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
  13: [2] -> [12] : -10+i <= 0, cost: 1
   2: [3] -> [5] : -25+i == 0, cost: 1
   5: [3] -> [4] : (-25+i < 0 \/ -25+i > 0), cost: 1
   6: [4] -> [8] : -30+i <= 0, cost: 1
   9: [4] -> [10] : -30+i > 0, cost: 1
   3: [5] -> [6] : i'=30, T, cost: 1
   4: [6] -> [4] : T, cost: 1
  12: [7] -> [2] : T, cost: 1
   7: [8] -> [9] : i'=-1+i, T, cost: 1
   8: [9] -> [7] : T, cost: 1
  10: [10] -> [11] : i'=20, T, cost: 1
  11: [11] -> [7] : 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
  13: [2] -> [12] : -10+i <= 0, cost: 1
   5: [3] -> [4] : (-25+i < 0 \/ -25+i > 0), cost: 1
  15: [3] -> [4] : i'=30, -25+i == 0, cost: 1
  18: [4] -> [7] : i'=-1+i, -30+i <= 0, cost: 1
  19: [4] -> [7] : i'=20, -30+i > 0, cost: 1
  12: [7] -> [2] : T, cost: 1

	Eliminating location [5] by chaining:

	Applied chaining

	First rule:
	[3] -> [5] : -25+i == 0, cost: 1
	Second rule:
	[5] -> [6] : i'=30, T, cost: 1
	New rule:
	[3] -> [6] : i'=30, -25+i == 0, cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	[3] -> [6] : i'=30, -25+i == 0, cost: 1
	Second rule:
	[6] -> [4] : T, cost: 1
	New rule:
	[3] -> [4] : i'=30, -25+i == 0, cost: 1
	
	Applied deletion

	Removed the following rules: 4 14
	
	Eliminating location [8] by chaining:

	Applied chaining

	First rule:
	[4] -> [8] : -30+i <= 0, cost: 1
	Second rule:
	[8] -> [9] : i'=-1+i, T, cost: 1
	New rule:
	[4] -> [9] : i'=-1+i, -30+i <= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 6 7
	
	Eliminating location [10] by chaining:

	Applied chaining

	First rule:
	[4] -> [10] : -30+i > 0, cost: 1
	Second rule:
	[10] -> [11] : i'=20, T, cost: 1
	New rule:
	[4] -> [11] : i'=20, -30+i > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 9 10
	
	Eliminating location [9] by chaining:

	Applied chaining

	First rule:
	[4] -> [9] : i'=-1+i, -30+i <= 0, cost: 1
	Second rule:
	[9] -> [7] : T, cost: 1
	New rule:
	[4] -> [7] : i'=-1+i, -30+i <= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 8 16
	
	Eliminating location [11] by chaining:

	Applied chaining

	First rule:
	[4] -> [11] : i'=20, -30+i > 0, cost: 1
	Second rule:
	[11] -> [7] : T, cost: 1
	New rule:
	[4] -> [7] : i'=20, -30+i > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 11 17

Step with 0

	Trace

	0[T]
	
	Blocked

	[{}, {}]

Step with 13

	Trace

	0[T], 13[(-10+i <= 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	0[T]
	
	Blocked

	[{}, {13[T]}]

Step with 1

	Trace

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

	[{}, {13[T]}, {}]

Step with 5

	Trace

	0[T], 1[(-10+i > 0)], 5[(-25+i > 0)]
	
	Blocked

	[{}, {13[T]}, {}, {}]

Step with 18

	Trace

	0[T], 1[(-10+i > 0)], 5[(-25+i > 0)], 18[(-30+i <= 0)]
	
	Blocked

	[{}, {13[T]}, {}, {}, {}]

Step with 12

	Trace

	0[T], 1[(-10+i > 0)], 5[(-25+i > 0)], 18[(-30+i <= 0)], 12[T]
	
	Blocked

	[{}, {13[T]}, {}, {}, {}, {}]

Accelerate

Start location: [1]
Program variables: i
   0: [1] -> [2] : i'=nondet, T, cost: 1
   1: [2] -> [3] : -10+i > 0, cost: 1
  13: [2] -> [12] : -10+i <= 0, cost: 1
  20: [2] -> [2] : i'=-n+i, (30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0), cost: 1
   5: [3] -> [4] : (-25+i < 0 \/ -25+i > 0), cost: 1
  15: [3] -> [4] : i'=30, -25+i == 0, cost: 1
  18: [4] -> [7] : i'=-1+i, -30+i <= 0, cost: 1
  19: [4] -> [7] : i'=20, -30+i > 0, cost: 1
  12: [7] -> [2] : T, cost: 1

	Loop Acceleration

	Original rule:
	[2] -> [2] : i'=-1+i, (-25+i > 0 /\ -30+i <= 0 /\ -10+i > 0), cost: 1
	New rule:
	[2] -> [2] : i'=-n+i, (30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0), cost: 1

		-25+i > 0 [0]: montonic decrease yields -24-n+i > 0
		
		-25+i > 0 [1]: eventual increase yields (1 <= 0 /\ -25+i > 0)
		
		30-i >= 0 [0]: monotonic increase yields 30-i >= 0
		
		-10+i > 0 [0]: monotonic increase yields -10+i > 0, dependencies: -25+i > 0
		
		Replacement map: {-25+i > 0 -> -24-n+i > 0, 30-i >= 0 -> 30-i >= 0, -10+i > 0 -> -10+i > 0}

	Trace

	0[T], 20[(30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0)]
	
	Blocked

	[{}, {13[T]}, {20[T]}]

Step with 1

	Trace

	0[T], 20[(30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0)], 1[(-10+i > 0)]
	
	Blocked

	[{}, {13[T]}, {13[T], 20[T]}, {}]

Step with 5

	Trace

	0[T], 20[(30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0)], 1[(-10+i > 0)], 5[(-25+i > 0)]
	
	Blocked

	[{}, {13[T]}, {13[T], 20[T]}, {}, {}]

Step with 18

	Trace

	0[T], 20[(30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0)], 1[(-10+i > 0)], 5[(-25+i > 0)], 18[(-30+i <= 0)]
	
	Blocked

	[{}, {13[T]}, {13[T], 20[T]}, {}, {}, {}]

Step with 12

	Trace

	0[T], 20[(30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0)], 1[(-10+i > 0)], 5[(-25+i > 0)], 18[(-30+i <= 0)], 12[T]
	
	Blocked

	[{}, {13[T]}, {13[T], 20[T]}, {}, {}, {}, {}]

Covered

	Trace

	0[T], 20[(30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0)], 1[(-10+i > 0)], 5[(-25+i > 0)], 18[(-30+i <= 0)]
	
	Blocked

	[{}, {13[T]}, {13[T], 20[T]}, {}, {}, {12[T]}]

Backtrack

	Trace

	0[T], 20[(30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0)], 1[(-10+i > 0)], 5[(-25+i > 0)]
	
	Blocked

	[{}, {13[T]}, {13[T], 20[T]}, {}, {18[T]}]

Backtrack

	Trace

	0[T], 20[(30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0)], 1[(-10+i > 0)]
	
	Blocked

	[{}, {13[T]}, {13[T], 20[T]}, {5[-25+i > 0]}]

Step with 15

	Trace

	0[T], 20[(30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0)], 1[(-10+i > 0)], 15[(-25+i == 0)]
	
	Blocked

	[{}, {13[T]}, {13[T], 20[T]}, {5[T]}, {}]

Step with 18

	Trace

	0[T], 20[(30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0)], 1[(-10+i > 0)], 15[(-25+i == 0)], 18[(-30+i <= 0)]
	
	Blocked

	[{}, {13[T]}, {13[T], 20[T]}, {5[T]}, {}, {}]

Step with 12

	Trace

	0[T], 20[(30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0)], 1[(-10+i > 0)], 15[(-25+i == 0)], 18[(-30+i <= 0)], 12[T]
	
	Blocked

	[{}, {13[T]}, {13[T], 20[T]}, {5[T]}, {}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Nonterm

Start location: [1]
Program variables: i
   0: [1] -> [2] : i'=nondet, T, cost: 1
   1: [2] -> [3] : -10+i > 0, cost: 1
  13: [2] -> [12] : -10+i <= 0, cost: 1
  20: [2] -> [2] : i'=-n+i, (30-i >= 0 /\ -10+i > 0 /\ -1+n >= 0 /\ -24-n+i > 0), cost: 1
  21: [2] -> LoAT_sink : (-26+i >= 0 /\ 30-i >= 0 /\ -10+i > 0 /\ -1+n2 >= 0), cost: NONTERM
   5: [3] -> [4] : (-25+i < 0 \/ -25+i > 0), cost: 1
  15: [3] -> [4] : i'=30, -25+i == 0, cost: 1
  18: [4] -> [7] : i'=-1+i, -30+i <= 0, cost: 1
  19: [4] -> [7] : i'=20, -30+i > 0, cost: 1
  12: [7] -> [2] : T, cost: 1

	Certificate of Non-Termination

	Original rule:
	[2] -> [2] : i'=29, (-26+i >= 0 /\ 30-i >= 0 /\ -10+i > 0), cost: 1
	New rule:
	[2] -> LoAT_sink : (-26+i >= 0 /\ 30-i >= 0 /\ -10+i > 0 /\ -1+n2 >= 0), cost: NONTERM

		-26+i >= 0 [0]: monotonic increase yields -26+i >= 0
		
		30-i >= 0 [0]: monotonic increase yields 30-i >= 0
		
		-10+i > 0 [0]: monotonic increase yields -10+i > 0
		
		Replacement map: {-26+i >= 0 -> -26+i >= 0, 30-i >= 0 -> 30-i >= 0, -10+i > 0 -> -10+i > 0}

Step with 21

	Trace

	0[T], 21[(-26+i >= 0 /\ 30-i >= 0 /\ -10+i > 0 /\ -1+n2 >= 0)]
	
	Blocked

	[{}, {13[T]}, {21[T]}]

Refute

	Counterexample

	[ i=26 ] 0 [ i=i ] 21
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b