/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 366 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) JBCTerminationSCC
        (8) SCCToIRSProof [SOUND, 113 ms]
        (9) IRSwT
        (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (11) IRSwT
        (12) IRSwTTerminationDigraphProof [EQUIVALENT, 44 ms]
        (13) IRSwT
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IRSwT
        (16) TempFilterProof [SOUND, 13 ms]
        (17) IntTRS
        (18) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) JBCTerminationSCC
        (21) SCCToIRSProof [SOUND, 65 ms]
        (22) IRSwT
        (23) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (24) IRSwT
        (25) IRSwTTerminationDigraphProof [EQUIVALENT, 49 ms]
        (26) IRSwT
        (27) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (28) IRSwT
        (29) TempFilterProof [SOUND, 48 ms]
        (30) IntTRS
        (31) RankingReductionPairProof [EQUIVALENT, 0 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:
f1306_0_iterate_EQ(EOS(STATIC_1306), o126[List3.next]o127, o126[List3.next]o125, o127[List3.next]o126, o127[List3.next]o125) -> f1308_0_iterate_Load(EOS(STATIC_1308), o126[List3.next]o127, o126[List3.next]o125, o127[List3.next]o126, o127[List3.next]o125) :|: TRUE
f1308_0_iterate_Load(EOS(STATIC_1308), o126[List3.next]o127, o126[List3.next]o125, o127[List3.next]o126, o127[List3.next]o125) -> f1312_0_iterate_FieldAccess(EOS(STATIC_1312), o126[List3.next]o127, o126[List3.next]o125, o127[List3.next]o126, o127[List3.next]o125) :|: TRUE
f1312_0_iterate_FieldAccess(EOS(STATIC_1312), o126[List3.next]o127, o126[List3.next]o125, o127[List3.next]o126, o127[List3.next]o125) -> f1328_0_iterate_FieldAccess(EOS(STATIC_1328), o126[List3.next]o127, o126[List3.next]o125, o127[List3.next]o125, o127[List3.next]o126) :|: o126[List3.next]o127 > 0 && o127[List3.next]o126 > 0
f1312_0_iterate_FieldAccess(EOS(STATIC_1312), o161[List3.next]o161, o161[List3.next]o125, o161[List3.next]o161, o161[List3.next]o125) -> f1330_0_iterate_FieldAccess(EOS(STATIC_1330), o161[List3.next]o125, o161[List3.next]o161) :|: TRUE
f1328_0_iterate_FieldAccess(EOS(STATIC_1328), o126[List3.next]o162, o126[List3.next]o125, o162[List3.next]o125, o162[List3.next]o126) -> f1336_0_iterate_FieldAccess(EOS(STATIC_1336), o126[List3.next]o125, o126[List3.next]o162, o163[List3.next]o125, o163[List3.next]o126) :|: o163[List3.next]o125 < o162[List3.next]o125 && o162[List3.next]o125 >= 0 && o163[List3.next]o126 < o162[List3.next]o126 && o162[List3.next]o126 >= 0
f1336_0_iterate_FieldAccess(EOS(STATIC_1336), o126[List3.next]o125, o126[List3.next]o162, o163[List3.next]o125, o163[List3.next]o126) -> f1339_0_iterate_Store(EOS(STATIC_1339), o126[List3.next]o125, o163[List3.next]o125, o163[List3.next]o126, o126[List3.next]o163) :|: o126[List3.next]o163 > o126[List3.next]o162 && o126[List3.next]o162 >= 0
f1339_0_iterate_Store(EOS(STATIC_1339), o126[List3.next]o125, o163[List3.next]o125, o163[List3.next]o126, o126[List3.next]o163) -> f1343_0_iterate_JMP(EOS(STATIC_1343), o126[List3.next]o125, o163[List3.next]o125, o163[List3.next]o126, o126[List3.next]o163) :|: TRUE
f1343_0_iterate_JMP(EOS(STATIC_1343), o126[List3.next]o125, o163[List3.next]o125, o163[List3.next]o126, o126[List3.next]o163) -> f1359_0_iterate_Load(EOS(STATIC_1359), o126[List3.next]o125, o163[List3.next]o125, o163[List3.next]o126, o126[List3.next]o163) :|: TRUE
f1359_0_iterate_Load(EOS(STATIC_1359), o126[List3.next]o125, o163[List3.next]o125, o163[List3.next]o126, o126[List3.next]o163) -> f1278_0_iterate_Load(EOS(STATIC_1278), o126[List3.next]o163, o126[List3.next]o125, o163[List3.next]o125, o163[List3.next]o126) :|: TRUE
f1278_0_iterate_Load(EOS(STATIC_1278), o126[List3.next]o127, o126[List3.next]o125, o127[List3.next]o125, o127[List3.next]o126) -> f1285_0_iterate_Load(EOS(STATIC_1285), o126[List3.next]o127, o126[List3.next]o125, o127[List3.next]o125, o127[List3.next]o126) :|: TRUE
f1285_0_iterate_Load(EOS(STATIC_1285), o126[List3.next]o127, o126[List3.next]o125, o127[List3.next]o125, o127[List3.next]o126) -> f1299_0_iterate_EQ(EOS(STATIC_1299), o126[List3.next]o127, o126[List3.next]o125, o127[List3.next]o125, o127[List3.next]o126) :|: TRUE
f1299_0_iterate_EQ(EOS(STATIC_1299), o126[List3.next]o127, o126[List3.next]o125, o127[List3.next]o125, o127[List3.next]o126) -> f1306_0_iterate_EQ(EOS(STATIC_1306), o126[List3.next]o127, o126[List3.next]o125, o127[List3.next]o126, o127[List3.next]o125) :|: o127[List3.next]o125 > 0
f1330_0_iterate_FieldAccess(EOS(STATIC_1330), o164[List3.next]o125, o164[List3.next]o164) -> f1338_0_iterate_FieldAccess(EOS(STATIC_1338), o165[List3.next]o125, o165[List3.next]o164) :|: o165[List3.next]o125 < o164[List3.next]o125 && o164[List3.next]o125 >= 0 && o165[List3.next]o164 < o164[List3.next]o164 && o164[List3.next]o164 >= 0
f1338_0_iterate_FieldAccess(EOS(STATIC_1338), o165[List3.next]o125, o165[List3.next]o164) -> f1341_0_iterate_Store(EOS(STATIC_1341), o165[List3.next]o125, o165[List3.next]o164) :|: TRUE
f1341_0_iterate_Store(EOS(STATIC_1341), o165[List3.next]o125, o165[List3.next]o164) -> f1347_0_iterate_JMP(EOS(STATIC_1347), o165[List3.next]o125, o165[List3.next]o164) :|: TRUE
f1347_0_iterate_JMP(EOS(STATIC_1347), o165[List3.next]o125, o165[List3.next]o164) -> f1380_0_iterate_Load(EOS(STATIC_1380), o165[List3.next]o125, o165[List3.next]o164) :|: TRUE
f1380_0_iterate_Load(EOS(STATIC_1380), o165[List3.next]o125, o165[List3.next]o164) -> f1278_0_iterate_Load(EOS(STATIC_1278), o164[List3.next]o165, o164[List3.next]o125, o165[List3.next]o125, o165[List3.next]o164) :|: o164[List3.next]o165 = 1
Combined rules. Obtained 2 IRulesP rules:
f1306_0_iterate_EQ(EOS(STATIC_1306), o126[List3.next]o127:0, o126[List3.next]o125:0, o126[List3.next]o127:0, o126[List3.next]o125:0) -> f1306_0_iterate_EQ(EOS(STATIC_1306), 1, o164[List3.next]o125:0, o165[List3.next]o164:0, o165[List3.next]o125:0) :|: o126[List3.next]o125:0 > -1 && o165[List3.next]o125:0 < o126[List3.next]o125:0 && o165[List3.next]o164:0 < o126[List3.next]o127:0 && o165[List3.next]o125:0 > 0 && o126[List3.next]o127:0 > -1
f1306_0_iterate_EQ(EOS(STATIC_1306), o126[List3.next]o127:0, o126[List3.next]o125:0, o127[List3.next]o126:0, o127[List3.next]o125:0) -> f1306_0_iterate_EQ(EOS(STATIC_1306), o126[List3.next]o163:0, o126[List3.next]o125:0, o163[List3.next]o126:0, o163[List3.next]o125:0) :|: o127[List3.next]o126:0 > 0 && o126[List3.next]o127:0 > 0 && o127[List3.next]o125:0 > -1 && o163[List3.next]o125:0 < o127[List3.next]o125:0 && o163[List3.next]o126:0 < o127[List3.next]o126:0 && o163[List3.next]o125:0 > 0 && o126[List3.next]o163:0 > o126[List3.next]o127:0
Filtered constant ground arguments:
   f1306_0_iterate_EQ(x1, x2, x3, x4, x5) -> f1306_0_iterate_EQ(x2, x3, x4, x5)
   EOS(x1) -> EOS
Finished conversion. Obtained 2 rules.P rules:
f1306_0_iterate_EQ(o126[List3.next]o127:0, o126[List3.next]o125:0, o126[List3.next]o127:0, o126[List3.next]o125:0) -> f1306_0_iterate_EQ(1, o164[List3.next]o125:0, o165[List3.next]o164:0, o165[List3.next]o125:0) :|: o165[List3.next]o125:0 < o126[List3.next]o125:0 && o126[List3.next]o125:0 > -1 && o165[List3.next]o164:0 < o126[List3.next]o127:0 && o126[List3.next]o127:0 > -1 && o165[List3.next]o125:0 > 0
f1306_0_iterate_EQ(o126[List3.next]o127:0, o126[List3.next]o125:0, o127[List3.next]o126:0, o127[List3.next]o125:0) -> f1306_0_iterate_EQ(o126[List3.next]o163:0, o126[List3.next]o125:0, o163[List3.next]o126:0, o163[List3.next]o125:0) :|: o126[List3.next]o127:0 > 0 && o127[List3.next]o126:0 > 0 && o127[List3.next]o125:0 > -1 && o163[List3.next]o125:0 < o127[List3.next]o125:0 && o163[List3.next]o126:0 < o127[List3.next]o126:0 && o126[List3.next]o163:0 > o126[List3.next]o127:0 && o163[List3.next]o125:0 > 0

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

(9)
Obligation:
Rules:
f1306_0_iterate_EQ(o126[List3.next]o127:0, o126[List3.next]o125:0, o126[List3.next]o127:0, o126[List3.next]o125:0) -> f1306_0_iterate_EQ(1, o164[List3.next]o125:0, o165[List3.next]o164:0, o165[List3.next]o125:0) :|: o165[List3.next]o125:0 < o126[List3.next]o125:0 && o126[List3.next]o125:0 > -1 && o165[List3.next]o164:0 < o126[List3.next]o127:0 && o126[List3.next]o127:0 > -1 && o165[List3.next]o125:0 > 0
f1306_0_iterate_EQ(x, x1, x2, x3) -> f1306_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:
f1306_0_iterate_EQ(o126[List3.next]o127:0, o126[List3.next]o125:0, o126[List3.next]o127:0, o126[List3.next]o125:0) -> f1306_0_iterate_EQ(1, o164[List3.next]o125:0, o165[List3.next]o164:0, o165[List3.next]o125:0) :|: o165[List3.next]o125:0 < o126[List3.next]o125:0 && o126[List3.next]o125:0 > -1 && o165[List3.next]o164:0 < o126[List3.next]o127:0 && o126[List3.next]o127:0 > -1 && o165[List3.next]o125:0 > 0
f1306_0_iterate_EQ(x, x1, x2, x3) -> f1306_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) f1306_0_iterate_EQ(o126[List3.next]o127:0, o126[List3.next]o125:0, o126[List3.next]o127:0, o126[List3.next]o125:0) -> f1306_0_iterate_EQ(1, o164[List3.next]o125:0, o165[List3.next]o164:0, o165[List3.next]o125:0) :|: o165[List3.next]o125:0 < o126[List3.next]o125:0 && o126[List3.next]o125:0 > -1 && o165[List3.next]o164:0 < o126[List3.next]o127:0 && o126[List3.next]o127:0 > -1 && o165[List3.next]o125:0 > 0
(2) f1306_0_iterate_EQ(x, x1, x2, x3) -> f1306_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) f1306_0_iterate_EQ(o126[List3.next]o127:0, o126[List3.next]o125:0, o126[List3.next]o127:0, o126[List3.next]o125:0) -> f1306_0_iterate_EQ(1, o164[List3.next]o125:0, o165[List3.next]o164:0, o165[List3.next]o125:0) :|: o165[List3.next]o125:0 < o126[List3.next]o125:0 && o126[List3.next]o125:0 > -1 && o165[List3.next]o164:0 < o126[List3.next]o127:0 && o126[List3.next]o127:0 > -1 && o165[List3.next]o125:0 > 0
(2) f1306_0_iterate_EQ(x, x1, x2, x3) -> f1306_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:
f1306_0_iterate_EQ(x:0, x1:0, x2:0, x3:0) -> f1306_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
f1306_0_iterate_EQ(o126[List3.next]o127:0:0, o126[List3.next]o125:0:0, o126[List3.next]o127:0:0, o126[List3.next]o125:0:0) -> f1306_0_iterate_EQ(1, o164[List3.next]o125:0:0, o165[List3.next]o164:0:0, o165[List3.next]o125:0:0) :|: o126[List3.next]o127:0:0 > -1 && o165[List3.next]o125:0:0 > 0 && o165[List3.next]o164:0:0 < o126[List3.next]o127:0:0 && o126[List3.next]o125:0:0 > -1 && o165[List3.next]o125:0:0 < o126[List3.next]o125:0:0

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

(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1306_0_iterate_EQ(VARIABLE, VARIABLE, INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(17)
Obligation:
Rules:
f1306_0_iterate_EQ(x:0, x1:0, x2:0, x3:0) -> f1306_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
f1306_0_iterate_EQ(o126[List3.next]o127:0:0, o126[List3.next]o125:0:0, o126[List3.next]o127:0:0, o126[List3.next]o125:0:0) -> f1306_0_iterate_EQ(c, o164[List3.next]o125:0:0, o165[List3.next]o164:0:0, o165[List3.next]o125:0:0) :|: c = 1 && (o126[List3.next]o127:0:0 > -1 && o165[List3.next]o125:0:0 > 0 && o165[List3.next]o164:0:0 < o126[List3.next]o127:0:0 && o126[List3.next]o125:0:0 > -1 && o165[List3.next]o125:0:0 < o126[List3.next]o125:0:0)

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

(18) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f1306_0_iterate_EQ ] = f1306_0_iterate_EQ_4

The following rules are decreasing:
f1306_0_iterate_EQ(x:0, x1:0, x2:0, x3:0) -> f1306_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
f1306_0_iterate_EQ(o126[List3.next]o127:0:0, o126[List3.next]o125:0:0, o126[List3.next]o127:0:0, o126[List3.next]o125:0:0) -> f1306_0_iterate_EQ(c, o164[List3.next]o125:0:0, o165[List3.next]o164:0:0, o165[List3.next]o125:0:0) :|: c = 1 && (o126[List3.next]o127:0:0 > -1 && o165[List3.next]o125:0:0 > 0 && o165[List3.next]o164:0:0 < o126[List3.next]o127:0:0 && o126[List3.next]o125:0:0 > -1 && o165[List3.next]o125:0:0 < o126[List3.next]o125:0:0)

The following rules are bounded:
f1306_0_iterate_EQ(x:0, x1:0, x2:0, x3:0) -> f1306_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
f1306_0_iterate_EQ(o126[List3.next]o127:0:0, o126[List3.next]o125:0:0, o126[List3.next]o127:0:0, o126[List3.next]o125:0:0) -> f1306_0_iterate_EQ(c, o164[List3.next]o125:0:0, o165[List3.next]o164:0:0, o165[List3.next]o125:0:0) :|: c = 1 && (o126[List3.next]o127:0:0 > -1 && o165[List3.next]o125:0:0 > 0 && o165[List3.next]o164:0:0 < o126[List3.next]o127:0:0 && o126[List3.next]o125:0:0 > -1 && o165[List3.next]o125:0:0 < o126[List3.next]o125:0:0)


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

(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:
f1011_0_main_Inc(EOS(STATIC_1011), i84, i84, o82[List3.next]o81) -> f1014_0_main_LE(EOS(STATIC_1014), i84 + -1, i84, o82[List3.next]o81) :|: TRUE
f1014_0_main_LE(EOS(STATIC_1014), i88, i92, o82[List3.next]o81) -> f1021_0_main_LE(EOS(STATIC_1021), i88, i92, o82[List3.next]o81) :|: TRUE
f1021_0_main_LE(EOS(STATIC_1021), i88, i92, o82[List3.next]o81) -> f1023_0_main_Load(EOS(STATIC_1023), i88, o82[List3.next]o81) :|: i92 > 0
f1023_0_main_Load(EOS(STATIC_1023), i88, o82[List3.next]o81) -> f1025_0_main_New(EOS(STATIC_1025), i88, o82[List3.next]o81) :|: TRUE
f1025_0_main_New(EOS(STATIC_1025), i88, o82[List3.next]o81) -> f1027_0_main_Duplicate(EOS(STATIC_1027), i88, o82[List3.next]o81) :|: TRUE
f1027_0_main_Duplicate(EOS(STATIC_1027), i88, o82[List3.next]o81) -> f1037_0_main_InvokeMethod(EOS(STATIC_1037), i88, o82[List3.next]o81) :|: TRUE
f1037_0_main_InvokeMethod(EOS(STATIC_1037), i88, o82[List3.next]o81) -> f1055_0__init__Load(EOS(STATIC_1055), i88, o82[List3.next]o81) :|: TRUE
f1055_0__init__Load(EOS(STATIC_1055), i88, o82[List3.next]o81) -> f1063_0__init__InvokeMethod(EOS(STATIC_1063), i88, o82[List3.next]o81) :|: TRUE
f1063_0__init__InvokeMethod(EOS(STATIC_1063), i88, o82[List3.next]o81) -> f1064_0__init__Return(EOS(STATIC_1064), i88, o82[List3.next]o81) :|: TRUE
f1064_0__init__Return(EOS(STATIC_1064), i88, o82[List3.next]o81) -> f1067_0_main_FieldAccess(EOS(STATIC_1067), i88, o82[List3.next]o81) :|: TRUE
f1067_0_main_FieldAccess(EOS(STATIC_1067), i88, o82[List3.next]o81) -> f1070_0_main_FieldAccess(EOS(STATIC_1070), i88, o82[List3.next]o81) :|: o82[List3.next]o81 > 0
f1067_0_main_FieldAccess(EOS(STATIC_1067), i88, o101[List3.next]o101) -> f1071_0_main_FieldAccess(EOS(STATIC_1071), i88) :|: TRUE
f1070_0_main_FieldAccess(EOS(STATIC_1070), i88, o82[List3.next]o81) -> f1075_0_main_Load(EOS(STATIC_1075), i88, o82[List3.next]o81) :|: TRUE
f1075_0_main_Load(EOS(STATIC_1075), i88, o82[List3.next]o81) -> f1090_0_main_FieldAccess(EOS(STATIC_1090), i88, o82[List3.next]o81) :|: TRUE
f1090_0_main_FieldAccess(EOS(STATIC_1090), i88, o82[List3.next]o81) -> f1103_0_main_Store(EOS(STATIC_1103), i88, o82[List3.next]o85) :|: o82[List3.next]o85 > o82[List3.next]o81 && o82[List3.next]o81 >= 0
f1103_0_main_Store(EOS(STATIC_1103), i88, o82[List3.next]o85) -> f1114_0_main_JMP(EOS(STATIC_1114), i88, o82[List3.next]o85) :|: TRUE
f1114_0_main_JMP(EOS(STATIC_1114), i88, o82[List3.next]o85) -> f1191_0_main_Load(EOS(STATIC_1191), i88, o82[List3.next]o85) :|: TRUE
f1191_0_main_Load(EOS(STATIC_1191), i88, o82[List3.next]o85) -> f1000_0_main_Load(EOS(STATIC_1000), i88, o82[List3.next]o85) :|: TRUE
f1000_0_main_Load(EOS(STATIC_1000), i84, o82[List3.next]o81) -> f1011_0_main_Inc(EOS(STATIC_1011), i84, i84, o82[List3.next]o81) :|: TRUE
f1071_0_main_FieldAccess(EOS(STATIC_1071), i88) -> f1081_0_main_Load(EOS(STATIC_1081), i88) :|: TRUE
f1081_0_main_Load(EOS(STATIC_1081), i88) -> f1093_0_main_FieldAccess(EOS(STATIC_1093), i88) :|: TRUE
f1093_0_main_FieldAccess(EOS(STATIC_1093), i88) -> f1107_0_main_Store(EOS(STATIC_1107), i88) :|: TRUE
f1107_0_main_Store(EOS(STATIC_1107), i88) -> f1118_0_main_JMP(EOS(STATIC_1118), i88) :|: TRUE
f1118_0_main_JMP(EOS(STATIC_1118), i88) -> f1219_0_main_Load(EOS(STATIC_1219), i88) :|: TRUE
f1219_0_main_Load(EOS(STATIC_1219), i88) -> f1000_0_main_Load(EOS(STATIC_1000), i88, o101[List3.next]o85) :|: o101[List3.next]o85 = 1
Combined rules. Obtained 2 IRulesP rules:
f1011_0_main_Inc(EOS(STATIC_1011), i84:0, i84:0, o82[List3.next]o81:0) -> f1011_0_main_Inc(EOS(STATIC_1011), i84:0 - 1, i84:0 - 1, o82[List3.next]o85:0) :|: o82[List3.next]o81:0 > 0 && o82[List3.next]o85:0 > o82[List3.next]o81:0 && i84:0 > 0
f1011_0_main_Inc(EOS(STATIC_1011), i84:0, i84:0, o82[List3.next]o81:0) -> f1011_0_main_Inc(EOS(STATIC_1011), i84:0 - 1, i84:0 - 1, 1) :|: i84:0 > 0
Filtered constant ground arguments:
   f1011_0_main_Inc(x1, x2, x3, x4) -> f1011_0_main_Inc(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f1011_0_main_Inc(x1, x2, x3) -> f1011_0_main_Inc(x2, x3)
Finished conversion. Obtained 2 rules.P rules:
f1011_0_main_Inc(i84:0, o82[List3.next]o81:0) -> f1011_0_main_Inc(i84:0 - 1, o82[List3.next]o85:0) :|: o82[List3.next]o85:0 > o82[List3.next]o81:0 && i84:0 > 0 && o82[List3.next]o81:0 > 0
f1011_0_main_Inc(i84:0, o82[List3.next]o81:0) -> f1011_0_main_Inc(i84:0 - 1, 1) :|: i84:0 > 0

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

(22)
Obligation:
Rules:
f1011_0_main_Inc(i84:0, o82[List3.next]o81:0) -> f1011_0_main_Inc(i84:0 - 1, o82[List3.next]o85:0) :|: o82[List3.next]o85:0 > o82[List3.next]o81:0 && i84:0 > 0 && o82[List3.next]o81:0 > 0
f1011_0_main_Inc(x, x1) -> f1011_0_main_Inc(x - 1, 1) :|: x > 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:
f1011_0_main_Inc(i84:0, o82[List3.next]o81:0) -> f1011_0_main_Inc(arith, o82[List3.next]o85:0) :|: o82[List3.next]o85:0 > o82[List3.next]o81:0 && i84:0 > 0 && o82[List3.next]o81:0 > 0 && arith = i84:0 - 1
f1011_0_main_Inc(x2, x3) -> f1011_0_main_Inc(x4, 1) :|: x2 > 0 && x4 = x2 - 1

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(25) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1011_0_main_Inc(i84:0, o82[List3.next]o81:0) -> f1011_0_main_Inc(arith, o82[List3.next]o85:0) :|: o82[List3.next]o85:0 > o82[List3.next]o81:0 && i84:0 > 0 && o82[List3.next]o81:0 > 0 && arith = i84:0 - 1
(2) f1011_0_main_Inc(x2, x3) -> f1011_0_main_Inc(x4, 1) :|: x2 > 0 && x4 = x2 - 1

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

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

(26)
Obligation:

Termination digraph:
Nodes:
(1) f1011_0_main_Inc(i84:0, o82[List3.next]o81:0) -> f1011_0_main_Inc(arith, o82[List3.next]o85:0) :|: o82[List3.next]o85:0 > o82[List3.next]o81:0 && i84:0 > 0 && o82[List3.next]o81:0 > 0 && arith = i84:0 - 1
(2) f1011_0_main_Inc(x2, x3) -> f1011_0_main_Inc(x4, 1) :|: x2 > 0 && x4 = x2 - 1

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

This digraph is fully evaluated!

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

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

(28)
Obligation:
Rules:
f1011_0_main_Inc(i84:0:0, o82[List3.next]o81:0:0) -> f1011_0_main_Inc(i84:0:0 - 1, o82[List3.next]o85:0:0) :|: o82[List3.next]o85:0:0 > o82[List3.next]o81:0:0 && i84:0:0 > 0 && o82[List3.next]o81:0:0 > 0
f1011_0_main_Inc(x2:0, x3:0) -> f1011_0_main_Inc(x2:0 - 1, 1) :|: x2:0 > 0

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

(29) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1011_0_main_Inc(INTEGER, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(30)
Obligation:
Rules:
f1011_0_main_Inc(i84:0:0, o82[List3.next]o81:0:0) -> f1011_0_main_Inc(c, o82[List3.next]o85:0:0) :|: c = i84:0:0 - 1 && (o82[List3.next]o85:0:0 > o82[List3.next]o81:0:0 && i84:0:0 > 0 && o82[List3.next]o81:0:0 > 0)
f1011_0_main_Inc(x2:0, x3:0) -> f1011_0_main_Inc(c1, c2) :|: c2 = 1 && c1 = x2:0 - 1 && x2:0 > 0

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

(31) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f1011_0_main_Inc ] = f1011_0_main_Inc_1

The following rules are decreasing:
f1011_0_main_Inc(i84:0:0, o82[List3.next]o81:0:0) -> f1011_0_main_Inc(c, o82[List3.next]o85:0:0) :|: c = i84:0:0 - 1 && (o82[List3.next]o85:0:0 > o82[List3.next]o81:0:0 && i84:0:0 > 0 && o82[List3.next]o81:0:0 > 0)
f1011_0_main_Inc(x2:0, x3:0) -> f1011_0_main_Inc(c1, c2) :|: c2 = 1 && c1 = x2:0 - 1 && x2:0 > 0

The following rules are bounded:
f1011_0_main_Inc(i84:0:0, o82[List3.next]o81:0:0) -> f1011_0_main_Inc(c, o82[List3.next]o85:0:0) :|: c = i84:0:0 - 1 && (o82[List3.next]o85:0:0 > o82[List3.next]o81:0:0 && i84:0:0 > 0 && o82[List3.next]o81:0:0 > 0)
f1011_0_main_Inc(x2:0, x3:0) -> f1011_0_main_Inc(c1, c2) :|: c2 = 1 && c1 = x2:0 - 1 && x2:0 > 0


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

(32)
YES