NO

Initial ITS

Start location: [1]
Program variables: i
   0: [1] -> [2] : i'=0, T, cost: 1
   1: [2] -> [3] : -100+i < 0, cost: 1
   9: [2] -> [9] : -100+i >= 0, cost: 1
   2: [3] -> [5] : -50+i < 0, cost: 1
   5: [3] -> [7] : -50+i >= 0, cost: 1
   8: [4] -> [2] : T, cost: 1
   3: [5] -> [6] : i'=51, T, cost: 1
   4: [6] -> [4] : T, cost: 1
   6: [7] -> [8] : i'=49, T, cost: 1
   7: [8] -> [4] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: i
   0: [1] -> [2] : i'=0, T, cost: 1
   1: [2] -> [3] : -100+i < 0, cost: 1
   9: [2] -> [9] : -100+i >= 0, cost: 1
  12: [3] -> [4] : i'=51, -50+i < 0, cost: 1
  13: [3] -> [4] : i'=49, -50+i >= 0, cost: 1
   8: [4] -> [2] : T, cost: 1

	Eliminating location [5] by chaining:

	Applied chaining

	First rule:
	[3] -> [5] : -50+i < 0, cost: 1
	Second rule:
	[5] -> [6] : i'=51, T, cost: 1
	New rule:
	[3] -> [6] : i'=51, -50+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 2 3
	
	Eliminating location [7] by chaining:

	Applied chaining

	First rule:
	[3] -> [7] : -50+i >= 0, cost: 1
	Second rule:
	[7] -> [8] : i'=49, T, cost: 1
	New rule:
	[3] -> [8] : i'=49, -50+i >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 5 6
	
	Eliminating location [6] by chaining:

	Applied chaining

	First rule:
	[3] -> [6] : i'=51, -50+i < 0, cost: 1
	Second rule:
	[6] -> [4] : T, cost: 1
	New rule:
	[3] -> [4] : i'=51, -50+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 4 10
	
	Eliminating location [8] by chaining:

	Applied chaining

	First rule:
	[3] -> [8] : i'=49, -50+i >= 0, cost: 1
	Second rule:
	[8] -> [4] : T, cost: 1
	New rule:
	[3] -> [4] : i'=49, -50+i >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 7 11

Step with 0

	Trace

	0[T]
	
	Blocked

	[{}, {}]

Step with 1

	Trace

	0[T], 1[(-100+i < 0)]
	
	Blocked

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

Step with 12

	Trace

	0[T], 1[(-100+i < 0)], 12[(-50+i < 0)]
	
	Blocked

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

Step with 8

	Trace

	0[T], 1[(-100+i < 0)], 12[(-50+i < 0)], 8[T]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Step with 1

	Trace

	0[T], 1[(-100+i < 0)], 12[(-50+i < 0)], 8[T], 1[(-100+i < 0)]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Step with 13

	Trace

	0[T], 1[(-100+i < 0)], 12[(-50+i < 0)], 8[T], 1[(-100+i < 0)], 13[(-50+i >= 0)]
	
	Blocked

	[{}, {9[T]}, {}, {}, {}, {12[T]}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 8

	Trace

	0[T], 1[(-100+i < 0)], 12[(-50+i < 0)], 8[T], 1[(-100+i < 0)], 13[(-50+i >= 0)], 8[T]
	
	Blocked

	[{}, {9[T]}, {}, {}, {}, {12[T]}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Nonterm

Start location: [1]
Program variables: i
   0: [1] -> [2] : i'=0, T, cost: 1
   1: [2] -> [3] : -100+i < 0, cost: 1
   9: [2] -> [9] : -100+i >= 0, cost: 1
  14: [2] -> LoAT_sink : (100-i > 0 /\ 50-i > 0 /\ -1+n >= 0), cost: NONTERM
  12: [3] -> [4] : i'=51, -50+i < 0, cost: 1
  13: [3] -> [4] : i'=49, -50+i >= 0, cost: 1
   8: [4] -> [2] : T, cost: 1

	Certificate of Non-Termination

	Original rule:
	[2] -> [2] : i'=49, (-50+i < 0 /\ -100+i < 0), cost: 1
	New rule:
	[2] -> LoAT_sink : (100-i > 0 /\ 50-i > 0 /\ -1+n >= 0), cost: NONTERM

		100-i > 0 [0]: monotonic increase yields 100-i > 0
		
		50-i > 0 [0]: monotonic increase yields 50-i > 0
		
		Replacement map: {100-i > 0 -> 100-i > 0, 50-i > 0 -> 50-i > 0}

Step with 14

	Trace

	0[T], 14[(100-i > 0 /\ 50-i > 0 /\ -1+n >= 0)]
	
	Blocked

	[{}, {9[T]}, {14[T]}]

Refute

	Counterexample

	[ i=0 ] 0 [ i=i ] 14
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b