6.93/2.76	YES
6.93/2.79	proof of /export/starexec/sandbox/benchmark/theBenchmark.jar
6.93/2.79	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.93/2.79	
6.93/2.79	
6.93/2.79	termination of the given Bare JBC problem could be proven:
6.93/2.79	
6.93/2.79	(0) Bare JBC problem
6.93/2.79	(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
6.93/2.79	(2) JBC problem
6.93/2.79	(3) JBCToGraph [EQUIVALENT, 349 ms]
6.93/2.79	(4) JBCTerminationGraph
6.93/2.79	(5) TerminationGraphToSCCProof [SOUND, 0 ms]
6.93/2.79	(6) AND
6.93/2.79	    (7) JBCTerminationSCC
6.93/2.79	        (8) SCCToQDPProof [SOUND, 127 ms]
6.93/2.79	        (9) QDP
6.93/2.79	        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
6.93/2.79	        (11) YES
6.93/2.79	    (12) JBCTerminationSCC
6.93/2.79	        (13) SCCToIRSProof [SOUND, 96 ms]
6.93/2.79	        (14) IRSwT
6.93/2.79	        (15) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
6.93/2.79	        (16) IRSwT
6.93/2.79	        (17) IRSwTTerminationDigraphProof [EQUIVALENT, 29 ms]
6.93/2.79	        (18) IRSwT
6.93/2.79	        (19) IntTRSCompressionProof [EQUIVALENT, 0 ms]
6.93/2.79	        (20) IRSwT
6.93/2.79	        (21) TempFilterProof [SOUND, 18 ms]
6.93/2.79	        (22) IntTRS
6.93/2.79	        (23) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
6.93/2.79	        (24) YES
6.93/2.79	
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(0)
6.93/2.79	Obligation:
6.93/2.79	need to prove termination of the following program:
6.93/2.79	public class List1 {
6.93/2.79		List1 pred, next;
6.93/2.79	
6.93/2.79		List1(List1 pred) {
6.93/2.79			if (pred != null) {
6.93/2.79				pred.next = this;
6.93/2.79			}
6.93/2.79			this.pred = pred;
6.93/2.79		}
6.93/2.79	
6.93/2.79		static int length(List1 l) {
6.93/2.79			int r = 1;
6.93/2.79			while (null != (l = l.next))
6.93/2.79				r++;
6.93/2.79			return r;
6.93/2.79		}
6.93/2.79	
6.93/2.79		public static void main(String[] args) {
6.93/2.79			//Create doubly-linked list:
6.93/2.79			int length = args.length;
6.93/2.79			List1 cur = new List1(null);
6.93/2.79			List1 first = cur;
6.93/2.79			while (length-- > 0) {
6.93/2.79				cur = new List1(cur);
6.93/2.79			}
6.93/2.79	
6.93/2.79			length(first);		
6.93/2.79		}
6.93/2.79	}
6.93/2.79	
6.93/2.79	
6.93/2.79	
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(1) BareJBCToJBCProof (EQUIVALENT)
6.93/2.79	initialized classpath
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(2)
6.93/2.79	Obligation:
6.93/2.79	need to prove termination of the following program:
6.93/2.79	public class List1 {
6.93/2.79		List1 pred, next;
6.93/2.79	
6.93/2.79		List1(List1 pred) {
6.93/2.79			if (pred != null) {
6.93/2.79				pred.next = this;
6.93/2.79			}
6.93/2.79			this.pred = pred;
6.93/2.79		}
6.93/2.79	
6.93/2.79		static int length(List1 l) {
6.93/2.79			int r = 1;
6.93/2.79			while (null != (l = l.next))
6.93/2.79				r++;
6.93/2.79			return r;
6.93/2.79		}
6.93/2.79	
6.93/2.79		public static void main(String[] args) {
6.93/2.79			//Create doubly-linked list:
6.93/2.79			int length = args.length;
6.93/2.79			List1 cur = new List1(null);
6.93/2.79			List1 first = cur;
6.93/2.79			while (length-- > 0) {
6.93/2.79				cur = new List1(cur);
6.93/2.79			}
6.93/2.79	
6.93/2.79			length(first);		
6.93/2.79		}
6.93/2.79	}
6.93/2.79	
6.93/2.79	
6.93/2.79	
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(3) JBCToGraph (EQUIVALENT)
6.93/2.79	Constructed TerminationGraph.
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(4)
6.93/2.79	Obligation:
6.93/2.79	Termination Graph based on JBC Program:
6.93/2.79	List1.main([Ljava/lang/String;)V: Graph of 79 nodes with 2 SCCs.
6.93/2.79	
6.93/2.79	
6.93/2.79	
6.93/2.79	
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(5) TerminationGraphToSCCProof (SOUND)
6.93/2.79	Splitted TerminationGraph to 2 SCCss.
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(6)
6.93/2.79	Complex Obligation (AND)
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(7)
6.93/2.79	Obligation:
6.93/2.79	SCC of termination graph based on JBC Program.
6.93/2.79	SCC contains nodes from the following methods: List1.main([Ljava/lang/String;)V
6.93/2.79	SCC calls the following helper methods: 
6.93/2.79	Performed SCC analyses:
6.93/2.79	*Used field analysis yielded the following read fields:
6.93/2.79	*List1: [next]
6.93/2.79	*Marker field analysis yielded the following relations that could be markers:
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(8) SCCToQDPProof (SOUND)
6.93/2.79	Transformed TerminationGraph SCC to QDP. Log: 
6.93/2.79	Generated 11 rules for P and 0 rules for R.P rules:
6.93/2.79	f1254_0_length_Load(EOS(STATIC_1254), java.lang.Object(o184sub)) -> f1257_0_length_FieldAccess(EOS(STATIC_1257), java.lang.Object(o184sub)) :|: TRUE
6.93/2.79	f1257_0_length_FieldAccess(EOS(STATIC_1257), java.lang.Object(List1(EOC, o189))) -> f1259_0_length_FieldAccess(EOS(STATIC_1259), java.lang.Object(List1(EOC, o189))) :|: TRUE
6.93/2.79	f1259_0_length_FieldAccess(EOS(STATIC_1259), java.lang.Object(List1(EOC, o189))) -> f1260_0_length_Duplicate(EOS(STATIC_1260), o189) :|: TRUE
6.93/2.79	f1260_0_length_Duplicate(EOS(STATIC_1260), o189) -> f1261_0_length_Store(EOS(STATIC_1261), o189, o189) :|: TRUE
6.93/2.79	f1261_0_length_Store(EOS(STATIC_1261), o189, o189) -> f1262_0_length_EQ(EOS(STATIC_1262), o189, o189) :|: TRUE
6.93/2.79	f1262_0_length_EQ(EOS(STATIC_1262), java.lang.Object(o190sub), java.lang.Object(o190sub)) -> f1263_0_length_EQ(EOS(STATIC_1263), java.lang.Object(o190sub), java.lang.Object(o190sub)) :|: TRUE
6.93/2.79	f1263_0_length_EQ(EOS(STATIC_1263), java.lang.Object(o190sub), java.lang.Object(o190sub)) -> f1265_0_length_Inc(EOS(STATIC_1265), java.lang.Object(o190sub)) :|: TRUE
6.93/2.79	f1265_0_length_Inc(EOS(STATIC_1265), java.lang.Object(o190sub)) -> f1267_0_length_JMP(EOS(STATIC_1267), java.lang.Object(o190sub)) :|: TRUE
6.93/2.79	f1267_0_length_JMP(EOS(STATIC_1267), java.lang.Object(o190sub)) -> f1270_0_length_ConstantStackPush(EOS(STATIC_1270), java.lang.Object(o190sub)) :|: TRUE
6.93/2.79	f1270_0_length_ConstantStackPush(EOS(STATIC_1270), java.lang.Object(o190sub)) -> f1251_0_length_ConstantStackPush(EOS(STATIC_1251), java.lang.Object(o190sub)) :|: TRUE
6.93/2.79	f1251_0_length_ConstantStackPush(EOS(STATIC_1251), java.lang.Object(o184sub)) -> f1254_0_length_Load(EOS(STATIC_1254), java.lang.Object(o184sub)) :|: TRUE
6.93/2.79	R rules:
6.93/2.79	Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules:
6.93/2.79	f1254_0_length_Load(EOS(STATIC_1254), java.lang.Object(List1(EOC, java.lang.Object(o190sub:0)))) -> f1254_0_length_Load(EOS(STATIC_1254), java.lang.Object(o190sub:0)) :|: TRUE
6.93/2.79	R rules:
6.93/2.79	Filtered ground terms:
6.93/2.79	   f1254_0_length_Load(x1, x2) -> f1254_0_length_Load(x2)
6.93/2.79	   EOS(x1) -> EOS
6.93/2.79	   List1(x1, x2) -> List1(x2)
6.93/2.79	Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules:
6.93/2.79	F1254_0_LENGTH_LOAD(java.lang.Object(List1(java.lang.Object(o190sub:0:0)))) -> F1254_0_LENGTH_LOAD(java.lang.Object(o190sub:0:0)) :|: TRUE
6.93/2.79	R rules:
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(9)
6.93/2.79	Obligation:
6.93/2.79	Q DP problem:
6.93/2.79	The TRS P consists of the following rules:
6.93/2.79	
6.93/2.79	   F1254_0_LENGTH_LOAD(java.lang.Object(List1(java.lang.Object(o190sub:0:0)))) -> F1254_0_LENGTH_LOAD(java.lang.Object(o190sub:0:0))
6.93/2.79	
6.93/2.79	R is empty.
6.93/2.79	Q is empty.
6.93/2.79	We have to consider all minimal (P,Q,R)-chains.
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(10) QDPSizeChangeProof (EQUIVALENT)
6.93/2.79	By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 
6.93/2.79	
6.93/2.79	From the DPs we obtained the following set of size-change graphs:
6.93/2.79	*F1254_0_LENGTH_LOAD(java.lang.Object(List1(java.lang.Object(o190sub:0:0)))) -> F1254_0_LENGTH_LOAD(java.lang.Object(o190sub:0:0))
6.93/2.79	The graph contains the following edges 1 > 1
6.93/2.79	
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(11)
6.93/2.79	YES
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(12)
6.93/2.79	Obligation:
6.93/2.79	SCC of termination graph based on JBC Program.
6.93/2.79	SCC contains nodes from the following methods: List1.main([Ljava/lang/String;)V
6.93/2.79	SCC calls the following helper methods: 
6.93/2.79	Performed SCC analyses:
6.93/2.79	*Used field analysis yielded the following read fields:
6.93/2.79	
6.93/2.79	*Marker field analysis yielded the following relations that could be markers:
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(13) SCCToIRSProof (SOUND)
6.93/2.79	Transformed FIGraph SCCs to intTRSs. Log: 
6.93/2.79	Generated rules. Obtained 33 IRulesP rules:
6.93/2.79	f904_0_main_Inc(EOS(STATIC_904), i76, i76, o119[List1.next]o117) -> f908_0_main_LE(EOS(STATIC_908), i76 + -1, i76, o119[List1.next]o117) :|: TRUE
6.93/2.79	f908_0_main_LE(EOS(STATIC_908), i84, i87, o119[List1.next]o117) -> f915_0_main_LE(EOS(STATIC_915), i84, i87, o119[List1.next]o117) :|: TRUE
6.93/2.79	f915_0_main_LE(EOS(STATIC_915), i84, i87, o119[List1.next]o117) -> f921_0_main_New(EOS(STATIC_921), i84, o119[List1.next]o117) :|: i87 > 0
6.93/2.79	f921_0_main_New(EOS(STATIC_921), i84, o119[List1.next]o117) -> f926_0_main_Duplicate(EOS(STATIC_926), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f926_0_main_Duplicate(EOS(STATIC_926), i84, o119[List1.next]o117) -> f931_0_main_Load(EOS(STATIC_931), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f931_0_main_Load(EOS(STATIC_931), i84, o119[List1.next]o117) -> f934_0_main_InvokeMethod(EOS(STATIC_934), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f934_0_main_InvokeMethod(EOS(STATIC_934), i84, o119[List1.next]o117) -> f939_0__init__Load(EOS(STATIC_939), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f939_0__init__Load(EOS(STATIC_939), i84, o119[List1.next]o117) -> f948_0__init__InvokeMethod(EOS(STATIC_948), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f948_0__init__InvokeMethod(EOS(STATIC_948), i84, o119[List1.next]o117) -> f954_0__init__Load(EOS(STATIC_954), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f954_0__init__Load(EOS(STATIC_954), i84, o119[List1.next]o117) -> f962_0__init__NULL(EOS(STATIC_962), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f962_0__init__NULL(EOS(STATIC_962), i84, o119[List1.next]o117) -> f967_0__init__Load(EOS(STATIC_967), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f967_0__init__Load(EOS(STATIC_967), i84, o119[List1.next]o117) -> f972_0__init__Load(EOS(STATIC_972), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f972_0__init__Load(EOS(STATIC_972), i84, o119[List1.next]o117) -> f977_0__init__FieldAccess(EOS(STATIC_977), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f977_0__init__FieldAccess(EOS(STATIC_977), i84, o119[List1.next]o117) -> f996_0__init__FieldAccess(EOS(STATIC_996), i84, o119[List1.next]o117) :|: o119[List1.next]o117 > 0
6.93/2.79	f977_0__init__FieldAccess(EOS(STATIC_977), i84, o136[List1.next]o136) -> f997_0__init__FieldAccess(EOS(STATIC_997), i84) :|: TRUE
6.93/2.79	f996_0__init__FieldAccess(EOS(STATIC_996), i84, o119[List1.next]o117) -> f1000_0__init__Load(EOS(STATIC_1000), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f1000_0__init__Load(EOS(STATIC_1000), i84, o119[List1.next]o117) -> f1006_0__init__Load(EOS(STATIC_1006), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f1006_0__init__Load(EOS(STATIC_1006), i84, o119[List1.next]o117) -> f1020_0__init__FieldAccess(EOS(STATIC_1020), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f1020_0__init__FieldAccess(EOS(STATIC_1020), i84, o119[List1.next]o117) -> f1023_0__init__Return(EOS(STATIC_1023), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f1023_0__init__Return(EOS(STATIC_1023), i84, o119[List1.next]o117) -> f1026_0_main_Store(EOS(STATIC_1026), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f1026_0_main_Store(EOS(STATIC_1026), i84, o119[List1.next]o117) -> f1030_0_main_JMP(EOS(STATIC_1030), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f1030_0_main_JMP(EOS(STATIC_1030), i84, o119[List1.next]o117) -> f1033_0_main_Load(EOS(STATIC_1033), i84, o119[List1.next]o117) :|: TRUE
6.93/2.79	f1033_0_main_Load(EOS(STATIC_1033), i84, o119[List1.next]o117) -> f900_0_main_Load(EOS(STATIC_900), i84, o119[List1.next]o124) :|: TRUE
6.93/2.79	f900_0_main_Load(EOS(STATIC_900), i76, o119[List1.next]o117) -> f904_0_main_Inc(EOS(STATIC_904), i76, i76, o119[List1.next]o117) :|: TRUE
6.93/2.79	f997_0__init__FieldAccess(EOS(STATIC_997), i84) -> f1001_0__init__FieldAccess(EOS(STATIC_1001), i84) :|: TRUE
6.93/2.79	f1001_0__init__FieldAccess(EOS(STATIC_1001), i84) -> f1014_0__init__Load(EOS(STATIC_1014), i84) :|: TRUE
6.93/2.79	f1014_0__init__Load(EOS(STATIC_1014), i84) -> f1021_0__init__Load(EOS(STATIC_1021), i84) :|: TRUE
6.93/2.79	f1021_0__init__Load(EOS(STATIC_1021), i84) -> f1024_0__init__FieldAccess(EOS(STATIC_1024), i84) :|: TRUE
6.93/2.79	f1024_0__init__FieldAccess(EOS(STATIC_1024), i84) -> f1028_0__init__Return(EOS(STATIC_1028), i84) :|: TRUE
6.93/2.79	f1028_0__init__Return(EOS(STATIC_1028), i84) -> f1031_0_main_Store(EOS(STATIC_1031), i84) :|: TRUE
6.93/2.79	f1031_0_main_Store(EOS(STATIC_1031), i84) -> f1034_0_main_JMP(EOS(STATIC_1034), i84) :|: TRUE
6.93/2.79	f1034_0_main_JMP(EOS(STATIC_1034), i84) -> f1174_0_main_Load(EOS(STATIC_1174), i84) :|: TRUE
6.93/2.79	f1174_0_main_Load(EOS(STATIC_1174), i84) -> f900_0_main_Load(EOS(STATIC_900), i84, o139[List1.next]o124) :|: o139[List1.next]o124 = 1
6.93/2.79	Combined rules. Obtained 2 IRulesP rules:
6.93/2.79	f904_0_main_Inc(EOS(STATIC_904), i76:0, i76:0, o119[List1.next]o117:0) -> f904_0_main_Inc(EOS(STATIC_904), i76:0 - 1, i76:0 - 1, o119[List1.next]o124:0) :|: o119[List1.next]o117:0 > 0 && i76:0 > 0
6.93/2.79	f904_0_main_Inc(EOS(STATIC_904), i76:0, i76:0, o119[List1.next]o117:0) -> f904_0_main_Inc(EOS(STATIC_904), i76:0 - 1, i76:0 - 1, 1) :|: i76:0 > 0
6.93/2.79	Filtered constant ground arguments:
6.93/2.79	   f904_0_main_Inc(x1, x2, x3, x4) -> f904_0_main_Inc(x2, x3, x4)
6.93/2.79	   EOS(x1) -> EOS
6.93/2.79	Filtered duplicate arguments:
6.93/2.79	   f904_0_main_Inc(x1, x2, x3) -> f904_0_main_Inc(x2, x3)
6.93/2.79	Finished conversion. Obtained 2 rules.P rules:
6.93/2.79	f904_0_main_Inc(i76:0, o119[List1.next]o117:0) -> f904_0_main_Inc(i76:0 - 1, o119[List1.next]o124:0) :|: o119[List1.next]o117:0 > 0 && i76:0 > 0
6.93/2.79	f904_0_main_Inc(i76:0, o119[List1.next]o117:0) -> f904_0_main_Inc(i76:0 - 1, 1) :|: i76:0 > 0
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(14)
6.93/2.79	Obligation:
6.93/2.79	Rules:
6.93/2.79	f904_0_main_Inc(i76:0, o119[List1.next]o117:0) -> f904_0_main_Inc(i76:0 - 1, o119[List1.next]o124:0) :|: o119[List1.next]o117:0 > 0 && i76:0 > 0
6.93/2.79	f904_0_main_Inc(x, x1) -> f904_0_main_Inc(x - 1, 1) :|: x > 0
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(15) IRSFormatTransformerProof (EQUIVALENT)
6.93/2.79	Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(16)
6.93/2.79	Obligation:
6.93/2.79	Rules:
6.93/2.79	f904_0_main_Inc(i76:0, o119[List1.next]o117:0) -> f904_0_main_Inc(arith, o119[List1.next]o124:0) :|: o119[List1.next]o117:0 > 0 && i76:0 > 0 && arith = i76:0 - 1
6.93/2.79	f904_0_main_Inc(x2, x3) -> f904_0_main_Inc(x4, 1) :|: x2 > 0 && x4 = x2 - 1
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(17) IRSwTTerminationDigraphProof (EQUIVALENT)
6.93/2.79	Constructed termination digraph!
6.93/2.79	Nodes:
6.93/2.79	(1) f904_0_main_Inc(i76:0, o119[List1.next]o117:0) -> f904_0_main_Inc(arith, o119[List1.next]o124:0) :|: o119[List1.next]o117:0 > 0 && i76:0 > 0 && arith = i76:0 - 1
6.93/2.79	(2) f904_0_main_Inc(x2, x3) -> f904_0_main_Inc(x4, 1) :|: x2 > 0 && x4 = x2 - 1
6.93/2.79	
6.93/2.79	Arcs:
6.93/2.79	(1) -> (1), (2)
6.93/2.79	(2) -> (1), (2)
6.93/2.79	
6.93/2.79	This digraph is fully evaluated!
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(18)
6.93/2.79	Obligation:
6.93/2.79	
6.93/2.79	Termination digraph:
6.93/2.79	Nodes:
6.93/2.79	(1) f904_0_main_Inc(i76:0, o119[List1.next]o117:0) -> f904_0_main_Inc(arith, o119[List1.next]o124:0) :|: o119[List1.next]o117:0 > 0 && i76:0 > 0 && arith = i76:0 - 1
6.93/2.79	(2) f904_0_main_Inc(x2, x3) -> f904_0_main_Inc(x4, 1) :|: x2 > 0 && x4 = x2 - 1
6.93/2.79	
6.93/2.79	Arcs:
6.93/2.79	(1) -> (1), (2)
6.93/2.79	(2) -> (1), (2)
6.93/2.79	
6.93/2.79	This digraph is fully evaluated!
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(19) IntTRSCompressionProof (EQUIVALENT)
6.93/2.79	Compressed rules.
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(20)
6.93/2.79	Obligation:
6.93/2.79	Rules:
6.93/2.79	f904_0_main_Inc(i76:0:0, o119[List1.next]o117:0:0) -> f904_0_main_Inc(i76:0:0 - 1, o119[List1.next]o124:0:0) :|: o119[List1.next]o117:0:0 > 0 && i76:0:0 > 0
6.93/2.79	f904_0_main_Inc(x2:0, x3:0) -> f904_0_main_Inc(x2:0 - 1, 1) :|: x2:0 > 0
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(21) TempFilterProof (SOUND)
6.93/2.79	Used the following sort dictionary for filtering: 
6.93/2.79	f904_0_main_Inc(INTEGER, VARIABLE)
6.93/2.79	Replaced non-predefined constructor symbols by 0.
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(22)
6.93/2.79	Obligation:
6.93/2.79	Rules:
6.93/2.79	f904_0_main_Inc(i76:0:0, o119[List1.next]o117:0:0) -> f904_0_main_Inc(c, o119[List1.next]o124:0:0) :|: c = i76:0:0 - 1 && (o119[List1.next]o117:0:0 > 0 && i76:0:0 > 0)
6.93/2.79	f904_0_main_Inc(x2:0, x3:0) -> f904_0_main_Inc(c1, c2) :|: c2 = 1 && c1 = x2:0 - 1 && x2:0 > 0
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(23) PolynomialOrderProcessor (EQUIVALENT)
6.93/2.79	Found the following polynomial interpretation:
6.93/2.79	[f904_0_main_Inc(x, x1)] = x
6.93/2.79	
6.93/2.79	The following rules are decreasing:
6.93/2.79	f904_0_main_Inc(i76:0:0, o119[List1.next]o117:0:0) -> f904_0_main_Inc(c, o119[List1.next]o124:0:0) :|: c = i76:0:0 - 1 && (o119[List1.next]o117:0:0 > 0 && i76:0:0 > 0)
6.93/2.79	f904_0_main_Inc(x2:0, x3:0) -> f904_0_main_Inc(c1, c2) :|: c2 = 1 && c1 = x2:0 - 1 && x2:0 > 0
6.93/2.79	The following rules are bounded:
6.93/2.79	f904_0_main_Inc(i76:0:0, o119[List1.next]o117:0:0) -> f904_0_main_Inc(c, o119[List1.next]o124:0:0) :|: c = i76:0:0 - 1 && (o119[List1.next]o117:0:0 > 0 && i76:0:0 > 0)
6.93/2.79	f904_0_main_Inc(x2:0, x3:0) -> f904_0_main_Inc(c1, c2) :|: c2 = 1 && c1 = x2:0 - 1 && x2:0 > 0
6.93/2.79	
6.93/2.79	----------------------------------------
6.93/2.79	
6.93/2.79	(24)
6.93/2.79	YES
7.25/2.83	EOF