NO

Initial ITS

Start location: [1]
Program variables: x
   0: [1] -> [2] : x'=nondet, T, cost: 1
   1: [2] -> [3] : x >= 0, cost: 1
   4: [2] -> [5] : x < 0, cost: 1
   2: [3] -> [4] : x'=nondet1+x, T, cost: 1
   3: [4] -> [2] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: x
   0: [1] -> [2] : x'=nondet, T, cost: 1
   4: [2] -> [5] : x < 0, cost: 1
   6: [2] -> [2] : x'=nondet1+x, x >= 0, cost: 1

	Eliminating location [3] by chaining:

	Applied chaining

	First rule:
	[2] -> [3] : x >= 0, cost: 1
	Second rule:
	[3] -> [4] : x'=nondet1+x, T, cost: 1
	New rule:
	[2] -> [4] : x'=nondet1+x, x >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 1 2
	
	Eliminating location [4] by chaining:

	Applied chaining

	First rule:
	[2] -> [4] : x'=nondet1+x, x >= 0, cost: 1
	Second rule:
	[4] -> [2] : T, cost: 1
	New rule:
	[2] -> [2] : x'=nondet1+x, x >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 3 5

Step with 0

	Trace

	0[T]
	
	Blocked

	[{}, {}]

Step with 4

	Trace

	0[T], 4[(x < 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	0[T]
	
	Blocked

	[{}, {4[T]}]

Step with 6

	Trace

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

	[{}, {4[T]}, {}]

Nonterm

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

	Certificate of Non-Termination

	Original rule:
	[2] -> [2] : x'=nondet1+x, (x >= 0), cost: 1
	New rule:
	[2] -> LoAT_sink : (-nondet1 <= 0 /\ x >= 0), cost: NONTERM

		x >= 0 [0]: eventual decrease yields ((-1+n)*nondet1+x >= 0 /\ x >= 0)
		
		x >= 0 [1]: eventual increase yields (-nondet1 <= 0 /\ x >= 0)
		
		Replacement map: {x >= 0 -> (-nondet1 <= 0 /\ x >= 0)}

	Loop Acceleration

	Original rule:
	[2] -> [2] : x'=nondet1+x, (x >= 0), cost: 1
	New rule:
	[2] -> [2] : x'=nondet1*n+x, (-1+n >= 0 /\ (-1+n)*nondet1+x >= 0 /\ x >= 0), cost: 1

		x >= 0 [0]: eventual decrease yields ((-1+n)*nondet1+x >= 0 /\ x >= 0)
		
		x >= 0 [1]: eventual increase yields (-nondet1 <= 0 /\ x >= 0)
		
		Replacement map: {x >= 0 -> ((-1+n)*nondet1+x >= 0 /\ x >= 0)}

Step with 7

	Trace

	0[T], 7[(-nondet1 <= 0 /\ x >= 0)]
	
	Blocked

	[{}, {4[T]}, {7[T]}]

Refute

	Counterexample

	[ x=0 ] 0 [ x=x ] 7
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b