NO

Initial ITS

Start location: l5
Program variables: nd^0 p^0 x^0
   0: l0 -> l1 : nd^0'=nd^post1, p^0'=p^post1, x^0'=x^post1, (nd^0-nd^post1 == 0 /\ nd^0 <= 0 /\ -2+p^post1 == 0 /\ -x^post1+x^0 == 0), cost: 1
   1: l0 -> l1 : nd^0'=nd^post2, p^0'=p^post2, x^0'=x^post2, (-1+p^post2 == 0 /\ nd^0-nd^post2 == 0 /\ 1-nd^0 <= 0 /\ -x^post2+x^0 == 0), cost: 1
   2: l1 -> l0 : nd^0'=nd^post3, p^0'=p^post3, x^0'=x^post3, (0 == 0 /\ -p^post3+p^0 == 0 /\ -x^post3+x^0 == 0), cost: 1
   3: l2 -> l3 : nd^0'=nd^post4, p^0'=p^post4, x^0'=x^post4, (2+x^post4-x^0 == 0 /\ -p^post4+p^0 == 0 /\ nd^0 <= 0 /\ nd^0-nd^post4 == 0), cost: 1
   4: l2 -> l3 : nd^0'=nd^post5, p^0'=p^post5, x^0'=x^post5, (1+x^post5-x^0 == 0 /\ p^0-p^post5 == 0 /\ 1-nd^0 <= 0 /\ -nd^post5+nd^0 == 0), cost: 1
   5: l3 -> l1 : nd^0'=nd^post6, p^0'=p^post6, x^0'=x^post6, (-nd^post6+nd^0 == 0 /\ p^0-p^post6 == 0 /\ x^0 <= 0 /\ -x^post6+x^0 == 0), cost: 1
   6: l3 -> l2 : nd^0'=nd^post7, p^0'=p^post7, x^0'=x^post7, (0 == 0 /\ p^0-p^post7 == 0 /\ 1-x^0 <= 0 /\ -x^post7+x^0 == 0), cost: 1
   7: l4 -> l3 : nd^0'=nd^post8, p^0'=p^post8, x^0'=x^post8, (p^post8 == 0 /\ -nd^post8+nd^0 == 0 /\ x^0-x^post8 == 0), cost: 1
   8: l5 -> l4 : nd^0'=nd^post9, p^0'=p^post9, x^0'=x^post9, (-nd^post9+nd^0 == 0 /\ p^0-p^post9 == 0 /\ x^0-x^post9 == 0), cost: 1

Chained Linear Paths

Start location: l5
Program variables: nd^0 p^0 x^0
   0: l0 -> l1 : nd^0'=nd^post1, p^0'=p^post1, x^0'=x^post1, (nd^0-nd^post1 == 0 /\ nd^0 <= 0 /\ -2+p^post1 == 0 /\ -x^post1+x^0 == 0), cost: 1
   1: l0 -> l1 : nd^0'=nd^post2, p^0'=p^post2, x^0'=x^post2, (-1+p^post2 == 0 /\ nd^0-nd^post2 == 0 /\ 1-nd^0 <= 0 /\ -x^post2+x^0 == 0), cost: 1
   2: l1 -> l0 : nd^0'=nd^post3, p^0'=p^post3, x^0'=x^post3, (0 == 0 /\ -p^post3+p^0 == 0 /\ -x^post3+x^0 == 0), cost: 1
   3: l2 -> l3 : nd^0'=nd^post4, p^0'=p^post4, x^0'=x^post4, (2+x^post4-x^0 == 0 /\ -p^post4+p^0 == 0 /\ nd^0 <= 0 /\ nd^0-nd^post4 == 0), cost: 1
   4: l2 -> l3 : nd^0'=nd^post5, p^0'=p^post5, x^0'=x^post5, (1+x^post5-x^0 == 0 /\ p^0-p^post5 == 0 /\ 1-nd^0 <= 0 /\ -nd^post5+nd^0 == 0), cost: 1
   5: l3 -> l1 : nd^0'=nd^post6, p^0'=p^post6, x^0'=x^post6, (-nd^post6+nd^0 == 0 /\ p^0-p^post6 == 0 /\ x^0 <= 0 /\ -x^post6+x^0 == 0), cost: 1
   6: l3 -> l2 : nd^0'=nd^post7, p^0'=p^post7, x^0'=x^post7, (0 == 0 /\ p^0-p^post7 == 0 /\ 1-x^0 <= 0 /\ -x^post7+x^0 == 0), cost: 1
   9: l5 -> l3 : nd^0'=nd^post8, p^0'=p^post8, x^0'=x^post8, (-nd^post9+nd^0 == 0 /\ p^post8 == 0 /\ p^0-p^post9 == 0 /\ nd^post9-nd^post8 == 0 /\ x^0-x^post9 == 0 /\ x^post9-x^post8 == 0), cost: 1

	Eliminating location l4 by chaining:

	Applied chaining

	First rule:
	l5 -> l4 : nd^0'=nd^post9, p^0'=p^post9, x^0'=x^post9, (-nd^post9+nd^0 == 0 /\ p^0-p^post9 == 0 /\ x^0-x^post9 == 0), cost: 1
	Second rule:
	l4 -> l3 : nd^0'=nd^post8, p^0'=p^post8, x^0'=x^post8, (p^post8 == 0 /\ -nd^post8+nd^0 == 0 /\ x^0-x^post8 == 0), cost: 1
	New rule:
	l5 -> l3 : nd^0'=nd^post8, p^0'=p^post8, x^0'=x^post8, (-nd^post9+nd^0 == 0 /\ p^post8 == 0 /\ p^0-p^post9 == 0 /\ nd^post9-nd^post8 == 0 /\ x^0-x^post9 == 0 /\ x^post9-x^post8 == 0), cost: 1
	
	Applied deletion

	Removed the following rules: 7 8

Simplified Transitions

Start location: l5
Program variables: nd^0 p^0 x^0
  10: l0 -> l1 : p^0'=2, nd^0 <= 0, cost: 1
  11: l0 -> l1 : p^0'=1, 1-nd^0 <= 0, cost: 1
  12: l1 -> l0 : nd^0'=nd^post3, T, cost: 1
  13: l2 -> l3 : x^0'=-2+x^0, nd^0 <= 0, cost: 1
  14: l2 -> l3 : x^0'=-1+x^0, 1-nd^0 <= 0, cost: 1
  15: l3 -> l1 : x^0 <= 0, cost: 1
  16: l3 -> l2 : nd^0'=nd^post7, 1-x^0 <= 0, cost: 1
  17: l5 -> l3 : p^0'=0, T, cost: 1

	Propagated Equalities

	Original rule:
	l0 -> l1 : nd^0'=nd^post1, p^0'=p^post1, x^0'=x^post1, (nd^0-nd^post1 == 0 /\ nd^0 <= 0 /\ -2+p^post1 == 0 /\ -x^post1+x^0 == 0), cost: 1
	New rule:
	l0 -> l1 : nd^0'=nd^0, p^0'=2, x^0'=x^0, (0 == 0 /\ nd^0 <= 0), cost: 1
	
		propagated equality nd^post1 = nd^0
		
		propagated equality p^post1 = 2
		
		propagated equality x^post1 = x^0
		
	Simplified Guard

	Original rule:
	l0 -> l1 : nd^0'=nd^0, p^0'=2, x^0'=x^0, (0 == 0 /\ nd^0 <= 0), cost: 1
	New rule:
	l0 -> l1 : nd^0'=nd^0, p^0'=2, x^0'=x^0, nd^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l0 -> l1 : nd^0'=nd^0, p^0'=2, x^0'=x^0, nd^0 <= 0, cost: 1
	New rule:
	l0 -> l1 : p^0'=2, nd^0 <= 0, cost: 1
	
	Propagated Equalities

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

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

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

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

	Original rule:
	l1 -> l0 : nd^0'=nd^post3, p^0'=p^0, x^0'=x^0, 0 == 0, cost: 1
	New rule:
	l1 -> l0 : nd^0'=nd^post3, p^0'=p^0, x^0'=x^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l1 -> l0 : nd^0'=nd^post3, p^0'=p^0, x^0'=x^0, T, cost: 1
	New rule:
	l1 -> l0 : nd^0'=nd^post3, T, cost: 1
	
	Propagated Equalities

	Original rule:
	l2 -> l3 : nd^0'=nd^post4, p^0'=p^post4, x^0'=x^post4, (2+x^post4-x^0 == 0 /\ -p^post4+p^0 == 0 /\ nd^0 <= 0 /\ nd^0-nd^post4 == 0), cost: 1
	New rule:
	l2 -> l3 : nd^0'=nd^0, p^0'=p^0, x^0'=-2+x^0, (0 == 0 /\ nd^0 <= 0), cost: 1
	
		propagated equality x^post4 = -2+x^0
		
		propagated equality p^post4 = p^0
		
		propagated equality nd^post4 = nd^0
		
	Simplified Guard

	Original rule:
	l2 -> l3 : nd^0'=nd^0, p^0'=p^0, x^0'=-2+x^0, (0 == 0 /\ nd^0 <= 0), cost: 1
	New rule:
	l2 -> l3 : nd^0'=nd^0, p^0'=p^0, x^0'=-2+x^0, nd^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l2 -> l3 : nd^0'=nd^0, p^0'=p^0, x^0'=-2+x^0, nd^0 <= 0, cost: 1
	New rule:
	l2 -> l3 : x^0'=-2+x^0, nd^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l2 -> l3 : nd^0'=nd^post5, p^0'=p^post5, x^0'=x^post5, (1+x^post5-x^0 == 0 /\ p^0-p^post5 == 0 /\ 1-nd^0 <= 0 /\ -nd^post5+nd^0 == 0), cost: 1
	New rule:
	l2 -> l3 : nd^0'=nd^0, p^0'=p^0, x^0'=-1+x^0, (0 == 0 /\ 1-nd^0 <= 0), cost: 1
	
		propagated equality x^post5 = -1+x^0
		
		propagated equality p^post5 = p^0
		
		propagated equality nd^post5 = nd^0
		
	Simplified Guard

	Original rule:
	l2 -> l3 : nd^0'=nd^0, p^0'=p^0, x^0'=-1+x^0, (0 == 0 /\ 1-nd^0 <= 0), cost: 1
	New rule:
	l2 -> l3 : nd^0'=nd^0, p^0'=p^0, x^0'=-1+x^0, 1-nd^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l2 -> l3 : nd^0'=nd^0, p^0'=p^0, x^0'=-1+x^0, 1-nd^0 <= 0, cost: 1
	New rule:
	l2 -> l3 : x^0'=-1+x^0, 1-nd^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l3 -> l1 : nd^0'=nd^post6, p^0'=p^post6, x^0'=x^post6, (-nd^post6+nd^0 == 0 /\ p^0-p^post6 == 0 /\ x^0 <= 0 /\ -x^post6+x^0 == 0), cost: 1
	New rule:
	l3 -> l1 : nd^0'=nd^0, p^0'=p^0, x^0'=x^0, (0 == 0 /\ x^0 <= 0), cost: 1
	
		propagated equality nd^post6 = nd^0
		
		propagated equality p^post6 = p^0
		
		propagated equality x^post6 = x^0
		
	Simplified Guard

	Original rule:
	l3 -> l1 : nd^0'=nd^0, p^0'=p^0, x^0'=x^0, (0 == 0 /\ x^0 <= 0), cost: 1
	New rule:
	l3 -> l1 : nd^0'=nd^0, p^0'=p^0, x^0'=x^0, x^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l3 -> l1 : nd^0'=nd^0, p^0'=p^0, x^0'=x^0, x^0 <= 0, cost: 1
	New rule:
	l3 -> l1 : x^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l3 -> l2 : nd^0'=nd^post7, p^0'=p^post7, x^0'=x^post7, (0 == 0 /\ p^0-p^post7 == 0 /\ 1-x^0 <= 0 /\ -x^post7+x^0 == 0), cost: 1
	New rule:
	l3 -> l2 : nd^0'=nd^post7, p^0'=p^0, x^0'=x^0, (0 == 0 /\ 1-x^0 <= 0), cost: 1
	
		propagated equality p^post7 = p^0
		
		propagated equality x^post7 = x^0
		
	Simplified Guard

	Original rule:
	l3 -> l2 : nd^0'=nd^post7, p^0'=p^0, x^0'=x^0, (0 == 0 /\ 1-x^0 <= 0), cost: 1
	New rule:
	l3 -> l2 : nd^0'=nd^post7, p^0'=p^0, x^0'=x^0, 1-x^0 <= 0, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l3 -> l2 : nd^0'=nd^post7, p^0'=p^0, x^0'=x^0, 1-x^0 <= 0, cost: 1
	New rule:
	l3 -> l2 : nd^0'=nd^post7, 1-x^0 <= 0, cost: 1
	
	Propagated Equalities

	Original rule:
	l5 -> l3 : nd^0'=nd^post8, p^0'=p^post8, x^0'=x^post8, (-nd^post9+nd^0 == 0 /\ p^post8 == 0 /\ p^0-p^post9 == 0 /\ nd^post9-nd^post8 == 0 /\ x^0-x^post9 == 0 /\ x^post9-x^post8 == 0), cost: 1
	New rule:
	l5 -> l3 : nd^0'=nd^post9, p^0'=0, x^0'=x^post9, (0 == 0 /\ -nd^post9+nd^0 == 0 /\ p^0-p^post9 == 0 /\ x^0-x^post9 == 0), cost: 1
	
		propagated equality p^post8 = 0
		
		propagated equality nd^post8 = nd^post9
		
		propagated equality x^post8 = x^post9
		
	Propagated Equalities

	Original rule:
	l5 -> l3 : nd^0'=nd^post9, p^0'=0, x^0'=x^post9, (0 == 0 /\ -nd^post9+nd^0 == 0 /\ p^0-p^post9 == 0 /\ x^0-x^post9 == 0), cost: 1
	New rule:
	l5 -> l3 : nd^0'=nd^0, p^0'=0, x^0'=x^0, 0 == 0, cost: 1
	
		propagated equality nd^post9 = nd^0
		
		propagated equality p^post9 = p^0
		
		propagated equality x^post9 = x^0
		
	Simplified Guard

	Original rule:
	l5 -> l3 : nd^0'=nd^0, p^0'=0, x^0'=x^0, 0 == 0, cost: 1
	New rule:
	l5 -> l3 : nd^0'=nd^0, p^0'=0, x^0'=x^0, T, cost: 1
	
	Removed Trivial Updates

	Original rule:
	l5 -> l3 : nd^0'=nd^0, p^0'=0, x^0'=x^0, T, cost: 1
	New rule:
	l5 -> l3 : p^0'=0, T, cost: 1

Step with 17

	Trace

	17[T]
	
	Blocked

	[{}, {}]

Step with 15

	Trace

	17[T], 15[(x^0 <= 0)]
	
	Blocked

	[{}, {}, {}]

Step with 12

	Trace

	17[T], 15[(x^0 <= 0)], 12[T]
	
	Blocked

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

Step with 10

	Trace

	17[T], 15[(x^0 <= 0)], 12[T], 10[(nd^0 <= 0)]
	
	Blocked

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

Nonterm

Start location: l5
Program variables: nd^0 p^0 x^0
  10: l0 -> l1 : p^0'=2, nd^0 <= 0, cost: 1
  11: l0 -> l1 : p^0'=1, 1-nd^0 <= 0, cost: 1
  12: l1 -> l0 : nd^0'=nd^post3, T, cost: 1
  18: l1 -> LoAT_sink : (-1+n >= 0 /\ -nd^post31 >= 0), cost: NONTERM
  13: l2 -> l3 : x^0'=-2+x^0, nd^0 <= 0, cost: 1
  14: l2 -> l3 : x^0'=-1+x^0, 1-nd^0 <= 0, cost: 1
  15: l3 -> l1 : x^0 <= 0, cost: 1
  16: l3 -> l2 : nd^0'=nd^post7, 1-x^0 <= 0, cost: 1
  17: l5 -> l3 : p^0'=0, T, cost: 1

	Certificate of Non-Termination

	Original rule:
	l1 -> l1 : nd^0'=nd^post31, p^0'=2, nd^post31 <= 0, cost: 1
	New rule:
	l1 -> LoAT_sink : (-1+n >= 0 /\ -nd^post31 >= 0), cost: NONTERM

		-nd^post31 >= 0 [0]: monotonic increase yields -nd^post31 >= 0
		
		Replacement map: {-nd^post31 >= 0 -> -nd^post31 >= 0}

Step with 18

	Trace

	17[T], 15[(x^0 <= 0)], 18[(-1+n >= 0 /\ -nd^post31 >= 0)]
	
	Blocked

	[{}, {}, {}, {18[T]}]

Refute

	Counterexample

	[ nd^0=0 p^0=0 x^0=0 ] 17 [ nd^0=0 p^0=0 x^0=0 ] 15 [ nd^0=0 p^0=p^0 x^0=0 ] 18
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b