/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 503 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 104 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) IRSwTChainingProof [EQUIVALENT, 0 ms]
(16) IRSwT
(17) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms]
(18) IRSwT
(19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(20) IRSwT
(21) IRSwTChainingProof [EQUIVALENT, 0 ms]
(22) IRSwT
(23) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms]
(24) IRSwT
(25) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(26) IRSwT
(27) TempFilterProof [SOUND, 36 ms]
(28) IntTRS
(29) PolynomialOrderProcessor [EQUIVALENT, 8 ms]
(30) YES


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

(0)
Obligation:
need to prove termination of the following program:
public class Et3 {
    public static void main(String[] args) {
		Random.args = args;
	    int a =  Random.random(); 
	   	int b =  Random.random();
	   	loop(a,b);
	}
	public static void loop(int a, int b) {
	   	if (a > 0) {
	   	    a = a + b;
	   	    b = b - 1;
			loop(a,b);
	   	}
    }
}


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

  public static int random() {
      if (index >= args.length)
	  return 0;

      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 Et3 {
    public static void main(String[] args) {
		Random.args = args;
	    int a =  Random.random(); 
	   	int b =  Random.random();
	   	loop(a,b);
	}
	public static void loop(int a, int b) {
	   	if (a > 0) {
	   	    a = a + b;
	   	    b = b - 1;
			loop(a,b);
	   	}
    }
}


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

  public static int random() {
      if (index >= args.length)
	  return 0;

      String string = args[index];
      index++;
      return string.length();
  }
}



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

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

(4)
Obligation:
Termination Graph based on JBC Program:
Et3.main([Ljava/lang/String;)V: Graph of 229 nodes with 0 SCCs.



Et3.loop(II)V: Graph of 23 nodes with 0 SCCs.





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

(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: Et3.loop(II)V
SCC calls the following helper methods: Et3.loop(II)V
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:
f1451_0_loop_LE(EOS(STATIC_1451), i269, i265, i269, i265, i269) -> f1456_0_loop_LE(EOS(STATIC_1456), i269, i265, i269, i265, i269) :|: TRUE
f1456_0_loop_LE(EOS(STATIC_1456), i269, i265, i269, i265, i269) -> f1461_0_loop_Load(EOS(STATIC_1461), i269, i265, i269, i265) :|: i269 > 0
f1461_0_loop_Load(EOS(STATIC_1461), i269, i265, i269, i265) -> f1465_0_loop_Load(EOS(STATIC_1465), i269, i265, i265, i269) :|: TRUE
f1465_0_loop_Load(EOS(STATIC_1465), i269, i265, i265, i269) -> f1607_0_loop_IntArithmetic(EOS(STATIC_1607), i269, i265, i265, i269, i265) :|: TRUE
f1607_0_loop_IntArithmetic(EOS(STATIC_1607), i269, i265, i265, i269, i265) -> f1697_0_loop_Store(EOS(STATIC_1697), i269, i265, i265, i269 + i265) :|: i269 > 0
f1697_0_loop_Store(EOS(STATIC_1697), i269, i265, i265, i315) -> f1699_0_loop_Load(EOS(STATIC_1699), i269, i265, i315, i265) :|: TRUE
f1699_0_loop_Load(EOS(STATIC_1699), i269, i265, i315, i265) -> f1702_0_loop_ConstantStackPush(EOS(STATIC_1702), i269, i265, i315, i265) :|: TRUE
f1702_0_loop_ConstantStackPush(EOS(STATIC_1702), i269, i265, i315, i265) -> f1705_0_loop_IntArithmetic(EOS(STATIC_1705), i269, i265, i315, i265, 1) :|: TRUE
f1705_0_loop_IntArithmetic(EOS(STATIC_1705), i269, i265, i315, i265, matching1) -> f1708_0_loop_Store(EOS(STATIC_1708), i269, i265, i315, i265 - 1) :|: TRUE && matching1 = 1
f1708_0_loop_Store(EOS(STATIC_1708), i269, i265, i315, i317) -> f1711_0_loop_Load(EOS(STATIC_1711), i269, i265, i315, i317) :|: TRUE
f1711_0_loop_Load(EOS(STATIC_1711), i269, i265, i315, i317) -> f1713_0_loop_Load(EOS(STATIC_1713), i269, i265, i317, i315) :|: TRUE
f1713_0_loop_Load(EOS(STATIC_1713), i269, i265, i317, i315) -> f1716_0_loop_InvokeMethod(EOS(STATIC_1716), i269, i265, i315, i317) :|: TRUE
f1716_0_loop_InvokeMethod(EOS(STATIC_1716), i269, i265, i315, i317) -> f1718_0_loop_Load(EOS(STATIC_1718), i315, i317, i315, i317) :|: i269 >= 1 && i317 < i265
f1716_0_loop_InvokeMethod(EOS(STATIC_1716), i269, i265, i315, i317) -> f1718_1_loop_Load(EOS(STATIC_1718), i269, i265, i315, i317) :|: i269 >= 1 && i317 < i265
f1718_0_loop_Load(EOS(STATIC_1718), i315, i317, i315, i317) -> f1722_0_loop_Load(EOS(STATIC_1722), i315, i317, i315, i317) :|: TRUE
f1722_0_loop_Load(EOS(STATIC_1722), i315, i317, i315, i317) -> f1446_0_loop_Load(EOS(STATIC_1446), i315, i317, i315, i317) :|: TRUE
f1446_0_loop_Load(EOS(STATIC_1446), i264, i265, i264, i265) -> f1451_0_loop_LE(EOS(STATIC_1451), i264, i265, i264, i265, i264) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f1451_0_loop_LE(EOS(STATIC_1451), i269:0, i265:0, i269:0, i265:0, i269:0) -> f1451_0_loop_LE(EOS(STATIC_1451), i269:0 + i265:0, i265:0 - 1, i269:0 + i265:0, i265:0 - 1, i269:0 + i265:0) :|: i269:0 > 0 && i265:0 - 1 < i265:0
Removed following non-SCC rules:
f1451_0_loop_LE(EOS(STATIC_1451), i269:0, i265:0, i269:0, i265:0, i269:0) -> f1718_1_loop_Load(EOS(STATIC_1718), i269:0, i265:0, i269:0 + i265:0, i265:0 - 1) :|: i269:0 > 0 && i265:0 - 1 < i265:0
Filtered constant ground arguments:
   f1451_0_loop_LE(x1, x2, x3, x4, x5, x6) -> f1451_0_loop_LE(x2, x3, x4, x5, x6)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f1451_0_loop_LE(x1, x2, x3, x4, x5) -> f1451_0_loop_LE(x4, x5)
Finished conversion. Obtained 1 rules.P rules:
f1451_0_loop_LE(i265:0, i269:0) -> f1451_0_loop_LE(i265:0 - 1, i269:0 + i265:0) :|: i269:0 > 0 && i265:0 - 1 < i265:0

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

(8)
Obligation:
Rules:
f1451_0_loop_LE(i265:0, i269:0) -> f1451_0_loop_LE(i265:0 - 1, i269:0 + i265:0) :|: i269:0 > 0 && i265:0 - 1 < i265:0

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

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

(10)
Obligation:
Rules:
f1451_0_loop_LE(i265:0, i269:0) -> f1451_0_loop_LE(arith, arith1) :|: i269:0 > 0 && i265:0 - 1 < i265:0 && arith = i265:0 - 1 && arith1 = i269:0 + i265:0

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1451_0_loop_LE(i265:0, i269:0) -> f1451_0_loop_LE(arith, arith1) :|: i269:0 > 0 && i265:0 - 1 < i265:0 && arith = i265:0 - 1 && arith1 = i269:0 + i265:0

Arcs:
(1) -> (1)

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f1451_0_loop_LE(i265:0, i269:0) -> f1451_0_loop_LE(arith, arith1) :|: i269:0 > 0 && i265:0 - 1 < i265:0 && arith = i265:0 - 1 && arith1 = i269:0 + i265:0

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(14)
Obligation:
Rules:
f1451_0_loop_LE(i265:0:0, i269:0:0) -> f1451_0_loop_LE(i265:0:0 - 1, i269:0:0 + i265:0:0) :|: i269:0:0 > 0 && i265:0:0 - 1 < i265:0:0

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

(15) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(16)
Obligation:
Rules:
f1451_0_loop_LE(x, x1) -> f1451_0_loop_LE(x + -2, x1 + 2 * x + -1) :|: TRUE && x1 >= 1 && x1 + x >= 1

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

(17) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1451_0_loop_LE(x, x1) -> f1451_0_loop_LE(x + -2, x1 + 2 * x + -1) :|: TRUE && x1 >= 1 && x1 + x >= 1

Arcs:
(1) -> (1)

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

(18)
Obligation:

Termination digraph:
Nodes:
(1) f1451_0_loop_LE(x, x1) -> f1451_0_loop_LE(x + -2, x1 + 2 * x + -1) :|: TRUE && x1 >= 1 && x1 + x >= 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(20)
Obligation:
Rules:
f1451_0_loop_LE(x:0, x1:0) -> f1451_0_loop_LE(x:0 - 2, x1:0 + 2 * x:0 - 1) :|: x1:0 + x:0 >= 1 && x1:0 > 0

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

(21) IRSwTChainingProof (EQUIVALENT)
Chaining!
----------------------------------------

(22)
Obligation:
Rules:
f1451_0_loop_LE(x, x1) -> f1451_0_loop_LE(x + -4, x1 + 4 * x + -6) :|: TRUE && x1 + x >= 1 && x1 >= 1 && x1 + 3 * x >= 4 && x1 + 2 * x >= 2

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

(23) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1451_0_loop_LE(x, x1) -> f1451_0_loop_LE(x + -4, x1 + 4 * x + -6) :|: TRUE && x1 + x >= 1 && x1 >= 1 && x1 + 3 * x >= 4 && x1 + 2 * x >= 2

Arcs:
(1) -> (1)

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

(24)
Obligation:

Termination digraph:
Nodes:
(1) f1451_0_loop_LE(x, x1) -> f1451_0_loop_LE(x + -4, x1 + 4 * x + -6) :|: TRUE && x1 + x >= 1 && x1 >= 1 && x1 + 3 * x >= 4 && x1 + 2 * x >= 2

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(26)
Obligation:
Rules:
f1451_0_loop_LE(x:0, x1:0) -> f1451_0_loop_LE(x:0 - 4, x1:0 + 4 * x:0 - 6) :|: x1:0 + 3 * x:0 >= 4 && x1:0 + 2 * x:0 >= 2 && x1:0 + x:0 >= 1 && x1:0 > 0

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

(27) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1451_0_loop_LE(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(28)
Obligation:
Rules:
f1451_0_loop_LE(x:0, x1:0) -> f1451_0_loop_LE(c, c1) :|: c1 = x1:0 + 4 * x:0 - 6 && c = x:0 - 4 && (x1:0 + 3 * x:0 >= 4 && x1:0 + 2 * x:0 >= 2 && x1:0 + x:0 >= 1 && x1:0 > 0)

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

(29) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f1451_0_loop_LE(x, x1)] = -2 + 2*x + x^2 + 2*x1

The following rules are decreasing:
f1451_0_loop_LE(x:0, x1:0) -> f1451_0_loop_LE(c, c1) :|: c1 = x1:0 + 4 * x:0 - 6 && c = x:0 - 4 && (x1:0 + 3 * x:0 >= 4 && x1:0 + 2 * x:0 >= 2 && x1:0 + x:0 >= 1 && x1:0 > 0)
The following rules are bounded:
f1451_0_loop_LE(x:0, x1:0) -> f1451_0_loop_LE(c, c1) :|: c1 = x1:0 + 4 * x:0 - 6 && c = x:0 - 4 && (x1:0 + 3 * x:0 >= 4 && x1:0 + 2 * x:0 >= 2 && x1:0 + x:0 >= 1 && x1:0 > 0)

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

(30)
YES