NO

Initial ITS

Start location: l6
Program variables: l^0 n^0 o^0
   0: l0 -> l1 : l^0'=l^post1, n^0'=n^post1, o^0'=o^post1, (1+o^0-n^0 <= 0 /\ -n^post1+n^0 == 0 /\ -o^post1+o^0 == 0 /\ l^0-l^post1 == 0), cost: 1
   1: l0 -> l2 : l^0'=l^post2, n^0'=n^post2, o^0'=o^post2, (-o^0+n^0 <= 0 /\ -n^post2+n^0 == 0 /\ l^0-l^post2 == 0 /\ -o^post2+o^0 == 0), cost: 1
   4: l1 -> l4 : l^0'=l^post5, n^0'=n^post5, o^0'=o^post5, (l^0-l^post5 == 0 /\ -n^post5+n^0 == 0 /\ -o^post5+o^0 == 0 /\ 1-l^0 <= 0 /\ -1+l^0 <= 0), cost: 1
   5: l1 -> l3 : l^0'=l^post6, n^0'=n^post6, o^0'=o^post6, (-1+l^post6 == 0 /\ o^post6-n^0 == 0 /\ -n^post6+n^0 == 0), cost: 1
   2: l3 -> l0 : l^0'=l^post3, n^0'=n^post3, o^0'=o^post3, (0 <= 0 /\ -n^post3+n^0 == 0 /\ l^0-l^post3 == 0 /\ -o^post3+o^0 == 0), cost: 1
   3: l3 -> l0 : l^0'=l^post4, n^0'=n^post4, o^0'=o^post4, (-o^post4+o^0 == 0 /\ -1+n^post4-n^0 == 0 /\ l^post4 == 0), cost: 1
   6: l5 -> l1 : l^0'=l^post7, n^0'=n^post7, o^0'=o^post7, (l^post7 == 0 /\ -n^post7+n^0 == 0 /\ -o^post7+o^0 == 0), cost: 1
   7: l6 -> l5 : l^0'=l^post8, n^0'=n^post8, o^0'=o^post8, (o^0-o^post8 == 0 /\ -n^post8+n^0 == 0 /\ l^0-l^post8 == 0), cost: 1

Chained Linear Paths

Start location: l6
Program variables: l^0 n^0 o^0
   0: l0 -> l1 : l^0'=l^post1, n^0'=n^post1, o^0'=o^post1, (1+o^0-n^0 <= 0 /\ -n^post1+n^0 == 0 /\ -o^post1+o^0 == 0 /\ l^0-l^post1 == 0), cost: 1
   1: l0 -> l2 : l^0'=l^post2, n^0'=n^post2, o^0'=o^post2, (-o^0+n^0 <= 0 /\ -n^post2+n^0 == 0 /\ l^0-l^post2 == 0 /\ -o^post2+o^0 == 0), cost: 1
   4: l1 -> l4 : l^0'=l^post5, n^0'=n^post5, o^0'=o^post5, (l^0-l^post5 == 0 /\ -n^post5+n^0 == 0 /\ -o^post5+o^0 == 0 /\ 1-l^0 <= 0 /\ -1+l^0 <= 0), cost: 1
   5: l1 -> l3 : l^0'=l^post6, n^0'=n^post6, o^0'=o^post6, (-1+l^post6 == 0 /\ o^post6-n^0 == 0 /\ -n^post6+n^0 == 0), cost: 1
   2: l3 -> l0 : l^0'=l^post3, n^0'=n^post3, o^0'=o^post3, (0 <= 0 /\ -n^post3+n^0 == 0 /\ l^0-l^post3 == 0 /\ -o^post3+o^0 == 0), cost: 1
   3: l3 -> l0 : l^0'=l^post4, n^0'=n^post4, o^0'=o^post4, (-o^post4+o^0 == 0 /\ -1+n^post4-n^0 == 0 /\ l^post4 == 0), cost: 1
   8: l6 -> l1 : l^0'=l^post7, n^0'=n^post7, o^0'=o^post7, (o^0-o^post8 == 0 /\ -o^post7+o^post8 == 0 /\ n^post8-n^post7 == 0 /\ -n^post8+n^0 == 0 /\ l^post7 == 0 /\ l^0-l^post8 == 0), cost: 1

	Eliminating location l5 by chaining:

	Applied chaining

	First rule:
	l6 -> l5 : l^0'=l^post8, n^0'=n^post8, o^0'=o^post8, (o^0-o^post8 == 0 /\ -n^post8+n^0 == 0 /\ l^0-l^post8 == 0), cost: 1
	Second rule:
	l5 -> l1 : l^0'=l^post7, n^0'=n^post7, o^0'=o^post7, (l^post7 == 0 /\ -n^post7+n^0 == 0 /\ -o^post7+o^0 == 0), cost: 1
	New rule:
	l6 -> l1 : l^0'=l^post7, n^0'=n^post7, o^0'=o^post7, (o^0-o^post8 == 0 /\ -o^post7+o^post8 == 0 /\ n^post8-n^post7 == 0 /\ -n^post8+n^0 == 0 /\ l^post7 == 0 /\ l^0-l^post8 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 6 7

Simplified Transitions

Start location: l6
Program variables: l^0 n^0 o^0
   9: l0 -> l1 : 1+o^0-n^0 <= 0, cost: 1
  10: l0 -> l2 : -o^0+n^0 <= 0, cost: 1
  13: l1 -> l4 : (1-l^0 <= 0 /\ 1-l^0 == 0 /\ -1+l^0 <= 0), cost: 1
  14: l1 -> l3 : l^0'=1, o^0'=n^0, T, cost: 1
  11: l3 -> l0 : T, cost: 1
  12: l3 -> l0 : l^0'=0, n^0'=1+n^0, T, cost: 1
  15: l6 -> l1 : l^0'=0, T, cost: 1

	Propagated Equalities

	Original rule:
	l0 -> l1 : l^0'=l^post1, n^0'=n^post1, o^0'=o^post1, (1+o^0-n^0 <= 0 /\ -n^post1+n^0 == 0 /\ -o^post1+o^0 == 0 /\ l^0-l^post1 == 0), cost: 1
	New rule:
	l0 -> l1 : l^0'=l^0, n^0'=n^0, o^0'=o^0, (0 == 0 /\ 1+o^0-n^0 <= 0), cost: 1
	
		propagated equality n^post1 = n^0
		
		propagated equality o^post1 = o^0
		
		propagated equality l^post1 = l^0
		
	Simplified Guard

	Original rule:
	l0 -> l1 : l^0'=l^0, n^0'=n^0, o^0'=o^0, (0 == 0 /\ 1+o^0-n^0 <= 0), cost: 1
	New rule:
	l0 -> l1 : l^0'=l^0, n^0'=n^0, o^0'=o^0, 1+o^0-n^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l0 -> l1 : l^0'=l^0, n^0'=n^0, o^0'=o^0, 1+o^0-n^0 <= 0, cost: 1
	New rule:
	l0 -> l1 : 1+o^0-n^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l0 -> l2 : l^0'=l^post2, n^0'=n^post2, o^0'=o^post2, (-o^0+n^0 <= 0 /\ -n^post2+n^0 == 0 /\ l^0-l^post2 == 0 /\ -o^post2+o^0 == 0), cost: 1
	New rule:
	l0 -> l2 : l^0'=l^0, n^0'=n^0, o^0'=o^0, (0 == 0 /\ -o^0+n^0 <= 0), cost: 1
	
		propagated equality n^post2 = n^0
		
		propagated equality l^post2 = l^0
		
		propagated equality o^post2 = o^0
		
	Simplified Guard

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

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

	Original rule:
	l3 -> l0 : l^0'=l^post3, n^0'=n^post3, o^0'=o^post3, (0 <= 0 /\ -n^post3+n^0 == 0 /\ l^0-l^post3 == 0 /\ -o^post3+o^0 == 0), cost: 1
	New rule:
	l3 -> l0 : l^0'=l^0, n^0'=n^0, o^0'=o^0, (0 <= 0 /\ 0 == 0), cost: 1
	
		propagated equality n^post3 = n^0
		
		propagated equality l^post3 = l^0
		
		propagated equality o^post3 = o^0
		
	Simplified Guard

	Original rule:
	l3 -> l0 : l^0'=l^0, n^0'=n^0, o^0'=o^0, (0 <= 0 /\ 0 == 0), cost: 1
	New rule:
	l3 -> l0 : l^0'=l^0, n^0'=n^0, o^0'=o^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l3 -> l0 : l^0'=l^0, n^0'=n^0, o^0'=o^0, T, cost: 1
	New rule:
	l3 -> l0 : T, cost: 1
	
	Propagated Equalities

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

	Original rule:
	l3 -> l0 : l^0'=0, n^0'=1+n^0, o^0'=o^0, 0 == 0, cost: 1
	New rule:
	l3 -> l0 : l^0'=0, n^0'=1+n^0, o^0'=o^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l3 -> l0 : l^0'=0, n^0'=1+n^0, o^0'=o^0, T, cost: 1
	New rule:
	l3 -> l0 : l^0'=0, n^0'=1+n^0, T, cost: 1
	
	made implied equalities explicit

	Original rule:
	l1 -> l4 : l^0'=l^post5, n^0'=n^post5, o^0'=o^post5, (l^0-l^post5 == 0 /\ -n^post5+n^0 == 0 /\ -o^post5+o^0 == 0 /\ 1-l^0 <= 0 /\ -1+l^0 <= 0), cost: 1
	New rule:
	l1 -> l4 : l^0'=l^post5, n^0'=n^post5, o^0'=o^post5, (l^0-l^post5 == 0 /\ -n^post5+n^0 == 0 /\ -o^post5+o^0 == 0 /\ 1-l^0 <= 0 /\ 1-l^0 == 0 /\ -1+l^0 <= 0), cost: 1
	
	Propagated Equalities

	Original rule:
	l1 -> l4 : l^0'=l^post5, n^0'=n^post5, o^0'=o^post5, (l^0-l^post5 == 0 /\ -n^post5+n^0 == 0 /\ -o^post5+o^0 == 0 /\ 1-l^0 <= 0 /\ 1-l^0 == 0 /\ -1+l^0 <= 0), cost: 1
	New rule:
	l1 -> l4 : l^0'=l^0, n^0'=n^0, o^0'=o^0, (0 == 0 /\ 1-l^0 <= 0 /\ 1-l^0 == 0 /\ -1+l^0 <= 0), cost: 1
	
		propagated equality l^post5 = l^0
		
		propagated equality n^post5 = n^0
		
		propagated equality o^post5 = o^0
		
	Simplified Guard

	Original rule:
	l1 -> l4 : l^0'=l^0, n^0'=n^0, o^0'=o^0, (0 == 0 /\ 1-l^0 <= 0 /\ 1-l^0 == 0 /\ -1+l^0 <= 0), cost: 1
	New rule:
	l1 -> l4 : l^0'=l^0, n^0'=n^0, o^0'=o^0, (1-l^0 <= 0 /\ 1-l^0 == 0 /\ -1+l^0 <= 0), cost: 1
	
	made implied equalities explicit

	Original rule:
	l1 -> l4 : l^0'=l^0, n^0'=n^0, o^0'=o^0, (1-l^0 <= 0 /\ 1-l^0 == 0 /\ -1+l^0 <= 0), cost: 1
	New rule:
	l1 -> l4 : l^0'=l^0, n^0'=n^0, o^0'=o^0, (1-l^0 <= 0 /\ 1-l^0 == 0 /\ -1+l^0 <= 0), cost: 1
	
	Removed Trivial Updates

	Original rule:
	l1 -> l4 : l^0'=l^0, n^0'=n^0, o^0'=o^0, (1-l^0 <= 0 /\ 1-l^0 == 0 /\ -1+l^0 <= 0), cost: 1
	New rule:
	l1 -> l4 : (1-l^0 <= 0 /\ 1-l^0 == 0 /\ -1+l^0 <= 0), cost: 1
	
	Propagated Equalities

	Original rule:
	l1 -> l3 : l^0'=l^post6, n^0'=n^post6, o^0'=o^post6, (-1+l^post6 == 0 /\ o^post6-n^0 == 0 /\ -n^post6+n^0 == 0), cost: 1
	New rule:
	l1 -> l3 : l^0'=1, n^0'=n^0, o^0'=n^0, 0 == 0, cost: 1
	
		propagated equality l^post6 = 1
		
		propagated equality o^post6 = n^0
		
		propagated equality n^post6 = n^0
		
	Simplified Guard

	Original rule:
	l1 -> l3 : l^0'=1, n^0'=n^0, o^0'=n^0, 0 == 0, cost: 1
	New rule:
	l1 -> l3 : l^0'=1, n^0'=n^0, o^0'=n^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l1 -> l3 : l^0'=1, n^0'=n^0, o^0'=n^0, T, cost: 1
	New rule:
	l1 -> l3 : l^0'=1, o^0'=n^0, T, cost: 1
	
	Propagated Equalities

	Original rule:
	l6 -> l1 : l^0'=l^post7, n^0'=n^post7, o^0'=o^post7, (o^0-o^post8 == 0 /\ -o^post7+o^post8 == 0 /\ n^post8-n^post7 == 0 /\ -n^post8+n^0 == 0 /\ l^post7 == 0 /\ l^0-l^post8 == 0), cost: 1
	New rule:
	l6 -> l1 : l^0'=0, n^0'=n^post8, o^0'=o^post8, (0 == 0 /\ o^0-o^post8 == 0 /\ -n^post8+n^0 == 0 /\ l^0-l^post8 == 0), cost: 1
	
		propagated equality o^post7 = o^post8
		
		propagated equality n^post7 = n^post8
		
		propagated equality l^post7 = 0
		
	Propagated Equalities

	Original rule:
	l6 -> l1 : l^0'=0, n^0'=n^post8, o^0'=o^post8, (0 == 0 /\ o^0-o^post8 == 0 /\ -n^post8+n^0 == 0 /\ l^0-l^post8 == 0), cost: 1
	New rule:
	l6 -> l1 : l^0'=0, n^0'=n^0, o^0'=o^0, 0 == 0, cost: 1
	
		propagated equality o^post8 = o^0
		
		propagated equality n^post8 = n^0
		
		propagated equality l^post8 = l^0
		
	Simplified Guard

	Original rule:
	l6 -> l1 : l^0'=0, n^0'=n^0, o^0'=o^0, 0 == 0, cost: 1
	New rule:
	l6 -> l1 : l^0'=0, n^0'=n^0, o^0'=o^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l6 -> l1 : l^0'=0, n^0'=n^0, o^0'=o^0, T, cost: 1
	New rule:
	l6 -> l1 : l^0'=0, T, cost: 1

Step with 15

	Trace

	15[T]
	
	Blocked

	[{}, {}]

Step with 14

	Trace

	15[T], 14[T]
	
	Blocked

	[{}, {13[T]}, {}]

Step with 11

	Trace

	15[T], 14[T], 11[T]
	
	Blocked

	[{}, {13[T]}, {}, {}]

Step with 10

	Trace

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

	[{}, {13[T]}, {}, {}, {}]

Backtrack

	Trace

	15[T], 14[T], 11[T]
	
	Blocked

	[{}, {13[T]}, {}, {10[T]}]

Backtrack

	Trace

	15[T], 14[T]
	
	Blocked

	[{}, {13[T]}, {11[T]}]

Step with 12

	Trace

	15[T], 14[T], 12[T]
	
	Blocked

	[{}, {13[T]}, {11[T]}, {}]

Step with 9

	Trace

	15[T], 14[T], 12[T], 9[(1+o^0-n^0 <= 0)]
	
	Blocked

	[{}, {13[T]}, {11[T]}, {10[T]}, {}]

Nonterm

Start location: l6
Program variables: l^0 n^0 o^0
   9: l0 -> l1 : 1+o^0-n^0 <= 0, cost: 1
  10: l0 -> l2 : -o^0+n^0 <= 0, cost: 1
  13: l1 -> l4 : (1-l^0 <= 0 /\ 1-l^0 == 0 /\ -1+l^0 <= 0), cost: 1
  14: l1 -> l3 : l^0'=1, o^0'=n^0, T, cost: 1
  16: l1 -> LoAT_sink : -1+n >= 0, cost: NONTERM
  17: l1 -> l1 : l^0'=0, n^0'=n+n^0, o^0'=-1+n+n^0, -1+n >= 0, cost: 1
  11: l3 -> l0 : T, cost: 1
  12: l3 -> l0 : l^0'=0, n^0'=1+n^0, T, cost: 1
  15: l6 -> l1 : l^0'=0, T, cost: 1

	Certificate of Non-Termination

	Original rule:
	l1 -> l1 : l^0'=0, n^0'=1+n^0, o^0'=n^0, T, cost: 1
	New rule:
	l1 -> LoAT_sink : -1+n >= 0, cost: NONTERM

		Replacement map: {}

	Loop Acceleration

	Original rule:
	l1 -> l1 : l^0'=0, n^0'=1+n^0, o^0'=n^0, T, cost: 1
	New rule:
	l1 -> l1 : l^0'=0, n^0'=n+n^0, o^0'=-1+n+n^0, -1+n >= 0, cost: 1

		Replacement map: {}

Step with 16

	Trace

	15[T], 16[-1+n >= 0]
	
	Blocked

	[{}, {13[T]}, {16[T]}]

Refute

	Counterexample

	[ l^0=0 n^0=0 o^0=0 ] 15 [ l^0=l^0 n^0=0 o^0=0 ] 16
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b