NO

Initial ITS

Start location: [1]
Program variables: i
   0: [1] -> [2] : i'=nondet, T, cost: 1
   1: [2] -> [3] : -10+i < 0, cost: 1
   7: [2] -> [7] : -10+i >= 0, cost: 1
   2: [3] -> [5] : (-3+i < 0 \/ -3+i > 0), cost: 1
   5: [3] -> [4] : (-3+i <= 0 /\ -3+i >= 0), cost: 1
   6: [4] -> [2] : T, cost: 1
   3: [5] -> [6] : i'=1+i, T, cost: 1
   4: [6] -> [4] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: i
   0: [1] -> [2] : i'=nondet, T, cost: 1
   1: [2] -> [3] : -10+i < 0, cost: 1
   7: [2] -> [7] : -10+i >= 0, cost: 1
   5: [3] -> [4] : (-3+i <= 0 /\ -3+i >= 0), cost: 1
   9: [3] -> [4] : i'=1+i, (-3+i < 0 \/ -3+i > 0), cost: 1
   6: [4] -> [2] : T, cost: 1

	Eliminating location [5] by chaining:

	Applied chaining

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

	Removed the following rules: 2 3
	
	Eliminating location [6] by chaining:

	Applied chaining

	First rule:
	[3] -> [6] : i'=1+i, (-3+i < 0 \/ -3+i > 0), cost: 1
	Second rule:
	[6] -> [4] : T, cost: 1
	New rule:
	[3] -> [4] : i'=1+i, (-3+i < 0 \/ -3+i > 0), cost: 1
	
	Applied deletion

	Removed the following rules: 4 8

Step with 0

	Trace

	0[T]
	
	Blocked

	[{}, {}]

Step with 7

	Trace

	0[T], 7[(-10+i >= 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	0[T]
	
	Blocked

	[{}, {7[T]}]

Step with 1

	Trace

	0[T], 1[(-10+i < 0)]
	
	Blocked

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

Step with 5

	Trace

	0[T], 1[(-10+i < 0)], 5[(-3+i <= 0 /\ -3+i >= 0)]
	
	Blocked

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

Step with 6

	Trace

	0[T], 1[(-10+i < 0)], 5[(-3+i <= 0 /\ -3+i >= 0)], 6[T]
	
	Blocked

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

Nonterm

Start location: [1]
Program variables: i
   0: [1] -> [2] : i'=nondet, T, cost: 1
   1: [2] -> [3] : -10+i < 0, cost: 1
   7: [2] -> [7] : -10+i >= 0, cost: 1
  10: [2] -> LoAT_sink : (10-i > 0 /\ -3+i >= 0 /\ 3-i >= 0 /\ -1+n >= 0), cost: NONTERM
   5: [3] -> [4] : (-3+i <= 0 /\ -3+i >= 0), cost: 1
   9: [3] -> [4] : i'=1+i, (-3+i < 0 \/ -3+i > 0), cost: 1
   6: [4] -> [2] : T, cost: 1

	Certificate of Non-Termination

	Original rule:
	[2] -> [2] : (-3+i <= 0 /\ -3+i >= 0 /\ -10+i < 0), cost: 1
	New rule:
	[2] -> LoAT_sink : (10-i > 0 /\ -3+i >= 0 /\ 3-i >= 0 /\ -1+n >= 0), cost: NONTERM

		10-i > 0 [0]: monotonic increase yields 10-i > 0
		
		-3+i >= 0 [0]: monotonic increase yields -3+i >= 0
		
		3-i >= 0 [0]: monotonic increase yields 3-i >= 0
		
		Replacement map: {10-i > 0 -> 10-i > 0, -3+i >= 0 -> -3+i >= 0, 3-i >= 0 -> 3-i >= 0}

Step with 10

	Trace

	0[T], 10[(10-i > 0 /\ -3+i >= 0 /\ 3-i >= 0 /\ -1+n >= 0)]
	
	Blocked

	[{}, {7[T]}, {10[T]}]

Refute

	Counterexample

	[ i=3 ] 0 [ i=i ] 10
	
NO

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