7.32/2.81	YES
7.32/2.86	proof of /export/starexec/sandbox/benchmark/theBenchmark.jar
7.32/2.86	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
7.32/2.86	
7.32/2.86	
7.32/2.86	termination of the given Bare JBC problem could be proven:
7.32/2.86	
7.32/2.86	(0) Bare JBC problem
7.32/2.86	(1) BareJBCToJBCProof [EQUIVALENT, 95 ms]
7.32/2.86	(2) JBC problem
7.32/2.86	(3) JBCToGraph [EQUIVALENT, 367 ms]
7.32/2.86	(4) JBCTerminationGraph
7.32/2.86	(5) TerminationGraphToSCCProof [SOUND, 0 ms]
7.32/2.86	(6) JBCTerminationSCC
7.32/2.86	(7) SCCToIRSProof [SOUND, 109 ms]
7.32/2.86	(8) IRSwT
7.32/2.86	(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
7.32/2.86	(10) IRSwT
7.32/2.86	(11) IRSwTTerminationDigraphProof [EQUIVALENT, 54 ms]
7.32/2.86	(12) IRSwT
7.32/2.86	(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
7.32/2.86	(14) IRSwT
7.32/2.86	(15) TempFilterProof [SOUND, 49 ms]
7.32/2.86	(16) IntTRS
7.32/2.86	(17) PolynomialOrderProcessor [EQUIVALENT, 1 ms]
7.32/2.86	(18) IntTRS
7.32/2.86	(19) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
7.32/2.86	(20) YES
7.32/2.86	
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(0)
7.32/2.86	Obligation:
7.32/2.86	need to prove termination of the following program:
7.32/2.86	/**
7.32/2.86	 * Example taken from "A Term Rewriting Approach to the Automated Termination
7.32/2.86	 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
7.32/2.86	 * and converted to Java.
7.32/2.86	 */
7.32/2.86	
7.32/2.86	public class PastaC1 {
7.32/2.86	    public static void main(String[] args) {
7.32/2.86	        Random.args = args;
7.32/2.86	        int x = Random.random();
7.32/2.86	
7.32/2.86			while (x >= 0) {
7.32/2.86				int y = 1;
7.32/2.86				while (x > y) {
7.32/2.86					y = 2*y;
7.32/2.86				}
7.32/2.86				x--;
7.32/2.86			}
7.32/2.86	    }
7.32/2.86	}
7.32/2.86	
7.32/2.86	
7.32/2.86	public class Random {
7.32/2.86	  static String[] args;
7.32/2.86	  static int index = 0;
7.32/2.86	
7.32/2.86	  public static int random() {
7.32/2.86	    String string = args[index];
7.32/2.86	    index++;
7.32/2.86	    return string.length();
7.32/2.86	  }
7.32/2.86	}
7.32/2.86	
7.32/2.86	
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(1) BareJBCToJBCProof (EQUIVALENT)
7.32/2.86	initialized classpath
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(2)
7.32/2.86	Obligation:
7.32/2.86	need to prove termination of the following program:
7.32/2.86	/**
7.32/2.86	 * Example taken from "A Term Rewriting Approach to the Automated Termination
7.32/2.86	 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
7.32/2.86	 * and converted to Java.
7.32/2.86	 */
7.32/2.86	
7.32/2.86	public class PastaC1 {
7.32/2.86	    public static void main(String[] args) {
7.32/2.86	        Random.args = args;
7.32/2.86	        int x = Random.random();
7.32/2.86	
7.32/2.86			while (x >= 0) {
7.32/2.86				int y = 1;
7.32/2.86				while (x > y) {
7.32/2.86					y = 2*y;
7.32/2.86				}
7.32/2.86				x--;
7.32/2.86			}
7.32/2.86	    }
7.32/2.86	}
7.32/2.86	
7.32/2.86	
7.32/2.86	public class Random {
7.32/2.86	  static String[] args;
7.32/2.86	  static int index = 0;
7.32/2.86	
7.32/2.86	  public static int random() {
7.32/2.86	    String string = args[index];
7.32/2.86	    index++;
7.32/2.86	    return string.length();
7.32/2.86	  }
7.32/2.86	}
7.32/2.86	
7.32/2.86	
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(3) JBCToGraph (EQUIVALENT)
7.32/2.86	Constructed TerminationGraph.
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(4)
7.32/2.86	Obligation:
7.32/2.86	Termination Graph based on JBC Program:
7.32/2.86	PastaC1.main([Ljava/lang/String;)V: Graph of 124 nodes with 1 SCC.
7.32/2.86	
7.32/2.86	
7.32/2.86	
7.32/2.86	
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(5) TerminationGraphToSCCProof (SOUND)
7.32/2.86	Splitted TerminationGraph to 1 SCCs.
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(6)
7.32/2.86	Obligation:
7.32/2.86	SCC of termination graph based on JBC Program.
7.32/2.86	SCC contains nodes from the following methods: PastaC1.main([Ljava/lang/String;)V
7.32/2.86	SCC calls the following helper methods: 
7.32/2.86	Performed SCC analyses:
7.32/2.86	*Used field analysis yielded the following read fields:
7.32/2.86	
7.32/2.86	*Marker field analysis yielded the following relations that could be markers:
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(7) SCCToIRSProof (SOUND)
7.32/2.86	Transformed FIGraph SCCs to intTRSs. Log: 
7.32/2.86	Generated rules. Obtained 23 IRulesP rules:
7.32/2.86	f813_0_main_LT(EOS(STATIC_813), i83, i83) -> f817_0_main_LT(EOS(STATIC_817), i83, i83) :|: TRUE
7.32/2.86	f817_0_main_LT(EOS(STATIC_817), i83, i83) -> f819_0_main_ConstantStackPush(EOS(STATIC_819), i83) :|: i83 >= 0
7.32/2.86	f819_0_main_ConstantStackPush(EOS(STATIC_819), i83) -> f821_0_main_Store(EOS(STATIC_821), i83, 1) :|: TRUE
7.32/2.86	f821_0_main_Store(EOS(STATIC_821), i83, matching1) -> f823_0_main_Load(EOS(STATIC_823), i83, 1) :|: TRUE && matching1 = 1
7.32/2.86	f823_0_main_Load(EOS(STATIC_823), i83, matching1) -> f905_0_main_Load(EOS(STATIC_905), i83, 1) :|: TRUE && matching1 = 1
7.32/2.86	f905_0_main_Load(EOS(STATIC_905), i92, i93) -> f954_0_main_Load(EOS(STATIC_954), i92, i93) :|: TRUE
7.32/2.86	f954_0_main_Load(EOS(STATIC_954), i102, i103) -> f984_0_main_Load(EOS(STATIC_984), i102, i103) :|: TRUE
7.32/2.86	f984_0_main_Load(EOS(STATIC_984), i111, i112) -> f985_0_main_Load(EOS(STATIC_985), i111, i112, i111) :|: TRUE
7.32/2.86	f985_0_main_Load(EOS(STATIC_985), i111, i112, i111) -> f986_0_main_LE(EOS(STATIC_986), i111, i112, i111, i112) :|: TRUE
7.32/2.86	f986_0_main_LE(EOS(STATIC_986), i111, i112, i111, i112) -> f991_0_main_LE(EOS(STATIC_991), i111, i112, i111, i112) :|: i111 <= i112
7.32/2.86	f986_0_main_LE(EOS(STATIC_986), i111, i112, i111, i112) -> f992_0_main_LE(EOS(STATIC_992), i111, i112, i111, i112) :|: i111 > i112
7.32/2.86	f991_0_main_LE(EOS(STATIC_991), i111, i112, i111, i112) -> f998_0_main_Inc(EOS(STATIC_998), i111) :|: i111 <= i112
7.32/2.86	f998_0_main_Inc(EOS(STATIC_998), i111) -> f1004_0_main_JMP(EOS(STATIC_1004), i111 + -1) :|: TRUE
7.32/2.86	f1004_0_main_JMP(EOS(STATIC_1004), i118) -> f1008_0_main_Load(EOS(STATIC_1008), i118) :|: TRUE
7.32/2.86	f1008_0_main_Load(EOS(STATIC_1008), i118) -> f808_0_main_Load(EOS(STATIC_808), i118) :|: TRUE
7.32/2.86	f808_0_main_Load(EOS(STATIC_808), i80) -> f813_0_main_LT(EOS(STATIC_813), i80, i80) :|: TRUE
7.32/2.86	f992_0_main_LE(EOS(STATIC_992), i111, i112, i111, i112) -> f1003_0_main_ConstantStackPush(EOS(STATIC_1003), i111, i112) :|: i111 > i112
7.32/2.86	f1003_0_main_ConstantStackPush(EOS(STATIC_1003), i111, i112) -> f1006_0_main_Load(EOS(STATIC_1006), i111, i112, 2) :|: TRUE
7.32/2.86	f1006_0_main_Load(EOS(STATIC_1006), i111, i112, matching1) -> f1009_0_main_IntArithmetic(EOS(STATIC_1009), i111, 2, i112) :|: TRUE && matching1 = 2
7.32/2.86	f1009_0_main_IntArithmetic(EOS(STATIC_1009), i111, matching1, i112) -> f1010_0_main_Store(EOS(STATIC_1010), i111, 2 * i112) :|: i112 >= 1 && matching1 = 2
7.32/2.86	f1010_0_main_Store(EOS(STATIC_1010), i111, i120) -> f1012_0_main_JMP(EOS(STATIC_1012), i111, i120) :|: TRUE
7.32/2.86	f1012_0_main_JMP(EOS(STATIC_1012), i111, i120) -> f1021_0_main_Load(EOS(STATIC_1021), i111, i120) :|: TRUE
7.32/2.86	f1021_0_main_Load(EOS(STATIC_1021), i111, i120) -> f984_0_main_Load(EOS(STATIC_984), i111, i120) :|: TRUE
7.32/2.86	Combined rules. Obtained 2 IRulesP rules:
7.32/2.86	f986_0_main_LE(EOS(STATIC_986), i111:0, i112:0, i111:0, i112:0) -> f986_0_main_LE(EOS(STATIC_986), i111:0 - 1, 1, i111:0 - 1, 1) :|: i111:0 > 0 && i112:0 >= i111:0
7.32/2.86	f986_0_main_LE(EOS(STATIC_986), i111:0, i112:0, i111:0, i112:0) -> f986_0_main_LE(EOS(STATIC_986), i111:0, 2 * i112:0, i111:0, 2 * i112:0) :|: i112:0 < i111:0 && i112:0 > 0
7.32/2.86	Filtered constant ground arguments:
7.32/2.86	   f986_0_main_LE(x1, x2, x3, x4, x5) -> f986_0_main_LE(x2, x3, x4, x5)
7.32/2.86	   EOS(x1) -> EOS
7.32/2.86	Filtered duplicate arguments:
7.32/2.86	   f986_0_main_LE(x1, x2, x3, x4) -> f986_0_main_LE(x3, x4)
7.32/2.86	Finished conversion. Obtained 2 rules.P rules:
7.32/2.86	f986_0_main_LE(i111:0, i112:0) -> f986_0_main_LE(i111:0 - 1, 1) :|: i111:0 > 0 && i112:0 >= i111:0
7.32/2.86	f986_0_main_LE(i111:0, i112:0) -> f986_0_main_LE(i111:0, 2 * i112:0) :|: i112:0 < i111:0 && i112:0 > 0
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(8)
7.32/2.86	Obligation:
7.32/2.86	Rules:
7.32/2.86	f986_0_main_LE(i111:0, i112:0) -> f986_0_main_LE(i111:0 - 1, 1) :|: i111:0 > 0 && i112:0 >= i111:0
7.32/2.86	f986_0_main_LE(x, x1) -> f986_0_main_LE(x, 2 * x1) :|: x1 < x && x1 > 0
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(9) IRSFormatTransformerProof (EQUIVALENT)
7.32/2.86	Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(10)
7.32/2.86	Obligation:
7.32/2.86	Rules:
7.32/2.86	f986_0_main_LE(i111:0, i112:0) -> f986_0_main_LE(arith, 1) :|: i111:0 > 0 && i112:0 >= i111:0 && arith = i111:0 - 1
7.32/2.86	f986_0_main_LE(x2, x3) -> f986_0_main_LE(x2, x4) :|: x3 < x2 && x3 > 0 && x4 = 2 * x3
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(11) IRSwTTerminationDigraphProof (EQUIVALENT)
7.32/2.86	Constructed termination digraph!
7.32/2.86	Nodes:
7.32/2.86	(1) f986_0_main_LE(i111:0, i112:0) -> f986_0_main_LE(arith, 1) :|: i111:0 > 0 && i112:0 >= i111:0 && arith = i111:0 - 1
7.32/2.86	(2) f986_0_main_LE(x2, x3) -> f986_0_main_LE(x2, x4) :|: x3 < x2 && x3 > 0 && x4 = 2 * x3
7.32/2.86	
7.32/2.86	Arcs:
7.32/2.86	(1) -> (1), (2)
7.32/2.86	(2) -> (1), (2)
7.32/2.86	
7.32/2.86	This digraph is fully evaluated!
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(12)
7.32/2.86	Obligation:
7.32/2.86	
7.32/2.86	Termination digraph:
7.32/2.86	Nodes:
7.32/2.86	(1) f986_0_main_LE(i111:0, i112:0) -> f986_0_main_LE(arith, 1) :|: i111:0 > 0 && i112:0 >= i111:0 && arith = i111:0 - 1
7.32/2.86	(2) f986_0_main_LE(x2, x3) -> f986_0_main_LE(x2, x4) :|: x3 < x2 && x3 > 0 && x4 = 2 * x3
7.32/2.86	
7.32/2.86	Arcs:
7.32/2.86	(1) -> (1), (2)
7.32/2.86	(2) -> (1), (2)
7.32/2.86	
7.32/2.86	This digraph is fully evaluated!
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(13) IntTRSCompressionProof (EQUIVALENT)
7.32/2.86	Compressed rules.
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(14)
7.32/2.86	Obligation:
7.32/2.86	Rules:
7.32/2.86	f986_0_main_LE(x2:0, x3:0) -> f986_0_main_LE(x2:0, 2 * x3:0) :|: x3:0 < x2:0 && x3:0 > 0
7.32/2.86	f986_0_main_LE(i111:0:0, i112:0:0) -> f986_0_main_LE(i111:0:0 - 1, 1) :|: i111:0:0 > 0 && i112:0:0 >= i111:0:0
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(15) TempFilterProof (SOUND)
7.32/2.86	Used the following sort dictionary for filtering: 
7.32/2.86	f986_0_main_LE(INTEGER, VARIABLE)
7.32/2.86	Replaced non-predefined constructor symbols by 0.
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(16)
7.32/2.86	Obligation:
7.32/2.86	Rules:
7.32/2.86	f986_0_main_LE(x2:0, x3:0) -> f986_0_main_LE(x2:0, c) :|: c = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0)
7.32/2.86	f986_0_main_LE(i111:0:0, i112:0:0) -> f986_0_main_LE(c1, c2) :|: c2 = 1 && c1 = i111:0:0 - 1 && (i111:0:0 > 0 && i112:0:0 >= i111:0:0)
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(17) PolynomialOrderProcessor (EQUIVALENT)
7.32/2.86	Found the following polynomial interpretation:
7.32/2.86	[f986_0_main_LE(x, x1)] = x
7.32/2.86	
7.32/2.86	The following rules are decreasing:
7.32/2.86	f986_0_main_LE(i111:0:0, i112:0:0) -> f986_0_main_LE(c1, c2) :|: c2 = 1 && c1 = i111:0:0 - 1 && (i111:0:0 > 0 && i112:0:0 >= i111:0:0)
7.32/2.86	The following rules are bounded:
7.32/2.86	f986_0_main_LE(x2:0, x3:0) -> f986_0_main_LE(x2:0, c) :|: c = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0)
7.32/2.86	f986_0_main_LE(i111:0:0, i112:0:0) -> f986_0_main_LE(c1, c2) :|: c2 = 1 && c1 = i111:0:0 - 1 && (i111:0:0 > 0 && i112:0:0 >= i111:0:0)
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(18)
7.32/2.86	Obligation:
7.32/2.86	Rules:
7.32/2.86	f986_0_main_LE(x2:0, x3:0) -> f986_0_main_LE(x2:0, c) :|: c = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0)
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(19) PolynomialOrderProcessor (EQUIVALENT)
7.32/2.86	Found the following polynomial interpretation:
7.32/2.86	[f986_0_main_LE(x, x1)] = -1 + x - x1
7.32/2.86	
7.32/2.86	The following rules are decreasing:
7.32/2.86	f986_0_main_LE(x2:0, x3:0) -> f986_0_main_LE(x2:0, c) :|: c = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0)
7.32/2.86	The following rules are bounded:
7.32/2.86	f986_0_main_LE(x2:0, x3:0) -> f986_0_main_LE(x2:0, c) :|: c = 2 * x3:0 && (x3:0 < x2:0 && x3:0 > 0)
7.32/2.86	
7.32/2.86	----------------------------------------
7.32/2.86	
7.32/2.86	(20)
7.32/2.86	YES
7.58/2.90	EOF