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


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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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1098 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 54 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 7 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 17 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(18) YES


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(0)
Obligation:
need to prove termination of the following program:
public class LogMult{

  public static int log(int x, int y) {

    int res = 1;

    if (x < 0 || y < 1) return 0;
    else {
      while (x > y) { 
        y = y*y;
        res = 2*res;
      }
    }
    return res;

  }





  public static void main(String[] args) {
    Random.args = args;

    int x = Random.random();
    log(x,2);
  }
}


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

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



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

(1) BareJBCToJBCProof (EQUIVALENT)
initialized classpath
----------------------------------------

(2)
Obligation:
need to prove termination of the following program:
public class LogMult{

  public static int log(int x, int y) {

    int res = 1;

    if (x < 0 || y < 1) return 0;
    else {
      while (x > y) { 
        y = y*y;
        res = 2*res;
      }
    }
    return res;

  }





  public static void main(String[] args) {
    Random.args = args;

    int x = Random.random();
    log(x,2);
  }
}


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

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



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

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

(4)
Obligation:
Termination Graph based on JBC Program:
LogMult.main([Ljava/lang/String;)V: Graph of 130 nodes with 1 SCC.





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(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: LogMult.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
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 14 IRulesP rules:
f437_0_log_Load(EOS(STATIC_437), i60, i61, i60) -> f439_0_log_LE(EOS(STATIC_439), i60, i61, i60, i61) :|: TRUE
f439_0_log_LE(EOS(STATIC_439), i60, i61, i60, i61) -> f453_0_log_LE(EOS(STATIC_453), i60, i61, i60, i61) :|: i60 > i61
f453_0_log_LE(EOS(STATIC_453), i60, i61, i60, i61) -> f457_0_log_Load(EOS(STATIC_457), i60, i61) :|: i60 > i61
f457_0_log_Load(EOS(STATIC_457), i60, i61) -> f460_0_log_Load(EOS(STATIC_460), i60, i61, i61) :|: TRUE
f460_0_log_Load(EOS(STATIC_460), i60, i61, i61) -> f462_0_log_IntArithmetic(EOS(STATIC_462), i60, i61, i61) :|: TRUE
f462_0_log_IntArithmetic(EOS(STATIC_462), i60, i61, i61) -> f469_0_log_Store(EOS(STATIC_469), i60, i61 * i61) :|: i61 > 1 && i61 > 1
f469_0_log_Store(EOS(STATIC_469), i60, i71) -> f472_0_log_ConstantStackPush(EOS(STATIC_472), i60, i71) :|: TRUE
f472_0_log_ConstantStackPush(EOS(STATIC_472), i60, i71) -> f473_0_log_Load(EOS(STATIC_473), i60, i71) :|: TRUE
f473_0_log_Load(EOS(STATIC_473), i60, i71) -> f474_0_log_IntArithmetic(EOS(STATIC_474), i60, i71) :|: TRUE
f474_0_log_IntArithmetic(EOS(STATIC_474), i60, i71) -> f475_0_log_Store(EOS(STATIC_475), i60, i71) :|: TRUE
f475_0_log_Store(EOS(STATIC_475), i60, i71) -> f477_0_log_JMP(EOS(STATIC_477), i60, i71) :|: TRUE
f477_0_log_JMP(EOS(STATIC_477), i60, i71) -> f490_0_log_Load(EOS(STATIC_490), i60, i71) :|: TRUE
f490_0_log_Load(EOS(STATIC_490), i60, i71) -> f433_0_log_Load(EOS(STATIC_433), i60, i71) :|: TRUE
f433_0_log_Load(EOS(STATIC_433), i60, i61) -> f437_0_log_Load(EOS(STATIC_437), i60, i61, i60) :|: TRUE
Combined rules. Obtained 1 IRulesP rules:
f437_0_log_Load(EOS(STATIC_437), i60:0, i61:0, i60:0) -> f437_0_log_Load(EOS(STATIC_437), i60:0, i61:0 * i61:0, i60:0) :|: i61:0 < i60:0 && i61:0 > 1
Filtered constant ground arguments:
   f437_0_log_Load(x1, x2, x3, x4) -> f437_0_log_Load(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f437_0_log_Load(x1, x2, x3) -> f437_0_log_Load(x2, x3)
Finished conversion. Obtained 1 rules.P rules:
f437_0_log_Load(i61:0, i60:0) -> f437_0_log_Load(i61:0 * i61:0, i60:0) :|: i61:0 < i60:0 && i61:0 > 1

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(8)
Obligation:
Rules:
f437_0_log_Load(i61:0, i60:0) -> f437_0_log_Load(i61:0 * i61:0, i60:0) :|: i61:0 < i60:0 && i61:0 > 1

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

(10)
Obligation:
Rules:
f437_0_log_Load(i61:0, i60:0) -> f437_0_log_Load(arith, i60:0) :|: i61:0 < i60:0 && i61:0 > 1 && arith = i61:0 * i61:0

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(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f437_0_log_Load(i61:0, i60:0) -> f437_0_log_Load(arith, i60:0) :|: i61:0 < i60:0 && i61:0 > 1 && arith = i61:0 * i61:0

Arcs:
(1) -> (1)

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f437_0_log_Load(i61:0, i60:0) -> f437_0_log_Load(arith, i60:0) :|: i61:0 < i60:0 && i61:0 > 1 && arith = i61:0 * i61:0

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(14)
Obligation:
Rules:
f437_0_log_Load(i61:0:0, i60:0:0) -> f437_0_log_Load(i61:0:0 * i61:0:0, i60:0:0) :|: i61:0:0 < i60:0:0 && i61:0:0 > 1

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f437_0_log_Load(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f437_0_log_Load(i61:0:0, i60:0:0) -> f437_0_log_Load(c, i60:0:0) :|: c = i61:0:0 * i61:0:0 && (i61:0:0 < i60:0:0 && i61:0:0 > 1)

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f437_0_log_Load(x, x1)] = -x + x1

The following rules are decreasing:
f437_0_log_Load(i61:0:0, i60:0:0) -> f437_0_log_Load(c, i60:0:0) :|: c = i61:0:0 * i61:0:0 && (i61:0:0 < i60:0:0 && i61:0:0 > 1)
The following rules are bounded:
f437_0_log_Load(i61:0:0, i60:0:0) -> f437_0_log_Load(c, i60:0:0) :|: c = i61:0:0 * i61:0:0 && (i61:0:0 < i60:0:0 && i61:0:0 > 1)

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(18)
YES