NO

Initial ITS

Start location: [1]
Program variables: c x
   0: [1] -> [2] : x'=nondet, T, cost: 1
   1: [2] -> [3] : c'=nondet1, T, cost: 1
   2: [3] -> [5] : c == 0, cost: 1
   8: [3] -> [4] : (c < 0 \/ c > 0), cost: 1
   3: [5] -> [6] : x >= 0, cost: 1
   6: [5] -> [8] : x < 0, cost: 1
   4: [6] -> [7] : x'=c+x, T, cost: 1
   5: [7] -> [5] : T, cost: 1
   7: [8] -> [4] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: c x
   9: [1] -> [3] : c'=nondet1, x'=nondet, T, cost: 1
   2: [3] -> [5] : c == 0, cost: 1
   8: [3] -> [4] : (c < 0 \/ c > 0), cost: 1
  11: [5] -> [4] : x < 0, cost: 1
  12: [5] -> [5] : x'=c+x, x >= 0, cost: 1

	Eliminating location [2] by chaining:

	Applied chaining

	First rule:
	[1] -> [2] : x'=nondet, T, cost: 1
	Second rule:
	[2] -> [3] : c'=nondet1, T, cost: 1
	New rule:
	[1] -> [3] : c'=nondet1, x'=nondet, T, cost: 1
	
	Applied deletion

	Removed the following rules: 0 1
	
	Eliminating location [6] by chaining:

	Applied chaining

	First rule:
	[5] -> [6] : x >= 0, cost: 1
	Second rule:
	[6] -> [7] : x'=c+x, T, cost: 1
	New rule:
	[5] -> [7] : x'=c+x, x >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 3 4
	
	Eliminating location [8] by chaining:

	Applied chaining

	First rule:
	[5] -> [8] : x < 0, cost: 1
	Second rule:
	[8] -> [4] : T, cost: 1
	New rule:
	[5] -> [4] : x < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 6 7
	
	Eliminating location [7] by chaining:

	Applied chaining

	First rule:
	[5] -> [7] : x'=c+x, x >= 0, cost: 1
	Second rule:
	[7] -> [5] : T, cost: 1
	New rule:
	[5] -> [5] : x'=c+x, x >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 5 10

Step with 9

	Trace

	9[T]
	
	Blocked

	[{}, {}]

Step with 2

	Trace

	9[T], 2[(c == 0)]
	
	Blocked

	[{}, {}, {}]

Step with 11

	Trace

	9[T], 2[(c == 0)], 11[(x < 0)]
	
	Blocked

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

Backtrack

	Trace

	9[T], 2[(c == 0)]
	
	Blocked

	[{}, {}, {11[T]}]

Step with 12

	Trace

	9[T], 2[(c == 0)], 12[(x >= 0)]
	
	Blocked

	[{}, {}, {11[T]}, {}]

Nonterm

Start location: [1]
Program variables: c x
   9: [1] -> [3] : c'=nondet1, x'=nondet, T, cost: 1
   2: [3] -> [5] : c == 0, cost: 1
   8: [3] -> [4] : (c < 0 \/ c > 0), cost: 1
  11: [5] -> [4] : x < 0, cost: 1
  12: [5] -> [5] : x'=c+x, x >= 0, cost: 1
  13: [5] -> LoAT_sink : (-c <= 0 /\ x >= 0), cost: NONTERM
  14: [5] -> [5] : x'=n*c+x, (-1+n >= 0 /\ (-1+n)*c+x >= 0 /\ x >= 0), cost: 1

	Certificate of Non-Termination

	Original rule:
	[5] -> [5] : x'=c+x, (x >= 0), cost: 1
	New rule:
	[5] -> LoAT_sink : (-c <= 0 /\ x >= 0), cost: NONTERM

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

	Loop Acceleration

	Original rule:
	[5] -> [5] : x'=c+x, (x >= 0), cost: 1
	New rule:
	[5] -> [5] : x'=n*c+x, (-1+n >= 0 /\ (-1+n)*c+x >= 0 /\ x >= 0), cost: 1

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

Step with 13

	Trace

	9[T], 2[(c == 0)], 13[(-c <= 0 /\ x >= 0)]
	
	Blocked

	[{}, {}, {11[T]}, {13[T]}]

Refute

	Counterexample

	[ c=0 x=0 ] 9 [ c=0 x=0 ] 2 [ c=c x=x ] 13
	
NO

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