8.06/3.14	YES
8.06/3.15	proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar
8.06/3.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.06/3.15	
8.06/3.15	
8.06/3.15	termination of the given Bare JBC problem could be proven:
8.06/3.15	
8.06/3.15	(0) Bare JBC problem
8.06/3.15	(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
8.06/3.15	(2) JBC problem
8.06/3.15	(3) JBCToGraph [EQUIVALENT, 343 ms]
8.06/3.15	(4) JBCTerminationGraph
8.06/3.15	(5) TerminationGraphToSCCProof [SOUND, 0 ms]
8.06/3.15	(6) JBCTerminationSCC
8.06/3.15	(7) SCCToIRSProof [SOUND, 73 ms]
8.06/3.15	(8) IRSwT
8.06/3.15	(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
8.06/3.15	(10) IRSwT
8.06/3.15	(11) IRSwTTerminationDigraphProof [EQUIVALENT, 51 ms]
8.06/3.15	(12) IRSwT
8.06/3.15	(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
8.06/3.15	(14) IRSwT
8.06/3.15	(15) TempFilterProof [SOUND, 45 ms]
8.06/3.15	(16) IntTRS
8.06/3.15	(17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
8.06/3.15	(18) IntTRS
8.06/3.15	(19) RankingReductionPairProof [EQUIVALENT, 0 ms]
8.06/3.15	(20) YES
8.06/3.15	
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(0)
8.06/3.15	Obligation:
8.06/3.15	need to prove termination of the following program:
8.06/3.15	public class GCD2 {
8.06/3.15	  public static int mod(int a, int b) {
8.06/3.15	    if (a == b) {
8.06/3.15	      return 0;
8.06/3.15	    }
8.06/3.15	    while(a>b) {
8.06/3.15	      a -= b;
8.06/3.15	    }
8.06/3.15	    return a;
8.06/3.15	  }
8.06/3.15	
8.06/3.15	  public static int gcd(int a, int b) {
8.06/3.15	    int tmp;
8.06/3.15	    while(b != 0 && a >= 0 && b >= 0) {
8.06/3.15	      tmp = b;
8.06/3.15	      b = mod(a, b);
8.06/3.15	      a = tmp;
8.06/3.15	    }
8.06/3.15	    return a;
8.06/3.15	  }
8.06/3.15	
8.06/3.15	  public static void main(String[] args) {
8.06/3.15	    Random.args = args;
8.06/3.15	    int x = Random.random();
8.06/3.15	    int y = Random.random();
8.06/3.15	    gcd(x, y);
8.06/3.15	  }
8.06/3.15	}
8.06/3.15	
8.06/3.15	
8.06/3.15	public class Random {
8.06/3.15	  static String[] args;
8.06/3.15	  static int index = 0;
8.06/3.15	
8.06/3.15	  public static int random() {
8.06/3.15	    String string = args[index];
8.06/3.15	    index++;
8.06/3.15	    return string.length();
8.06/3.15	  }
8.06/3.15	}
8.06/3.15	
8.06/3.15	
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(1) BareJBCToJBCProof (EQUIVALENT)
8.06/3.15	initialized classpath
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(2)
8.06/3.15	Obligation:
8.06/3.15	need to prove termination of the following program:
8.06/3.15	public class GCD2 {
8.06/3.15	  public static int mod(int a, int b) {
8.06/3.15	    if (a == b) {
8.06/3.15	      return 0;
8.06/3.15	    }
8.06/3.15	    while(a>b) {
8.06/3.15	      a -= b;
8.06/3.15	    }
8.06/3.15	    return a;
8.06/3.15	  }
8.06/3.15	
8.06/3.15	  public static int gcd(int a, int b) {
8.06/3.15	    int tmp;
8.06/3.15	    while(b != 0 && a >= 0 && b >= 0) {
8.06/3.15	      tmp = b;
8.06/3.15	      b = mod(a, b);
8.06/3.15	      a = tmp;
8.06/3.15	    }
8.06/3.15	    return a;
8.06/3.15	  }
8.06/3.15	
8.06/3.15	  public static void main(String[] args) {
8.06/3.15	    Random.args = args;
8.06/3.15	    int x = Random.random();
8.06/3.15	    int y = Random.random();
8.06/3.15	    gcd(x, y);
8.06/3.15	  }
8.06/3.15	}
8.06/3.15	
8.06/3.15	
8.06/3.15	public class Random {
8.06/3.15	  static String[] args;
8.06/3.15	  static int index = 0;
8.06/3.15	
8.06/3.15	  public static int random() {
8.06/3.15	    String string = args[index];
8.06/3.15	    index++;
8.06/3.15	    return string.length();
8.06/3.15	  }
8.06/3.15	}
8.06/3.15	
8.06/3.15	
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(3) JBCToGraph (EQUIVALENT)
8.06/3.15	Constructed TerminationGraph.
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(4)
8.06/3.15	Obligation:
8.06/3.15	Termination Graph based on JBC Program:
8.06/3.15	GCD2.main([Ljava/lang/String;)V: Graph of 213 nodes with 1 SCC.
8.06/3.15	
8.06/3.15	
8.06/3.15	
8.06/3.15	
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(5) TerminationGraphToSCCProof (SOUND)
8.06/3.15	Splitted TerminationGraph to 1 SCCs.
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(6)
8.06/3.15	Obligation:
8.06/3.15	SCC of termination graph based on JBC Program.
8.06/3.15	SCC contains nodes from the following methods: GCD2.main([Ljava/lang/String;)V
8.06/3.15	SCC calls the following helper methods: 
8.06/3.15	Performed SCC analyses:
8.06/3.15	*Used field analysis yielded the following read fields:
8.06/3.15	
8.06/3.15	*Marker field analysis yielded the following relations that could be markers:
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(7) SCCToIRSProof (SOUND)
8.06/3.15	Transformed FIGraph SCCs to intTRSs. Log: 
8.06/3.15	Generated rules. Obtained 42 IRulesP rules:
8.06/3.15	f337_0_gcd_EQ(EOS(STATIC_337), i19, i45, i45) -> f340_0_gcd_EQ(EOS(STATIC_340), i19, i45, i45) :|: TRUE
8.06/3.15	f340_0_gcd_EQ(EOS(STATIC_340), i19, i45, i45) -> f344_0_gcd_Load(EOS(STATIC_344), i19, i45) :|: i45 > 0
8.06/3.15	f344_0_gcd_Load(EOS(STATIC_344), i19, i45) -> f348_0_gcd_LT(EOS(STATIC_348), i19, i45, i19) :|: TRUE
8.06/3.15	f348_0_gcd_LT(EOS(STATIC_348), i19, i45, i19) -> f352_0_gcd_Load(EOS(STATIC_352), i19, i45) :|: i19 >= 0
8.06/3.15	f352_0_gcd_Load(EOS(STATIC_352), i19, i45) -> f356_0_gcd_LT(EOS(STATIC_356), i19, i45, i45) :|: TRUE
8.06/3.15	f356_0_gcd_LT(EOS(STATIC_356), i19, i45, i45) -> f360_0_gcd_Load(EOS(STATIC_360), i19, i45) :|: i45 >= 0
8.06/3.15	f360_0_gcd_Load(EOS(STATIC_360), i19, i45) -> f364_0_gcd_Store(EOS(STATIC_364), i19, i45, i45) :|: TRUE
8.06/3.15	f364_0_gcd_Store(EOS(STATIC_364), i19, i45, i45) -> f367_0_gcd_Load(EOS(STATIC_367), i19, i45, i45) :|: TRUE
8.06/3.15	f367_0_gcd_Load(EOS(STATIC_367), i19, i45, i45) -> f369_0_gcd_Load(EOS(STATIC_369), i45, i45, i19) :|: TRUE
8.06/3.15	f369_0_gcd_Load(EOS(STATIC_369), i45, i45, i19) -> f371_0_gcd_InvokeMethod(EOS(STATIC_371), i45, i19, i45) :|: TRUE
8.06/3.15	f371_0_gcd_InvokeMethod(EOS(STATIC_371), i45, i19, i45) -> f373_0_mod_Load(EOS(STATIC_373), i45, i19, i45) :|: TRUE
8.06/3.15	f373_0_mod_Load(EOS(STATIC_373), i45, i19, i45) -> f375_0_mod_Load(EOS(STATIC_375), i45, i19, i45, i19) :|: TRUE
8.06/3.15	f375_0_mod_Load(EOS(STATIC_375), i45, i19, i45, i19) -> f376_0_mod_NE(EOS(STATIC_376), i45, i19, i45, i19, i45) :|: TRUE
8.06/3.15	f376_0_mod_NE(EOS(STATIC_376), i45, i19, i45, i19, i45) -> f377_0_mod_NE(EOS(STATIC_377), i45, i19, i45, i19, i45) :|: !(i19 = i45)
8.06/3.15	f376_0_mod_NE(EOS(STATIC_376), i45, i45, i45, i45, i45) -> f378_0_mod_NE(EOS(STATIC_378), i45, i45, i45, i45, i45) :|: i19 = i45
8.06/3.15	f377_0_mod_NE(EOS(STATIC_377), i45, i19, i45, i19, i45) -> f382_0_mod_Load(EOS(STATIC_382), i45, i19, i45) :|: !(i19 = i45)
8.06/3.15	f382_0_mod_Load(EOS(STATIC_382), i45, i19, i45) -> f478_0_mod_Load(EOS(STATIC_478), i45, i19, i45) :|: TRUE
8.06/3.15	f478_0_mod_Load(EOS(STATIC_478), i45, i53, i45) -> f497_0_mod_Load(EOS(STATIC_497), i45, i53, i45, i53) :|: TRUE
8.06/3.15	f497_0_mod_Load(EOS(STATIC_497), i45, i53, i45, i53) -> f1040_0_mod_LE(EOS(STATIC_1040), i45, i53, i45, i53, i45) :|: TRUE
8.06/3.15	f1040_0_mod_LE(EOS(STATIC_1040), i45, i53, i45, i53, i45) -> f1048_0_mod_LE(EOS(STATIC_1048), i45, i53, i45, i53, i45) :|: i53 <= i45
8.06/3.15	f1040_0_mod_LE(EOS(STATIC_1040), i45, i53, i45, i53, i45) -> f1049_0_mod_LE(EOS(STATIC_1049), i45, i53, i45, i53, i45) :|: i53 > i45
8.06/3.15	f1048_0_mod_LE(EOS(STATIC_1048), i45, i53, i45, i53, i45) -> f1051_0_mod_Load(EOS(STATIC_1051), i45, i53) :|: i53 <= i45
8.06/3.15	f1051_0_mod_Load(EOS(STATIC_1051), i45, i53) -> f1062_0_mod_Return(EOS(STATIC_1062), i45, i53) :|: TRUE
8.06/3.15	f1062_0_mod_Return(EOS(STATIC_1062), i45, i53) -> f1074_0_gcd_Store(EOS(STATIC_1074), i45, i53) :|: TRUE
8.06/3.15	f1074_0_gcd_Store(EOS(STATIC_1074), i45, i53) -> f1076_0_gcd_Load(EOS(STATIC_1076), i53, i45) :|: TRUE
8.06/3.15	f1076_0_gcd_Load(EOS(STATIC_1076), i53, i45) -> f1083_0_gcd_Store(EOS(STATIC_1083), i53, i45) :|: TRUE
8.06/3.15	f1083_0_gcd_Store(EOS(STATIC_1083), i53, i45) -> f1085_0_gcd_JMP(EOS(STATIC_1085), i45, i53) :|: TRUE
8.06/3.15	f1085_0_gcd_JMP(EOS(STATIC_1085), i45, i53) -> f1095_0_gcd_Load(EOS(STATIC_1095), i45, i53) :|: TRUE
8.06/3.15	f1095_0_gcd_Load(EOS(STATIC_1095), i45, i53) -> f332_0_gcd_Load(EOS(STATIC_332), i45, i53) :|: TRUE
8.06/3.15	f332_0_gcd_Load(EOS(STATIC_332), i19, i43) -> f337_0_gcd_EQ(EOS(STATIC_337), i19, i43, i43) :|: TRUE
8.06/3.15	f1049_0_mod_LE(EOS(STATIC_1049), i45, i53, i45, i53, i45) -> f1059_0_mod_Load(EOS(STATIC_1059), i45, i53, i45) :|: i53 > i45
8.06/3.15	f1059_0_mod_Load(EOS(STATIC_1059), i45, i53, i45) -> f1064_0_mod_Load(EOS(STATIC_1064), i45, i45, i53) :|: TRUE
8.06/3.15	f1064_0_mod_Load(EOS(STATIC_1064), i45, i45, i53) -> f1075_0_mod_IntArithmetic(EOS(STATIC_1075), i45, i45, i53, i45) :|: TRUE
8.06/3.15	f1075_0_mod_IntArithmetic(EOS(STATIC_1075), i45, i45, i53, i45) -> f1082_0_mod_Store(EOS(STATIC_1082), i45, i45, i53 - i45) :|: i53 > 0 && i45 > 0
8.06/3.15	f1082_0_mod_Store(EOS(STATIC_1082), i45, i45, i81) -> f1084_0_mod_JMP(EOS(STATIC_1084), i45, i81, i45) :|: TRUE
8.06/3.15	f1084_0_mod_JMP(EOS(STATIC_1084), i45, i81, i45) -> f1090_0_mod_Load(EOS(STATIC_1090), i45, i81, i45) :|: TRUE
8.06/3.15	f1090_0_mod_Load(EOS(STATIC_1090), i45, i81, i45) -> f478_0_mod_Load(EOS(STATIC_478), i45, i81, i45) :|: TRUE
8.06/3.15	f378_0_mod_NE(EOS(STATIC_378), i45, i45, i45, i45, i45) -> f384_0_mod_ConstantStackPush(EOS(STATIC_384), i45) :|: TRUE
8.06/3.15	f384_0_mod_ConstantStackPush(EOS(STATIC_384), i45) -> f387_0_mod_Return(EOS(STATIC_387), i45, 0) :|: TRUE
8.06/3.15	f387_0_mod_Return(EOS(STATIC_387), i45, matching1) -> f389_0_gcd_Store(EOS(STATIC_389), i45, 0) :|: TRUE && matching1 = 0
8.06/3.15	f389_0_gcd_Store(EOS(STATIC_389), i45, matching1) -> f425_0_gcd_Store(EOS(STATIC_425), i45, 0) :|: TRUE && matching1 = 0
8.06/3.15	f425_0_gcd_Store(EOS(STATIC_425), i45, i19) -> f1074_0_gcd_Store(EOS(STATIC_1074), i45, i19) :|: TRUE
8.06/3.15	Combined rules. Obtained 5 IRulesP rules:
8.06/3.15	f1040_0_mod_LE(EOS(STATIC_1040), i45:0, i53:0, i45:0, i53:0, i45:0) -> f337_0_gcd_EQ(EOS(STATIC_337), i45:0, i53:0, i53:0) :|: i53:0 <= i45:0
8.06/3.15	f337_0_gcd_EQ(EOS(STATIC_337), i19:0, i45:0, i45:0) -> f1040_0_mod_LE(EOS(STATIC_1040), i45:0, i19:0, i45:0, i19:0, i45:0) :|: i45:0 > 0 && i19:0 > -1 && i45:0 > i19:0
8.06/3.15	f337_0_gcd_EQ(EOS(STATIC_337), i19:0, i45:0, i45:0) -> f1040_0_mod_LE(EOS(STATIC_1040), i45:0, i19:0, i45:0, i19:0, i45:0) :|: i45:0 > 0 && i19:0 > -1 && i45:0 < i19:0
8.06/3.15	f337_0_gcd_EQ(EOS(STATIC_337), i19:0, i19:0, i19:0) -> f337_0_gcd_EQ(EOS(STATIC_337), i19:0, 0, 0) :|: i19:0 > 0
8.06/3.15	f1040_0_mod_LE(EOS(STATIC_1040), i45:0, i53:0, i45:0, i53:0, i45:0) -> f1040_0_mod_LE(EOS(STATIC_1040), i45:0, i53:0 - i45:0, i45:0, i53:0 - i45:0, i45:0) :|: i53:0 > i45:0 && i53:0 > 0 && i45:0 > 0
8.06/3.15	Filtered constant ground arguments:
8.06/3.15	   f1040_0_mod_LE(x1, x2, x3, x4, x5, x6) -> f1040_0_mod_LE(x2, x3, x4, x5, x6)
8.06/3.15	   f337_0_gcd_EQ(x1, x2, x3, x4) -> f337_0_gcd_EQ(x2, x3, x4)
8.06/3.15	Filtered duplicate arguments:
8.06/3.15	   f1040_0_mod_LE(x1, x2, x3, x4, x5) -> f1040_0_mod_LE(x4, x5)
8.06/3.15	   f337_0_gcd_EQ(x1, x2, x3) -> f337_0_gcd_EQ(x1, x3)
8.06/3.15	Finished conversion. Obtained 5 rules.P rules:
8.06/3.15	f1040_0_mod_LE(i53:0, i45:0) -> f337_0_gcd_EQ(i45:0, i53:0) :|: i53:0 <= i45:0
8.06/3.15	f337_0_gcd_EQ(i19:0, i45:0) -> f1040_0_mod_LE(i19:0, i45:0) :|: i19:0 > -1 && i45:0 > i19:0 && i45:0 > 0
8.06/3.15	f337_0_gcd_EQ(i19:0, i45:0) -> f1040_0_mod_LE(i19:0, i45:0) :|: i19:0 > -1 && i45:0 < i19:0 && i45:0 > 0
8.06/3.15	f337_0_gcd_EQ(i19:0, i19:0) -> f337_0_gcd_EQ(i19:0, 0) :|: i19:0 > 0
8.06/3.15	f1040_0_mod_LE(i53:0, i45:0) -> f1040_0_mod_LE(i53:0 - i45:0, i45:0) :|: i53:0 > 0 && i45:0 > 0 && i53:0 > i45:0
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(8)
8.06/3.15	Obligation:
8.06/3.15	Rules:
8.06/3.15	f1040_0_mod_LE(i53:0, i45:0) -> f337_0_gcd_EQ(i45:0, i53:0) :|: i53:0 <= i45:0
8.06/3.15	f337_0_gcd_EQ(x, x1) -> f1040_0_mod_LE(x, x1) :|: x > -1 && x1 > x && x1 > 0
8.06/3.15	f337_0_gcd_EQ(x2, x3) -> f1040_0_mod_LE(x2, x3) :|: x2 > -1 && x3 < x2 && x3 > 0
8.06/3.15	f337_0_gcd_EQ(i19:0, i19:0) -> f337_0_gcd_EQ(i19:0, 0) :|: i19:0 > 0
8.06/3.15	f1040_0_mod_LE(x4, x5) -> f1040_0_mod_LE(x4 - x5, x5) :|: x4 > 0 && x5 > 0 && x4 > x5
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(9) IRSFormatTransformerProof (EQUIVALENT)
8.06/3.15	Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(10)
8.06/3.15	Obligation:
8.06/3.15	Rules:
8.06/3.15	f1040_0_mod_LE(i53:0, i45:0) -> f337_0_gcd_EQ(i45:0, i53:0) :|: i53:0 <= i45:0
8.06/3.15	f337_0_gcd_EQ(x, x1) -> f1040_0_mod_LE(x, x1) :|: x > -1 && x1 > x && x1 > 0
8.06/3.15	f337_0_gcd_EQ(x2, x3) -> f1040_0_mod_LE(x2, x3) :|: x2 > -1 && x3 < x2 && x3 > 0
8.06/3.15	f337_0_gcd_EQ(i19:0, i19:0) -> f337_0_gcd_EQ(i19:0, 0) :|: i19:0 > 0
8.06/3.15	f1040_0_mod_LE(x4, x5) -> f1040_0_mod_LE(arith, x5) :|: x4 > 0 && x5 > 0 && x4 > x5 && arith = x4 - x5
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(11) IRSwTTerminationDigraphProof (EQUIVALENT)
8.06/3.15	Constructed termination digraph!
8.06/3.15	Nodes:
8.06/3.15	(1) f1040_0_mod_LE(i53:0, i45:0) -> f337_0_gcd_EQ(i45:0, i53:0) :|: i53:0 <= i45:0
8.06/3.15	(2) f337_0_gcd_EQ(x, x1) -> f1040_0_mod_LE(x, x1) :|: x > -1 && x1 > x && x1 > 0
8.06/3.15	(3) f337_0_gcd_EQ(x2, x3) -> f1040_0_mod_LE(x2, x3) :|: x2 > -1 && x3 < x2 && x3 > 0
8.06/3.15	(4) f337_0_gcd_EQ(i19:0, i19:0) -> f337_0_gcd_EQ(i19:0, 0) :|: i19:0 > 0
8.06/3.15	(5) f1040_0_mod_LE(x4, x5) -> f1040_0_mod_LE(arith, x5) :|: x4 > 0 && x5 > 0 && x4 > x5 && arith = x4 - x5
8.06/3.15	
8.06/3.15	Arcs:
8.06/3.15	(1) -> (3), (4)
8.06/3.15	(2) -> (1)
8.06/3.15	(3) -> (5)
8.06/3.15	(5) -> (1), (5)
8.06/3.15	
8.06/3.15	This digraph is fully evaluated!
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(12)
8.06/3.15	Obligation:
8.06/3.15	
8.06/3.15	Termination digraph:
8.06/3.15	Nodes:
8.06/3.15	(1) f1040_0_mod_LE(i53:0, i45:0) -> f337_0_gcd_EQ(i45:0, i53:0) :|: i53:0 <= i45:0
8.06/3.15	(2) f1040_0_mod_LE(x4, x5) -> f1040_0_mod_LE(arith, x5) :|: x4 > 0 && x5 > 0 && x4 > x5 && arith = x4 - x5
8.06/3.15	(3) f337_0_gcd_EQ(x2, x3) -> f1040_0_mod_LE(x2, x3) :|: x2 > -1 && x3 < x2 && x3 > 0
8.06/3.15	
8.06/3.15	Arcs:
8.06/3.15	(1) -> (3)
8.06/3.15	(2) -> (1), (2)
8.06/3.15	(3) -> (2)
8.06/3.15	
8.06/3.15	This digraph is fully evaluated!
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(13) IntTRSCompressionProof (EQUIVALENT)
8.06/3.15	Compressed rules.
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(14)
8.06/3.15	Obligation:
8.06/3.15	Rules:
8.06/3.15	f1040_0_mod_LE(x4:0, x5:0) -> f1040_0_mod_LE(x4:0 - x5:0, x5:0) :|: x4:0 > 0 && x5:0 > 0 && x5:0 < x4:0
8.06/3.15	f1040_0_mod_LE(i53:0:0, i45:0:0) -> f1040_0_mod_LE(i45:0:0, i53:0:0) :|: i45:0:0 > -1 && i53:0:0 < i45:0:0 && i53:0:0 > 0
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(15) TempFilterProof (SOUND)
8.06/3.15	Used the following sort dictionary for filtering: 
8.06/3.15	f1040_0_mod_LE(INTEGER, INTEGER)
8.06/3.15	Replaced non-predefined constructor symbols by 0.
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(16)
8.06/3.15	Obligation:
8.06/3.15	Rules:
8.06/3.15	f1040_0_mod_LE(x4:0, x5:0) -> f1040_0_mod_LE(c, x5:0) :|: c = x4:0 - x5:0 && (x4:0 > 0 && x5:0 > 0 && x5:0 < x4:0)
8.06/3.15	f1040_0_mod_LE(i53:0:0, i45:0:0) -> f1040_0_mod_LE(i45:0:0, i53:0:0) :|: i45:0:0 > -1 && i53:0:0 < i45:0:0 && i53:0:0 > 0
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(17) PolynomialOrderProcessor (EQUIVALENT)
8.06/3.15	Found the following polynomial interpretation:
8.06/3.15	[f1040_0_mod_LE(x, x1)] = -2 + x1
8.06/3.15	
8.06/3.15	The following rules are decreasing:
8.06/3.15	f1040_0_mod_LE(i53:0:0, i45:0:0) -> f1040_0_mod_LE(i45:0:0, i53:0:0) :|: i45:0:0 > -1 && i53:0:0 < i45:0:0 && i53:0:0 > 0
8.06/3.15	The following rules are bounded:
8.06/3.15	f1040_0_mod_LE(i53:0:0, i45:0:0) -> f1040_0_mod_LE(i45:0:0, i53:0:0) :|: i45:0:0 > -1 && i53:0:0 < i45:0:0 && i53:0:0 > 0
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(18)
8.06/3.15	Obligation:
8.06/3.15	Rules:
8.06/3.15	f1040_0_mod_LE(x4:0, x5:0) -> f1040_0_mod_LE(c, x5:0) :|: c = x4:0 - x5:0 && (x4:0 > 0 && x5:0 > 0 && x5:0 < x4:0)
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(19) RankingReductionPairProof (EQUIVALENT)
8.06/3.15	Interpretation:
8.06/3.15	[ f1040_0_mod_LE ] = f1040_0_mod_LE_1
8.06/3.15	
8.06/3.15	The following rules are decreasing:
8.06/3.15	f1040_0_mod_LE(x4:0, x5:0) -> f1040_0_mod_LE(c, x5:0) :|: c = x4:0 - x5:0 && (x4:0 > 0 && x5:0 > 0 && x5:0 < x4:0)
8.06/3.15	
8.06/3.15	The following rules are bounded:
8.06/3.15	f1040_0_mod_LE(x4:0, x5:0) -> f1040_0_mod_LE(c, x5:0) :|: c = x4:0 - x5:0 && (x4:0 > 0 && x5:0 > 0 && x5:0 < x4:0)
8.06/3.15	
8.06/3.15	
8.06/3.15	----------------------------------------
8.06/3.15	
8.06/3.15	(20)
8.06/3.15	YES
8.41/3.18	EOF