NO

Initial ITS

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

Chained Linear Paths

Start location: l3
Program variables: x^0 y^0
   0: l0 -> l1 : x^0'=x^post1, y^0'=y^post1, (y^0-y^post1 == 0 /\ 1-x^0 <= 0 /\ -x^post1+x^0 == 0), cost: 1
   1: l1 -> l0 : x^0'=x^post2, y^0'=y^post2, (0 == 0 /\ 1+y^post2-y^0 == 0), cost: 1
   2: l1 -> l0 : x^0'=x^post3, y^0'=y^post3, (y^0-y^post3 == 0 /\ 1+x^post3-x^0 == 0), cost: 1
   5: l3 -> l0 : x^0'=x^post4, y^0'=y^post4, (x^0-x^post5 == 0 /\ y^post5-y^post4 == 0 /\ -y^post5+y^0 == 0 /\ -x^post4+x^post5 == 0), cost: 1

	Eliminating location l2 by chaining:

	Applied chaining

	First rule:
	l3 -> l2 : x^0'=x^post5, y^0'=y^post5, (x^0-x^post5 == 0 /\ -y^post5+y^0 == 0), cost: 1
	Second rule:
	l2 -> l0 : x^0'=x^post4, y^0'=y^post4, (-x^post4+x^0 == 0 /\ y^0-y^post4 == 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^post4, y^0'=y^post4, (x^0-x^post5 == 0 /\ y^post5-y^post4 == 0 /\ -y^post5+y^0 == 0 /\ -x^post4+x^post5 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 3 4

Simplified Transitions

Start location: l3
Program variables: x^0 y^0
   6: l0 -> l1 : 1-x^0 <= 0, cost: 1
   7: l1 -> l0 : x^0'=x^post2, y^0'=-1+y^0, T, cost: 1
   8: l1 -> l0 : x^0'=-1+x^0, T, cost: 1
   9: l3 -> l0 : T, cost: 1

	Propagated Equalities

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

	Original rule:
	l0 -> l1 : x^0'=x^0, y^0'=y^0, (0 == 0 /\ 1-x^0 <= 0), cost: 1
	New rule:
	l0 -> l1 : x^0'=x^0, y^0'=y^0, 1-x^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l0 -> l1 : x^0'=x^0, y^0'=y^0, 1-x^0 <= 0, cost: 1
	New rule:
	l0 -> l1 : 1-x^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l1 -> l0 : x^0'=x^post2, y^0'=y^post2, (0 == 0 /\ 1+y^post2-y^0 == 0), cost: 1
	New rule:
	l1 -> l0 : x^0'=x^post2, y^0'=-1+y^0, 0 == 0, cost: 1
	
		propagated equality y^post2 = -1+y^0
		
	Simplified Guard

	Original rule:
	l1 -> l0 : x^0'=x^post2, y^0'=-1+y^0, 0 == 0, cost: 1
	New rule:
	l1 -> l0 : x^0'=x^post2, y^0'=-1+y^0, T, cost: 1
	
	Propagated Equalities

	Original rule:
	l1 -> l0 : x^0'=x^post3, y^0'=y^post3, (y^0-y^post3 == 0 /\ 1+x^post3-x^0 == 0), cost: 1
	New rule:
	l1 -> l0 : x^0'=-1+x^0, y^0'=y^0, 0 == 0, cost: 1
	
		propagated equality y^post3 = y^0
		
		propagated equality x^post3 = -1+x^0
		
	Simplified Guard

	Original rule:
	l1 -> l0 : x^0'=-1+x^0, y^0'=y^0, 0 == 0, cost: 1
	New rule:
	l1 -> l0 : x^0'=-1+x^0, y^0'=y^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l1 -> l0 : x^0'=-1+x^0, y^0'=y^0, T, cost: 1
	New rule:
	l1 -> l0 : x^0'=-1+x^0, T, cost: 1
	
	Propagated Equalities

	Original rule:
	l3 -> l0 : x^0'=x^post4, y^0'=y^post4, (x^0-x^post5 == 0 /\ y^post5-y^post4 == 0 /\ -y^post5+y^0 == 0 /\ -x^post4+x^post5 == 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^post5, y^0'=y^post5, (0 == 0 /\ x^0-x^post5 == 0 /\ -y^post5+y^0 == 0), cost: 1
	
		propagated equality y^post4 = y^post5
		
		propagated equality x^post4 = x^post5
		
	Propagated Equalities

	Original rule:
	l3 -> l0 : x^0'=x^post5, y^0'=y^post5, (0 == 0 /\ x^0-x^post5 == 0 /\ -y^post5+y^0 == 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^0, y^0'=y^0, 0 == 0, cost: 1
	
		propagated equality x^post5 = x^0
		
		propagated equality y^post5 = y^0
		
	Simplified Guard

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

	Original rule:
	l3 -> l0 : x^0'=x^0, y^0'=y^0, T, cost: 1
	New rule:
	l3 -> l0 : T, cost: 1

Step with 9

	Trace

	9[T]
	
	Blocked

	[{}, {}]

Step with 6

	Trace

	9[T], 6[(1-x^0 <= 0)]
	
	Blocked

	[{}, {}, {}]

Step with 7

	Trace

	9[T], 6[(1-x^0 <= 0)], 7[T]
	
	Blocked

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

Nonterm

Start location: l3
Program variables: x^0 y^0
   6: l0 -> l1 : 1-x^0 <= 0, cost: 1
  10: l0 -> LoAT_sink : (-1+x^0 >= 0 /\ x^0-x^post2 <= 0), cost: NONTERM
  11: l0 -> l0 : x^0'=x^post2, y^0'=y^0-n, (-1+n >= 0 /\ -1+x^0 >= 0 /\ -1+x^post2 >= 0), cost: 1
   7: l1 -> l0 : x^0'=x^post2, y^0'=-1+y^0, T, cost: 1
   8: l1 -> l0 : x^0'=-1+x^0, T, cost: 1
   9: l3 -> l0 : T, cost: 1

	Certificate of Non-Termination

	Original rule:
	l0 -> l0 : x^0'=x^post2, y^0'=-1+y^0, 1-x^0 <= 0, cost: 1
	New rule:
	l0 -> LoAT_sink : (-1+x^0 >= 0 /\ x^0-x^post2 <= 0), cost: NONTERM

		-1+x^0 >= 0 [0]: eventual decrease yields (-1+x^0 >= 0 /\ -1+x^post2 >= 0)
		
		-1+x^0 >= 0 [1]: eventual increase yields (-1+x^0 >= 0 /\ x^0-x^post2 <= 0)
		
		Replacement map: {-1+x^0 >= 0 -> (-1+x^0 >= 0 /\ x^0-x^post2 <= 0)}

	Loop Acceleration

	Original rule:
	l0 -> l0 : x^0'=x^post2, y^0'=-1+y^0, 1-x^0 <= 0, cost: 1
	New rule:
	l0 -> l0 : x^0'=x^post2, y^0'=y^0-n, (-1+n >= 0 /\ -1+x^0 >= 0 /\ -1+x^post2 >= 0), cost: 1

		-1+x^0 >= 0 [0]: eventual decrease yields (-1+x^0 >= 0 /\ -1+x^post2 >= 0)
		
		-1+x^0 >= 0 [1]: eventual increase yields (-1+x^0 >= 0 /\ x^0-x^post2 <= 0)
		
		Replacement map: {-1+x^0 >= 0 -> (-1+x^0 >= 0 /\ -1+x^post2 >= 0)}

Step with 10

	Trace

	9[T], 10[(-1+x^0 >= 0 /\ x^0-x^post2 <= 0)]
	
	Blocked

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

Refute

	Counterexample

	[ x^0=1 y^0=0 ] 9 [ x^0=1 y^0=0 ] 10
	
NO

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