 - 2 * x13:0 > -2 && x12:0 > 0 && x12:0 < x11:0 && x11:0 - 2 * x13:0 = 0 && x11:0 > 1 && x10:0 < 2
The following rules are bounded:
f682_0_power_GT'(x10:0, x11:0) -> f682_0_power_GT(x10:0, x12:0) :|: x11:0 - 2 * x12:0 > -2 && x11:0 - 2 * x12:0 < 2 && x11:0 - 2 * x13:0 < 2 && x11:0 - 2 * x13:0 > -2 && x12:0 > 0 && x12:0 < x11:0 && x11:0 - 2 * x13:0 = 0 && x11:0 > 1 && x10:0 < 2
f682_0_power_GT(x6:0, x7:0) -> f682_0_power_GT'(x6:0, x7:0) :|: x9:0 > 0 && x9:0 < x7:0 && x7:0 - 2 * x8:0 = 0 && x7:0 > 1 && x6:0 < 2
f682_0_power_GT(x:0, x1:0) -> f682_0_power_GT'(x:0, x1:0) :|: x1:0 - 1 < x1:0 && x1:0 - 2 * x2:0 = 1 && x1:0 > 1 && x:0 < 2

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(28)
Obligation:
Rules:
f682_0_power_GT(x6:0, x7:0) -> f682_0_power_GT'(x6:0, x7:0) :|: x9:0 > 0 && x9:0 < x7:0 && x7:0 - 2 * x8:0 = 0 && x7:0 > 1 && x6:0 < 2
f682_0_power_GT(x:0, x1:0) -> f682_0_power_GT'(x:0, x1:0) :|: x1:0 - 1 < x1:0 && x1:0 - 2 * x2:0 = 1 && x1:0 > 1 && x:0 < 2

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(29) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f682_0_power_GT(x, x1)] = 1
[f682_0_power_GT'(x2, x3)] = 0

The following rules are decreasing:
f682_0_power_GT(x6:0, x7:0) -> f682_0_power_GT'(x6:0, x7:0) :|: x9:0 > 0 && x9:0 < x7:0 && x7:0 - 2 * x8:0 = 0 && x7:0 > 1 && x6:0 < 2
f682_0_power_GT(x:0, x1:0) -> f682_0_power_GT'(x:0, x1:0) :|: x1:0 - 1 < x1:0 && x1:0 - 2 * x2:0 = 1 && x1:0 > 1 && x:0 < 2
The following rules are bounded:
f682_0_power_GT(x6:0, x7:0) -> f682_0_power_GT'(x6:0, x7:0) :|: x9:0 > 0 && x9:0 < x7:0 && x7:0 - 2 * x8:0 = 0 && x7:0 > 1 && x6:0 < 2
f682_0_power_GT(x:0, x1:0) -> f682_0_power_GT'(x:0, x1:0) :|: x1:0 - 1 < x1:0 && x1:0 - 2 * x2:0 = 1 && x1:0 > 1 && x:0 < 2

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(30)
YES