NO

Initial ITS

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

Chained Linear Paths

Start location: [1]
Program variables: n sum
   7: [1] -> [3] : n'=nondet, sum'=0, T, cost: 1
   6: [3] -> [7] : (n <= 0 /\ n >= 0), cost: 1
  10: [3] -> [3] : n'=-1+n, sum'=sum+n, (n < 0 \/ n > 0), cost: 1

	Eliminating location [2] by chaining:

	Applied chaining

	First rule:
	[1] -> [2] : n'=nondet, T, cost: 1
	Second rule:
	[2] -> [3] : sum'=0, T, cost: 1
	New rule:
	[1] -> [3] : n'=nondet, sum'=0, T, cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	[3] -> [4] : (n < 0 \/ n > 0), cost: 1
	Second rule:
	[4] -> [5] : sum'=sum+n, T, cost: 1
	New rule:
	[3] -> [5] : sum'=sum+n, (n < 0 \/ n > 0), cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	[3] -> [5] : sum'=sum+n, (n < 0 \/ n > 0), cost: 1
	Second rule:
	[5] -> [6] : n'=-1+n, T, cost: 1
	New rule:
	[3] -> [6] : n'=-1+n, sum'=sum+n, (n < 0 \/ n > 0), cost: 1
	
	Applied deletion

	Removed the following rules: 4 8
	
	Eliminating location [6] by chaining:

	Applied chaining

	First rule:
	[3] -> [6] : n'=-1+n, sum'=sum+n, (n < 0 \/ n > 0), cost: 1
	Second rule:
	[6] -> [3] : T, cost: 1
	New rule:
	[3] -> [3] : n'=-1+n, sum'=sum+n, (n < 0 \/ n > 0), cost: 1
	
	Applied deletion

	Removed the following rules: 5 9

Step with 7

	Trace

	7[T]
	
	Blocked

	[{}, {}]

Step with 6

	Trace

	7[T], 6[(n <= 0 /\ n >= 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	7[T]
	
	Blocked

	[{}, {6[T]}]

Step with 10

	Trace

	7[T], 10[(n > 0)]
	
	Blocked

	[{}, {6[T]}, {}]

Accelerate

Start location: [1]
Program variables: n sum
   7: [1] -> [3] : n'=nondet, sum'=0, T, cost: 1
   6: [3] -> [7] : (n <= 0 /\ n >= 0), cost: 1
  10: [3] -> [3] : n'=-1+n, sum'=sum+n, (n < 0 \/ n > 0), cost: 1
  11: [3] -> [3] : n'=-n4+n, sum'=-1/2*n4^2+n4*n+sum+1/2*n4, (-1+n4 >= 0 /\ 1-n4+n > 0), cost: 1

	Loop Acceleration

	Original rule:
	[3] -> [3] : n'=-1+n, sum'=sum+n, (n > 0), cost: 1
	New rule:
	[3] -> [3] : n'=-n4+n, sum'=-1/2*n4^2+n4*n+sum+1/2*n4, (-1+n4 >= 0 /\ 1-n4+n > 0), cost: 1

		n > 0 [0]: montonic decrease yields 1-n4+n > 0
		
		n > 0 [1]: eventual increase yields (1 <= 0 /\ n > 0)
		
		Replacement map: {n > 0 -> 1-n4+n > 0}

	Trace

	7[T], 11[(-1+n4 >= 0 /\ 1-n4+n > 0)]
	
	Blocked

	[{}, {6[T]}, {10[n > 0], 11[T]}]

Step with 6

	Trace

	7[T], 11[(-1+n4 >= 0 /\ 1-n4+n > 0)], 6[(n <= 0 /\ n >= 0)]
	
	Blocked

	[{}, {6[T]}, {10[n > 0], 11[T]}, {}]

Backtrack

	Trace

	7[T], 11[(-1+n4 >= 0 /\ 1-n4+n > 0)]
	
	Blocked

	[{}, {6[T]}, {6[T], 10[n > 0], 11[T]}]

Backtrack

	Trace

	7[T]
	
	Blocked

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

Step with 10

	Trace

	7[T], 10[(n < 0)]
	
	Blocked

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

Nonterm

Start location: [1]
Program variables: n sum
   7: [1] -> [3] : n'=nondet, sum'=0, T, cost: 1
   6: [3] -> [7] : (n <= 0 /\ n >= 0), cost: 1
  10: [3] -> [3] : n'=-1+n, sum'=sum+n, (n < 0 \/ n > 0), cost: 1
  11: [3] -> [3] : n'=-n4+n, sum'=-1/2*n4^2+n4*n+sum+1/2*n4, (-1+n4 >= 0 /\ 1-n4+n > 0), cost: 1
  12: [3] -> LoAT_sink : (-1+n8 >= 0 /\ -n > 0), cost: NONTERM
  13: [3] -> [3] : n'=-n8+n, sum'=-1/2*n8^2+1/2*n8+n8*n+sum, (-1+n8 >= 0 /\ -n > 0), cost: 1

	Certificate of Non-Termination

	Original rule:
	[3] -> [3] : n'=-1+n, sum'=sum+n, (n < 0), cost: 1
	New rule:
	[3] -> LoAT_sink : (-1+n8 >= 0 /\ -n > 0), cost: NONTERM

		-n > 0 [0]: monotonic increase yields -n > 0
		
		Replacement map: {-n > 0 -> -n > 0}

	Loop Acceleration

	Original rule:
	[3] -> [3] : n'=-1+n, sum'=sum+n, (n < 0), cost: 1
	New rule:
	[3] -> [3] : n'=-n8+n, sum'=-1/2*n8^2+1/2*n8+n8*n+sum, (-1+n8 >= 0 /\ -n > 0), cost: 1

		-n > 0 [0]: monotonic increase yields -n > 0
		
		Replacement map: {-n > 0 -> -n > 0}

Step with 12

	Trace

	7[T], 12[(-1+n8 >= 0 /\ -n > 0)]
	
	Blocked

	[{}, {6[T], 11[T]}, {12[T]}]

Refute

	Counterexample

	[ n=-1 sum=0 ] 7 [ n=n sum=sum ] 12
	
NO

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