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

Chained Linear Paths

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

	Eliminating location l0 by chaining:

	Applied chaining

	First rule:
	l4 -> l0 : x_1^0'=x_1^post5, y_1^0'=y_1^post5, (-y_1^post5+y_1^0 == 0 /\ x_1^0-x_1^post5 == 0), cost: 1
	Second rule:
	l0 -> l1 : x_1^0'=x_1^post1, y_1^0'=y_1^post1, (-1+y_1^post1 == 0 /\ -1+x_1^post1 == 0), cost: 1
	New rule:
	l4 -> l1 : x_1^0'=x_1^post1, y_1^0'=y_1^post1, (-1+y_1^post1 == 0 /\ -1+x_1^post1 == 0 /\ -y_1^post5+y_1^0 == 0 /\ x_1^0-x_1^post5 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 0 4
	
	Eliminating location l2 by chaining:

	Applied chaining

	First rule:
	l1 -> l2 : x_1^0'=x_1^post2, y_1^0'=y_1^post2, (-1-x_1^0+x_1^post2 == 0 /\ -y_1^post2+y_1^0 == 0), cost: 1
	Second rule:
	l2 -> l1 : x_1^0'=x_1^post3, y_1^0'=y_1^post3, (y_1^0-y_1^post3 == 0 /\ x_1^0-x_1^post3 == 0), cost: 1
	New rule:
	l1 -> l1 : x_1^0'=x_1^post3, y_1^0'=y_1^post3, (-x_1^post3+x_1^post2 == 0 /\ y_1^post2-y_1^post3 == 0 /\ -1-x_1^0+x_1^post2 == 0 /\ -y_1^post2+y_1^0 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 1 2

Simplified Transitions

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

	Propagated Equalities

	Original rule:
	l1 -> l3 : x_1^0'=x_1^post4, y_1^0'=y_1^post4, (2 <= 0 /\ -y_1^post4+y_1^0 == 0 /\ -x_1^post4+x_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 y_1^post4 = y_1^0
		
		propagated equality x_1^post4 = x_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, (-1+y_1^post1 == 0 /\ -1+x_1^post1 == 0 /\ -y_1^post5+y_1^0 == 0 /\ x_1^0-x_1^post5 == 0), cost: 1
	New rule:
	l4 -> l1 : x_1^0'=1, y_1^0'=1, (0 == 0 /\ -y_1^post5+y_1^0 == 0 /\ x_1^0-x_1^post5 == 0), cost: 1
	
		propagated equality y_1^post1 = 1
		
		propagated equality x_1^post1 = 1
		
	Propagated Equalities

	Original rule:
	l4 -> l1 : x_1^0'=1, y_1^0'=1, (0 == 0 /\ -y_1^post5+y_1^0 == 0 /\ x_1^0-x_1^post5 == 0), cost: 1
	New rule:
	l4 -> l1 : x_1^0'=1, y_1^0'=1, 0 == 0, cost: 1
	
		propagated equality y_1^post5 = y_1^0
		
		propagated equality x_1^post5 = x_1^0
		
	Simplified Guard

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

	Original rule:
	l1 -> l1 : x_1^0'=x_1^post3, y_1^0'=y_1^post3, (-x_1^post3+x_1^post2 == 0 /\ y_1^post2-y_1^post3 == 0 /\ -1-x_1^0+x_1^post2 == 0 /\ -y_1^post2+y_1^0 == 0), cost: 1
	New rule:
	l1 -> l1 : x_1^0'=x_1^post2, y_1^0'=y_1^post2, (0 == 0 /\ -1-x_1^0+x_1^post2 == 0 /\ -y_1^post2+y_1^0 == 0), cost: 1
	
		propagated equality x_1^post3 = x_1^post2
		
		propagated equality y_1^post3 = y_1^post2
		
	Propagated Equalities

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

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

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

Step with 8

	Trace

	8[T]
	
	Blocked

	[{}, {}]

Step with 9

	Trace

	8[T], 9[T]
	
	Blocked

	[{}, {7[T]}, {}]

Nonterm

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

	Certificate of Non-Termination

	Original rule:
	l1 -> l1 : x_1^0'=1+x_1^0, T, cost: 1
	New rule:
	l1 -> LoAT_sink : -1+n >= 0, cost: NONTERM

		Replacement map: {}

	Loop Acceleration

	Original rule:
	l1 -> l1 : x_1^0'=1+x_1^0, T, cost: 1
	New rule:
	l1 -> l1 : x_1^0'=n+x_1^0, -1+n >= 0, cost: 1

		Replacement map: {}

Step with 10

	Trace

	8[T], 10[-1+n >= 0]
	
	Blocked

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

Refute

	Counterexample

	[ x_1^0=1 y_1^0=1 ] 8 [ x_1^0=x_1^0 y_1^0=y_1^0 ] 10
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b