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


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.jar
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


termination of the given Bare JBC problem could be proven:

(0) Bare JBC problem
(1) BareJBCToJBCProof [EQUIVALENT, 95 ms]
(2) JBC problem
(3) JBCToGraph [EQUIVALENT, 376 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 1 ms]
(6) AND
    (7) JBCTerminationSCC
        (8) SCCToIRSProof [SOUND, 57 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, 15 ms]
        (17) IntTRS
        (18) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (19) YES
    (20) JBCTerminationSCC
        (21) SCCToQDPProof [SOUND, 252 ms]
        (22) QDP
        (23) MRRProof [EQUIVALENT, 0 ms]
        (24) QDP
        (25) PisEmptyProof [EQUIVALENT, 0 ms]
        (26) YES


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

(0)
Obligation:
need to prove termination of the following program:
package AlternatingGrowReduce2;

public class AlternatingGrowReduce2 {
	AlternatingGrowReduce2 next;

	public static void main(String[] argv) {
		Random.args = argv;
		AlternatingGrowReduce2 list = createList(Random.random());

		int mode = 0;
		while (list != null) {
			if (mode == 0) {
				list = list.next;
			} else if (mode == 1) {
				list = new AlternatingGrowReduce2(list);
			} else if (mode > 1) {
				list = list.next;
			}

			mode++;
			if (mode > 2) {
				mode = 0;
			}
		}
	}

	public AlternatingGrowReduce2(AlternatingGrowReduce2 old) {
		this.next = old;
	}

	public static AlternatingGrowReduce2 createList(int length) {
		AlternatingGrowReduce2 res = new AlternatingGrowReduce2(null);
		while (length > 0) {
			res = new AlternatingGrowReduce2(res);
			length--;
		}
		return res;
	}
}


package AlternatingGrowReduce2;

public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}



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

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

(2)
Obligation:
need to prove termination of the following program:
package AlternatingGrowReduce2;

public class AlternatingGrowReduce2 {
	AlternatingGrowReduce2 next;

	public static void main(String[] argv) {
		Random.args = argv;
		AlternatingGrowReduce2 list = createList(Random.random());

		int mode = 0;
		while (list != null) {
			if (mode == 0) {
				list = list.next;
			} else if (mode == 1) {
				list = new AlternatingGrowReduce2(list);
			} else if (mode > 1) {
				list = list.next;
			}

			mode++;
			if (mode > 2) {
				mode = 0;
			}
		}
	}

	public AlternatingGrowReduce2(AlternatingGrowReduce2 old) {
		this.next = old;
	}

	public static AlternatingGrowReduce2 createList(int length) {
		AlternatingGrowReduce2 res = new AlternatingGrowReduce2(null);
		while (length > 0) {
			res = new AlternatingGrowReduce2(res);
			length--;
		}
		return res;
	}
}


package AlternatingGrowReduce2;

public class Random {
  static String[] args;
  static int index = 0;

  public static int random() {
    String string = args[index];
    index++;
    return string.length();
  }
}



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

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

(4)
Obligation:
Termination Graph based on JBC Program:
AlternatingGrowReduce2.AlternatingGrowReduce2.main([Ljava/lang/String;)V: Graph of 165 nodes with 1 SCC.



AlternatingGrowReduce2.AlternatingGrowReduce2.createList(I)LAlternatingGrowReduce2/AlternatingGrowReduce2;: Graph of 34 nodes with 1 SCC.





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

(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: AlternatingGrowReduce2.AlternatingGrowReduce2.createList(I)LAlternatingGrowReduce2/AlternatingGrowReduce2;
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:
f530_0_createList_LE(EOS(STATIC_530), i63, i63) -> f537_0_createList_LE(EOS(STATIC_537), i63, i63) :|: TRUE
f537_0_createList_LE(EOS(STATIC_537), i63, i63) -> f544_0_createList_New(EOS(STATIC_544), i63) :|: i63 > 0
f544_0_createList_New(EOS(STATIC_544), i63) -> f550_0_createList_Duplicate(EOS(STATIC_550), i63) :|: TRUE
f550_0_createList_Duplicate(EOS(STATIC_550), i63) -> f556_0_createList_Load(EOS(STATIC_556), i63) :|: TRUE
f556_0_createList_Load(EOS(STATIC_556), i63) -> f612_0_createList_InvokeMethod(EOS(STATIC_612), i63) :|: TRUE
f612_0_createList_InvokeMethod(EOS(STATIC_612), i63) -> f634_0__init__Load(EOS(STATIC_634), i63) :|: TRUE
f634_0__init__Load(EOS(STATIC_634), i63) -> f638_0__init__InvokeMethod(EOS(STATIC_638), i63) :|: TRUE
f638_0__init__InvokeMethod(EOS(STATIC_638), i63) -> f640_0__init__Load(EOS(STATIC_640), i63) :|: TRUE
f640_0__init__Load(EOS(STATIC_640), i63) -> f644_0__init__Load(EOS(STATIC_644), i63) :|: TRUE
f644_0__init__Load(EOS(STATIC_644), i63) -> f650_0__init__FieldAccess(EOS(STATIC_650), i63) :|: TRUE
f650_0__init__FieldAccess(EOS(STATIC_650), i63) -> f661_0__init__Return(EOS(STATIC_661), i63) :|: TRUE
f661_0__init__Return(EOS(STATIC_661), i63) -> f666_0_createList_Store(EOS(STATIC_666), i63) :|: TRUE
f666_0_createList_Store(EOS(STATIC_666), i63) -> f668_0_createList_Inc(EOS(STATIC_668), i63) :|: TRUE
f668_0_createList_Inc(EOS(STATIC_668), i63) -> f672_0_createList_JMP(EOS(STATIC_672), i63 + -1) :|: TRUE
f672_0_createList_JMP(EOS(STATIC_672), i79) -> f704_0_createList_Load(EOS(STATIC_704), i79) :|: TRUE
f704_0_createList_Load(EOS(STATIC_704), i79) -> f524_0_createList_Load(EOS(STATIC_524), i79) :|: TRUE
f524_0_createList_Load(EOS(STATIC_524), i58) -> f530_0_createList_LE(EOS(STATIC_530), i58, i58) :|: TRUE
Combined rules. Obtained 1 IRulesP rules:
f530_0_createList_LE(EOS(STATIC_530), i63:0, i63:0) -> f530_0_createList_LE(EOS(STATIC_530), i63:0 - 1, i63:0 - 1) :|: i63:0 > 0
Filtered constant ground arguments:
   f530_0_createList_LE(x1, x2, x3) -> f530_0_createList_LE(x2, x3)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f530_0_createList_LE(x1, x2) -> f530_0_createList_LE(x2)
Finished conversion. Obtained 1 rules.P rules:
f530_0_createList_LE(i63:0) -> f530_0_createList_LE(i63:0 - 1) :|: i63:0 > 0

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

(9)
Obligation:
Rules:
f530_0_createList_LE(i63:0) -> f530_0_createList_LE(i63:0 - 1) :|: i63:0 > 0

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

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

(11)
Obligation:
Rules:
f530_0_createList_LE(i63:0) -> f530_0_createList_LE(arith) :|: i63:0 > 0 && arith = i63:0 - 1

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

(12) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f530_0_createList_LE(i63:0) -> f530_0_createList_LE(arith) :|: i63:0 > 0 && arith = i63:0 - 1

Arcs:
(1) -> (1)

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

(13)
Obligation:

Termination digraph:
Nodes:
(1) f530_0_createList_LE(i63:0) -> f530_0_createList_LE(arith) :|: i63:0 > 0 && arith = i63:0 - 1

Arcs:
(1) -> (1)

This digraph is fully evaluated!

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

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

(15)
Obligation:
Rules:
f530_0_createList_LE(i63:0:0) -> f530_0_createList_LE(i63:0:0 - 1) :|: i63:0:0 > 0

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

(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f530_0_createList_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(17)
Obligation:
Rules:
f530_0_createList_LE(i63:0:0) -> f530_0_createList_LE(c) :|: c = i63:0:0 - 1 && i63:0:0 > 0

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

(18) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f530_0_createList_LE(x)] = x

The following rules are decreasing:
f530_0_createList_LE(i63:0:0) -> f530_0_createList_LE(c) :|: c = i63:0:0 - 1 && i63:0:0 > 0
The following rules are bounded:
f530_0_createList_LE(i63:0:0) -> f530_0_createList_LE(c) :|: c = i63:0:0 - 1 && i63:0:0 > 0

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

(19)
YES

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

(20)
Obligation:
SCC of termination graph based on JBC Program.
SCC contains nodes from the following methods: AlternatingGrowReduce2.AlternatingGrowReduce2.main([Ljava/lang/String;)V
SCC calls the following helper methods: 
Performed SCC analyses:
*Used field analysis yielded the following read fields:
*AlternatingGrowReduce2.AlternatingGrowReduce2: [next]
*Marker field analysis yielded the following relations that could be markers:

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

(21) SCCToQDPProof (SOUND)
Transformed TerminationGraph SCC to QDP. Log: 
Generated rules. Obtained 56 IRulesP rules:
f902_0_main_NULL(EOS(STATIC_902), java.lang.Object(o158sub), i89, java.lang.Object(o158sub)) -> f903_0_main_NULL(EOS(STATIC_903), java.lang.Object(o158sub), i89, java.lang.Object(o158sub)) :|: TRUE
f903_0_main_NULL(EOS(STATIC_903), java.lang.Object(o158sub), i89, java.lang.Object(o158sub)) -> f905_0_main_Load(EOS(STATIC_905), java.lang.Object(o158sub), i89) :|: TRUE
f905_0_main_Load(EOS(STATIC_905), java.lang.Object(o158sub), i89) -> f907_0_main_NE(EOS(STATIC_907), java.lang.Object(o158sub), i89, i89) :|: TRUE
f907_0_main_NE(EOS(STATIC_907), java.lang.Object(o158sub), i91, i91) -> f910_0_main_NE(EOS(STATIC_910), java.lang.Object(o158sub), i91, i91) :|: TRUE
f907_0_main_NE(EOS(STATIC_907), java.lang.Object(o158sub), matching1, matching2) -> f911_0_main_NE(EOS(STATIC_911), java.lang.Object(o158sub), 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f910_0_main_NE(EOS(STATIC_910), java.lang.Object(o158sub), i91, i91) -> f912_0_main_Load(EOS(STATIC_912), java.lang.Object(o158sub), i91) :|: i91 > 0
f912_0_main_Load(EOS(STATIC_912), java.lang.Object(o158sub), i91) -> f914_0_main_ConstantStackPush(EOS(STATIC_914), java.lang.Object(o158sub), i91, i91) :|: TRUE
f914_0_main_ConstantStackPush(EOS(STATIC_914), java.lang.Object(o158sub), i91, i91) -> f917_0_main_NE(EOS(STATIC_917), java.lang.Object(o158sub), i91, i91, 1) :|: TRUE
f917_0_main_NE(EOS(STATIC_917), java.lang.Object(o158sub), matching1, matching2, matching3) -> f939_0_main_NE(EOS(STATIC_939), java.lang.Object(o158sub), 1, 1, 1) :|: i91 = 1 && matching1 = 1 && matching2 = 1 && matching3 = 1
f917_0_main_NE(EOS(STATIC_917), java.lang.Object(o158sub), matching1, matching2, matching3) -> f941_0_main_NE(EOS(STATIC_941), java.lang.Object(o158sub), 2, 2, 1) :|: i91 = 2 && matching1 = 2 && matching2 = 2 && matching3 = 1
f939_0_main_NE(EOS(STATIC_939), java.lang.Object(o158sub), matching1, matching2, matching3) -> f945_0_main_New(EOS(STATIC_945), java.lang.Object(o158sub), 1) :|: TRUE && matching1 = 1 && matching2 = 1 && matching3 = 1
f945_0_main_New(EOS(STATIC_945), java.lang.Object(o158sub), matching1) -> f953_0_main_Duplicate(EOS(STATIC_953), java.lang.Object(o158sub), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) :|: TRUE && matching1 = 1
f953_0_main_Duplicate(EOS(STATIC_953), java.lang.Object(o158sub), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) -> f958_0_main_Load(EOS(STATIC_958), java.lang.Object(o158sub), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) :|: TRUE && matching1 = 1
f958_0_main_Load(EOS(STATIC_958), java.lang.Object(o158sub), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) -> f961_0_main_InvokeMethod(EOS(STATIC_961), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o158sub)) :|: TRUE && matching1 = 1
f961_0_main_InvokeMethod(EOS(STATIC_961), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o158sub)) -> f965_0__init__Load(EOS(STATIC_965), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o158sub)) :|: TRUE && matching1 = 1
f965_0__init__Load(EOS(STATIC_965), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o158sub)) -> f995_0__init__InvokeMethod(EOS(STATIC_995), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o158sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) :|: TRUE && matching1 = 1
f995_0__init__InvokeMethod(EOS(STATIC_995), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o158sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) -> f1000_0__init__Load(EOS(STATIC_1000), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o158sub)) :|: TRUE && matching1 = 1
f1000_0__init__Load(EOS(STATIC_1000), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o158sub)) -> f1006_0__init__Load(EOS(STATIC_1006), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o158sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) :|: TRUE && matching1 = 1
f1006_0__init__Load(EOS(STATIC_1006), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o158sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) -> f1011_0__init__FieldAccess(EOS(STATIC_1011), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o158sub)) :|: TRUE && matching1 = 1
f1011_0__init__FieldAccess(EOS(STATIC_1011), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o158sub)) -> f1015_0__init__Return(EOS(STATIC_1015), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub)))) :|: TRUE && matching1 = 1
f1015_0__init__Return(EOS(STATIC_1015), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub)))) -> f1017_0_main_Store(EOS(STATIC_1017), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub)))) :|: TRUE && matching1 = 1
f1017_0_main_Store(EOS(STATIC_1017), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub)))) -> f1026_0_main_JMP(EOS(STATIC_1026), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), 1) :|: TRUE && matching1 = 1
f1026_0_main_JMP(EOS(STATIC_1026), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), matching1) -> f1032_0_main_Inc(EOS(STATIC_1032), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), 1) :|: TRUE && matching1 = 1
f1032_0_main_Inc(EOS(STATIC_1032), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), matching1) -> f1038_0_main_Load(EOS(STATIC_1038), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), 2) :|: TRUE && matching1 = 1
f1038_0_main_Load(EOS(STATIC_1038), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), matching1) -> f1073_0_main_ConstantStackPush(EOS(STATIC_1073), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), 2, 2) :|: TRUE && matching1 = 2
f1073_0_main_ConstantStackPush(EOS(STATIC_1073), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), matching1, matching2) -> f1080_0_main_LE(EOS(STATIC_1080), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), 2, 2, 2) :|: TRUE && matching1 = 2 && matching2 = 2
f1080_0_main_LE(EOS(STATIC_1080), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), matching1, matching2, matching3) -> f1089_0_main_Load(EOS(STATIC_1089), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), 2) :|: TRUE && matching1 = 2 && matching2 = 2 && matching3 = 2
f1089_0_main_Load(EOS(STATIC_1089), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), matching1) -> f900_0_main_Load(EOS(STATIC_900), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub))), 2) :|: TRUE && matching1 = 2
f900_0_main_Load(EOS(STATIC_900), o155, i89) -> f902_0_main_NULL(EOS(STATIC_902), o155, i89, o155) :|: TRUE
f941_0_main_NE(EOS(STATIC_941), java.lang.Object(o158sub), matching1, matching2, matching3) -> f948_0_main_Load(EOS(STATIC_948), java.lang.Object(o158sub), 2) :|: TRUE && matching1 = 2 && matching2 = 2 && matching3 = 1
f948_0_main_Load(EOS(STATIC_948), java.lang.Object(o158sub), matching1) -> f955_0_main_ConstantStackPush(EOS(STATIC_955), java.lang.Object(o158sub), 2, 2) :|: TRUE && matching1 = 2
f955_0_main_ConstantStackPush(EOS(STATIC_955), java.lang.Object(o158sub), matching1, matching2) -> f959_0_main_LE(EOS(STATIC_959), java.lang.Object(o158sub), 2, 2) :|: TRUE && matching1 = 2 && matching2 = 2
f959_0_main_LE(EOS(STATIC_959), java.lang.Object(o158sub), matching1, matching2) -> f963_0_main_Load(EOS(STATIC_963), java.lang.Object(o158sub), 2) :|: TRUE && matching1 = 2 && matching2 = 2
f963_0_main_Load(EOS(STATIC_963), java.lang.Object(o158sub), matching1) -> f967_0_main_FieldAccess(EOS(STATIC_967), 2, java.lang.Object(o158sub)) :|: TRUE && matching1 = 2
f967_0_main_FieldAccess(EOS(STATIC_967), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o164))) -> f974_0_main_FieldAccess(EOS(STATIC_974), 2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o164))) :|: TRUE && matching1 = 2
f974_0_main_FieldAccess(EOS(STATIC_974), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o164))) -> f998_0_main_Store(EOS(STATIC_998), 2, o164) :|: TRUE && matching1 = 2
f998_0_main_Store(EOS(STATIC_998), matching1, o164) -> f1004_0_main_Inc(EOS(STATIC_1004), o164, 2) :|: TRUE && matching1 = 2
f1004_0_main_Inc(EOS(STATIC_1004), o164, matching1) -> f1009_0_main_Load(EOS(STATIC_1009), o164) :|: TRUE && matching1 = 2
f1009_0_main_Load(EOS(STATIC_1009), o164) -> f1013_0_main_ConstantStackPush(EOS(STATIC_1013), o164) :|: TRUE
f1013_0_main_ConstantStackPush(EOS(STATIC_1013), o164) -> f1016_0_main_LE(EOS(STATIC_1016), o164) :|: TRUE
f1016_0_main_LE(EOS(STATIC_1016), o164) -> f1023_0_main_ConstantStackPush(EOS(STATIC_1023), o164) :|: TRUE
f1023_0_main_ConstantStackPush(EOS(STATIC_1023), o164) -> f1028_0_main_Store(EOS(STATIC_1028), o164, 0) :|: TRUE
f1028_0_main_Store(EOS(STATIC_1028), o164, matching1) -> f1034_0_main_JMP(EOS(STATIC_1034), o164, 0) :|: TRUE && matching1 = 0
f1034_0_main_JMP(EOS(STATIC_1034), o164, matching1) -> f1060_0_main_Load(EOS(STATIC_1060), o164, 0) :|: TRUE && matching1 = 0
f1060_0_main_Load(EOS(STATIC_1060), o164, matching1) -> f900_0_main_Load(EOS(STATIC_900), o164, 0) :|: TRUE && matching1 = 0
f911_0_main_NE(EOS(STATIC_911), java.lang.Object(o158sub), matching1, matching2) -> f913_0_main_Load(EOS(STATIC_913), java.lang.Object(o158sub), 0) :|: TRUE && matching1 = 0 && matching2 = 0
f913_0_main_Load(EOS(STATIC_913), java.lang.Object(o158sub), matching1) -> f915_0_main_FieldAccess(EOS(STATIC_915), 0, java.lang.Object(o158sub)) :|: TRUE && matching1 = 0
f915_0_main_FieldAccess(EOS(STATIC_915), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o160))) -> f921_0_main_FieldAccess(EOS(STATIC_921), 0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o160))) :|: TRUE && matching1 = 0
f921_0_main_FieldAccess(EOS(STATIC_921), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o160))) -> f943_0_main_Store(EOS(STATIC_943), 0, o160) :|: TRUE && matching1 = 0
f943_0_main_Store(EOS(STATIC_943), matching1, o160) -> f950_0_main_JMP(EOS(STATIC_950), o160, 0) :|: TRUE && matching1 = 0
f950_0_main_JMP(EOS(STATIC_950), o160, matching1) -> f957_0_main_Inc(EOS(STATIC_957), o160, 0) :|: TRUE && matching1 = 0
f957_0_main_Inc(EOS(STATIC_957), o160, matching1) -> f960_0_main_Load(EOS(STATIC_960), o160, 1) :|: TRUE && matching1 = 0
f960_0_main_Load(EOS(STATIC_960), o160, matching1) -> f964_0_main_ConstantStackPush(EOS(STATIC_964), o160, 1, 1) :|: TRUE && matching1 = 1
f964_0_main_ConstantStackPush(EOS(STATIC_964), o160, matching1, matching2) -> f970_0_main_LE(EOS(STATIC_970), o160, 1, 1) :|: TRUE && matching1 = 1 && matching2 = 1
f970_0_main_LE(EOS(STATIC_970), o160, matching1, matching2) -> f993_0_main_Load(EOS(STATIC_993), o160, 1) :|: TRUE && matching1 = 1 && matching2 = 1
f993_0_main_Load(EOS(STATIC_993), o160, matching1) -> f900_0_main_Load(EOS(STATIC_900), o160, 1) :|: TRUE && matching1 = 1
Combined rules. Obtained 3 IRulesP rules:
f902_0_main_NULL(EOS(STATIC_902), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o164:0)), 2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o164:0))) -> f902_0_main_NULL(EOS(STATIC_902), o164:0, 0, o164:0) :|: TRUE
f902_0_main_NULL(EOS(STATIC_902), java.lang.Object(o158sub:0), 1, java.lang.Object(o158sub:0)) -> f902_0_main_NULL(EOS(STATIC_902), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub:0))), 2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o158sub:0)))) :|: TRUE
f902_0_main_NULL(EOS(STATIC_902), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o160:0)), 0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o160:0))) -> f902_0_main_NULL(EOS(STATIC_902), o160:0, 1, o160:0) :|: TRUE
Filtered constant ground arguments:
   f902_0_main_NULL(x1, x2, x3, x4) -> f902_0_main_NULL(x2, x3, x4)
   EOS(x1) -> EOS
   AlternatingGrowReduce2.AlternatingGrowReduce2(x1, x2) -> AlternatingGrowReduce2.AlternatingGrowReduce2(x2)
Filtered duplicate arguments:
   f902_0_main_NULL(x1, x2, x3) -> f902_0_main_NULL(x2, x3)

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(22)
Obligation:
Q DP problem:
The TRS P consists of the following rules:

   f902_0_main_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(o164:0))) -> f902_0_main_NULL(0, o164:0)
   f902_0_main_NULL(1, java.lang.Object(o158sub:0)) -> f902_0_main_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(java.lang.Object(o158sub:0))))
   f902_0_main_NULL(0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(o160:0))) -> f902_0_main_NULL(1, o160:0)

R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(23) MRRProof (EQUIVALENT)
By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented.

Strictly oriented dependency pairs:

   f902_0_main_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(o164:0))) -> f902_0_main_NULL(0, o164:0)
   f902_0_main_NULL(1, java.lang.Object(o158sub:0)) -> f902_0_main_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(java.lang.Object(o158sub:0))))
   f902_0_main_NULL(0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(o160:0))) -> f902_0_main_NULL(1, o160:0)


Used ordering: Knuth-Bendix order [KBO] with precedence:2 > f902_0_main_NULL_2 > AlternatingGrowReduce2.AlternatingGrowReduce2_1 > 0 > 1 > java.lang.Object_1

and weight map:

   2=1
   0=2
   1=3
   java.lang.Object_1=1
   AlternatingGrowReduce2.AlternatingGrowReduce2_1=1
   f902_0_main_NULL_2=0

The variable weight is 1

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(24)
Obligation:
Q DP problem:
P is empty.
R is empty.
Q is empty.
We have to consider all minimal (P,Q,R)-chains.
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(25) PisEmptyProof (EQUIVALENT)
The TRS P is empty. Hence, there is no (P,Q,R) chain.
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(26)
YES