/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1066 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 102 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 16 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:
f452_0_log_Load(EOS(STATIC_452), i62, i63, i62) -> f454_0_log_LE(EOS(STATIC_454), i62, i63, i62, i63) :|: TRUE
f454_0_log_LE(EOS(STATIC_454), i62, i63, i62, i63) -> f460_0_log_LE(EOS(STATIC_460), i62, i63, i62, i63) :|: i62 > i63
f460_0_log_LE(EOS(STATIC_460), i62, i63, i62, i63) -> f471_0_log_Load(EOS(STATIC_471), i62, i63) :|: i62 > i63
f471_0_log_Load(EOS(STATIC_471), i62, i63) -> f476_0_log_Load(EOS(STATIC_476), i62, i63, i63) :|: TRUE
f476_0_log_Load(EOS(STATIC_476), i62, i63, i63) -> f478_0_log_IntArithmetic(EOS(STATIC_478), i62, i63, i63) :|: TRUE
f478_0_log_IntArithmetic(EOS(STATIC_478), i62, i63, i63) -> f480_0_log_Store(EOS(STATIC_480), i62, i63 * i63) :|: i63 > 1 && i63 > 1
f480_0_log_Store(EOS(STATIC_480), i62, i71) -> f482_0_log_ConstantStackPush(EOS(STATIC_482), i62, i71) :|: TRUE
f482_0_log_ConstantStackPush(EOS(STATIC_482), i62, i71) -> f483_0_log_Load(EOS(STATIC_483), i62, i71) :|: TRUE
f483_0_log_Load(EOS(STATIC_483), i62, i71) -> f484_0_log_IntArithmetic(EOS(STATIC_484), i62, i71) :|: TRUE
f484_0_log_IntArithmetic(EOS(STATIC_484), i62, i71) -> f485_0_log_Store(EOS(STATIC_485), i62, i71) :|: TRUE
f485_0_log_Store(EOS(STATIC_485), i62, i71) -> f486_0_log_JMP(EOS(STATIC_486), i62, i71) :|: TRUE
f486_0_log_JMP(EOS(STATIC_486), i62, i71) -> f496_0_log_Load(EOS(STATIC_496), i62, i71) :|: TRUE
f496_0_log_Load(EOS(STATIC_496), i62, i71) -> f451_0_log_Load(EOS(STATIC_451), i62, i71) :|: TRUE
f451_0_log_Load(EOS(STATIC_451), i62, i63) -> f452_0_log_Load(EOS(STATIC_452), i62, i63, i62) :|: TRUE
Combined rules. Obtained 1 IRulesP rules:
f452_0_log_Load(EOS(STATIC_452), i62:0, i63:0, i62:0) -> f452_0_log_Load(EOS(STATIC_452), i62:0, i63:0 * i63:0, i62:0) :|: i63:0 < i62:0 && i63:0 > 1
Filtered constant ground arguments:
   f452_0_log_Load(x1, x2, x3, x4) -> f452_0_log_Load(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f452_0_log_Load(x1, x2, x3) -> f452_0_log_Load(x2, x3)
Finished conversion. Obtained 1 rules.P rules:
f452_0_log_Load(i63:0, i62:0) -> f452_0_log_Load(i63:0 * i63:0, i62:0) :|: i63:0 < i62:0 && i63:0 > 1

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(8)
Obligation:
Rules:
f452_0_log_Load(i63:0, i62:0) -> f452_0_log_Load(i63:0 * i63:0, i62:0) :|: i63:0 < i62:0 && i63:0 > 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:
f452_0_log_Load(i63:0, i62:0) -> f452_0_log_Load(arith, i62:0) :|: i63:0 < i62:0 && i63:0 > 1 && arith = i63:0 * i63:0

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(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f452_0_log_Load(i63:0, i62:0) -> f452_0_log_Load(arith, i62:0) :|: i63:0 < i62:0 && i63:0 > 1 && arith = i63:0 * i63:0

Arcs:
(1) -> (1)

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f452_0_log_Load(i63:0, i62:0) -> f452_0_log_Load(arith, i62:0) :|: i63:0 < i62:0 && i63:0 > 1 && arith = i63:0 * i63:0

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(14)
Obligation:
Rules:
f452_0_log_Load(i63:0:0, i62:0:0) -> f452_0_log_Load(i63:0:0 * i63:0:0, i62:0:0) :|: i63:0:0 < i62:0:0 && i63:0:0 > 1

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f452_0_log_Load(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f452_0_log_Load(i63:0:0, i62:0:0) -> f452_0_log_Load(c, i62:0:0) :|: c = i63:0:0 * i63:0:0 && (i63:0:0 < i62:0:0 && i63:0:0 > 1)

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f452_0_log_Load(x, x1)] = -x + x1

The following rules are decreasing:
f452_0_log_Load(i63:0:0, i62:0:0) -> f452_0_log_Load(c, i62:0:0) :|: c = i63:0:0 * i63:0:0 && (i63:0:0 < i62:0:0 && i63:0:0 > 1)
The following rules are bounded:
f452_0_log_Load(i63:0:0, i62:0:0) -> f452_0_log_Load(c, i62:0:0) :|: c = i63:0:0 * i63:0:0 && (i63:0:0 < i62:0:0 && i63:0:0 > 1)

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(18)
YES