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


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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


termination of the given Bare JBC problem could not be shown:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 815 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) JBCTerminationSCC
        (8) SCCToIRSProof [SOUND, 37 ms]
        (9) IRSwT
        (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (11) IRSwT
        (12) IRSwTTerminationDigraphProof [EQUIVALENT, 13 ms]
        (13) IRSwT
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IRSwT
        (16) TempFilterProof [SOUND, 9 ms]
        (17) IntTRS
        (18) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (19) YES
    (20) JBCTerminationSCC
        (21) SCCToIRSProof [SOUND, 81 ms]
        (22) IRSwT
        (23) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (24) IRSwT
        (25) IRSwTTerminationDigraphProof [EQUIVALENT, 64 ms]
        (26) IRSwT
        (27) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (28) IRSwT
        (29) FilterProof [EQUIVALENT, 0 ms]
        (30) IntTRS
        (31) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (32) IntTRS
        (33) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
        (34) NO
    (35) JBCTerminationSCC
        (36) SCCToIRSProof [SOUND, 95 ms]
        (37) IRSwT
        (38) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (39) IRSwT
        (40) IRSwTTerminationDigraphProof [EQUIVALENT, 58 ms]
        (41) IRSwT
        (42) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (43) IRSwT
        (44) FilterProof [EQUIVALENT, 0 ms]
        (45) IntTRS
        (46) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (47) IntTRS
        (48) IntTRSPeriodicNontermProof [COMPLETE, 0 ms]
        (49) NO


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

(0)
Obligation:
need to prove termination of the following program:
/**
 * Parts of the below code have been adapted from
 *
 * http://www0.cs.ucl.ac.uk/staff/p.ohearn/Talks/SAStalk.pdf
 *
 * Based on the motivating example of the paper
 *
 * Automatic termination proofs for programs with shape-shifting heaps
 * Josh Berdine, Byron Cook, Dino Distefano, and Peter W. O’Hearn
 * In Proc. CAV'06, LNCS 4144, pp. 386 - 400, 2006.
 */
public class Kernel93 {
    /**
     * A reference to the next list element.
     */
    private Kernel93 next;
    
    public static void main(String[] args) {
        int random1 = args[0].length();
        int random2 = args[1].length();

        //slide68(random1, random2);
        //slide88(random1, random2);
        slide93(random1, random2);
        //slide95(random1, random2);
    }
    
    /**
     * Create a new list element.
     * @param n a reference to the next element.
     */
    public Kernel93(final Kernel93 n) {
        this.next = n;
    }
    
    /**
     * Create a new cyclical list of a length x.
     * @param x some length
     * @return cyclical list of length max(1, x)
     */
    public static Kernel93 create(int x) {
        Kernel93 last, current;
        last = current = new Kernel93(null);
        while (--x > 0)
            current = new Kernel93(current);
        return last.next = current;
    }

    /**
     * Check if the last bit of x is > 0.
     */
    private static boolean check(int x) {
        return x % 2 > 0;
    }

    public static void slide68(int random1, int random2) {
        Kernel93 h = create(random1);
        Kernel93 p = h;
        Kernel93 c = p.next;
        while (c != h) {
            Kernel93 o = c;
            c = c.next;
            if (check(random2)) { // nondet()
                p.next = c;
                //dispose(o);
                o = null;
                // Java's garbage collector will notice that the object
                // previously referenced by o is not referenced any more
                // and will release it (of course, in the next loop iteration
                // this would happen anyway); obviously, this does not have
                // quite the impact of a proper "dispose" operation, which
                // also renders all other pointer invalid that happen to point
                // to the same address
            } else {
                p = o;
            }

            // get a fresh random bit to the end of random2
            random2 = random2 / 2;
       }
    }

    public static void slide88(int random1, int random2) {
        Kernel93 h = create(random1);
        Kernel93 p = h;
        Kernel93 c = p.next;
        while (c != h) {
            Kernel93 o = c;
            //c = c.next;
            if (check(random2)) { // nondet()
                Kernel93 e = o.next;
                p.next = e;
                //dispose(o);
                o = null;
                // Java's garbage collector will notice that the object
                // previously referenced by o is not referenced any more
                // and will release it
                c = o;
                // for a faithful translation of the original C code,
                // let c point to whatever o points to -- the interesting
                // aspect is that dereferencing this memory location 
                // henceforth is a very bad idea (in C, obviously, this would
                // not necessarily lead to a clean exception at runtime)
            } else {
                p = o;
            }
            c = c.next;

            // get a fresh random bit to the end of random2
            random2 = random2 / 2;
        }
    }

    /**
     * Non-terminating.
     */
    public static void slide93(int random1, int random2) {
        Kernel93 h = create(random1);
        Kernel93 p = h;
        Kernel93 c = p.next;
        while (c != h) {
            Kernel93 o = c;
            //c = c.next;

            if (check(random2)) { // nondet()
                Kernel93 e = o.next;
                p.next = e;
                o.next = o;
            } else {
                p = o;
            }
            c = c.next;

            // get a fresh random bit to the end of random2
            random2 = random2 / 2;
        }
    }

    public static void slide95(int random1, int random2) {
        Kernel93 h = create(random1);
        Kernel93 p = h;
        Kernel93 c = p.next;
        while (c != h) {
            Kernel93 o = c;
            c = c.next;

            if (check(random2)) { // nondet()
                Kernel93 e = o.next;
                p.next = e;
                o.next = o;
            } else {
                p = o;
            }

            // get a fresh random bit to the end of random2
            random2 = random2 / 2;
        }
    }

}



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

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

(2)
Obligation:
need to prove termination of the following program:
/**
 * Parts of the below code have been adapted from
 *
 * http://www0.cs.ucl.ac.uk/staff/p.ohearn/Talks/SAStalk.pdf
 *
 * Based on the motivating example of the paper
 *
 * Automatic termination proofs for programs with shape-shifting heaps
 * Josh Berdine, Byron Cook, Dino Distefano, and Peter W. O’Hearn
 * In Proc. CAV'06, LNCS 4144, pp. 386 - 400, 2006.
 */
public class Kernel93 {
    /**
     * A reference to the next list element.
     */
    private Kernel93 next;
    
    public static void main(String[] args) {
        int random1 = args[0].length();
        int random2 = args[1].length();

        //slide68(random1, random2);
        //slide88(random1, random2);
        slide93(random1, random2);
        //slide95(random1, random2);
    }
    
    /**
     * Create a new list element.
     * @param n a reference to the next element.
     */
    public Kernel93(final Kernel93 n) {
        this.next = n;
    }
    
    /**
     * Create a new cyclical list of a length x.
     * @param x some length
     * @return cyclical list of length max(1, x)
     */
    public static Kernel93 create(int x) {
        Kernel93 last, current;
        last = current = new Kernel93(null);
        while (--x > 0)
            current = new Kernel93(current);
        return last.next = current;
    }

    /**
     * Check if the last bit of x is > 0.
     */
    private static boolean check(int x) {
        return x % 2 > 0;
    }

    public static void slide68(int random1, int random2) {
        Kernel93 h = create(random1);
        Kernel93 p = h;
        Kernel93 c = p.next;
        while (c != h) {
            Kernel93 o = c;
            c = c.next;
            if (check(random2)) { // nondet()
                p.next = c;
                //dispose(o);
                o = null;
                // Java's garbage collector will notice that the object
                // previously referenced by o is not referenced any more
                // and will release it (of course, in the next loop iteration
                // this would happen anyway); obviously, this does not have
                // quite the impact of a proper "dispose" operation, which
                // also renders all other pointer invalid that happen to point
                // to the same address
            } else {
                p = o;
            }

            // get a fresh random bit to the end of random2
            random2 = random2 / 2;
       }
    }

    public static void slide88(int random1, int random2) {
        Kernel93 h = create(random1);
        Kernel93 p = h;
        Kernel93 c = p.next;
        while (c != h) {
            Kernel93 o = c;
            //c = c.next;
            if (check(random2)) { // nondet()
                Kernel93 e = o.next;
                p.next = e;
                //dispose(o);
                o = null;
                // Java's garbage collector will notice that the object
                // previously referenced by o is not referenced any more
                // and will release it
                c = o;
                // for a faithful translation of the original C code,
                // let c point to whatever o points to -- the interesting
                // aspect is that dereferencing this memory location 
                // henceforth is a very bad idea (in C, obviously, this would
                // not necessarily lead to a clean exception at runtime)
            } else {
                p = o;
            }
            c = c.next;

            // get a fresh random bit to the end of random2
            random2 = random2 / 2;
        }
    }

    /**
     * Non-terminating.
     */
    public static void slide93(int random1, int random2) {
        Kernel93 h = create(random1);
        Kernel93 p = h;
        Kernel93 c = p.next;
        while (c != h) {
            Kernel93 o = c;
            //c = c.next;

            if (check(random2)) { // nondet()
                Kernel93 e = o.next;
                p.next = e;
                o.next = o;
            } else {
                p = o;
            }
            c = c.next;

            // get a fresh random bit to the end of random2
            random2 = random2 / 2;
        }
    }

    public static void slide95(int random1, int random2) {
        Kernel93 h = create(random1);
        Kernel93 p = h;
        Kernel93 c = p.next;
        while (c != h) {
            Kernel93 o = c;
            c = c.next;

            if (check(random2)) { // nondet()
                Kernel93 e = o.next;
                p.next = e;
                o.next = o;
            } else {
                p = o;
            }

            // get a fresh random bit to the end of random2
            random2 = random2 / 2;
        }
    }

}



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

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

(4)
Obligation:
Termination Graph based on JBC Program:
Kernel93.main([Ljava/lang/String;)V: Graph of 297 nodes with 2 SCCs.



Kernel93.create(I)LKernel93;: Graph of 42 nodes with 1 SCC.





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

(5) TerminationGraphToSCCProof (SOUND)
Splitted TerminationGraph to 3 SCCss.
----------------------------------------

(6)
Complex Obligation (AND)

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

(7)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: Kernel93.create(I)LKernel93;
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:

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

(8) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 17 IRulesP rules:
f907_0_create_Load(EOS(STATIC_907), i84, o74[Kernel93.next]o73) -> f912_0_create_LE(EOS(STATIC_912), i84, i84, o74[Kernel93.next]o73) :|: TRUE
f912_0_create_LE(EOS(STATIC_912), i86, i86, o74[Kernel93.next]o73) -> f920_0_create_LE(EOS(STATIC_920), i86, i86, o74[Kernel93.next]o73) :|: TRUE
f920_0_create_LE(EOS(STATIC_920), i86, i86, o74[Kernel93.next]o73) -> f927_0_create_New(EOS(STATIC_927), i86, o74[Kernel93.next]o73) :|: i86 > 0
f927_0_create_New(EOS(STATIC_927), i86, o74[Kernel93.next]o73) -> f935_0_create_Duplicate(EOS(STATIC_935), i86, o74[Kernel93.next]o73) :|: TRUE
f935_0_create_Duplicate(EOS(STATIC_935), i86, o74[Kernel93.next]o73) -> f941_0_create_Load(EOS(STATIC_941), i86, o74[Kernel93.next]o73) :|: TRUE
f941_0_create_Load(EOS(STATIC_941), i86, o74[Kernel93.next]o73) -> f945_0_create_InvokeMethod(EOS(STATIC_945), i86, o74[Kernel93.next]o73) :|: TRUE
f945_0_create_InvokeMethod(EOS(STATIC_945), i86, o74[Kernel93.next]o73) -> f965_0__init__Load(EOS(STATIC_965), i86, o74[Kernel93.next]o73) :|: TRUE
f965_0__init__Load(EOS(STATIC_965), i86, o74[Kernel93.next]o73) -> f996_0__init__InvokeMethod(EOS(STATIC_996), i86, o74[Kernel93.next]o73) :|: TRUE
f996_0__init__InvokeMethod(EOS(STATIC_996), i86, o74[Kernel93.next]o73) -> f1004_0__init__Load(EOS(STATIC_1004), i86, o74[Kernel93.next]o73) :|: TRUE
f1004_0__init__Load(EOS(STATIC_1004), i86, o74[Kernel93.next]o73) -> f1025_0__init__Load(EOS(STATIC_1025), i86, o74[Kernel93.next]o73) :|: TRUE
f1025_0__init__Load(EOS(STATIC_1025), i86, o74[Kernel93.next]o73) -> f1028_0__init__FieldAccess(EOS(STATIC_1028), i86, o74[Kernel93.next]o73) :|: TRUE
f1028_0__init__FieldAccess(EOS(STATIC_1028), i86, o74[Kernel93.next]o73) -> f1035_0__init__Return(EOS(STATIC_1035), i86, o74[Kernel93.next]o73) :|: TRUE
f1035_0__init__Return(EOS(STATIC_1035), i86, o74[Kernel93.next]o73) -> f1040_0_create_Store(EOS(STATIC_1040), i86, o74[Kernel93.next]o73) :|: TRUE
f1040_0_create_Store(EOS(STATIC_1040), i86, o74[Kernel93.next]o73) -> f1045_0_create_JMP(EOS(STATIC_1045), i86, o74[Kernel93.next]o73) :|: TRUE
f1045_0_create_JMP(EOS(STATIC_1045), i86, o74[Kernel93.next]o73) -> f1158_0_create_Inc(EOS(STATIC_1158), i86, o74[Kernel93.next]o73) :|: TRUE
f1158_0_create_Inc(EOS(STATIC_1158), i86, o74[Kernel93.next]o73) -> f899_0_create_Inc(EOS(STATIC_899), i86, o82[Kernel93.next]o73) :|: TRUE
f899_0_create_Inc(EOS(STATIC_899), i55, o74[Kernel93.next]o73) -> f907_0_create_Load(EOS(STATIC_907), i55 + -1, o74[Kernel93.next]o73) :|: TRUE
Combined rules. Obtained 1 IRulesP rules:
f907_0_create_Load(EOS(STATIC_907), i84:0, o74[Kernel93.next]o73:0) -> f907_0_create_Load(EOS(STATIC_907), i84:0 - 1, o82[Kernel93.next]o73:0) :|: i84:0 > 0
Filtered constant ground arguments:
   f907_0_create_Load(x1, x2, x3) -> f907_0_create_Load(x2, x3)
   EOS(x1) -> EOS
Filtered unneeded arguments:
   f907_0_create_Load(x1, x2) -> f907_0_create_Load(x1)
Finished conversion. Obtained 1 rules.P rules:
f907_0_create_Load(i84:0) -> f907_0_create_Load(i84:0 - 1) :|: i84:0 > 0

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

(9)
Obligation:
Rules:
f907_0_create_Load(i84:0) -> f907_0_create_Load(i84:0 - 1) :|: i84:0 > 0

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

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

(11)
Obligation:
Rules:
f907_0_create_Load(i84:0) -> f907_0_create_Load(arith) :|: i84:0 > 0 && arith = i84:0 - 1

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

(12) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f907_0_create_Load(i84:0) -> f907_0_create_Load(arith) :|: i84:0 > 0 && arith = i84:0 - 1

Arcs:
(1) -> (1)

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

(13)
Obligation:

Termination digraph:
Nodes:
(1) f907_0_create_Load(i84:0) -> f907_0_create_Load(arith) :|: i84:0 > 0 && arith = i84:0 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(15)
Obligation:
Rules:
f907_0_create_Load(i84:0:0) -> f907_0_create_Load(i84:0:0 - 1) :|: i84:0:0 > 0

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

(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f907_0_create_Load(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(17)
Obligation:
Rules:
f907_0_create_Load(i84:0:0) -> f907_0_create_Load(c) :|: c = i84:0:0 - 1 && i84:0:0 > 0

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

(18) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f907_0_create_Load(x)] = x

The following rules are decreasing:
f907_0_create_Load(i84:0:0) -> f907_0_create_Load(c) :|: c = i84:0:0 - 1 && i84:0:0 > 0
The following rules are bounded:
f907_0_create_Load(i84:0:0) -> f907_0_create_Load(c) :|: c = i84:0:0 - 1 && i84:0:0 > 0

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

(19)
YES

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

(20)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: Kernel93.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*Kernel93: [next]
*Marker field analysis yielded the following relations that could be markers:

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

(21) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 77 IRulesP rules:
f6678_0_slide93_EQ(EOS(STATIC_6678), i623) -> f6680_0_slide93_Load(EOS(STATIC_6680), i623) :|: TRUE
f6680_0_slide93_Load(EOS(STATIC_6680), i623) -> f6682_0_slide93_Store(EOS(STATIC_6682), i623) :|: TRUE
f6682_0_slide93_Store(EOS(STATIC_6682), i623) -> f6683_0_slide93_Load(EOS(STATIC_6683), i623) :|: TRUE
f6683_0_slide93_Load(EOS(STATIC_6683), i623) -> f6684_0_slide93_InvokeMethod(EOS(STATIC_6684), i623, i623) :|: TRUE
f6684_0_slide93_InvokeMethod(EOS(STATIC_6684), i623, i623) -> f6685_0_check_Load(EOS(STATIC_6685), i623, i623) :|: TRUE
f6685_0_check_Load(EOS(STATIC_6685), i623, i623) -> f6686_0_check_ConstantStackPush(EOS(STATIC_6686), i623, i623) :|: TRUE
f6686_0_check_ConstantStackPush(EOS(STATIC_6686), i623, i623) -> f6687_0_check_IntArithmetic(EOS(STATIC_6687), i623, i623, 2) :|: TRUE
f6687_0_check_IntArithmetic(EOS(STATIC_6687), i623, i623, matching1) -> f6688_0_check_LE(EOS(STATIC_6688), i623, i623 % 2) :|: TRUE && matching1 = 2
f6688_0_check_LE(EOS(STATIC_6688), i623, matching1) -> f6689_0_check_LE(EOS(STATIC_6689), i623, 0) :|: TRUE && matching1 = 0
f6688_0_check_LE(EOS(STATIC_6688), i623, matching1) -> f6690_0_check_LE(EOS(STATIC_6690), i623, 1) :|: TRUE && matching1 = 1
f6689_0_check_LE(EOS(STATIC_6689), i623, matching1) -> f6691_0_check_ConstantStackPush(EOS(STATIC_6691), i623) :|: 0 <= 0 && matching1 = 0
f6691_0_check_ConstantStackPush(EOS(STATIC_6691), i623) -> f6693_0_check_Return(EOS(STATIC_6693), i623, 0) :|: TRUE
f6693_0_check_Return(EOS(STATIC_6693), i623, matching1) -> f6695_0_slide93_EQ(EOS(STATIC_6695), i623, 0) :|: TRUE && matching1 = 0
f6695_0_slide93_EQ(EOS(STATIC_6695), i623, matching1) -> f6735_0_slide93_Load(EOS(STATIC_6735), i623) :|: TRUE && matching1 = 0
f6735_0_slide93_Load(EOS(STATIC_6735), i623) -> f6745_0_slide93_Store(EOS(STATIC_6745), i623) :|: TRUE
f6745_0_slide93_Store(EOS(STATIC_6745), i623) -> f6759_0_slide93_Load(EOS(STATIC_6759), i623) :|: TRUE
f6759_0_slide93_Load(EOS(STATIC_6759), i623) -> f6768_0_slide93_FieldAccess(EOS(STATIC_6768), i623) :|: TRUE
f6768_0_slide93_FieldAccess(EOS(STATIC_6768), i623) -> f6814_0_slide93_Store(EOS(STATIC_6814), i623) :|: TRUE
f6814_0_slide93_Store(EOS(STATIC_6814), i623) -> f6828_0_slide93_Load(EOS(STATIC_6828), i623) :|: TRUE
f6828_0_slide93_Load(EOS(STATIC_6828), i623) -> f6839_0_slide93_ConstantStackPush(EOS(STATIC_6839), i623) :|: TRUE
f6839_0_slide93_ConstantStackPush(EOS(STATIC_6839), i623) -> f6908_0_slide93_IntArithmetic(EOS(STATIC_6908), i623, 2) :|: TRUE
f6908_0_slide93_IntArithmetic(EOS(STATIC_6908), i623, matching1) -> f6920_0_slide93_Store(EOS(STATIC_6920), i713) :|: i713 = i623 / 2 && i713 <= i623 && matching1 = 2
f6920_0_slide93_Store(EOS(STATIC_6920), i713) -> f6960_0_slide93_JMP(EOS(STATIC_6960), i713) :|: TRUE
f6960_0_slide93_JMP(EOS(STATIC_6960), i713) -> f6975_0_slide93_Load(EOS(STATIC_6975), i713) :|: TRUE
f6975_0_slide93_Load(EOS(STATIC_6975), i713) -> f6639_0_slide93_Load(EOS(STATIC_6639), i713) :|: TRUE
f6639_0_slide93_Load(EOS(STATIC_6639), i623) -> f6676_0_slide93_Load(EOS(STATIC_6676), i623) :|: TRUE
f6676_0_slide93_Load(EOS(STATIC_6676), i623) -> f6677_0_slide93_EQ(EOS(STATIC_6677), i623) :|: TRUE
f6677_0_slide93_EQ(EOS(STATIC_6677), i623) -> f6678_0_slide93_EQ(EOS(STATIC_6678), i623) :|: TRUE
f6690_0_check_LE(EOS(STATIC_6690), i623, matching1) -> f6692_0_check_ConstantStackPush(EOS(STATIC_6692), i623) :|: 1 > 0 && matching1 = 1
f6692_0_check_ConstantStackPush(EOS(STATIC_6692), i623) -> f6694_0_check_JMP(EOS(STATIC_6694), i623, 1) :|: TRUE
f6694_0_check_JMP(EOS(STATIC_6694), i623, matching1) -> f6730_0_check_Return(EOS(STATIC_6730), i623, 1) :|: TRUE && matching1 = 1
f6730_0_check_Return(EOS(STATIC_6730), i623, matching1) -> f6741_0_slide93_EQ(EOS(STATIC_6741), i623, 1) :|: TRUE && matching1 = 1
f6741_0_slide93_EQ(EOS(STATIC_6741), i623, matching1) -> f6749_0_slide93_Load(EOS(STATIC_6749), i623) :|: 1 > 0 && matching1 = 1
f6749_0_slide93_Load(EOS(STATIC_6749), i623) -> f6763_0_slide93_FieldAccess(EOS(STATIC_6763), i623) :|: TRUE
f6763_0_slide93_FieldAccess(EOS(STATIC_6763), i623) -> f6793_0_slide93_Store(EOS(STATIC_6793), i623) :|: TRUE
f6793_0_slide93_Store(EOS(STATIC_6793), i623) -> f6820_0_slide93_Load(EOS(STATIC_6820), i623) :|: TRUE
f6820_0_slide93_Load(EOS(STATIC_6820), i623) -> f6832_0_slide93_Load(EOS(STATIC_6832), i623) :|: TRUE
f6832_0_slide93_Load(EOS(STATIC_6832), i623) -> f6852_0_slide93_FieldAccess(EOS(STATIC_6852), i623) :|: TRUE
f6852_0_slide93_FieldAccess(EOS(STATIC_6852), i623) -> f6916_0_slide93_FieldAccess(EOS(STATIC_6916), i623) :|: TRUE
f6916_0_slide93_FieldAccess(EOS(STATIC_6916), i623) -> f6958_0_slide93_FieldAccess(EOS(STATIC_6958), i623) :|: TRUE
f6916_0_slide93_FieldAccess(EOS(STATIC_6916), i623) -> f6959_0_slide93_FieldAccess(EOS(STATIC_6959), i623) :|: TRUE
f6958_0_slide93_FieldAccess(EOS(STATIC_6958), i623) -> f6961_0_slide93_FieldAccess(EOS(STATIC_6961), i623) :|: TRUE
f6958_0_slide93_FieldAccess(EOS(STATIC_6958), i623) -> f6962_0_slide93_FieldAccess(EOS(STATIC_6962), i623) :|: TRUE
f6961_0_slide93_FieldAccess(EOS(STATIC_6961), i623) -> f6988_0_slide93_Load(EOS(STATIC_6988), i623) :|: TRUE
f6988_0_slide93_Load(EOS(STATIC_6988), i623) -> f7007_0_slide93_Load(EOS(STATIC_7007), i623) :|: TRUE
f7007_0_slide93_Load(EOS(STATIC_7007), i623) -> f7026_0_slide93_FieldAccess(EOS(STATIC_7026), i623) :|: TRUE
f7026_0_slide93_FieldAccess(EOS(STATIC_7026), i623) -> f7035_0_slide93_JMP(EOS(STATIC_7035), i623) :|: TRUE
f7035_0_slide93_JMP(EOS(STATIC_7035), i623) -> f7038_0_slide93_Load(EOS(STATIC_7038), i623) :|: TRUE
f7038_0_slide93_Load(EOS(STATIC_7038), i623) -> f7041_0_slide93_FieldAccess(EOS(STATIC_7041), i623) :|: TRUE
f7041_0_slide93_FieldAccess(EOS(STATIC_7041), i623) -> f7043_0_slide93_Store(EOS(STATIC_7043), i623) :|: TRUE
f7043_0_slide93_Store(EOS(STATIC_7043), i623) -> f7045_0_slide93_Load(EOS(STATIC_7045), i623) :|: TRUE
f7045_0_slide93_Load(EOS(STATIC_7045), i623) -> f7049_0_slide93_ConstantStackPush(EOS(STATIC_7049), i623) :|: TRUE
f7049_0_slide93_ConstantStackPush(EOS(STATIC_7049), i623) -> f7057_0_slide93_IntArithmetic(EOS(STATIC_7057), i623, 2) :|: TRUE
f7057_0_slide93_IntArithmetic(EOS(STATIC_7057), i623, matching1) -> f7066_0_slide93_Store(EOS(STATIC_7066), i776) :|: i776 = i623 / 2 && i776 <= i623 && matching1 = 2
f7066_0_slide93_Store(EOS(STATIC_7066), i776) -> f7079_0_slide93_JMP(EOS(STATIC_7079), i776) :|: TRUE
f7079_0_slide93_JMP(EOS(STATIC_7079), i776) -> f7154_0_slide93_Load(EOS(STATIC_7154), i776) :|: TRUE
f7154_0_slide93_Load(EOS(STATIC_7154), i776) -> f6639_0_slide93_Load(EOS(STATIC_6639), i776) :|: TRUE
f6962_0_slide93_FieldAccess(EOS(STATIC_6962), i623) -> f6997_0_slide93_Load(EOS(STATIC_6997), i623) :|: TRUE
f6997_0_slide93_Load(EOS(STATIC_6997), i623) -> f7023_0_slide93_Load(EOS(STATIC_7023), i623) :|: TRUE
f7023_0_slide93_Load(EOS(STATIC_7023), i623) -> f7033_0_slide93_FieldAccess(EOS(STATIC_7033), i623) :|: TRUE
f7033_0_slide93_FieldAccess(EOS(STATIC_7033), i623) -> f7036_0_slide93_JMP(EOS(STATIC_7036), i623) :|: TRUE
f7036_0_slide93_JMP(EOS(STATIC_7036), i623) -> f7039_0_slide93_Load(EOS(STATIC_7039), i623) :|: TRUE
f7039_0_slide93_Load(EOS(STATIC_7039), i623) -> f6759_0_slide93_Load(EOS(STATIC_6759), i623) :|: TRUE
f6959_0_slide93_FieldAccess(EOS(STATIC_6959), i623) -> f6963_0_slide93_Load(EOS(STATIC_6963), i623) :|: TRUE
f6963_0_slide93_Load(EOS(STATIC_6963), i623) -> f7001_0_slide93_Load(EOS(STATIC_7001), i623) :|: TRUE
f7001_0_slide93_Load(EOS(STATIC_7001), i623) -> f7024_0_slide93_FieldAccess(EOS(STATIC_7024), i623) :|: TRUE
f7024_0_slide93_FieldAccess(EOS(STATIC_7024), i623) -> f7034_0_slide93_JMP(EOS(STATIC_7034), i623) :|: TRUE
f7034_0_slide93_JMP(EOS(STATIC_7034), i623) -> f7037_0_slide93_Load(EOS(STATIC_7037), i623) :|: TRUE
f7037_0_slide93_Load(EOS(STATIC_7037), i623) -> f7040_0_slide93_FieldAccess(EOS(STATIC_7040), i623) :|: TRUE
f7040_0_slide93_FieldAccess(EOS(STATIC_7040), i623) -> f7042_0_slide93_Store(EOS(STATIC_7042), i623) :|: TRUE
f7042_0_slide93_Store(EOS(STATIC_7042), i623) -> f7044_0_slide93_Load(EOS(STATIC_7044), i623) :|: TRUE
f7044_0_slide93_Load(EOS(STATIC_7044), i623) -> f7046_0_slide93_ConstantStackPush(EOS(STATIC_7046), i623) :|: TRUE
f7046_0_slide93_ConstantStackPush(EOS(STATIC_7046), i623) -> f7050_0_slide93_IntArithmetic(EOS(STATIC_7050), i623, 2) :|: TRUE
f7050_0_slide93_IntArithmetic(EOS(STATIC_7050), i623, matching1) -> f7058_0_slide93_Store(EOS(STATIC_7058), i775) :|: i775 = i623 / 2 && i775 <= i623 && matching1 = 2
f7058_0_slide93_Store(EOS(STATIC_7058), i775) -> f7071_0_slide93_JMP(EOS(STATIC_7071), i775) :|: TRUE
f7071_0_slide93_JMP(EOS(STATIC_7071), i775) -> f7153_0_slide93_Load(EOS(STATIC_7153), i775) :|: TRUE
f7153_0_slide93_Load(EOS(STATIC_7153), i775) -> f6639_0_slide93_Load(EOS(STATIC_6639), i775) :|: TRUE
Combined rules. Obtained 4 IRulesP rules:
f6678_0_slide93_EQ(EOS(STATIC_6678), i623:0) -> f6678_0_slide93_EQ'(EOS(STATIC_6678), i623:0) :|: i623:0 >= div1 && i623:0 - 2 * div = 1
f6678_0_slide93_EQ'(EOS(STATIC_6678), i623:0) -> f6678_0_slide93_EQ(EOS(STATIC_6678), div1) :|: i623:0 - 2 * div = 1 && i623:0 >= div1 && i623:0 - 2 * div > -2 && i623:0 - 2 * div < 2 && i623:0 - 2 * div1 < 2 && i623:0 - 2 * div1 > -2
f6678_0_slide93_EQ(EOS(STATIC_6678), i623:0) -> f6678_0_slide93_EQ'(EOS(STATIC_6678), i623:0) :|: i623:0 >= div1 && i623:0 - 2 * div = 0
f6678_0_slide93_EQ'(EOS(STATIC_6678), i623:0) -> f6678_0_slide93_EQ(EOS(STATIC_6678), div1) :|: i623:0 - 2 * div = 0 && i623:0 >= div1 && i623:0 - 2 * div > -2 && i623:0 - 2 * div < 2 && i623:0 - 2 * div1 < 2 && i623:0 - 2 * div1 > -2
Filtered constant ground arguments:
   f6678_0_slide93_EQ(x1, x2) -> f6678_0_slide93_EQ(x2)
   f6678_0_slide93_EQ'(x1, x2) -> f6678_0_slide93_EQ'(x2)
   EOS(x1) -> EOS
Finished conversion. Obtained 4 rules.P rules:
f6678_0_slide93_EQ(i623:0) -> f6678_0_slide93_EQ'(i623:0) :|: i623:0 >= div1 && i623:0 - 2 * div = 1
f6678_0_slide93_EQ'(i623:0) -> f6678_0_slide93_EQ(div1) :|: i623:0 >= div1 && i623:0 - 2 * div = 1 && i623:0 - 2 * div > -2 && i623:0 - 2 * div < 2 && i623:0 - 2 * div1 > -2 && i623:0 - 2 * div1 < 2
f6678_0_slide93_EQ(i623:0) -> f6678_0_slide93_EQ'(i623:0) :|: i623:0 >= div1 && i623:0 - 2 * div = 0
f6678_0_slide93_EQ'(i623:0) -> f6678_0_slide93_EQ(div1) :|: i623:0 >= div1 && i623:0 - 2 * div = 0 && i623:0 - 2 * div > -2 && i623:0 - 2 * div < 2 && i623:0 - 2 * div1 > -2 && i623:0 - 2 * div1 < 2

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

(22)
Obligation:
Rules:
f6678_0_slide93_EQ(x) -> f6678_0_slide93_EQ'(x) :|: x >= x1 && x - 2 * x2 = 1
f6678_0_slide93_EQ'(x3) -> f6678_0_slide93_EQ(x4) :|: x3 >= x4 && x3 - 2 * x5 = 1 && x3 - 2 * x5 > -2 && x3 - 2 * x5 < 2 && x3 - 2 * x4 > -2 && x3 - 2 * x4 < 2
f6678_0_slide93_EQ(x6) -> f6678_0_slide93_EQ'(x6) :|: x6 >= x7 && x6 - 2 * x8 = 0
f6678_0_slide93_EQ'(x9) -> f6678_0_slide93_EQ(x10) :|: x9 >= x10 && x9 - 2 * x11 = 0 && x9 - 2 * x11 > -2 && x9 - 2 * x11 < 2 && x9 - 2 * x10 > -2 && x9 - 2 * x10 < 2

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

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

(24)
Obligation:
Rules:
f6678_0_slide93_EQ(x) -> f6678_0_slide93_EQ'(x) :|: x >= x1 && x - 2 * x2 = 1
f6678_0_slide93_EQ'(x3) -> f6678_0_slide93_EQ(x4) :|: x3 >= x4 && x3 - 2 * x5 = 1 && x3 - 2 * x5 > -2 && x3 - 2 * x5 < 2 && x3 - 2 * x4 > -2 && x3 - 2 * x4 < 2
f6678_0_slide93_EQ(x6) -> f6678_0_slide93_EQ'(x6) :|: x6 >= x7 && x6 - 2 * x8 = 0
f6678_0_slide93_EQ'(x9) -> f6678_0_slide93_EQ(x10) :|: x9 >= x10 && x9 - 2 * x11 = 0 && x9 - 2 * x11 > -2 && x9 - 2 * x11 < 2 && x9 - 2 * x10 > -2 && x9 - 2 * x10 < 2

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

(25) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f6678_0_slide93_EQ(x) -> f6678_0_slide93_EQ'(x) :|: x >= x1 && x - 2 * x2 = 1
(2) f6678_0_slide93_EQ'(x3) -> f6678_0_slide93_EQ(x4) :|: x3 >= x4 && x3 - 2 * x5 = 1 && x3 - 2 * x5 > -2 && x3 - 2 * x5 < 2 && x3 - 2 * x4 > -2 && x3 - 2 * x4 < 2
(3) f6678_0_slide93_EQ(x6) -> f6678_0_slide93_EQ'(x6) :|: x6 >= x7 && x6 - 2 * x8 = 0
(4) f6678_0_slide93_EQ'(x9) -> f6678_0_slide93_EQ(x10) :|: x9 >= x10 && x9 - 2 * x11 = 0 && x9 - 2 * x11 > -2 && x9 - 2 * x11 < 2 && x9 - 2 * x10 > -2 && x9 - 2 * x10 < 2

Arcs:
(1) -> (2)
(2) -> (1), (3)
(3) -> (4)
(4) -> (1), (3)

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

(26)
Obligation:

Termination digraph:
Nodes:
(1) f6678_0_slide93_EQ(x) -> f6678_0_slide93_EQ'(x) :|: x >= x1 && x - 2 * x2 = 1
(2) f6678_0_slide93_EQ'(x9) -> f6678_0_slide93_EQ(x10) :|: x9 >= x10 && x9 - 2 * x11 = 0 && x9 - 2 * x11 > -2 && x9 - 2 * x11 < 2 && x9 - 2 * x10 > -2 && x9 - 2 * x10 < 2
(3) f6678_0_slide93_EQ(x6) -> f6678_0_slide93_EQ'(x6) :|: x6 >= x7 && x6 - 2 * x8 = 0
(4) f6678_0_slide93_EQ'(x3) -> f6678_0_slide93_EQ(x4) :|: x3 >= x4 && x3 - 2 * x5 = 1 && x3 - 2 * x5 > -2 && x3 - 2 * x5 < 2 && x3 - 2 * x4 > -2 && x3 - 2 * x4 < 2

Arcs:
(1) -> (4)
(2) -> (1), (3)
(3) -> (2)
(4) -> (1), (3)

This digraph is fully evaluated!

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

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

(28)
Obligation:
Rules:
f6678_0_slide93_EQ(x6:0) -> f6678_0_slide93_EQ'(x6:0) :|: x7:0 <= x6:0 && x6:0 - 2 * x8:0 = 0
f6678_0_slide93_EQ'(x3:0) -> f6678_0_slide93_EQ(x4:0) :|: x3:0 - 2 * x4:0 > -2 && x3:0 - 2 * x4:0 < 2 && x3:0 - 2 * x5:0 < 2 && x3:0 - 2 * x5:0 > -2 && x3:0 - 2 * x5:0 = 1 && x4:0 <= x3:0
f6678_0_slide93_EQ(x:0) -> f6678_0_slide93_EQ'(x:0) :|: x:0 >= x1:0 && x:0 - 2 * x2:0 = 1
f6678_0_slide93_EQ'(x9:0) -> f6678_0_slide93_EQ(x10:0) :|: x9:0 - 2 * x10:0 > -2 && x9:0 - 2 * x10:0 < 2 && x9:0 - 2 * x11:0 < 2 && x9:0 - 2 * x11:0 > -2 && x9:0 - 2 * x11:0 = 0 && x9:0 >= x10:0

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

(29) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f6678_0_slide93_EQ(INTEGER)
f6678_0_slide93_EQ'(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(30)
Obligation:
Rules:
f6678_0_slide93_EQ(x6:0) -> f6678_0_slide93_EQ'(x6:0) :|: x7:0 <= x6:0 && x6:0 - 2 * x8:0 = 0
f6678_0_slide93_EQ'(x3:0) -> f6678_0_slide93_EQ(x4:0) :|: x3:0 - 2 * x4:0 > -2 && x3:0 - 2 * x4:0 < 2 && x3:0 - 2 * x5:0 < 2 && x3:0 - 2 * x5:0 > -2 && x3:0 - 2 * x5:0 = 1 && x4:0 <= x3:0
f6678_0_slide93_EQ(x:0) -> f6678_0_slide93_EQ'(x:0) :|: x:0 >= x1:0 && x:0 - 2 * x2:0 = 1
f6678_0_slide93_EQ'(x9:0) -> f6678_0_slide93_EQ(x10:0) :|: x9:0 - 2 * x10:0 > -2 && x9:0 - 2 * x10:0 < 2 && x9:0 - 2 * x11:0 < 2 && x9:0 - 2 * x11:0 > -2 && x9:0 - 2 * x11:0 = 0 && x9:0 >= x10:0

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

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

(32)
Obligation:
Rules:
f6678_0_slide93_EQ'(x3:0:0) -> f6678_0_slide93_EQ(x4:0:0) :|: x3:0:0 - 2 * x5:0:0 = 1 && x4:0:0 <= x3:0:0 && x3:0:0 - 2 * x5:0:0 > -2 && x3:0:0 - 2 * x5:0:0 < 2 && x3:0:0 - 2 * x4:0:0 < 2 && x3:0:0 - 2 * x4:0:0 > -2
f6678_0_slide93_EQ(x6:0:0) -> f6678_0_slide93_EQ'(x6:0:0) :|: x7:0:0 <= x6:0:0 && x6:0:0 - 2 * x8:0:0 = 0
f6678_0_slide93_EQ(x:0:0) -> f6678_0_slide93_EQ'(x:0:0) :|: x:0:0 >= x1:0:0 && x:0:0 - 2 * x2:0:0 = 1
f6678_0_slide93_EQ'(x9:0:0) -> f6678_0_slide93_EQ(x10:0:0) :|: x9:0:0 - 2 * x11:0:0 = 0 && x9:0:0 >= x10:0:0 && x9:0:0 - 2 * x11:0:0 > -2 && x9:0:0 - 2 * x11:0:0 < 2 && x9:0:0 - 2 * x10:0:0 < 2 && x9:0:0 - 2 * x10:0:0 > -2

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

(33) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x3:0:0) -> f(2, x4:0:0) :|: pc = 1 && (x3:0:0 - 2 * x5:0:0 = 1 && x4:0:0 <= x3:0:0 && x3:0:0 - 2 * x5:0:0 > -2 && x3:0:0 - 2 * x5:0:0 < 2 && x3:0:0 - 2 * x4:0:0 < 2 && x3:0:0 - 2 * x4:0:0 > -2)
f(pc, x6:0:0) -> f(1, x6:0:0) :|: pc = 2 && (x7:0:0 <= x6:0:0 && x6:0:0 - 2 * x8:0:0 = 0)
f(pc, x:0:0) -> f(1, x:0:0) :|: pc = 2 && (x:0:0 >= x1:0:0 && x:0:0 - 2 * x2:0:0 = 1)
f(pc, x9:0:0) -> f(2, x10:0:0) :|: pc = 1 && (x9:0:0 - 2 * x11:0:0 = 0 && x9:0:0 >= x10:0:0 && x9:0:0 - 2 * x11:0:0 > -2 && x9:0:0 - 2 * x11:0:0 < 2 && x9:0:0 - 2 * x10:0:0 < 2 && x9:0:0 - 2 * x10:0:0 > -2)
Witness term starting non-terminating reduction: f(2, -1)
----------------------------------------

(34)
NO

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

(35)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: Kernel93.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*Kernel93: [next]
*Marker field analysis yielded the following relations that could be markers:

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

(36) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 57 IRulesP rules:
f5823_0_slide93_EQ(EOS(STATIC_5823), i460, o1522[Kernel93.next]o1522) -> f5836_0_slide93_Load(EOS(STATIC_5836), i460, o1522[Kernel93.next]o1522) :|: TRUE
f5836_0_slide93_Load(EOS(STATIC_5836), i460, o1522[Kernel93.next]o1522) -> f5852_0_slide93_Store(EOS(STATIC_5852), i460, o1522[Kernel93.next]o1522) :|: TRUE
f5852_0_slide93_Store(EOS(STATIC_5852), i460, o1522[Kernel93.next]o1522) -> f5863_0_slide93_Load(EOS(STATIC_5863), i460, o1522[Kernel93.next]o1522) :|: TRUE
f5863_0_slide93_Load(EOS(STATIC_5863), i460, o1522[Kernel93.next]o1522) -> f5870_0_slide93_InvokeMethod(EOS(STATIC_5870), i460, i460, o1522[Kernel93.next]o1522) :|: TRUE
f5870_0_slide93_InvokeMethod(EOS(STATIC_5870), i460, i460, o1522[Kernel93.next]o1522) -> f5873_0_check_Load(EOS(STATIC_5873), i460, i460, o1522[Kernel93.next]o1522) :|: TRUE
f5873_0_check_Load(EOS(STATIC_5873), i460, i460, o1522[Kernel93.next]o1522) -> f5878_0_check_ConstantStackPush(EOS(STATIC_5878), i460, i460, o1522[Kernel93.next]o1522) :|: TRUE
f5878_0_check_ConstantStackPush(EOS(STATIC_5878), i460, i460, o1522[Kernel93.next]o1522) -> f5881_0_check_IntArithmetic(EOS(STATIC_5881), i460, i460, 2, o1522[Kernel93.next]o1522) :|: TRUE
f5881_0_check_IntArithmetic(EOS(STATIC_5881), i460, i460, matching1, o1522[Kernel93.next]o1522) -> f5884_0_check_LE(EOS(STATIC_5884), i460, i460 % 2, o1522[Kernel93.next]o1522) :|: TRUE && matching1 = 2
f5884_0_check_LE(EOS(STATIC_5884), i460, matching1, o1522[Kernel93.next]o1522) -> f5887_0_check_LE(EOS(STATIC_5887), i460, 0, o1522[Kernel93.next]o1522) :|: TRUE && matching1 = 0
f5884_0_check_LE(EOS(STATIC_5884), i460, matching1, o1522[Kernel93.next]o1522) -> f5888_0_check_LE(EOS(STATIC_5888), i460, 1, o1522[Kernel93.next]o1522) :|: TRUE && matching1 = 1
f5887_0_check_LE(EOS(STATIC_5887), i460, matching1, o1522[Kernel93.next]o1522) -> f5891_0_check_ConstantStackPush(EOS(STATIC_5891), i460, o1522[Kernel93.next]o1522) :|: 0 <= 0 && matching1 = 0
f5891_0_check_ConstantStackPush(EOS(STATIC_5891), i460, o1522[Kernel93.next]o1522) -> f5895_0_check_Return(EOS(STATIC_5895), i460, 0, o1522[Kernel93.next]o1522) :|: TRUE
f5895_0_check_Return(EOS(STATIC_5895), i460, matching1, o1522[Kernel93.next]o1522) -> f5899_0_slide93_EQ(EOS(STATIC_5899), i460, 0, o1522[Kernel93.next]o1522) :|: TRUE && matching1 = 0
f5899_0_slide93_EQ(EOS(STATIC_5899), i460, matching1, o1522[Kernel93.next]o1522) -> f5904_0_slide93_Load(EOS(STATIC_5904), i460, o1522[Kernel93.next]o1522) :|: TRUE && matching1 = 0
f5904_0_slide93_Load(EOS(STATIC_5904), i460, o1522[Kernel93.next]o1522) -> f5932_0_slide93_Store(EOS(STATIC_5932), i460, o1522[Kernel93.next]o1522) :|: TRUE
f5932_0_slide93_Store(EOS(STATIC_5932), i460, o1522[Kernel93.next]o1522) -> f5942_0_slide93_Load(EOS(STATIC_5942), i460, o1522[Kernel93.next]o1522) :|: TRUE
f5942_0_slide93_Load(EOS(STATIC_5942), i460, o1522[Kernel93.next]o1522) -> f5969_0_slide93_FieldAccess(EOS(STATIC_5969), i460, o1522[Kernel93.next]o1522) :|: TRUE
f5969_0_slide93_FieldAccess(EOS(STATIC_5969), i460, o1721[Kernel93.next]o1721) -> f5977_0_slide93_FieldAccess(EOS(STATIC_5977), i460, o1722[Kernel93.next]o1721) :|: o1722[Kernel93.next]o1721 < o1721[Kernel93.next]o1721 && o1721[Kernel93.next]o1721 >= 0
f5977_0_slide93_FieldAccess(EOS(STATIC_5977), i460, o1722[Kernel93.next]o1721) -> f6016_0_slide93_FieldAccess(EOS(STATIC_6016), i460, o1722[Kernel93.next]o1721) :|: o1722[Kernel93.next]o1721 > 0
f6016_0_slide93_FieldAccess(EOS(STATIC_6016), i460, o1722[Kernel93.next]o1721) -> f6024_0_slide93_Store(EOS(STATIC_6024), i460, o1722[Kernel93.next]o1721) :|: TRUE
f6024_0_slide93_Store(EOS(STATIC_6024), i460, o1722[Kernel93.next]o1721) -> f6028_0_slide93_Load(EOS(STATIC_6028), i460, o1722[Kernel93.next]o1721) :|: TRUE
f6028_0_slide93_Load(EOS(STATIC_6028), i460, o1722[Kernel93.next]o1721) -> f6032_0_slide93_ConstantStackPush(EOS(STATIC_6032), i460, o1722[Kernel93.next]o1721) :|: TRUE
f6032_0_slide93_ConstantStackPush(EOS(STATIC_6032), i460, o1722[Kernel93.next]o1721) -> f6036_0_slide93_IntArithmetic(EOS(STATIC_6036), i460, 2, o1722[Kernel93.next]o1721) :|: TRUE
f6036_0_slide93_IntArithmetic(EOS(STATIC_6036), i460, matching1, o1722[Kernel93.next]o1721) -> f6089_0_slide93_Store(EOS(STATIC_6089), i534, o1722[Kernel93.next]o1721) :|: i534 = i460 / 2 && i534 <= i460 && matching1 = 2
f6089_0_slide93_Store(EOS(STATIC_6089), i534, o1722[Kernel93.next]o1721) -> f6143_0_slide93_JMP(EOS(STATIC_6143), i534, o1722[Kernel93.next]o1721) :|: TRUE
f6143_0_slide93_JMP(EOS(STATIC_6143), i534, o1722[Kernel93.next]o1721) -> f6180_0_slide93_Load(EOS(STATIC_6180), i534, o1722[Kernel93.next]o1721) :|: TRUE
f6180_0_slide93_Load(EOS(STATIC_6180), i534, o1722[Kernel93.next]o1721) -> f5776_0_slide93_Load(EOS(STATIC_5776), i534, o1722[Kernel93.next]o1722) :|: TRUE
f5776_0_slide93_Load(EOS(STATIC_5776), i460, o1522[Kernel93.next]o1522) -> f5785_0_slide93_Load(EOS(STATIC_5785), i460, o1522[Kernel93.next]o1522) :|: TRUE
f5785_0_slide93_Load(EOS(STATIC_5785), i460, o1522[Kernel93.next]o1522) -> f5801_0_slide93_EQ(EOS(STATIC_5801), i460, o1522[Kernel93.next]o1522) :|: TRUE
f5801_0_slide93_EQ(EOS(STATIC_5801), i460, o1522[Kernel93.next]o1522) -> f5823_0_slide93_EQ(EOS(STATIC_5823), i460, o1522[Kernel93.next]o1522) :|: o1522[Kernel93.next]o1522 > 0
f5888_0_check_LE(EOS(STATIC_5888), i460, matching1, o1522[Kernel93.next]o1522) -> f5892_0_check_ConstantStackPush(EOS(STATIC_5892), i460, o1522[Kernel93.next]o1522) :|: 1 > 0 && matching1 = 1
f5892_0_check_ConstantStackPush(EOS(STATIC_5892), i460, o1522[Kernel93.next]o1522) -> f5896_0_check_JMP(EOS(STATIC_5896), i460, 1, o1522[Kernel93.next]o1522) :|: TRUE
f5896_0_check_JMP(EOS(STATIC_5896), i460, matching1, o1522[Kernel93.next]o1522) -> f5900_0_check_Return(EOS(STATIC_5900), i460, 1, o1522[Kernel93.next]o1522) :|: TRUE && matching1 = 1
f5900_0_check_Return(EOS(STATIC_5900), i460, matching1, o1522[Kernel93.next]o1522) -> f5913_0_slide93_EQ(EOS(STATIC_5913), i460, 1, o1522[Kernel93.next]o1522) :|: TRUE && matching1 = 1
f5913_0_slide93_EQ(EOS(STATIC_5913), i460, matching1, o1522[Kernel93.next]o1522) -> f5938_0_slide93_Load(EOS(STATIC_5938), i460, o1522[Kernel93.next]o1522) :|: 1 > 0 && matching1 = 1
f5938_0_slide93_Load(EOS(STATIC_5938), i460, o1522[Kernel93.next]o1522) -> f5958_0_slide93_FieldAccess(EOS(STATIC_5958), i460, o1522[Kernel93.next]o1522) :|: TRUE
f5958_0_slide93_FieldAccess(EOS(STATIC_5958), i460, o1719[Kernel93.next]o1719) -> f5974_0_slide93_FieldAccess(EOS(STATIC_5974), i460, o1720[Kernel93.next]o1719) :|: o1720[Kernel93.next]o1719 < o1719[Kernel93.next]o1719 && o1719[Kernel93.next]o1719 >= 0
f5974_0_slide93_FieldAccess(EOS(STATIC_5974), i460, o1720[Kernel93.next]o1719) -> f5997_0_slide93_FieldAccess(EOS(STATIC_5997), i460, o1720[Kernel93.next]o1719) :|: o1720[Kernel93.next]o1719 > 0
f5997_0_slide93_FieldAccess(EOS(STATIC_5997), i460, o1720[Kernel93.next]o1719) -> f6022_0_slide93_Store(EOS(STATIC_6022), i460, o1720[Kernel93.next]o1719) :|: TRUE
f6022_0_slide93_Store(EOS(STATIC_6022), i460, o1720[Kernel93.next]o1719) -> f6026_0_slide93_Load(EOS(STATIC_6026), i460, o1720[Kernel93.next]o1719) :|: TRUE
f6026_0_slide93_Load(EOS(STATIC_6026), i460, o1720[Kernel93.next]o1719) -> f6030_0_slide93_Load(EOS(STATIC_6030), i460, o1720[Kernel93.next]o1719) :|: TRUE
f6030_0_slide93_Load(EOS(STATIC_6030), i460, o1720[Kernel93.next]o1719) -> f6034_0_slide93_FieldAccess(EOS(STATIC_6034), i460, o1720[Kernel93.next]o1719) :|: TRUE
f6034_0_slide93_FieldAccess(EOS(STATIC_6034), i460, o1720[Kernel93.next]o1719) -> f6064_0_slide93_FieldAccess(EOS(STATIC_6064), i460, o1720[Kernel93.next]o1719) :|: TRUE
f6064_0_slide93_FieldAccess(EOS(STATIC_6064), i460, o1720[Kernel93.next]o1719) -> f6133_0_slide93_Load(EOS(STATIC_6133), i460) :|: TRUE
f6133_0_slide93_Load(EOS(STATIC_6133), i460) -> f6145_0_slide93_Load(EOS(STATIC_6145), i460) :|: TRUE
f6145_0_slide93_Load(EOS(STATIC_6145), i460) -> f6249_0_slide93_FieldAccess(EOS(STATIC_6249), i460) :|: TRUE
f6249_0_slide93_FieldAccess(EOS(STATIC_6249), i460) -> f6278_0_slide93_JMP(EOS(STATIC_6278), i460) :|: TRUE
f6278_0_slide93_JMP(EOS(STATIC_6278), i460) -> f6322_0_slide93_Load(EOS(STATIC_6322), i460) :|: TRUE
f6322_0_slide93_Load(EOS(STATIC_6322), i460) -> f6357_0_slide93_FieldAccess(EOS(STATIC_6357), i460) :|: TRUE
f6357_0_slide93_FieldAccess(EOS(STATIC_6357), i460) -> f6389_0_slide93_Store(EOS(STATIC_6389), i460) :|: TRUE
f6389_0_slide93_Store(EOS(STATIC_6389), i460) -> f6417_0_slide93_Load(EOS(STATIC_6417), i460) :|: TRUE
f6417_0_slide93_Load(EOS(STATIC_6417), i460) -> f6445_0_slide93_ConstantStackPush(EOS(STATIC_6445), i460) :|: TRUE
f6445_0_slide93_ConstantStackPush(EOS(STATIC_6445), i460) -> f6476_0_slide93_IntArithmetic(EOS(STATIC_6476), i460, 2) :|: TRUE
f6476_0_slide93_IntArithmetic(EOS(STATIC_6476), i460, matching1) -> f6501_0_slide93_Store(EOS(STATIC_6501), i592) :|: i592 = i460 / 2 && i592 <= i460 && matching1 = 2
f6501_0_slide93_Store(EOS(STATIC_6501), i592) -> f6536_0_slide93_JMP(EOS(STATIC_6536), i592) :|: TRUE
f6536_0_slide93_JMP(EOS(STATIC_6536), i592) -> f6584_0_slide93_Load(EOS(STATIC_6584), i592) :|: TRUE
f6584_0_slide93_Load(EOS(STATIC_6584), i592) -> f5776_0_slide93_Load(EOS(STATIC_5776), i592, o1719[Kernel93.next]o1719) :|: o1719[Kernel93.next]o1719 = 1
Combined rules. Obtained 4 IRulesP rules:
f5823_0_slide93_EQ(EOS(STATIC_5823), i460:0, o1522[Kernel93.next]o1522:0) -> f5823_0_slide93_EQ'(EOS(STATIC_5823), i460:0, o1522[Kernel93.next]o1522:0) :|: i460:0 - 2 * div = 1 && o1522[Kernel93.next]o1522:0 > -1 && o1720[Kernel93.next]o1719:0 < o1522[Kernel93.next]o1522:0 && i460:0 >= div1 && o1720[Kernel93.next]o1719:0 > 0
f5823_0_slide93_EQ'(EOS(STATIC_5823), i460:0, o1522[Kernel93.next]o1522:0) -> f5823_0_slide93_EQ(EOS(STATIC_5823), div1, 1) :|: i460:0 - 2 * div = 1 && o1522[Kernel93.next]o1522:0 > -1 && o1720[Kernel93.next]o1719:0 < o1522[Kernel93.next]o1522:0 && o1720[Kernel93.next]o1719:0 > 0 && i460:0 >= div1 && i460:0 - 2 * div > -2 && i460:0 - 2 * div < 2 && i460:0 - 2 * div1 < 2 && i460:0 - 2 * div1 > -2
f5823_0_slide93_EQ(EOS(STATIC_5823), i460:0, o1522[Kernel93.next]o1522:0) -> f5823_0_slide93_EQ'(EOS(STATIC_5823), i460:0, o1522[Kernel93.next]o1522:0) :|: i460:0 - 2 * div = 0 && o1522[Kernel93.next]o1522:0 > -1 && o1722[Kernel93.next]o1721:0 < o1522[Kernel93.next]o1522:0 && o1722[Kernel93.next]o1721:0 > 0 && o1722[Kernel93.next]o1722:0 > 0 && i460:0 >= div1
f5823_0_slide93_EQ'(EOS(STATIC_5823), i460:0, o1522[Kernel93.next]o1522:0) -> f5823_0_slide93_EQ(EOS(STATIC_5823), div1, o1722[Kernel93.next]o1722:0) :|: i460:0 - 2 * div = 0 && o1522[Kernel93.next]o1522:0 > -1 && o1722[Kernel93.next]o1721:0 < o1522[Kernel93.next]o1522:0 && o1722[Kernel93.next]o1721:0 > 0 && i460:0 >= div1 && o1722[Kernel93.next]o1722:0 > 0 && i460:0 - 2 * div > -2 && i460:0 - 2 * div < 2 && i460:0 - 2 * div1 < 2 && i460:0 - 2 * div1 > -2
Filtered constant ground arguments:
   f5823_0_slide93_EQ(x1, x2, x3) -> f5823_0_slide93_EQ(x2, x3)
   f5823_0_slide93_EQ'(x1, x2, x3) -> f5823_0_slide93_EQ'(x2, x3)
   EOS(x1) -> EOS
Finished conversion. Obtained 4 rules.P rules:
f5823_0_slide93_EQ(i460:0, o1522[Kernel93.next]o1522:0) -> f5823_0_slide93_EQ'(i460:0, o1522[Kernel93.next]o1522:0) :|: o1522[Kernel93.next]o1522:0 > -1 && i460:0 - 2 * div = 1 && o1720[Kernel93.next]o1719:0 < o1522[Kernel93.next]o1522:0 && o1720[Kernel93.next]o1719:0 > 0 && i460:0 >= div1
f5823_0_slide93_EQ'(i460:0, o1522[Kernel93.next]o1522:0) -> f5823_0_slide93_EQ(div1, 1) :|: o1522[Kernel93.next]o1522:0 > -1 && i460:0 - 2 * div = 1 && o1720[Kernel93.next]o1719:0 < o1522[Kernel93.next]o1522:0 && o1720[Kernel93.next]o1719:0 > 0 && i460:0 >= div1 && i460:0 - 2 * div > -2 && i460:0 - 2 * div < 2 && i460:0 - 2 * div1 > -2 && i460:0 - 2 * div1 < 2
f5823_0_slide93_EQ(i460:0, o1522[Kernel93.next]o1522:0) -> f5823_0_slide93_EQ'(i460:0, o1522[Kernel93.next]o1522:0) :|: o1522[Kernel93.next]o1522:0 > -1 && i460:0 - 2 * div = 0 && o1722[Kernel93.next]o1721:0 < o1522[Kernel93.next]o1522:0 && o1722[Kernel93.next]o1721:0 > 0 && i460:0 >= div1 && o1722[Kernel93.next]o1722:0 > 0
f5823_0_slide93_EQ'(i460:0, o1522[Kernel93.next]o1522:0) -> f5823_0_slide93_EQ(div1, o1722[Kernel93.next]o1722:0) :|: o1522[Kernel93.next]o1522:0 > -1 && i460:0 - 2 * div = 0 && o1722[Kernel93.next]o1721:0 < o1522[Kernel93.next]o1522:0 && o1722[Kernel93.next]o1721:0 > 0 && i460:0 >= div1 && o1722[Kernel93.next]o1722:0 > 0 && i460:0 - 2 * div > -2 && i460:0 - 2 * div < 2 && i460:0 - 2 * div1 > -2 && i460:0 - 2 * div1 < 2

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

(37)
Obligation:
Rules:
f5823_0_slide93_EQ(x, x1) -> f5823_0_slide93_EQ'(x, x1) :|: x1 > -1 && x - 2 * x2 = 1 && x3 < x1 && x3 > 0 && x >= x4
f5823_0_slide93_EQ'(x5, x6) -> f5823_0_slide93_EQ(x7, 1) :|: x6 > -1 && x5 - 2 * x8 = 1 && x9 < x6 && x9 > 0 && x5 >= x7 && x5 - 2 * x8 > -2 && x5 - 2 * x8 < 2 && x5 - 2 * x7 > -2 && x5 - 2 * x7 < 2
f5823_0_slide93_EQ(x10, x11) -> f5823_0_slide93_EQ'(x10, x11) :|: x11 > -1 && x10 - 2 * x12 = 0 && x13 < x11 && x13 > 0 && x10 >= x14 && x15 > 0
f5823_0_slide93_EQ'(x16, x17) -> f5823_0_slide93_EQ(x18, x19) :|: x17 > -1 && x16 - 2 * x20 = 0 && x21 < x17 && x21 > 0 && x16 >= x18 && x19 > 0 && x16 - 2 * x20 > -2 && x16 - 2 * x20 < 2 && x16 - 2 * x18 > -2 && x16 - 2 * x18 < 2

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

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

(39)
Obligation:
Rules:
f5823_0_slide93_EQ(x, x1) -> f5823_0_slide93_EQ'(x, x1) :|: x1 > -1 && x - 2 * x2 = 1 && x3 < x1 && x3 > 0 && x >= x4
f5823_0_slide93_EQ'(x5, x6) -> f5823_0_slide93_EQ(x7, 1) :|: x6 > -1 && x5 - 2 * x8 = 1 && x9 < x6 && x9 > 0 && x5 >= x7 && x5 - 2 * x8 > -2 && x5 - 2 * x8 < 2 && x5 - 2 * x7 > -2 && x5 - 2 * x7 < 2
f5823_0_slide93_EQ(x10, x11) -> f5823_0_slide93_EQ'(x10, x11) :|: x11 > -1 && x10 - 2 * x12 = 0 && x13 < x11 && x13 > 0 && x10 >= x14 && x15 > 0
f5823_0_slide93_EQ'(x16, x17) -> f5823_0_slide93_EQ(x18, x19) :|: x17 > -1 && x16 - 2 * x20 = 0 && x21 < x17 && x21 > 0 && x16 >= x18 && x19 > 0 && x16 - 2 * x20 > -2 && x16 - 2 * x20 < 2 && x16 - 2 * x18 > -2 && x16 - 2 * x18 < 2

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

(40) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f5823_0_slide93_EQ(x, x1) -> f5823_0_slide93_EQ'(x, x1) :|: x1 > -1 && x - 2 * x2 = 1 && x3 < x1 && x3 > 0 && x >= x4
(2) f5823_0_slide93_EQ'(x5, x6) -> f5823_0_slide93_EQ(x7, 1) :|: x6 > -1 && x5 - 2 * x8 = 1 && x9 < x6 && x9 > 0 && x5 >= x7 && x5 - 2 * x8 > -2 && x5 - 2 * x8 < 2 && x5 - 2 * x7 > -2 && x5 - 2 * x7 < 2
(3) f5823_0_slide93_EQ(x10, x11) -> f5823_0_slide93_EQ'(x10, x11) :|: x11 > -1 && x10 - 2 * x12 = 0 && x13 < x11 && x13 > 0 && x10 >= x14 && x15 > 0
(4) f5823_0_slide93_EQ'(x16, x17) -> f5823_0_slide93_EQ(x18, x19) :|: x17 > -1 && x16 - 2 * x20 = 0 && x21 < x17 && x21 > 0 && x16 >= x18 && x19 > 0 && x16 - 2 * x20 > -2 && x16 - 2 * x20 < 2 && x16 - 2 * x18 > -2 && x16 - 2 * x18 < 2

Arcs:
(1) -> (2)
(3) -> (4)
(4) -> (1), (3)

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

(41)
Obligation:

Termination digraph:
Nodes:
(1) f5823_0_slide93_EQ(x10, x11) -> f5823_0_slide93_EQ'(x10, x11) :|: x11 > -1 && x10 - 2 * x12 = 0 && x13 < x11 && x13 > 0 && x10 >= x14 && x15 > 0
(2) f5823_0_slide93_EQ'(x16, x17) -> f5823_0_slide93_EQ(x18, x19) :|: x17 > -1 && x16 - 2 * x20 = 0 && x21 < x17 && x21 > 0 && x16 >= x18 && x19 > 0 && x16 - 2 * x20 > -2 && x16 - 2 * x20 < 2 && x16 - 2 * x18 > -2 && x16 - 2 * x18 < 2

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

This digraph is fully evaluated!

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

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

(43)
Obligation:
Rules:
f5823_0_slide93_EQ(x10:0, x11:0) -> f5823_0_slide93_EQ(x18:0, x19:0) :|: x10:0 - 2 * x18:0 < 2 && x15:0 > 0 && x14:0 <= x10:0 && x10:0 - 2 * x18:0 > -2 && x13:0 > 0 && x10:0 - 2 * x20:0 < 2 && x13:0 < x11:0 && x10:0 - 2 * x20:0 > -2 && x10:0 - 2 * x12:0 = 0 && x19:0 > 0 && x18:0 <= x10:0 && x21:0 > 0 && x21:0 < x11:0 && x10:0 - 2 * x20:0 = 0 && x11:0 > -1

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

(44) FilterProof (EQUIVALENT)
Used the following sort dictionary for filtering: 
f5823_0_slide93_EQ(INTEGER, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(45)
Obligation:
Rules:
f5823_0_slide93_EQ(x10:0, x11:0) -> f5823_0_slide93_EQ(x18:0, x19:0) :|: x10:0 - 2 * x18:0 < 2 && x15:0 > 0 && x14:0 <= x10:0 && x10:0 - 2 * x18:0 > -2 && x13:0 > 0 && x10:0 - 2 * x20:0 < 2 && x13:0 < x11:0 && x10:0 - 2 * x20:0 > -2 && x10:0 - 2 * x12:0 = 0 && x19:0 > 0 && x18:0 <= x10:0 && x21:0 > 0 && x21:0 < x11:0 && x10:0 - 2 * x20:0 = 0 && x11:0 > -1

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

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

(47)
Obligation:
Rules:
f5823_0_slide93_EQ(x10:0:0, x11:0:0) -> f5823_0_slide93_EQ(x18:0:0, x19:0:0) :|: x10:0:0 - 2 * x20:0:0 = 0 && x11:0:0 > -1 && x21:0:0 < x11:0:0 && x21:0:0 > 0 && x18:0:0 <= x10:0:0 && x19:0:0 > 0 && x10:0:0 - 2 * x12:0:0 = 0 && x10:0:0 - 2 * x20:0:0 > -2 && x13:0:0 < x11:0:0 && x10:0:0 - 2 * x20:0:0 < 2 && x13:0:0 > 0 && x10:0:0 - 2 * x18:0:0 > -2 && x14:0:0 <= x10:0:0 && x15:0:0 > 0 && x10:0:0 - 2 * x18:0:0 < 2

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

(48) IntTRSPeriodicNontermProof (COMPLETE)
Normalized system to the following form:
f(pc, x10:0:0, x11:0:0) -> f(1, x18:0:0, x19:0:0) :|: pc = 1 && (x10:0:0 - 2 * x20:0:0 = 0 && x11:0:0 > -1 && x21:0:0 < x11:0:0 && x21:0:0 > 0 && x18:0:0 <= x10:0:0 && x19:0:0 > 0 && x10:0:0 - 2 * x12:0:0 = 0 && x10:0:0 - 2 * x20:0:0 > -2 && x13:0:0 < x11:0:0 && x10:0:0 - 2 * x20:0:0 < 2 && x13:0:0 > 0 && x10:0:0 - 2 * x18:0:0 > -2 && x14:0:0 <= x10:0:0 && x15:0:0 > 0 && x10:0:0 - 2 * x18:0:0 < 2)
Witness term starting non-terminating reduction: f(1, 0, 15)
----------------------------------------

(49)
NO