7.51/2.81	YES
7.51/2.83	proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar
7.51/2.83	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
7.51/2.83	
7.51/2.83	
7.51/2.83	termination of the given Bare JBC problem could be proven:
7.51/2.83	
7.51/2.83	(0) Bare JBC problem
7.51/2.83	(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
7.51/2.83	(2) JBC problem
7.51/2.83	(3) JBCToGraph [EQUIVALENT, 351 ms]
7.51/2.83	(4) JBCTerminationGraph
7.51/2.83	(5) TerminationGraphToSCCProof [SOUND, 0 ms]
7.51/2.83	(6) JBCTerminationSCC
7.51/2.83	(7) SCCToIRSProof [SOUND, 126 ms]
7.51/2.83	(8) IRSwT
7.51/2.83	(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
7.51/2.83	(10) IRSwT
7.51/2.83	(11) IRSwTTerminationDigraphProof [EQUIVALENT, 53 ms]
7.51/2.83	(12) AND
7.51/2.83	    (13) IRSwT
7.51/2.83	        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
7.51/2.83	        (15) IRSwT
7.51/2.83	        (16) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
7.51/2.83	        (17) IRSwT
7.51/2.83	        (18) TempFilterProof [SOUND, 29 ms]
7.51/2.83	        (19) IntTRS
7.51/2.83	        (20) PolynomialOrderProcessor [EQUIVALENT, 12 ms]
7.51/2.83	        (21) YES
7.51/2.83	    (22) IRSwT
7.51/2.83	        (23) IntTRSCompressionProof [EQUIVALENT, 0 ms]
7.51/2.83	        (24) IRSwT
7.51/2.83	        (25) TempFilterProof [SOUND, 13 ms]
7.51/2.83	        (26) IntTRS
7.51/2.83	        (27) PolynomialOrderProcessor [EQUIVALENT, 4 ms]
7.51/2.83	        (28) YES
7.51/2.83	
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(0)
7.51/2.83	Obligation:
7.51/2.83	need to prove termination of the following program:
7.51/2.83	/**
7.51/2.83	 * Example taken from "A Term Rewriting Approach to the Automated Termination
7.51/2.83	 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
7.51/2.83	 * and converted to Java.
7.51/2.83	 */
7.51/2.83	
7.51/2.83	public class PastaC11 {
7.51/2.83	    public static void main(String[] args) {
7.51/2.83	        Random.args = args;
7.51/2.83	        int x = Random.random();
7.51/2.83	        int y = Random.random();
7.51/2.83	
7.51/2.83	        while (true) {
7.51/2.83				if (x >= 0) {
7.51/2.83					x--;
7.51/2.83					y = Random.random();
7.51/2.83				} else if (y >= 0) {
7.51/2.83					y--;
7.51/2.83				} else {
7.51/2.83					break;
7.51/2.83				}
7.51/2.83	        }
7.51/2.83	    } 
7.51/2.83	}
7.51/2.83	
7.51/2.83	
7.51/2.83	public class Random {
7.51/2.83	  static String[] args;
7.51/2.83	  static int index = 0;
7.51/2.83	
7.51/2.83	  public static int random() {
7.51/2.83	    String string = args[index];
7.51/2.83	    index++;
7.51/2.83	    return string.length();
7.51/2.83	  }
7.51/2.83	}
7.51/2.83	
7.51/2.83	
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(1) BareJBCToJBCProof (EQUIVALENT)
7.51/2.83	initialized classpath
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(2)
7.51/2.83	Obligation:
7.51/2.83	need to prove termination of the following program:
7.51/2.83	/**
7.51/2.83	 * Example taken from "A Term Rewriting Approach to the Automated Termination
7.51/2.83	 * Analysis of Imperative Programs" (http://www.cs.unm.edu/~spf/papers/2009-02.pdf)
7.51/2.83	 * and converted to Java.
7.51/2.83	 */
7.51/2.83	
7.51/2.83	public class PastaC11 {
7.51/2.83	    public static void main(String[] args) {
7.51/2.83	        Random.args = args;
7.51/2.83	        int x = Random.random();
7.51/2.83	        int y = Random.random();
7.51/2.83	
7.51/2.83	        while (true) {
7.51/2.83				if (x >= 0) {
7.51/2.83					x--;
7.51/2.83					y = Random.random();
7.51/2.83				} else if (y >= 0) {
7.51/2.83					y--;
7.51/2.83				} else {
7.51/2.83					break;
7.51/2.83				}
7.51/2.83	        }
7.51/2.83	    } 
7.51/2.83	}
7.51/2.83	
7.51/2.83	
7.51/2.83	public class Random {
7.51/2.83	  static String[] args;
7.51/2.83	  static int index = 0;
7.51/2.83	
7.51/2.83	  public static int random() {
7.51/2.83	    String string = args[index];
7.51/2.83	    index++;
7.51/2.83	    return string.length();
7.51/2.83	  }
7.51/2.83	}
7.51/2.83	
7.51/2.83	
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(3) JBCToGraph (EQUIVALENT)
7.51/2.83	Constructed TerminationGraph.
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(4)
7.51/2.83	Obligation:
7.51/2.83	Termination Graph based on JBC Program:
7.51/2.83	PastaC11.main([Ljava/lang/String;)V: Graph of 249 nodes with 1 SCC.
7.51/2.83	
7.51/2.83	
7.51/2.83	
7.51/2.83	
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(5) TerminationGraphToSCCProof (SOUND)
7.51/2.83	Splitted TerminationGraph to 1 SCCs.
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(6)
7.51/2.83	Obligation:
7.51/2.83	SCC of termination graph based on JBC Program.
7.51/2.83	SCC contains nodes from the following methods: PastaC11.main([Ljava/lang/String;)V
7.51/2.83	SCC calls the following helper methods: 
7.51/2.83	Performed SCC analyses:
7.51/2.83	*Used field analysis yielded the following read fields:
7.51/2.83	*java.lang.String: [count]
7.51/2.83	*Marker field analysis yielded the following relations that could be markers:
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(7) SCCToIRSProof (SOUND)
7.51/2.83	Transformed FIGraph SCCs to intTRSs. Log: 
7.51/2.83	Generated rules. Obtained 34 IRulesP rules:
7.51/2.83	f1193_0_main_LT(EOS(STATIC_1193(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), matching1, i126, matching2) -> f1198_0_main_LT(EOS(STATIC_1198(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), -1, i126, -1) :|: TRUE && matching1 = -1 && matching2 = -1
7.51/2.83	f1193_0_main_LT(EOS(STATIC_1193(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i212, i126, i212) -> f1199_0_main_LT(EOS(STATIC_1199(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i212, i126, i212) :|: TRUE
7.51/2.83	f1198_0_main_LT(EOS(STATIC_1198(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), matching1, i126, matching2) -> f1202_0_main_Load(EOS(STATIC_1202(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), -1, i126) :|: -1 < 0 && matching1 = -1 && matching2 = -1
7.51/2.83	f1202_0_main_Load(EOS(STATIC_1202(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), matching1, i126) -> f1206_0_main_LT(EOS(STATIC_1206(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), -1, i126, i126) :|: TRUE && matching1 = -1
7.51/2.83	f1206_0_main_LT(EOS(STATIC_1206(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), matching1, i215, i215) -> f1213_0_main_LT(EOS(STATIC_1213(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), -1, i215, i215) :|: TRUE && matching1 = -1
7.51/2.83	f1213_0_main_LT(EOS(STATIC_1213(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), matching1, i215, i215) -> f1219_0_main_Inc(EOS(STATIC_1219(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), -1, i215) :|: i215 >= 0 && matching1 = -1
7.51/2.83	f1219_0_main_Inc(EOS(STATIC_1219(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), matching1, i215) -> f1225_0_main_JMP(EOS(STATIC_1225(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), -1, i215 + -1) :|: TRUE && matching1 = -1
7.51/2.83	f1225_0_main_JMP(EOS(STATIC_1225(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), matching1, i217) -> f1325_0_main_Load(EOS(STATIC_1325(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), -1, i217) :|: TRUE && matching1 = -1
7.51/2.83	f1325_0_main_Load(EOS(STATIC_1325(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), matching1, i217) -> f1189_0_main_Load(EOS(STATIC_1189(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), -1, i217) :|: TRUE && matching1 = -1
7.51/2.83	f1189_0_main_Load(EOS(STATIC_1189(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i125, i126) -> f1193_0_main_LT(EOS(STATIC_1193(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i125, i126, i125) :|: TRUE
7.51/2.83	f1199_0_main_LT(EOS(STATIC_1199(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i212, i126, i212) -> f1203_0_main_Inc(EOS(STATIC_1203(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i212) :|: i212 >= 0
7.51/2.83	f1203_0_main_Inc(EOS(STATIC_1203(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i212) -> f1209_0_main_InvokeMethod(EOS(STATIC_1209(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i212 + -1) :|: TRUE
7.51/2.83	f1209_0_main_InvokeMethod(EOS(STATIC_1209(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214) -> f1215_0_random_FieldAccess(EOS(STATIC_1215(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214) :|: TRUE
7.51/2.83	f1215_0_random_FieldAccess(EOS(STATIC_1215(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214) -> f1228_0_random_FieldAccess(EOS(STATIC_1228(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(ARRAY(i6))) :|: TRUE
7.51/2.83	f1228_0_random_FieldAccess(EOS(STATIC_1228(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(ARRAY(i6))) -> f1335_0_random_ArrayAccess(EOS(STATIC_1335(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(ARRAY(i6))) :|: TRUE
7.51/2.83	f1335_0_random_ArrayAccess(EOS(STATIC_1335(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(ARRAY(i6))) -> f1337_0_random_ArrayAccess(EOS(STATIC_1337(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(ARRAY(i6))) :|: TRUE
7.51/2.83	f1337_0_random_ArrayAccess(EOS(STATIC_1337(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(ARRAY(i6))) -> f1344_0_random_Store(EOS(STATIC_1344(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) :|: TRUE
7.51/2.83	f1344_0_random_Store(EOS(STATIC_1344(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) -> f1351_0_random_FieldAccess(EOS(STATIC_1351(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) :|: TRUE
7.51/2.83	f1351_0_random_FieldAccess(EOS(STATIC_1351(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) -> f1354_0_random_ConstantStackPush(EOS(STATIC_1354(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) :|: TRUE
7.51/2.83	f1354_0_random_ConstantStackPush(EOS(STATIC_1354(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) -> f1365_0_random_IntArithmetic(EOS(STATIC_1365(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) :|: TRUE
7.51/2.83	f1365_0_random_IntArithmetic(EOS(STATIC_1365(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) -> f1371_0_random_FieldAccess(EOS(STATIC_1371(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) :|: TRUE
7.51/2.83	f1371_0_random_FieldAccess(EOS(STATIC_1371(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) -> f1375_0_random_Load(EOS(STATIC_1375(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) :|: TRUE
7.51/2.83	f1375_0_random_Load(EOS(STATIC_1375(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) -> f1388_0_random_InvokeMethod(EOS(STATIC_1388(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, o108) :|: TRUE
7.51/2.83	f1388_0_random_InvokeMethod(EOS(STATIC_1388(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(o115sub)) -> f1390_0_random_InvokeMethod(EOS(STATIC_1390(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(o115sub)) :|: TRUE
7.51/2.83	f1390_0_random_InvokeMethod(EOS(STATIC_1390(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(o116sub)) -> f1393_0_random_InvokeMethod(EOS(STATIC_1393(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(o116sub)) :|: TRUE
7.51/2.83	f1393_0_random_InvokeMethod(EOS(STATIC_1393(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(o116sub)) -> f1404_0_length_Load(EOS(STATIC_1404(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(o116sub)) :|: TRUE
7.51/2.83	f1404_0_length_Load(EOS(STATIC_1404(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(o116sub)) -> f1421_0_length_FieldAccess(EOS(STATIC_1421(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(o116sub)) :|: TRUE
7.51/2.83	f1421_0_length_FieldAccess(EOS(STATIC_1421(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(java.lang.String(EOC, i278))) -> f1433_0_length_FieldAccess(EOS(STATIC_1433(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(java.lang.String(EOC, i278))) :|: i278 >= 0
7.51/2.83	f1433_0_length_FieldAccess(EOS(STATIC_1433(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, java.lang.Object(java.lang.String(EOC, i278))) -> f1441_0_length_Return(EOS(STATIC_1441(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, i278) :|: TRUE
7.51/2.83	f1441_0_length_Return(EOS(STATIC_1441(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, i278) -> f1452_0_random_Return(EOS(STATIC_1452(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, i278) :|: TRUE
7.51/2.83	f1452_0_random_Return(EOS(STATIC_1452(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, i278) -> f1460_0_main_Store(EOS(STATIC_1460(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, i278) :|: TRUE
7.51/2.83	f1460_0_main_Store(EOS(STATIC_1460(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, i278) -> f1462_0_main_JMP(EOS(STATIC_1462(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, i278) :|: TRUE
7.51/2.83	f1462_0_main_JMP(EOS(STATIC_1462(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, i278) -> f1465_0_main_Load(EOS(STATIC_1465(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, i278) :|: TRUE
7.51/2.83	f1465_0_main_Load(EOS(STATIC_1465(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, i278) -> f1189_0_main_Load(EOS(STATIC_1189(java.lang.Object(ARRAY(i6)))), java.lang.Object(ARRAY(i6)), i214, i278) :|: TRUE
7.51/2.83	Combined rules. Obtained 2 IRulesP rules:
7.51/2.83	f1193_0_main_LT(EOS(STATIC_1193(java.lang.Object(ARRAY(i6:0)))), java.lang.Object(ARRAY(i6:0)), -1, i126:0, -1) -> f1193_0_main_LT(EOS(STATIC_1193(java.lang.Object(ARRAY(i6:0)))), java.lang.Object(ARRAY(i6:0)), -1, i126:0 - 1, -1) :|: i126:0 > -1
7.51/2.83	f1193_0_main_LT(EOS(STATIC_1193(java.lang.Object(ARRAY(i6:0)))), java.lang.Object(ARRAY(i6:0)), i212:0, i126:0, i212:0) -> f1193_0_main_LT(EOS(STATIC_1193(java.lang.Object(ARRAY(i6:0)))), java.lang.Object(ARRAY(i6:0)), i212:0 - 1, i278:0, i212:0 - 1) :|: i278:0 > -1 && i212:0 > -1
7.51/2.83	Filtered duplicate arguments:
7.51/2.83	   f1193_0_main_LT(x1, x2, x3, x4, x5) -> f1193_0_main_LT(x1, x2, x4, x5)
7.51/2.83	Filtered unneeded arguments:
7.51/2.83	   f1193_0_main_LT(x1, x2, x3, x4) -> f1193_0_main_LT(x3, x4)
7.51/2.83	Finished conversion. Obtained 2 rules.P rules:
7.51/2.83	f1193_0_main_LT(i126:0, cons_-1) -> f1193_0_main_LT(i126:0 - 1, -1) :|: i126:0 > -1 && cons_-1 = -1
7.51/2.83	f1193_0_main_LT(i126:0, i212:0) -> f1193_0_main_LT(i278:0, i212:0 - 1) :|: i278:0 > -1 && i212:0 > -1
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(8)
7.51/2.83	Obligation:
7.51/2.83	Rules:
7.51/2.83	f1193_0_main_LT(i126:0, cons_-1) -> f1193_0_main_LT(i126:0 - 1, -1) :|: i126:0 > -1 && cons_-1 = -1
7.51/2.83	f1193_0_main_LT(x, x1) -> f1193_0_main_LT(x2, x1 - 1) :|: x2 > -1 && x1 > -1
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(9) IRSFormatTransformerProof (EQUIVALENT)
7.51/2.83	Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(10)
7.51/2.83	Obligation:
7.51/2.83	Rules:
7.51/2.83	f1193_0_main_LT(i126:0, cons_-1) -> f1193_0_main_LT(arith, -1) :|: i126:0 > -1 && cons_-1 = -1 && arith = i126:0 - 1
7.51/2.83	f1193_0_main_LT(x3, x4) -> f1193_0_main_LT(x5, x6) :|: x5 > -1 && x4 > -1 && x6 = x4 - 1
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(11) IRSwTTerminationDigraphProof (EQUIVALENT)
7.51/2.83	Constructed termination digraph!
7.51/2.83	Nodes:
7.51/2.83	(1) f1193_0_main_LT(i126:0, cons_-1) -> f1193_0_main_LT(arith, -1) :|: i126:0 > -1 && cons_-1 = -1 && arith = i126:0 - 1
7.51/2.83	(2) f1193_0_main_LT(x3, x4) -> f1193_0_main_LT(x5, x6) :|: x5 > -1 && x4 > -1 && x6 = x4 - 1
7.51/2.83	
7.51/2.83	Arcs:
7.51/2.83	(1) -> (1)
7.51/2.83	(2) -> (1), (2)
7.51/2.83	
7.51/2.83	This digraph is fully evaluated!
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(12)
7.51/2.83	Complex Obligation (AND)
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(13)
7.51/2.83	Obligation:
7.51/2.83	
7.51/2.83	Termination digraph:
7.51/2.83	Nodes:
7.51/2.83	(1) f1193_0_main_LT(x3, x4) -> f1193_0_main_LT(x5, x6) :|: x5 > -1 && x4 > -1 && x6 = x4 - 1
7.51/2.83	
7.51/2.83	Arcs:
7.51/2.83	(1) -> (1)
7.51/2.83	
7.51/2.83	This digraph is fully evaluated!
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(14) IntTRSCompressionProof (EQUIVALENT)
7.51/2.83	Compressed rules.
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(15)
7.51/2.83	Obligation:
7.51/2.83	Rules:
7.51/2.83	f1193_0_main_LT(x3:0, x4:0) -> f1193_0_main_LT(x5:0, x4:0 - 1) :|: x5:0 > -1 && x4:0 > -1
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(16) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
7.51/2.83	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
7.51/2.83	
7.51/2.83	   f1193_0_main_LT(x1, x2) -> f1193_0_main_LT(x2)
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(17)
7.51/2.83	Obligation:
7.51/2.83	Rules:
7.51/2.83	f1193_0_main_LT(x4:0) -> f1193_0_main_LT(x4:0 - 1) :|: x5:0 > -1 && x4:0 > -1
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(18) TempFilterProof (SOUND)
7.51/2.83	Used the following sort dictionary for filtering: 
7.51/2.83	f1193_0_main_LT(INTEGER)
7.51/2.83	Replaced non-predefined constructor symbols by 0.
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(19)
7.51/2.83	Obligation:
7.51/2.83	Rules:
7.51/2.83	f1193_0_main_LT(x4:0) -> f1193_0_main_LT(c) :|: c = x4:0 - 1 && (x5:0 > -1 && x4:0 > -1)
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(20) PolynomialOrderProcessor (EQUIVALENT)
7.51/2.83	Found the following polynomial interpretation:
7.51/2.83	[f1193_0_main_LT(x)] = x
7.51/2.83	
7.51/2.83	The following rules are decreasing:
7.51/2.83	f1193_0_main_LT(x4:0) -> f1193_0_main_LT(c) :|: c = x4:0 - 1 && (x5:0 > -1 && x4:0 > -1)
7.51/2.83	The following rules are bounded:
7.51/2.83	f1193_0_main_LT(x4:0) -> f1193_0_main_LT(c) :|: c = x4:0 - 1 && (x5:0 > -1 && x4:0 > -1)
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(21)
7.51/2.83	YES
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(22)
7.51/2.83	Obligation:
7.51/2.83	
7.51/2.83	Termination digraph:
7.51/2.83	Nodes:
7.51/2.83	(1) f1193_0_main_LT(i126:0, cons_-1) -> f1193_0_main_LT(arith, -1) :|: i126:0 > -1 && cons_-1 = -1 && arith = i126:0 - 1
7.51/2.83	
7.51/2.83	Arcs:
7.51/2.83	(1) -> (1)
7.51/2.83	
7.51/2.83	This digraph is fully evaluated!
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(23) IntTRSCompressionProof (EQUIVALENT)
7.51/2.83	Compressed rules.
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(24)
7.51/2.83	Obligation:
7.51/2.83	Rules:
7.51/2.83	f1193_0_main_LT(i126:0:0, cons_-1) -> f1193_0_main_LT(i126:0:0 - 1, -1) :|: i126:0:0 > -1 && cons_-1 = -1
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(25) TempFilterProof (SOUND)
7.51/2.83	Used the following sort dictionary for filtering: 
7.51/2.83	f1193_0_main_LT(INTEGER, VARIABLE)
7.51/2.83	Replaced non-predefined constructor symbols by 0.
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(26)
7.51/2.83	Obligation:
7.51/2.83	Rules:
7.51/2.83	f1193_0_main_LT(i126:0:0, c) -> f1193_0_main_LT(c1, c2) :|: c2 = -1 && (c1 = i126:0:0 - 1 && c = -1) && (i126:0:0 > -1 && cons_-1 = -1)
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(27) PolynomialOrderProcessor (EQUIVALENT)
7.51/2.83	Found the following polynomial interpretation:
7.51/2.83	[f1193_0_main_LT(x, x1)] = x
7.51/2.83	
7.51/2.83	The following rules are decreasing:
7.51/2.83	f1193_0_main_LT(i126:0:0, c) -> f1193_0_main_LT(c1, c2) :|: c2 = -1 && (c1 = i126:0:0 - 1 && c = -1) && (i126:0:0 > -1 && cons_-1 = -1)
7.51/2.83	The following rules are bounded:
7.51/2.83	f1193_0_main_LT(i126:0:0, c) -> f1193_0_main_LT(c1, c2) :|: c2 = -1 && (c1 = i126:0:0 - 1 && c = -1) && (i126:0:0 > -1 && cons_-1 = -1)
7.51/2.83	
7.51/2.83	----------------------------------------
7.51/2.83	
7.51/2.83	(28)
7.51/2.83	YES
7.74/2.88	EOF