6.00/2.48	YES
6.31/2.49	proof of /export/starexec/sandbox/benchmark/theBenchmark.jar
6.31/2.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.31/2.49	
6.31/2.49	
6.31/2.49	termination of the given Bare JBC problem could be proven:
6.31/2.49	
6.31/2.49	(0) Bare JBC problem
6.31/2.49	(1) BareJBCToJBCProof [EQUIVALENT, 91 ms]
6.31/2.49	(2) JBC problem
6.31/2.49	(3) JBCToGraph [EQUIVALENT, 246 ms]
6.31/2.49	(4) JBCTerminationGraph
6.31/2.49	(5) TerminationGraphToSCCProof [SOUND, 0 ms]
6.31/2.49	(6) JBCTerminationSCC
6.31/2.49	(7) SCCToIRSProof [SOUND, 122 ms]
6.31/2.49	(8) IRSwT
6.31/2.49	(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
6.31/2.49	(10) IRSwT
6.31/2.49	(11) IRSwTTerminationDigraphProof [EQUIVALENT, 25 ms]
6.31/2.49	(12) IRSwT
6.31/2.49	(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.31/2.49	(14) IRSwT
6.31/2.49	(15) FilterProof [EQUIVALENT, 0 ms]
6.31/2.49	(16) IntTRS
6.31/2.49	(17) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.31/2.49	(18) IntTRS
6.31/2.49	(19) RankingReductionPairProof [EQUIVALENT, 0 ms]
6.31/2.49	(20) YES
6.31/2.49	
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(0)
6.31/2.49	Obligation:
6.31/2.49	need to prove termination of the following program:
6.31/2.49	package example_2;
6.31/2.49	
6.31/2.49	
6.31/2.49	public class Test {
6.31/2.49	
6.31/2.49		public static int divBy(int x){
6.31/2.49			int r = 0;
6.31/2.49			int y;
6.31/2.49			while (x > 0) {
6.31/2.49				y = 2;
6.31/2.49				x = x/y;
6.31/2.49				r = r + x;
6.31/2.49			}
6.31/2.49			return r;
6.31/2.49		}
6.31/2.49	
6.31/2.49		public static void main(String[] args) {
6.31/2.49			if (args.length > 0) {
6.31/2.49			        int x = args[0].length();
6.31/2.49				int r = divBy(x);
6.31/2.49				// System.out.println("Result: " + r);
6.31/2.49			}
6.31/2.49			// else System.out.println("Error: Incorrect call");
6.31/2.49		}
6.31/2.49	}
6.31/2.49	
6.31/2.49	
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(1) BareJBCToJBCProof (EQUIVALENT)
6.31/2.49	initialized classpath
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(2)
6.31/2.49	Obligation:
6.31/2.49	need to prove termination of the following program:
6.31/2.49	package example_2;
6.31/2.49	
6.31/2.49	
6.31/2.49	public class Test {
6.31/2.49	
6.31/2.49		public static int divBy(int x){
6.31/2.49			int r = 0;
6.31/2.49			int y;
6.31/2.49			while (x > 0) {
6.31/2.49				y = 2;
6.31/2.49				x = x/y;
6.31/2.49				r = r + x;
6.31/2.49			}
6.31/2.49			return r;
6.31/2.49		}
6.31/2.49	
6.31/2.49		public static void main(String[] args) {
6.31/2.49			if (args.length > 0) {
6.31/2.49			        int x = args[0].length();
6.31/2.49				int r = divBy(x);
6.31/2.49				// System.out.println("Result: " + r);
6.31/2.49			}
6.31/2.49			// else System.out.println("Error: Incorrect call");
6.31/2.49		}
6.31/2.49	}
6.31/2.49	
6.31/2.49	
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(3) JBCToGraph (EQUIVALENT)
6.31/2.49	Constructed TerminationGraph.
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(4)
6.31/2.49	Obligation:
6.31/2.49	Termination Graph based on JBC Program:
6.31/2.49	example_2.Test.main([Ljava/lang/String;)V: Graph of 67 nodes with 1 SCC.
6.31/2.49	
6.31/2.49	
6.31/2.49	
6.31/2.49	
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(5) TerminationGraphToSCCProof (SOUND)
6.31/2.49	Splitted TerminationGraph to 1 SCCs.
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(6)
6.31/2.49	Obligation:
6.31/2.49	SCC of termination graph based on JBC Program.
6.31/2.49	SCC contains nodes from the following methods: example_2.Test.main([Ljava/lang/String;)V
6.31/2.49	SCC calls the following helper methods: 
6.31/2.49	Performed SCC analyses:
6.31/2.49	*Used field analysis yielded the following read fields:
6.31/2.49	
6.31/2.49	*Marker field analysis yielded the following relations that could be markers:
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(7) SCCToIRSProof (SOUND)
6.31/2.49	Transformed FIGraph SCCs to intTRSs. Log: 
6.31/2.49	Generated rules. Obtained 15 IRulesP rules:
6.31/2.49	f996_0_divBy_LE(EOS(STATIC_996), i163, i163) -> f998_0_divBy_LE(EOS(STATIC_998), i163, i163) :|: TRUE
6.31/2.49	f998_0_divBy_LE(EOS(STATIC_998), i163, i163) -> f1000_0_divBy_ConstantStackPush(EOS(STATIC_1000), i163) :|: i163 > 0
6.31/2.49	f1000_0_divBy_ConstantStackPush(EOS(STATIC_1000), i163) -> f1005_0_divBy_Store(EOS(STATIC_1005), i163, 2) :|: TRUE
6.31/2.49	f1005_0_divBy_Store(EOS(STATIC_1005), i163, matching1) -> f1010_0_divBy_Load(EOS(STATIC_1010), i163, 2) :|: TRUE && matching1 = 2
6.31/2.49	f1010_0_divBy_Load(EOS(STATIC_1010), i163, matching1) -> f1017_0_divBy_Load(EOS(STATIC_1017), 2, i163) :|: TRUE && matching1 = 2
6.31/2.49	f1017_0_divBy_Load(EOS(STATIC_1017), matching1, i163) -> f1021_0_divBy_IntArithmetic(EOS(STATIC_1021), i163, 2) :|: TRUE && matching1 = 2
6.31/2.49	f1021_0_divBy_IntArithmetic(EOS(STATIC_1021), i163, matching1) -> f1024_0_divBy_Store(EOS(STATIC_1024), i165) :|: i165 = i163 / 2 && i163 >= 1 && i165 < i163 && matching1 = 2
6.31/2.49	f1024_0_divBy_Store(EOS(STATIC_1024), i165) -> f1027_0_divBy_Load(EOS(STATIC_1027), i165) :|: TRUE
6.31/2.49	f1027_0_divBy_Load(EOS(STATIC_1027), i165) -> f1029_0_divBy_Load(EOS(STATIC_1029), i165) :|: TRUE
6.31/2.49	f1029_0_divBy_Load(EOS(STATIC_1029), i165) -> f1030_0_divBy_IntArithmetic(EOS(STATIC_1030), i165, i165) :|: TRUE
6.31/2.49	f1030_0_divBy_IntArithmetic(EOS(STATIC_1030), i165, i165) -> f1033_0_divBy_Store(EOS(STATIC_1033), i165) :|: i165 >= 0
6.31/2.49	f1033_0_divBy_Store(EOS(STATIC_1033), i165) -> f1036_0_divBy_JMP(EOS(STATIC_1036), i165) :|: TRUE
6.31/2.49	f1036_0_divBy_JMP(EOS(STATIC_1036), i165) -> f1087_0_divBy_Load(EOS(STATIC_1087), i165) :|: TRUE
6.31/2.49	f1087_0_divBy_Load(EOS(STATIC_1087), i165) -> f949_0_divBy_Load(EOS(STATIC_949), i165) :|: TRUE
6.31/2.49	f949_0_divBy_Load(EOS(STATIC_949), i144) -> f996_0_divBy_LE(EOS(STATIC_996), i144, i144) :|: TRUE
6.31/2.49	Combined rules. Obtained 2 IRulesP rules:
6.31/2.49	f996_0_divBy_LE(EOS(STATIC_996), i163:0, i163:0) -> f996_0_divBy_LE'(EOS(STATIC_996), i163:0, i163:0) :|: i163:0 > 0 && div > -1 && i163:0 > div
6.31/2.49	f996_0_divBy_LE'(EOS(STATIC_996), i163:0, i163:0) -> f996_0_divBy_LE(EOS(STATIC_996), div, div) :|: i163:0 > 0 && i163:0 > div && div > -1 && i163:0 - 2 * div < 2 && i163:0 - 2 * div > -2
6.31/2.49	Filtered constant ground arguments:
6.31/2.49	   f996_0_divBy_LE(x1, x2, x3) -> f996_0_divBy_LE(x2, x3)
6.31/2.49	   f996_0_divBy_LE'(x1, x2, x3) -> f996_0_divBy_LE'(x2, x3)
6.31/2.49	   EOS(x1) -> EOS
6.31/2.49	Filtered duplicate arguments:
6.31/2.49	   f996_0_divBy_LE(x1, x2) -> f996_0_divBy_LE(x2)
6.31/2.49	   f996_0_divBy_LE'(x1, x2) -> f996_0_divBy_LE'(x2)
6.31/2.49	Finished conversion. Obtained 2 rules.P rules:
6.31/2.49	f996_0_divBy_LE(i163:0) -> f996_0_divBy_LE'(i163:0) :|: div > -1 && i163:0 > div && i163:0 > 0
6.31/2.49	f996_0_divBy_LE'(i163:0) -> f996_0_divBy_LE(div) :|: i163:0 > div && i163:0 > 0 && div > -1 && i163:0 - 2 * div > -2 && i163:0 - 2 * div < 2
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(8)
6.31/2.49	Obligation:
6.31/2.49	Rules:
6.31/2.49	f996_0_divBy_LE(x) -> f996_0_divBy_LE'(x) :|: x1 > -1 && x > x1 && x > 0
6.31/2.49	f996_0_divBy_LE'(x2) -> f996_0_divBy_LE(x3) :|: x2 > x3 && x2 > 0 && x3 > -1 && x2 - 2 * x3 > -2 && x2 - 2 * x3 < 2
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(9) IRSFormatTransformerProof (EQUIVALENT)
6.31/2.49	Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(10)
6.31/2.49	Obligation:
6.31/2.49	Rules:
6.31/2.49	f996_0_divBy_LE(x) -> f996_0_divBy_LE'(x) :|: x1 > -1 && x > x1 && x > 0
6.31/2.49	f996_0_divBy_LE'(x2) -> f996_0_divBy_LE(x3) :|: x2 > x3 && x2 > 0 && x3 > -1 && x2 - 2 * x3 > -2 && x2 - 2 * x3 < 2
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(11) IRSwTTerminationDigraphProof (EQUIVALENT)
6.31/2.49	Constructed termination digraph!
6.31/2.49	Nodes:
6.31/2.49	(1) f996_0_divBy_LE(x) -> f996_0_divBy_LE'(x) :|: x1 > -1 && x > x1 && x > 0
6.31/2.49	(2) f996_0_divBy_LE'(x2) -> f996_0_divBy_LE(x3) :|: x2 > x3 && x2 > 0 && x3 > -1 && x2 - 2 * x3 > -2 && x2 - 2 * x3 < 2
6.31/2.49	
6.31/2.49	Arcs:
6.31/2.49	(1) -> (2)
6.31/2.49	(2) -> (1)
6.31/2.49	
6.31/2.49	This digraph is fully evaluated!
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(12)
6.31/2.49	Obligation:
6.31/2.49	
6.31/2.49	Termination digraph:
6.31/2.49	Nodes:
6.31/2.49	(1) f996_0_divBy_LE(x) -> f996_0_divBy_LE'(x) :|: x1 > -1 && x > x1 && x > 0
6.31/2.49	(2) f996_0_divBy_LE'(x2) -> f996_0_divBy_LE(x3) :|: x2 > x3 && x2 > 0 && x3 > -1 && x2 - 2 * x3 > -2 && x2 - 2 * x3 < 2
6.31/2.49	
6.31/2.49	Arcs:
6.31/2.49	(1) -> (2)
6.31/2.49	(2) -> (1)
6.31/2.49	
6.31/2.49	This digraph is fully evaluated!
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(13) IntTRSCompressionProof (EQUIVALENT)
6.31/2.49	Compressed rules.
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(14)
6.31/2.49	Obligation:
6.31/2.49	Rules:
6.31/2.49	f996_0_divBy_LE(x:0) -> f996_0_divBy_LE(x3:0) :|: x:0 - 2 * x3:0 < 2 && x1:0 > -1 && x:0 > x1:0 && x:0 - 2 * x3:0 > -2 && x3:0 > -1 && x:0 > 0 && x:0 > x3:0
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(15) FilterProof (EQUIVALENT)
6.31/2.49	Used the following sort dictionary for filtering: 
6.31/2.49	f996_0_divBy_LE(INTEGER)
6.31/2.49	Replaced non-predefined constructor symbols by 0.
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(16)
6.31/2.49	Obligation:
6.31/2.49	Rules:
6.31/2.49	f996_0_divBy_LE(x:0) -> f996_0_divBy_LE(x3:0) :|: x:0 - 2 * x3:0 < 2 && x1:0 > -1 && x:0 > x1:0 && x:0 - 2 * x3:0 > -2 && x3:0 > -1 && x:0 > 0 && x:0 > x3:0
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(17) IntTRSCompressionProof (EQUIVALENT)
6.31/2.49	Compressed rules.
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(18)
6.31/2.49	Obligation:
6.31/2.49	Rules:
6.31/2.49	f996_0_divBy_LE(x:0:0) -> f996_0_divBy_LE(x3:0:0) :|: x:0:0 > 0 && x:0:0 > x3:0:0 && x3:0:0 > -1 && x:0:0 - 2 * x3:0:0 > -2 && x:0:0 > x1:0:0 && x1:0:0 > -1 && x:0:0 - 2 * x3:0:0 < 2
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(19) RankingReductionPairProof (EQUIVALENT)
6.31/2.49	Interpretation:
6.31/2.49	[ f996_0_divBy_LE ] = f996_0_divBy_LE_1
6.31/2.49	
6.31/2.49	The following rules are decreasing:
6.31/2.49	f996_0_divBy_LE(x:0:0) -> f996_0_divBy_LE(x3:0:0) :|: x:0:0 > 0 && x:0:0 > x3:0:0 && x3:0:0 > -1 && x:0:0 - 2 * x3:0:0 > -2 && x:0:0 > x1:0:0 && x1:0:0 > -1 && x:0:0 - 2 * x3:0:0 < 2
6.31/2.49	
6.31/2.49	The following rules are bounded:
6.31/2.49	f996_0_divBy_LE(x:0:0) -> f996_0_divBy_LE(x3:0:0) :|: x:0:0 > 0 && x:0:0 > x3:0:0 && x3:0:0 > -1 && x:0:0 - 2 * x3:0:0 > -2 && x:0:0 > x1:0:0 && x1:0:0 > -1 && x:0:0 - 2 * x3:0:0 < 2
6.31/2.49	
6.31/2.49	
6.31/2.49	----------------------------------------
6.31/2.49	
6.31/2.49	(20)
6.31/2.49	YES
6.48/2.65	EOF