NO

Initial ITS

Start location: [1]
Program variables: i j t
   0: [1] -> [2] : i'=nondet, T, cost: 1
   1: [2] -> [3] : j'=nondet1, T, cost: 1
   2: [3] -> [4] : t'=0, T, cost: 1
   3: [4] -> [5] : (j > 0 /\ i > 0), cost: 1
  18: [4] -> [17] : (j <= 0 \/ i <= 0), cost: 1
   4: [5] -> [7] : -j+i < 0, cost: 1
   9: [5] -> [11] : -j+i >= 0, cost: 1
  17: [6] -> [4] : T, cost: 1
   5: [7] -> [8] : t'=i, T, cost: 1
   6: [8] -> [9] : i'=j, T, cost: 1
   7: [9] -> [10] : j'=t, T, cost: 1
   8: [10] -> [6] : T, cost: 1
  10: [11] -> [13] : -j+i > 0, cost: 1
  13: [11] -> [15] : -j+i <= 0, cost: 1
  16: [12] -> [6] : T, cost: 1
  11: [13] -> [14] : j'=i, T, cost: 1
  12: [14] -> [12] : T, cost: 1
  14: [15] -> [16] : i'=-1+i, T, cost: 1
  15: [16] -> [12] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: i j t
  20: [1] -> [4] : i'=nondet, j'=nondet1, t'=0, T, cost: 1
   3: [4] -> [5] : (j > 0 /\ i > 0), cost: 1
  18: [4] -> [17] : (j <= 0 \/ i <= 0), cost: 1
   9: [5] -> [11] : -j+i >= 0, cost: 1
  24: [5] -> [6] : i'=j, j'=i, t'=i, -j+i < 0, cost: 1
  17: [6] -> [4] : T, cost: 1
  27: [11] -> [12] : j'=i, -j+i > 0, cost: 1
  28: [11] -> [12] : i'=-1+i, -j+i <= 0, cost: 1
  16: [12] -> [6] : T, cost: 1

	Eliminating location [2] by chaining:

	Applied chaining

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

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

	Applied chaining

	First rule:
	[1] -> [3] : i'=nondet, j'=nondet1, T, cost: 1
	Second rule:
	[3] -> [4] : t'=0, T, cost: 1
	New rule:
	[1] -> [4] : i'=nondet, j'=nondet1, t'=0, T, cost: 1
	
	Applied deletion

	Removed the following rules: 2 19
	
	Eliminating location [7] by chaining:

	Applied chaining

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

	Removed the following rules: 4 5
	
	Eliminating location [8] by chaining:

	Applied chaining

	First rule:
	[5] -> [8] : t'=i, -j+i < 0, cost: 1
	Second rule:
	[8] -> [9] : i'=j, T, cost: 1
	New rule:
	[5] -> [9] : i'=j, t'=i, -j+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 6 21
	
	Eliminating location [9] by chaining:

	Applied chaining

	First rule:
	[5] -> [9] : i'=j, t'=i, -j+i < 0, cost: 1
	Second rule:
	[9] -> [10] : j'=t, T, cost: 1
	New rule:
	[5] -> [10] : i'=j, j'=i, t'=i, -j+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 7 22
	
	Eliminating location [10] by chaining:

	Applied chaining

	First rule:
	[5] -> [10] : i'=j, j'=i, t'=i, -j+i < 0, cost: 1
	Second rule:
	[10] -> [6] : T, cost: 1
	New rule:
	[5] -> [6] : i'=j, j'=i, t'=i, -j+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 8 23
	
	Eliminating location [13] by chaining:

	Applied chaining

	First rule:
	[11] -> [13] : -j+i > 0, cost: 1
	Second rule:
	[13] -> [14] : j'=i, T, cost: 1
	New rule:
	[11] -> [14] : j'=i, -j+i > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 10 11
	
	Eliminating location [15] by chaining:

	Applied chaining

	First rule:
	[11] -> [15] : -j+i <= 0, cost: 1
	Second rule:
	[15] -> [16] : i'=-1+i, T, cost: 1
	New rule:
	[11] -> [16] : i'=-1+i, -j+i <= 0, cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	[11] -> [14] : j'=i, -j+i > 0, cost: 1
	Second rule:
	[14] -> [12] : T, cost: 1
	New rule:
	[11] -> [12] : j'=i, -j+i > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 12 25
	
	Eliminating location [16] by chaining:

	Applied chaining

	First rule:
	[11] -> [16] : i'=-1+i, -j+i <= 0, cost: 1
	Second rule:
	[16] -> [12] : T, cost: 1
	New rule:
	[11] -> [12] : i'=-1+i, -j+i <= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 15 26

Step with 20

	Trace

	20[T]
	
	Blocked

	[{}, {}]

Step with 18

	Trace

	20[T], 18[(j <= 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	20[T]
	
	Blocked

	[{}, {18[j <= 0]}]

Step with 18

	Trace

	20[T], 18[(i <= 0)]
	
	Blocked

	[{}, {18[j <= 0]}, {}]

Backtrack

	Trace

	20[T]
	
	Blocked

	[{}, {18[(j <= 0 /\ i <= 0)]}]

Step with 3

	Trace

	20[T], 3[(j > 0 /\ i > 0)]
	
	Blocked

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

Step with 9

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)]
	
	Blocked

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

Step with 27

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)]
	
	Blocked

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

Step with 16

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T]
	
	Blocked

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

Step with 17

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Step with 3

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Step with 9

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Step with 28

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 28[(-j+i <= 0)]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Step with 16

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 28[(-j+i <= 0)], 16[T]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Step with 17

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 28[(-j+i <= 0)], 16[T], 17[T]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Acceleration Failed

marked recursive suffix as redundant

Step with 3

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 28[(-j+i <= 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Acceleration Failed

marked recursive suffix as redundant

Step with 24

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 28[(-j+i <= 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {}, {}, {}, {27[T]}, {}, {}, {}, {9[T]}, {}]

Acceleration Failed

marked recursive suffix as redundant

Restart

Step with 20

	Trace

	20[T]
	
	Blocked

	[{}, {}]

Step with 18

	Trace

	20[T], 18[(j <= 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	20[T]
	
	Blocked

	[{}, {18[j <= 0]}]

Step with 18

	Trace

	20[T], 18[(i <= 0)]
	
	Blocked

	[{}, {18[j <= 0]}, {}]

Backtrack

	Trace

	20[T]
	
	Blocked

	[{}, {18[(j <= 0 /\ i <= 0)]}]

Step with 3

	Trace

	20[T], 3[(j > 0 /\ i > 0)]
	
	Blocked

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

Step with 24

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)]
	
	Blocked

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

Step with 17

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)], 17[T]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Step with 3

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)], 17[T], 3[(j > 0 /\ i > 0)]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Step with 9

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {24[T]}, {}]

Step with 27

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {24[T]}, {28[T]}, {}]

Step with 16

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {24[T]}, {28[T]}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 17

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {24[T]}, {28[T]}, {}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 3

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {24[T]}, {28[T]}, {}, {}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 9

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {24[T]}, {28[T]}, {}, {}, {}, {}, {}]

Step with 28

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 28[(-j+i <= 0)]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {24[T]}, {28[T]}, {}, {}, {}, {}, {27[T]}, {}]

Step with 16

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 28[(-j+i <= 0)], 16[T]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {24[T]}, {28[T]}, {}, {}, {}, {}, {27[T]}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 17

	Trace

	20[T], 3[(j > 0 /\ i > 0)], 24[(-j+i < 0)], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 27[(-j+i > 0)], 16[T], 17[T], 3[(j > 0 /\ i > 0)], 9[(-j+i >= 0)], 28[(-j+i <= 0)], 16[T], 17[T]
	
	Blocked

	[{}, {18[T]}, {}, {}, {}, {24[T]}, {28[T]}, {}, {}, {}, {}, {27[T]}, {}, {}, {}]

Nonterm

Start location: [1]
Program variables: i j t
  20: [1] -> [4] : i'=nondet, j'=nondet1, t'=0, T, cost: 1
   3: [4] -> [5] : (j > 0 /\ i > 0), cost: 1
  18: [4] -> [17] : (j <= 0 \/ i <= 0), cost: 1
  29: [4] -> LoAT_sink : (1 > 0 /\ 1 >= 0 /\ j-i > 0 /\ j-i >= 0 /\ -1+n >= 0 /\ -1+j > 0 /\ j > 0 /\ i > 0), cost: NONTERM
  30: [4] -> [4] : i'=-1+j, t'=-1+j, (j-i > 0 /\ j-i >= 0 /\ -1+j > 0 /\ j > 0 /\ i > 0), cost: 1
   9: [5] -> [11] : -j+i >= 0, cost: 1
  24: [5] -> [6] : i'=j, j'=i, t'=i, -j+i < 0, cost: 1
  17: [6] -> [4] : T, cost: 1
  27: [11] -> [12] : j'=i, -j+i > 0, cost: 1
  28: [11] -> [12] : i'=-1+i, -j+i <= 0, cost: 1
  16: [12] -> [6] : T, cost: 1

	unrolling

	Original rule:
	[4] -> [4] : i'=-1+j, t'=i, (j-i > 0 /\ j-i >= 0 /\ -j+i < 0 /\ j > 0 /\ i > 0), cost: 1
	New rule:
	[4] -> [4] : i'=-1+j, t'=-1+j, (1 > 0 /\ 1 >= 0 /\ j-i > 0 /\ j-i >= 0 /\ -j+i < 0 /\ -1 < 0 /\ -1+j > 0 /\ j > 0 /\ i > 0), cost: 1
	
	Certificate of Non-Termination

	Original rule:
	[4] -> [4] : i'=-1+j, t'=-1+j, (1 > 0 /\ 1 >= 0 /\ j-i > 0 /\ j-i >= 0 /\ -j+i < 0 /\ -1 < 0 /\ -1+j > 0 /\ j > 0 /\ i > 0), cost: 1
	New rule:
	[4] -> LoAT_sink : (1 > 0 /\ 1 >= 0 /\ j-i > 0 /\ j-i >= 0 /\ -1+n >= 0 /\ -1+j > 0 /\ j > 0 /\ i > 0), cost: NONTERM

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

	Loop Acceleration

	Original rule:
	[4] -> [4] : i'=-1+j, t'=-1+j, (1 > 0 /\ 1 >= 0 /\ j-i > 0 /\ j-i >= 0 /\ -j+i < 0 /\ -1 < 0 /\ -1+j > 0 /\ j > 0 /\ i > 0), cost: 1
	New rule:
	[4] -> [4] : i'=-1+j, t'=-1+j, (1 > 0 /\ 1 >= 0 /\ j-i > 0 /\ j-i >= 0 /\ -1+n >= 0 /\ -1+j > 0 /\ j > 0 /\ i > 0), cost: 1

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

	Simplified Guard

	Original rule:
	[4] -> [4] : i'=-1+j, t'=-1+j, (1 > 0 /\ 1 >= 0 /\ j-i > 0 /\ j-i >= 0 /\ -1+n >= 0 /\ -1+j > 0 /\ j > 0 /\ i > 0), cost: 1
	New rule:
	[4] -> [4] : i'=-1+j, t'=-1+j, (j-i > 0 /\ j-i >= 0 /\ -1+n >= 0 /\ -1+j > 0 /\ j > 0 /\ i > 0), cost: 1
	
	Eliminated Temporary Variables via Transitive Closure

	Original rule:
	[4] -> [4] : i'=-1+j, t'=-1+j, (j-i > 0 /\ j-i >= 0 /\ -1+n >= 0 /\ -1+j > 0 /\ j > 0 /\ i > 0), cost: 1
	New rule:
	[4] -> [4] : i'=-1+j, t'=-1+j, (j-i > 0 /\ j-i >= 0 /\ -1+j > 0 /\ j > 0 /\ i > 0), cost: 1

Step with 29

	Trace

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

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

Refute

	Counterexample

	[ i=1 j=2 t=0 ] 20 [ i=i j=j t=t ] 29
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b