Termination of the given JBC could be disproven:

(0) Obligation:

JBC Problem based on JBC Program:

package simple.upAndDownIneq;

public class Main {

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

	}

}


package simple.upAndDownIneq;

public class UpAndDownIneq {
	
	public static void upAndDown(int i) {
		int up = 0;
		while (0 <= i && i <= 10) {
			if (i >= 10) {
				up = 0;
			}
			if (i <= 0) {
				up = 1;
			}
			if (up >= 1) {
				i++;
			} else {
				i--;
			}
		}
	}
	
}

(1) JBCNonTerm (EQUIVALENT transformation)

Reached a loop using the following run:
0:

java.lang.String = serialPersistentFields, CASE_INSENSITIVE_ORDER
[a143(lv_0_0)]
<simple.upAndDownIneq.Main.main||0: load ADDR args||args: a143|| ->
	String.serialVersionUID: iconstLong_-6849794470754667710
	String.serialPersistentFields: a145
	String.CASE_INSENSITIVE_ORDER: o93
	String$CaseInsensitiveComparator.serialVersionUID: iconstLong_8575799808933029326
	RuntimeException.serialVersionUID: iconstLong_-7034897190745766939
	Exception.serialVersionUID: iconstLong_-3387516993124229948
	Throwable.serialVersionUID: iconstLong_-3042686055658047285
	i114: [0,+inf)(2){0,+inf}
	a143([java.lang.String...]): length i114
	a145([java.io.ObjectStreamField|]): length iconst_0
	o93!: String$CaseInsensitiveComparator()
Relations: 

1:

java.lang.String = serialPersistentFields, CASE_INSENSITIVE_ORDER
[a143(lv_0_0)]
<simple.upAndDownIneq.Main.main||1: arraylength|| - ||a143>
	String.serialVersionUID: iconstLong_-6849794470754667710
	String.serialPersistentFields: a145
	String.CASE_INSENSITIVE_ORDER: o93
	String$CaseInsensitiveComparator.serialVersionUID: iconstLong_8575799808933029326
	RuntimeException.serialVersionUID: iconstLong_-7034897190745766939
	Exception.serialVersionUID: iconstLong_-3387516993124229948
	Throwable.serialVersionUID: iconstLong_-3042686055658047285
	i114: [0,+inf)(2){0,+inf}
	a143([java.lang.String...]): length i114
	a145([java.io.ObjectStreamField|]): length iconst_0
	o93!: String$CaseInsensitiveComparator()
Relations: 

2:

java.lang.String = serialPersistentFields, CASE_INSENSITIVE_ORDER
[a143(lv_0_0)]
<simple.upAndDownIneq.Main.main||2: simple.upAndDownIneq.UpAndDownIneq.upAndDown(I)V|| - ||i114>
	String.serialVersionUID: iconstLong_-6849794470754667710
	String.serialPersistentFields: a145
	String.CASE_INSENSITIVE_ORDER: o93
	String$CaseInsensitiveComparator.serialVersionUID: iconstLong_8575799808933029326
	RuntimeException.serialVersionUID: iconstLong_-7034897190745766939
	Exception.serialVersionUID: iconstLong_-3387516993124229948
	Throwable.serialVersionUID: iconstLong_-3042686055658047285
	i114: [0,+inf)(2){0,+inf}
	a143([java.lang.String...]): length i114
	a145([java.io.ObjectStreamField|]): length iconst_0
	o93!: String$CaseInsensitiveComparator()
Relations: 

3:

<simple.upAndDownIneq.UpAndDownIneq.upAndDown||0: push 0||i: i114|| ->
java.lang.String = serialPersistentFields, CASE_INSENSITIVE_ORDER
[a143(lv_0_0)]
<simple.upAndDownIneq.Main.main||2: simple.upAndDownIneq.UpAndDownIneq.upAndDown|| - ||i114>
	String.serialVersionUID: iconstLong_-6849794470754667710
	String.serialPersistentFields: a145
	String.CASE_INSENSITIVE_ORDER: o93
	String$CaseInsensitiveComparator.serialVersionUID: iconstLong_8575799808933029326
	RuntimeException.serialVersionUID: iconstLong_-7034897190745766939
	Exception.serialVersionUID: iconstLong_-3387516993124229948
	Throwable.serialVersionUID: iconstLong_-3042686055658047285
	i114: [0,+inf)(2){0,+inf}
	a143([java.lang.String...]): length i114
	a145([java.io.ObjectStreamField|]): length iconst_0
	o93!: String$CaseInsensitiveComparator()
Relations: 

4:

<simple.upAndDownIneq.UpAndDownIneq.upAndDown||1: store INT to up||i: i114||iconst_0>
java.lang.String = serialPersistentFields, CASE_INSENSITIVE_ORDER
[a143(lv_0_0)]
<simple.upAndDownIneq.Main.main||2: simple.upAndDownIneq.UpAndDownIneq.upAndDown|| - ||i114>
	String.serialVersionUID: iconstLong_-6849794470754667710
	String.serialPersistentFields: a145
	String.CASE_INSENSITIVE_ORDER: o93
	String$CaseInsensitiveComparator.serialVersionUID: iconstLong_8575799808933029326
	RuntimeException.serialVersionUID: iconstLong_-7034897190745766939
	Exception.serialVersionUID: iconstLong_-3387516993124229948
	Throwable.serialVersionUID: iconstLong_-3042686055658047285
	i114: [0,+inf)(2){0,+inf}
	a143([java.lang.String...]): length i114
	a145([java.io.ObjectStreamField|]): length iconst_0
	o93!: String$CaseInsensitiveComparator()
Relations: 

5:

<simple.upAndDownIneq.UpAndDownIneq.upAndDown||2: push 0||i: i114, up: iconst_0|| ->
java.lang.String = serialPersistentFields, CASE_INSENSITIVE_ORDER
[a143(lv_0_0)]
<simple.upAndDownIneq.Main.main||2: simple.upAndDownIneq.UpAndDownIneq.upAndDown|| - ||i114>
	String.serialVersionUID: iconstLong_-6849794470754667710
	String.serialPersistentFields: a145
	String.CASE_INSENSITIVE_ORDER: o93
	String$CaseInsensitiveComparator.serialVersionUID: iconstLong_8575799808933029326
	RuntimeException.serialVersionUID: iconstLong_-7034897190745766939
	Exception.serialVersionUID: iconstLong_-3387516993124229948
	Throwable.serialVersionUID: iconstLong_-3042686055658047285
	i114: [0,+inf)(2){0,+inf}
	a143([java.lang.String...]): length i114
	a145([java.io.ObjectStreamField|]): length iconst_0
	o93!: String$CaseInsensitiveComparator()
Relations: 

Start state of loop:

<simple.upAndDownIneq.UpAndDownIneq.upAndDown||2: push 0||i: i54, up: i55|| ->
java.lang.String = serialPersistentFields, CASE_INSENSITIVE_ORDER
[a61(lv_0_0)]
<simple.upAndDownIneq.Main.main||2: simple.upAndDownIneq.UpAndDownIneq.upAndDown|| - ||i17>
	String.serialVersionUID: iconstLong_-6849794470754667710
	String.serialPersistentFields: a60
	String.CASE_INSENSITIVE_ORDER: o43
	String$CaseInsensitiveComparator.serialVersionUID: iconstLong_8575799808933029326
	RuntimeException.serialVersionUID: iconstLong_-7034897190745766939
	Exception.serialVersionUID: iconstLong_-3387516993124229948
	Throwable.serialVersionUID: iconstLong_-3042686055658047285
	a60([java.io.ObjectStreamField|]): length iconst_0
	o43!: String$CaseInsensitiveComparator()
	i54: [0,+inf)(2){-1,+inf}
	i55: [0,1](1){0,1}
	i17: [0,+inf)(1){0,+inf}
	a61([java.lang.String...]): length i17
Relations: 

In the loop head node, references [i54, iconst_0, i55] were interesting.
By SMT, we could prove
((0 <= initial_i54 and 0 <= initial_i55 and initial_i55 <= 1 and 0 <= initial_i17) and ((((path1_i54 = path1_i74 and path1_i74 = path1_i77 and path1_i77 = path1_i79 and path1_i80 = (path1_i79 + -1) and path1_i80 = res_i54 and 0 = res_i55 and path1_i17 = res_i17 and path1_i54 = initial_i54 and path1_i55 = initial_i55 and path1_i17 = initial_i17) and (0 <= path1_i54 and T and path1_i74 <= 10 and T and path1_i77 < 10 and path1_i79 > 0 and path1_i55 = 0 and path1_i55 = 0)) or ((path2_i54 = path2_i74 and path2_i74 = path2_i77 and path2_i77 = path2_i79 and path2_i81 = (path2_i79 + 1) and path2_i81 = res_i54 and 1 = res_i55 and path2_i17 = res_i17 and path2_i54 = initial_i54 and path2_i55 = initial_i55 and path2_i17 = initial_i17) and (0 <= path2_i54 and T and path2_i74 <= 10 and T and path2_i77 < 10 and path2_i79 > 0 and path2_i55 = 1 and path2_i55 = 1)) or ((path3_i54 = path3_i74 and 9 = res_i54 and 0 = res_i55 and path3_i17 = res_i17 and path3_i54 = initial_i54 and path3_i55 = initial_i55 and path3_i17 = initial_i17) and (0 <= path3_i54 and T and path3_i74 <= 10 and path3_i74 = 10 and path3_i74 = 10 and 10 > 0)) or ((path4_i54 = path4_i74 and path4_i74 = path4_i77 and 1 = res_i54 and 1 = res_i55 and path4_i17 = res_i17 and path4_i54 = initial_i54 and path4_i55 = initial_i55 and path4_i17 = initial_i17) and (0 <= path4_i54 and T and path4_i74 <= 10 and T and path4_i77 < 10 and path4_i77 = 0 and 0 <= 0))) and (((res_i54 = res_i74 and res_i74 = res_i77 and res_i77 = res_i79 and res_i80 = (res_i79 + -1)) and !(0 <= res_i54 and T and res_i74 <= 10 and T and res_i77 < 10 and res_i79 > 0 and res_i55 = 0 and res_i55 = 0)) and ((res_i54 = res_i74 and res_i74 = res_i77 and res_i77 = res_i79 and res_i81 = (res_i79 + 1)) and !(0 <= res_i54 and T and res_i74 <= 10 and T and res_i77 < 10 and res_i79 > 0 and res_i55 = 1 and res_i55 = 1)) and (res_i54 = res_i74 and !(0 <= res_i54 and T and res_i74 <= 10 and res_i74 = 10 and res_i74 = 10 and 10 > 0)) and ((res_i54 = res_i74 and res_i74 = res_i77) and !(0 <= res_i54 and T and res_i74 <= 10 and T and res_i77 < 10 and res_i77 = 0 and 0 <= 0)))))
to be UNSAT. Consequently, the loop will not terminate.

(2) NO