/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.jar /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.jar
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


termination of the given Bare JBC problem could be proven:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 357 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) JBCTerminationSCC
        (8) SCCToIRSProof [SOUND, 63 ms]
        (9) IRSwT
        (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (11) IRSwT
        (12) IRSwTTerminationDigraphProof [EQUIVALENT, 33 ms]
        (13) IRSwT
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IRSwT
        (16) TempFilterProof [SOUND, 27 ms]
        (17) IntTRS
        (18) RankingReductionPairProof [EQUIVALENT, 7 ms]
        (19) YES
    (20) JBCTerminationSCC
        (21) SCCToIRSProof [SOUND, 42 ms]
        (22) IRSwT
        (23) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (24) IRSwT
        (25) IRSwTTerminationDigraphProof [EQUIVALENT, 20 ms]
        (26) IRSwT
        (27) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (28) IRSwT
        (29) TempFilterProof [SOUND, 46 ms]
        (30) IntTRS
        (31) RankingReductionPairProof [EQUIVALENT, 17 ms]
        (32) YES


----------------------------------------

(0)
Obligation:
need to prove termination of the following program:
public class List3 {
	private List3 next;

	void iterate() {
		List3 current = this.next;
	        while (current != this) {
	                current = current.next;
	        }
	}

	public static void main(String[] args) {
		//Create cyclic list:
		int length = args.length;
		List3 cur = new List3();
		List3 first = cur;
		while (length-- > 0) {
			cur.next = new List3();
			cur = cur.next;
		}
		cur.next = first;

		cur.iterate();
	}
}



----------------------------------------

(1) BareJBCToJBCProof (EQUIVALENT)
initialized classpath
----------------------------------------

(2)
Obligation:
need to prove termination of the following program:
public class List3 {
	private List3 next;

	void iterate() {
		List3 current = this.next;
	        while (current != this) {
	                current = current.next;
	        }
	}

	public static void main(String[] args) {
		//Create cyclic list:
		int length = args.length;
		List3 cur = new List3();
		List3 first = cur;
		while (length-- > 0) {
			cur.next = new List3();
			cur = cur.next;
		}
		cur.next = first;

		cur.iterate();
	}
}



----------------------------------------

(3) JBCToGraph (EQUIVALENT)
Constructed TerminationGraph.
----------------------------------------

(4)
Obligation:
Termination Graph based on JBC Program:
List3.main([Ljava/lang/String;)V: Graph of 81 nodes with 2 SCCs.





----------------------------------------

(5) TerminationGraphToSCCProof (SOUND)
Splitted TerminationGraph to 2 SCCss.
----------------------------------------

(6)
Complex Obligation (AND)

----------------------------------------

(7)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: List3.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*List3: [next]
*Marker field analysis yielded the following relations that could be markers:

----------------------------------------

(8) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 17 IRulesP rules:
f1501_0_iterate_EQ(EOS(STATIC_1501), o131[List3.next]o132, o131[List3.next]o130, o132[List3.next]o131, o132[List3.next]o130) -> f1503_0_iterate_Load(EOS(STATIC_1503), o131[List3.next]o132, o131[List3.next]o130, o132[List3.next]o131, o132[List3.next]o130) :|: TRUE
f1503_0_iterate_Load(EOS(STATIC_1503), o131[List3.next]o132, o131[List3.next]o130, o132[List3.next]o131, o132[List3.next]o130) -> f1512_0_iterate_FieldAccess(EOS(STATIC_1512), o131[List3.next]o132, o131[List3.next]o130, o132[List3.next]o131, o132[List3.next]o130) :|: TRUE
f1512_0_iterate_FieldAccess(EOS(STATIC_1512), o131[List3.next]o132, o131[List3.next]o130, o132[List3.next]o131, o132[List3.next]o130) -> f1534_0_iterate_FieldAccess(EOS(STATIC_1534), o131[List3.next]o132, o131[List3.next]o130, o132[List3.next]o130, o132[List3.next]o131) :|: o131[List3.next]o132 > 0 && o132[List3.next]o131 > 0
f1512_0_iterate_FieldAccess(EOS(STATIC_1512), o162[List3.next]o162, o162[List3.next]o130, o162[List3.next]o162, o162[List3.next]o130) -> f1535_0_iterate_FieldAccess(EOS(STATIC_1535), o162[List3.next]o130, o162[List3.next]o162) :|: TRUE
f1534_0_iterate_FieldAccess(EOS(STATIC_1534), o131[List3.next]o164, o131[List3.next]o130, o164[List3.next]o130, o164[List3.next]o131) -> f1536_0_iterate_FieldAccess(EOS(STATIC_1536), o131[List3.next]o130, o131[List3.next]o164, o165[List3.next]o130, o165[List3.next]o131) :|: o165[List3.next]o130 < o164[List3.next]o130 && o164[List3.next]o130 >= 0 && o165[List3.next]o131 < o164[List3.next]o131 && o164[List3.next]o131 >= 0
f1536_0_iterate_FieldAccess(EOS(STATIC_1536), o131[List3.next]o130, o131[List3.next]o164, o165[List3.next]o130, o165[List3.next]o131) -> f1538_0_iterate_Store(EOS(STATIC_1538), o131[List3.next]o130, o165[List3.next]o130, o165[List3.next]o131, o131[List3.next]o165) :|: o131[List3.next]o165 > o131[List3.next]o164 && o131[List3.next]o164 >= 0
f1538_0_iterate_Store(EOS(STATIC_1538), o131[List3.next]o130, o165[List3.next]o130, o165[List3.next]o131, o131[List3.next]o165) -> f1541_0_iterate_JMP(EOS(STATIC_1541), o131[List3.next]o130, o165[List3.next]o130, o165[List3.next]o131, o131[List3.next]o165) :|: TRUE
f1541_0_iterate_JMP(EOS(STATIC_1541), o131[List3.next]o130, o165[List3.next]o130, o165[List3.next]o131, o131[List3.next]o165) -> f1572_0_iterate_Load(EOS(STATIC_1572), o131[List3.next]o130, o165[List3.next]o130, o165[List3.next]o131, o131[List3.next]o165) :|: TRUE
f1572_0_iterate_Load(EOS(STATIC_1572), o131[List3.next]o130, o165[List3.next]o130, o165[List3.next]o131, o131[List3.next]o165) -> f1435_0_iterate_Load(EOS(STATIC_1435), o131[List3.next]o165, o131[List3.next]o130, o165[List3.next]o130, o165[List3.next]o131) :|: TRUE
f1435_0_iterate_Load(EOS(STATIC_1435), o131[List3.next]o132, o131[List3.next]o130, o132[List3.next]o130, o132[List3.next]o131) -> f1445_0_iterate_Load(EOS(STATIC_1445), o131[List3.next]o132, o131[List3.next]o130, o132[List3.next]o130, o132[List3.next]o131) :|: TRUE
f1445_0_iterate_Load(EOS(STATIC_1445), o131[List3.next]o132, o131[List3.next]o130, o132[List3.next]o130, o132[List3.next]o131) -> f1478_0_iterate_EQ(EOS(STATIC_1478), o131[List3.next]o132, o131[List3.next]o130, o132[List3.next]o130, o132[List3.next]o131) :|: TRUE
f1478_0_iterate_EQ(EOS(STATIC_1478), o131[List3.next]o132, o131[List3.next]o130, o132[List3.next]o130, o132[List3.next]o131) -> f1501_0_iterate_EQ(EOS(STATIC_1501), o131[List3.next]o132, o131[List3.next]o130, o132[List3.next]o131, o132[List3.next]o130) :|: o132[List3.next]o130 > 0
f1535_0_iterate_FieldAccess(EOS(STATIC_1535), o166[List3.next]o130, o166[List3.next]o166) -> f1537_0_iterate_FieldAccess(EOS(STATIC_1537), o167[List3.next]o130, o167[List3.next]o166) :|: o167[List3.next]o130 < o166[List3.next]o130 && o166[List3.next]o130 >= 0 && o167[List3.next]o166 < o166[List3.next]o166 && o166[List3.next]o166 >= 0
f1537_0_iterate_FieldAccess(EOS(STATIC_1537), o167[List3.next]o130, o167[List3.next]o166) -> f1539_0_iterate_Store(EOS(STATIC_1539), o167[List3.next]o130, o167[List3.next]o166) :|: TRUE
f1539_0_iterate_Store(EOS(STATIC_1539), o167[List3.next]o130, o167[List3.next]o166) -> f1545_0_iterate_JMP(EOS(STATIC_1545), o167[List3.next]o130, o167[List3.next]o166) :|: TRUE
f1545_0_iterate_JMP(EOS(STATIC_1545), o167[List3.next]o130, o167[List3.next]o166) -> f1592_0_iterate_Load(EOS(STATIC_1592), o167[List3.next]o130, o167[List3.next]o166) :|: TRUE
f1592_0_iterate_Load(EOS(STATIC_1592), o167[List3.next]o130, o167[List3.next]o166) -> f1435_0_iterate_Load(EOS(STATIC_1435), o166[List3.next]o167, o166[List3.next]o130, o167[List3.next]o130, o167[List3.next]o166) :|: o166[List3.next]o167 = 1
Combined rules. Obtained 2 IRulesP rules:
f1501_0_iterate_EQ(EOS(STATIC_1501), o131[List3.next]o132:0, o131[List3.next]o130:0, o131[List3.next]o132:0, o131[List3.next]o130:0) -> f1501_0_iterate_EQ(EOS(STATIC_1501), 1, o166[List3.next]o130:0, o167[List3.next]o166:0, o167[List3.next]o130:0) :|: o131[List3.next]o130:0 > -1 && o167[List3.next]o130:0 < o131[List3.next]o130:0 && o167[List3.next]o166:0 < o131[List3.next]o132:0 && o167[List3.next]o130:0 > 0 && o131[List3.next]o132:0 > -1
f1501_0_iterate_EQ(EOS(STATIC_1501), o131[List3.next]o132:0, o131[List3.next]o130:0, o132[List3.next]o131:0, o132[List3.next]o130:0) -> f1501_0_iterate_EQ(EOS(STATIC_1501), o131[List3.next]o165:0, o131[List3.next]o130:0, o165[List3.next]o131:0, o165[List3.next]o130:0) :|: o132[List3.next]o131:0 > 0 && o131[List3.next]o132:0 > 0 && o132[List3.next]o130:0 > -1 && o165[List3.next]o130:0 < o132[List3.next]o130:0 && o165[List3.next]o131:0 < o132[List3.next]o131:0 && o165[List3.next]o130:0 > 0 && o131[List3.next]o165:0 > o131[List3.next]o132:0
Filtered constant ground arguments:
   f1501_0_iterate_EQ(x1, x2, x3, x4, x5) -> f1501_0_iterate_EQ(x2, x3, x4, x5)
   EOS(x1) -> EOS
Finished conversion. Obtained 2 rules.P rules:
f1501_0_iterate_EQ(o131[List3.next]o132:0, o131[List3.next]o130:0, o131[List3.next]o132:0, o131[List3.next]o130:0) -> f1501_0_iterate_EQ(1, o166[List3.next]o130:0, o167[List3.next]o166:0, o167[List3.next]o130:0) :|: o167[List3.next]o130:0 < o131[List3.next]o130:0 && o131[List3.next]o130:0 > -1 && o167[List3.next]o166:0 < o131[List3.next]o132:0 && o131[List3.next]o132:0 > -1 && o167[List3.next]o130:0 > 0
f1501_0_iterate_EQ(o131[List3.next]o132:0, o131[List3.next]o130:0, o132[List3.next]o131:0, o132[List3.next]o130:0) -> f1501_0_iterate_EQ(o131[List3.next]o165:0, o131[List3.next]o130:0, o165[List3.next]o131:0, o165[List3.next]o130:0) :|: o131[List3.next]o132:0 > 0 && o132[List3.next]o131:0 > 0 && o132[List3.next]o130:0 > -1 && o165[List3.next]o130:0 < o132[List3.next]o130:0 && o165[List3.next]o131:0 < o132[List3.next]o131:0 && o131[List3.next]o165:0 > o131[List3.next]o132:0 && o165[List3.next]o130:0 > 0

----------------------------------------

(9)
Obligation:
Rules:
f1501_0_iterate_EQ(o131[List3.next]o132:0, o131[List3.next]o130:0, o131[List3.next]o132:0, o131[List3.next]o130:0) -> f1501_0_iterate_EQ(1, o166[List3.next]o130:0, o167[List3.next]o166:0, o167[List3.next]o130:0) :|: o167[List3.next]o130:0 < o131[List3.next]o130:0 && o131[List3.next]o130:0 > -1 && o167[List3.next]o166:0 < o131[List3.next]o132:0 && o131[List3.next]o132:0 > -1 && o167[List3.next]o130:0 > 0
f1501_0_iterate_EQ(x, x1, x2, x3) -> f1501_0_iterate_EQ(x4, x1, x5, x6) :|: x > 0 && x2 > 0 && x3 > -1 && x6 < x3 && x5 < x2 && x4 > x && x6 > 0

----------------------------------------

(10) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(11)
Obligation:
Rules:
f1501_0_iterate_EQ(o131[List3.next]o132:0, o131[List3.next]o130:0, o131[List3.next]o132:0, o131[List3.next]o130:0) -> f1501_0_iterate_EQ(1, o166[List3.next]o130:0, o167[List3.next]o166:0, o167[List3.next]o130:0) :|: o167[List3.next]o130:0 < o131[List3.next]o130:0 && o131[List3.next]o130:0 > -1 && o167[List3.next]o166:0 < o131[List3.next]o132:0 && o131[List3.next]o132:0 > -1 && o167[List3.next]o130:0 > 0
f1501_0_iterate_EQ(x, x1, x2, x3) -> f1501_0_iterate_EQ(x4, x1, x5, x6) :|: x > 0 && x2 > 0 && x3 > -1 && x6 < x3 && x5 < x2 && x4 > x && x6 > 0

----------------------------------------

(12) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1501_0_iterate_EQ(o131[List3.next]o132:0, o131[List3.next]o130:0, o131[List3.next]o132:0, o131[List3.next]o130:0) -> f1501_0_iterate_EQ(1, o166[List3.next]o130:0, o167[List3.next]o166:0, o167[List3.next]o130:0) :|: o167[List3.next]o130:0 < o131[List3.next]o130:0 && o131[List3.next]o130:0 > -1 && o167[List3.next]o166:0 < o131[List3.next]o132:0 && o131[List3.next]o132:0 > -1 && o167[List3.next]o130:0 > 0
(2) f1501_0_iterate_EQ(x, x1, x2, x3) -> f1501_0_iterate_EQ(x4, x1, x5, x6) :|: x > 0 && x2 > 0 && x3 > -1 && x6 < x3 && x5 < x2 && x4 > x && x6 > 0

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!
----------------------------------------

(13)
Obligation:

Termination digraph:
Nodes:
(1) f1501_0_iterate_EQ(o131[List3.next]o132:0, o131[List3.next]o130:0, o131[List3.next]o132:0, o131[List3.next]o130:0) -> f1501_0_iterate_EQ(1, o166[List3.next]o130:0, o167[List3.next]o166:0, o167[List3.next]o130:0) :|: o167[List3.next]o130:0 < o131[List3.next]o130:0 && o131[List3.next]o130:0 > -1 && o167[List3.next]o166:0 < o131[List3.next]o132:0 && o131[List3.next]o132:0 > -1 && o167[List3.next]o130:0 > 0
(2) f1501_0_iterate_EQ(x, x1, x2, x3) -> f1501_0_iterate_EQ(x4, x1, x5, x6) :|: x > 0 && x2 > 0 && x3 > -1 && x6 < x3 && x5 < x2 && x4 > x && x6 > 0

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!

----------------------------------------

(14) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(15)
Obligation:
Rules:
f1501_0_iterate_EQ(o131[List3.next]o132:0:0, o131[List3.next]o130:0:0, o131[List3.next]o132:0:0, o131[List3.next]o130:0:0) -> f1501_0_iterate_EQ(1, o166[List3.next]o130:0:0, o167[List3.next]o166:0:0, o167[List3.next]o130:0:0) :|: o131[List3.next]o132:0:0 > -1 && o167[List3.next]o130:0:0 > 0 && o167[List3.next]o166:0:0 < o131[List3.next]o132:0:0 && o131[List3.next]o130:0:0 > -1 && o167[List3.next]o130:0:0 < o131[List3.next]o130:0:0
f1501_0_iterate_EQ(x:0, x1:0, x2:0, x3:0) -> f1501_0_iterate_EQ(x4:0, x1:0, x5:0, x6:0) :|: x:0 < x4:0 && x6:0 > 0 && x5:0 < x2:0 && x6:0 < x3:0 && x3:0 > -1 && x2:0 > 0 && x:0 > 0

----------------------------------------

(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1501_0_iterate_EQ(VARIABLE, VARIABLE, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(17)
Obligation:
Rules:
f1501_0_iterate_EQ(o131[List3.next]o132:0:0, o131[List3.next]o130:0:0, o131[List3.next]o132:0:0, o131[List3.next]o130:0:0) -> f1501_0_iterate_EQ(c, o166[List3.next]o130:0:0, o167[List3.next]o166:0:0, o167[List3.next]o130:0:0) :|: c = 1 && (o131[List3.next]o132:0:0 > -1 && o167[List3.next]o130:0:0 > 0 && o167[List3.next]o166:0:0 < o131[List3.next]o132:0:0 && o131[List3.next]o130:0:0 > -1 && o167[List3.next]o130:0:0 < o131[List3.next]o130:0:0)
f1501_0_iterate_EQ(x:0, x1:0, x2:0, x3:0) -> f1501_0_iterate_EQ(x4:0, x1:0, x5:0, x6:0) :|: x:0 < x4:0 && x6:0 > 0 && x5:0 < x2:0 && x6:0 < x3:0 && x3:0 > -1 && x2:0 > 0 && x:0 > 0

----------------------------------------

(18) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f1501_0_iterate_EQ ] = f1501_0_iterate_EQ_3

The following rules are decreasing:
f1501_0_iterate_EQ(o131[List3.next]o132:0:0, o131[List3.next]o130:0:0, o131[List3.next]o132:0:0, o131[List3.next]o130:0:0) -> f1501_0_iterate_EQ(c, o166[List3.next]o130:0:0, o167[List3.next]o166:0:0, o167[List3.next]o130:0:0) :|: c = 1 && (o131[List3.next]o132:0:0 > -1 && o167[List3.next]o130:0:0 > 0 && o167[List3.next]o166:0:0 < o131[List3.next]o132:0:0 && o131[List3.next]o130:0:0 > -1 && o167[List3.next]o130:0:0 < o131[List3.next]o130:0:0)
f1501_0_iterate_EQ(x:0, x1:0, x2:0, x3:0) -> f1501_0_iterate_EQ(x4:0, x1:0, x5:0, x6:0) :|: x:0 < x4:0 && x6:0 > 0 && x5:0 < x2:0 && x6:0 < x3:0 && x3:0 > -1 && x2:0 > 0 && x:0 > 0

The following rules are bounded:
f1501_0_iterate_EQ(o131[List3.next]o132:0:0, o131[List3.next]o130:0:0, o131[List3.next]o132:0:0, o131[List3.next]o130:0:0) -> f1501_0_iterate_EQ(c, o166[List3.next]o130:0:0, o167[List3.next]o166:0:0, o167[List3.next]o130:0:0) :|: c = 1 && (o131[List3.next]o132:0:0 > -1 && o167[List3.next]o130:0:0 > 0 && o167[List3.next]o166:0:0 < o131[List3.next]o132:0:0 && o131[List3.next]o130:0:0 > -1 && o167[List3.next]o130:0:0 < o131[List3.next]o130:0:0)
f1501_0_iterate_EQ(x:0, x1:0, x2:0, x3:0) -> f1501_0_iterate_EQ(x4:0, x1:0, x5:0, x6:0) :|: x:0 < x4:0 && x6:0 > 0 && x5:0 < x2:0 && x6:0 < x3:0 && x3:0 > -1 && x2:0 > 0 && x:0 > 0


----------------------------------------

(19)
YES

----------------------------------------

(20)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: List3.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*List3: [next]
*Marker field analysis yielded the following relations that could be markers:

----------------------------------------

(21) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 25 IRulesP rules:
f1134_0_main_Inc(EOS(STATIC_1134), i84, i84, o82[List3.next]o81) -> f1138_0_main_LE(EOS(STATIC_1138), i84 + -1, i84, o82[List3.next]o81) :|: TRUE
f1138_0_main_LE(EOS(STATIC_1138), i96, i99, o82[List3.next]o81) -> f1144_0_main_LE(EOS(STATIC_1144), i96, i99, o82[List3.next]o81) :|: TRUE
f1144_0_main_LE(EOS(STATIC_1144), i96, i99, o82[List3.next]o81) -> f1152_0_main_Load(EOS(STATIC_1152), i96, o82[List3.next]o81) :|: i99 > 0
f1152_0_main_Load(EOS(STATIC_1152), i96, o82[List3.next]o81) -> f1154_0_main_New(EOS(STATIC_1154), i96, o82[List3.next]o81) :|: TRUE
f1154_0_main_New(EOS(STATIC_1154), i96, o82[List3.next]o81) -> f1156_0_main_Duplicate(EOS(STATIC_1156), i96, o82[List3.next]o81) :|: TRUE
f1156_0_main_Duplicate(EOS(STATIC_1156), i96, o82[List3.next]o81) -> f1159_0_main_InvokeMethod(EOS(STATIC_1159), i96, o82[List3.next]o81) :|: TRUE
f1159_0_main_InvokeMethod(EOS(STATIC_1159), i96, o82[List3.next]o81) -> f1162_0__init__Load(EOS(STATIC_1162), i96, o82[List3.next]o81) :|: TRUE
f1162_0__init__Load(EOS(STATIC_1162), i96, o82[List3.next]o81) -> f1167_0__init__InvokeMethod(EOS(STATIC_1167), i96, o82[List3.next]o81) :|: TRUE
f1167_0__init__InvokeMethod(EOS(STATIC_1167), i96, o82[List3.next]o81) -> f1168_0__init__Return(EOS(STATIC_1168), i96, o82[List3.next]o81) :|: TRUE
f1168_0__init__Return(EOS(STATIC_1168), i96, o82[List3.next]o81) -> f1173_0_main_FieldAccess(EOS(STATIC_1173), i96, o82[List3.next]o81) :|: TRUE
f1173_0_main_FieldAccess(EOS(STATIC_1173), i96, o82[List3.next]o81) -> f1194_0_main_FieldAccess(EOS(STATIC_1194), i96, o82[List3.next]o81) :|: o82[List3.next]o81 > 0
f1173_0_main_FieldAccess(EOS(STATIC_1173), i96, o102[List3.next]o102) -> f1195_0_main_FieldAccess(EOS(STATIC_1195), i96) :|: TRUE
f1194_0_main_FieldAccess(EOS(STATIC_1194), i96, o82[List3.next]o81) -> f1208_0_main_Load(EOS(STATIC_1208), i96, o82[List3.next]o81) :|: TRUE
f1208_0_main_Load(EOS(STATIC_1208), i96, o82[List3.next]o81) -> f1220_0_main_FieldAccess(EOS(STATIC_1220), i96, o82[List3.next]o81) :|: TRUE
f1220_0_main_FieldAccess(EOS(STATIC_1220), i96, o82[List3.next]o81) -> f1237_0_main_Store(EOS(STATIC_1237), i96, o82[List3.next]o87) :|: o82[List3.next]o87 > o82[List3.next]o81 && o82[List3.next]o81 >= 0
f1237_0_main_Store(EOS(STATIC_1237), i96, o82[List3.next]o87) -> f1248_0_main_JMP(EOS(STATIC_1248), i96, o82[List3.next]o87) :|: TRUE
f1248_0_main_JMP(EOS(STATIC_1248), i96, o82[List3.next]o87) -> f1315_0_main_Load(EOS(STATIC_1315), i96, o82[List3.next]o87) :|: TRUE
f1315_0_main_Load(EOS(STATIC_1315), i96, o82[List3.next]o87) -> f1126_0_main_Load(EOS(STATIC_1126), i96, o82[List3.next]o87) :|: TRUE
f1126_0_main_Load(EOS(STATIC_1126), i84, o82[List3.next]o81) -> f1134_0_main_Inc(EOS(STATIC_1134), i84, i84, o82[List3.next]o81) :|: TRUE
f1195_0_main_FieldAccess(EOS(STATIC_1195), i96) -> f1211_0_main_Load(EOS(STATIC_1211), i96) :|: TRUE
f1211_0_main_Load(EOS(STATIC_1211), i96) -> f1225_0_main_FieldAccess(EOS(STATIC_1225), i96) :|: TRUE
f1225_0_main_FieldAccess(EOS(STATIC_1225), i96) -> f1241_0_main_Store(EOS(STATIC_1241), i96) :|: TRUE
f1241_0_main_Store(EOS(STATIC_1241), i96) -> f1252_0_main_JMP(EOS(STATIC_1252), i96) :|: TRUE
f1252_0_main_JMP(EOS(STATIC_1252), i96) -> f1352_0_main_Load(EOS(STATIC_1352), i96) :|: TRUE
f1352_0_main_Load(EOS(STATIC_1352), i96) -> f1126_0_main_Load(EOS(STATIC_1126), i96, o102[List3.next]o87) :|: o102[List3.next]o87 = 1
Combined rules. Obtained 2 IRulesP rules:
f1134_0_main_Inc(EOS(STATIC_1134), i84:0, i84:0, o82[List3.next]o81:0) -> f1134_0_main_Inc(EOS(STATIC_1134), i84:0 - 1, i84:0 - 1, 1) :|: i84:0 > 0
f1134_0_main_Inc(EOS(STATIC_1134), i84:0, i84:0, o82[List3.next]o81:0) -> f1134_0_main_Inc(EOS(STATIC_1134), i84:0 - 1, i84:0 - 1, o82[List3.next]o87:0) :|: o82[List3.next]o81:0 > 0 && o82[List3.next]o87:0 > o82[List3.next]o81:0 && i84:0 > 0
Filtered constant ground arguments:
   f1134_0_main_Inc(x1, x2, x3, x4) -> f1134_0_main_Inc(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f1134_0_main_Inc(x1, x2, x3) -> f1134_0_main_Inc(x2, x3)
Finished conversion. Obtained 2 rules.P rules:
f1134_0_main_Inc(i84:0, o82[List3.next]o81:0) -> f1134_0_main_Inc(i84:0 - 1, 1) :|: i84:0 > 0
f1134_0_main_Inc(i84:0, o82[List3.next]o81:0) -> f1134_0_main_Inc(i84:0 - 1, o82[List3.next]o87:0) :|: o82[List3.next]o87:0 > o82[List3.next]o81:0 && i84:0 > 0 && o82[List3.next]o81:0 > 0

----------------------------------------

(22)
Obligation:
Rules:
f1134_0_main_Inc(i84:0, o82[List3.next]o81:0) -> f1134_0_main_Inc(i84:0 - 1, 1) :|: i84:0 > 0
f1134_0_main_Inc(x, x1) -> f1134_0_main_Inc(x - 1, x2) :|: x2 > x1 && x > 0 && x1 > 0

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(23) IRSFormatTransformerProof (EQUIVALENT)
Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %).
----------------------------------------

(24)
Obligation:
Rules:
f1134_0_main_Inc(i84:0, o82[List3.next]o81:0) -> f1134_0_main_Inc(arith, 1) :|: i84:0 > 0 && arith = i84:0 - 1
f1134_0_main_Inc(x3, x4) -> f1134_0_main_Inc(x5, x6) :|: x6 > x4 && x3 > 0 && x4 > 0 && x5 = x3 - 1

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(25) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1134_0_main_Inc(i84:0, o82[List3.next]o81:0) -> f1134_0_main_Inc(arith, 1) :|: i84:0 > 0 && arith = i84:0 - 1
(2) f1134_0_main_Inc(x3, x4) -> f1134_0_main_Inc(x5, x6) :|: x6 > x4 && x3 > 0 && x4 > 0 && x5 = x3 - 1

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!
----------------------------------------

(26)
Obligation:

Termination digraph:
Nodes:
(1) f1134_0_main_Inc(i84:0, o82[List3.next]o81:0) -> f1134_0_main_Inc(arith, 1) :|: i84:0 > 0 && arith = i84:0 - 1
(2) f1134_0_main_Inc(x3, x4) -> f1134_0_main_Inc(x5, x6) :|: x6 > x4 && x3 > 0 && x4 > 0 && x5 = x3 - 1

Arcs:
(1) -> (1), (2)
(2) -> (1), (2)

This digraph is fully evaluated!

----------------------------------------

(27) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
----------------------------------------

(28)
Obligation:
Rules:
f1134_0_main_Inc(i84:0:0, o82[List3.next]o81:0:0) -> f1134_0_main_Inc(i84:0:0 - 1, 1) :|: i84:0:0 > 0
f1134_0_main_Inc(x3:0, x4:0) -> f1134_0_main_Inc(x3:0 - 1, x6:0) :|: x6:0 > x4:0 && x3:0 > 0 && x4:0 > 0

----------------------------------------

(29) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1134_0_main_Inc(INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(30)
Obligation:
Rules:
f1134_0_main_Inc(i84:0:0, o82[List3.next]o81:0:0) -> f1134_0_main_Inc(c, c1) :|: c1 = 1 && c = i84:0:0 - 1 && i84:0:0 > 0
f1134_0_main_Inc(x3:0, x4:0) -> f1134_0_main_Inc(c2, x6:0) :|: c2 = x3:0 - 1 && (x6:0 > x4:0 && x3:0 > 0 && x4:0 > 0)

----------------------------------------

(31) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f1134_0_main_Inc ] = f1134_0_main_Inc_1

The following rules are decreasing:
f1134_0_main_Inc(i84:0:0, o82[List3.next]o81:0:0) -> f1134_0_main_Inc(c, c1) :|: c1 = 1 && c = i84:0:0 - 1 && i84:0:0 > 0
f1134_0_main_Inc(x3:0, x4:0) -> f1134_0_main_Inc(c2, x6:0) :|: c2 = x3:0 - 1 && (x6:0 > x4:0 && x3:0 > 0 && x4:0 > 0)

The following rules are bounded:
f1134_0_main_Inc(i84:0:0, o82[List3.next]o81:0:0) -> f1134_0_main_Inc(c, c1) :|: c1 = 1 && c = i84:0:0 - 1 && i84:0:0 > 0
f1134_0_main_Inc(x3:0, x4:0) -> f1134_0_main_Inc(c2, x6:0) :|: c2 = x3:0 - 1 && (x6:0 > x4:0 && x3:0 > 0 && x4:0 > 0)


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(32)
YES