NO

Initial ITS

Start location: [1]
Program variables: c x
   0: [1] -> [2] : c'=5, T, cost: 1
   1: [2] -> [3] : x'=nondet, T, cost: 1
   2: [3] -> [4] : x >= 0, cost: 1
   5: [3] -> [6] : x < 0, cost: 1
   3: [4] -> [5] : x'=x+c, T, cost: 1
   4: [5] -> [3] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: c x
   6: [1] -> [3] : c'=5, x'=nondet, T, cost: 1
   5: [3] -> [6] : x < 0, cost: 1
   8: [3] -> [3] : x'=x+c, x >= 0, cost: 1

	Eliminating location [2] by chaining:

	Applied chaining

	First rule:
	[1] -> [2] : c'=5, T, cost: 1
	Second rule:
	[2] -> [3] : x'=nondet, T, cost: 1
	New rule:
	[1] -> [3] : c'=5, x'=nondet, T, cost: 1
	
	Applied deletion

	Removed the following rules: 0 1
	
	Eliminating location [4] by chaining:

	Applied chaining

	First rule:
	[3] -> [4] : x >= 0, cost: 1
	Second rule:
	[4] -> [5] : x'=x+c, T, cost: 1
	New rule:
	[3] -> [5] : x'=x+c, x >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 2 3
	
	Eliminating location [5] by chaining:

	Applied chaining

	First rule:
	[3] -> [5] : x'=x+c, x >= 0, cost: 1
	Second rule:
	[5] -> [3] : T, cost: 1
	New rule:
	[3] -> [3] : x'=x+c, x >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 4 7

Step with 6

	Trace

	6[T]
	
	Blocked

	[{}, {}]

Step with 5

	Trace

	6[T], 5[(x < 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	6[T]
	
	Blocked

	[{}, {5[T]}]

Step with 8

	Trace

	6[T], 8[(x >= 0)]
	
	Blocked

	[{}, {5[T]}, {}]

Nonterm

Start location: [1]
Program variables: c x
   6: [1] -> [3] : c'=5, x'=nondet, T, cost: 1
   5: [3] -> [6] : x < 0, cost: 1
   8: [3] -> [3] : x'=x+c, x >= 0, cost: 1
   9: [3] -> LoAT_sink : (-c <= 0 /\ x >= 0), cost: NONTERM
  10: [3] -> [3] : x'=x+n*c, (x+(-1+n)*c >= 0 /\ -1+n >= 0 /\ x >= 0), cost: 1

	Certificate of Non-Termination

	Original rule:
	[3] -> [3] : x'=x+c, (x >= 0), cost: 1
	New rule:
	[3] -> LoAT_sink : (-c <= 0 /\ x >= 0), cost: NONTERM

		x >= 0 [0]: eventual decrease yields (x+(-1+n)*c >= 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:
	[3] -> [3] : x'=x+c, (x >= 0), cost: 1
	New rule:
	[3] -> [3] : x'=x+n*c, (x+(-1+n)*c >= 0 /\ -1+n >= 0 /\ x >= 0), cost: 1

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

Step with 9

	Trace

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

	[{}, {5[T]}, {9[T]}]

Refute

	Counterexample

	[ c=5 x=0 ] 6 [ c=c x=x ] 9
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b