NO

Initial ITS

Start location: l4
Program variables: x_1^0 y_1^0
   0: l0 -> l1 : x_1^0'=x_1^post1, y_1^0'=y_1^post1, (-2+x_1^post1 == 0 /\ -y_1^post1+y_1^0 == 0), cost: 1
   3: l1 -> l2 : x_1^0'=x_1^post4, y_1^0'=y_1^post4, (0 == 0 /\ -x_1^post4+x_1^0 == 0), cost: 1
   4: l1 -> l3 : x_1^0'=x_1^post5, y_1^0'=y_1^post5, (2 <= 0 /\ x_1^0-x_1^post5 == 0 /\ -y_1^post5+y_1^0 == 0), cost: 1
   1: l2 -> l1 : x_1^0'=x_1^post2, y_1^0'=y_1^post2, (-y_1^post2+y_1^0 == 0 /\ y_1^0 <= 0 /\ 1-x_1^0+x_1^post2 == 0), cost: 1
   2: l2 -> l1 : x_1^0'=x_1^post3, y_1^0'=y_1^post3, (-1+x_1^post3-x_1^0 == 0 /\ -y_1^post3+y_1^0 == 0 /\ 1-y_1^0 <= 0), cost: 1
   5: l4 -> l0 : x_1^0'=x_1^post6, y_1^0'=y_1^post6, (-y_1^post6+y_1^0 == 0 /\ -x_1^post6+x_1^0 == 0), cost: 1

Chained Linear Paths

Start location: l4
Program variables: x_1^0 y_1^0
   3: l1 -> l2 : x_1^0'=x_1^post4, y_1^0'=y_1^post4, (0 == 0 /\ -x_1^post4+x_1^0 == 0), cost: 1
   4: l1 -> l3 : x_1^0'=x_1^post5, y_1^0'=y_1^post5, (2 <= 0 /\ x_1^0-x_1^post5 == 0 /\ -y_1^post5+y_1^0 == 0), cost: 1
   1: l2 -> l1 : x_1^0'=x_1^post2, y_1^0'=y_1^post2, (-y_1^post2+y_1^0 == 0 /\ y_1^0 <= 0 /\ 1-x_1^0+x_1^post2 == 0), cost: 1
   2: l2 -> l1 : x_1^0'=x_1^post3, y_1^0'=y_1^post3, (-1+x_1^post3-x_1^0 == 0 /\ -y_1^post3+y_1^0 == 0 /\ 1-y_1^0 <= 0), cost: 1
   6: l4 -> l1 : x_1^0'=x_1^post1, y_1^0'=y_1^post1, (-y_1^post6+y_1^0 == 0 /\ -y_1^post1+y_1^post6 == 0 /\ -2+x_1^post1 == 0 /\ -x_1^post6+x_1^0 == 0), cost: 1

	Eliminating location l0 by chaining:

	Applied chaining

	First rule:
	l4 -> l0 : x_1^0'=x_1^post6, y_1^0'=y_1^post6, (-y_1^post6+y_1^0 == 0 /\ -x_1^post6+x_1^0 == 0), cost: 1
	Second rule:
	l0 -> l1 : x_1^0'=x_1^post1, y_1^0'=y_1^post1, (-2+x_1^post1 == 0 /\ -y_1^post1+y_1^0 == 0), cost: 1
	New rule:
	l4 -> l1 : x_1^0'=x_1^post1, y_1^0'=y_1^post1, (-y_1^post6+y_1^0 == 0 /\ -y_1^post1+y_1^post6 == 0 /\ -2+x_1^post1 == 0 /\ -x_1^post6+x_1^0 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 0 5

Simplified Transitions

Start location: l4
Program variables: x_1^0 y_1^0
   9: l1 -> l2 : y_1^0'=y_1^post4, T, cost: 1
  10: l1 -> l3 : _|_, cost: 1
   7: l2 -> l1 : x_1^0'=-1+x_1^0, y_1^0 <= 0, cost: 1
   8: l2 -> l1 : x_1^0'=1+x_1^0, 1-y_1^0 <= 0, cost: 1
  11: l4 -> l1 : x_1^0'=2, T, cost: 1

	Propagated Equalities

	Original rule:
	l2 -> l1 : x_1^0'=x_1^post2, y_1^0'=y_1^post2, (-y_1^post2+y_1^0 == 0 /\ y_1^0 <= 0 /\ 1-x_1^0+x_1^post2 == 0), cost: 1
	New rule:
	l2 -> l1 : x_1^0'=-1+x_1^0, y_1^0'=y_1^0, (0 == 0 /\ y_1^0 <= 0), cost: 1
	
		propagated equality y_1^post2 = y_1^0
		
		propagated equality x_1^post2 = -1+x_1^0
		
	Simplified Guard

	Original rule:
	l2 -> l1 : x_1^0'=-1+x_1^0, y_1^0'=y_1^0, (0 == 0 /\ y_1^0 <= 0), cost: 1
	New rule:
	l2 -> l1 : x_1^0'=-1+x_1^0, y_1^0'=y_1^0, y_1^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l2 -> l1 : x_1^0'=-1+x_1^0, y_1^0'=y_1^0, y_1^0 <= 0, cost: 1
	New rule:
	l2 -> l1 : x_1^0'=-1+x_1^0, y_1^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l2 -> l1 : x_1^0'=x_1^post3, y_1^0'=y_1^post3, (-1+x_1^post3-x_1^0 == 0 /\ -y_1^post3+y_1^0 == 0 /\ 1-y_1^0 <= 0), cost: 1
	New rule:
	l2 -> l1 : x_1^0'=1+x_1^0, y_1^0'=y_1^0, (0 == 0 /\ 1-y_1^0 <= 0), cost: 1
	
		propagated equality x_1^post3 = 1+x_1^0
		
		propagated equality y_1^post3 = y_1^0
		
	Simplified Guard

	Original rule:
	l2 -> l1 : x_1^0'=1+x_1^0, y_1^0'=y_1^0, (0 == 0 /\ 1-y_1^0 <= 0), cost: 1
	New rule:
	l2 -> l1 : x_1^0'=1+x_1^0, y_1^0'=y_1^0, 1-y_1^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l2 -> l1 : x_1^0'=1+x_1^0, y_1^0'=y_1^0, 1-y_1^0 <= 0, cost: 1
	New rule:
	l2 -> l1 : x_1^0'=1+x_1^0, 1-y_1^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l1 -> l2 : x_1^0'=x_1^post4, y_1^0'=y_1^post4, (0 == 0 /\ -x_1^post4+x_1^0 == 0), cost: 1
	New rule:
	l1 -> l2 : x_1^0'=x_1^0, y_1^0'=y_1^post4, 0 == 0, cost: 1
	
		propagated equality x_1^post4 = x_1^0
		
	Simplified Guard

	Original rule:
	l1 -> l2 : x_1^0'=x_1^0, y_1^0'=y_1^post4, 0 == 0, cost: 1
	New rule:
	l1 -> l2 : x_1^0'=x_1^0, y_1^0'=y_1^post4, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l1 -> l2 : x_1^0'=x_1^0, y_1^0'=y_1^post4, T, cost: 1
	New rule:
	l1 -> l2 : y_1^0'=y_1^post4, T, cost: 1
	
	Propagated Equalities

	Original rule:
	l1 -> l3 : x_1^0'=x_1^post5, y_1^0'=y_1^post5, (2 <= 0 /\ x_1^0-x_1^post5 == 0 /\ -y_1^post5+y_1^0 == 0), cost: 1
	New rule:
	l1 -> l3 : x_1^0'=x_1^0, y_1^0'=y_1^0, (0 == 0 /\ 2 <= 0), cost: 1
	
		propagated equality x_1^post5 = x_1^0
		
		propagated equality y_1^post5 = y_1^0
		
	Simplified Guard

	Original rule:
	l1 -> l3 : x_1^0'=x_1^0, y_1^0'=y_1^0, (0 == 0 /\ 2 <= 0), cost: 1
	New rule:
	l1 -> l3 : x_1^0'=x_1^0, y_1^0'=y_1^0, _|_, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l1 -> l3 : x_1^0'=x_1^0, y_1^0'=y_1^0, _|_, cost: 1
	New rule:
	l1 -> l3 : _|_, cost: 1
	
	Propagated Equalities

	Original rule:
	l4 -> l1 : x_1^0'=x_1^post1, y_1^0'=y_1^post1, (-y_1^post6+y_1^0 == 0 /\ -y_1^post1+y_1^post6 == 0 /\ -2+x_1^post1 == 0 /\ -x_1^post6+x_1^0 == 0), cost: 1
	New rule:
	l4 -> l1 : x_1^0'=2, y_1^0'=y_1^post6, (0 == 0 /\ -y_1^post6+y_1^0 == 0 /\ -x_1^post6+x_1^0 == 0), cost: 1
	
		propagated equality y_1^post1 = y_1^post6
		
		propagated equality x_1^post1 = 2
		
	Propagated Equalities

	Original rule:
	l4 -> l1 : x_1^0'=2, y_1^0'=y_1^post6, (0 == 0 /\ -y_1^post6+y_1^0 == 0 /\ -x_1^post6+x_1^0 == 0), cost: 1
	New rule:
	l4 -> l1 : x_1^0'=2, y_1^0'=y_1^0, 0 == 0, cost: 1
	
		propagated equality y_1^post6 = y_1^0
		
		propagated equality x_1^post6 = x_1^0
		
	Simplified Guard

	Original rule:
	l4 -> l1 : x_1^0'=2, y_1^0'=y_1^0, 0 == 0, cost: 1
	New rule:
	l4 -> l1 : x_1^0'=2, y_1^0'=y_1^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l4 -> l1 : x_1^0'=2, y_1^0'=y_1^0, T, cost: 1
	New rule:
	l4 -> l1 : x_1^0'=2, T, cost: 1

Step with 11

	Trace

	11[T]
	
	Blocked

	[{}, {}]

Step with 9

	Trace

	11[T], 9[T]
	
	Blocked

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

Step with 7

	Trace

	11[T], 9[T], 7[(y_1^0 <= 0)]
	
	Blocked

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

Nonterm

Start location: l4
Program variables: x_1^0 y_1^0
   9: l1 -> l2 : y_1^0'=y_1^post4, T, cost: 1
  10: l1 -> l3 : _|_, cost: 1
  12: l1 -> LoAT_sink : (-1+n >= 0 /\ -y_1^post41 >= 0), cost: NONTERM
  13: l1 -> l1 : x_1^0'=-n+x_1^0, y_1^0'=y_1^post41, (-1+n >= 0 /\ -y_1^post41 >= 0), cost: 1
   7: l2 -> l1 : x_1^0'=-1+x_1^0, y_1^0 <= 0, cost: 1
   8: l2 -> l1 : x_1^0'=1+x_1^0, 1-y_1^0 <= 0, cost: 1
  11: l4 -> l1 : x_1^0'=2, T, cost: 1

	Certificate of Non-Termination

	Original rule:
	l1 -> l1 : x_1^0'=-1+x_1^0, y_1^0'=y_1^post41, y_1^post41 <= 0, cost: 1
	New rule:
	l1 -> LoAT_sink : (-1+n >= 0 /\ -y_1^post41 >= 0), cost: NONTERM

		-y_1^post41 >= 0 [0]: monotonic increase yields -y_1^post41 >= 0
		
		Replacement map: {-y_1^post41 >= 0 -> -y_1^post41 >= 0}

	Loop Acceleration

	Original rule:
	l1 -> l1 : x_1^0'=-1+x_1^0, y_1^0'=y_1^post41, y_1^post41 <= 0, cost: 1
	New rule:
	l1 -> l1 : x_1^0'=-n+x_1^0, y_1^0'=y_1^post41, (-1+n >= 0 /\ -y_1^post41 >= 0), cost: 1

		-y_1^post41 >= 0 [0]: monotonic increase yields -y_1^post41 >= 0
		
		Replacement map: {-y_1^post41 >= 0 -> -y_1^post41 >= 0}

Step with 12

	Trace

	11[T], 12[(-1+n >= 0 /\ -y_1^post41 >= 0)]
	
	Blocked

	[{}, {10[T]}, {12[T]}]

Refute

	Counterexample

	[ x_1^0=2 y_1^0=0 ] 11 [ x_1^0=x_1^0 y_1^0=0 ] 12
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b