/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 622 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) JBCTerminationSCC
        (8) SCCToIRSProof [SOUND, 43 ms]
        (9) IRSwT
        (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (11) IRSwT
        (12) IRSwTTerminationDigraphProof [EQUIVALENT, 11 ms]
        (13) IRSwT
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IRSwT
        (16) TempFilterProof [SOUND, 2 ms]
        (17) IRSwT
        (18) IRSwTToQDPProof [SOUND, 0 ms]
        (19) QDP
        (20) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (21) YES
    (22) JBCTerminationSCC
        (23) SCCToQDPProof [SOUND, 100 ms]
        (24) QDP
        (25) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (26) YES
    (27) JBCTerminationSCC
        (28) SCCToIRSProof [SOUND, 45 ms]
        (29) IRSwT
        (30) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (31) IRSwT
        (32) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms]
        (33) IRSwT
        (34) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (35) IRSwT
        (36) TempFilterProof [SOUND, 5 ms]
        (37) IntTRS
        (38) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (39) YES
    (40) JBCTerminationSCC
        (41) SCCToIRSProof [SOUND, 44 ms]
        (42) IRSwT
        (43) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (44) IRSwT
        (45) IRSwTTerminationDigraphProof [EQUIVALENT, 24 ms]
        (46) IRSwT
        (47) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (48) IRSwT
        (49) TempFilterProof [SOUND, 45 ms]
        (50) IntTRS
        (51) RankingReductionPairProof [EQUIVALENT, 26 ms]
        (52) IntTRS
        (53) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (54) YES


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

(0)
Obligation:
need to prove termination of the following program:
public class Test7 {
    public static void main(String[] args) {
	List[] ls = { List.mk(args.length), List.mk(args.length), List.mk(args.length) };

	for (int k = 0; k < ls.length; k++) {
	    int len = length(ls[0]);
	    for (int i = 0; i < len; i++)
		bubble(ls[0]);
	}
    }

    private static void bubble(List l) {
	for (List cursor = l; cursor != null && cursor.getTail() != null; cursor = cursor.getTail())
	    if (cursor.head > cursor.getTail().head) {
		int temp = cursor.head;
		cursor.head = cursor.getTail().head;
		cursor.getTail().head = temp;
	    }
    }

    private static int length(List list) {
	int len = 0;

	while (list != null) {
	    list = list.getTail();
	    len++;
	}

	return len;
    }
}

public class List {
    public int head;
    private List tail;

    public List(int head, List tail) {
	this.head = head;
	this.tail = tail;
    }

    public List getTail() {
	return tail;
    }

    public static List mk(int len) {
	List result = null;

	while (len-- > 0)
	    result = new List(len, result);

	return result;
    }
}


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

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

(2)
Obligation:
need to prove termination of the following program:
public class Test7 {
    public static void main(String[] args) {
	List[] ls = { List.mk(args.length), List.mk(args.length), List.mk(args.length) };

	for (int k = 0; k < ls.length; k++) {
	    int len = length(ls[0]);
	    for (int i = 0; i < len; i++)
		bubble(ls[0]);
	}
    }

    private static void bubble(List l) {
	for (List cursor = l; cursor != null && cursor.getTail() != null; cursor = cursor.getTail())
	    if (cursor.head > cursor.getTail().head) {
		int temp = cursor.head;
		cursor.head = cursor.getTail().head;
		cursor.getTail().head = temp;
	    }
    }

    private static int length(List list) {
	int len = 0;

	while (list != null) {
	    list = list.getTail();
	    len++;
	}

	return len;
    }
}

public class List {
    public int head;
    private List tail;

    public List(int head, List tail) {
	this.head = head;
	this.tail = tail;
    }

    public List getTail() {
	return tail;
    }

    public static List mk(int len) {
	List result = null;

	while (len-- > 0)
	    result = new List(len, result);

	return result;
    }
}


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

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

(4)
Obligation:
Termination Graph based on JBC Program:
Test7.main([Ljava/lang/String;)V: Graph of 83 nodes with 1 SCC.



List.mk(I)LList;: Graph of 54 nodes with 1 SCC.



Test7.length(LList;)I: Graph of 22 nodes with 1 SCC.



Test7.bubble(LList;)V: Graph of 63 nodes with 1 SCC.





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

(5) TerminationGraphToSCCProof (SOUND)
Splitted TerminationGraph to 4 SCCss.
----------------------------------------

(6)
Complex Obligation (AND)

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

(7)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: Test7.bubble(LList;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*List: [tail, head]
*Marker field analysis yielded the following relations that could be markers:

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

(8) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 55 IRulesP rules:
f3176_0_bubble_NULL(EOS(STATIC_3176), java.lang.Object(o465sub), java.lang.Object(o465sub)) -> f3177_0_bubble_NULL(EOS(STATIC_3177), java.lang.Object(o465sub), java.lang.Object(o465sub)) :|: TRUE
f3177_0_bubble_NULL(EOS(STATIC_3177), java.lang.Object(o465sub), java.lang.Object(o465sub)) -> f3179_0_bubble_Load(EOS(STATIC_3179), java.lang.Object(o465sub)) :|: TRUE
f3179_0_bubble_Load(EOS(STATIC_3179), java.lang.Object(o465sub)) -> f3181_0_bubble_InvokeMethod(EOS(STATIC_3181), java.lang.Object(o465sub), java.lang.Object(o465sub)) :|: TRUE
f3181_0_bubble_InvokeMethod(EOS(STATIC_3181), java.lang.Object(o465sub), java.lang.Object(o465sub)) -> f3183_0_getTail_Load(EOS(STATIC_3183), java.lang.Object(o465sub), java.lang.Object(o465sub)) :|: TRUE
f3183_0_getTail_Load(EOS(STATIC_3183), java.lang.Object(o465sub), java.lang.Object(o465sub)) -> f3188_0_getTail_FieldAccess(EOS(STATIC_3188), java.lang.Object(o465sub), java.lang.Object(o465sub)) :|: TRUE
f3188_0_getTail_FieldAccess(EOS(STATIC_3188), java.lang.Object(List(EOC, o471, i497)), java.lang.Object(List(EOC, o471, i497))) -> f3190_0_getTail_FieldAccess(EOS(STATIC_3190), java.lang.Object(List(EOC, o471, i497)), java.lang.Object(List(EOC, o471, i497))) :|: TRUE
f3190_0_getTail_FieldAccess(EOS(STATIC_3190), java.lang.Object(List(EOC, o471, i497)), java.lang.Object(List(EOC, o471, i497))) -> f3192_0_getTail_Return(EOS(STATIC_3192), java.lang.Object(List(EOC, o471, i497)), o471) :|: TRUE
f3192_0_getTail_Return(EOS(STATIC_3192), java.lang.Object(List(EOC, o471, i497)), o471) -> f3194_0_bubble_NULL(EOS(STATIC_3194), java.lang.Object(List(EOC, o471, i497)), o471) :|: TRUE
f3194_0_bubble_NULL(EOS(STATIC_3194), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), java.lang.Object(o472sub)) -> f3197_0_bubble_NULL(EOS(STATIC_3197), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), java.lang.Object(o472sub)) :|: TRUE
f3197_0_bubble_NULL(EOS(STATIC_3197), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), java.lang.Object(o472sub)) -> f3200_0_bubble_Load(EOS(STATIC_3200), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497))) :|: TRUE
f3200_0_bubble_Load(EOS(STATIC_3200), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497))) -> f3206_0_bubble_FieldAccess(EOS(STATIC_3206), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497))) :|: TRUE
f3206_0_bubble_FieldAccess(EOS(STATIC_3206), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497))) -> f3207_0_bubble_Load(EOS(STATIC_3207), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), i497) :|: TRUE
f3207_0_bubble_Load(EOS(STATIC_3207), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), i497) -> f3208_0_bubble_InvokeMethod(EOS(STATIC_3208), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(o472sub), i497))) :|: TRUE
f3208_0_bubble_InvokeMethod(EOS(STATIC_3208), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(o472sub), i497))) -> f3209_0_getTail_Load(EOS(STATIC_3209), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(o472sub), i497))) :|: TRUE
f3209_0_getTail_Load(EOS(STATIC_3209), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(o472sub), i497))) -> f3210_0_getTail_FieldAccess(EOS(STATIC_3210), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(o472sub), i497))) :|: TRUE
f3210_0_getTail_FieldAccess(EOS(STATIC_3210), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(o472sub), i497))) -> f3211_0_getTail_Return(EOS(STATIC_3211), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), i497, java.lang.Object(o472sub)) :|: TRUE
f3211_0_getTail_Return(EOS(STATIC_3211), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), i497, java.lang.Object(o472sub)) -> f3212_0_bubble_FieldAccess(EOS(STATIC_3212), java.lang.Object(List(EOC, java.lang.Object(o472sub), i497)), i497, java.lang.Object(o472sub)) :|: TRUE
f3212_0_bubble_FieldAccess(EOS(STATIC_3212), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, o476, i498))) -> f3213_0_bubble_FieldAccess(EOS(STATIC_3213), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, o476, i498))) :|: TRUE
f3213_0_bubble_FieldAccess(EOS(STATIC_3213), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, o476, i498))) -> f3214_0_bubble_LE(EOS(STATIC_3214), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, i498) :|: TRUE
f3214_0_bubble_LE(EOS(STATIC_3214), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, i498) -> f3215_0_bubble_LE(EOS(STATIC_3215), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, i498) :|: i497 <= i498
f3214_0_bubble_LE(EOS(STATIC_3214), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, i498) -> f3216_0_bubble_LE(EOS(STATIC_3216), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, i498) :|: i497 > i498
f3215_0_bubble_LE(EOS(STATIC_3215), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, i498) -> f3218_0_bubble_Load(EOS(STATIC_3218), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) :|: i497 <= i498
f3218_0_bubble_Load(EOS(STATIC_3218), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) -> f3225_0_bubble_InvokeMethod(EOS(STATIC_3225), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) :|: TRUE
f3225_0_bubble_InvokeMethod(EOS(STATIC_3225), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) -> f3230_0_getTail_Load(EOS(STATIC_3230), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) :|: TRUE
f3230_0_getTail_Load(EOS(STATIC_3230), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) -> f3239_0_getTail_FieldAccess(EOS(STATIC_3239), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) :|: TRUE
f3239_0_getTail_FieldAccess(EOS(STATIC_3239), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) -> f3245_0_getTail_Return(EOS(STATIC_3245), java.lang.Object(List(EOC, o476, i498))) :|: TRUE
f3245_0_getTail_Return(EOS(STATIC_3245), java.lang.Object(List(EOC, o476, i498))) -> f3249_0_bubble_Store(EOS(STATIC_3249), java.lang.Object(List(EOC, o476, i498))) :|: TRUE
f3249_0_bubble_Store(EOS(STATIC_3249), java.lang.Object(List(EOC, o476, i498))) -> f3254_0_bubble_JMP(EOS(STATIC_3254), java.lang.Object(List(EOC, o476, i498))) :|: TRUE
f3254_0_bubble_JMP(EOS(STATIC_3254), java.lang.Object(List(EOC, o476, i498))) -> f3260_0_bubble_Load(EOS(STATIC_3260), java.lang.Object(List(EOC, o476, i498))) :|: TRUE
f3260_0_bubble_Load(EOS(STATIC_3260), java.lang.Object(List(EOC, o476, i498))) -> f3175_0_bubble_Load(EOS(STATIC_3175), java.lang.Object(List(EOC, o476, i498))) :|: TRUE
f3175_0_bubble_Load(EOS(STATIC_3175), o461) -> f3176_0_bubble_NULL(EOS(STATIC_3176), o461, o461) :|: TRUE
f3216_0_bubble_LE(EOS(STATIC_3216), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, i498) -> f3223_0_bubble_Load(EOS(STATIC_3223), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) :|: i497 > i498
f3223_0_bubble_Load(EOS(STATIC_3223), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) -> f3227_0_bubble_FieldAccess(EOS(STATIC_3227), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) :|: TRUE
f3227_0_bubble_FieldAccess(EOS(STATIC_3227), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) -> f3232_0_bubble_Store(EOS(STATIC_3232), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497) :|: TRUE
f3232_0_bubble_Store(EOS(STATIC_3232), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497) -> f3235_0_bubble_Load(EOS(STATIC_3235), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497) :|: TRUE
f3235_0_bubble_Load(EOS(STATIC_3235), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497) -> f3241_0_bubble_Load(EOS(STATIC_3241), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) :|: TRUE
f3241_0_bubble_Load(EOS(STATIC_3241), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) -> f3247_0_bubble_InvokeMethod(EOS(STATIC_3247), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) :|: TRUE
f3247_0_bubble_InvokeMethod(EOS(STATIC_3247), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) -> f3252_0_getTail_Load(EOS(STATIC_3252), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) :|: TRUE
f3252_0_getTail_Load(EOS(STATIC_3252), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) -> f3261_0_getTail_FieldAccess(EOS(STATIC_3261), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) :|: TRUE
f3261_0_getTail_FieldAccess(EOS(STATIC_3261), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497))) -> f3262_0_getTail_Return(EOS(STATIC_3262), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), java.lang.Object(List(EOC, o476, i498))) :|: TRUE
f3262_0_getTail_Return(EOS(STATIC_3262), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), java.lang.Object(List(EOC, o476, i498))) -> f3263_0_bubble_FieldAccess(EOS(STATIC_3263), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), java.lang.Object(List(EOC, o476, i498))) :|: TRUE
f3263_0_bubble_FieldAccess(EOS(STATIC_3263), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), java.lang.Object(List(EOC, o476, i498))) -> f3264_0_bubble_FieldAccess(EOS(STATIC_3264), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i498) :|: TRUE
f3264_0_bubble_FieldAccess(EOS(STATIC_3264), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i497)), i498) -> f3265_0_bubble_Load(EOS(STATIC_3265), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), i497) :|: TRUE
f3265_0_bubble_Load(EOS(STATIC_3265), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), i497) -> f3266_0_bubble_InvokeMethod(EOS(STATIC_3266), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498))) :|: TRUE
f3266_0_bubble_InvokeMethod(EOS(STATIC_3266), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498))) -> f3267_0_getTail_Load(EOS(STATIC_3267), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498))) :|: TRUE
f3267_0_getTail_Load(EOS(STATIC_3267), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498))) -> f3268_0_getTail_FieldAccess(EOS(STATIC_3268), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498))) :|: TRUE
f3268_0_getTail_FieldAccess(EOS(STATIC_3268), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), i497, java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498))) -> f3269_0_getTail_Return(EOS(STATIC_3269), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), i497, java.lang.Object(List(EOC, o476, i498))) :|: TRUE
f3269_0_getTail_Return(EOS(STATIC_3269), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), i497, java.lang.Object(List(EOC, o476, i498))) -> f3270_0_bubble_Load(EOS(STATIC_3270), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), i497, java.lang.Object(List(EOC, o476, i498))) :|: TRUE
f3270_0_bubble_Load(EOS(STATIC_3270), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), i497, java.lang.Object(List(EOC, o476, i498))) -> f3271_0_bubble_FieldAccess(EOS(STATIC_3271), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), java.lang.Object(List(EOC, o476, i498)), i497) :|: TRUE
f3271_0_bubble_FieldAccess(EOS(STATIC_3271), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i498)), i498)), java.lang.Object(List(EOC, o476, i498)), i497) -> f3272_0_bubble_Load(EOS(STATIC_3272), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i497)), i498))) :|: TRUE
f3272_0_bubble_Load(EOS(STATIC_3272), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i497)), i498))) -> f3276_0_bubble_InvokeMethod(EOS(STATIC_3276), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i497)), i498))) :|: TRUE
f3276_0_bubble_InvokeMethod(EOS(STATIC_3276), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i497)), i498))) -> f3277_0_getTail_Load(EOS(STATIC_3277), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i497)), i498))) :|: TRUE
f3277_0_getTail_Load(EOS(STATIC_3277), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i497)), i498))) -> f3278_0_getTail_FieldAccess(EOS(STATIC_3278), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i497)), i498))) :|: TRUE
f3278_0_getTail_FieldAccess(EOS(STATIC_3278), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476, i497)), i498))) -> f3279_0_getTail_Return(EOS(STATIC_3279), java.lang.Object(List(EOC, o476, i497))) :|: TRUE
f3279_0_getTail_Return(EOS(STATIC_3279), java.lang.Object(List(EOC, o476, i497))) -> f3245_0_getTail_Return(EOS(STATIC_3245), java.lang.Object(List(EOC, o476, i497))) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f3176_0_bubble_NULL(EOS(STATIC_3176), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476:0, i498:0)), i497:0)), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476:0, i498:0)), i497:0))) -> f3176_0_bubble_NULL(EOS(STATIC_3176), java.lang.Object(List(EOC, o476:0, i498:0)), java.lang.Object(List(EOC, o476:0, i498:0))) :|: i498:0 >= i497:0
f3176_0_bubble_NULL(EOS(STATIC_3176), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476:0, i498:0)), i497:0)), java.lang.Object(List(EOC, java.lang.Object(List(EOC, o476:0, i498:0)), i497:0))) -> f3176_0_bubble_NULL(EOS(STATIC_3176), java.lang.Object(List(EOC, o476:0, i497:0)), java.lang.Object(List(EOC, o476:0, i497:0))) :|: i498:0 < i497:0
Filtered constant ground arguments:
   f3176_0_bubble_NULL(x1, x2, x3) -> f3176_0_bubble_NULL(x2, x3)
   EOS(x1) -> EOS
   List(x1, x2, x3) -> List(x2, x3)
Filtered duplicate arguments:
   f3176_0_bubble_NULL(x1, x2) -> f3176_0_bubble_NULL(x2)
Finished conversion. Obtained 2 rules.P rules:
f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(o476:0, i498:0)), i497:0)), i497:0) -> f3176_0_bubble_NULL(java.lang.Object(List(o476:0, i498:0)), i498:0) :|: i498:0 >= i497:0
f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(o476:0, i498:0)), i497:0)), i497:0) -> f3176_0_bubble_NULL(java.lang.Object(List(o476:0, i497:0)), i497:0) :|: i498:0 < i497:0

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

(9)
Obligation:
Rules:
f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(o476:0, i498:0)), i497:0)), i497:0) -> f3176_0_bubble_NULL(java.lang.Object(List(o476:0, i498:0)), i498:0) :|: i498:0 >= i497:0
f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(x, x1)), x2)), x2) -> f3176_0_bubble_NULL(java.lang.Object(List(x, x2)), x2) :|: x1 < x2

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

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

(11)
Obligation:
Rules:
f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(o476:0, i498:0)), i497:0)), i497:0) -> f3176_0_bubble_NULL(java.lang.Object(List(o476:0, i498:0)), i498:0) :|: i498:0 >= i497:0
f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(x, x1)), x2)), x2) -> f3176_0_bubble_NULL(java.lang.Object(List(x, x2)), x2) :|: x1 < x2

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

(12) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(o476:0, i498:0)), i497:0)), i497:0) -> f3176_0_bubble_NULL(java.lang.Object(List(o476:0, i498:0)), i498:0) :|: i498:0 >= i497:0
(2) f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(x, x1)), x2)), x2) -> f3176_0_bubble_NULL(java.lang.Object(List(x, x2)), x2) :|: x1 < x2

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

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

(13)
Obligation:

Termination digraph:
Nodes:
(1) f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(o476:0, i498:0)), i497:0)), i497:0) -> f3176_0_bubble_NULL(java.lang.Object(List(o476:0, i498:0)), i498:0) :|: i498:0 >= i497:0
(2) f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(x, x1)), x2)), x2) -> f3176_0_bubble_NULL(java.lang.Object(List(x, x2)), x2) :|: x1 < x2

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

This digraph is fully evaluated!

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

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

(15)
Obligation:
Rules:
f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(x:0, x1:0)), x2:0)), x2:0) -> f3176_0_bubble_NULL(java.lang.Object(List(x:0, x2:0)), x2:0) :|: x2:0 > x1:0
f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(o476:0:0, i498:0:0)), i497:0:0)), i497:0:0) -> f3176_0_bubble_NULL(java.lang.Object(List(o476:0:0, i498:0:0)), i498:0:0) :|: i498:0:0 >= i497:0:0

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

(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f3176_0_bubble_NULL(VARIABLE, INTEGER)
java.lang.Object(VARIABLE)
List(VARIABLE, INTEGER)
Removed predefined arithmetic.
----------------------------------------

(17)
Obligation:
Rules:
f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(x:0))))) -> f3176_0_bubble_NULL(java.lang.Object(List(x:0)))

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

(18) IRSwTToQDPProof (SOUND)
Removed the integers and created a QDP-Problem.
----------------------------------------

(19)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(x:0))))) -> f3176_0_bubble_NULL(java.lang.Object(List(x:0)))

R is empty.
Q is empty.
We have to consider all (P,Q,R)-chains.
----------------------------------------

(20) QDPSizeChangeProof (EQUIVALENT)
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. 

From the DPs we obtained the following set of size-change graphs:
*f3176_0_bubble_NULL(java.lang.Object(List(java.lang.Object(List(x:0))))) -> f3176_0_bubble_NULL(java.lang.Object(List(x:0)))
The graph contains the following edges 1 > 1


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

(21)
YES

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

(22)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: Test7.length(LList;)I
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*List: [tail]
*Marker field analysis yielded the following relations that could be markers:

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

(23) SCCToQDPProof (SOUND)
Transformed TerminationGraph SCC to QDP. Log: 
Generated 13 rules for P and 0 rules for R.P rules:
f1878_0_length_NULL(EOS(STATIC_1878), java.lang.Object(o247sub), java.lang.Object(o247sub)) -> f1883_0_length_NULL(EOS(STATIC_1883), java.lang.Object(o247sub), java.lang.Object(o247sub)) :|: TRUE
f1883_0_length_NULL(EOS(STATIC_1883), java.lang.Object(o247sub), java.lang.Object(o247sub)) -> f1887_0_length_Load(EOS(STATIC_1887), java.lang.Object(o247sub)) :|: TRUE
f1887_0_length_Load(EOS(STATIC_1887), java.lang.Object(o247sub)) -> f1891_0_length_InvokeMethod(EOS(STATIC_1891), java.lang.Object(o247sub)) :|: TRUE
f1891_0_length_InvokeMethod(EOS(STATIC_1891), java.lang.Object(o247sub)) -> f1922_0_getTail_Load(EOS(STATIC_1922), java.lang.Object(o247sub)) :|: TRUE
f1922_0_getTail_Load(EOS(STATIC_1922), java.lang.Object(o247sub)) -> f1937_0_getTail_FieldAccess(EOS(STATIC_1937), java.lang.Object(o247sub)) :|: TRUE
f1937_0_getTail_FieldAccess(EOS(STATIC_1937), java.lang.Object(List(EOC, o261))) -> f1942_0_getTail_FieldAccess(EOS(STATIC_1942), java.lang.Object(List(EOC, o261))) :|: TRUE
f1942_0_getTail_FieldAccess(EOS(STATIC_1942), java.lang.Object(List(EOC, o261))) -> f1951_0_getTail_Return(EOS(STATIC_1951), o261) :|: TRUE
f1951_0_getTail_Return(EOS(STATIC_1951), o261) -> f1953_0_length_Store(EOS(STATIC_1953), o261) :|: TRUE
f1953_0_length_Store(EOS(STATIC_1953), o261) -> f1957_0_length_Inc(EOS(STATIC_1957), o261) :|: TRUE
f1957_0_length_Inc(EOS(STATIC_1957), o261) -> f1962_0_length_JMP(EOS(STATIC_1962), o261) :|: TRUE
f1962_0_length_JMP(EOS(STATIC_1962), o261) -> f1986_0_length_Load(EOS(STATIC_1986), o261) :|: TRUE
f1986_0_length_Load(EOS(STATIC_1986), o261) -> f1876_0_length_Load(EOS(STATIC_1876), o261) :|: TRUE
f1876_0_length_Load(EOS(STATIC_1876), o241) -> f1878_0_length_NULL(EOS(STATIC_1878), o241, o241) :|: TRUE
R rules:
Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules:
f1878_0_length_NULL(EOS(STATIC_1878), java.lang.Object(List(EOC, o261:0)), java.lang.Object(List(EOC, o261:0))) -> f1878_0_length_NULL(EOS(STATIC_1878), o261:0, o261:0) :|: TRUE
R rules:
Filtered ground terms:
   f1878_0_length_NULL(x1, x2, x3) -> f1878_0_length_NULL(x2, x3)
   EOS(x1) -> EOS
   List(x1, x2) -> List(x2)
Filtered duplicate args:
   f1878_0_length_NULL(x1, x2) -> f1878_0_length_NULL(x2)
Combined rules. Obtained 1 conditional rules for P and 0 conditional rules for R.P rules:
F1878_0_LENGTH_NULL(java.lang.Object(List(o261:0:0))) -> F1878_0_LENGTH_NULL(o261:0:0) :|: TRUE
R rules:

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

(24)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   F1878_0_LENGTH_NULL(java.lang.Object(List(o261:0:0))) -> F1878_0_LENGTH_NULL(o261:0:0)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
----------------------------------------

(25) QDPSizeChangeProof (EQUIVALENT)
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. 

From the DPs we obtained the following set of size-change graphs:
*F1878_0_LENGTH_NULL(java.lang.Object(List(o261:0:0))) -> F1878_0_LENGTH_NULL(o261:0:0)
The graph contains the following edges 1 > 1


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

(26)
YES

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

(27)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: List.mk(I)LList;
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:

*Marker field analysis yielded the following relations that could be markers:

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

(28) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 21 IRulesP rules:
f1196_0_mk_Inc(EOS(STATIC_1196), i220, java.lang.Object(List(EOC)), i220) -> f1206_0_mk_LE(EOS(STATIC_1206), i220 + -1, java.lang.Object(List(EOC)), i220) :|: TRUE
f1206_0_mk_LE(EOS(STATIC_1206), i248, java.lang.Object(List(EOC)), i260) -> f1211_0_mk_LE(EOS(STATIC_1211), i248, java.lang.Object(List(EOC)), i260) :|: TRUE
f1211_0_mk_LE(EOS(STATIC_1211), i248, java.lang.Object(List(EOC)), i260) -> f1222_0_mk_New(EOS(STATIC_1222), i248, java.lang.Object(List(EOC))) :|: i260 > 0
f1222_0_mk_New(EOS(STATIC_1222), i248, java.lang.Object(List(EOC))) -> f1246_0_mk_Duplicate(EOS(STATIC_1246), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) :|: TRUE
f1246_0_mk_Duplicate(EOS(STATIC_1246), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) -> f1252_0_mk_Load(EOS(STATIC_1252), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) :|: TRUE
f1252_0_mk_Load(EOS(STATIC_1252), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) -> f1267_0_mk_Load(EOS(STATIC_1267), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248) :|: TRUE
f1267_0_mk_Load(EOS(STATIC_1267), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248) -> f1278_0_mk_InvokeMethod(EOS(STATIC_1278), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248, java.lang.Object(List(EOC))) :|: TRUE
f1278_0_mk_InvokeMethod(EOS(STATIC_1278), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248, java.lang.Object(List(EOC))) -> f1281_0__init__Load(EOS(STATIC_1281), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248, java.lang.Object(List(EOC))) :|: TRUE
f1281_0__init__Load(EOS(STATIC_1281), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248, java.lang.Object(List(EOC))) -> f1289_0__init__InvokeMethod(EOS(STATIC_1289), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) :|: TRUE
f1289_0__init__InvokeMethod(EOS(STATIC_1289), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) -> f1294_0__init__Load(EOS(STATIC_1294), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248, java.lang.Object(List(EOC))) :|: TRUE
f1294_0__init__Load(EOS(STATIC_1294), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248, java.lang.Object(List(EOC))) -> f1299_0__init__Load(EOS(STATIC_1299), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) :|: TRUE
f1299_0__init__Load(EOS(STATIC_1299), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) -> f1306_0__init__FieldAccess(EOS(STATIC_1306), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248) :|: TRUE
f1306_0__init__FieldAccess(EOS(STATIC_1306), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), i248) -> f1308_0__init__Load(EOS(STATIC_1308), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) :|: TRUE
f1308_0__init__Load(EOS(STATIC_1308), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) -> f1311_0__init__Load(EOS(STATIC_1311), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) :|: TRUE
f1311_0__init__Load(EOS(STATIC_1311), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) -> f1314_0__init__FieldAccess(EOS(STATIC_1314), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) :|: TRUE
f1314_0__init__FieldAccess(EOS(STATIC_1314), i248, java.lang.Object(List(EOC)), java.lang.Object(List(EOC)), java.lang.Object(List(EOC))) -> f1317_0__init__Return(EOS(STATIC_1317), i248, java.lang.Object(List(EOC))) :|: TRUE
f1317_0__init__Return(EOS(STATIC_1317), i248, java.lang.Object(List(EOC))) -> f1320_0_mk_Store(EOS(STATIC_1320), i248, java.lang.Object(List(EOC))) :|: TRUE
f1320_0_mk_Store(EOS(STATIC_1320), i248, java.lang.Object(List(EOC))) -> f1323_0_mk_JMP(EOS(STATIC_1323), i248, java.lang.Object(List(EOC))) :|: TRUE
f1323_0_mk_JMP(EOS(STATIC_1323), i248, java.lang.Object(List(EOC))) -> f1346_0_mk_Load(EOS(STATIC_1346), i248, java.lang.Object(List(EOC))) :|: TRUE
f1346_0_mk_Load(EOS(STATIC_1346), i248, java.lang.Object(List(EOC))) -> f1189_0_mk_Load(EOS(STATIC_1189), i248, java.lang.Object(List(EOC))) :|: TRUE
f1189_0_mk_Load(EOS(STATIC_1189), i220, java.lang.Object(List(EOC))) -> f1196_0_mk_Inc(EOS(STATIC_1196), i220, java.lang.Object(List(EOC)), i220) :|: TRUE
Combined rules. Obtained 1 IRulesP rules:
f1196_0_mk_Inc(EOS(STATIC_1196), i220:0, java.lang.Object(List(EOC)), i220:0) -> f1196_0_mk_Inc(EOS(STATIC_1196), i220:0 - 1, java.lang.Object(List(EOC)), i220:0 - 1) :|: i220:0 > 0
Filtered constant ground arguments:
   f1196_0_mk_Inc(x1, x2, x3, x4) -> f1196_0_mk_Inc(x2, x4)
   EOS(x1) -> EOS
   java.lang.Object(x1) -> java.lang.Object
   List(x1) -> List
Filtered duplicate arguments:
   f1196_0_mk_Inc(x1, x2) -> f1196_0_mk_Inc(x2)
Finished conversion. Obtained 1 rules.P rules:
f1196_0_mk_Inc(i220:0) -> f1196_0_mk_Inc(i220:0 - 1) :|: i220:0 > 0

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

(29)
Obligation:
Rules:
f1196_0_mk_Inc(i220:0) -> f1196_0_mk_Inc(i220:0 - 1) :|: i220:0 > 0

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

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

(31)
Obligation:
Rules:
f1196_0_mk_Inc(i220:0) -> f1196_0_mk_Inc(arith) :|: i220:0 > 0 && arith = i220:0 - 1

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

(32) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f1196_0_mk_Inc(i220:0) -> f1196_0_mk_Inc(arith) :|: i220:0 > 0 && arith = i220:0 - 1

Arcs:
(1) -> (1)

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

(33)
Obligation:

Termination digraph:
Nodes:
(1) f1196_0_mk_Inc(i220:0) -> f1196_0_mk_Inc(arith) :|: i220:0 > 0 && arith = i220:0 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

(35)
Obligation:
Rules:
f1196_0_mk_Inc(i220:0:0) -> f1196_0_mk_Inc(i220:0:0 - 1) :|: i220:0:0 > 0

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(36) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f1196_0_mk_Inc(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(37)
Obligation:
Rules:
f1196_0_mk_Inc(i220:0:0) -> f1196_0_mk_Inc(c) :|: c = i220:0:0 - 1 && i220:0:0 > 0

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

(38) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f1196_0_mk_Inc ] = f1196_0_mk_Inc_1

The following rules are decreasing:
f1196_0_mk_Inc(i220:0:0) -> f1196_0_mk_Inc(c) :|: c = i220:0:0 - 1 && i220:0:0 > 0

The following rules are bounded:
f1196_0_mk_Inc(i220:0:0) -> f1196_0_mk_Inc(c) :|: c = i220:0:0 - 1 && i220:0:0 > 0


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

(39)
YES

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

(40)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: Test7.main([Ljava/lang/String;)V
SCC calls the following helper methods: Test7.length(LList;)I, Test7.bubble(LList;)V
Performed SCC analyses:
*Used field analysis yielded the following read fields:

*Marker field analysis yielded the following relations that could be markers:

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

(41) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 40 IRulesP rules:
f2155_0_main_Load(EOS(STATIC_2155), java.lang.Object(ARRAY(matching1)), i367, i367) -> f2157_0_main_ArrayLength(EOS(STATIC_2157), java.lang.Object(ARRAY(3)), i367, i367, java.lang.Object(ARRAY(3))) :|: TRUE && matching1 = 3
f2157_0_main_ArrayLength(EOS(STATIC_2157), java.lang.Object(ARRAY(matching1)), i367, i367, java.lang.Object(ARRAY(matching2))) -> f2159_0_main_GE(EOS(STATIC_2159), java.lang.Object(ARRAY(3)), i367, i367, 3) :|: 3 >= 0 && matching1 = 3 && matching2 = 3
f2159_0_main_GE(EOS(STATIC_2159), java.lang.Object(ARRAY(matching1)), i369, i369, matching2) -> f2168_0_main_GE(EOS(STATIC_2168), java.lang.Object(ARRAY(3)), i369, i369, 3) :|: TRUE && matching1 = 3 && matching2 = 3
f2168_0_main_GE(EOS(STATIC_2168), java.lang.Object(ARRAY(matching1)), i369, i369, matching2) -> f2176_0_main_Load(EOS(STATIC_2176), java.lang.Object(ARRAY(3)), i369) :|: i369 < 3 && matching1 = 3 && matching2 = 3
f2176_0_main_Load(EOS(STATIC_2176), java.lang.Object(ARRAY(matching1)), i369) -> f2187_0_main_ConstantStackPush(EOS(STATIC_2187), java.lang.Object(ARRAY(3)), i369, java.lang.Object(ARRAY(3))) :|: TRUE && matching1 = 3
f2187_0_main_ConstantStackPush(EOS(STATIC_2187), java.lang.Object(ARRAY(matching1)), i369, java.lang.Object(ARRAY(matching2))) -> f2191_0_main_ArrayAccess(EOS(STATIC_2191), java.lang.Object(ARRAY(3)), i369, java.lang.Object(ARRAY(3)), 0) :|: TRUE && matching1 = 3 && matching2 = 3
f2191_0_main_ArrayAccess(EOS(STATIC_2191), java.lang.Object(ARRAY(matching1)), i369, java.lang.Object(ARRAY(matching2)), matching3) -> f2192_0_main_InvokeMethod(EOS(STATIC_2192), java.lang.Object(ARRAY(3)), i369, o272) :|: 0 < 3 && matching1 = 3 && matching2 = 3 && matching3 = 0
f2192_0_main_InvokeMethod(EOS(STATIC_2192), java.lang.Object(ARRAY(matching1)), i369, o272) -> f2193_0_length_ConstantStackPush(EOS(STATIC_2193), o272, o272) :|: TRUE && matching1 = 3
f2192_0_main_InvokeMethod(EOS(STATIC_2192), java.lang.Object(ARRAY(matching1)), i369, o272) -> f2193_1_length_ConstantStackPush(EOS(STATIC_2193), java.lang.Object(ARRAY(3)), i369, o272) :|: TRUE && matching1 = 3
f2193_0_length_ConstantStackPush(EOS(STATIC_2193), o272, o272) -> f3511_0_length_ConstantStackPush(EOS(STATIC_3511), o272, o272) :|: TRUE
f2207_0_length_Return(EOS(STATIC_2207), java.lang.Object(ARRAY(matching1)), i369, i374) -> f2211_0_main_Store(EOS(STATIC_2211), java.lang.Object(ARRAY(3)), i369, i374) :|: TRUE && matching1 = 3
f2211_0_main_Store(EOS(STATIC_2211), java.lang.Object(ARRAY(matching1)), i369, i374) -> f2212_0_main_ConstantStackPush(EOS(STATIC_2212), java.lang.Object(ARRAY(3)), i369, i374) :|: TRUE && matching1 = 3
f2212_0_main_ConstantStackPush(EOS(STATIC_2212), java.lang.Object(ARRAY(matching1)), i369, i374) -> f2213_0_main_Store(EOS(STATIC_2213), java.lang.Object(ARRAY(3)), i369, i374, 0) :|: TRUE && matching1 = 3
f2213_0_main_Store(EOS(STATIC_2213), java.lang.Object(ARRAY(matching1)), i369, i374, matching2) -> f2214_0_main_Load(EOS(STATIC_2214), java.lang.Object(ARRAY(3)), i369, i374, 0) :|: TRUE && matching1 = 3 && matching2 = 0
f2214_0_main_Load(EOS(STATIC_2214), java.lang.Object(ARRAY(matching1)), i369, i374, matching2) -> f2376_0_main_Load(EOS(STATIC_2376), java.lang.Object(ARRAY(3)), i369, i374, 0) :|: TRUE && matching1 = 3 && matching2 = 0
f2376_0_main_Load(EOS(STATIC_2376), java.lang.Object(ARRAY(matching1)), i369, i410, i411) -> f2731_0_main_Load(EOS(STATIC_2731), java.lang.Object(ARRAY(3)), i369, i410, i411) :|: TRUE && matching1 = 3
f2731_0_main_Load(EOS(STATIC_2731), java.lang.Object(ARRAY(matching1)), i369, i454, i455) -> f2848_0_main_Load(EOS(STATIC_2848), java.lang.Object(ARRAY(3)), i369, i454, i455) :|: TRUE && matching1 = 3
f2848_0_main_Load(EOS(STATIC_2848), java.lang.Object(ARRAY(matching1)), i369, i465, i466) -> f2850_0_main_Load(EOS(STATIC_2850), java.lang.Object(ARRAY(3)), i369, i465, i466, i466) :|: TRUE && matching1 = 3
f2850_0_main_Load(EOS(STATIC_2850), java.lang.Object(ARRAY(matching1)), i369, i465, i466, i466) -> f2853_0_main_GE(EOS(STATIC_2853), java.lang.Object(ARRAY(3)), i369, i465, i466, i466, i465) :|: TRUE && matching1 = 3
f2853_0_main_GE(EOS(STATIC_2853), java.lang.Object(ARRAY(matching1)), i369, i465, i466, i466, i465) -> f2889_0_main_GE(EOS(STATIC_2889), java.lang.Object(ARRAY(3)), i369, i465, i466, i466, i465) :|: i466 >= i465 && matching1 = 3
f2853_0_main_GE(EOS(STATIC_2853), java.lang.Object(ARRAY(matching1)), i369, i465, i466, i466, i465) -> f2890_0_main_GE(EOS(STATIC_2890), java.lang.Object(ARRAY(3)), i369, i465, i466, i466, i465) :|: i466 < i465 && matching1 = 3
f2889_0_main_GE(EOS(STATIC_2889), java.lang.Object(ARRAY(matching1)), i369, i465, i466, i466, i465) -> f2899_0_main_Inc(EOS(STATIC_2899), java.lang.Object(ARRAY(3)), i369) :|: i466 >= i465 && matching1 = 3
f2899_0_main_Inc(EOS(STATIC_2899), java.lang.Object(ARRAY(matching1)), i369) -> f2909_0_main_JMP(EOS(STATIC_2909), java.lang.Object(ARRAY(3)), i369 + 1) :|: TRUE && matching1 = 3
f2909_0_main_JMP(EOS(STATIC_2909), java.lang.Object(ARRAY(matching1)), i470) -> f2929_0_main_Load(EOS(STATIC_2929), java.lang.Object(ARRAY(3)), i470) :|: TRUE && matching1 = 3
f2929_0_main_Load(EOS(STATIC_2929), java.lang.Object(ARRAY(matching1)), i470) -> f2150_0_main_Load(EOS(STATIC_2150), java.lang.Object(ARRAY(3)), i470) :|: TRUE && matching1 = 3
f2150_0_main_Load(EOS(STATIC_2150), java.lang.Object(ARRAY(matching1)), i367) -> f2155_0_main_Load(EOS(STATIC_2155), java.lang.Object(ARRAY(3)), i367, i367) :|: TRUE && matching1 = 3
f2890_0_main_GE(EOS(STATIC_2890), java.lang.Object(ARRAY(matching1)), i369, i465, i466, i466, i465) -> f2906_0_main_Load(EOS(STATIC_2906), java.lang.Object(ARRAY(3)), i369, i465, i466) :|: i466 < i465 && matching1 = 3
f2906_0_main_Load(EOS(STATIC_2906), java.lang.Object(ARRAY(matching1)), i369, i465, i466) -> f2911_0_main_ConstantStackPush(EOS(STATIC_2911), java.lang.Object(ARRAY(3)), i369, i465, i466, java.lang.Object(ARRAY(3))) :|: TRUE && matching1 = 3
f2911_0_main_ConstantStackPush(EOS(STATIC_2911), java.lang.Object(ARRAY(matching1)), i369, i465, i466, java.lang.Object(ARRAY(matching2))) -> f2931_0_main_ArrayAccess(EOS(STATIC_2931), java.lang.Object(ARRAY(3)), i369, i465, i466, java.lang.Object(ARRAY(3)), 0) :|: TRUE && matching1 = 3 && matching2 = 3
f2931_0_main_ArrayAccess(EOS(STATIC_2931), java.lang.Object(ARRAY(matching1)), i369, i465, i466, java.lang.Object(ARRAY(matching2)), matching3) -> f2970_0_main_InvokeMethod(EOS(STATIC_2970), java.lang.Object(ARRAY(3)), i369, i465, i466, o383) :|: 0 < 3 && matching1 = 3 && matching2 = 3 && matching3 = 0
f2970_0_main_InvokeMethod(EOS(STATIC_2970), java.lang.Object(ARRAY(matching1)), i369, i465, i466, o383) -> f2972_0_bubble_Load(EOS(STATIC_2972), o383, o383) :|: i465 >= 1 && i466 < i465 && matching1 = 3
f2970_0_main_InvokeMethod(EOS(STATIC_2970), java.lang.Object(ARRAY(matching1)), i369, i465, i466, o383) -> f2972_1_bubble_Load(EOS(STATIC_2972), java.lang.Object(ARRAY(3)), i369, i465, i466, o383) :|: i465 >= 1 && i466 < i465 && matching1 = 3
f2972_0_bubble_Load(EOS(STATIC_2972), o383, o383) -> f3563_0_bubble_Load(EOS(STATIC_3563), o383, o383) :|: TRUE
f3187_0_bubble_Return(EOS(STATIC_3187), java.lang.Object(ARRAY(matching1)), i369, i465, i466) -> f3018_0_bubble_Return(EOS(STATIC_3018), java.lang.Object(ARRAY(3)), i369, i465, i466) :|: TRUE && matching1 = 3
f3018_0_bubble_Return(EOS(STATIC_3018), java.lang.Object(ARRAY(matching1)), i369, i465, i466) -> f3031_0_main_Inc(EOS(STATIC_3031), java.lang.Object(ARRAY(3)), i369, i465, i466) :|: TRUE && matching1 = 3
f3031_0_main_Inc(EOS(STATIC_3031), java.lang.Object(ARRAY(matching1)), i369, i465, i466) -> f3049_0_main_JMP(EOS(STATIC_3049), java.lang.Object(ARRAY(3)), i369, i465, i466 + 1) :|: TRUE && matching1 = 3
f3049_0_main_JMP(EOS(STATIC_3049), java.lang.Object(ARRAY(matching1)), i369, i465, i475) -> f3068_0_main_Load(EOS(STATIC_3068), java.lang.Object(ARRAY(3)), i369, i465, i475) :|: TRUE && matching1 = 3
f3068_0_main_Load(EOS(STATIC_3068), java.lang.Object(ARRAY(matching1)), i369, i465, i475) -> f2848_0_main_Load(EOS(STATIC_2848), java.lang.Object(ARRAY(3)), i369, i465, i475) :|: TRUE && matching1 = 3
f2193_1_length_ConstantStackPush(EOS(STATIC_2193), java.lang.Object(ARRAY(matching1)), i369, o286) -> f2207_0_length_Return(EOS(STATIC_2207), java.lang.Object(ARRAY(3)), i369, i374) :|: TRUE && matching1 = 3
f2972_1_bubble_Load(EOS(STATIC_2972), java.lang.Object(ARRAY(matching1)), i369, i465, i466, o383) -> f3187_0_bubble_Return(EOS(STATIC_3187), java.lang.Object(ARRAY(3)), i369, i465, i466) :|: TRUE && matching1 = 3
Combined rules. Obtained 4 IRulesP rules:
f2853_0_main_GE(EOS(STATIC_2853), java.lang.Object(ARRAY(3)), i369:0, i465:0, i466:0, i466:0, i465:0) -> f2853_0_main_GE(EOS(STATIC_2853), java.lang.Object(ARRAY(3)), i369:0, i465:0, i466:0 + 1, i466:0 + 1, i465:0) :|: i466:0 < i465:0 && i465:0 > 0
f2853_0_main_GE(EOS(STATIC_2853), java.lang.Object(ARRAY(3)), i369:0, i465:0, i466:0, i466:0, i465:0) -> f2853_0_main_GE(EOS(STATIC_2853), java.lang.Object(ARRAY(3)), i369:0 + 1, i374:0, 0, 0, i374:0) :|: i369:0 < 2 && i466:0 >= i465:0
Removed following non-SCC rules:
f2853_0_main_GE(EOS(STATIC_2853), java.lang.Object(ARRAY(3)), i369:0, i465:0, i466:0, i466:0, i465:0) -> f3511_0_length_ConstantStackPush(EOS(STATIC_3511), o272:0, o272:0) :|: i369:0 < 2 && i466:0 >= i465:0
f2853_0_main_GE(EOS(STATIC_2853), java.lang.Object(ARRAY(3)), i369:0, i465:0, i466:0, i466:0, i465:0) -> f3563_0_bubble_Load(EOS(STATIC_3563), o383:0, o383:0) :|: i466:0 < i465:0 && i465:0 > 0
Filtered constant ground arguments:
   f2853_0_main_GE(x1, x2, x3, x4, x5, x6, x7) -> f2853_0_main_GE(x3, x4, x5, x6, x7)
   EOS(x1) -> EOS
   java.lang.Object(x1) -> java.lang.Object
   ARRAY(x1) -> ARRAY
Filtered duplicate arguments:
   f2853_0_main_GE(x1, x2, x3, x4, x5) -> f2853_0_main_GE(x1, x4, x5)
Finished conversion. Obtained 2 rules.P rules:
f2853_0_main_GE(i369:0, i466:0, i465:0) -> f2853_0_main_GE(i369:0, i466:0 + 1, i465:0) :|: i466:0 < i465:0 && i465:0 > 0
f2853_0_main_GE(i369:0, i466:0, i465:0) -> f2853_0_main_GE(i369:0 + 1, 0, i374:0) :|: i369:0 < 2 && i466:0 >= i465:0

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

(42)
Obligation:
Rules:
f2853_0_main_GE(i369:0, i466:0, i465:0) -> f2853_0_main_GE(i369:0, i466:0 + 1, i465:0) :|: i466:0 < i465:0 && i465:0 > 0
f2853_0_main_GE(x, x1, x2) -> f2853_0_main_GE(x + 1, 0, x3) :|: x < 2 && x1 >= x2

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

(44)
Obligation:
Rules:
f2853_0_main_GE(i369:0, i466:0, i465:0) -> f2853_0_main_GE(i369:0, arith, i465:0) :|: i466:0 < i465:0 && i465:0 > 0 && arith = i466:0 + 1
f2853_0_main_GE(x4, x5, x6) -> f2853_0_main_GE(x7, 0, x8) :|: x4 < 2 && x5 >= x6 && x7 = x4 + 1

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(45) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f2853_0_main_GE(i369:0, i466:0, i465:0) -> f2853_0_main_GE(i369:0, arith, i465:0) :|: i466:0 < i465:0 && i465:0 > 0 && arith = i466:0 + 1
(2) f2853_0_main_GE(x4, x5, x6) -> f2853_0_main_GE(x7, 0, x8) :|: x4 < 2 && x5 >= x6 && x7 = x4 + 1

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

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

(46)
Obligation:

Termination digraph:
Nodes:
(1) f2853_0_main_GE(i369:0, i466:0, i465:0) -> f2853_0_main_GE(i369:0, arith, i465:0) :|: i466:0 < i465:0 && i465:0 > 0 && arith = i466:0 + 1
(2) f2853_0_main_GE(x4, x5, x6) -> f2853_0_main_GE(x7, 0, x8) :|: x4 < 2 && x5 >= x6 && x7 = x4 + 1

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

This digraph is fully evaluated!

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

(48)
Obligation:
Rules:
f2853_0_main_GE(i369:0:0, i466:0:0, i465:0:0) -> f2853_0_main_GE(i369:0:0, i466:0:0 + 1, i465:0:0) :|: i466:0:0 < i465:0:0 && i465:0:0 > 0
f2853_0_main_GE(x4:0, x5:0, x6:0) -> f2853_0_main_GE(x4:0 + 1, 0, x8:0) :|: x4:0 < 2 && x6:0 <= x5:0

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(49) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f2853_0_main_GE(VARIABLE, VARIABLE, VARIABLE)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(50)
Obligation:
Rules:
f2853_0_main_GE(i369:0:0, i466:0:0, i465:0:0) -> f2853_0_main_GE(i369:0:0, c, i465:0:0) :|: c = i466:0:0 + 1 && (i466:0:0 < i465:0:0 && i465:0:0 > 0)
f2853_0_main_GE(x4:0, x5:0, x6:0) -> f2853_0_main_GE(c1, c2, x8:0) :|: c2 = 0 && c1 = x4:0 + 1 && (x4:0 < 2 && x6:0 <= x5:0)

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(51) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f2853_0_main_GE ] = -1*f2853_0_main_GE_1 + 1

The following rules are decreasing:
f2853_0_main_GE(x4:0, x5:0, x6:0) -> f2853_0_main_GE(c1, c2, x8:0) :|: c2 = 0 && c1 = x4:0 + 1 && (x4:0 < 2 && x6:0 <= x5:0)

The following rules are bounded:
f2853_0_main_GE(x4:0, x5:0, x6:0) -> f2853_0_main_GE(c1, c2, x8:0) :|: c2 = 0 && c1 = x4:0 + 1 && (x4:0 < 2 && x6:0 <= x5:0)


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(52)
Obligation:
Rules:
f2853_0_main_GE(i369:0:0, i466:0:0, i465:0:0) -> f2853_0_main_GE(i369:0:0, c, i465:0:0) :|: c = i466:0:0 + 1 && (i466:0:0 < i465:0:0 && i465:0:0 > 0)

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(53) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f2853_0_main_GE ] = -1*f2853_0_main_GE_2 + f2853_0_main_GE_3

The following rules are decreasing:
f2853_0_main_GE(i369:0:0, i466:0:0, i465:0:0) -> f2853_0_main_GE(i369:0:0, c, i465:0:0) :|: c = i466:0:0 + 1 && (i466:0:0 < i465:0:0 && i465:0:0 > 0)

The following rules are bounded:
f2853_0_main_GE(i369:0:0, i466:0:0, i465:0:0) -> f2853_0_main_GE(i369:0:0, c, i465:0:0) :|: c = i466:0:0 + 1 && (i466:0:0 < i465:0:0 && i465:0:0 > 0)


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(54)
YES