9.59/3.97	YES
9.59/3.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.jar
9.59/3.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.59/3.98	
9.59/3.98	
9.59/3.98	termination of the given Bare JBC problem could be proven:
9.59/3.98	
9.59/3.98	(0) Bare JBC problem
9.59/3.98	(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
9.59/3.98	(2) JBC problem
9.59/3.98	(3) JBCToGraph [EQUIVALENT, 375 ms]
9.59/3.98	(4) JBCTerminationGraph
9.59/3.98	(5) TerminationGraphToSCCProof [SOUND, 0 ms]
9.59/3.98	(6) JBCTerminationSCC
9.59/3.98	(7) SCCToIRSProof [SOUND, 83 ms]
9.59/3.98	(8) IRSwT
9.59/3.98	(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
9.59/3.98	(10) IRSwT
9.59/3.98	(11) IRSwTTerminationDigraphProof [EQUIVALENT, 12 ms]
9.59/3.98	(12) AND
9.59/3.98	    (13) IRSwT
9.59/3.98	        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
9.59/3.98	        (15) IRSwT
9.59/3.98	        (16) TempFilterProof [SOUND, 13 ms]
9.59/3.98	        (17) IntTRS
9.59/3.98	        (18) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
9.59/3.98	        (19) YES
9.59/3.98	    (20) IRSwT
9.59/3.98	        (21) IntTRSCompressionProof [EQUIVALENT, 0 ms]
9.59/3.98	        (22) IRSwT
9.59/3.98	        (23) TempFilterProof [SOUND, 3 ms]
9.59/3.98	        (24) IntTRS
9.59/3.98	        (25) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
9.59/3.98	        (26) YES
9.59/3.98	
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(0)
9.59/3.98	Obligation:
9.59/3.98	need to prove termination of the following program:
9.59/3.98	/**
9.59/3.98	 * Example taken from "A Term Rewriting Approach to the Automated Termination
9.59/3.98	 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
9.59/3.98	 * and converted to Java.
9.59/3.98	 */
9.59/3.98	
9.59/3.98	public class PastaB10 {
9.59/3.98	    public static void main(String[] args) {
9.59/3.98	        Random.args = args;
9.59/3.98	        int x = Random.random();
9.59/3.98	        int y = Random.random();
9.59/3.98	
9.59/3.98	        while (x + y > 0) {
9.59/3.98	            if (x > 0) {
9.59/3.98	                x--;
9.59/3.98	            } else if (y > 0) {
9.59/3.98	                y--;
9.59/3.98	            } else {
9.59/3.98	                continue;
9.59/3.98	            }            
9.59/3.98	        }
9.59/3.98	    }
9.59/3.98	}
9.59/3.98	
9.59/3.98	
9.59/3.98	public class Random {
9.59/3.98	  static String[] args;
9.59/3.98	  static int index = 0;
9.59/3.98	
9.59/3.98	  public static int random() {
9.59/3.98	    String string = args[index];
9.59/3.98	    index++;
9.59/3.98	    return string.length();
9.59/3.98	  }
9.59/3.98	}
9.59/3.98	
9.59/3.98	
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(1) BareJBCToJBCProof (EQUIVALENT)
9.59/3.98	initialized classpath
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(2)
9.59/3.98	Obligation:
9.59/3.98	need to prove termination of the following program:
9.59/3.98	/**
9.59/3.98	 * Example taken from "A Term Rewriting Approach to the Automated Termination
9.59/3.98	 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
9.59/3.98	 * and converted to Java.
9.59/3.98	 */
9.59/3.98	
9.59/3.98	public class PastaB10 {
9.59/3.98	    public static void main(String[] args) {
9.59/3.98	        Random.args = args;
9.59/3.98	        int x = Random.random();
9.59/3.98	        int y = Random.random();
9.59/3.98	
9.59/3.98	        while (x + y > 0) {
9.59/3.98	            if (x > 0) {
9.59/3.98	                x--;
9.59/3.98	            } else if (y > 0) {
9.59/3.98	                y--;
9.59/3.98	            } else {
9.59/3.98	                continue;
9.59/3.98	            }            
9.59/3.98	        }
9.59/3.98	    }
9.59/3.98	}
9.59/3.98	
9.59/3.98	
9.59/3.98	public class Random {
9.59/3.98	  static String[] args;
9.59/3.98	  static int index = 0;
9.59/3.98	
9.59/3.98	  public static int random() {
9.59/3.98	    String string = args[index];
9.59/3.98	    index++;
9.59/3.98	    return string.length();
9.59/3.98	  }
9.59/3.98	}
9.59/3.98	
9.59/3.98	
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(3) JBCToGraph (EQUIVALENT)
9.59/3.98	Constructed TerminationGraph.
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(4)
9.59/3.98	Obligation:
9.59/3.98	Termination Graph based on JBC Program:
9.59/3.98	PastaB10.main([Ljava/lang/String;)V: Graph of 187 nodes with 1 SCC.
9.59/3.98	
9.59/3.98	
9.59/3.98	
9.59/3.98	
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(5) TerminationGraphToSCCProof (SOUND)
9.59/3.98	Splitted TerminationGraph to 1 SCCs.
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(6)
9.59/3.98	Obligation:
9.59/3.98	SCC of termination graph based on JBC Program.
9.59/3.98	SCC contains nodes from the following methods: PastaB10.main([Ljava/lang/String;)V
9.59/3.98	SCC calls the following helper methods: 
9.59/3.98	Performed SCC analyses:
9.59/3.98	*Used field analysis yielded the following read fields:
9.59/3.98	
9.59/3.98	*Marker field analysis yielded the following relations that could be markers:
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(7) SCCToIRSProof (SOUND)
9.59/3.98	Transformed FIGraph SCCs to intTRSs. Log: 
9.59/3.98	Generated rules. Obtained 22 IRulesP rules:
9.59/3.98	f362_0_main_Load(EOS(STATIC_362), i19, i50, i19) -> f371_0_main_IntArithmetic(EOS(STATIC_371), i19, i50, i19, i50) :|: TRUE
9.59/3.98	f371_0_main_IntArithmetic(EOS(STATIC_371), i19, i50, i19, i50) -> f385_0_main_LE(EOS(STATIC_385), i19, i50, i19 + i50) :|: i19 >= 0 && i50 >= 0
9.59/3.98	f385_0_main_LE(EOS(STATIC_385), i19, i50, i62) -> f398_0_main_LE(EOS(STATIC_398), i19, i50, i62) :|: TRUE
9.59/3.98	f398_0_main_LE(EOS(STATIC_398), i19, i50, i62) -> f432_0_main_Load(EOS(STATIC_432), i19, i50) :|: i62 > 0
9.59/3.98	f432_0_main_Load(EOS(STATIC_432), i19, i50) -> f451_0_main_LE(EOS(STATIC_451), i19, i50, i19) :|: TRUE
9.59/3.98	f451_0_main_LE(EOS(STATIC_451), matching1, i50, matching2) -> f460_0_main_LE(EOS(STATIC_460), 0, i50, 0) :|: TRUE && matching1 = 0 && matching2 = 0
9.59/3.98	f451_0_main_LE(EOS(STATIC_451), i72, i50, i72) -> f461_0_main_LE(EOS(STATIC_461), i72, i50, i72) :|: TRUE
9.59/3.98	f460_0_main_LE(EOS(STATIC_460), matching1, i50, matching2) -> f481_0_main_Load(EOS(STATIC_481), 0, i50) :|: 0 <= 0 && matching1 = 0 && matching2 = 0
9.59/3.98	f481_0_main_Load(EOS(STATIC_481), matching1, i50) -> f492_0_main_LE(EOS(STATIC_492), 0, i50, i50) :|: TRUE && matching1 = 0
9.59/3.98	f492_0_main_LE(EOS(STATIC_492), matching1, matching2, matching3) -> f507_0_main_LE(EOS(STATIC_507), 0, 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0 && matching3 = 0
9.59/3.98	f492_0_main_LE(EOS(STATIC_492), matching1, i80, i80) -> f508_0_main_LE(EOS(STATIC_508), 0, i80, i80) :|: TRUE && matching1 = 0
9.59/3.98	f507_0_main_LE(EOS(STATIC_507), matching1, matching2, matching3) -> f1261_0_main_Load(EOS(STATIC_1261), 0, 0) :|: 0 <= 0 && matching1 = 0 && matching2 = 0 && matching3 = 0
9.59/3.98	f1261_0_main_Load(EOS(STATIC_1261), matching1, matching2) -> f351_0_main_Load(EOS(STATIC_351), 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0
9.59/3.98	f351_0_main_Load(EOS(STATIC_351), i19, i50) -> f362_0_main_Load(EOS(STATIC_362), i19, i50, i19) :|: TRUE
9.59/3.98	f508_0_main_LE(EOS(STATIC_508), matching1, i80, i80) -> f1268_0_main_Inc(EOS(STATIC_1268), 0, i80) :|: i80 > 0 && matching1 = 0
9.59/3.98	f1268_0_main_Inc(EOS(STATIC_1268), matching1, i80) -> f9262_0_main_JMP(EOS(STATIC_9262), 0, i80 + -1) :|: TRUE && matching1 = 0
9.59/3.98	f9262_0_main_JMP(EOS(STATIC_9262), matching1, i1395) -> f9265_0_main_Load(EOS(STATIC_9265), 0, i1395) :|: TRUE && matching1 = 0
9.59/3.98	f9265_0_main_Load(EOS(STATIC_9265), matching1, i1395) -> f351_0_main_Load(EOS(STATIC_351), 0, i1395) :|: TRUE && matching1 = 0
9.59/3.98	f461_0_main_LE(EOS(STATIC_461), i72, i50, i72) -> f483_0_main_Inc(EOS(STATIC_483), i72, i50) :|: i72 > 0
9.59/3.98	f483_0_main_Inc(EOS(STATIC_483), i72, i50) -> f495_0_main_JMP(EOS(STATIC_495), i72 + -1, i50) :|: TRUE
9.59/3.98	f495_0_main_JMP(EOS(STATIC_495), i78, i50) -> f651_0_main_Load(EOS(STATIC_651), i78, i50) :|: TRUE
9.59/3.98	f651_0_main_Load(EOS(STATIC_651), i78, i50) -> f351_0_main_Load(EOS(STATIC_351), i78, i50) :|: TRUE
9.59/3.98	Combined rules. Obtained 2 IRulesP rules:
9.59/3.98	f362_0_main_Load(EOS(STATIC_362), i19:0, i50:0, i19:0) -> f362_0_main_Load(EOS(STATIC_362), i19:0 - 1, i50:0, i19:0 - 1) :|: i19:0 > 0 && i19:0 + i50:0 > 0 && i50:0 > -1
9.59/3.98	f362_0_main_Load(EOS(STATIC_362), 0, i50:0, 0) -> f362_0_main_Load(EOS(STATIC_362), 0, i50:0 - 1, 0) :|: i50:0 > 0
9.59/3.98	Filtered constant ground arguments:
9.59/3.98	   f362_0_main_Load(x1, x2, x3, x4) -> f362_0_main_Load(x2, x3, x4)
9.59/3.98	   EOS(x1) -> EOS
9.59/3.98	Filtered duplicate arguments:
9.59/3.98	   f362_0_main_Load(x1, x2, x3) -> f362_0_main_Load(x2, x3)
9.59/3.98	Finished conversion. Obtained 2 rules.P rules:
9.59/3.98	f362_0_main_Load(i50:0, i19:0) -> f362_0_main_Load(i50:0, i19:0 - 1) :|: i19:0 + i50:0 > 0 && i50:0 > -1 && i19:0 > 0
9.59/3.98	f362_0_main_Load(i50:0, cons_0) -> f362_0_main_Load(i50:0 - 1, 0) :|: i50:0 > 0 && cons_0 = 0
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(8)
9.59/3.98	Obligation:
9.59/3.98	Rules:
9.59/3.98	f362_0_main_Load(i50:0, i19:0) -> f362_0_main_Load(i50:0, i19:0 - 1) :|: i19:0 + i50:0 > 0 && i50:0 > -1 && i19:0 > 0
9.59/3.98	f362_0_main_Load(x, x1) -> f362_0_main_Load(x - 1, 0) :|: x > 0 && x1 = 0
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(9) IRSFormatTransformerProof (EQUIVALENT)
9.59/3.98	Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(10)
9.59/3.98	Obligation:
9.59/3.98	Rules:
9.59/3.98	f362_0_main_Load(i50:0, i19:0) -> f362_0_main_Load(i50:0, arith) :|: i19:0 + i50:0 > 0 && i50:0 > -1 && i19:0 > 0 && arith = i19:0 - 1
9.59/3.98	f362_0_main_Load(x2, x3) -> f362_0_main_Load(x4, 0) :|: x2 > 0 && x3 = 0 && x4 = x2 - 1
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(11) IRSwTTerminationDigraphProof (EQUIVALENT)
9.59/3.98	Constructed termination digraph!
9.59/3.98	Nodes:
9.59/3.98	(1) f362_0_main_Load(i50:0, i19:0) -> f362_0_main_Load(i50:0, arith) :|: i19:0 + i50:0 > 0 && i50:0 > -1 && i19:0 > 0 && arith = i19:0 - 1
9.59/3.98	(2) f362_0_main_Load(x2, x3) -> f362_0_main_Load(x4, 0) :|: x2 > 0 && x3 = 0 && x4 = x2 - 1
9.59/3.98	
9.59/3.98	Arcs:
9.59/3.98	(1) -> (1), (2)
9.59/3.98	(2) -> (2)
9.59/3.98	
9.59/3.98	This digraph is fully evaluated!
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(12)
9.59/3.98	Complex Obligation (AND)
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(13)
9.59/3.98	Obligation:
9.59/3.98	
9.59/3.98	Termination digraph:
9.59/3.98	Nodes:
9.59/3.98	(1) f362_0_main_Load(i50:0, i19:0) -> f362_0_main_Load(i50:0, arith) :|: i19:0 + i50:0 > 0 && i50:0 > -1 && i19:0 > 0 && arith = i19:0 - 1
9.59/3.98	
9.59/3.98	Arcs:
9.59/3.98	(1) -> (1)
9.59/3.98	
9.59/3.98	This digraph is fully evaluated!
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(14) IntTRSCompressionProof (EQUIVALENT)
9.59/3.98	Compressed rules.
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(15)
9.59/3.98	Obligation:
9.59/3.98	Rules:
9.59/3.98	f362_0_main_Load(i50:0:0, i19:0:0) -> f362_0_main_Load(i50:0:0, i19:0:0 - 1) :|: i19:0:0 + i50:0:0 > 0 && i50:0:0 > -1 && i19:0:0 > 0
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(16) TempFilterProof (SOUND)
9.59/3.98	Used the following sort dictionary for filtering: 
9.59/3.98	f362_0_main_Load(INTEGER, INTEGER)
9.59/3.98	Replaced non-predefined constructor symbols by 0.
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(17)
9.59/3.98	Obligation:
9.59/3.98	Rules:
9.59/3.98	f362_0_main_Load(i50:0:0, i19:0:0) -> f362_0_main_Load(i50:0:0, c) :|: c = i19:0:0 - 1 && (i19:0:0 + i50:0:0 > 0 && i50:0:0 > -1 && i19:0:0 > 0)
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(18) PolynomialOrderProcessor (EQUIVALENT)
9.59/3.98	Found the following polynomial interpretation:
9.59/3.98	[f362_0_main_Load(x, x1)] = x + x1
9.59/3.98	
9.59/3.98	The following rules are decreasing:
9.59/3.98	f362_0_main_Load(i50:0:0, i19:0:0) -> f362_0_main_Load(i50:0:0, c) :|: c = i19:0:0 - 1 && (i19:0:0 + i50:0:0 > 0 && i50:0:0 > -1 && i19:0:0 > 0)
9.59/3.98	The following rules are bounded:
9.59/3.98	f362_0_main_Load(i50:0:0, i19:0:0) -> f362_0_main_Load(i50:0:0, c) :|: c = i19:0:0 - 1 && (i19:0:0 + i50:0:0 > 0 && i50:0:0 > -1 && i19:0:0 > 0)
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(19)
9.59/3.98	YES
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(20)
9.59/3.98	Obligation:
9.59/3.98	
9.59/3.98	Termination digraph:
9.59/3.98	Nodes:
9.59/3.98	(1) f362_0_main_Load(x2, x3) -> f362_0_main_Load(x4, 0) :|: x2 > 0 && x3 = 0 && x4 = x2 - 1
9.59/3.98	
9.59/3.98	Arcs:
9.59/3.98	(1) -> (1)
9.59/3.98	
9.59/3.98	This digraph is fully evaluated!
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(21) IntTRSCompressionProof (EQUIVALENT)
9.59/3.98	Compressed rules.
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(22)
9.59/3.98	Obligation:
9.59/3.98	Rules:
9.59/3.98	f362_0_main_Load(x2:0, cons_0) -> f362_0_main_Load(x2:0 - 1, 0) :|: x2:0 > 0 && cons_0 = 0
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(23) TempFilterProof (SOUND)
9.59/3.98	Used the following sort dictionary for filtering: 
9.59/3.98	f362_0_main_Load(INTEGER, VARIABLE)
9.59/3.98	Replaced non-predefined constructor symbols by 0.
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(24)
9.59/3.98	Obligation:
9.59/3.98	Rules:
9.59/3.98	f362_0_main_Load(x2:0, c) -> f362_0_main_Load(c1, c2) :|: c2 = 0 && (c1 = x2:0 - 1 && c = 0) && (x2:0 > 0 && cons_0 = 0)
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(25) PolynomialOrderProcessor (EQUIVALENT)
9.59/3.98	Found the following polynomial interpretation:
9.59/3.98	[f362_0_main_Load(x, x1)] = x + c1*x1
9.59/3.98	
9.59/3.98	The following rules are decreasing:
9.59/3.98	f362_0_main_Load(x2:0, c) -> f362_0_main_Load(c1, c2) :|: c2 = 0 && (c1 = x2:0 - 1 && c = 0) && (x2:0 > 0 && cons_0 = 0)
9.59/3.98	The following rules are bounded:
9.59/3.98	f362_0_main_Load(x2:0, c) -> f362_0_main_Load(c1, c2) :|: c2 = 0 && (c1 = x2:0 - 1 && c = 0) && (x2:0 > 0 && cons_0 = 0)
9.59/3.98	
9.59/3.98	----------------------------------------
9.59/3.98	
9.59/3.98	(26)
9.59/3.98	YES
9.86/4.02	EOF