NO

Initial ITS

Start location: l5
Program variables: n^0 x^0
   0: l0 -> l1 : n^0'=n^post1, x^0'=x^post1, (x^0-x^post1 == 0 /\ -n^post1+n^0 == 0), cost: 1
   1: l1 -> l0 : n^0'=n^post2, x^0'=x^post2, (-x^post2+x^0 == 0 /\ n^0-n^post2 == 0), cost: 1
   2: l2 -> l0 : n^0'=n^post3, x^0'=x^post3, (-1+x^post3 == 0 /\ n^0-n^post3 == 0 /\ x^1 == 0 /\ n^0 <= 0), cost: 1
   3: l2 -> l3 : n^0'=n^post4, x^0'=x^post4, (1-n^0 <= 0 /\ x^0-x^post4 == 0 /\ -n^post4+n^0 == 0), cost: 1
   4: l3 -> l2 : n^0'=n^post5, x^0'=x^post5, (-n^post5+n^0 == 0 /\ x^0-x^post5 == 0), cost: 1
   5: l4 -> l2 : n^0'=n^post6, x^0'=x^post6, (0 == 0 /\ -1+x^post6 == 0), cost: 1
   6: l5 -> l4 : n^0'=n^post7, x^0'=x^post7, (x^0-x^post7 == 0 /\ -n^post7+n^0 == 0), cost: 1

Chained Linear Paths

Start location: l5
Program variables: n^0 x^0
   9: l0 -> l0 : n^0'=n^post2, x^0'=x^post2, (n^post1-n^post2 == 0 /\ x^0-x^post1 == 0 /\ -n^post1+n^0 == 0 /\ -x^post2+x^post1 == 0), cost: 1
   2: l2 -> l0 : n^0'=n^post3, x^0'=x^post3, (-1+x^post3 == 0 /\ n^0-n^post3 == 0 /\ x^1 == 0 /\ n^0 <= 0), cost: 1
   8: l2 -> l2 : n^0'=n^post5, x^0'=x^post5, (-x^post5+x^post4 == 0 /\ 1-n^0 <= 0 /\ -n^post5+n^post4 == 0 /\ x^0-x^post4 == 0 /\ -n^post4+n^0 == 0), cost: 1
   7: l5 -> l2 : n^0'=n^post6, x^0'=x^post6, (0 == 0 /\ x^0-x^post7 == 0 /\ -n^post7+n^0 == 0 /\ -1+x^post6 == 0), cost: 1

	Eliminating location l4 by chaining:

	Applied chaining

	First rule:
	l5 -> l4 : n^0'=n^post7, x^0'=x^post7, (x^0-x^post7 == 0 /\ -n^post7+n^0 == 0), cost: 1
	Second rule:
	l4 -> l2 : n^0'=n^post6, x^0'=x^post6, (0 == 0 /\ -1+x^post6 == 0), cost: 1
	New rule:
	l5 -> l2 : n^0'=n^post6, x^0'=x^post6, (0 == 0 /\ x^0-x^post7 == 0 /\ -n^post7+n^0 == 0 /\ -1+x^post6 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 5 6
	
	Eliminating location l3 by chaining:

	Applied chaining

	First rule:
	l2 -> l3 : n^0'=n^post4, x^0'=x^post4, (1-n^0 <= 0 /\ x^0-x^post4 == 0 /\ -n^post4+n^0 == 0), cost: 1
	Second rule:
	l3 -> l2 : n^0'=n^post5, x^0'=x^post5, (-n^post5+n^0 == 0 /\ x^0-x^post5 == 0), cost: 1
	New rule:
	l2 -> l2 : n^0'=n^post5, x^0'=x^post5, (-x^post5+x^post4 == 0 /\ 1-n^0 <= 0 /\ -n^post5+n^post4 == 0 /\ x^0-x^post4 == 0 /\ -n^post4+n^0 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 3 4
	
	Eliminating location l1 by chaining:

	Applied chaining

	First rule:
	l0 -> l1 : n^0'=n^post1, x^0'=x^post1, (x^0-x^post1 == 0 /\ -n^post1+n^0 == 0), cost: 1
	Second rule:
	l1 -> l0 : n^0'=n^post2, x^0'=x^post2, (-x^post2+x^0 == 0 /\ n^0-n^post2 == 0), cost: 1
	New rule:
	l0 -> l0 : n^0'=n^post2, x^0'=x^post2, (n^post1-n^post2 == 0 /\ x^0-x^post1 == 0 /\ -n^post1+n^0 == 0 /\ -x^post2+x^post1 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 0 1

Simplified Transitions

Start location: l5
Program variables: n^0 x^0
  13: l0 -> l0 : T, cost: 1
  10: l2 -> l0 : x^0'=1, n^0 <= 0, cost: 1
  12: l2 -> l2 : 1-n^0 <= 0, cost: 1
  11: l5 -> l2 : n^0'=n^post6, x^0'=1, T, cost: 1

	Propagated Equalities

	Original rule:
	l2 -> l0 : n^0'=n^post3, x^0'=x^post3, (-1+x^post3 == 0 /\ n^0-n^post3 == 0 /\ x^1 == 0 /\ n^0 <= 0), cost: 1
	New rule:
	l2 -> l0 : n^0'=n^0, x^0'=1, (0 == 0 /\ x^1 == 0 /\ n^0 <= 0), cost: 1
	
		propagated equality x^post3 = 1
		
		propagated equality n^post3 = n^0
		
	Propagated Equalities

	Original rule:
	l2 -> l0 : n^0'=n^0, x^0'=1, (0 == 0 /\ x^1 == 0 /\ n^0 <= 0), cost: 1
	New rule:
	l2 -> l0 : n^0'=n^0, x^0'=1, (0 == 0 /\ n^0 <= 0), cost: 1
	
		propagated equality x^1 = 0
		
	Simplified Guard

	Original rule:
	l2 -> l0 : n^0'=n^0, x^0'=1, (0 == 0 /\ n^0 <= 0), cost: 1
	New rule:
	l2 -> l0 : n^0'=n^0, x^0'=1, n^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l2 -> l0 : n^0'=n^0, x^0'=1, n^0 <= 0, cost: 1
	New rule:
	l2 -> l0 : x^0'=1, n^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l5 -> l2 : n^0'=n^post6, x^0'=x^post6, (0 == 0 /\ x^0-x^post7 == 0 /\ -n^post7+n^0 == 0 /\ -1+x^post6 == 0), cost: 1
	New rule:
	l5 -> l2 : n^0'=n^post6, x^0'=1, (0 == 0 /\ x^0-x^post7 == 0 /\ -n^post7+n^0 == 0), cost: 1
	
		propagated equality x^post6 = 1
		
	Propagated Equalities

	Original rule:
	l5 -> l2 : n^0'=n^post6, x^0'=1, (0 == 0 /\ x^0-x^post7 == 0 /\ -n^post7+n^0 == 0), cost: 1
	New rule:
	l5 -> l2 : n^0'=n^post6, x^0'=1, 0 == 0, cost: 1
	
		propagated equality x^post7 = x^0
		
		propagated equality n^post7 = n^0
		
	Simplified Guard

	Original rule:
	l5 -> l2 : n^0'=n^post6, x^0'=1, 0 == 0, cost: 1
	New rule:
	l5 -> l2 : n^0'=n^post6, x^0'=1, T, cost: 1
	
	Propagated Equalities

	Original rule:
	l2 -> l2 : n^0'=n^post5, x^0'=x^post5, (-x^post5+x^post4 == 0 /\ 1-n^0 <= 0 /\ -n^post5+n^post4 == 0 /\ x^0-x^post4 == 0 /\ -n^post4+n^0 == 0), cost: 1
	New rule:
	l2 -> l2 : n^0'=n^post4, x^0'=x^post4, (0 == 0 /\ 1-n^0 <= 0 /\ x^0-x^post4 == 0 /\ -n^post4+n^0 == 0), cost: 1
	
		propagated equality x^post5 = x^post4
		
		propagated equality n^post5 = n^post4
		
	Propagated Equalities

	Original rule:
	l2 -> l2 : n^0'=n^post4, x^0'=x^post4, (0 == 0 /\ 1-n^0 <= 0 /\ x^0-x^post4 == 0 /\ -n^post4+n^0 == 0), cost: 1
	New rule:
	l2 -> l2 : n^0'=n^0, x^0'=x^0, (0 == 0 /\ 1-n^0 <= 0), cost: 1
	
		propagated equality x^post4 = x^0
		
		propagated equality n^post4 = n^0
		
	Simplified Guard

	Original rule:
	l2 -> l2 : n^0'=n^0, x^0'=x^0, (0 == 0 /\ 1-n^0 <= 0), cost: 1
	New rule:
	l2 -> l2 : n^0'=n^0, x^0'=x^0, 1-n^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l2 -> l2 : n^0'=n^0, x^0'=x^0, 1-n^0 <= 0, cost: 1
	New rule:
	l2 -> l2 : 1-n^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l0 -> l0 : n^0'=n^post2, x^0'=x^post2, (n^post1-n^post2 == 0 /\ x^0-x^post1 == 0 /\ -n^post1+n^0 == 0 /\ -x^post2+x^post1 == 0), cost: 1
	New rule:
	l0 -> l0 : n^0'=n^post1, x^0'=x^post1, (0 == 0 /\ x^0-x^post1 == 0 /\ -n^post1+n^0 == 0), cost: 1
	
		propagated equality n^post2 = n^post1
		
		propagated equality x^post2 = x^post1
		
	Propagated Equalities

	Original rule:
	l0 -> l0 : n^0'=n^post1, x^0'=x^post1, (0 == 0 /\ x^0-x^post1 == 0 /\ -n^post1+n^0 == 0), cost: 1
	New rule:
	l0 -> l0 : n^0'=n^0, x^0'=x^0, 0 == 0, cost: 1
	
		propagated equality x^post1 = x^0
		
		propagated equality n^post1 = n^0
		
	Simplified Guard

	Original rule:
	l0 -> l0 : n^0'=n^0, x^0'=x^0, 0 == 0, cost: 1
	New rule:
	l0 -> l0 : n^0'=n^0, x^0'=x^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l0 -> l0 : n^0'=n^0, x^0'=x^0, T, cost: 1
	New rule:
	l0 -> l0 : T, cost: 1

Step with 11

	Trace

	11[T]
	
	Blocked

	[{}, {}]

Step with 10

	Trace

	11[T], 10[(n^0 <= 0)]
	
	Blocked

	[{}, {}, {}]

Step with 13

	Trace

	11[T], 10[(n^0 <= 0)], 13[T]
	
	Blocked

	[{}, {}, {}, {}]

Nonterm

Start location: l5
Program variables: n^0 x^0
  13: l0 -> l0 : T, cost: 1
  14: l0 -> LoAT_sink : -1+n >= 0, cost: NONTERM
  10: l2 -> l0 : x^0'=1, n^0 <= 0, cost: 1
  12: l2 -> l2 : 1-n^0 <= 0, cost: 1
  11: l5 -> l2 : n^0'=n^post6, x^0'=1, T, cost: 1

	Certificate of Non-Termination

	Original rule:
	l0 -> l0 : T, cost: 1
	New rule:
	l0 -> LoAT_sink : -1+n >= 0, cost: NONTERM

		Replacement map: {}

Step with 14

	Trace

	11[T], 10[(n^0 <= 0)], 14[-1+n >= 0]
	
	Blocked

	[{}, {}, {}, {14[T]}]

Refute

	Counterexample

	[ n^0=0 x^0=1 ] 11 [ n^0=0 x^0=1 ] 10 [ n^0=n^0 x^0=x^0 ] 14
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b