Termination of the given JBC could be disproven:

(0) Obligation:

JBC Problem based on JBC Program:

package simple.alternatingIncr;

public class AlternatingIncr {

	public static void increase(int i) {
		while (i > 0) {
			if (i % 2 == 0) {
				i--;
			} else {
				i = i+3;
			}
		}
	}
}


package simple.alternatingIncr;

public class Main {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		AlternatingIncr.increase(args.length);

	}

}

(1) JBCNonTerm (EQUIVALENT transformation)

Reached a loop using the following run:
0:

java.lang.String = serialPersistentFields, CASE_INSENSITIVE_ORDER
[a50(lv_0_0)]
<simple.alternatingIncr.Main.main||0: load ADDR args||args: a50|| ->
	String.serialVersionUID: iconstLong_-6849794470754667710
	String.serialPersistentFields: a52
	String.CASE_INSENSITIVE_ORDER: o26
	String$CaseInsensitiveComparator.serialVersionUID: iconstLong_8575799808933029326
	RuntimeException.serialVersionUID: iconstLong_-7034897190745766939
	Exception.serialVersionUID: iconstLong_-3387516993124229948
	Throwable.serialVersionUID: iconstLong_-3042686055658047285
	i202: [0,+inf)(1){0,+inf}
	a50([java.lang.String...]): length i202
	a52([java.io.ObjectStreamField|]): length iconst_0
	o26!: String$CaseInsensitiveComparator()
Relations: 

1:

java.lang.String = serialPersistentFields, CASE_INSENSITIVE_ORDER
[a50(lv_0_0)]
<simple.alternatingIncr.Main.main||1: arraylength|| - ||a50>
	String.serialVersionUID: iconstLong_-6849794470754667710
	String.serialPersistentFields: a52
	String.CASE_INSENSITIVE_ORDER: o26
	String$CaseInsensitiveComparator.serialVersionUID: iconstLong_8575799808933029326
	RuntimeException.serialVersionUID: iconstLong_-7034897190745766939
	Exception.serialVersionUID: iconstLong_-3387516993124229948
	Throwable.serialVersionUID: iconstLong_-3042686055658047285
	i202: [0,+inf)(1){0,+inf}
	a50([java.lang.String...]): length i202
	a52([java.io.ObjectStreamField|]): length iconst_0
	o26!: String$CaseInsensitiveComparator()
Relations: 

2:

java.lang.String = serialPersistentFields, CASE_INSENSITIVE_ORDER
[a50(lv_0_0)]
<simple.alternatingIncr.Main.main||2: simple.alternatingIncr.AlternatingIncr.increase(I)V|| - ||i202>
	String.serialVersionUID: iconstLong_-6849794470754667710
	String.serialPersistentFields: a52
	String.CASE_INSENSITIVE_ORDER: o26
	String$CaseInsensitiveComparator.serialVersionUID: iconstLong_8575799808933029326
	RuntimeException.serialVersionUID: iconstLong_-7034897190745766939
	Exception.serialVersionUID: iconstLong_-3387516993124229948
	Throwable.serialVersionUID: iconstLong_-3042686055658047285
	i202: [0,+inf)(1){0,+inf}
	a50([java.lang.String...]): length i202
	a52([java.io.ObjectStreamField|]): length iconst_0
	o26!: String$CaseInsensitiveComparator()
Relations: 

3:

<simple.alternatingIncr.AlternatingIncr.increase||0: load INT i||i: i202|| ->
java.lang.String = serialPersistentFields, CASE_INSENSITIVE_ORDER
[a50(lv_0_0)]
<simple.alternatingIncr.Main.main||2: simple.alternatingIncr.AlternatingIncr.increase|| - ||i202>
	String.serialVersionUID: iconstLong_-6849794470754667710
	String.serialPersistentFields: a52
	String.CASE_INSENSITIVE_ORDER: o26
	String$CaseInsensitiveComparator.serialVersionUID: iconstLong_8575799808933029326
	RuntimeException.serialVersionUID: iconstLong_-7034897190745766939
	Exception.serialVersionUID: iconstLong_-3387516993124229948
	Throwable.serialVersionUID: iconstLong_-3042686055658047285
	i202: [0,+inf)(1){0,+inf}
	a50([java.lang.String...]): length i202
	a52([java.io.ObjectStreamField|]): length iconst_0
	o26!: String$CaseInsensitiveComparator()
Relations: 

Start state of loop:

<simple.alternatingIncr.AlternatingIncr.increase||0: load INT i||i: i13|| ->
java.lang.String = serialPersistentFields, CASE_INSENSITIVE_ORDER
[a6(lv_0_0)]
<simple.alternatingIncr.Main.main||2: simple.alternatingIncr.AlternatingIncr.increase|| - ||i15>
	String.serialVersionUID: iconstLong_-6849794470754667710
	String.serialPersistentFields: a5
	String.CASE_INSENSITIVE_ORDER: o3
	String$CaseInsensitiveComparator.serialVersionUID: iconstLong_8575799808933029326
	RuntimeException.serialVersionUID: iconstLong_-7034897190745766939
	Exception.serialVersionUID: iconstLong_-3387516993124229948
	Throwable.serialVersionUID: iconstLong_-3042686055658047285
	a5([java.io.ObjectStreamField|]): length iconst_0
	o3!: String$CaseInsensitiveComparator()
	i13: [0,+inf){-1,+inf}
	i15: [0,+inf)(1){0,+inf}
	a6([java.lang.String...]): length i15
Relations: 

In the loop head node, references [i13, iconst_0] were interesting.
By SMT, we could prove
((0 <= initial_i13 and 0 <= initial_i15) and ((((path1_i13 = path1_i27 and path1_i29 = (path1_i27 % 2) and path1_i32 = (path1_i27 + -1) and path1_i32 = res_i13 and path1_i15 = res_i15 and path1_i13 = initial_i13 and path1_i15 = initial_i15) and (path1_i27 > 0 and path1_i29 = 0 and T)) or ((path2_i13 = path2_i27 and path2_i29 = (path2_i27 % 2) and path2_i40 = (path2_i27 + 3) and path2_i40 = res_i13 and path2_i15 = res_i15 and path2_i13 = initial_i13 and path2_i15 = initial_i15) and (path2_i27 > 0 and path2_i29 = 1 and 1 > 0))) and (((res_i13 = res_i27 and res_i29 = (res_i27 % 2) and res_i32 = (res_i27 + -1)) and !(res_i27 > 0 and res_i29 = 0 and T)) and ((res_i13 = res_i27 and res_i29 = (res_i27 % 2) and res_i40 = (res_i27 + 3)) and !(res_i27 > 0 and res_i29 = 1 and 1 > 0)))))
to be UNSAT. Consequently, the loop will not terminate.

(2) NO