/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


termination of the given Bare JBC problem could be proven:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 98 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 364 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 67 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 40 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 60 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 12 ms]
(18) IntTRS
(19) RankingReductionPairProof [EQUIVALENT, 0 ms]
(20) YES


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(0)
Obligation:
need to prove termination of the following program:
public class Mod {
  public static void main(String[] args) {
    int x = args[0].length();
    int y = args[1].length();
    mod(x, y);
  }
  public static int mod(int x, int y) {
   
    while (x >= y && y > 0) {
      x = minus(x,y);
     
    }
    return x;
  }

  public static int minus(int x, int y) {
    while (y != 0) {
      if (y > 0)  {
        y--;
        x--;
      } else  {
        y++;
        x++;
      }
    }
    return x;
  }

}



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

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

(2)
Obligation:
need to prove termination of the following program:
public class Mod {
  public static void main(String[] args) {
    int x = args[0].length();
    int y = args[1].length();
    mod(x, y);
  }
  public static int mod(int x, int y) {
   
    while (x >= y && y > 0) {
      x = minus(x,y);
     
    }
    return x;
  }

  public static int minus(int x, int y) {
    while (y != 0) {
      if (y > 0)  {
        y--;
        x--;
      } else  {
        y++;
        x++;
      }
    }
    return x;
  }

}



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

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

(4)
Obligation:
Termination Graph based on JBC Program:
Mod.main([Ljava/lang/String;)V: Graph of 152 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: Mod.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 27 IRulesP rules:
f195_0_mod_Load(EOS(STATIC_195), i12, i30, i12) -> f198_0_mod_LT(EOS(STATIC_198), i12, i30, i12, i30) :|: TRUE
f198_0_mod_LT(EOS(STATIC_198), i12, i30, i12, i30) -> f205_0_mod_LT(EOS(STATIC_205), i12, i30, i12, i30) :|: i12 >= i30
f205_0_mod_LT(EOS(STATIC_205), i12, i30, i12, i30) -> f212_0_mod_Load(EOS(STATIC_212), i12, i30) :|: i12 >= i30
f212_0_mod_Load(EOS(STATIC_212), i12, i30) -> f225_0_mod_LE(EOS(STATIC_225), i12, i30, i30) :|: TRUE
f225_0_mod_LE(EOS(STATIC_225), i36, i35, i35) -> f241_0_mod_LE(EOS(STATIC_241), i36, i35, i35) :|: TRUE
f241_0_mod_LE(EOS(STATIC_241), i36, i35, i35) -> f287_0_mod_Load(EOS(STATIC_287), i36, i35) :|: i35 > 0
f287_0_mod_Load(EOS(STATIC_287), i36, i35) -> f291_0_mod_Load(EOS(STATIC_291), i35, i36) :|: TRUE
f291_0_mod_Load(EOS(STATIC_291), i35, i36) -> f294_0_mod_InvokeMethod(EOS(STATIC_294), i35, i36, i35) :|: TRUE
f294_0_mod_InvokeMethod(EOS(STATIC_294), i35, i36, i35) -> f299_0_minus_Load(EOS(STATIC_299), i35, i36, i35) :|: TRUE
f299_0_minus_Load(EOS(STATIC_299), i35, i36, i35) -> f378_0_minus_Load(EOS(STATIC_378), i35, i36, i35) :|: TRUE
f378_0_minus_Load(EOS(STATIC_378), i35, i52, i53) -> f379_0_minus_EQ(EOS(STATIC_379), i35, i52, i53, i53) :|: TRUE
f379_0_minus_EQ(EOS(STATIC_379), i35, i63, i62, i62) -> f383_0_minus_EQ(EOS(STATIC_383), i35, i63, i62, i62) :|: TRUE
f379_0_minus_EQ(EOS(STATIC_379), i35, i52, matching1, matching2) -> f384_0_minus_EQ(EOS(STATIC_384), i35, i52, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f383_0_minus_EQ(EOS(STATIC_383), i35, i63, i62, i62) -> f385_0_minus_Load(EOS(STATIC_385), i35, i63, i62) :|: i62 > 0
f385_0_minus_Load(EOS(STATIC_385), i35, i63, i62) -> f390_0_minus_LE(EOS(STATIC_390), i35, i63, i62, i62) :|: TRUE
f390_0_minus_LE(EOS(STATIC_390), i35, i63, i62, i62) -> f393_0_minus_Inc(EOS(STATIC_393), i35, i63, i62) :|: i62 > 0
f393_0_minus_Inc(EOS(STATIC_393), i35, i63, i62) -> f395_0_minus_Inc(EOS(STATIC_395), i35, i63, i62 + -1) :|: TRUE
f395_0_minus_Inc(EOS(STATIC_395), i35, i63, i67) -> f398_0_minus_JMP(EOS(STATIC_398), i35, i63 + -1, i67) :|: TRUE
f398_0_minus_JMP(EOS(STATIC_398), i35, i68, i67) -> f443_0_minus_Load(EOS(STATIC_443), i35, i68, i67) :|: TRUE
f443_0_minus_Load(EOS(STATIC_443), i35, i68, i67) -> f378_0_minus_Load(EOS(STATIC_378), i35, i68, i67) :|: TRUE
f384_0_minus_EQ(EOS(STATIC_384), i35, i52, matching1, matching2) -> f387_0_minus_Load(EOS(STATIC_387), i35, i52) :|: TRUE && matching1 = 0 && matching2 = 0
f387_0_minus_Load(EOS(STATIC_387), i35, i52) -> f392_0_minus_Return(EOS(STATIC_392), i35, i52) :|: TRUE
f392_0_minus_Return(EOS(STATIC_392), i35, i52) -> f394_0_mod_Store(EOS(STATIC_394), i35, i52) :|: TRUE
f394_0_mod_Store(EOS(STATIC_394), i35, i52) -> f397_0_mod_JMP(EOS(STATIC_397), i52, i35) :|: TRUE
f397_0_mod_JMP(EOS(STATIC_397), i52, i35) -> f408_0_mod_Load(EOS(STATIC_408), i52, i35) :|: TRUE
f408_0_mod_Load(EOS(STATIC_408), i52, i35) -> f189_0_mod_Load(EOS(STATIC_189), i52, i35) :|: TRUE
f189_0_mod_Load(EOS(STATIC_189), i12, i30) -> f195_0_mod_Load(EOS(STATIC_195), i12, i30, i12) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f379_0_minus_EQ(EOS(STATIC_379), i35:0, i52:0, 0, 0) -> f379_0_minus_EQ(EOS(STATIC_379), i35:0, i52:0, i35:0, i35:0) :|: i52:0 >= i35:0 && i35:0 > 0
f379_0_minus_EQ(EOS(STATIC_379), i35:0, i63:0, i62:0, i62:0) -> f379_0_minus_EQ(EOS(STATIC_379), i35:0, i63:0 - 1, i62:0 - 1, i62:0 - 1) :|: i62:0 > 0
Filtered constant ground arguments:
   f379_0_minus_EQ(x1, x2, x3, x4, x5) -> f379_0_minus_EQ(x2, x3, x4, x5)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f379_0_minus_EQ(x1, x2, x3, x4) -> f379_0_minus_EQ(x1, x2, x4)
Finished conversion. Obtained 2 rules.P rules:
f379_0_minus_EQ(i35:0, i52:0, cons_0) -> f379_0_minus_EQ(i35:0, i52:0, i35:0) :|: i52:0 >= i35:0 && i35:0 > 0 && cons_0 = 0
f379_0_minus_EQ(i35:0, i63:0, i62:0) -> f379_0_minus_EQ(i35:0, i63:0 - 1, i62:0 - 1) :|: i62:0 > 0

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

(8)
Obligation:
Rules:
f379_0_minus_EQ(i35:0, i52:0, cons_0) -> f379_0_minus_EQ(i35:0, i52:0, i35:0) :|: i52:0 >= i35:0 && i35:0 > 0 && cons_0 = 0
f379_0_minus_EQ(x, x1, x2) -> f379_0_minus_EQ(x, x1 - 1, x2 - 1) :|: x2 > 0

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

(10)
Obligation:
Rules:
f379_0_minus_EQ(i35:0, i52:0, cons_0) -> f379_0_minus_EQ(i35:0, i52:0, i35:0) :|: i52:0 >= i35:0 && i35:0 > 0 && cons_0 = 0
f379_0_minus_EQ(x, x1, x2) -> f379_0_minus_EQ(x, arith, arith1) :|: x2 > 0 && arith = x1 - 1 && arith1 = x2 - 1

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f379_0_minus_EQ(i35:0, i52:0, cons_0) -> f379_0_minus_EQ(i35:0, i52:0, i35:0) :|: i52:0 >= i35:0 && i35:0 > 0 && cons_0 = 0
(2) f379_0_minus_EQ(x, x1, x2) -> f379_0_minus_EQ(x, arith, arith1) :|: x2 > 0 && arith = x1 - 1 && arith1 = x2 - 1

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

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f379_0_minus_EQ(i35:0, i52:0, cons_0) -> f379_0_minus_EQ(i35:0, i52:0, i35:0) :|: i52:0 >= i35:0 && i35:0 > 0 && cons_0 = 0
(2) f379_0_minus_EQ(x, x1, x2) -> f379_0_minus_EQ(x, arith, arith1) :|: x2 > 0 && arith = x1 - 1 && arith1 = x2 - 1

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

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f379_0_minus_EQ(i35:0:0, i52:0:0, cons_0) -> f379_0_minus_EQ(i35:0:0, i52:0:0, i35:0:0) :|: i52:0:0 >= i35:0:0 && i35:0:0 > 0 && cons_0 = 0
f379_0_minus_EQ(x:0, x1:0, x2:0) -> f379_0_minus_EQ(x:0, x1:0 - 1, x2:0 - 1) :|: x2:0 > 0

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

(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f379_0_minus_EQ(VARIABLE, VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(16)
Obligation:
Rules:
f379_0_minus_EQ(i35:0:0, i52:0:0, c) -> f379_0_minus_EQ(i35:0:0, i52:0:0, i35:0:0) :|: c = 0 && (i52:0:0 >= i35:0:0 && i35:0:0 > 0 && cons_0 = 0)
f379_0_minus_EQ(x:0, x1:0, x2:0) -> f379_0_minus_EQ(x:0, c1, c2) :|: c2 = x2:0 - 1 && c1 = x1:0 - 1 && x2:0 > 0

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f379_0_minus_EQ(x, x1, x2)] = x + x1 - x2

The following rules are decreasing:
f379_0_minus_EQ(i35:0:0, i52:0:0, c) -> f379_0_minus_EQ(i35:0:0, i52:0:0, i35:0:0) :|: c = 0 && (i52:0:0 >= i35:0:0 && i35:0:0 > 0 && cons_0 = 0)
The following rules are bounded:
f379_0_minus_EQ(i35:0:0, i52:0:0, c) -> f379_0_minus_EQ(i35:0:0, i52:0:0, i35:0:0) :|: c = 0 && (i52:0:0 >= i35:0:0 && i35:0:0 > 0 && cons_0 = 0)

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

(18)
Obligation:
Rules:
f379_0_minus_EQ(x:0, x1:0, x2:0) -> f379_0_minus_EQ(x:0, c1, c2) :|: c2 = x2:0 - 1 && c1 = x1:0 - 1 && x2:0 > 0

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(19) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f379_0_minus_EQ ] = f379_0_minus_EQ_3

The following rules are decreasing:
f379_0_minus_EQ(x:0, x1:0, x2:0) -> f379_0_minus_EQ(x:0, c1, c2) :|: c2 = x2:0 - 1 && c1 = x1:0 - 1 && x2:0 > 0

The following rules are bounded:
f379_0_minus_EQ(x:0, x1:0, x2:0) -> f379_0_minus_EQ(x:0, c1, c2) :|: c2 = x2:0 - 1 && c1 = x1:0 - 1 && x2:0 > 0


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(20)
YES