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


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YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 306 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 119 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, 43 ms]
(16) IntTRS
(17) RankingReductionPairProof [EQUIVALENT, 23 ms]
(18) YES


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(0)
Obligation:
need to prove termination of the following program:
public class AG313 {
  public static void main(String[] args) {
    int x, y;
    x = args[0].length();
    y = args[1].length() + 1;
    quot(x,y);

  }


  public static int quot(int x, int y) {
    int i = 0;
    if(x==0) return 0;
    while (x > 0 && y > 0) {
      i += 1;
      x = (x - 1)- (y - 1);

    }
    return i;
  }
}



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(1) BareJBCToJBCProof (EQUIVALENT)
initialized classpath
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(2)
Obligation:
need to prove termination of the following program:
public class AG313 {
  public static void main(String[] args) {
    int x, y;
    x = args[0].length();
    y = args[1].length() + 1;
    quot(x,y);

  }


  public static int quot(int x, int y) {
    int i = 0;
    if(x==0) return 0;
    while (x > 0 && y > 0) {
      i += 1;
      x = (x - 1)- (y - 1);

    }
    return i;
  }
}



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(3) JBCToGraph (EQUIVALENT)
Constructed TerminationGraph.
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(4)
Obligation:
Termination Graph based on JBC Program:
AG313.main([Ljava/lang/String;)V: Graph of 156 nodes with 1 SCC.





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(5) TerminationGraphToSCCProof (SOUND)
Splitted TerminationGraph to 1 SCCs.
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(6)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: AG313.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:

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(7) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 16 IRulesP rules:
f1276_0_quot_LE(EOS(STATIC_1276), i297, i34, i297) -> f1280_0_quot_LE(EOS(STATIC_1280), i297, i34, i297) :|: TRUE
f1280_0_quot_LE(EOS(STATIC_1280), i297, i34, i297) -> f1284_0_quot_Load(EOS(STATIC_1284), i297, i34) :|: i297 > 0
f1284_0_quot_Load(EOS(STATIC_1284), i297, i34) -> f1289_0_quot_LE(EOS(STATIC_1289), i297, i34, i34) :|: TRUE
f1289_0_quot_LE(EOS(STATIC_1289), i297, i34, i34) -> f1313_0_quot_Inc(EOS(STATIC_1313), i297, i34) :|: i34 > 0
f1313_0_quot_Inc(EOS(STATIC_1313), i297, i34) -> f1318_0_quot_Load(EOS(STATIC_1318), i297, i34) :|: TRUE
f1318_0_quot_Load(EOS(STATIC_1318), i297, i34) -> f1322_0_quot_ConstantStackPush(EOS(STATIC_1322), i34, i297) :|: TRUE
f1322_0_quot_ConstantStackPush(EOS(STATIC_1322), i34, i297) -> f1325_0_quot_IntArithmetic(EOS(STATIC_1325), i34, i297, 1) :|: TRUE
f1325_0_quot_IntArithmetic(EOS(STATIC_1325), i34, i297, matching1) -> f1327_0_quot_Load(EOS(STATIC_1327), i34, i297 - 1) :|: i297 > 0 && matching1 = 1
f1327_0_quot_Load(EOS(STATIC_1327), i34, i309) -> f1329_0_quot_ConstantStackPush(EOS(STATIC_1329), i34, i309, i34) :|: TRUE
f1329_0_quot_ConstantStackPush(EOS(STATIC_1329), i34, i309, i34) -> f1332_0_quot_IntArithmetic(EOS(STATIC_1332), i34, i309, i34, 1) :|: TRUE
f1332_0_quot_IntArithmetic(EOS(STATIC_1332), i34, i309, i34, matching1) -> f1334_0_quot_IntArithmetic(EOS(STATIC_1334), i34, i309, i34 - 1) :|: i34 > 0 && matching1 = 1
f1334_0_quot_IntArithmetic(EOS(STATIC_1334), i34, i309, i310) -> f1336_0_quot_Store(EOS(STATIC_1336), i34, i309 - i310) :|: i309 >= 0 && i310 >= 0
f1336_0_quot_Store(EOS(STATIC_1336), i34, i311) -> f1339_0_quot_JMP(EOS(STATIC_1339), i311, i34) :|: TRUE
f1339_0_quot_JMP(EOS(STATIC_1339), i311, i34) -> f1383_0_quot_Load(EOS(STATIC_1383), i311, i34) :|: TRUE
f1383_0_quot_Load(EOS(STATIC_1383), i311, i34) -> f1270_0_quot_Load(EOS(STATIC_1270), i311, i34) :|: TRUE
f1270_0_quot_Load(EOS(STATIC_1270), i283, i34) -> f1276_0_quot_LE(EOS(STATIC_1276), i283, i34, i283) :|: TRUE
Combined rules. Obtained 1 IRulesP rules:
f1276_0_quot_LE(EOS(STATIC_1276), i297:0, i34:0, i297:0) -> f1276_0_quot_LE(EOS(STATIC_1276), i297:0 - 1 - (i34:0 - 1), i34:0, i297:0 - 1 - (i34:0 - 1)) :|: i297:0 > 0 && i34:0 > 0
Filtered constant ground arguments:
   f1276_0_quot_LE(x1, x2, x3, x4) -> f1276_0_quot_LE(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f1276_0_quot_LE(x1, x2, x3) -> f1276_0_quot_LE(x2, x3)
Finished conversion. Obtained 1 rules.P rules:
f1276_0_quot_LE(i34:0, i297:0) -> f1276_0_quot_LE(i34:0, i297:0 - 1 - (i34:0 - 1)) :|: i297:0 > 0 && i34:0 > 0

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(8)
Obligation:
Rules:
f1276_0_quot_LE(i34:0, i297:0) -> f1276_0_quot_LE(i34:0, i297:0 - 1 - (i34:0 - 1)) :|: i297:0 > 0 && i34:0 > 0

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(9) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
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(10)
Obligation:
Rules:
f1276_0_quot_LE(i34:0, i297:0) -> f1276_0_quot_LE(i34:0, arith) :|: i297:0 > 0 && i34:0 > 0 && arith = i297:0 - 1 - (i34:0 - 1)

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(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1276_0_quot_LE(i34:0, i297:0) -> f1276_0_quot_LE(i34:0, arith) :|: i297:0 > 0 && i34:0 > 0 && arith = i297:0 - 1 - (i34:0 - 1)

Arcs:
(1) -> (1)

This digraph is fully evaluated!
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(12)
Obligation:

Termination digraph:
Nodes:
(1) f1276_0_quot_LE(i34:0, i297:0) -> f1276_0_quot_LE(i34:0, arith) :|: i297:0 > 0 && i34:0 > 0 && arith = i297:0 - 1 - (i34:0 - 1)

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f1276_0_quot_LE(i34:0:0, i297:0:0) -> f1276_0_quot_LE(i34:0:0, i297:0:0 - 1 - (i34:0:0 - 1)) :|: i297:0:0 > 0 && i34:0:0 > 0

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1276_0_quot_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
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(16)
Obligation:
Rules:
f1276_0_quot_LE(i34:0:0, i297:0:0) -> f1276_0_quot_LE(i34:0:0, c) :|: c = i297:0:0 - 1 - (i34:0:0 - 1) && (i297:0:0 > 0 && i34:0:0 > 0)

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(17) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f1276_0_quot_LE ] = f1276_0_quot_LE_2

The following rules are decreasing:
f1276_0_quot_LE(i34:0:0, i297:0:0) -> f1276_0_quot_LE(i34:0:0, c) :|: c = i297:0:0 - 1 - (i34:0:0 - 1) && (i297:0:0 > 0 && i34:0:0 > 0)

The following rules are bounded:
f1276_0_quot_LE(i34:0:0, i297:0:0) -> f1276_0_quot_LE(i34:0:0, c) :|: c = i297:0:0 - 1 - (i34:0:0 - 1) && (i297:0:0 > 0 && i34:0:0 > 0)


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(18)
YES