NO

Initial ITS

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

Chained Linear Paths

Start location: l4
Program variables: x^0 y^0 z^0
   7: l0 -> l0 : x^0'=x^post2, y^0'=y^post2, z^0'=z^post2, (2+y^post1-y^0 == 0 /\ -y^post2+y^post1 == 0 /\ -z^post1+z^0 == 0 /\ -z^post2+z^post1 == 0 /\ -y^0+x^post1-x^0 == 0 /\ -x^post2+x^post1 == 0), cost: 1
   8: l0 -> l0 : x^0'=x^post4, y^0'=y^post4, z^0'=z^post4, (x^post3-z^0-x^0 == 0 /\ -y^post4+y^post3 == 0 /\ -1+y^post3-y^0 == 0 /\ -x^post4+x^post3 == 0 /\ 2+z^post3-z^0 == 0 /\ -z^post4+z^post3 == 0), cost: 1
   6: l4 -> l0 : x^0'=x^post5, y^0'=y^post5, z^0'=z^post5, (y^post6-y^post5 == 0 /\ -x^post6 <= 0 /\ z^post6-z^post5 == 0 /\ -z^post6+z^0 == 0 /\ x^post6-x^post5 == 0 /\ -x^post6+x^0 == 0 /\ y^0-y^post6 == 0), cost: 1

	Eliminating location l3 by chaining:

	Applied chaining

	First rule:
	l4 -> l3 : x^0'=x^post6, y^0'=y^post6, z^0'=z^post6, (-z^post6+z^0 == 0 /\ -x^post6+x^0 == 0 /\ y^0-y^post6 == 0), cost: 1
	Second rule:
	l3 -> l0 : x^0'=x^post5, y^0'=y^post5, z^0'=z^post5, (-x^post5+x^0 == 0 /\ y^0-y^post5 == 0 /\ -z^post5+z^0 == 0 /\ -x^0 <= 0), cost: 1
	New rule:
	l4 -> l0 : x^0'=x^post5, y^0'=y^post5, z^0'=z^post5, (y^post6-y^post5 == 0 /\ -x^post6 <= 0 /\ z^post6-z^post5 == 0 /\ -z^post6+z^0 == 0 /\ x^post6-x^post5 == 0 /\ -x^post6+x^0 == 0 /\ y^0-y^post6 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 4 5
	
	Eliminating location l1 by chaining:

	Applied chaining

	First rule:
	l0 -> l1 : x^0'=x^post1, y^0'=y^post1, z^0'=z^post1, (2+y^post1-y^0 == 0 /\ -z^post1+z^0 == 0 /\ -y^0+x^post1-x^0 == 0), cost: 1
	Second rule:
	l1 -> l0 : x^0'=x^post2, y^0'=y^post2, z^0'=z^post2, (-z^post2+z^0 == 0 /\ -x^post2+x^0 == 0 /\ -y^post2+y^0 == 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=x^post2, y^0'=y^post2, z^0'=z^post2, (2+y^post1-y^0 == 0 /\ -y^post2+y^post1 == 0 /\ -z^post1+z^0 == 0 /\ -z^post2+z^post1 == 0 /\ -y^0+x^post1-x^0 == 0 /\ -x^post2+x^post1 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 0 1
	
	Eliminating location l2 by chaining:

	Applied chaining

	First rule:
	l0 -> l2 : x^0'=x^post3, y^0'=y^post3, z^0'=z^post3, (x^post3-z^0-x^0 == 0 /\ -1+y^post3-y^0 == 0 /\ 2+z^post3-z^0 == 0), cost: 1
	Second rule:
	l2 -> l0 : x^0'=x^post4, y^0'=y^post4, z^0'=z^post4, (-x^post4+x^0 == 0 /\ -y^post4+y^0 == 0 /\ -z^post4+z^0 == 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=x^post4, y^0'=y^post4, z^0'=z^post4, (x^post3-z^0-x^0 == 0 /\ -y^post4+y^post3 == 0 /\ -1+y^post3-y^0 == 0 /\ -x^post4+x^post3 == 0 /\ 2+z^post3-z^0 == 0 /\ -z^post4+z^post3 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 2 3

Simplified Transitions

Start location: l4
Program variables: x^0 y^0 z^0
  10: l0 -> l0 : x^0'=y^0+x^0, y^0'=-2+y^0, T, cost: 1
  11: l0 -> l0 : x^0'=z^0+x^0, y^0'=1+y^0, z^0'=-2+z^0, T, cost: 1
   9: l4 -> l0 : -x^0 <= 0, cost: 1

	Propagated Equalities

	Original rule:
	l4 -> l0 : x^0'=x^post5, y^0'=y^post5, z^0'=z^post5, (y^post6-y^post5 == 0 /\ -x^post6 <= 0 /\ z^post6-z^post5 == 0 /\ -z^post6+z^0 == 0 /\ x^post6-x^post5 == 0 /\ -x^post6+x^0 == 0 /\ y^0-y^post6 == 0), cost: 1
	New rule:
	l4 -> l0 : x^0'=x^post6, y^0'=y^post6, z^0'=z^post6, (0 == 0 /\ -x^post6 <= 0 /\ -z^post6+z^0 == 0 /\ -x^post6+x^0 == 0 /\ y^0-y^post6 == 0), cost: 1
	
		propagated equality y^post5 = y^post6
		
		propagated equality z^post5 = z^post6
		
		propagated equality x^post5 = x^post6
		
	Propagated Equalities

	Original rule:
	l4 -> l0 : x^0'=x^post6, y^0'=y^post6, z^0'=z^post6, (0 == 0 /\ -x^post6 <= 0 /\ -z^post6+z^0 == 0 /\ -x^post6+x^0 == 0 /\ y^0-y^post6 == 0), cost: 1
	New rule:
	l4 -> l0 : x^0'=x^0, y^0'=y^0, z^0'=z^0, (0 == 0 /\ -x^0 <= 0), cost: 1
	
		propagated equality z^post6 = z^0
		
		propagated equality x^post6 = x^0
		
		propagated equality y^post6 = y^0
		
	Simplified Guard

	Original rule:
	l4 -> l0 : x^0'=x^0, y^0'=y^0, z^0'=z^0, (0 == 0 /\ -x^0 <= 0), cost: 1
	New rule:
	l4 -> l0 : x^0'=x^0, y^0'=y^0, z^0'=z^0, -x^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l4 -> l0 : x^0'=x^0, y^0'=y^0, z^0'=z^0, -x^0 <= 0, cost: 1
	New rule:
	l4 -> l0 : -x^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l0 -> l0 : x^0'=x^post2, y^0'=y^post2, z^0'=z^post2, (2+y^post1-y^0 == 0 /\ -y^post2+y^post1 == 0 /\ -z^post1+z^0 == 0 /\ -z^post2+z^post1 == 0 /\ -y^0+x^post1-x^0 == 0 /\ -x^post2+x^post1 == 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=x^post1, y^0'=y^post1, z^0'=z^post1, (0 == 0 /\ 2+y^post1-y^0 == 0 /\ -z^post1+z^0 == 0 /\ -y^0+x^post1-x^0 == 0), cost: 1
	
		propagated equality y^post2 = y^post1
		
		propagated equality z^post2 = z^post1
		
		propagated equality x^post2 = x^post1
		
	Propagated Equalities

	Original rule:
	l0 -> l0 : x^0'=x^post1, y^0'=y^post1, z^0'=z^post1, (0 == 0 /\ 2+y^post1-y^0 == 0 /\ -z^post1+z^0 == 0 /\ -y^0+x^post1-x^0 == 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=y^0+x^0, y^0'=-2+y^0, z^0'=z^0, 0 == 0, cost: 1
	
		propagated equality y^post1 = -2+y^0
		
		propagated equality z^post1 = z^0
		
		propagated equality x^post1 = y^0+x^0
		
	Simplified Guard

	Original rule:
	l0 -> l0 : x^0'=y^0+x^0, y^0'=-2+y^0, z^0'=z^0, 0 == 0, cost: 1
	New rule:
	l0 -> l0 : x^0'=y^0+x^0, y^0'=-2+y^0, z^0'=z^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l0 -> l0 : x^0'=y^0+x^0, y^0'=-2+y^0, z^0'=z^0, T, cost: 1
	New rule:
	l0 -> l0 : x^0'=y^0+x^0, y^0'=-2+y^0, T, cost: 1
	
	Propagated Equalities

	Original rule:
	l0 -> l0 : x^0'=x^post4, y^0'=y^post4, z^0'=z^post4, (x^post3-z^0-x^0 == 0 /\ -y^post4+y^post3 == 0 /\ -1+y^post3-y^0 == 0 /\ -x^post4+x^post3 == 0 /\ 2+z^post3-z^0 == 0 /\ -z^post4+z^post3 == 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=x^post3, y^0'=y^post3, z^0'=z^post3, (0 == 0 /\ x^post3-z^0-x^0 == 0 /\ -1+y^post3-y^0 == 0 /\ 2+z^post3-z^0 == 0), cost: 1
	
		propagated equality y^post4 = y^post3
		
		propagated equality x^post4 = x^post3
		
		propagated equality z^post4 = z^post3
		
	Propagated Equalities

	Original rule:
	l0 -> l0 : x^0'=x^post3, y^0'=y^post3, z^0'=z^post3, (0 == 0 /\ x^post3-z^0-x^0 == 0 /\ -1+y^post3-y^0 == 0 /\ 2+z^post3-z^0 == 0), cost: 1
	New rule:
	l0 -> l0 : x^0'=z^0+x^0, y^0'=1+y^0, z^0'=-2+z^0, 0 == 0, cost: 1
	
		propagated equality x^post3 = z^0+x^0
		
		propagated equality y^post3 = 1+y^0
		
		propagated equality z^post3 = -2+z^0
		
	Simplified Guard

	Original rule:
	l0 -> l0 : x^0'=z^0+x^0, y^0'=1+y^0, z^0'=-2+z^0, 0 == 0, cost: 1
	New rule:
	l0 -> l0 : x^0'=z^0+x^0, y^0'=1+y^0, z^0'=-2+z^0, T, cost: 1

Step with 9

	Trace

	9[(-x^0 <= 0)]
	
	Blocked

	[{}, {}]

Step with 10

	Trace

	9[(-x^0 <= 0)], 10[T]
	
	Blocked

	[{}, {}, {}]

Nonterm

Start location: l4
Program variables: x^0 y^0 z^0
  10: l0 -> l0 : x^0'=y^0+x^0, y^0'=-2+y^0, T, cost: 1
  11: l0 -> l0 : x^0'=z^0+x^0, y^0'=1+y^0, z^0'=-2+z^0, T, cost: 1
  12: l0 -> LoAT_sink : -1+n >= 0, cost: NONTERM
  13: l0 -> l0 : x^0'=-n^2+y^0*n+n+x^0, y^0'=y^0-2*n, -1+n >= 0, cost: 1
   9: l4 -> l0 : -x^0 <= 0, cost: 1

	Certificate of Non-Termination

	Original rule:
	l0 -> l0 : x^0'=y^0+x^0, y^0'=-2+y^0, T, cost: 1
	New rule:
	l0 -> LoAT_sink : -1+n >= 0, cost: NONTERM

		Replacement map: {}

	Loop Acceleration

	Original rule:
	l0 -> l0 : x^0'=y^0+x^0, y^0'=-2+y^0, T, cost: 1
	New rule:
	l0 -> l0 : x^0'=-n^2+y^0*n+n+x^0, y^0'=y^0-2*n, -1+n >= 0, cost: 1

		Replacement map: {}

Step with 12

	Trace

	9[(-x^0 <= 0)], 12[-1+n >= 0]
	
	Blocked

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

Refute

	Counterexample

	[ x^0=0 y^0=0 z^0=0 ] 9 [ x^0=0 y^0=0 z^0=0 ] 12
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b