/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 318 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) JBCTerminationSCC
        (8) SCCToIRSProof [SOUND, 35 ms]
        (9) IRSwT
        (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (11) IRSwT
        (12) IRSwTTerminationDigraphProof [EQUIVALENT, 3 ms]
        (13) IRSwT
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IRSwT
        (16) TempFilterProof [SOUND, 13 ms]
        (17) IntTRS
        (18) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (19) YES
    (20) JBCTerminationSCC
        (21) SCCToIRSProof [SOUND, 103 ms]
        (22) IRSwT
        (23) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (24) IRSwT
        (25) IRSwTTerminationDigraphProof [EQUIVALENT, 48 ms]
        (26) IRSwT
        (27) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (28) IRSwT
        (29) TempFilterProof [SOUND, 23 ms]
        (30) IntTRS
        (31) PolynomialOrderProcessor [EQUIVALENT, 6 ms]
        (32) IntTRS
        (33) RankingReductionPairProof [EQUIVALENT, 0 ms]
        (34) YES


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

(0)
Obligation:
need to prove termination of the following program:
public class Test10 {
    public static void main(String[] args) {
	rec(args.length);
    }

    private static void rec(long l) {
	if (l > 0) {
	    for (int i = (int) l ; i < 100; i++)
		test(i);

	    rec (l - 1);
	}
    }

    private static void test(int i) {
	descend(i);
	descend(i);
	descend(i);
	descend(i);
	descend(i);
	descend(i);
	descend(i);
	descend(i);
    }

    private static void descend(int i) {
	if (i > 0)
	    descend(i - 1);
    }
}


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

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

(2)
Obligation:
need to prove termination of the following program:
public class Test10 {
    public static void main(String[] args) {
	rec(args.length);
    }

    private static void rec(long l) {
	if (l > 0) {
	    for (int i = (int) l ; i < 100; i++)
		test(i);

	    rec (l - 1);
	}
    }

    private static void test(int i) {
	descend(i);
	descend(i);
	descend(i);
	descend(i);
	descend(i);
	descend(i);
	descend(i);
	descend(i);
    }

    private static void descend(int i) {
	if (i > 0)
	    descend(i - 1);
    }
}


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

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

(4)
Obligation:
Termination Graph based on JBC Program:
Test10.main([Ljava/lang/String;)V: Graph of 11 nodes with 0 SCCs.



Test10.rec(J)V: Graph of 73 nodes with 1 SCC.



Test10.descend(I)V: Graph of 16 nodes with 0 SCCs.





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

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

(6)
Complex Obligation (AND)

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

(7)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: Test10.descend(I)V
SCC calls the following helper methods: Test10.descend(I)V
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 10 IRulesP rules:
f466_0_descend_LE(EOS(STATIC_466), i91, i91, i91) -> f470_0_descend_LE(EOS(STATIC_470), i91, i91, i91) :|: TRUE
f470_0_descend_LE(EOS(STATIC_470), i91, i91, i91) -> f477_0_descend_Load(EOS(STATIC_477), i91, i91) :|: i91 > 0
f477_0_descend_Load(EOS(STATIC_477), i91, i91) -> f480_0_descend_ConstantStackPush(EOS(STATIC_480), i91, i91) :|: TRUE
f480_0_descend_ConstantStackPush(EOS(STATIC_480), i91, i91) -> f482_0_descend_IntArithmetic(EOS(STATIC_482), i91, i91, 1) :|: TRUE
f482_0_descend_IntArithmetic(EOS(STATIC_482), i91, i91, matching1) -> f484_0_descend_InvokeMethod(EOS(STATIC_484), i91, i91 - 1) :|: i91 > 0 && matching1 = 1
f484_0_descend_InvokeMethod(EOS(STATIC_484), i91, i93) -> f485_0_descend_Load(EOS(STATIC_485), i93, i93) :|: i91 >= 1 && i93 < i91
f484_0_descend_InvokeMethod(EOS(STATIC_484), i91, i93) -> f485_1_descend_Load(EOS(STATIC_485), i91, i93) :|: i91 >= 1 && i93 < i91
f485_0_descend_Load(EOS(STATIC_485), i93, i93) -> f486_0_descend_Load(EOS(STATIC_486), i93, i93) :|: TRUE
f486_0_descend_Load(EOS(STATIC_486), i93, i93) -> f463_0_descend_Load(EOS(STATIC_463), i93, i93) :|: TRUE
f463_0_descend_Load(EOS(STATIC_463), i89, i89) -> f466_0_descend_LE(EOS(STATIC_466), i89, i89, i89) :|: TRUE
Combined rules. Obtained 2 IRulesP rules:
f466_0_descend_LE(EOS(STATIC_466), i91:0, i91:0, i91:0) -> f466_0_descend_LE(EOS(STATIC_466), i91:0 - 1, i91:0 - 1, i91:0 - 1) :|: i91:0 > 0 && i91:0 - 1 < i91:0
Removed following non-SCC rules:
f466_0_descend_LE(EOS(STATIC_466), i91:0, i91:0, i91:0) -> f485_1_descend_Load(EOS(STATIC_485), i91:0, i91:0 - 1) :|: i91:0 > 0 && i91:0 - 1 < i91:0
Filtered constant ground arguments:
   f466_0_descend_LE(x1, x2, x3, x4) -> f466_0_descend_LE(x2, x3, x4)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f466_0_descend_LE(x1, x2, x3) -> f466_0_descend_LE(x3)
Finished conversion. Obtained 1 rules.P rules:
f466_0_descend_LE(i91:0) -> f466_0_descend_LE(i91:0 - 1) :|: i91:0 > 0 && i91:0 - 1 < i91:0

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

(9)
Obligation:
Rules:
f466_0_descend_LE(i91:0) -> f466_0_descend_LE(i91:0 - 1) :|: i91:0 > 0 && i91:0 - 1 < i91:0

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

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

(11)
Obligation:
Rules:
f466_0_descend_LE(i91:0) -> f466_0_descend_LE(arith) :|: i91:0 > 0 && i91:0 - 1 < i91:0 && arith = i91:0 - 1

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

(12) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f466_0_descend_LE(i91:0) -> f466_0_descend_LE(arith) :|: i91:0 > 0 && i91:0 - 1 < i91:0 && arith = i91:0 - 1

Arcs:
(1) -> (1)

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

(13)
Obligation:

Termination digraph:
Nodes:
(1) f466_0_descend_LE(i91:0) -> f466_0_descend_LE(arith) :|: i91:0 > 0 && i91:0 - 1 < i91:0 && arith = i91:0 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(15)
Obligation:
Rules:
f466_0_descend_LE(i91:0:0) -> f466_0_descend_LE(i91:0:0 - 1) :|: i91:0:0 > 0 && i91:0:0 - 1 < i91:0:0

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

(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f466_0_descend_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(17)
Obligation:
Rules:
f466_0_descend_LE(i91:0:0) -> f466_0_descend_LE(c) :|: c = i91:0:0 - 1 && (i91:0:0 > 0 && i91:0:0 - 1 < i91:0:0)

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

(18) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f466_0_descend_LE(x)] = x

The following rules are decreasing:
f466_0_descend_LE(i91:0:0) -> f466_0_descend_LE(c) :|: c = i91:0:0 - 1 && (i91:0:0 > 0 && i91:0:0 - 1 < i91:0:0)
The following rules are bounded:
f466_0_descend_LE(i91:0:0) -> f466_0_descend_LE(c) :|: c = i91:0:0 - 1 && (i91:0:0 > 0 && i91:0:0 - 1 < i91:0:0)

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

(19)
YES

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

(20)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: Test10.rec(J)V
SCC calls the following helper methods: Test10.descend(I)V, Test10.rec(J)V
Performed SCC analyses:
*Used field analysis yielded the following read fields:

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

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

(21) SCCToIRSProof (SOUND)
Transformed FIGraph SCCs to intTRSs. Log: 
Generated rules. Obtained 75 IRulesP rules:
f17_0_rec_ConstantStackPush(EOS(STATIC_17), i4, i4, i4) -> f18_0_rec_Cmp(EOS(STATIC_18), i4, i4, i4, 0) :|: TRUE
f18_0_rec_Cmp(EOS(STATIC_18), i5, i5, i5, matching1) -> f21_0_rec_Cmp(EOS(STATIC_21), i5, i5, i5, 0) :|: TRUE && matching1 = 0
f21_0_rec_Cmp(EOS(STATIC_21), i5, i5, i5, matching1) -> f31_0_rec_LE(EOS(STATIC_31), i5, i5, 1) :|: TRUE && matching1 = 0
f31_0_rec_LE(EOS(STATIC_31), i5, i5, matching1) -> f33_0_rec_Load(EOS(STATIC_33), i5, i5) :|: 1 > 0 && matching1 = 1
f33_0_rec_Load(EOS(STATIC_33), i5, i5) -> f35_0_rec_TypeCast(EOS(STATIC_35), i5, i5, i5) :|: TRUE
f35_0_rec_TypeCast(EOS(STATIC_35), i5, i5, i5) -> f48_0_rec_Store(EOS(STATIC_48), i5, i5, i10) :|: i10 = i5
f48_0_rec_Store(EOS(STATIC_48), i5, i5, i10) -> f50_0_rec_Load(EOS(STATIC_50), i5, i5, i10) :|: TRUE
f50_0_rec_Load(EOS(STATIC_50), i5, i5, i10) -> f52_0_rec_ConstantStackPush(EOS(STATIC_52), i5, i5, i10, i10) :|: TRUE
f52_0_rec_ConstantStackPush(EOS(STATIC_52), i5, i5, i10, i10) -> f55_0_rec_GE(EOS(STATIC_55), i5, i5, i10, i10, 100) :|: TRUE
f55_0_rec_GE(EOS(STATIC_55), i5, i5, i12, i12, matching1) -> f60_0_rec_GE(EOS(STATIC_60), i5, i5, i12, i12, 100) :|: TRUE && matching1 = 100
f55_0_rec_GE(EOS(STATIC_55), i5, i5, i13, i13, matching1) -> f61_0_rec_GE(EOS(STATIC_61), i5, i5, i13, i13, 100) :|: TRUE && matching1 = 100
f60_0_rec_GE(EOS(STATIC_60), i5, i5, i12, i12, matching1) -> f65_0_rec_Load(EOS(STATIC_65), i5, i5, i12) :|: i12 < 100 && matching1 = 100
f65_0_rec_Load(EOS(STATIC_65), i5, i5, i12) -> f69_0_rec_InvokeMethod(EOS(STATIC_69), i5, i5, i12, i12) :|: TRUE
f69_0_rec_InvokeMethod(EOS(STATIC_69), i5, i5, i12, i12) -> f72_0_test_Load(EOS(STATIC_72), i5, i5, i12, i12) :|: TRUE
f72_0_test_Load(EOS(STATIC_72), i5, i5, i12, i12) -> f75_0_test_InvokeMethod(EOS(STATIC_75), i5, i5, i12, i12, i12) :|: TRUE
f75_0_test_InvokeMethod(EOS(STATIC_75), i5, i5, i12, i12, i12) -> f77_0_descend_Load(EOS(STATIC_77), i12, i12) :|: i12 >= 1
f75_0_test_InvokeMethod(EOS(STATIC_75), i5, i5, i12, i12, i12) -> f77_1_descend_Load(EOS(STATIC_77), i5, i5, i12, i12, i12) :|: i12 >= 1
f77_0_descend_Load(EOS(STATIC_77), i12, i12) -> f2837_0_descend_Load(EOS(STATIC_2837), i12, i12) :|: TRUE
f676_0_descend_Return(EOS(STATIC_676), i5, i5, i124, i124) -> f682_0_test_Load(EOS(STATIC_682), i5, i5, i124, i124) :|: TRUE
f682_0_test_Load(EOS(STATIC_682), i5, i5, i124, i124) -> f684_0_test_InvokeMethod(EOS(STATIC_684), i5, i5, i124, i124, i124) :|: TRUE
f684_0_test_InvokeMethod(EOS(STATIC_684), i5, i5, i124, i124, i124) -> f686_0_descend_Load(EOS(STATIC_686), i124, i124) :|: i124 >= 1
f684_0_test_InvokeMethod(EOS(STATIC_684), i5, i5, i124, i124, i124) -> f686_1_descend_Load(EOS(STATIC_686), i5, i5, i124, i124, i124) :|: i124 >= 1
f686_0_descend_Load(EOS(STATIC_686), i124, i124) -> f2854_0_descend_Load(EOS(STATIC_2854), i124, i124) :|: TRUE
f956_0_descend_Return(EOS(STATIC_956), i5, i5, i136, i136) -> f959_0_test_Load(EOS(STATIC_959), i5, i5, i136, i136) :|: TRUE
f959_0_test_Load(EOS(STATIC_959), i5, i5, i136, i136) -> f960_0_test_InvokeMethod(EOS(STATIC_960), i5, i5, i136, i136, i136) :|: TRUE
f960_0_test_InvokeMethod(EOS(STATIC_960), i5, i5, i136, i136, i136) -> f961_0_descend_Load(EOS(STATIC_961), i136, i136) :|: i136 >= 1
f960_0_test_InvokeMethod(EOS(STATIC_960), i5, i5, i136, i136, i136) -> f961_1_descend_Load(EOS(STATIC_961), i5, i5, i136, i136, i136) :|: i136 >= 1
f961_0_descend_Load(EOS(STATIC_961), i136, i136) -> f2870_0_descend_Load(EOS(STATIC_2870), i136, i136) :|: TRUE
f1764_0_descend_Return(EOS(STATIC_1764), i5, i5, i184, i184) -> f1765_0_test_Load(EOS(STATIC_1765), i5, i5, i184, i184) :|: TRUE
f1765_0_test_Load(EOS(STATIC_1765), i5, i5, i184, i184) -> f1766_0_test_InvokeMethod(EOS(STATIC_1766), i5, i5, i184, i184, i184) :|: TRUE
f1766_0_test_InvokeMethod(EOS(STATIC_1766), i5, i5, i184, i184, i184) -> f1767_0_descend_Load(EOS(STATIC_1767), i184, i184) :|: i184 >= 1
f1766_0_test_InvokeMethod(EOS(STATIC_1766), i5, i5, i184, i184, i184) -> f1767_1_descend_Load(EOS(STATIC_1767), i5, i5, i184, i184, i184) :|: i184 >= 1
f1767_0_descend_Load(EOS(STATIC_1767), i184, i184) -> f2886_0_descend_Load(EOS(STATIC_2886), i184, i184) :|: TRUE
f2568_0_descend_Return(EOS(STATIC_2568), i5, i5, i301, i301) -> f2570_0_test_Load(EOS(STATIC_2570), i5, i5, i301, i301) :|: TRUE
f2570_0_test_Load(EOS(STATIC_2570), i5, i5, i301, i301) -> f2571_0_test_InvokeMethod(EOS(STATIC_2571), i5, i5, i301, i301, i301) :|: TRUE
f2571_0_test_InvokeMethod(EOS(STATIC_2571), i5, i5, i301, i301, i301) -> f2574_0_descend_Load(EOS(STATIC_2574), i301, i301) :|: i301 >= 1
f2571_0_test_InvokeMethod(EOS(STATIC_2571), i5, i5, i301, i301, i301) -> f2574_1_descend_Load(EOS(STATIC_2574), i5, i5, i301, i301, i301) :|: i301 >= 1
f2574_0_descend_Load(EOS(STATIC_2574), i301, i301) -> f2902_0_descend_Load(EOS(STATIC_2902), i301, i301) :|: TRUE
f2598_0_descend_Return(EOS(STATIC_2598), i5, i5, i422, i422) -> f2600_0_test_Load(EOS(STATIC_2600), i5, i5, i422, i422) :|: TRUE
f2600_0_test_Load(EOS(STATIC_2600), i5, i5, i422, i422) -> f2603_0_test_InvokeMethod(EOS(STATIC_2603), i5, i5, i422, i422, i422) :|: TRUE
f2603_0_test_InvokeMethod(EOS(STATIC_2603), i5, i5, i422, i422, i422) -> f2605_0_descend_Load(EOS(STATIC_2605), i422, i422) :|: i422 >= 1
f2603_0_test_InvokeMethod(EOS(STATIC_2603), i5, i5, i422, i422, i422) -> f2605_1_descend_Load(EOS(STATIC_2605), i5, i5, i422, i422, i422) :|: i422 >= 1
f2605_0_descend_Load(EOS(STATIC_2605), i422, i422) -> f2918_0_descend_Load(EOS(STATIC_2918), i422, i422) :|: TRUE
f2625_0_descend_Return(EOS(STATIC_2625), i5, i5, i433, i433) -> f2628_0_test_Load(EOS(STATIC_2628), i5, i5, i433, i433) :|: TRUE
f2628_0_test_Load(EOS(STATIC_2628), i5, i5, i433, i433) -> f2630_0_test_InvokeMethod(EOS(STATIC_2630), i5, i5, i433, i433, i433) :|: TRUE
f2630_0_test_InvokeMethod(EOS(STATIC_2630), i5, i5, i433, i433, i433) -> f2631_0_descend_Load(EOS(STATIC_2631), i433, i433) :|: i433 >= 1
f2630_0_test_InvokeMethod(EOS(STATIC_2630), i5, i5, i433, i433, i433) -> f2631_1_descend_Load(EOS(STATIC_2631), i5, i5, i433, i433, i433) :|: i433 >= 1
f2631_0_descend_Load(EOS(STATIC_2631), i433, i433) -> f2934_0_descend_Load(EOS(STATIC_2934), i433, i433) :|: TRUE
f2640_0_descend_Return(EOS(STATIC_2640), i5, i5, i440, i440) -> f2641_0_test_Load(EOS(STATIC_2641), i5, i5, i440, i440) :|: TRUE
f2641_0_test_Load(EOS(STATIC_2641), i5, i5, i440, i440) -> f2642_0_test_InvokeMethod(EOS(STATIC_2642), i5, i5, i440, i440) :|: TRUE
f2642_0_test_InvokeMethod(EOS(STATIC_2642), i5, i5, i440, i440) -> f2643_0_descend_Load(EOS(STATIC_2643), i440, i440) :|: i440 >= 1
f2642_0_test_InvokeMethod(EOS(STATIC_2642), i5, i5, i440, i440) -> f2643_1_descend_Load(EOS(STATIC_2643), i5, i5, i440, i440) :|: i440 >= 1
f2643_0_descend_Load(EOS(STATIC_2643), i440, i440) -> f2951_0_descend_Load(EOS(STATIC_2951), i440, i440) :|: TRUE
f2646_0_descend_Return(EOS(STATIC_2646), i5, i5, i445) -> f2647_0_test_Return(EOS(STATIC_2647), i5, i5, i445) :|: TRUE
f2647_0_test_Return(EOS(STATIC_2647), i5, i5, i445) -> f2648_0_rec_Inc(EOS(STATIC_2648), i5, i5, i445) :|: TRUE
f2648_0_rec_Inc(EOS(STATIC_2648), i5, i5, i445) -> f2649_0_rec_JMP(EOS(STATIC_2649), i5, i5, i445 + 1) :|: TRUE
f2649_0_rec_JMP(EOS(STATIC_2649), i5, i5, i446) -> f2688_0_rec_Load(EOS(STATIC_2688), i5, i5, i446) :|: TRUE
f2688_0_rec_Load(EOS(STATIC_2688), i5, i5, i446) -> f50_0_rec_Load(EOS(STATIC_50), i5, i5, i446) :|: TRUE
f61_0_rec_GE(EOS(STATIC_61), i5, i5, i13, i13, matching1) -> f66_0_rec_Load(EOS(STATIC_66), i5, i5) :|: i13 >= 100 && matching1 = 100
f66_0_rec_Load(EOS(STATIC_66), i5, i5) -> f71_0_rec_ConstantStackPush(EOS(STATIC_71), i5, i5) :|: TRUE
f71_0_rec_ConstantStackPush(EOS(STATIC_71), i5, i5) -> f73_0_rec_IntArithmetic(EOS(STATIC_73), i5, i5, 1) :|: TRUE
f73_0_rec_IntArithmetic(EOS(STATIC_73), i5, i5, matching1) -> f74_0_rec_InvokeMethod(EOS(STATIC_74), i5, i5 - 1) :|: i5 > 0 && matching1 = 1
f74_0_rec_InvokeMethod(EOS(STATIC_74), i5, i15) -> f76_0_rec_Load(EOS(STATIC_76), i15, i15) :|: i15 < i5
f74_0_rec_InvokeMethod(EOS(STATIC_74), i5, i15) -> f76_1_rec_Load(EOS(STATIC_76), i5, i15) :|: i15 < i5
f76_0_rec_Load(EOS(STATIC_76), i15, i15) -> f78_0_rec_Load(EOS(STATIC_78), i15, i15) :|: TRUE
f78_0_rec_Load(EOS(STATIC_78), i15, i15) -> f16_0_rec_Load(EOS(STATIC_16), i15, i15) :|: TRUE
f16_0_rec_Load(EOS(STATIC_16), i4, i4) -> f17_0_rec_ConstantStackPush(EOS(STATIC_17), i4, i4, i4) :|: TRUE
f77_1_descend_Load(EOS(STATIC_77), i5, i5, i124, i124, i124) -> f676_0_descend_Return(EOS(STATIC_676), i5, i5, i124, i124) :|: TRUE
f686_1_descend_Load(EOS(STATIC_686), i5, i5, i136, i136, i136) -> f956_0_descend_Return(EOS(STATIC_956), i5, i5, i136, i136) :|: TRUE
f961_1_descend_Load(EOS(STATIC_961), i5, i5, i184, i184, i184) -> f1764_0_descend_Return(EOS(STATIC_1764), i5, i5, i184, i184) :|: TRUE
f1767_1_descend_Load(EOS(STATIC_1767), i5, i5, i301, i301, i301) -> f2568_0_descend_Return(EOS(STATIC_2568), i5, i5, i301, i301) :|: TRUE
f2574_1_descend_Load(EOS(STATIC_2574), i5, i5, i422, i422, i422) -> f2598_0_descend_Return(EOS(STATIC_2598), i5, i5, i422, i422) :|: TRUE
f2605_1_descend_Load(EOS(STATIC_2605), i5, i5, i433, i433, i433) -> f2625_0_descend_Return(EOS(STATIC_2625), i5, i5, i433, i433) :|: TRUE
f2631_1_descend_Load(EOS(STATIC_2631), i5, i5, i440, i440, i440) -> f2640_0_descend_Return(EOS(STATIC_2640), i5, i5, i440, i440) :|: TRUE
f2643_1_descend_Load(EOS(STATIC_2643), i5, i5, i445, i445) -> f2646_0_descend_Return(EOS(STATIC_2646), i5, i5, i445) :|: TRUE
Combined rules. Obtained 11 IRulesP rules:
f55_0_rec_GE(EOS(STATIC_55), i5:0, i5:0, i13:0, i13:0, 100) -> f55_0_rec_GE(EOS(STATIC_55), i5:0 - 1, i5:0 - 1, i5:0 - 1, i5:0 - 1, 100) :|: i13:0 > 99 && i5:0 - 1 < i5:0 && i5:0 > 0
f55_0_rec_GE(EOS(STATIC_55), i5:0, i5:0, i12:0, i12:0, 100) -> f55_0_rec_GE(EOS(STATIC_55), i5:0, i5:0, i12:0 + 1, i12:0 + 1, 100) :|: i12:0 < 100 && i12:0 > 0
Removed following non-SCC rules:
f55_0_rec_GE(EOS(STATIC_55), i5:0, i5:0, i13:0, i13:0, 100) -> f76_1_rec_Load(EOS(STATIC_76), i5:0, i5:0 - 1) :|: i13:0 > 99 && i5:0 - 1 < i5:0 && i5:0 > 0
f55_0_rec_GE(EOS(STATIC_55), i5:0, i5:0, i12:0, i12:0, 100) -> f2837_0_descend_Load(EOS(STATIC_2837), i12:0, i12:0) :|: i12:0 > 0 && i12:0 < 100
f55_0_rec_GE(EOS(STATIC_55), i5:0, i5:0, i12:0, i12:0, 100) -> f2934_0_descend_Load(EOS(STATIC_2934), i12:0, i12:0) :|: i12:0 < 100 && i12:0 > 0
f55_0_rec_GE(EOS(STATIC_55), i5:0, i5:0, i12:0, i12:0, 100) -> f2870_0_descend_Load(EOS(STATIC_2870), i12:0, i12:0) :|: i12:0 < 100 && i12:0 > 0
f55_0_rec_GE(EOS(STATIC_55), i5:0, i5:0, i12:0, i12:0, 100) -> f2886_0_descend_Load(EOS(STATIC_2886), i12:0, i12:0) :|: i12:0 < 100 && i12:0 > 0
f55_0_rec_GE(EOS(STATIC_55), i5:0, i5:0, i12:0, i12:0, 100) -> f2951_0_descend_Load(EOS(STATIC_2951), i12:0, i12:0) :|: i12:0 < 100 && i12:0 > 0
f55_0_rec_GE(EOS(STATIC_55), i5:0, i5:0, i12:0, i12:0, 100) -> f2902_0_descend_Load(EOS(STATIC_2902), i12:0, i12:0) :|: i12:0 < 100 && i12:0 > 0
f55_0_rec_GE(EOS(STATIC_55), i5:0, i5:0, i12:0, i12:0, 100) -> f2854_0_descend_Load(EOS(STATIC_2854), i12:0, i12:0) :|: i12:0 < 100 && i12:0 > 0
f55_0_rec_GE(EOS(STATIC_55), i5:0, i5:0, i12:0, i12:0, 100) -> f2918_0_descend_Load(EOS(STATIC_2918), i12:0, i12:0) :|: i12:0 < 100 && i12:0 > 0
Filtered constant ground arguments:
   f55_0_rec_GE(x1, x2, x3, x4, x5, x6) -> f55_0_rec_GE(x2, x3, x4, x5)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f55_0_rec_GE(x1, x2, x3, x4) -> f55_0_rec_GE(x2, x4)
Finished conversion. Obtained 2 rules.P rules:
f55_0_rec_GE(i5:0, i13:0) -> f55_0_rec_GE(i5:0 - 1, i5:0 - 1) :|: i5:0 - 1 < i5:0 && i5:0 > 0 && i13:0 > 99
f55_0_rec_GE(i5:0, i12:0) -> f55_0_rec_GE(i5:0, i12:0 + 1) :|: i12:0 < 100 && i12:0 > 0

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(22)
Obligation:
Rules:
f55_0_rec_GE(i5:0, i13:0) -> f55_0_rec_GE(i5:0 - 1, i5:0 - 1) :|: i5:0 - 1 < i5:0 && i5:0 > 0 && i13:0 > 99
f55_0_rec_GE(x, x1) -> f55_0_rec_GE(x, x1 + 1) :|: x1 < 100 && x1 > 0

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

(24)
Obligation:
Rules:
f55_0_rec_GE(i5:0, i13:0) -> f55_0_rec_GE(arith, arith) :|: i5:0 - 1 < i5:0 && i5:0 > 0 && i13:0 > 99 && arith = i5:0 - 1 && arith = i5:0 - 1
f55_0_rec_GE(x2, x3) -> f55_0_rec_GE(x2, x4) :|: x3 < 100 && x3 > 0 && x4 = x3 + 1

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(25) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f55_0_rec_GE(i5:0, i13:0) -> f55_0_rec_GE(arith, arith) :|: i5:0 - 1 < i5:0 && i5:0 > 0 && i13:0 > 99 && arith = i5:0 - 1 && arith = i5:0 - 1
(2) f55_0_rec_GE(x2, x3) -> f55_0_rec_GE(x2, x4) :|: x3 < 100 && x3 > 0 && x4 = x3 + 1

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

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

(26)
Obligation:

Termination digraph:
Nodes:
(1) f55_0_rec_GE(i5:0, i13:0) -> f55_0_rec_GE(arith, arith) :|: i5:0 - 1 < i5:0 && i5:0 > 0 && i13:0 > 99 && arith = i5:0 - 1 && arith = i5:0 - 1
(2) f55_0_rec_GE(x2, x3) -> f55_0_rec_GE(x2, x4) :|: x3 < 100 && x3 > 0 && x4 = x3 + 1

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

This digraph is fully evaluated!

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

(28)
Obligation:
Rules:
f55_0_rec_GE(i5:0:0, i13:0:0) -> f55_0_rec_GE(i5:0:0 - 1, i5:0:0 - 1) :|: i5:0:0 - 1 < i5:0:0 && i5:0:0 > 0 && i13:0:0 > 99
f55_0_rec_GE(x2:0, x3:0) -> f55_0_rec_GE(x2:0, x3:0 + 1) :|: x3:0 < 100 && x3:0 > 0

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(29) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f55_0_rec_GE(VARIABLE, INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(30)
Obligation:
Rules:
f55_0_rec_GE(i5:0:0, i13:0:0) -> f55_0_rec_GE(c, c1) :|: c1 = i5:0:0 - 1 && c = i5:0:0 - 1 && (i5:0:0 - 1 < i5:0:0 && i5:0:0 > 0 && i13:0:0 > 99)
f55_0_rec_GE(x2:0, x3:0) -> f55_0_rec_GE(x2:0, c2) :|: c2 = x3:0 + 1 && (x3:0 < 100 && x3:0 > 0)

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(31) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f55_0_rec_GE(x, x1)] = -1 + x

The following rules are decreasing:
f55_0_rec_GE(i5:0:0, i13:0:0) -> f55_0_rec_GE(c, c1) :|: c1 = i5:0:0 - 1 && c = i5:0:0 - 1 && (i5:0:0 - 1 < i5:0:0 && i5:0:0 > 0 && i13:0:0 > 99)
The following rules are bounded:
f55_0_rec_GE(i5:0:0, i13:0:0) -> f55_0_rec_GE(c, c1) :|: c1 = i5:0:0 - 1 && c = i5:0:0 - 1 && (i5:0:0 - 1 < i5:0:0 && i5:0:0 > 0 && i13:0:0 > 99)

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(32)
Obligation:
Rules:
f55_0_rec_GE(x2:0, x3:0) -> f55_0_rec_GE(x2:0, c2) :|: c2 = x3:0 + 1 && (x3:0 < 100 && x3:0 > 0)

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(33) RankingReductionPairProof (EQUIVALENT)
Interpretation:
[ f55_0_rec_GE ] = -1*f55_0_rec_GE_2

The following rules are decreasing:
f55_0_rec_GE(x2:0, x3:0) -> f55_0_rec_GE(x2:0, c2) :|: c2 = x3:0 + 1 && (x3:0 < 100 && x3:0 > 0)

The following rules are bounded:
f55_0_rec_GE(x2:0, x3:0) -> f55_0_rec_GE(x2:0, c2) :|: c2 = x3:0 + 1 && (x3:0 < 100 && x3:0 > 0)


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(34)
YES