unknown

Initial ITS

Start location: [1]
Program variables: i j k n
   0: [1] -> [2] : k'=nondet, T, cost: 1
   1: [2] -> [3] : i'=nondet1, T, cost: 1
   2: [3] -> [4] : j'=nondet2, T, cost: 1
   3: [4] -> [5] : n'=nondet3, T, cost: 1
   4: [5] -> [7] : -1+k >= 0, cost: 1
  16: [5] -> [6] : -1+k < 0, cost: 1
   5: [7] -> [8] : i'=0, T, cost: 1
   6: [8] -> [9] : -n+i < 0, cost: 1
  14: [8] -> [15] : -n+i >= 0, cost: 1
   7: [9] -> [10] : j'=0, T, cost: 1
   8: [10] -> [11] : j-i <= 0, cost: 1
  11: [10] -> [13] : j-i > 0, cost: 1
   9: [11] -> [12] : j'=j+k, T, cost: 1
  10: [12] -> [10] : T, cost: 1
  12: [13] -> [14] : i'=1+i, T, cost: 1
  13: [14] -> [8] : T, cost: 1
  15: [15] -> [6] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: i j k n
  19: [1] -> [5] : i'=nondet1, j'=nondet2, k'=nondet, n'=nondet3, T, cost: 1
  16: [5] -> [6] : -1+k < 0, cost: 1
  20: [5] -> [8] : i'=0, -1+k >= 0, cost: 1
  21: [8] -> [10] : j'=0, -n+i < 0, cost: 1
  22: [8] -> [6] : -n+i >= 0, cost: 1
  25: [10] -> [10] : j'=j+k, j-i <= 0, cost: 1
  26: [10] -> [8] : i'=1+i, j-i > 0, cost: 1

	Eliminating location [2] by chaining:

	Applied chaining

	First rule:
	[1] -> [2] : k'=nondet, T, cost: 1
	Second rule:
	[2] -> [3] : i'=nondet1, T, cost: 1
	New rule:
	[1] -> [3] : i'=nondet1, k'=nondet, T, cost: 1
	
	Applied deletion

	Removed the following rules: 0 1
	
	Eliminating location [3] by chaining:

	Applied chaining

	First rule:
	[1] -> [3] : i'=nondet1, k'=nondet, T, cost: 1
	Second rule:
	[3] -> [4] : j'=nondet2, T, cost: 1
	New rule:
	[1] -> [4] : i'=nondet1, j'=nondet2, k'=nondet, T, cost: 1
	
	Applied deletion

	Removed the following rules: 2 17
	
	Eliminating location [4] by chaining:

	Applied chaining

	First rule:
	[1] -> [4] : i'=nondet1, j'=nondet2, k'=nondet, T, cost: 1
	Second rule:
	[4] -> [5] : n'=nondet3, T, cost: 1
	New rule:
	[1] -> [5] : i'=nondet1, j'=nondet2, k'=nondet, n'=nondet3, T, cost: 1
	
	Applied deletion

	Removed the following rules: 3 18
	
	Eliminating location [7] by chaining:

	Applied chaining

	First rule:
	[5] -> [7] : -1+k >= 0, cost: 1
	Second rule:
	[7] -> [8] : i'=0, T, cost: 1
	New rule:
	[5] -> [8] : i'=0, -1+k >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 4 5
	
	Eliminating location [9] by chaining:

	Applied chaining

	First rule:
	[8] -> [9] : -n+i < 0, cost: 1
	Second rule:
	[9] -> [10] : j'=0, T, cost: 1
	New rule:
	[8] -> [10] : j'=0, -n+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 6 7
	
	Eliminating location [15] by chaining:

	Applied chaining

	First rule:
	[8] -> [15] : -n+i >= 0, cost: 1
	Second rule:
	[15] -> [6] : T, cost: 1
	New rule:
	[8] -> [6] : -n+i >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 14 15
	
	Eliminating location [11] by chaining:

	Applied chaining

	First rule:
	[10] -> [11] : j-i <= 0, cost: 1
	Second rule:
	[11] -> [12] : j'=j+k, T, cost: 1
	New rule:
	[10] -> [12] : j'=j+k, j-i <= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 8 9
	
	Eliminating location [13] by chaining:

	Applied chaining

	First rule:
	[10] -> [13] : j-i > 0, cost: 1
	Second rule:
	[13] -> [14] : i'=1+i, T, cost: 1
	New rule:
	[10] -> [14] : i'=1+i, j-i > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 11 12
	
	Eliminating location [12] by chaining:

	Applied chaining

	First rule:
	[10] -> [12] : j'=j+k, j-i <= 0, cost: 1
	Second rule:
	[12] -> [10] : T, cost: 1
	New rule:
	[10] -> [10] : j'=j+k, j-i <= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 10 23
	
	Eliminating location [14] by chaining:

	Applied chaining

	First rule:
	[10] -> [14] : i'=1+i, j-i > 0, cost: 1
	Second rule:
	[14] -> [8] : T, cost: 1
	New rule:
	[10] -> [8] : i'=1+i, j-i > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 13 24

Step with 19

	Trace

	19[T]
	
	Blocked

	[{}, {}]

Step with 16

	Trace

	19[T], 16[(-1+k < 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	19[T]
	
	Blocked

	[{}, {16[T]}]

Step with 20

	Trace

	19[T], 20[(-1+k >= 0)]
	
	Blocked

	[{}, {16[T]}, {}]

Step with 22

	Trace

	19[T], 20[(-1+k >= 0)], 22[(-n+i >= 0)]
	
	Blocked

	[{}, {16[T]}, {}, {}]

Backtrack

	Trace

	19[T], 20[(-1+k >= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}]

Step with 21

	Trace

	19[T], 20[(-1+k >= 0)], 21[(-n+i < 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {}]

Step with 25

	Trace

	19[T], 20[(-1+k >= 0)], 21[(-n+i < 0)], 25[(j-i <= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {}, {}]

Accelerate

Start location: [1]
Program variables: i j k n
  19: [1] -> [5] : i'=nondet1, j'=nondet2, k'=nondet, n'=nondet3, T, cost: 1
  16: [5] -> [6] : -1+k < 0, cost: 1
  20: [5] -> [8] : i'=0, -1+k >= 0, cost: 1
  21: [8] -> [10] : j'=0, -n+i < 0, cost: 1
  22: [8] -> [6] : -n+i >= 0, cost: 1
  25: [10] -> [10] : j'=j+k, j-i <= 0, cost: 1
  26: [10] -> [8] : i'=1+i, j-i > 0, cost: 1
  27: [10] -> LoAT_sink : (-j+i >= 0 /\ k <= 0), cost: NONTERM
  28: [10] -> [10] : j'=n7*k+j, (-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0), cost: 1

	Certificate of Non-Termination

	Original rule:
	[10] -> [10] : j'=j+k, (j-i <= 0), cost: 1
	New rule:
	[10] -> LoAT_sink : (-j+i >= 0 /\ k <= 0), cost: NONTERM

		-j+i >= 0 [0]: eventual decrease yields (-(-1+n7)*k-j+i >= 0 /\ -j+i >= 0)
		
		-j+i >= 0 [1]: eventual increase yields (-j+i >= 0 /\ k <= 0)
		
		Replacement map: {-j+i >= 0 -> (-j+i >= 0 /\ k <= 0)}

	Loop Acceleration

	Original rule:
	[10] -> [10] : j'=j+k, (j-i <= 0), cost: 1
	New rule:
	[10] -> [10] : j'=n7*k+j, (-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0), cost: 1

		-j+i >= 0 [0]: eventual decrease yields (-(-1+n7)*k-j+i >= 0 /\ -j+i >= 0)
		
		-j+i >= 0 [1]: eventual increase yields (-j+i >= 0 /\ k <= 0)
		
		Replacement map: {-j+i >= 0 -> (-(-1+n7)*k-j+i >= 0 /\ -j+i >= 0)}

	Trace

	19[T], 20[(-1+k >= 0)], 21[(-n+i < 0)], 28[(-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {}, {25[T], 28[T]}]

Step with 26

	Trace

	19[T], 20[(-1+k >= 0)], 21[(-n+i < 0)], 28[(-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0)], 26[(j-i > 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {}, {25[T], 27[T], 28[T]}, {}]

Accelerate

Start location: [1]
Program variables: i j k n
  19: [1] -> [5] : i'=nondet1, j'=nondet2, k'=nondet, n'=nondet3, T, cost: 1
  16: [5] -> [6] : -1+k < 0, cost: 1
  20: [5] -> [8] : i'=0, -1+k >= 0, cost: 1
  21: [8] -> [10] : j'=0, -n+i < 0, cost: 1
  22: [8] -> [6] : -n+i >= 0, cost: 1
  29: [8] -> [8] : i'=n10+i, j'=n71*k, (1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0), cost: 1
  25: [10] -> [10] : j'=j+k, j-i <= 0, cost: 1
  26: [10] -> [8] : i'=1+i, j-i > 0, cost: 1
  27: [10] -> LoAT_sink : (-j+i >= 0 /\ k <= 0), cost: NONTERM
  28: [10] -> [10] : j'=n7*k+j, (-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0), cost: 1

	Loop Acceleration

	Original rule:
	[8] -> [8] : i'=1+i, j'=n71*k, (n71*k-i > 0 /\ -n+i < 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0), cost: 1
	New rule:
	[8] -> [8] : i'=n10+i, j'=n71*k, (1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0), cost: 1

		n-i > 0 [0]: montonic decrease yields 1+n-n10-i > 0
		
		n-i > 0 [1]: eventual increase yields (1 <= 0 /\ n-i > 0)
		
		n71*k-i > 0 [0]: montonic decrease yields 1+n71*k-n10-i > 0
		
		n71*k-i > 0 [1]: eventual increase yields (1 <= 0 /\ n71*k-i > 0)
		
		-(-1+n71)*k+i >= 0 [0]: monotonic increase yields -(-1+n71)*k+i >= 0
		
		-1+n71 >= 0 [0]: monotonic increase yields -1+n71 >= 0
		
		i >= 0 [0]: monotonic increase yields i >= 0
		
		Replacement map: {n-i > 0 -> 1+n-n10-i > 0, n71*k-i > 0 -> 1+n71*k-n10-i > 0, -(-1+n71)*k+i >= 0 -> -(-1+n71)*k+i >= 0, -1+n71 >= 0 -> -1+n71 >= 0, i >= 0 -> i >= 0}

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {29[T]}]

Step with 22

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)], 22[(-n+i >= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {29[T]}, {}]

Backtrack

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {22[T], 29[T]}]

Step with 21

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)], 21[(-n+i < 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {22[T], 29[T]}, {}]

Step with 28

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)], 21[(-n+i < 0)], 28[(-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {22[T], 29[T]}, {26[T], 27[T]}, {28[T]}]

Step with 25

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)], 21[(-n+i < 0)], 28[(-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0)], 25[(j-i <= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {22[T], 29[T]}, {26[T], 27[T]}, {27[T], 28[T]}, {}]

Covered

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)], 21[(-n+i < 0)], 28[(-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {22[T], 29[T]}, {26[T], 27[T]}, {25[T], 27[T], 28[T]}]

Step with 26

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)], 21[(-n+i < 0)], 28[(-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0)], 26[(j-i > 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {22[T], 29[T]}, {26[T], 27[T]}, {25[T], 27[T], 28[T]}, {}]

Covered

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)], 21[(-n+i < 0)], 28[(-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {22[T], 29[T]}, {26[T], 27[T]}, {25[T], 26[T], 27[T], 28[T]}]

Backtrack

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)], 21[(-n+i < 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {22[T], 29[T]}, {26[T], 27[T], 28[T]}]

Step with 25

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)], 21[(-n+i < 0)], 25[(j-i <= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {22[T], 29[T]}, {26[T], 27[T], 28[T]}, {}]

Covered

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)], 21[(-n+i < 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {22[T], 29[T]}, {25[T], 26[T], 27[T], 28[T]}]

Backtrack

	Trace

	19[T], 20[(-1+k >= 0)], 29[(1+n71*k-n10-i > 0 /\ 1+n-n10-i > 0 /\ -1+n10 >= 0 /\ -(-1+n71)*k+i >= 0 /\ -1+n71 >= 0 /\ i >= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T]}, {21[T], 22[T], 29[T]}]

Backtrack

	Trace

	19[T], 20[(-1+k >= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T], 29[T]}]

Step with 21

	Trace

	19[T], 20[(-1+k >= 0)], 21[(-n+i < 0)]
	
	Blocked

	[{}, {16[T]}, {22[T], 29[T]}, {}]

Step with 25

	Trace

	19[T], 20[(-1+k >= 0)], 21[(-n+i < 0)], 25[(j-i <= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T], 29[T]}, {27[T]}, {}]

Covered

	Trace

	19[T], 20[(-1+k >= 0)], 21[(-n+i < 0)]
	
	Blocked

	[{}, {16[T]}, {22[T], 29[T]}, {25[T], 27[T]}]

Step with 28

	Trace

	19[T], 20[(-1+k >= 0)], 21[(-n+i < 0)], 28[(-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T], 29[T]}, {25[T], 26[T], 27[T]}, {28[T]}]

Step with 26

	Trace

	19[T], 20[(-1+k >= 0)], 21[(-n+i < 0)], 28[(-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0)], 26[(j-i > 0)]
	
	Blocked

	[{}, {16[T]}, {22[T], 29[T]}, {25[T], 26[T], 27[T]}, {25[T], 27[T], 28[T]}, {}]

Covered

	Trace

	19[T], 20[(-1+k >= 0)], 21[(-n+i < 0)], 28[(-(-1+n7)*k-j+i >= 0 /\ -1+n7 >= 0 /\ -j+i >= 0)]
	
	Blocked

	[{}, {16[T]}, {22[T], 29[T]}, {25[T], 26[T], 27[T]}, {25[T], 26[T], 27[T], 28[T]}]

Backtrack

	Trace

	19[T], 20[(-1+k >= 0)], 21[(-n+i < 0)]
	
	Blocked

	[{}, {16[T]}, {22[T], 29[T]}, {25[T], 26[T], 27[T], 28[T]}]

Backtrack

	Trace

	19[T], 20[(-1+k >= 0)]
	
	Blocked

	[{}, {16[T]}, {21[T], 22[T], 29[T]}]

Backtrack

	Trace

	19[T]
	
	Blocked

	[{}, {16[T], 20[T]}]

Backtrack

	Trace

	Blocked

	[{19[T]}]

Accept

unknown

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b