6.66/2.66	YES
6.66/2.68	proof of /export/starexec/sandbox/benchmark/theBenchmark.jar
6.66/2.68	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.66/2.68	
6.66/2.68	
6.66/2.68	termination of the given Bare JBC problem could be proven:
6.66/2.68	
6.66/2.68	(0) Bare JBC problem
6.66/2.68	(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
6.66/2.68	(2) JBC problem
6.66/2.68	(3) JBCToGraph [EQUIVALENT, 321 ms]
6.66/2.68	(4) JBCTerminationGraph
6.66/2.68	(5) TerminationGraphToSCCProof [SOUND, 0 ms]
6.66/2.68	(6) JBCTerminationSCC
6.66/2.68	(7) SCCToIRSProof [SOUND, 109 ms]
6.66/2.68	(8) IRSwT
6.66/2.68	(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
6.66/2.68	(10) IRSwT
6.66/2.68	(11) IRSwTTerminationDigraphProof [EQUIVALENT, 22 ms]
6.66/2.68	(12) IRSwT
6.66/2.68	(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.66/2.68	(14) IRSwT
6.66/2.68	(15) FilterProof [EQUIVALENT, 0 ms]
6.66/2.68	(16) IntTRS
6.66/2.68	(17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.66/2.68	(18) IntTRS
6.66/2.68	(19) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
6.66/2.68	(20) YES
6.66/2.68	
6.66/2.68	
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(0)
6.66/2.68	Obligation:
6.66/2.68	need to prove termination of the following program:
6.66/2.68	public class LogIterative {
6.66/2.68	  public static int log(int x, int y) {
6.66/2.68	    int res = 0;
6.66/2.68	    while (x >= y && y > 1) {
6.66/2.68	      res++;
6.66/2.68	      x = x/y;
6.66/2.68	    }
6.66/2.68	    return res;
6.66/2.68	  } 
6.66/2.68	
6.66/2.68	  public static void main(String[] args) {
6.66/2.68	    Random.args = args;
6.66/2.68	    int x = Random.random();
6.66/2.68	    int y = Random.random();
6.66/2.68	    log(x, y);
6.66/2.68	  }
6.66/2.68	}
6.66/2.68	
6.66/2.68	
6.66/2.68	public class Random {
6.66/2.68	  static String[] args;
6.66/2.68	  static int index = 0;
6.66/2.68	
6.66/2.68	  public static int random() {
6.66/2.68	    String string = args[index];
6.66/2.68	    index++;
6.66/2.68	    return string.length();
6.66/2.68	  }
6.66/2.68	}
6.66/2.68	
6.66/2.68	
6.66/2.68	
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(1) BareJBCToJBCProof (EQUIVALENT)
6.66/2.68	initialized classpath
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(2)
6.66/2.68	Obligation:
6.66/2.68	need to prove termination of the following program:
6.66/2.68	public class LogIterative {
6.66/2.68	  public static int log(int x, int y) {
6.66/2.68	    int res = 0;
6.66/2.68	    while (x >= y && y > 1) {
6.66/2.68	      res++;
6.66/2.68	      x = x/y;
6.66/2.68	    }
6.66/2.68	    return res;
6.66/2.68	  } 
6.66/2.68	
6.66/2.68	  public static void main(String[] args) {
6.66/2.68	    Random.args = args;
6.66/2.68	    int x = Random.random();
6.66/2.68	    int y = Random.random();
6.66/2.68	    log(x, y);
6.66/2.68	  }
6.66/2.68	}
6.66/2.68	
6.66/2.68	
6.66/2.68	public class Random {
6.66/2.68	  static String[] args;
6.66/2.68	  static int index = 0;
6.66/2.68	
6.66/2.68	  public static int random() {
6.66/2.68	    String string = args[index];
6.66/2.68	    index++;
6.66/2.68	    return string.length();
6.66/2.68	  }
6.66/2.68	}
6.66/2.68	
6.66/2.68	
6.66/2.68	
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(3) JBCToGraph (EQUIVALENT)
6.66/2.68	Constructed TerminationGraph.
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(4)
6.66/2.68	Obligation:
6.66/2.68	Termination Graph based on JBC Program:
6.66/2.68	LogIterative.main([Ljava/lang/String;)V: Graph of 195 nodes with 1 SCC.
6.66/2.68	
6.66/2.68	
6.66/2.68	
6.66/2.68	
6.66/2.68	
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(5) TerminationGraphToSCCProof (SOUND)
6.66/2.68	Splitted TerminationGraph to 1 SCCs.
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(6)
6.66/2.68	Obligation:
6.66/2.68	SCC of termination graph based on JBC Program.
6.66/2.68	SCC contains nodes from the following methods: LogIterative.main([Ljava/lang/String;)V
6.66/2.68	SCC calls the following helper methods: 
6.66/2.68	Performed SCC analyses:
6.66/2.68	*Used field analysis yielded the following read fields:
6.66/2.68	
6.66/2.68	*Marker field analysis yielded the following relations that could be markers:
6.66/2.68	
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(7) SCCToIRSProof (SOUND)
6.66/2.68	Transformed FIGraph SCCs to intTRSs. Log: 
6.66/2.68	Generated rules. Obtained 15 IRulesP rules:
6.66/2.68	f595_0_log_Load(EOS(STATIC_595), i92, i93, i92) -> f596_0_log_LT(EOS(STATIC_596), i92, i93, i92, i93) :|: TRUE
6.66/2.68	f596_0_log_LT(EOS(STATIC_596), i92, i93, i92, i93) -> f601_0_log_LT(EOS(STATIC_601), i92, i93, i92, i93) :|: i92 >= i93
6.66/2.68	f601_0_log_LT(EOS(STATIC_601), i92, i93, i92, i93) -> f608_0_log_Load(EOS(STATIC_608), i92, i93) :|: i92 >= i93
6.66/2.68	f608_0_log_Load(EOS(STATIC_608), i92, i93) -> f612_0_log_ConstantStackPush(EOS(STATIC_612), i92, i93, i93) :|: TRUE
6.66/2.68	f612_0_log_ConstantStackPush(EOS(STATIC_612), i92, i93, i93) -> f617_0_log_LE(EOS(STATIC_617), i92, i93, i93, 1) :|: TRUE
6.66/2.68	f617_0_log_LE(EOS(STATIC_617), i104, i103, i103, matching1) -> f625_0_log_LE(EOS(STATIC_625), i104, i103, i103, 1) :|: TRUE && matching1 = 1
6.66/2.68	f625_0_log_LE(EOS(STATIC_625), i104, i103, i103, matching1) -> f643_0_log_Inc(EOS(STATIC_643), i104, i103) :|: i103 > 1 && matching1 = 1
6.66/2.68	f643_0_log_Inc(EOS(STATIC_643), i104, i103) -> f646_0_log_Load(EOS(STATIC_646), i104, i103) :|: TRUE
6.66/2.68	f646_0_log_Load(EOS(STATIC_646), i104, i103) -> f648_0_log_Load(EOS(STATIC_648), i103, i104) :|: TRUE
6.66/2.68	f648_0_log_Load(EOS(STATIC_648), i103, i104) -> f649_0_log_IntArithmetic(EOS(STATIC_649), i103, i104, i103) :|: TRUE
6.66/2.68	f649_0_log_IntArithmetic(EOS(STATIC_649), i103, i104, i103) -> f650_0_log_Store(EOS(STATIC_650), i103, i107) :|: i107 = i104 / i103 && i104 > 1 && i103 > 1 && i107 < i104
6.66/2.68	f650_0_log_Store(EOS(STATIC_650), i103, i107) -> f651_0_log_JMP(EOS(STATIC_651), i107, i103) :|: TRUE
6.66/2.68	f651_0_log_JMP(EOS(STATIC_651), i107, i103) -> f673_0_log_Load(EOS(STATIC_673), i107, i103) :|: TRUE
6.66/2.68	f673_0_log_Load(EOS(STATIC_673), i107, i103) -> f592_0_log_Load(EOS(STATIC_592), i107, i103) :|: TRUE
6.66/2.68	f592_0_log_Load(EOS(STATIC_592), i92, i93) -> f595_0_log_Load(EOS(STATIC_595), i92, i93, i92) :|: TRUE
6.66/2.68	Combined rules. Obtained 2 IRulesP rules:
6.66/2.68	f595_0_log_Load(EOS(STATIC_595), i92:0, i93:0, i92:0) -> f595_0_log_Load'(EOS(STATIC_595), i92:0, i93:0, i92:0) :|: i93:0 <= i92:0 && i93:0 > 1 && i92:0 > 1 && i92:0 > div
6.66/2.68	f595_0_log_Load'(EOS(STATIC_595), i92:0, i93:0, i92:0) -> f595_0_log_Load(EOS(STATIC_595), div, i93:0, div) :|: i93:0 <= i92:0 && i93:0 > 1 && i92:0 > 1 && i92:0 > div && i93:0 > i92:0 - i93:0 * div && i92:0 - i93:0 * div + i93:0 > 0
6.66/2.68	Filtered constant ground arguments:
6.66/2.68	   f595_0_log_Load(x1, x2, x3, x4) -> f595_0_log_Load(x2, x3, x4)
6.66/2.68	   f595_0_log_Load'(x1, x2, x3, x4) -> f595_0_log_Load'(x2, x3, x4)
6.66/2.68	   EOS(x1) -> EOS
6.66/2.68	Filtered duplicate arguments:
6.66/2.68	   f595_0_log_Load(x1, x2, x3) -> f595_0_log_Load(x2, x3)
6.66/2.68	   f595_0_log_Load'(x1, x2, x3) -> f595_0_log_Load'(x2, x3)
6.66/2.68	Finished conversion. Obtained 2 rules.P rules:
6.66/2.68	f595_0_log_Load(i93:0, i92:0) -> f595_0_log_Load'(i93:0, i92:0) :|: i93:0 > 1 && i93:0 <= i92:0 && i92:0 > div && i92:0 > 1
6.66/2.68	f595_0_log_Load'(i93:0, i92:0) -> f595_0_log_Load(i93:0, div) :|: i93:0 > 1 && i93:0 <= i92:0 && i92:0 > 1 && i92:0 > div && i92:0 - i93:0 * div + i93:0 > 0 && i93:0 > i92:0 - i93:0 * div
6.66/2.68	
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(8)
6.66/2.68	Obligation:
6.66/2.68	Rules:
6.66/2.68	f595_0_log_Load(x, x1) -> f595_0_log_Load'(x, x1) :|: x > 1 && x <= x1 && x1 > x2 && x1 > 1
6.66/2.68	f595_0_log_Load'(x3, x4) -> f595_0_log_Load(x3, x5) :|: x3 > 1 && x3 <= x4 && x4 > 1 && x4 > x5 && x4 - x3 * x5 + x3 > 0 && x3 > x4 - x3 * x5
6.66/2.68	
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(9) IRSFormatTransformerProof (EQUIVALENT)
6.66/2.68	Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(10)
6.66/2.68	Obligation:
6.66/2.68	Rules:
6.66/2.68	f595_0_log_Load(x, x1) -> f595_0_log_Load'(x, x1) :|: x > 1 && x <= x1 && x1 > x2 && x1 > 1
6.66/2.68	f595_0_log_Load'(x3, x4) -> f595_0_log_Load(x3, x5) :|: x3 > 1 && x3 <= x4 && x4 > 1 && x4 > x5 && x4 - x3 * x5 + x3 > 0 && x3 > x4 - x3 * x5
6.66/2.68	
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(11) IRSwTTerminationDigraphProof (EQUIVALENT)
6.66/2.68	Constructed termination digraph!
6.66/2.68	Nodes:
6.66/2.68	(1) f595_0_log_Load(x, x1) -> f595_0_log_Load'(x, x1) :|: x > 1 && x <= x1 && x1 > x2 && x1 > 1
6.66/2.68	(2) f595_0_log_Load'(x3, x4) -> f595_0_log_Load(x3, x5) :|: x3 > 1 && x3 <= x4 && x4 > 1 && x4 > x5 && x4 - x3 * x5 + x3 > 0 && x3 > x4 - x3 * x5
6.66/2.68	
6.66/2.68	Arcs:
6.66/2.68	(1) -> (2)
6.66/2.68	(2) -> (1)
6.66/2.68	
6.66/2.68	This digraph is fully evaluated!
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(12)
6.66/2.68	Obligation:
6.66/2.68	
6.66/2.68	Termination digraph:
6.66/2.68	Nodes:
6.66/2.68	(1) f595_0_log_Load(x, x1) -> f595_0_log_Load'(x, x1) :|: x > 1 && x <= x1 && x1 > x2 && x1 > 1
6.66/2.68	(2) f595_0_log_Load'(x3, x4) -> f595_0_log_Load(x3, x5) :|: x3 > 1 && x3 <= x4 && x4 > 1 && x4 > x5 && x4 - x3 * x5 + x3 > 0 && x3 > x4 - x3 * x5
6.66/2.68	
6.66/2.68	Arcs:
6.66/2.68	(1) -> (2)
6.66/2.68	(2) -> (1)
6.66/2.68	
6.66/2.68	This digraph is fully evaluated!
6.66/2.68	
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(13) IntTRSCompressionProof (EQUIVALENT)
6.66/2.68	Compressed rules.
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(14)
6.66/2.68	Obligation:
6.66/2.68	Rules:
6.66/2.68	f595_0_log_Load(x:0, x1:0) -> f595_0_log_Load(x:0, x5:0) :|: x:0 > x1:0 - x:0 * x5:0 && x2:0 < x1:0 && x1:0 - x:0 * x5:0 + x:0 > 0 && x5:0 < x1:0 && x1:0 > 1 && x:0 <= x1:0 && x:0 > 1
6.66/2.68	
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(15) FilterProof (EQUIVALENT)
6.66/2.68	Used the following sort dictionary for filtering: 
6.66/2.68	f595_0_log_Load(INTEGER, INTEGER)
6.66/2.68	Replaced non-predefined constructor symbols by 0.
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(16)
6.66/2.68	Obligation:
6.66/2.68	Rules:
6.66/2.68	f595_0_log_Load(x:0, x1:0) -> f595_0_log_Load(x:0, x5:0) :|: x:0 > x1:0 - x:0 * x5:0 && x2:0 < x1:0 && x1:0 - x:0 * x5:0 + x:0 > 0 && x5:0 < x1:0 && x1:0 > 1 && x:0 <= x1:0 && x:0 > 1
6.66/2.68	
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(17) IntTRSCompressionProof (EQUIVALENT)
6.66/2.68	Compressed rules.
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(18)
6.66/2.68	Obligation:
6.66/2.68	Rules:
6.66/2.68	f595_0_log_Load(x:0:0, x1:0:0) -> f595_0_log_Load(x:0:0, x5:0:0) :|: x:0:0 <= x1:0:0 && x:0:0 > 1 && x1:0:0 > 1 && x5:0:0 < x1:0:0 && x1:0:0 - x:0:0 * x5:0:0 + x:0:0 > 0 && x2:0:0 < x1:0:0 && x:0:0 > x1:0:0 - x:0:0 * x5:0:0
6.66/2.68	
6.66/2.68	----------------------------------------
6.66/2.68	
6.66/2.68	(19) PolynomialOrderProcessor (EQUIVALENT)
6.66/2.68	Found the following polynomial interpretation:
6.66/2.68	[f595_0_log_Load(x, x1)] = x1
6.66/2.68	
6.66/2.68	The following rules are decreasing:
6.66/2.68	f595_0_log_Load(x:0:0, x1:0:0) -> f595_0_log_Load(x:0:0, x5:0:0) :|: x:0:0 <= x1:0:0 && x:0:0 > 1 && x1:0:0 > 1 && x5:0:0 < x1:0:0 && x1:0:0 - x:0:0 * x5:0:0 + x:0:0 > 0 && x2:0:0 < x1:0:0 && x:0:0 > x1:0:0 - x:0:0 * x5:0:0
6.95/2.68	The following rules are bounded:
6.95/2.68	f595_0_log_Load(x:0:0, x1:0:0) -> f595_0_log_Load(x:0:0, x5:0:0) :|: x:0:0 <= x1:0:0 && x:0:0 > 1 && x1:0:0 > 1 && x5:0:0 < x1:0:0 && x1:0:0 - x:0:0 * x5:0:0 + x:0:0 > 0 && x2:0:0 < x1:0:0 && x:0:0 > x1:0:0 - x:0:0 * x5:0:0
6.95/2.68	
6.95/2.68	----------------------------------------
6.95/2.68	
6.95/2.68	(20)
6.95/2.68	YES
6.95/2.71	EOF