NO

Initial ITS

Start location: l3
Program variables: x^0 x_next^0
   0: l0 -> l1 : x^0'=x^post1, x_next^0'=x_next^post1, (0 == 0 /\ -x_next^post1+x^post1 == 0 /\ 1-x_next^post1+x^1 <= 0 /\ -x_next^1+x^1 == 0 /\ -1+x_next^post1-x^1 <= 0), cost: 1
   1: l1 -> l0 : x^0'=x^post2, x_next^0'=x_next^post2, (-x^post2+x^0 == 0 /\ x_next^0-x_next^post2 == 0), cost: 1
   2: l2 -> l0 : x^0'=x^post3, x_next^0'=x_next^post3, (x_next^0-x_next^post3 == 0 /\ -x^post3+x^0 == 0), cost: 1
   3: l3 -> l2 : x^0'=x^post4, x_next^0'=x_next^post4, (-x_next^post4+x_next^0 == 0 /\ -x^post4+x^0 == 0), cost: 1

Chained Linear Paths

Start location: l3
Program variables: x^0 x_next^0
   5: l0 -> l0 : x^0'=x^post2, x_next^0'=x_next^post2, (0 == 0 /\ -x_next^post1+x^post1 == 0 /\ -x^post2+x^post1 == 0 /\ 1-x_next^post1+x^1 <= 0 /\ x_next^post1-x_next^post2 == 0 /\ -x_next^1+x^1 == 0 /\ -1+x_next^post1-x^1 <= 0), cost: 1
   4: l3 -> l0 : x^0'=x^post3, x_next^0'=x_next^post3, (-x_next^post4+x_next^0 == 0 /\ -x^post4+x^0 == 0 /\ x_next^post4-x_next^post3 == 0 /\ -x^post3+x^post4 == 0), cost: 1

	Eliminating location l2 by chaining:

	Applied chaining

	First rule:
	l3 -> l2 : x^0'=x^post4, x_next^0'=x_next^post4, (-x_next^post4+x_next^0 == 0 /\ -x^post4+x^0 == 0), cost: 1
	Second rule:
	l2 -> l0 : x^0'=x^post3, x_next^0'=x_next^post3, (x_next^0-x_next^post3 == 0 /\ -x^post3+x^0 == 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^post3, x_next^0'=x_next^post3, (-x_next^post4+x_next^0 == 0 /\ -x^post4+x^0 == 0 /\ x_next^post4-x_next^post3 == 0 /\ -x^post3+x^post4 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 2 3
	
	Eliminating location l1 by chaining:

	Applied chaining

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

	Removed the following rules: 0 1

Simplified Transitions

Start location: l3
Program variables: x^0 x_next^0
   7: l0 -> l0 : x^0'=x_next^post1, x_next^0'=x_next^post1, T, cost: 1
   6: l3 -> l0 : T, cost: 1

	Propagated Equalities

	Original rule:
	l3 -> l0 : x^0'=x^post3, x_next^0'=x_next^post3, (-x_next^post4+x_next^0 == 0 /\ -x^post4+x^0 == 0 /\ x_next^post4-x_next^post3 == 0 /\ -x^post3+x^post4 == 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^post4, x_next^0'=x_next^post4, (0 == 0 /\ -x_next^post4+x_next^0 == 0 /\ -x^post4+x^0 == 0), cost: 1
	
		propagated equality x_next^post3 = x_next^post4
		
		propagated equality x^post3 = x^post4
		
	Propagated Equalities

	Original rule:
	l3 -> l0 : x^0'=x^post4, x_next^0'=x_next^post4, (0 == 0 /\ -x_next^post4+x_next^0 == 0 /\ -x^post4+x^0 == 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^0, x_next^0'=x_next^0, 0 == 0, cost: 1
	
		propagated equality x_next^post4 = x_next^0
		
		propagated equality x^post4 = x^0
		
	Simplified Guard

	Original rule:
	l3 -> l0 : x^0'=x^0, x_next^0'=x_next^0, 0 == 0, cost: 1
	New rule:
	l3 -> l0 : x^0'=x^0, x_next^0'=x_next^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l3 -> l0 : x^0'=x^0, x_next^0'=x_next^0, T, cost: 1
	New rule:
	l3 -> l0 : T, cost: 1
	
	made implied equalities explicit

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

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

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

	Original rule:
	l0 -> l0 : x^0'=x_next^post1, x_next^0'=x_next^post1, (0 <= 0 /\ 0 == 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=x_next^post1, x_next^0'=x_next^post1, T, cost: 1

Step with 6

	Trace

	6[T]
	
	Blocked

	[{}, {}]

Step with 7

	Trace

	6[T], 7[T]
	
	Blocked

	[{}, {}, {}]

Nonterm

Start location: l3
Program variables: x^0 x_next^0
   7: l0 -> l0 : x^0'=x_next^post1, x_next^0'=x_next^post1, T, cost: 1
   8: l0 -> LoAT_sink : -1+n >= 0, cost: NONTERM
   6: l3 -> l0 : T, cost: 1

	Certificate of Non-Termination

	Original rule:
	l0 -> l0 : x^0'=x_next^post1, x_next^0'=x_next^post1, T, cost: 1
	New rule:
	l0 -> LoAT_sink : -1+n >= 0, cost: NONTERM

		Replacement map: {}

Step with 8

	Trace

	6[T], 8[-1+n >= 0]
	
	Blocked

	[{}, {}, {8[T]}]

Refute

	Counterexample

	[ x^0=0 x_next^0=0 ] 6 [ x^0=0 x_next^0=0 ] 8
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b