NO

Initial ITS

Start location: l4
Program variables: x^0
   0: l0 -> l2 : x^0'=x^post1, 1+x^post1-x^0 == 0, cost: 1
   1: l2 -> l1 : x^0'=x^post2, (-x^post2+x^0 == 0 /\ -299+x^0 <= 0), cost: 1
   2: l2 -> l1 : x^0'=x^post3, (-x^post3+x^0 == 0 /\ 301-x^0 <= 0), cost: 1
   3: l1 -> l0 : x^0'=x^post4, -x^post4+x^0 == 0, cost: 1
   4: l3 -> l0 : x^0'=x^post5, -100+x^post5 == 0, cost: 1
   5: l4 -> l3 : x^0'=x^post6, -x^post6+x^0 == 0, cost: 1

Chained Linear Paths

Start location: l4
Program variables: x^0
   0: l0 -> l2 : x^0'=x^post1, 1+x^post1-x^0 == 0, cost: 1
   1: l2 -> l1 : x^0'=x^post2, (-x^post2+x^0 == 0 /\ -299+x^0 <= 0), cost: 1
   2: l2 -> l1 : x^0'=x^post3, (-x^post3+x^0 == 0 /\ 301-x^0 <= 0), cost: 1
   3: l1 -> l0 : x^0'=x^post4, -x^post4+x^0 == 0, cost: 1
   6: l4 -> l0 : x^0'=x^post5, (-x^post6+x^0 == 0 /\ -100+x^post5 == 0), cost: 1

	Eliminating location l3 by chaining:

	Applied chaining

	First rule:
	l4 -> l3 : x^0'=x^post6, -x^post6+x^0 == 0, cost: 1
	Second rule:
	l3 -> l0 : x^0'=x^post5, -100+x^post5 == 0, cost: 1
	New rule:
	l4 -> l0 : x^0'=x^post5, (-x^post6+x^0 == 0 /\ -100+x^post5 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 4 5

Simplified Transitions

Start location: l4
Program variables: x^0
   7: l0 -> l2 : x^0'=-1+x^0, T, cost: 1
   8: l2 -> l1 : -299+x^0 <= 0, cost: 1
   9: l2 -> l1 : 301-x^0 <= 0, cost: 1
  10: l1 -> l0 : T, cost: 1
  11: l4 -> l0 : x^0'=100, T, cost: 1

	Propagated Equalities

	Original rule:
	l0 -> l2 : x^0'=x^post1, 1+x^post1-x^0 == 0, cost: 1
	New rule:
	l0 -> l2 : x^0'=-1+x^0, 0 == 0, cost: 1
	
		propagated equality x^post1 = -1+x^0
		
	Simplified Guard

	Original rule:
	l0 -> l2 : x^0'=-1+x^0, 0 == 0, cost: 1
	New rule:
	l0 -> l2 : x^0'=-1+x^0, T, cost: 1
	
	Propagated Equalities

	Original rule:
	l2 -> l1 : x^0'=x^post2, (-x^post2+x^0 == 0 /\ -299+x^0 <= 0), cost: 1
	New rule:
	l2 -> l1 : x^0'=x^0, (0 == 0 /\ -299+x^0 <= 0), cost: 1
	
		propagated equality x^post2 = x^0
		
	Simplified Guard

	Original rule:
	l2 -> l1 : x^0'=x^0, (0 == 0 /\ -299+x^0 <= 0), cost: 1
	New rule:
	l2 -> l1 : x^0'=x^0, -299+x^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l2 -> l1 : x^0'=x^0, -299+x^0 <= 0, cost: 1
	New rule:
	l2 -> l1 : -299+x^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l2 -> l1 : x^0'=x^post3, (-x^post3+x^0 == 0 /\ 301-x^0 <= 0), cost: 1
	New rule:
	l2 -> l1 : x^0'=x^0, (0 == 0 /\ 301-x^0 <= 0), cost: 1
	
		propagated equality x^post3 = x^0
		
	Simplified Guard

	Original rule:
	l2 -> l1 : x^0'=x^0, (0 == 0 /\ 301-x^0 <= 0), cost: 1
	New rule:
	l2 -> l1 : x^0'=x^0, 301-x^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l2 -> l1 : x^0'=x^0, 301-x^0 <= 0, cost: 1
	New rule:
	l2 -> l1 : 301-x^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l1 -> l0 : x^0'=x^post4, -x^post4+x^0 == 0, cost: 1
	New rule:
	l1 -> l0 : x^0'=x^0, 0 == 0, cost: 1
	
		propagated equality x^post4 = x^0
		
	Simplified Guard

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

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

	Original rule:
	l4 -> l0 : x^0'=x^post5, (-x^post6+x^0 == 0 /\ -100+x^post5 == 0), cost: 1
	New rule:
	l4 -> l0 : x^0'=100, (0 == 0 /\ -x^post6+x^0 == 0), cost: 1
	
		propagated equality x^post5 = 100
		
	Propagated Equalities

	Original rule:
	l4 -> l0 : x^0'=100, (0 == 0 /\ -x^post6+x^0 == 0), cost: 1
	New rule:
	l4 -> l0 : x^0'=100, 0 == 0, cost: 1
	
		propagated equality x^post6 = x^0
		
	Simplified Guard

	Original rule:
	l4 -> l0 : x^0'=100, 0 == 0, cost: 1
	New rule:
	l4 -> l0 : x^0'=100, T, cost: 1

Step with 11

	Trace

	11[T]
	
	Blocked

	[{}, {}]

Step with 7

	Trace

	11[T], 7[T]
	
	Blocked

	[{}, {}, {}]

Step with 8

	Trace

	11[T], 7[T], 8[(-299+x^0 <= 0)]
	
	Blocked

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

Step with 10

	Trace

	11[T], 7[T], 8[(-299+x^0 <= 0)], 10[T]
	
	Blocked

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

Nonterm

Start location: l4
Program variables: x^0
   7: l0 -> l2 : x^0'=-1+x^0, T, cost: 1
  12: l0 -> LoAT_sink : (300-x^0 >= 0 /\ -1+n >= 0), cost: NONTERM
  13: l0 -> l0 : x^0'=-n+x^0, (300-x^0 >= 0 /\ -1+n >= 0), cost: 1
   8: l2 -> l1 : -299+x^0 <= 0, cost: 1
   9: l2 -> l1 : 301-x^0 <= 0, cost: 1
  10: l1 -> l0 : T, cost: 1
  11: l4 -> l0 : x^0'=100, T, cost: 1

	Certificate of Non-Termination

	Original rule:
	l0 -> l0 : x^0'=-1+x^0, -300+x^0 <= 0, cost: 1
	New rule:
	l0 -> LoAT_sink : (300-x^0 >= 0 /\ -1+n >= 0), cost: NONTERM

		300-x^0 >= 0 [0]: monotonic increase yields 300-x^0 >= 0
		
		Replacement map: {300-x^0 >= 0 -> 300-x^0 >= 0}

	Loop Acceleration

	Original rule:
	l0 -> l0 : x^0'=-1+x^0, -300+x^0 <= 0, cost: 1
	New rule:
	l0 -> l0 : x^0'=-n+x^0, (300-x^0 >= 0 /\ -1+n >= 0), cost: 1

		300-x^0 >= 0 [0]: monotonic increase yields 300-x^0 >= 0
		
		Replacement map: {300-x^0 >= 0 -> 300-x^0 >= 0}

Step with 12

	Trace

	11[T], 12[(300-x^0 >= 0 /\ -1+n >= 0)]
	
	Blocked

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

Refute

	Counterexample

	[ x^0=100 ] 11 [ x^0=x^0 ] 12
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b