NO

Initial ITS

Start location: l3
Program variables: x^0 y^0
   0: l0 -> l1 : x^0'=x^post1, y^0'=y^post1, (111-x^post1 <= 0 /\ -1000+x^post1-x^0 == 0 /\ -y^post1+y^0 == 0 /\ -3999+y^0 <= 0), cost: 1
   1: l1 -> l0 : x^0'=x^post2, y^0'=y^post2, (-y^post2+y^0 == 0 /\ x^0-x^post2 == 0), cost: 1
   2: l2 -> l0 : x^0'=x^post3, y^0'=y^post3, (-3000+y^post3 == 0 /\ x^0-x^post3 == 0), cost: 1
   3: l3 -> l2 : x^0'=x^post4, y^0'=y^post4, (-y^post4+y^0 == 0 /\ -x^post4+x^0 == 0), cost: 1

Chained Linear Paths

Start location: l3
Program variables: x^0 y^0
   5: l0 -> l0 : x^0'=x^post2, y^0'=y^post2, (111-x^post1 <= 0 /\ x^post1-x^post2 == 0 /\ -1000+x^post1-x^0 == 0 /\ -y^post1+y^0 == 0 /\ -y^post2+y^post1 == 0 /\ -3999+y^0 <= 0), cost: 1
   4: l3 -> l0 : x^0'=x^post3, y^0'=y^post3, (-3000+y^post3 == 0 /\ x^post4-x^post3 == 0 /\ -y^post4+y^0 == 0 /\ -x^post4+x^0 == 0), cost: 1

	Eliminating location l2 by chaining:

	Applied chaining

	First rule:
	l3 -> l2 : x^0'=x^post4, y^0'=y^post4, (-y^post4+y^0 == 0 /\ -x^post4+x^0 == 0), cost: 1
	Second rule:
	l2 -> l0 : x^0'=x^post3, y^0'=y^post3, (-3000+y^post3 == 0 /\ x^0-x^post3 == 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^post3, y^0'=y^post3, (-3000+y^post3 == 0 /\ x^post4-x^post3 == 0 /\ -y^post4+y^0 == 0 /\ -x^post4+x^0 == 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, y^0'=y^post1, (111-x^post1 <= 0 /\ -1000+x^post1-x^0 == 0 /\ -y^post1+y^0 == 0 /\ -3999+y^0 <= 0), cost: 1
	Second rule:
	l1 -> l0 : x^0'=x^post2, y^0'=y^post2, (-y^post2+y^0 == 0 /\ x^0-x^post2 == 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=x^post2, y^0'=y^post2, (111-x^post1 <= 0 /\ x^post1-x^post2 == 0 /\ -1000+x^post1-x^0 == 0 /\ -y^post1+y^0 == 0 /\ -y^post2+y^post1 == 0 /\ -3999+y^0 <= 0), cost: 1
	
	Applied deletion

	Removed the following rules: 0 1

Simplified Transitions

Start location: l3
Program variables: x^0 y^0
   7: l0 -> l0 : x^0'=1000+x^0, (-889-x^0 <= 0 /\ -3999+y^0 <= 0), cost: 1
   6: l3 -> l0 : y^0'=3000, T, cost: 1

	Propagated Equalities

	Original rule:
	l3 -> l0 : x^0'=x^post3, y^0'=y^post3, (-3000+y^post3 == 0 /\ x^post4-x^post3 == 0 /\ -y^post4+y^0 == 0 /\ -x^post4+x^0 == 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^post4, y^0'=3000, (0 == 0 /\ -y^post4+y^0 == 0 /\ -x^post4+x^0 == 0), cost: 1
	
		propagated equality y^post3 = 3000
		
		propagated equality x^post3 = x^post4
		
	Propagated Equalities

	Original rule:
	l3 -> l0 : x^0'=x^post4, y^0'=3000, (0 == 0 /\ -y^post4+y^0 == 0 /\ -x^post4+x^0 == 0), cost: 1
	New rule:
	l3 -> l0 : x^0'=x^0, y^0'=3000, 0 == 0, cost: 1
	
		propagated equality y^post4 = y^0
		
		propagated equality x^post4 = x^0
		
	Simplified Guard

	Original rule:
	l3 -> l0 : x^0'=x^0, y^0'=3000, 0 == 0, cost: 1
	New rule:
	l3 -> l0 : x^0'=x^0, y^0'=3000, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l3 -> l0 : x^0'=x^0, y^0'=3000, T, cost: 1
	New rule:
	l3 -> l0 : y^0'=3000, T, cost: 1
	
	Propagated Equalities

	Original rule:
	l0 -> l0 : x^0'=x^post2, y^0'=y^post2, (111-x^post1 <= 0 /\ x^post1-x^post2 == 0 /\ -1000+x^post1-x^0 == 0 /\ -y^post1+y^0 == 0 /\ -y^post2+y^post1 == 0 /\ -3999+y^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=x^post1, y^0'=y^post1, (0 == 0 /\ 111-x^post1 <= 0 /\ -1000+x^post1-x^0 == 0 /\ -y^post1+y^0 == 0 /\ -3999+y^0 <= 0), cost: 1
	
		propagated equality x^post2 = x^post1
		
		propagated equality y^post2 = y^post1
		
	Propagated Equalities

	Original rule:
	l0 -> l0 : x^0'=x^post1, y^0'=y^post1, (0 == 0 /\ 111-x^post1 <= 0 /\ -1000+x^post1-x^0 == 0 /\ -y^post1+y^0 == 0 /\ -3999+y^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=1000+x^0, y^0'=y^0, (0 == 0 /\ -889-x^0 <= 0 /\ -3999+y^0 <= 0), cost: 1
	
		propagated equality x^post1 = 1000+x^0
		
		propagated equality y^post1 = y^0
		
	Simplified Guard

	Original rule:
	l0 -> l0 : x^0'=1000+x^0, y^0'=y^0, (0 == 0 /\ -889-x^0 <= 0 /\ -3999+y^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=1000+x^0, y^0'=y^0, (-889-x^0 <= 0 /\ -3999+y^0 <= 0), cost: 1
	
	Removed Trivial Updates

	Original rule:
	l0 -> l0 : x^0'=1000+x^0, y^0'=y^0, (-889-x^0 <= 0 /\ -3999+y^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=1000+x^0, (-889-x^0 <= 0 /\ -3999+y^0 <= 0), cost: 1

Step with 6

	Trace

	6[T]
	
	Blocked

	[{}, {}]

Step with 7

	Trace

	6[T], 7[(-889-x^0 <= 0 /\ -3999+y^0 <= 0)]
	
	Blocked

	[{}, {}, {}]

Nonterm

Start location: l3
Program variables: x^0 y^0
   7: l0 -> l0 : x^0'=1000+x^0, (-889-x^0 <= 0 /\ -3999+y^0 <= 0), cost: 1
   8: l0 -> LoAT_sink : (889+x^0 >= 0 /\ -1+n >= 0 /\ 3999-y^0 >= 0), cost: NONTERM
   9: l0 -> l0 : x^0'=1000*n+x^0, (889+x^0 >= 0 /\ -1+n >= 0 /\ 3999-y^0 >= 0), cost: 1
   6: l3 -> l0 : y^0'=3000, T, cost: 1

	Certificate of Non-Termination

	Original rule:
	l0 -> l0 : x^0'=1000+x^0, (-889-x^0 <= 0 /\ -3999+y^0 <= 0), cost: 1
	New rule:
	l0 -> LoAT_sink : (889+x^0 >= 0 /\ -1+n >= 0 /\ 3999-y^0 >= 0), cost: NONTERM

		889+x^0 >= 0 [0]: monotonic increase yields 889+x^0 >= 0
		
		3999-y^0 >= 0 [0]: monotonic increase yields 3999-y^0 >= 0
		
		Replacement map: {889+x^0 >= 0 -> 889+x^0 >= 0, 3999-y^0 >= 0 -> 3999-y^0 >= 0}

	Loop Acceleration

	Original rule:
	l0 -> l0 : x^0'=1000+x^0, (-889-x^0 <= 0 /\ -3999+y^0 <= 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=1000*n+x^0, (889+x^0 >= 0 /\ -1+n >= 0 /\ 3999-y^0 >= 0), cost: 1

		889+x^0 >= 0 [0]: monotonic increase yields 889+x^0 >= 0
		
		3999-y^0 >= 0 [0]: monotonic increase yields 3999-y^0 >= 0
		
		Replacement map: {889+x^0 >= 0 -> 889+x^0 >= 0, 3999-y^0 >= 0 -> 3999-y^0 >= 0}

Step with 8

	Trace

	6[T], 8[(889+x^0 >= 0 /\ -1+n >= 0 /\ 3999-y^0 >= 0)]
	
	Blocked

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

Refute

	Counterexample

	[ x^0=0 y^0=3000 ] 6 [ x^0=0 y^0=y^0 ] 8
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b