/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 346 ms]
(4) JBCTerminationGraph
(5) TerminationGraphToSCCProof [SOUND, 0 ms]
(6) AND
    (7) JBCTerminationSCC
        (8) SCCToIRSProof [SOUND, 51 ms]
        (9) IRSwT
        (10) IRSFormatTransformerProof [EQUIVALENT, 0 ms]
        (11) IRSwT
        (12) IRSwTTerminationDigraphProof [EQUIVALENT, 18 ms]
        (13) IRSwT
        (14) IntTRSCompressionProof [EQUIVALENT, 0 ms]
        (15) IRSwT
        (16) TempFilterProof [SOUND, 37 ms]
        (17) IntTRS
        (18) PolynomialOrderProcessor [EQUIVALENT, 0 ms]
        (19) YES
    (20) JBCTerminationSCC
        (21) SCCToQDPProof [SOUND, 232 ms]
        (22) QDP
        (23) MRRProof [EQUIVALENT, 3 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:
f522_0_createList_LE(EOS(STATIC_522), i63, i63) -> f526_0_createList_LE(EOS(STATIC_526), i63, i63) :|: TRUE
f526_0_createList_LE(EOS(STATIC_526), i63, i63) -> f530_0_createList_New(EOS(STATIC_530), i63) :|: i63 > 0
f530_0_createList_New(EOS(STATIC_530), i63) -> f533_0_createList_Duplicate(EOS(STATIC_533), i63) :|: TRUE
f533_0_createList_Duplicate(EOS(STATIC_533), i63) -> f536_0_createList_Load(EOS(STATIC_536), i63) :|: TRUE
f536_0_createList_Load(EOS(STATIC_536), i63) -> f595_0_createList_InvokeMethod(EOS(STATIC_595), i63) :|: TRUE
f595_0_createList_InvokeMethod(EOS(STATIC_595), i63) -> f632_0__init__Load(EOS(STATIC_632), i63) :|: TRUE
f632_0__init__Load(EOS(STATIC_632), i63) -> f636_0__init__InvokeMethod(EOS(STATIC_636), i63) :|: TRUE
f636_0__init__InvokeMethod(EOS(STATIC_636), i63) -> f639_0__init__Load(EOS(STATIC_639), i63) :|: TRUE
f639_0__init__Load(EOS(STATIC_639), i63) -> f641_0__init__Load(EOS(STATIC_641), i63) :|: TRUE
f641_0__init__Load(EOS(STATIC_641), i63) -> f644_0__init__FieldAccess(EOS(STATIC_644), i63) :|: TRUE
f644_0__init__FieldAccess(EOS(STATIC_644), i63) -> f646_0__init__Return(EOS(STATIC_646), i63) :|: TRUE
f646_0__init__Return(EOS(STATIC_646), i63) -> f649_0_createList_Store(EOS(STATIC_649), i63) :|: TRUE
f649_0_createList_Store(EOS(STATIC_649), i63) -> f653_0_createList_Inc(EOS(STATIC_653), i63) :|: TRUE
f653_0_createList_Inc(EOS(STATIC_653), i63) -> f659_0_createList_JMP(EOS(STATIC_659), i63 + -1) :|: TRUE
f659_0_createList_JMP(EOS(STATIC_659), i79) -> f689_0_createList_Load(EOS(STATIC_689), i79) :|: TRUE
f689_0_createList_Load(EOS(STATIC_689), i79) -> f520_0_createList_Load(EOS(STATIC_520), i79) :|: TRUE
f520_0_createList_Load(EOS(STATIC_520), i56) -> f522_0_createList_LE(EOS(STATIC_522), i56, i56) :|: TRUE
Combined rules. Obtained 1 IRulesP rules:
f522_0_createList_LE(EOS(STATIC_522), i63:0, i63:0) -> f522_0_createList_LE(EOS(STATIC_522), i63:0 - 1, i63:0 - 1) :|: i63:0 > 0
Filtered constant ground arguments:
   f522_0_createList_LE(x1, x2, x3) -> f522_0_createList_LE(x2, x3)
   EOS(x1) -> EOS
Filtered duplicate arguments:
   f522_0_createList_LE(x1, x2) -> f522_0_createList_LE(x2)
Finished conversion. Obtained 1 rules.P rules:
f522_0_createList_LE(i63:0) -> f522_0_createList_LE(i63:0 - 1) :|: i63:0 > 0

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

(9)
Obligation:
Rules:
f522_0_createList_LE(i63:0) -> f522_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:
f522_0_createList_LE(i63:0) -> f522_0_createList_LE(arith) :|: i63:0 > 0 && arith = i63:0 - 1

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

(12) IRSwTTerminationDigraphProof (EQUIVALENT)
Constructed termination digraph!
Nodes:
(1) f522_0_createList_LE(i63:0) -> f522_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) f522_0_createList_LE(i63:0) -> f522_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:
f522_0_createList_LE(i63:0:0) -> f522_0_createList_LE(i63:0:0 - 1) :|: i63:0:0 > 0

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

(16) TempFilterProof (SOUND)
Used the following sort dictionary for filtering: 
f522_0_createList_LE(INTEGER)
Replaced non-predefined constructor symbols by 0.
----------------------------------------

(17)
Obligation:
Rules:
f522_0_createList_LE(i63:0:0) -> f522_0_createList_LE(c) :|: c = i63:0:0 - 1 && i63:0:0 > 0

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

(18) PolynomialOrderProcessor (EQUIVALENT)
Found the following polynomial interpretation:
[f522_0_createList_LE(x)] = x

The following rules are decreasing:
f522_0_createList_LE(i63:0:0) -> f522_0_createList_LE(c) :|: c = i63:0:0 - 1 && i63:0:0 > 0
The following rules are bounded:
f522_0_createList_LE(i63:0:0) -> f522_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:
f847_0_main_NULL(EOS(STATIC_847), java.lang.Object(o159sub), i87, java.lang.Object(o159sub)) -> f850_0_main_NULL(EOS(STATIC_850), java.lang.Object(o159sub), i87, java.lang.Object(o159sub)) :|: TRUE
f850_0_main_NULL(EOS(STATIC_850), java.lang.Object(o159sub), i87, java.lang.Object(o159sub)) -> f853_0_main_Load(EOS(STATIC_853), java.lang.Object(o159sub), i87) :|: TRUE
f853_0_main_Load(EOS(STATIC_853), java.lang.Object(o159sub), i87) -> f857_0_main_NE(EOS(STATIC_857), java.lang.Object(o159sub), i87, i87) :|: TRUE
f857_0_main_NE(EOS(STATIC_857), java.lang.Object(o159sub), i91, i91) -> f860_0_main_NE(EOS(STATIC_860), java.lang.Object(o159sub), i91, i91) :|: TRUE
f857_0_main_NE(EOS(STATIC_857), java.lang.Object(o159sub), matching1, matching2) -> f861_0_main_NE(EOS(STATIC_861), java.lang.Object(o159sub), 0, 0) :|: TRUE && matching1 = 0 && matching2 = 0
f860_0_main_NE(EOS(STATIC_860), java.lang.Object(o159sub), i91, i91) -> f862_0_main_Load(EOS(STATIC_862), java.lang.Object(o159sub), i91) :|: i91 > 0
f862_0_main_Load(EOS(STATIC_862), java.lang.Object(o159sub), i91) -> f864_0_main_ConstantStackPush(EOS(STATIC_864), java.lang.Object(o159sub), i91, i91) :|: TRUE
f864_0_main_ConstantStackPush(EOS(STATIC_864), java.lang.Object(o159sub), i91, i91) -> f867_0_main_NE(EOS(STATIC_867), java.lang.Object(o159sub), i91, i91, 1) :|: TRUE
f867_0_main_NE(EOS(STATIC_867), java.lang.Object(o159sub), matching1, matching2, matching3) -> f884_0_main_NE(EOS(STATIC_884), java.lang.Object(o159sub), 1, 1, 1) :|: i91 = 1 && matching1 = 1 && matching2 = 1 && matching3 = 1
f867_0_main_NE(EOS(STATIC_867), java.lang.Object(o159sub), matching1, matching2, matching3) -> f885_0_main_NE(EOS(STATIC_885), java.lang.Object(o159sub), 2, 2, 1) :|: i91 = 2 && matching1 = 2 && matching2 = 2 && matching3 = 1
f884_0_main_NE(EOS(STATIC_884), java.lang.Object(o159sub), matching1, matching2, matching3) -> f900_0_main_New(EOS(STATIC_900), java.lang.Object(o159sub), 1) :|: TRUE && matching1 = 1 && matching2 = 1 && matching3 = 1
f900_0_main_New(EOS(STATIC_900), java.lang.Object(o159sub), matching1) -> f907_0_main_Duplicate(EOS(STATIC_907), java.lang.Object(o159sub), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) :|: TRUE && matching1 = 1
f907_0_main_Duplicate(EOS(STATIC_907), java.lang.Object(o159sub), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) -> f911_0_main_Load(EOS(STATIC_911), java.lang.Object(o159sub), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) :|: TRUE && matching1 = 1
f911_0_main_Load(EOS(STATIC_911), java.lang.Object(o159sub), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) -> f919_0_main_InvokeMethod(EOS(STATIC_919), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o159sub)) :|: TRUE && matching1 = 1
f919_0_main_InvokeMethod(EOS(STATIC_919), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o159sub)) -> f931_0__init__Load(EOS(STATIC_931), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o159sub)) :|: TRUE && matching1 = 1
f931_0__init__Load(EOS(STATIC_931), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o159sub)) -> f940_0__init__InvokeMethod(EOS(STATIC_940), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o159sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) :|: TRUE && matching1 = 1
f940_0__init__InvokeMethod(EOS(STATIC_940), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o159sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) -> f947_0__init__Load(EOS(STATIC_947), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o159sub)) :|: TRUE && matching1 = 1
f947_0__init__Load(EOS(STATIC_947), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o159sub)) -> f951_0__init__Load(EOS(STATIC_951), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o159sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) :|: TRUE && matching1 = 1
f951_0__init__Load(EOS(STATIC_951), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o159sub), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL))) -> f957_0__init__FieldAccess(EOS(STATIC_957), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o159sub)) :|: TRUE && matching1 = 1
f957_0__init__FieldAccess(EOS(STATIC_957), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, NULL)), java.lang.Object(o159sub)) -> f967_0__init__Return(EOS(STATIC_967), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub)))) :|: TRUE && matching1 = 1
f967_0__init__Return(EOS(STATIC_967), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub)))) -> f971_0_main_Store(EOS(STATIC_971), 1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub)))) :|: TRUE && matching1 = 1
f971_0_main_Store(EOS(STATIC_971), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub)))) -> f980_0_main_JMP(EOS(STATIC_980), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), 1) :|: TRUE && matching1 = 1
f980_0_main_JMP(EOS(STATIC_980), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), matching1) -> f983_0_main_Inc(EOS(STATIC_983), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), 1) :|: TRUE && matching1 = 1
f983_0_main_Inc(EOS(STATIC_983), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), matching1) -> f986_0_main_Load(EOS(STATIC_986), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), 2) :|: TRUE && matching1 = 1
f986_0_main_Load(EOS(STATIC_986), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), matching1) -> f1015_0_main_ConstantStackPush(EOS(STATIC_1015), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), 2, 2) :|: TRUE && matching1 = 2
f1015_0_main_ConstantStackPush(EOS(STATIC_1015), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), matching1, matching2) -> f1021_0_main_LE(EOS(STATIC_1021), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), 2, 2, 2) :|: TRUE && matching1 = 2 && matching2 = 2
f1021_0_main_LE(EOS(STATIC_1021), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), matching1, matching2, matching3) -> f1030_0_main_Load(EOS(STATIC_1030), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), 2) :|: TRUE && matching1 = 2 && matching2 = 2 && matching3 = 2
f1030_0_main_Load(EOS(STATIC_1030), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), matching1) -> f844_0_main_Load(EOS(STATIC_844), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub))), 2) :|: TRUE && matching1 = 2
f844_0_main_Load(EOS(STATIC_844), o155, i87) -> f847_0_main_NULL(EOS(STATIC_847), o155, i87, o155) :|: TRUE
f885_0_main_NE(EOS(STATIC_885), java.lang.Object(o159sub), matching1, matching2, matching3) -> f903_0_main_Load(EOS(STATIC_903), java.lang.Object(o159sub), 2) :|: TRUE && matching1 = 2 && matching2 = 2 && matching3 = 1
f903_0_main_Load(EOS(STATIC_903), java.lang.Object(o159sub), matching1) -> f908_0_main_ConstantStackPush(EOS(STATIC_908), java.lang.Object(o159sub), 2, 2) :|: TRUE && matching1 = 2
f908_0_main_ConstantStackPush(EOS(STATIC_908), java.lang.Object(o159sub), matching1, matching2) -> f914_0_main_LE(EOS(STATIC_914), java.lang.Object(o159sub), 2, 2) :|: TRUE && matching1 = 2 && matching2 = 2
f914_0_main_LE(EOS(STATIC_914), java.lang.Object(o159sub), matching1, matching2) -> f928_0_main_Load(EOS(STATIC_928), java.lang.Object(o159sub), 2) :|: TRUE && matching1 = 2 && matching2 = 2
f928_0_main_Load(EOS(STATIC_928), java.lang.Object(o159sub), matching1) -> f932_0_main_FieldAccess(EOS(STATIC_932), 2, java.lang.Object(o159sub)) :|: TRUE && matching1 = 2
f932_0_main_FieldAccess(EOS(STATIC_932), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o165))) -> f934_0_main_FieldAccess(EOS(STATIC_934), 2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o165))) :|: TRUE && matching1 = 2
f934_0_main_FieldAccess(EOS(STATIC_934), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o165))) -> f944_0_main_Store(EOS(STATIC_944), 2, o165) :|: TRUE && matching1 = 2
f944_0_main_Store(EOS(STATIC_944), matching1, o165) -> f949_0_main_Inc(EOS(STATIC_949), o165, 2) :|: TRUE && matching1 = 2
f949_0_main_Inc(EOS(STATIC_949), o165, matching1) -> f955_0_main_Load(EOS(STATIC_955), o165) :|: TRUE && matching1 = 2
f955_0_main_Load(EOS(STATIC_955), o165) -> f961_0_main_ConstantStackPush(EOS(STATIC_961), o165) :|: TRUE
f961_0_main_ConstantStackPush(EOS(STATIC_961), o165) -> f970_0_main_LE(EOS(STATIC_970), o165) :|: TRUE
f970_0_main_LE(EOS(STATIC_970), o165) -> f978_0_main_ConstantStackPush(EOS(STATIC_978), o165) :|: TRUE
f978_0_main_ConstantStackPush(EOS(STATIC_978), o165) -> f982_0_main_Store(EOS(STATIC_982), o165, 0) :|: TRUE
f982_0_main_Store(EOS(STATIC_982), o165, matching1) -> f985_0_main_JMP(EOS(STATIC_985), o165, 0) :|: TRUE && matching1 = 0
f985_0_main_JMP(EOS(STATIC_985), o165, matching1) -> f1010_0_main_Load(EOS(STATIC_1010), o165, 0) :|: TRUE && matching1 = 0
f1010_0_main_Load(EOS(STATIC_1010), o165, matching1) -> f844_0_main_Load(EOS(STATIC_844), o165, 0) :|: TRUE && matching1 = 0
f861_0_main_NE(EOS(STATIC_861), java.lang.Object(o159sub), matching1, matching2) -> f863_0_main_Load(EOS(STATIC_863), java.lang.Object(o159sub), 0) :|: TRUE && matching1 = 0 && matching2 = 0
f863_0_main_Load(EOS(STATIC_863), java.lang.Object(o159sub), matching1) -> f865_0_main_FieldAccess(EOS(STATIC_865), 0, java.lang.Object(o159sub)) :|: TRUE && matching1 = 0
f865_0_main_FieldAccess(EOS(STATIC_865), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o161))) -> f868_0_main_FieldAccess(EOS(STATIC_868), 0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o161))) :|: TRUE && matching1 = 0
f868_0_main_FieldAccess(EOS(STATIC_868), matching1, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o161))) -> f888_0_main_Store(EOS(STATIC_888), 0, o161) :|: TRUE && matching1 = 0
f888_0_main_Store(EOS(STATIC_888), matching1, o161) -> f905_0_main_JMP(EOS(STATIC_905), o161, 0) :|: TRUE && matching1 = 0
f905_0_main_JMP(EOS(STATIC_905), o161, matching1) -> f909_0_main_Inc(EOS(STATIC_909), o161, 0) :|: TRUE && matching1 = 0
f909_0_main_Inc(EOS(STATIC_909), o161, matching1) -> f917_0_main_Load(EOS(STATIC_917), o161, 1) :|: TRUE && matching1 = 0
f917_0_main_Load(EOS(STATIC_917), o161, matching1) -> f930_0_main_ConstantStackPush(EOS(STATIC_930), o161, 1, 1) :|: TRUE && matching1 = 1
f930_0_main_ConstantStackPush(EOS(STATIC_930), o161, matching1, matching2) -> f933_0_main_LE(EOS(STATIC_933), o161, 1, 1) :|: TRUE && matching1 = 1 && matching2 = 1
f933_0_main_LE(EOS(STATIC_933), o161, matching1, matching2) -> f938_0_main_Load(EOS(STATIC_938), o161, 1) :|: TRUE && matching1 = 1 && matching2 = 1
f938_0_main_Load(EOS(STATIC_938), o161, matching1) -> f844_0_main_Load(EOS(STATIC_844), o161, 1) :|: TRUE && matching1 = 1
Combined rules. Obtained 3 IRulesP rules:
f847_0_main_NULL(EOS(STATIC_847), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o161:0)), 0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o161:0))) -> f847_0_main_NULL(EOS(STATIC_847), o161:0, 1, o161:0) :|: TRUE
f847_0_main_NULL(EOS(STATIC_847), java.lang.Object(o159sub:0), 1, java.lang.Object(o159sub:0)) -> f847_0_main_NULL(EOS(STATIC_847), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub:0))), 2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, java.lang.Object(o159sub:0)))) :|: TRUE
f847_0_main_NULL(EOS(STATIC_847), java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o165:0)), 2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(EOC, o165:0))) -> f847_0_main_NULL(EOS(STATIC_847), o165:0, 0, o165:0) :|: TRUE
Filtered constant ground arguments:
   f847_0_main_NULL(x1, x2, x3, x4) -> f847_0_main_NULL(x2, x3, x4)
   EOS(x1) -> EOS
   AlternatingGrowReduce2.AlternatingGrowReduce2(x1, x2) -> AlternatingGrowReduce2.AlternatingGrowReduce2(x2)
Filtered duplicate arguments:
   f847_0_main_NULL(x1, x2, x3) -> f847_0_main_NULL(x2, x3)

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

   f847_0_main_NULL(0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(o161:0))) -> f847_0_main_NULL(1, o161:0)
   f847_0_main_NULL(1, java.lang.Object(o159sub:0)) -> f847_0_main_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(java.lang.Object(o159sub:0))))
   f847_0_main_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(o165:0))) -> f847_0_main_NULL(0, o165:0)

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:

   f847_0_main_NULL(0, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(o161:0))) -> f847_0_main_NULL(1, o161:0)
   f847_0_main_NULL(1, java.lang.Object(o159sub:0)) -> f847_0_main_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(java.lang.Object(o159sub:0))))
   f847_0_main_NULL(2, java.lang.Object(AlternatingGrowReduce2.AlternatingGrowReduce2(o165:0))) -> f847_0_main_NULL(0, o165:0)


Used ordering: Knuth-Bendix order [KBO] with precedence:2 > 0 > 1 > java.lang.Object_1 > f847_0_main_NULL_2 > AlternatingGrowReduce2.AlternatingGrowReduce2_1

and weight map:

   0=2
   1=3
   2=1
   java.lang.Object_1=1
   AlternatingGrowReduce2.AlternatingGrowReduce2_1=1
   f847_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