13.01/9.54	YES
13.01/9.55	proof of /export/starexec/sandbox/benchmark/theBenchmark.jar
13.01/9.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
13.01/9.55	
13.01/9.55	
13.01/9.55	termination of the given Bare JBC problem could be proven:
13.01/9.55	
13.01/9.55	(0) Bare JBC problem
13.01/9.55	(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
13.01/9.55	(2) JBC problem
13.01/9.55	(3) JBCToGraph [EQUIVALENT, 1239 ms]
13.01/9.55	(4) JBCTerminationGraph
13.01/9.55	(5) TerminationGraphToSCCProof [SOUND, 0 ms]
13.01/9.55	(6) JBCTerminationSCC
13.01/9.55	(7) SCCToIRSProof [SOUND, 108 ms]
13.01/9.55	(8) IRSwT
13.01/9.55	(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
13.01/9.55	(10) IRSwT
13.01/9.55	(11) IRSwTTerminationDigraphProof [EQUIVALENT, 121 ms]
13.01/9.55	(12) IRSwT
13.01/9.55	(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
13.01/9.55	(14) IRSwT
13.01/9.55	(15) TempFilterProof [SOUND, 65 ms]
13.01/9.55	(16) IntTRS
13.01/9.55	(17) PolynomialOrderProcessor [EQUIVALENT, 18 ms]
13.01/9.55	(18) IntTRS
13.01/9.55	(19) RankingReductionPairProof [EQUIVALENT, 0 ms]
13.01/9.55	(20) YES
13.01/9.55	
13.01/9.55	
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(0)
13.01/9.55	Obligation:
13.01/9.55	need to prove termination of the following program:
13.01/9.55	/**
13.01/9.55	 * Example taken from "A Term Rewriting Approach to the Automated Termination
13.01/9.55	 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
13.01/9.55	 * and converted to Java.
13.01/9.55	 */
13.01/9.55	
13.01/9.55	public class PastaC5 {
13.01/9.55	    public static void main(String[] args) {
13.01/9.55	        Random.args = args;
13.01/9.55	        int x = Random.random();
13.01/9.55	        int y = Random.random();
13.01/9.55	
13.01/9.55	        if (x > 0 && y > 0) {
13.01/9.55	            while (x != y) {
13.01/9.55	                if (x > y) {
13.01/9.55	                    x = x - y;
13.01/9.55	                } else {
13.01/9.55	                    y = y - x;
13.01/9.55	                }
13.01/9.55	            }
13.01/9.55	        }
13.01/9.55	    }
13.01/9.55	}
13.01/9.55	
13.01/9.55	
13.01/9.55	public class Random {
13.01/9.55	  static String[] args;
13.01/9.55	  static int index = 0;
13.01/9.55	
13.01/9.55	  public static int random() {
13.01/9.55	    String string = args[index];
13.01/9.55	    index++;
13.01/9.55	    return string.length();
13.01/9.55	  }
13.01/9.55	}
13.01/9.55	
13.01/9.55	
13.01/9.55	
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(1) BareJBCToJBCProof (EQUIVALENT)
13.01/9.55	initialized classpath
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(2)
13.01/9.55	Obligation:
13.01/9.55	need to prove termination of the following program:
13.01/9.55	/**
13.01/9.55	 * Example taken from "A Term Rewriting Approach to the Automated Termination
13.01/9.55	 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
13.01/9.55	 * and converted to Java.
13.01/9.55	 */
13.01/9.55	
13.01/9.55	public class PastaC5 {
13.01/9.55	    public static void main(String[] args) {
13.01/9.55	        Random.args = args;
13.01/9.55	        int x = Random.random();
13.01/9.55	        int y = Random.random();
13.01/9.55	
13.01/9.55	        if (x > 0 && y > 0) {
13.01/9.55	            while (x != y) {
13.01/9.55	                if (x > y) {
13.01/9.55	                    x = x - y;
13.01/9.55	                } else {
13.01/9.55	                    y = y - x;
13.01/9.55	                }
13.01/9.55	            }
13.01/9.55	        }
13.01/9.55	    }
13.01/9.55	}
13.01/9.55	
13.01/9.55	
13.01/9.55	public class Random {
13.01/9.55	  static String[] args;
13.01/9.55	  static int index = 0;
13.01/9.55	
13.01/9.55	  public static int random() {
13.01/9.55	    String string = args[index];
13.01/9.55	    index++;
13.01/9.55	    return string.length();
13.01/9.55	  }
13.01/9.55	}
13.01/9.55	
13.01/9.55	
13.01/9.55	
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(3) JBCToGraph (EQUIVALENT)
13.01/9.55	Constructed TerminationGraph.
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(4)
13.01/9.55	Obligation:
13.01/9.55	Termination Graph based on JBC Program:
13.01/9.55	PastaC5.main([Ljava/lang/String;)V: Graph of 198 nodes with 1 SCC.
13.01/9.55	
13.01/9.55	
13.01/9.55	
13.01/9.55	
13.01/9.55	
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(5) TerminationGraphToSCCProof (SOUND)
13.01/9.55	Splitted TerminationGraph to 1 SCCs.
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(6)
13.01/9.55	Obligation:
13.01/9.55	SCC of termination graph based on JBC Program.
13.01/9.55	SCC contains nodes from the following methods: PastaC5.main([Ljava/lang/String;)V
13.01/9.55	SCC calls the following helper methods: 
13.01/9.55	Performed SCC analyses:
13.01/9.55	*Used field analysis yielded the following read fields:
13.01/9.55	
13.01/9.55	*Marker field analysis yielded the following relations that could be markers:
13.01/9.55	
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(7) SCCToIRSProof (SOUND)
13.01/9.55	Transformed FIGraph SCCs to intTRSs. Log: 
13.01/9.55	Generated rules. Obtained 22 IRulesP rules:
13.01/9.55	f337_0_main_EQ(EOS(STATIC_337), i46, i47, i46, i47) -> f351_0_main_Load(EOS(STATIC_351), i46, i47) :|: !(i46 = i47)
13.01/9.55	f351_0_main_Load(EOS(STATIC_351), i46, i47) -> f357_0_main_Load(EOS(STATIC_357), i46, i47, i46) :|: TRUE
13.01/9.55	f357_0_main_Load(EOS(STATIC_357), i46, i47, i46) -> f360_0_main_LE(EOS(STATIC_360), i46, i47, i46, i47) :|: TRUE
13.01/9.55	f360_0_main_LE(EOS(STATIC_360), i46, i47, i46, i47) -> f366_0_main_LE(EOS(STATIC_366), i46, i47, i46, i47) :|: i46 <= i47
13.01/9.55	f360_0_main_LE(EOS(STATIC_360), i46, i47, i46, i47) -> f367_0_main_LE(EOS(STATIC_367), i46, i47, i46, i47) :|: i46 > i47
13.01/9.55	f366_0_main_LE(EOS(STATIC_366), i46, i47, i46, i47) -> f370_0_main_Load(EOS(STATIC_370), i46, i47) :|: i46 < i47
13.01/9.55	f370_0_main_Load(EOS(STATIC_370), i46, i47) -> f377_0_main_Load(EOS(STATIC_377), i46, i47) :|: TRUE
13.01/9.55	f377_0_main_Load(EOS(STATIC_377), i46, i47) -> f384_0_main_IntArithmetic(EOS(STATIC_384), i46, i47, i46) :|: TRUE
13.01/9.55	f384_0_main_IntArithmetic(EOS(STATIC_384), i46, i47, i46) -> f387_0_main_Store(EOS(STATIC_387), i46, i47 - i46) :|: i47 > 0 && i46 > 0
13.01/9.55	f387_0_main_Store(EOS(STATIC_387), i46, i48) -> f390_0_main_JMP(EOS(STATIC_390), i46, i48) :|: TRUE
13.01/9.55	f390_0_main_JMP(EOS(STATIC_390), i46, i48) -> f417_0_main_Load(EOS(STATIC_417), i46, i48) :|: TRUE
13.01/9.55	f417_0_main_Load(EOS(STATIC_417), i46, i48) -> f325_0_main_Load(EOS(STATIC_325), i46, i48) :|: TRUE
13.01/9.55	f325_0_main_Load(EOS(STATIC_325), i46, i47) -> f328_0_main_Load(EOS(STATIC_328), i46, i47, i46) :|: TRUE
13.01/9.55	f328_0_main_Load(EOS(STATIC_328), i46, i47, i46) -> f331_0_main_EQ(EOS(STATIC_331), i46, i47, i46, i47) :|: TRUE
13.01/9.55	f331_0_main_EQ(EOS(STATIC_331), i46, i47, i46, i47) -> f337_0_main_EQ(EOS(STATIC_337), i46, i47, i46, i47) :|: !(i46 = i47)
13.01/9.55	f367_0_main_LE(EOS(STATIC_367), i46, i47, i46, i47) -> f372_0_main_Load(EOS(STATIC_372), i46, i47) :|: i46 > i47
13.01/9.55	f372_0_main_Load(EOS(STATIC_372), i46, i47) -> f380_0_main_Load(EOS(STATIC_380), i47, i46) :|: TRUE
13.01/9.55	f380_0_main_Load(EOS(STATIC_380), i47, i46) -> f385_0_main_IntArithmetic(EOS(STATIC_385), i47, i46, i47) :|: TRUE
13.01/9.55	f385_0_main_IntArithmetic(EOS(STATIC_385), i47, i46, i47) -> f389_0_main_Store(EOS(STATIC_389), i47, i46 - i47) :|: i46 > 0 && i47 > 0
13.01/9.55	f389_0_main_Store(EOS(STATIC_389), i47, i49) -> f391_0_main_JMP(EOS(STATIC_391), i49, i47) :|: TRUE
13.01/9.55	f391_0_main_JMP(EOS(STATIC_391), i49, i47) -> f418_0_main_Load(EOS(STATIC_418), i49, i47) :|: TRUE
13.01/9.55	f418_0_main_Load(EOS(STATIC_418), i49, i47) -> f325_0_main_Load(EOS(STATIC_325), i49, i47) :|: TRUE
13.01/9.55	Combined rules. Obtained 4 IRulesP rules:
13.01/9.55	f337_0_main_EQ(EOS(STATIC_337), i46:0, i47:0, i46:0, i47:0) -> f337_0_main_EQ(EOS(STATIC_337), i46:0 - i47:0, i47:0, i46:0 - i47:0, i47:0) :|: i47:0 < i46:0 && i47:0 > 0 && i47:0 > i46:0 - i47:0 && i46:0 > 0
13.01/9.55	f337_0_main_EQ(EOS(STATIC_337), i46:0, i47:0, i46:0, i47:0) -> f337_0_main_EQ(EOS(STATIC_337), i46:0 - i47:0, i47:0, i46:0 - i47:0, i47:0) :|: i47:0 < i46:0 && i47:0 > 0 && i47:0 < i46:0 - i47:0 && i46:0 > 0
13.01/9.55	f337_0_main_EQ(EOS(STATIC_337), i46:0, i47:0, i46:0, i47:0) -> f337_0_main_EQ(EOS(STATIC_337), i46:0, i47:0 - i46:0, i46:0, i47:0 - i46:0) :|: i47:0 > i46:0 && i46:0 > 0 && i47:0 - i46:0 > i46:0 && i47:0 > 0
13.01/9.55	f337_0_main_EQ(EOS(STATIC_337), i46:0, i47:0, i46:0, i47:0) -> f337_0_main_EQ(EOS(STATIC_337), i46:0, i47:0 - i46:0, i46:0, i47:0 - i46:0) :|: i47:0 > i46:0 && i46:0 > 0 && i47:0 - i46:0 < i46:0 && i47:0 > 0
13.01/9.55	Filtered constant ground arguments:
13.01/9.55	   f337_0_main_EQ(x1, x2, x3, x4, x5) -> f337_0_main_EQ(x2, x3, x4, x5)
13.01/9.55	   EOS(x1) -> EOS
13.01/9.55	Filtered duplicate arguments:
13.01/9.55	   f337_0_main_EQ(x1, x2, x3, x4) -> f337_0_main_EQ(x3, x4)
13.01/9.55	Finished conversion. Obtained 4 rules.P rules:
13.01/9.55	f337_0_main_EQ(i46:0, i47:0) -> f337_0_main_EQ(i46:0 - i47:0, i47:0) :|: i47:0 > 0 && i47:0 < i46:0 && i46:0 > 0 && i47:0 > i46:0 - i47:0
13.01/9.55	f337_0_main_EQ(i46:0, i47:0) -> f337_0_main_EQ(i46:0 - i47:0, i47:0) :|: i47:0 > 0 && i47:0 < i46:0 && i46:0 > 0 && i47:0 < i46:0 - i47:0
13.01/9.55	f337_0_main_EQ(i46:0, i47:0) -> f337_0_main_EQ(i46:0, i47:0 - i46:0) :|: i46:0 > 0 && i47:0 > i46:0 && i47:0 > 0 && i47:0 - i46:0 > i46:0
13.01/9.55	f337_0_main_EQ(i46:0, i47:0) -> f337_0_main_EQ(i46:0, i47:0 - i46:0) :|: i46:0 > 0 && i47:0 > i46:0 && i47:0 > 0 && i47:0 - i46:0 < i46:0
13.01/9.55	
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(8)
13.01/9.55	Obligation:
13.01/9.55	Rules:
13.01/9.55	f337_0_main_EQ(i46:0, i47:0) -> f337_0_main_EQ(i46:0 - i47:0, i47:0) :|: i47:0 > 0 && i47:0 < i46:0 && i46:0 > 0 && i47:0 > i46:0 - i47:0
13.01/9.55	f337_0_main_EQ(x, x1) -> f337_0_main_EQ(x - x1, x1) :|: x1 > 0 && x1 < x && x > 0 && x1 < x - x1
13.01/9.55	f337_0_main_EQ(x2, x3) -> f337_0_main_EQ(x2, x3 - x2) :|: x2 > 0 && x3 > x2 && x3 > 0 && x3 - x2 > x2
13.01/9.55	f337_0_main_EQ(x4, x5) -> f337_0_main_EQ(x4, x5 - x4) :|: x4 > 0 && x5 > x4 && x5 > 0 && x5 - x4 < x4
13.01/9.55	
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(9) IRSFormatTransformerProof (EQUIVALENT)
13.01/9.55	Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(10)
13.01/9.55	Obligation:
13.01/9.55	Rules:
13.01/9.55	f337_0_main_EQ(i46:0, i47:0) -> f337_0_main_EQ(arith, i47:0) :|: i47:0 > 0 && i47:0 < i46:0 && i46:0 > 0 && i47:0 > i46:0 - i47:0 && arith = i46:0 - i47:0
13.01/9.55	f337_0_main_EQ(x6, x7) -> f337_0_main_EQ(x8, x7) :|: x7 > 0 && x7 < x6 && x6 > 0 && x7 < x6 - x7 && x8 = x6 - x7
13.01/9.55	f337_0_main_EQ(x9, x10) -> f337_0_main_EQ(x9, x11) :|: x9 > 0 && x10 > x9 && x10 > 0 && x10 - x9 > x9 && x11 = x10 - x9
13.01/9.55	f337_0_main_EQ(x12, x13) -> f337_0_main_EQ(x12, x14) :|: x12 > 0 && x13 > x12 && x13 > 0 && x13 - x12 < x12 && x14 = x13 - x12
13.01/9.55	
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(11) IRSwTTerminationDigraphProof (EQUIVALENT)
13.01/9.55	Constructed termination digraph!
13.01/9.55	Nodes:
13.01/9.55	(1) f337_0_main_EQ(i46:0, i47:0) -> f337_0_main_EQ(arith, i47:0) :|: i47:0 > 0 && i47:0 < i46:0 && i46:0 > 0 && i47:0 > i46:0 - i47:0 && arith = i46:0 - i47:0
13.01/9.55	(2) f337_0_main_EQ(x6, x7) -> f337_0_main_EQ(x8, x7) :|: x7 > 0 && x7 < x6 && x6 > 0 && x7 < x6 - x7 && x8 = x6 - x7
13.01/9.55	(3) f337_0_main_EQ(x9, x10) -> f337_0_main_EQ(x9, x11) :|: x9 > 0 && x10 > x9 && x10 > 0 && x10 - x9 > x9 && x11 = x10 - x9
13.01/9.55	(4) f337_0_main_EQ(x12, x13) -> f337_0_main_EQ(x12, x14) :|: x12 > 0 && x13 > x12 && x13 > 0 && x13 - x12 < x12 && x14 = x13 - x12
13.01/9.55	
13.01/9.55	Arcs:
13.01/9.55	(1) -> (3), (4)
13.01/9.55	(2) -> (1), (2)
13.01/9.55	(3) -> (3), (4)
13.01/9.55	(4) -> (1), (2)
13.01/9.55	
13.01/9.55	This digraph is fully evaluated!
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(12)
13.01/9.55	Obligation:
13.01/9.55	
13.01/9.55	Termination digraph:
13.01/9.55	Nodes:
13.01/9.55	(1) f337_0_main_EQ(i46:0, i47:0) -> f337_0_main_EQ(arith, i47:0) :|: i47:0 > 0 && i47:0 < i46:0 && i46:0 > 0 && i47:0 > i46:0 - i47:0 && arith = i46:0 - i47:0
13.01/9.55	(2) f337_0_main_EQ(x6, x7) -> f337_0_main_EQ(x8, x7) :|: x7 > 0 && x7 < x6 && x6 > 0 && x7 < x6 - x7 && x8 = x6 - x7
13.01/9.55	(3) f337_0_main_EQ(x12, x13) -> f337_0_main_EQ(x12, x14) :|: x12 > 0 && x13 > x12 && x13 > 0 && x13 - x12 < x12 && x14 = x13 - x12
13.01/9.55	(4) f337_0_main_EQ(x9, x10) -> f337_0_main_EQ(x9, x11) :|: x9 > 0 && x10 > x9 && x10 > 0 && x10 - x9 > x9 && x11 = x10 - x9
13.01/9.55	
13.01/9.55	Arcs:
13.01/9.55	(1) -> (3), (4)
13.01/9.55	(2) -> (1), (2)
13.01/9.55	(3) -> (1), (2)
13.01/9.55	(4) -> (3), (4)
13.01/9.55	
13.01/9.55	This digraph is fully evaluated!
13.01/9.55	
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(13) IntTRSCompressionProof (EQUIVALENT)
13.01/9.55	Compressed rules.
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(14)
13.01/9.55	Obligation:
13.01/9.55	Rules:
13.01/9.55	f337_0_main_EQ(x9:0, x10:0) -> f337_0_main_EQ(x9:0, x10:0 - x9:0) :|: x10:0 > 0 && x9:0 < x10:0 - x9:0 && x9:0 < x10:0 && x9:0 > 0
13.01/9.55	f337_0_main_EQ(x6:0, x7:0) -> f337_0_main_EQ(x6:0 - x7:0, x7:0) :|: x6:0 > 0 && x7:0 < x6:0 - x7:0 && x7:0 < x6:0 && x7:0 > 0
13.01/9.55	f337_0_main_EQ(i46:0:0, i47:0:0) -> f337_0_main_EQ(i46:0:0 - i47:0:0, i47:0:0) :|: i46:0:0 > 0 && i47:0:0 > i46:0:0 - i47:0:0 && i47:0:0 < i46:0:0 && i47:0:0 > 0
13.01/9.55	f337_0_main_EQ(x12:0, x13:0) -> f337_0_main_EQ(x12:0, x13:0 - x12:0) :|: x13:0 > 0 && x13:0 - x12:0 < x12:0 && x13:0 > x12:0 && x12:0 > 0
13.01/9.55	
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(15) TempFilterProof (SOUND)
13.01/9.55	Used the following sort dictionary for filtering: 
13.01/9.55	f337_0_main_EQ(INTEGER, INTEGER)
13.01/9.55	Replaced non-predefined constructor symbols by 0.
13.01/9.55	----------------------------------------
13.01/9.55	
13.01/9.55	(16)
13.01/9.55	Obligation:
13.01/9.55	Rules:
13.01/9.55	f337_0_main_EQ(x9:0, x10:0) -> f337_0_main_EQ(x9:0, c) :|: c = x10:0 - x9:0 && (x10:0 > 0 && x9:0 < x10:0 - x9:0 && x9:0 < x10:0 && x9:0 > 0)
13.01/9.55	f337_0_main_EQ(x6:0, x7:0) -> f337_0_main_EQ(c1, x7:0) :|: c1 = x6:0 - x7:0 && (x6:0 > 0 && x7:0 < x6:0 - x7:0 && x7:0 < x6:0 && x7:0 > 0)
13.01/9.55	f337_0_main_EQ(i46:0:0, i47:0:0) -> f337_0_main_EQ(c2, i47:0:0) :|: c2 = i46:0:0 - i47:0:0 && (i46:0:0 > 0 && i47:0:0 > i46:0:0 - i47:0:0 && i47:0:0 < i46:0:0 && i47:0:0 > 0)
13.01/9.55	f337_0_main_EQ(x12:0, x13:0) -> f337_0_main_EQ(x12:0, c3) :|: c3 = x13:0 - x12:0 && (x13:0 > 0 && x13:0 - x12:0 < x12:0 && x13:0 > x12:0 && x12:0 > 0)
13.01/9.55	
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13.01/9.55	
13.01/9.55	(17) PolynomialOrderProcessor (EQUIVALENT)
13.01/9.55	Found the following polynomial interpretation:
13.01/9.55	[f337_0_main_EQ(x, x1)] = x1
13.01/9.55	
13.01/9.55	The following rules are decreasing:
13.01/9.55	f337_0_main_EQ(x9:0, x10:0) -> f337_0_main_EQ(x9:0, c) :|: c = x10:0 - x9:0 && (x10:0 > 0 && x9:0 < x10:0 - x9:0 && x9:0 < x10:0 && x9:0 > 0)
13.01/9.55	f337_0_main_EQ(x12:0, x13:0) -> f337_0_main_EQ(x12:0, c3) :|: c3 = x13:0 - x12:0 && (x13:0 > 0 && x13:0 - x12:0 < x12:0 && x13:0 > x12:0 && x12:0 > 0)
13.01/9.55	The following rules are bounded:
13.01/9.55	f337_0_main_EQ(x9:0, x10:0) -> f337_0_main_EQ(x9:0, c) :|: c = x10:0 - x9:0 && (x10:0 > 0 && x9:0 < x10:0 - x9:0 && x9:0 < x10:0 && x9:0 > 0)
13.01/9.55	f337_0_main_EQ(x6:0, x7:0) -> f337_0_main_EQ(c1, x7:0) :|: c1 = x6:0 - x7:0 && (x6:0 > 0 && x7:0 < x6:0 - x7:0 && x7:0 < x6:0 && x7:0 > 0)
13.01/9.55	f337_0_main_EQ(i46:0:0, i47:0:0) -> f337_0_main_EQ(c2, i47:0:0) :|: c2 = i46:0:0 - i47:0:0 && (i46:0:0 > 0 && i47:0:0 > i46:0:0 - i47:0:0 && i47:0:0 < i46:0:0 && i47:0:0 > 0)
13.01/9.55	f337_0_main_EQ(x12:0, x13:0) -> f337_0_main_EQ(x12:0, c3) :|: c3 = x13:0 - x12:0 && (x13:0 > 0 && x13:0 - x12:0 < x12:0 && x13:0 > x12:0 && x12:0 > 0)
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13.01/9.55	
13.01/9.55	(18)
13.01/9.55	Obligation:
13.01/9.55	Rules:
13.01/9.55	f337_0_main_EQ(x6:0, x7:0) -> f337_0_main_EQ(c1, x7:0) :|: c1 = x6:0 - x7:0 && (x6:0 > 0 && x7:0 < x6:0 - x7:0 && x7:0 < x6:0 && x7:0 > 0)
13.01/9.55	f337_0_main_EQ(i46:0:0, i47:0:0) -> f337_0_main_EQ(c2, i47:0:0) :|: c2 = i46:0:0 - i47:0:0 && (i46:0:0 > 0 && i47:0:0 > i46:0:0 - i47:0:0 && i47:0:0 < i46:0:0 && i47:0:0 > 0)
13.01/9.55	
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13.01/9.55	
13.01/9.55	(19) RankingReductionPairProof (EQUIVALENT)
13.01/9.55	Interpretation:
13.01/9.55	[ f337_0_main_EQ ] = f337_0_main_EQ_1
13.01/9.55	
13.01/9.55	The following rules are decreasing:
13.01/9.55	f337_0_main_EQ(x6:0, x7:0) -> f337_0_main_EQ(c1, x7:0) :|: c1 = x6:0 - x7:0 && (x6:0 > 0 && x7:0 < x6:0 - x7:0 && x7:0 < x6:0 && x7:0 > 0)
13.01/9.55	f337_0_main_EQ(i46:0:0, i47:0:0) -> f337_0_main_EQ(c2, i47:0:0) :|: c2 = i46:0:0 - i47:0:0 && (i46:0:0 > 0 && i47:0:0 > i46:0:0 - i47:0:0 && i47:0:0 < i46:0:0 && i47:0:0 > 0)
13.01/9.55	
13.01/9.55	The following rules are bounded:
13.01/9.55	f337_0_main_EQ(x6:0, x7:0) -> f337_0_main_EQ(c1, x7:0) :|: c1 = x6:0 - x7:0 && (x6:0 > 0 && x7:0 < x6:0 - x7:0 && x7:0 < x6:0 && x7:0 > 0)
13.01/9.55	f337_0_main_EQ(i46:0:0, i47:0:0) -> f337_0_main_EQ(c2, i47:0:0) :|: c2 = i46:0:0 - i47:0:0 && (i46:0:0 > 0 && i47:0:0 > i46:0:0 - i47:0:0 && i47:0:0 < i46:0:0 && i47:0:0 > 0)
13.01/9.55	
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13.01/9.55	
13.01/9.55	(20)
13.01/9.55	YES
13.19/9.59	EOF