Termination of the given JBC could be disproven:

(0) Obligation:

JBC Problem based on JBC Program:
Manifest-Version: 1.0 Created-By: 1.6.0_26 (Sun Microsystems Inc.) Main-Class: LoopingNonterm

public class LoopingNonterm {
 public static void main(String[] a) {
  int i = 0;
  int j = a.length;
  while (i < j) {
   i += a[i].length();
  }
 }
}

(1) JBCNonTerm (EQUIVALENT transformation)

Constructed a run with a repetition. States 5 and 19 are repetitions.
0:

<LoopingNonterm.main||0: push 0||a: a65|| ->
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

1:

<LoopingNonterm.main||1: store INT to i||a: a65||0>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

2:

<LoopingNonterm.main||2: load ADDR a||a: a65, i: 0|| ->
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

3:

<LoopingNonterm.main||3: arraylength||a: a65, i: 0||a65>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

4:

<LoopingNonterm.main||4: store INT to j||a: a65, i: 0||1>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

5:

<LoopingNonterm.main||5: load INT i||a: a65, i: 0, j: 1|| ->
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

6:

<LoopingNonterm.main||6: load INT j||a: a65, i: 0, j: 1||0>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

7:

<LoopingNonterm.main||7: GE||a: a65, i: 0, j: 1||0, 1>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

8:

<LoopingNonterm.main||10: load INT i||a: a65, i: 0, j: 1|| ->
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

9:

<LoopingNonterm.main||11: load ADDR a||a: a65, i: 0, j: 1||0>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

10:

<LoopingNonterm.main||12: load INT i||a: a65, i: 0, j: 1||0, a65>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

11:

<LoopingNonterm.main||13: Read ADDR from array||a: a65, j: 1||0, a65, 0>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

12:

<LoopingNonterm.main||14: java.lang.String.length()I||a: a65, j: 1||0, o78>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=i102, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	i102: #I
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

13:

<java.lang.String.length||0: load ADDR this||this: o78|| ->
<LoopingNonterm.main||14: java.lang.String.length||a: a65, j: 1||0, o78>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=i102, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	i102: #I
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

14:

<java.lang.String.length||1: Read from count|| - ||o78>
<LoopingNonterm.main||14: java.lang.String.length||a: a65, j: 1||0, o78>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=i102, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	i102: #I
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

15:

<java.lang.String.length||4: return INT|| - ||0>
<LoopingNonterm.main||14: java.lang.String.length||a: a65, j: 1||0, o78>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=i102, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	i102: #I
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

16:

<LoopingNonterm.main||17: ADD||a: a65, j: 1||0, 0>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

17:

<LoopingNonterm.main||18: store INT to i||a: a65, j: 1||0>
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

18:

<LoopingNonterm.main||19: jmp||a: a65, i: 0, j: 1|| ->
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

19:

<LoopingNonterm.main||5: load INT i||a: a65, i: 0, j: 1|| ->
	String.serialVersionUID: -6849794470754667710L
	String.serialPersistentFields: a63
	String.CASE_INSENSITIVE_ORDER: o80
	String$CaseInsensitiveComparator.serialVersionUID: 8575799808933029326L
	RuntimeException.serialVersionUID: -7034897190745766939L
	Exception.serialVersionUID: -3387516993124229948L
	Throwable.serialVersionUID: -3042686055658047285L
	o78(java.lang.String...): String(count=0, hash=#I, offset=0, value=a66?)
	o80!: String$CaseInsensitiveComparator()
	a63([java.io.ObjectStreamField|]): length 0
	a65([java.lang.String...]): {o78}
a66:: [CHAR]

(2) NO