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


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


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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


termination of the given Bare JBC problem could be proven:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 96 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 486 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) JBCTerminationSCC
(7) SCCToIRSProof [SOUND, 124 ms]
(8) IRSwT
(9) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
(10) IRSwT
(11) IRSwTTerminationDigraphProof [EQUIVALENT, 54 ms]
(12) IRSwT
(13) IntTRSCompressionProof [EQUIVALENT, 0 ms]
(14) IRSwT
(15) TempFilterProof [SOUND, 15 ms]
(16) IntTRS
(17) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
(18) YES


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

(0)
Obligation:
need to prove termination of the following program:
public class Fractale1 {
    public static void fractale(int i, Point p1, Point p2) {
	if (i > 0) {
	    int x3 = (p1.x + p1.y + p2.x - p2.y) / 2;
	    int y3 = (p2.x + p2.y + p1.y - p1.x) / 2;
	    Point p3 = new Point(x3, y3);
	    fractale(i-1, p1, p3);
	    fractale(i-1, p3, p2);
	}
    }

    public static void main(String args[]) {
	fractale(args.length, new Point(0, 0), new Point(200, 200));
    }
}

public class Point {
    
    public int x;
    public int y;

    public Point(int x, int y) {
	this.x = x;
	this.y = y;
    }
}


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

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

(2)
Obligation:
need to prove termination of the following program:
public class Fractale1 {
    public static void fractale(int i, Point p1, Point p2) {
	if (i > 0) {
	    int x3 = (p1.x + p1.y + p2.x - p2.y) / 2;
	    int y3 = (p2.x + p2.y + p1.y - p1.x) / 2;
	    Point p3 = new Point(x3, y3);
	    fractale(i-1, p1, p3);
	    fractale(i-1, p3, p2);
	}
    }

    public static void main(String args[]) {
	fractale(args.length, new Point(0, 0), new Point(200, 200));
    }
}

public class Point {
    
    public int x;
    public int y;

    public Point(int x, int y) {
	this.x = x;
	this.y = y;
    }
}


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

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

(4)
Obligation:
Termination Graph based on JBC Program:
Fractale1.main([Ljava/lang/String;)V: Graph of 40 nodes with 0 SCCs.



Fractale1.fractale(ILPoint;LPoint;)V: Graph of 73 nodes with 0 SCCs.





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

(5) TerminationGraphToSCCProof (SOUND)
Splitted TerminationGraph to 1 SCCs.
----------------------------------------

(6)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: Fractale1.fractale(ILPoint;LPoint;)V
SCC calls the following helper methods: Fractale1.fractale(ILPoint;LPoint;)V
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*Point: [x, y]
*Marker field analysis yielded the following relations that could be markers:

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

(7) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 70 IRulesP rules:
f2880_0_fractale_LE(EOS(STATIC_2880), i187, i187, i187) -> f2884_0_fractale_LE(EOS(STATIC_2884), i187, i187, i187) :|: TRUE
f2884_0_fractale_LE(EOS(STATIC_2884), i187, i187, i187) -> f2889_0_fractale_Load(EOS(STATIC_2889), i187, i187) :|: i187 > 0
f2889_0_fractale_Load(EOS(STATIC_2889), i187, i187) -> f2893_0_fractale_FieldAccess(EOS(STATIC_2893), i187, i187) :|: TRUE
f2893_0_fractale_FieldAccess(EOS(STATIC_2893), i187, i187) -> f2905_0_fractale_Load(EOS(STATIC_2905), i187, i187) :|: TRUE
f2905_0_fractale_Load(EOS(STATIC_2905), i187, i187) -> f2912_0_fractale_FieldAccess(EOS(STATIC_2912), i187, i187) :|: TRUE
f2912_0_fractale_FieldAccess(EOS(STATIC_2912), i187, i187) -> f2915_0_fractale_IntArithmetic(EOS(STATIC_2915), i187, i187) :|: TRUE
f2915_0_fractale_IntArithmetic(EOS(STATIC_2915), i187, i187) -> f2917_0_fractale_Load(EOS(STATIC_2917), i187, i187) :|: TRUE
f2917_0_fractale_Load(EOS(STATIC_2917), i187, i187) -> f2919_0_fractale_FieldAccess(EOS(STATIC_2919), i187, i187) :|: TRUE
f2919_0_fractale_FieldAccess(EOS(STATIC_2919), i187, i187) -> f2921_0_fractale_IntArithmetic(EOS(STATIC_2921), i187, i187) :|: TRUE
f2921_0_fractale_IntArithmetic(EOS(STATIC_2921), i187, i187) -> f2923_0_fractale_Load(EOS(STATIC_2923), i187, i187) :|: TRUE
f2923_0_fractale_Load(EOS(STATIC_2923), i187, i187) -> f2926_0_fractale_FieldAccess(EOS(STATIC_2926), i187, i187) :|: TRUE
f2926_0_fractale_FieldAccess(EOS(STATIC_2926), i187, i187) -> f2928_0_fractale_IntArithmetic(EOS(STATIC_2928), i187, i187) :|: TRUE
f2928_0_fractale_IntArithmetic(EOS(STATIC_2928), i187, i187) -> f2929_0_fractale_ConstantStackPush(EOS(STATIC_2929), i187, i187) :|: TRUE
f2929_0_fractale_ConstantStackPush(EOS(STATIC_2929), i187, i187) -> f2930_0_fractale_IntArithmetic(EOS(STATIC_2930), i187, i187) :|: TRUE
f2930_0_fractale_IntArithmetic(EOS(STATIC_2930), i187, i187) -> f2931_0_fractale_Store(EOS(STATIC_2931), i187, i187) :|: i194 = i193 / 2
f2931_0_fractale_Store(EOS(STATIC_2931), i187, i187) -> f2933_0_fractale_Load(EOS(STATIC_2933), i187, i187) :|: TRUE
f2933_0_fractale_Load(EOS(STATIC_2933), i187, i187) -> f2935_0_fractale_FieldAccess(EOS(STATIC_2935), i187, i187) :|: TRUE
f2935_0_fractale_FieldAccess(EOS(STATIC_2935), i187, i187) -> f2937_0_fractale_Load(EOS(STATIC_2937), i187, i187) :|: TRUE
f2937_0_fractale_Load(EOS(STATIC_2937), i187, i187) -> f2979_0_fractale_FieldAccess(EOS(STATIC_2979), i187, i187) :|: TRUE
f2979_0_fractale_FieldAccess(EOS(STATIC_2979), i187, i187) -> f2982_0_fractale_IntArithmetic(EOS(STATIC_2982), i187, i187) :|: TRUE
f2982_0_fractale_IntArithmetic(EOS(STATIC_2982), i187, i187) -> f2985_0_fractale_Load(EOS(STATIC_2985), i187, i187) :|: TRUE
f2985_0_fractale_Load(EOS(STATIC_2985), i187, i187) -> f2987_0_fractale_FieldAccess(EOS(STATIC_2987), i187, i187) :|: TRUE
f2987_0_fractale_FieldAccess(EOS(STATIC_2987), i187, i187) -> f2990_0_fractale_IntArithmetic(EOS(STATIC_2990), i187, i187) :|: TRUE
f2990_0_fractale_IntArithmetic(EOS(STATIC_2990), i187, i187) -> f2992_0_fractale_Load(EOS(STATIC_2992), i187, i187) :|: TRUE
f2992_0_fractale_Load(EOS(STATIC_2992), i187, i187) -> f2998_0_fractale_FieldAccess(EOS(STATIC_2998), i187, i187) :|: TRUE
f2998_0_fractale_FieldAccess(EOS(STATIC_2998), i187, i187) -> f3001_0_fractale_IntArithmetic(EOS(STATIC_3001), i187, i187) :|: TRUE
f3001_0_fractale_IntArithmetic(EOS(STATIC_3001), i187, i187) -> f3004_0_fractale_ConstantStackPush(EOS(STATIC_3004), i187, i187) :|: TRUE
f3004_0_fractale_ConstantStackPush(EOS(STATIC_3004), i187, i187) -> f3007_0_fractale_IntArithmetic(EOS(STATIC_3007), i187, i187) :|: TRUE
f3007_0_fractale_IntArithmetic(EOS(STATIC_3007), i187, i187) -> f3009_0_fractale_Store(EOS(STATIC_3009), i187, i187) :|: i200 = i199 / 2
f3009_0_fractale_Store(EOS(STATIC_3009), i187, i187) -> f3012_0_fractale_New(EOS(STATIC_3012), i187, i187) :|: TRUE
f3012_0_fractale_New(EOS(STATIC_3012), i187, i187) -> f3015_0_fractale_Duplicate(EOS(STATIC_3015), i187, i187) :|: TRUE
f3015_0_fractale_Duplicate(EOS(STATIC_3015), i187, i187) -> f3017_0_fractale_Load(EOS(STATIC_3017), i187, i187) :|: TRUE
f3017_0_fractale_Load(EOS(STATIC_3017), i187, i187) -> f3020_0_fractale_Load(EOS(STATIC_3020), i187, i187) :|: TRUE
f3020_0_fractale_Load(EOS(STATIC_3020), i187, i187) -> f3022_0_fractale_InvokeMethod(EOS(STATIC_3022), i187, i187) :|: TRUE
f3022_0_fractale_InvokeMethod(EOS(STATIC_3022), i187, i187) -> f3024_0__init__Load(EOS(STATIC_3024), i187, i187) :|: TRUE
f3024_0__init__Load(EOS(STATIC_3024), i187, i187) -> f3027_0__init__InvokeMethod(EOS(STATIC_3027), i187, i187) :|: TRUE
f3027_0__init__InvokeMethod(EOS(STATIC_3027), i187, i187) -> f3030_0__init__Load(EOS(STATIC_3030), i187, i187) :|: TRUE
f3030_0__init__Load(EOS(STATIC_3030), i187, i187) -> f3033_0__init__Load(EOS(STATIC_3033), i187, i187) :|: TRUE
f3033_0__init__Load(EOS(STATIC_3033), i187, i187) -> f3035_0__init__FieldAccess(EOS(STATIC_3035), i187, i187) :|: TRUE
f3035_0__init__FieldAccess(EOS(STATIC_3035), i187, i187) -> f3038_0__init__Load(EOS(STATIC_3038), i187, i187) :|: TRUE
f3038_0__init__Load(EOS(STATIC_3038), i187, i187) -> f3040_0__init__Load(EOS(STATIC_3040), i187, i187) :|: TRUE
f3040_0__init__Load(EOS(STATIC_3040), i187, i187) -> f3043_0__init__FieldAccess(EOS(STATIC_3043), i187, i187) :|: TRUE
f3043_0__init__FieldAccess(EOS(STATIC_3043), i187, i187) -> f3046_0__init__Return(EOS(STATIC_3046), i187, i187) :|: TRUE
f3046_0__init__Return(EOS(STATIC_3046), i187, i187) -> f3047_0_fractale_Store(EOS(STATIC_3047), i187, i187) :|: TRUE
f3047_0_fractale_Store(EOS(STATIC_3047), i187, i187) -> f3048_0_fractale_Load(EOS(STATIC_3048), i187, i187) :|: TRUE
f3048_0_fractale_Load(EOS(STATIC_3048), i187, i187) -> f3049_0_fractale_ConstantStackPush(EOS(STATIC_3049), i187, i187, i187) :|: TRUE
f3049_0_fractale_ConstantStackPush(EOS(STATIC_3049), i187, i187, i187) -> f3051_0_fractale_IntArithmetic(EOS(STATIC_3051), i187, i187, i187, 1) :|: TRUE
f3051_0_fractale_IntArithmetic(EOS(STATIC_3051), i187, i187, i187, matching1) -> f3053_0_fractale_Load(EOS(STATIC_3053), i187, i187, i187 - 1) :|: i187 > 0 && matching1 = 1
f3053_0_fractale_Load(EOS(STATIC_3053), i187, i187, i201) -> f3055_0_fractale_Load(EOS(STATIC_3055), i187, i187, i201) :|: TRUE
f3055_0_fractale_Load(EOS(STATIC_3055), i187, i187, i201) -> f3058_0_fractale_InvokeMethod(EOS(STATIC_3058), i187, i187, i201) :|: TRUE
f3058_0_fractale_InvokeMethod(EOS(STATIC_3058), i187, i187, i201) -> f3060_0_fractale_Load(EOS(STATIC_3060), i201, i201) :|: i187 >= 1 && i201 < i187
f3058_0_fractale_InvokeMethod(EOS(STATIC_3058), i187, i187, i201) -> f3060_1_fractale_Load(EOS(STATIC_3060), i187, i187, i201) :|: i187 >= 1 && i201 < i187
f3060_0_fractale_Load(EOS(STATIC_3060), i201, i201) -> f3062_0_fractale_Load(EOS(STATIC_3062), i201, i201) :|: TRUE
f3062_0_fractale_Load(EOS(STATIC_3062), i201, i201) -> f3120_0_fractale_Load(EOS(STATIC_3120), i201, i201) :|: TRUE
f3120_0_fractale_Load(EOS(STATIC_3120), i201, i201) -> f2870_0_fractale_Load(EOS(STATIC_2870), i201, i201) :|: TRUE
f2870_0_fractale_Load(EOS(STATIC_2870), i184, i184) -> f2880_0_fractale_LE(EOS(STATIC_2880), i184, i184, i184) :|: TRUE
f3849_0_fractale_Return(EOS(STATIC_3849), i187, i187) -> f3851_0_fractale_Load(EOS(STATIC_3851), i187, i187) :|: TRUE
f3851_0_fractale_Load(EOS(STATIC_3851), i187, i187) -> f3853_0_fractale_ConstantStackPush(EOS(STATIC_3853), i187, i187) :|: TRUE
f3853_0_fractale_ConstantStackPush(EOS(STATIC_3853), i187, i187) -> f3855_0_fractale_IntArithmetic(EOS(STATIC_3855), i187, i187, 1) :|: TRUE
f3855_0_fractale_IntArithmetic(EOS(STATIC_3855), i187, i187, matching1) -> f3857_0_fractale_Load(EOS(STATIC_3857), i187, i187 - 1) :|: i187 > 0 && matching1 = 1
f3857_0_fractale_Load(EOS(STATIC_3857), i187, i261) -> f3859_0_fractale_Load(EOS(STATIC_3859), i187, i261) :|: TRUE
f3859_0_fractale_Load(EOS(STATIC_3859), i187, i261) -> f3861_0_fractale_InvokeMethod(EOS(STATIC_3861), i187, i261) :|: TRUE
f3861_0_fractale_InvokeMethod(EOS(STATIC_3861), i187, i261) -> f3863_0_fractale_Load(EOS(STATIC_3863), i261, i261) :|: i187 >= 1 && i261 < i187
f3861_0_fractale_InvokeMethod(EOS(STATIC_3861), i187, i261) -> f3863_1_fractale_Load(EOS(STATIC_3863), i187, i261) :|: i187 >= 1 && i261 < i187
f3863_0_fractale_Load(EOS(STATIC_3863), i261, i261) -> f3867_0_fractale_Load(EOS(STATIC_3867), i261, i261) :|: TRUE
f3867_0_fractale_Load(EOS(STATIC_3867), i261, i261) -> f3903_0_fractale_Load(EOS(STATIC_3903), i261, i261) :|: TRUE
f3903_0_fractale_Load(EOS(STATIC_3903), i261, i261) -> f2870_0_fractale_Load(EOS(STATIC_2870), i261, i261) :|: TRUE
f5459_0_fractale_Return(EOS(STATIC_5459), i187, i187) -> f3849_0_fractale_Return(EOS(STATIC_3849), i187, i187) :|: TRUE
f3060_1_fractale_Load(EOS(STATIC_3060), i187, i187, i201) -> f3849_0_fractale_Return(EOS(STATIC_3849), i187, i187) :|: TRUE
f3060_1_fractale_Load(EOS(STATIC_3060), i187, i187, i201) -> f5459_0_fractale_Return(EOS(STATIC_5459), i187, i187) :|: TRUE
Combined rules. Obtained 5 IRulesP rules:
f2880_0_fractale_LE(EOS(STATIC_2880), i187:0, i187:0, i187:0) -> f2880_0_fractale_LE'(EOS(STATIC_2880), i187:0, i187:0, i187:0) :|: i187:0 > 0 && i187:0 - 1 < i187:0
f2880_0_fractale_LE'(EOS(STATIC_2880), i187:0, i187:0, i187:0) -> f3849_0_fractale_Return(EOS(STATIC_3849), i187:0, i187:0) :|: i187:0 > 0 && i187:0 - 1 < i187:0 && i193:0 - 2 * div > -2 && i193:0 - 2 * div < 2 && i199:0 - 2 * div1 < 2 && i199:0 - 2 * div1 > -2
f3849_0_fractale_Return(EOS(STATIC_3849), i187:0, i187:0) -> f2880_0_fractale_LE(EOS(STATIC_2880), i187:0 - 1, i187:0 - 1, i187:0 - 1) :|: i187:0 > 0 && i187:0 - 1 < i187:0
f2880_0_fractale_LE'(EOS(STATIC_2880), i187:0, i187:0, i187:0) -> f2880_0_fractale_LE(EOS(STATIC_2880), i187:0 - 1, i187:0 - 1, i187:0 - 1) :|: i187:0 > 0 && i187:0 - 1 < i187:0 && i193:0 - 2 * div > -2 && i193:0 - 2 * div < 2 && i199:0 - 2 * div1 < 2 && i199:0 - 2 * div1 > -2
Removed following non-SCC rules:
f3849_0_fractale_Return(EOS(STATIC_3849), i187:0, i187:0) -> f3863_1_fractale_Load(EOS(STATIC_3863), i187:0, i187:0 - 1) :|: i187:0 > 0 && i187:0 - 1 < i187:0
Filtered constant ground arguments:
   f2880_0_fractale_LE(x1, x2, x3, x4) -> f2880_0_fractale_LE(x2, x3, x4)
   f2880_0_fractale_LE'(x1, x2, x3, x4) -> f2880_0_fractale_LE'(x2, x3, x4)
   f3849_0_fractale_Return(x1, x2, x3) -> f3849_0_fractale_Return(x2, x3)
Filtered duplicate arguments:
   f2880_0_fractale_LE(x1, x2, x3) -> f2880_0_fractale_LE(x3)
   f2880_0_fractale_LE'(x1, x2, x3) -> f2880_0_fractale_LE'(x3)
   f3849_0_fractale_Return(x1, x2) -> f3849_0_fractale_Return(x2)
Finished conversion. Obtained 4 rules.P rules:
f2880_0_fractale_LE(i187:0) -> f2880_0_fractale_LE'(i187:0) :|: i187:0 > 0 && i187:0 - 1 < i187:0
f2880_0_fractale_LE'(i187:0) -> f3849_0_fractale_Return(i187:0) :|: i187:0 - 1 < i187:0 && i187:0 > 0 && i193:0 - 2 * div > -2 && i193:0 - 2 * div < 2 && i199:0 - 2 * div1 > -2 && i199:0 - 2 * div1 < 2
f3849_0_fractale_Return(i187:0) -> f2880_0_fractale_LE(i187:0 - 1) :|: i187:0 > 0 && i187:0 - 1 < i187:0
f2880_0_fractale_LE'(i187:0) -> f2880_0_fractale_LE(i187:0 - 1) :|: i187:0 - 1 < i187:0 && i187:0 > 0 && i193:0 - 2 * div > -2 && i193:0 - 2 * div < 2 && i199:0 - 2 * div1 > -2 && i199:0 - 2 * div1 < 2

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

(8)
Obligation:
Rules:
f2880_0_fractale_LE(i187:0) -> f2880_0_fractale_LE'(i187:0) :|: i187:0 > 0 && i187:0 - 1 < i187:0
f2880_0_fractale_LE'(x) -> f3849_0_fractale_Return(x) :|: x - 1 < x && x > 0 && x1 - 2 * x2 > -2 && x1 - 2 * x2 < 2 && x3 - 2 * x4 > -2 && x3 - 2 * x4 < 2
f3849_0_fractale_Return(x5) -> f2880_0_fractale_LE(x5 - 1) :|: x5 > 0 && x5 - 1 < x5
f2880_0_fractale_LE'(x6) -> f2880_0_fractale_LE(x6 - 1) :|: x6 - 1 < x6 && x6 > 0 && x7 - 2 * x8 > -2 && x7 - 2 * x8 < 2 && x9 - 2 * x10 > -2 && x9 - 2 * x10 < 2

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

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

(10)
Obligation:
Rules:
f2880_0_fractale_LE(i187:0) -> f2880_0_fractale_LE'(i187:0) :|: i187:0 > 0 && i187:0 - 1 < i187:0
f2880_0_fractale_LE'(x) -> f3849_0_fractale_Return(x) :|: x - 1 < x && x > 0 && x1 - 2 * x2 > -2 && x1 - 2 * x2 < 2 && x3 - 2 * x4 > -2 && x3 - 2 * x4 < 2
f3849_0_fractale_Return(x5) -> f2880_0_fractale_LE(arith) :|: x5 > 0 && x5 - 1 < x5 && arith = x5 - 1
f2880_0_fractale_LE'(x11) -> f2880_0_fractale_LE(x12) :|: x11 - 1 < x11 && x11 > 0 && x13 - 2 * x14 > -2 && x13 - 2 * x14 < 2 && x15 - 2 * x16 > -2 && x15 - 2 * x16 < 2 && x12 = x11 - 1

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

(11) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f2880_0_fractale_LE(i187:0) -> f2880_0_fractale_LE'(i187:0) :|: i187:0 > 0 && i187:0 - 1 < i187:0
(2) f2880_0_fractale_LE'(x) -> f3849_0_fractale_Return(x) :|: x - 1 < x && x > 0 && x1 - 2 * x2 > -2 && x1 - 2 * x2 < 2 && x3 - 2 * x4 > -2 && x3 - 2 * x4 < 2
(3) f3849_0_fractale_Return(x5) -> f2880_0_fractale_LE(arith) :|: x5 > 0 && x5 - 1 < x5 && arith = x5 - 1
(4) f2880_0_fractale_LE'(x11) -> f2880_0_fractale_LE(x12) :|: x11 - 1 < x11 && x11 > 0 && x13 - 2 * x14 > -2 && x13 - 2 * x14 < 2 && x15 - 2 * x16 > -2 && x15 - 2 * x16 < 2 && x12 = x11 - 1

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

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

(12)
Obligation:

Termination digraph:
Nodes:
(1) f2880_0_fractale_LE(i187:0) -> f2880_0_fractale_LE'(i187:0) :|: i187:0 > 0 && i187:0 - 1 < i187:0
(2) f2880_0_fractale_LE'(x11) -> f2880_0_fractale_LE(x12) :|: x11 - 1 < x11 && x11 > 0 && x13 - 2 * x14 > -2 && x13 - 2 * x14 < 2 && x15 - 2 * x16 > -2 && x15 - 2 * x16 < 2 && x12 = x11 - 1
(3) f3849_0_fractale_Return(x5) -> f2880_0_fractale_LE(arith) :|: x5 > 0 && x5 - 1 < x5 && arith = x5 - 1
(4) f2880_0_fractale_LE'(x) -> f3849_0_fractale_Return(x) :|: x - 1 < x && x > 0 && x1 - 2 * x2 > -2 && x1 - 2 * x2 < 2 && x3 - 2 * x4 > -2 && x3 - 2 * x4 < 2

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

This digraph is fully evaluated!

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(13) IntTRSCompressionProof (EQUIVALENT)
Compressed rules.
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(14)
Obligation:
Rules:
f2880_0_fractale_LE(i187:0:0) -> f2880_0_fractale_LE(i187:0:0 - 1) :|: x3:0 - 2 * x4:0 < 2 && x3:0 - 2 * x4:0 > -2 && x1:0 - 2 * x2:0 < 2 && x1:0 - 2 * x2:0 > -2 && i187:0:0 > 0 && i187:0:0 - 1 < i187:0:0

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(15) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f2880_0_fractale_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
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(16)
Obligation:
Rules:
f2880_0_fractale_LE(i187:0:0) -> f2880_0_fractale_LE(c) :|: c = i187:0:0 - 1 && (x3:0 - 2 * x4:0 < 2 && x3:0 - 2 * x4:0 > -2 && x1:0 - 2 * x2:0 < 2 && x1:0 - 2 * x2:0 > -2 && i187:0:0 > 0 && i187:0:0 - 1 < i187:0:0)

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(17) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f2880_0_fractale_LE(x)] = x

The following rules are decreasing:
f2880_0_fractale_LE(i187:0:0) -> f2880_0_fractale_LE(c) :|: c = i187:0:0 - 1 && (x3:0 - 2 * x4:0 < 2 && x3:0 - 2 * x4:0 > -2 && x1:0 - 2 * x2:0 < 2 && x1:0 - 2 * x2:0 > -2 && i187:0:0 > 0 && i187:0:0 - 1 < i187:0:0)
The following rules are bounded:
f2880_0_fractale_LE(i187:0:0) -> f2880_0_fractale_LE(c) :|: c = i187:0:0 - 1 && (x3:0 - 2 * x4:0 < 2 && x3:0 - 2 * x4:0 > -2 && x1:0 - 2 * x2:0 < 2 && x1:0 - 2 * x2:0 > -2 && i187:0:0 > 0 && i187:0:0 - 1 < i187:0:0)

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(18)
YES