NO

Initial ITS

Start location: [1]
Program variables: i w
   0: [1] -> [2] : i'=nondet, T, cost: 1
   1: [2] -> [3] : w'=5, T, cost: 1
   2: [3] -> [4] : (i < 0 \/ i > 0), cost: 1
  18: [3] -> [17] : (i <= 0 /\ i >= 0), cost: 1
   3: [4] -> [6] : w+i < 0, cost: 1
   7: [4] -> [9] : w+i >= 0, cost: 1
  16: [5] -> [16] : w'=1+w, T, cost: 1
   4: [6] -> [7] : i'=-1+i, T, cost: 1
   5: [7] -> [8] : i'=-i, T, cost: 1
   6: [8] -> [5] : T, cost: 1
   8: [9] -> [11] : -w+i > 0, cost: 1
  12: [9] -> [14] : -w+i <= 0, cost: 1
  15: [10] -> [5] : T, cost: 1
   9: [11] -> [12] : i'=1+i, T, cost: 1
  10: [12] -> [13] : i'=-i, T, cost: 1
  11: [13] -> [10] : T, cost: 1
  13: [14] -> [15] : i'=0, T, cost: 1
  14: [15] -> [10] : T, cost: 1
  17: [16] -> [3] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: i w
  19: [1] -> [3] : i'=nondet, w'=5, T, cost: 1
   2: [3] -> [4] : (i < 0 \/ i > 0), cost: 1
  18: [3] -> [17] : (i <= 0 /\ i >= 0), cost: 1
   7: [4] -> [9] : w+i >= 0, cost: 1
  22: [4] -> [5] : i'=1-i, w+i < 0, cost: 1
  23: [5] -> [3] : w'=1+w, T, cost: 1
  27: [9] -> [10] : i'=0, -w+i <= 0, cost: 1
  28: [9] -> [10] : i'=-1-i, -w+i > 0, cost: 1
  15: [10] -> [5] : T, cost: 1

	Eliminating location [2] by chaining:

	Applied chaining

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

	Removed the following rules: 0 1
	
	Eliminating location [6] by chaining:

	Applied chaining

	First rule:
	[4] -> [6] : w+i < 0, cost: 1
	Second rule:
	[6] -> [7] : i'=-1+i, T, cost: 1
	New rule:
	[4] -> [7] : i'=-1+i, w+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 3 4
	
	Eliminating location [7] by chaining:

	Applied chaining

	First rule:
	[4] -> [7] : i'=-1+i, w+i < 0, cost: 1
	Second rule:
	[7] -> [8] : i'=-i, T, cost: 1
	New rule:
	[4] -> [8] : i'=1-i, w+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 5 20
	
	Eliminating location [8] by chaining:

	Applied chaining

	First rule:
	[4] -> [8] : i'=1-i, w+i < 0, cost: 1
	Second rule:
	[8] -> [5] : T, cost: 1
	New rule:
	[4] -> [5] : i'=1-i, w+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 6 21
	
	Eliminating location [16] by chaining:

	Applied chaining

	First rule:
	[5] -> [16] : w'=1+w, T, cost: 1
	Second rule:
	[16] -> [3] : T, cost: 1
	New rule:
	[5] -> [3] : w'=1+w, T, cost: 1
	
	Applied deletion

	Removed the following rules: 16 17
	
	Eliminating location [11] by chaining:

	Applied chaining

	First rule:
	[9] -> [11] : -w+i > 0, cost: 1
	Second rule:
	[11] -> [12] : i'=1+i, T, cost: 1
	New rule:
	[9] -> [12] : i'=1+i, -w+i > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 8 9
	
	Eliminating location [14] by chaining:

	Applied chaining

	First rule:
	[9] -> [14] : -w+i <= 0, cost: 1
	Second rule:
	[14] -> [15] : i'=0, T, cost: 1
	New rule:
	[9] -> [15] : i'=0, -w+i <= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 12 13
	
	Eliminating location [12] by chaining:

	Applied chaining

	First rule:
	[9] -> [12] : i'=1+i, -w+i > 0, cost: 1
	Second rule:
	[12] -> [13] : i'=-i, T, cost: 1
	New rule:
	[9] -> [13] : i'=-1-i, -w+i > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 10 24
	
	Eliminating location [15] by chaining:

	Applied chaining

	First rule:
	[9] -> [15] : i'=0, -w+i <= 0, cost: 1
	Second rule:
	[15] -> [10] : T, cost: 1
	New rule:
	[9] -> [10] : i'=0, -w+i <= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 14 25
	
	Eliminating location [13] by chaining:

	Applied chaining

	First rule:
	[9] -> [13] : i'=-1-i, -w+i > 0, cost: 1
	Second rule:
	[13] -> [10] : T, cost: 1
	New rule:
	[9] -> [10] : i'=-1-i, -w+i > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 11 26

Step with 19

	Trace

	19[T]
	
	Blocked

	[{}, {}]

Step with 18

	Trace

	19[T], 18[(i <= 0 /\ i >= 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	19[T]
	
	Blocked

	[{}, {18[T]}]

Step with 2

	Trace

	19[T], 2[(i > 0)]
	
	Blocked

	[{}, {18[T]}, {}]

Step with 7

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)]
	
	Blocked

	[{}, {18[T]}, {}, {}]

Step with 27

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 27[(-w+i <= 0)]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}]

Step with 15

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 27[(-w+i <= 0)], 15[T]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {}]

Step with 23

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 27[(-w+i <= 0)], 15[T], 23[T]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 18

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 27[(-w+i <= 0)], 15[T], 23[T], 18[(i <= 0 /\ i >= 0)]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {}, {2[T]}, {}]

Backtrack

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 27[(-w+i <= 0)], 15[T], 23[T]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {}, {2[T], 18[T]}]

Backtrack

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 27[(-w+i <= 0)], 15[T]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {23[T]}]

Backtrack

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 27[(-w+i <= 0)]
	
	Blocked

	[{}, {18[T]}, {}, {}, {15[T]}]

Backtrack

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)]
	
	Blocked

	[{}, {18[T]}, {}, {27[T]}]

Step with 28

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 28[(-w+i > 0)]
	
	Blocked

	[{}, {18[T]}, {}, {27[T]}, {}]

Step with 15

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 28[(-w+i > 0)], 15[T]
	
	Blocked

	[{}, {18[T]}, {}, {27[T]}, {}, {}]

Step with 23

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 28[(-w+i > 0)], 15[T], 23[T]
	
	Blocked

	[{}, {18[T]}, {}, {27[T]}, {}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 2

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 28[(-w+i > 0)], 15[T], 23[T], 2[(i < 0)]
	
	Blocked

	[{}, {18[T]}, {}, {27[T]}, {}, {}, {18[T]}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 22

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 28[(-w+i > 0)], 15[T], 23[T], 2[(i < 0)], 22[(w+i < 0)]
	
	Blocked

	[{}, {18[T]}, {}, {27[T]}, {}, {}, {18[T]}, {7[T]}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 23

	Trace

	19[T], 2[(i > 0)], 7[(w+i >= 0)], 28[(-w+i > 0)], 15[T], 23[T], 2[(i < 0)], 22[(w+i < 0)], 23[T]
	
	Blocked

	[{}, {18[T]}, {}, {27[T]}, {}, {}, {18[T]}, {7[T]}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Nonterm

Start location: [1]
Program variables: i w
  19: [1] -> [3] : i'=nondet, w'=5, T, cost: 1
   2: [3] -> [4] : (i < 0 \/ i > 0), cost: 1
  18: [3] -> [17] : (i <= 0 /\ i >= 0), cost: 1
  29: [3] -> LoAT_sink : (w+i >= 0 /\ 1+i > 0 /\ -1+n >= 0 /\ -w+i > 0 /\ i > 0), cost: NONTERM
  30: [3] -> [3] : i'=2*n+i, w'=2*n+w, (w+i >= 0 /\ 1+i > 0 /\ -1+n >= 0 /\ -w+i > 0 /\ i > 0), cost: 1
   7: [4] -> [9] : w+i >= 0, cost: 1
  22: [4] -> [5] : i'=1-i, w+i < 0, cost: 1
  23: [5] -> [3] : w'=1+w, T, cost: 1
  27: [9] -> [10] : i'=0, -w+i <= 0, cost: 1
  28: [9] -> [10] : i'=-1-i, -w+i > 0, cost: 1
  15: [10] -> [5] : T, cost: 1

	Certificate of Non-Termination

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

		w+i >= 0 [0]: monotonic increase yields w+i >= 0
		
		1+i > 0 [0]: monotonic increase yields 1+i > 0
		
		-w+i > 0 [0]: monotonic increase yields -w+i > 0
		
		i > 0 [0]: monotonic increase yields i > 0, dependencies: 1+i > 0
		
		Replacement map: {w+i >= 0 -> w+i >= 0, 1+i > 0 -> 1+i > 0, -w+i > 0 -> -w+i > 0, i > 0 -> i > 0}

	Loop Acceleration

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

		w+i >= 0 [0]: monotonic increase yields w+i >= 0
		
		1+i > 0 [0]: monotonic increase yields 1+i > 0
		
		-w+i > 0 [0]: monotonic increase yields -w+i > 0
		
		i > 0 [0]: monotonic increase yields i > 0, dependencies: 1+i > 0
		
		Replacement map: {w+i >= 0 -> w+i >= 0, 1+i > 0 -> 1+i > 0, -w+i > 0 -> -w+i > 0, i > 0 -> i > 0}

Step with 29

	Trace

	19[T], 29[(w+i >= 0 /\ 1+i > 0 /\ -1+n >= 0 /\ -w+i > 0 /\ i > 0)]
	
	Blocked

	[{}, {18[T]}, {29[T]}]

Refute

	Counterexample

	[ i=6 w=5 ] 19 [ i=i w=w ] 29
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b