/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 375 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 105 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


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

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

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

    if (x < y) return x;
    else return y;
  }


  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    int res = 0;



    while (min(x-1,y) == y) {

      y++;
      res++;

    }


  }

}


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 MinusMin{

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

    if (x < y) return x;
    else return y;
  }


  public static void main(String[] args) {
    Random.args = args;
    int x = Random.random();
    int y = Random.random();
    int res = 0;



    while (min(x-1,y) == y) {

      y++;
      res++;

    }


  }

}


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:
MinusMin.main([Ljava/lang/String;)V: Graph of 194 nodes with 1 SCC.





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

(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: MinusMin.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 17 IRulesP rules:
f633_0_main_ConstantStackPush(EOS(STATIC_633), i19, i90, i19) -> f634_0_main_IntArithmetic(EOS(STATIC_634), i19, i90, i19, 1) :|: TRUE
f634_0_main_IntArithmetic(EOS(STATIC_634), i19, i90, i19, matching1) -> f646_0_main_Load(EOS(STATIC_646), i19, i90, i19 - 1) :|: i19 >= 0 && matching1 = 1
f646_0_main_Load(EOS(STATIC_646), i19, i90, i97) -> f647_0_main_InvokeMethod(EOS(STATIC_647), i19, i90, i97, i90) :|: TRUE
f647_0_main_InvokeMethod(EOS(STATIC_647), i19, i90, i97, i90) -> f648_0_min_Load(EOS(STATIC_648), i19, i90, i97, i90) :|: TRUE
f648_0_min_Load(EOS(STATIC_648), i19, i90, i97, i90) -> f649_0_min_Load(EOS(STATIC_649), i19, i90, i97, i90, i97) :|: TRUE
f649_0_min_Load(EOS(STATIC_649), i19, i90, i97, i90, i97) -> f650_0_min_GE(EOS(STATIC_650), i19, i90, i97, i90, i97, i90) :|: TRUE
f650_0_min_GE(EOS(STATIC_650), i19, i90, i97, i90, i97, i90) -> f651_0_min_GE(EOS(STATIC_651), i19, i90, i97, i90, i97, i90) :|: i97 >= i90
f651_0_min_GE(EOS(STATIC_651), i19, i90, i97, i90, i97, i90) -> f653_0_min_Load(EOS(STATIC_653), i19, i90, i90) :|: i97 >= i90
f653_0_min_Load(EOS(STATIC_653), i19, i90, i90) -> f655_0_min_Return(EOS(STATIC_655), i19, i90, i90) :|: TRUE
f655_0_min_Return(EOS(STATIC_655), i19, i90, i90) -> f657_0_main_Load(EOS(STATIC_657), i19, i90, i90) :|: TRUE
f657_0_main_Load(EOS(STATIC_657), i19, i90, i90) -> f674_0_main_NE(EOS(STATIC_674), i19, i90, i90, i90) :|: TRUE
f674_0_main_NE(EOS(STATIC_674), i19, i90, i90, i90) -> f698_0_main_Inc(EOS(STATIC_698), i19, i90) :|: TRUE
f698_0_main_Inc(EOS(STATIC_698), i19, i90) -> f710_0_main_Inc(EOS(STATIC_710), i19, i90 + 1) :|: TRUE
f710_0_main_Inc(EOS(STATIC_710), i19, i104) -> f713_0_main_JMP(EOS(STATIC_713), i19, i104) :|: TRUE
f713_0_main_JMP(EOS(STATIC_713), i19, i104) -> f730_0_main_Load(EOS(STATIC_730), i19, i104) :|: TRUE
f730_0_main_Load(EOS(STATIC_730), i19, i104) -> f632_0_main_Load(EOS(STATIC_632), i19, i104) :|: TRUE
f632_0_main_Load(EOS(STATIC_632), i19, i90) -> f633_0_main_ConstantStackPush(EOS(STATIC_633), i19, i90, i19) :|: TRUE
Combined rules. Obtained 1 IRulesP rules:
f633_0_main_ConstantStackPush(EOS(STATIC_633), i19:0, i90:0, i19:0) -> f633_0_main_ConstantStackPush(EOS(STATIC_633), i19:0, i90:0 + 1, i19:0) :|: i19:0 > -1 && i90:0 <= i19:0 - 1
Filtered constant ground arguments:
   f633_0_main_ConstantStackPush(x1, x2, x3, x4) -> f633_0_main_ConstantStackPush(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f633_0_main_ConstantStackPush(x1, x2, x3) -> f633_0_main_ConstantStackPush(x2, x3)
Finished conversion. Obtained 1 rules.P rules:
f633_0_main_ConstantStackPush(i90:0, i19:0) -> f633_0_main_ConstantStackPush(i90:0 + 1, i19:0) :|: i19:0 > -1 && i90:0 <= i19:0 - 1

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

(8)
Obligation:
Rules:
f633_0_main_ConstantStackPush(i90:0, i19:0) -> f633_0_main_ConstantStackPush(i90:0 + 1, i19:0) :|: i19:0 > -1 && i90:0 <= i19:0 - 1

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

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

(10)
Obligation:
Rules:
f633_0_main_ConstantStackPush(i90:0, i19:0) -> f633_0_main_ConstantStackPush(arith, i19:0) :|: i19:0 > -1 && i90:0 <= i19:0 - 1 && arith = i90:0 + 1

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f633_0_main_ConstantStackPush(i90:0, i19:0) -> f633_0_main_ConstantStackPush(arith, i19:0) :|: i19:0 > -1 && i90:0 <= i19:0 - 1 && arith = i90:0 + 1

Arcs:
(1) -> (1)

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f633_0_main_ConstantStackPush(i90:0, i19:0) -> f633_0_main_ConstantStackPush(arith, i19:0) :|: i19:0 > -1 && i90:0 <= i19:0 - 1 && arith = i90:0 + 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f633_0_main_ConstantStackPush(i90:0:0, i19:0:0) -> f633_0_main_ConstantStackPush(i90:0:0 + 1, i19:0:0) :|: i19:0:0 > -1 && i90:0:0 <= i19:0:0 - 1

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f633_0_main_ConstantStackPush(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f633_0_main_ConstantStackPush(i90:0:0, i19:0:0) -> f633_0_main_ConstantStackPush(c, i19:0:0) :|: c = i90:0:0 + 1 && (i19:0:0 > -1 && i90:0:0 <= i19:0:0 - 1)

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

(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f633_0_main_ConstantStackPush(x, x1)] = -x + x1

The following rules are decreasing:
f633_0_main_ConstantStackPush(i90:0:0, i19:0:0) -> f633_0_main_ConstantStackPush(c, i19:0:0) :|: c = i90:0:0 + 1 && (i19:0:0 > -1 && i90:0:0 <= i19:0:0 - 1)
The following rules are bounded:
f633_0_main_ConstantStackPush(i90:0:0, i19:0:0) -> f633_0_main_ConstantStackPush(c, i19:0:0) :|: c = i90:0:0 + 1 && (i19:0:0 > -1 && i90:0:0 <= i19:0:0 - 1)

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

(18)
YES