NO

Initial ITS

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

Chained Linear Paths

Start location: [1]
Program variables: i up
  19: [1] -> [3] : i'=nondet, up'=0, T, cost: 1
   2: [3] -> [4] : (-10+i <= 0 /\ -i <= 0), cost: 1
  18: [3] -> [16] : (-10+i > 0 \/ -i > 0), cost: 1
   6: [4] -> [5] : (-10+i < 0 \/ -10+i > 0), cost: 1
  21: [4] -> [5] : up'=0, -10+i == 0, cost: 1
  10: [5] -> [8] : (i < 0 \/ i > 0), cost: 1
  23: [5] -> [8] : up'=1, i == 0, cost: 1
  26: [8] -> [11] : i'=1+i, -1+up == 0, cost: 1
  27: [8] -> [11] : i'=-1+i, (-1+up < 0 \/ -1+up > 0), cost: 1
  17: [11] -> [3] : T, cost: 1

	Eliminating location [2] by chaining:

	Applied chaining

	First rule:
	[1] -> [2] : i'=nondet, T, cost: 1
	Second rule:
	[2] -> [3] : up'=0, T, cost: 1
	New rule:
	[1] -> [3] : i'=nondet, up'=0, T, cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	[4] -> [6] : -10+i == 0, cost: 1
	Second rule:
	[6] -> [7] : up'=0, T, cost: 1
	New rule:
	[4] -> [7] : up'=0, -10+i == 0, cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	[4] -> [7] : up'=0, -10+i == 0, cost: 1
	Second rule:
	[7] -> [5] : T, cost: 1
	New rule:
	[4] -> [5] : up'=0, -10+i == 0, cost: 1
	
	Applied deletion

	Removed the following rules: 5 20
	
	Eliminating location [9] by chaining:

	Applied chaining

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

	Removed the following rules: 7 8
	
	Eliminating location [10] by chaining:

	Applied chaining

	First rule:
	[5] -> [10] : up'=1, i == 0, cost: 1
	Second rule:
	[10] -> [8] : T, cost: 1
	New rule:
	[5] -> [8] : up'=1, i == 0, cost: 1
	
	Applied deletion

	Removed the following rules: 9 22
	
	Eliminating location [12] by chaining:

	Applied chaining

	First rule:
	[8] -> [12] : -1+up == 0, cost: 1
	Second rule:
	[12] -> [13] : i'=1+i, T, cost: 1
	New rule:
	[8] -> [13] : i'=1+i, -1+up == 0, cost: 1
	
	Applied deletion

	Removed the following rules: 11 12
	
	Eliminating location [14] by chaining:

	Applied chaining

	First rule:
	[8] -> [14] : (-1+up < 0 \/ -1+up > 0), cost: 1
	Second rule:
	[14] -> [15] : i'=-1+i, T, cost: 1
	New rule:
	[8] -> [15] : i'=-1+i, (-1+up < 0 \/ -1+up > 0), cost: 1
	
	Applied deletion

	Removed the following rules: 14 15
	
	Eliminating location [13] by chaining:

	Applied chaining

	First rule:
	[8] -> [13] : i'=1+i, -1+up == 0, cost: 1
	Second rule:
	[13] -> [11] : T, cost: 1
	New rule:
	[8] -> [11] : i'=1+i, -1+up == 0, cost: 1
	
	Applied deletion

	Removed the following rules: 13 24
	
	Eliminating location [15] by chaining:

	Applied chaining

	First rule:
	[8] -> [15] : i'=-1+i, (-1+up < 0 \/ -1+up > 0), cost: 1
	Second rule:
	[15] -> [11] : T, cost: 1
	New rule:
	[8] -> [11] : i'=-1+i, (-1+up < 0 \/ -1+up > 0), cost: 1
	
	Applied deletion

	Removed the following rules: 16 25

Step with 19

	Trace

	19[T]
	
	Blocked

	[{}, {}]

Step with 18

	Trace

	19[T], 18[(-i > 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	19[T]
	
	Blocked

	[{}, {18[-i > 0]}]

Step with 18

	Trace

	19[T], 18[(-10+i > 0)]
	
	Blocked

	[{}, {18[-i > 0]}, {}]

Backtrack

	Trace

	19[T]
	
	Blocked

	[{}, {18[(-10+i > 0 /\ -i > 0)]}]

Step with 2

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)]
	
	Blocked

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

Step with 6

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)]
	
	Blocked

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

Step with 10

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 10[(i > 0)]
	
	Blocked

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

Step with 27

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 10[(i > 0)], 27[(-1+up < 0)]
	
	Blocked

	[{}, {18[T]}, {}, {}, {26[T]}, {}]

Step with 17

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 10[(i > 0)], 27[(-1+up < 0)], 17[T]
	
	Blocked

	[{}, {18[T]}, {}, {}, {26[T]}, {}, {}]

Accelerate

Start location: [1]
Program variables: i up
  19: [1] -> [3] : i'=nondet, up'=0, T, cost: 1
   2: [3] -> [4] : (-10+i <= 0 /\ -i <= 0), cost: 1
  18: [3] -> [16] : (-10+i > 0 \/ -i > 0), cost: 1
  28: [3] -> [3] : i'=-n+i, (10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0), cost: 1
   6: [4] -> [5] : (-10+i < 0 \/ -10+i > 0), cost: 1
  21: [4] -> [5] : up'=0, -10+i == 0, cost: 1
  10: [5] -> [8] : (i < 0 \/ i > 0), cost: 1
  23: [5] -> [8] : up'=1, i == 0, cost: 1
  26: [8] -> [11] : i'=1+i, -1+up == 0, cost: 1
  27: [8] -> [11] : i'=-1+i, (-1+up < 0 \/ -1+up > 0), cost: 1
  17: [11] -> [3] : T, cost: 1

	Loop Acceleration

	Original rule:
	[3] -> [3] : i'=-1+i, (-1+up < 0 /\ -10+i < 0 /\ -10+i <= 0 /\ i > 0 /\ -i <= 0), cost: 1
	New rule:
	[3] -> [3] : i'=-n+i, (10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0), cost: 1

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

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)]
	
	Blocked

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

Step with 2

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)]
	
	Blocked

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

Step with 6

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)]
	
	Blocked

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

Step with 10

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 10[(i > 0)]
	
	Blocked

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

Step with 27

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 10[(i > 0)], 27[(-1+up < 0)]
	
	Blocked

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

Step with 17

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 10[(i > 0)], 27[(-1+up < 0)], 17[T]
	
	Blocked

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

Covered

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 10[(i > 0)], 27[(-1+up < 0)]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {}, {}, {17[T]}]

Backtrack

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 10[(i > 0)]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {}, {27[-1+up < 0]}]

Backtrack

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {10[i > 0]}]

Step with 23

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 23[(i == 0)]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {10[T]}, {}]

Step with 26

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 23[(i == 0)], 26[(-1+up == 0)]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {10[T]}, {27[T]}, {}]

Step with 17

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 23[(i == 0)], 26[(-1+up == 0)], 17[T]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {10[T]}, {27[T]}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Acceleration Failed

marked recursive suffix as redundant

Step with 2

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 23[(i == 0)], 26[(-1+up == 0)], 17[T], 2[(-10+i <= 0 /\ -i <= 0)]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {10[T]}, {27[T]}, {}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 6

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 23[(i == 0)], 26[(-1+up == 0)], 17[T], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {10[T]}, {27[T]}, {}, {}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 10

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 23[(i == 0)], 26[(-1+up == 0)], 17[T], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 10[(i > 0)]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {10[T]}, {27[T]}, {}, {}, {}, {23[T]}, {}]

Accelerate

Start location: [1]
Program variables: i up
  19: [1] -> [3] : i'=nondet, up'=0, T, cost: 1
   2: [3] -> [4] : (-10+i <= 0 /\ -i <= 0), cost: 1
  18: [3] -> [16] : (-10+i > 0 \/ -i > 0), cost: 1
  28: [3] -> [3] : i'=-n+i, (10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0), cost: 1
   6: [4] -> [5] : (-10+i < 0 \/ -10+i > 0), cost: 1
  21: [4] -> [5] : up'=0, -10+i == 0, cost: 1
  10: [5] -> [8] : (i < 0 \/ i > 0), cost: 1
  23: [5] -> [8] : up'=1, i == 0, cost: 1
  26: [8] -> [11] : i'=1+i, -1+up == 0, cost: 1
  27: [8] -> [11] : i'=-1+i, (-1+up < 0 \/ -1+up > 0), cost: 1
  29: [8] -> [8] : i'=n2+i, (10-n2-i > 0 /\ 1+i > 0 /\ 1+i >= 0 /\ 1-up >= 0 /\ -1+up >= 0 /\ -1+n2 >= 0 /\ 9-i >= 0), cost: 1
  17: [11] -> [3] : T, cost: 1

	Loop Acceleration

	Original rule:
	[8] -> [8] : i'=1+i, (-9+i < 0 /\ -9+i <= 0 /\ 1+i > 0 /\ -1-i <= 0 /\ -1+up == 0), cost: 1
	New rule:
	[8] -> [8] : i'=n2+i, (10-n2-i > 0 /\ 1+i > 0 /\ 1+i >= 0 /\ 1-up >= 0 /\ -1+up >= 0 /\ -1+n2 >= 0 /\ 9-i >= 0), cost: 1

		1+i > 0 [0]: monotonic increase yields 1+i > 0
		
		1+i >= 0 [0]: monotonic increase yields 1+i >= 0, dependencies: 1+i > 0
		
		1-up >= 0 [0]: monotonic increase yields 1-up >= 0
		
		-1+up >= 0 [0]: monotonic increase yields -1+up >= 0
		
		9-i > 0 [0]: montonic decrease yields 10-n2-i > 0
		
		9-i > 0 [1]: eventual increase yields (1 <= 0 /\ 9-i > 0)
		
		9-i >= 0 [0]: monotonic increase yields 9-i >= 0, dependencies: 9-i > 0
		
		Replacement map: {1+i > 0 -> 1+i > 0, 1+i >= 0 -> 1+i >= 0, 1-up >= 0 -> 1-up >= 0, -1+up >= 0 -> -1+up >= 0, 9-i > 0 -> 10-n2-i > 0, 9-i >= 0 -> 9-i >= 0}

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 23[(i == 0)], 29[(10-n2-i > 0 /\ 1+i > 0 /\ 1+i >= 0 /\ 1-up >= 0 /\ -1+up >= 0 /\ -1+n2 >= 0 /\ 9-i >= 0)]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {10[T]}, {27[T]}, {29[T]}]

Step with 26

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 23[(i == 0)], 29[(10-n2-i > 0 /\ 1+i > 0 /\ 1+i >= 0 /\ 1-up >= 0 /\ -1+up >= 0 /\ -1+n2 >= 0 /\ 9-i >= 0)], 26[(-1+up == 0)]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {10[T]}, {27[T]}, {29[T]}, {}]

Step with 17

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 23[(i == 0)], 29[(10-n2-i > 0 /\ 1+i > 0 /\ 1+i >= 0 /\ 1-up >= 0 /\ -1+up >= 0 /\ -1+n2 >= 0 /\ 9-i >= 0)], 26[(-1+up == 0)], 17[T]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {10[T]}, {27[T]}, {29[T]}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Acceleration Failed

marked recursive suffix as redundant

Step with 2

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 23[(i == 0)], 29[(10-n2-i > 0 /\ 1+i > 0 /\ 1+i >= 0 /\ 1-up >= 0 /\ -1+up >= 0 /\ -1+n2 >= 0 /\ 9-i >= 0)], 26[(-1+up == 0)], 17[T], 2[(-10+i <= 0 /\ -i <= 0)]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {10[T]}, {27[T]}, {29[T]}, {}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 6

	Trace

	19[T], 28[(10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0)], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)], 23[(i == 0)], 29[(10-n2-i > 0 /\ 1+i > 0 /\ 1+i >= 0 /\ 1-up >= 0 /\ -1+up >= 0 /\ -1+n2 >= 0 /\ 9-i >= 0)], 26[(-1+up == 0)], 17[T], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)]
	
	Blocked

	[{}, {18[T]}, {18[T], 28[T]}, {}, {10[T]}, {27[T]}, {29[T]}, {}, {}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Restart

Step with 19

	Trace

	19[T]
	
	Blocked

	[{}, {}]

Step with 18

	Trace

	19[T], 18[(-10+i > 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	19[T]
	
	Blocked

	[{}, {18[-10+i > 0]}]

Step with 18

	Trace

	19[T], 18[(-i > 0)]
	
	Blocked

	[{}, {18[-10+i > 0]}, {}]

Backtrack

	Trace

	19[T]
	
	Blocked

	[{}, {18[(-10+i > 0 /\ -i > 0)]}]

Step with 2

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)]
	
	Blocked

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

Step with 21

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 21[(-10+i == 0)]
	
	Blocked

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

Step with 10

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 21[(-10+i == 0)], 10[(i > 0)]
	
	Blocked

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

Step with 27

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 21[(-10+i == 0)], 10[(i > 0)], 27[(-1+up < 0)]
	
	Blocked

	[{}, {18[T]}, {}, {23[T]}, {26[T]}, {}]

Step with 17

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 21[(-10+i == 0)], 10[(i > 0)], 27[(-1+up < 0)], 17[T]
	
	Blocked

	[{}, {18[T]}, {}, {23[T]}, {26[T]}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 2

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 21[(-10+i == 0)], 10[(i > 0)], 27[(-1+up < 0)], 17[T], 2[(-10+i <= 0 /\ -i <= 0)]
	
	Blocked

	[{}, {18[T]}, {}, {23[T]}, {26[T]}, {}, {}, {}]

Acceleration Failed

marked recursive suffix as redundant

Step with 6

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 21[(-10+i == 0)], 10[(i > 0)], 27[(-1+up < 0)], 17[T], 2[(-10+i <= 0 /\ -i <= 0)], 6[(-10+i < 0)]
	
	Blocked

	[{}, {18[T]}, {}, {23[T]}, {26[T]}, {}, {}, {21[T]}, {}]

Accelerate

Start location: [1]
Program variables: i up
  19: [1] -> [3] : i'=nondet, up'=0, T, cost: 1
   2: [3] -> [4] : (-10+i <= 0 /\ -i <= 0), cost: 1
  18: [3] -> [16] : (-10+i > 0 \/ -i > 0), cost: 1
  28: [3] -> [3] : i'=-n+i, (10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0), cost: 1
   6: [4] -> [5] : (-10+i < 0 \/ -10+i > 0), cost: 1
  21: [4] -> [5] : up'=0, -10+i == 0, cost: 1
  10: [5] -> [8] : (i < 0 \/ i > 0), cost: 1
  23: [5] -> [8] : up'=1, i == 0, cost: 1
  30: [5] -> [5] : i'=-n3+i, (-n3+i >= 0 /\ 1-n3+i > 0 /\ 1-up > 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -1+n3 >= 0), cost: 1
  26: [8] -> [11] : i'=1+i, -1+up == 0, cost: 1
  27: [8] -> [11] : i'=-1+i, (-1+up < 0 \/ -1+up > 0), cost: 1
  29: [8] -> [8] : i'=n2+i, (10-n2-i > 0 /\ 1+i > 0 /\ 1+i >= 0 /\ 1-up >= 0 /\ -1+up >= 0 /\ -1+n2 >= 0 /\ 9-i >= 0), cost: 1
  17: [11] -> [3] : T, cost: 1

	Loop Acceleration

	Original rule:
	[5] -> [5] : i'=-1+i, (-11+i < 0 /\ -11+i <= 0 /\ -1+up < 0 /\ 1-i <= 0 /\ i > 0), cost: 1
	New rule:
	[5] -> [5] : i'=-n3+i, (-n3+i >= 0 /\ 1-n3+i > 0 /\ 1-up > 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -1+n3 >= 0), cost: 1

		1-up > 0 [0]: monotonic increase yields 1-up > 0
		
		11-i > 0 [0]: monotonic increase yields 11-i > 0
		
		11-i >= 0 [0]: monotonic increase yields 11-i >= 0, dependencies: 11-i > 0
		
		-1+i >= 0 [0]: montonic decrease yields -n3+i >= 0
		
		-1+i >= 0 [1]: eventual increase yields (1 <= 0 /\ -1+i >= 0)
		
		i > 0 [0]: montonic decrease yields 1-n3+i > 0
		
		i > 0 [1]: eventual increase yields (1 <= 0 /\ i > 0)
		
		Replacement map: {1-up > 0 -> 1-up > 0, 11-i > 0 -> 11-i > 0, 11-i >= 0 -> 11-i >= 0, -1+i >= 0 -> -n3+i >= 0, i > 0 -> 1-n3+i > 0}

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 21[(-10+i == 0)], 30[(-n3+i >= 0 /\ 1-n3+i > 0 /\ 1-up > 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -1+n3 >= 0)]
	
	Blocked

	[{}, {18[T]}, {}, {23[T]}, {30[T]}]

Step with 23

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 21[(-10+i == 0)], 30[(-n3+i >= 0 /\ 1-n3+i > 0 /\ 1-up > 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -1+n3 >= 0)], 23[(i == 0)]
	
	Blocked

	[{}, {18[T]}, {}, {23[T]}, {30[T]}, {}]

Step with 29

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 21[(-10+i == 0)], 30[(-n3+i >= 0 /\ 1-n3+i > 0 /\ 1-up > 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -1+n3 >= 0)], 23[(i == 0)], 29[(10-n2-i > 0 /\ 1+i > 0 /\ 1+i >= 0 /\ 1-up >= 0 /\ -1+up >= 0 /\ -1+n2 >= 0 /\ 9-i >= 0)]
	
	Blocked

	[{}, {18[T]}, {}, {23[T]}, {30[T]}, {27[T]}, {29[T]}]

Step with 26

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 21[(-10+i == 0)], 30[(-n3+i >= 0 /\ 1-n3+i > 0 /\ 1-up > 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -1+n3 >= 0)], 23[(i == 0)], 29[(10-n2-i > 0 /\ 1+i > 0 /\ 1+i >= 0 /\ 1-up >= 0 /\ -1+up >= 0 /\ -1+n2 >= 0 /\ 9-i >= 0)], 26[(-1+up == 0)]
	
	Blocked

	[{}, {18[T]}, {}, {23[T]}, {30[T]}, {27[T]}, {29[T]}, {}]

Step with 17

	Trace

	19[T], 2[(-10+i <= 0 /\ -i <= 0)], 21[(-10+i == 0)], 30[(-n3+i >= 0 /\ 1-n3+i > 0 /\ 1-up > 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -1+n3 >= 0)], 23[(i == 0)], 29[(10-n2-i > 0 /\ 1+i > 0 /\ 1+i >= 0 /\ 1-up >= 0 /\ -1+up >= 0 /\ -1+n2 >= 0 /\ 9-i >= 0)], 26[(-1+up == 0)], 17[T]
	
	Blocked

	[{}, {18[T]}, {}, {23[T]}, {30[T]}, {27[T]}, {29[T]}, {}, {}]

Nonterm

Start location: [1]
Program variables: i up
  19: [1] -> [3] : i'=nondet, up'=0, T, cost: 1
   2: [3] -> [4] : (-10+i <= 0 /\ -i <= 0), cost: 1
  18: [3] -> [16] : (-10+i > 0 \/ -i > 0), cost: 1
  28: [3] -> [3] : i'=-n+i, (10-i > 0 /\ 10-i >= 0 /\ 1-up > 0 /\ -1+n >= 0 /\ 1-n+i > 0 /\ i >= 0), cost: 1
  31: [3] -> LoAT_sink : (10-i >= 0 /\ -1+n22 >= 0 /\ -1-n22+i <= 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ 1+n22-i <= 0 /\ 10-n22 > 0 /\ -1+i >= 0 /\ i >= 0), cost: NONTERM
  32: [3] -> [3] : i'=10, up'=1, (10-i >= 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ -10+i == 0 /\ -1+i >= 0 /\ i >= 0), cost: 1
   6: [4] -> [5] : (-10+i < 0 \/ -10+i > 0), cost: 1
  21: [4] -> [5] : up'=0, -10+i == 0, cost: 1
  10: [5] -> [8] : (i < 0 \/ i > 0), cost: 1
  23: [5] -> [8] : up'=1, i == 0, cost: 1
  30: [5] -> [5] : i'=-n3+i, (-n3+i >= 0 /\ 1-n3+i > 0 /\ 1-up > 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -1+n3 >= 0), cost: 1
  26: [8] -> [11] : i'=1+i, -1+up == 0, cost: 1
  27: [8] -> [11] : i'=-1+i, (-1+up < 0 \/ -1+up > 0), cost: 1
  29: [8] -> [8] : i'=n2+i, (10-n2-i > 0 /\ 1+i > 0 /\ 1+i >= 0 /\ 1-up >= 0 /\ -1+up >= 0 /\ -1+n2 >= 0 /\ 9-i >= 0), cost: 1
  17: [11] -> [3] : T, cost: 1

	Certificate of Non-Termination

	Original rule:
	[3] -> [3] : i'=1+n22, up'=1, (-1+n22 >= 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -10+i <= 0 /\ -10+i == 0 /\ 10-n22 > 0 /\ -1+i >= 0 /\ -i <= 0), cost: 1
	New rule:
	[3] -> LoAT_sink : (10-i >= 0 /\ -1+n22 >= 0 /\ -1-n22+i <= 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ 1+n22-i <= 0 /\ 10-n22 > 0 /\ -1+i >= 0 /\ i >= 0), cost: NONTERM

		10-i >= 0 [0]: monotonic increase yields 10-i >= 0, dependencies: 10-n22 > 0
		
		10-i >= 0 [1]: montonic decrease yields 9-n22 >= 0, dependencies: 11-i > 0
		
		10-i >= 0 [2]: eventual decrease yields (10-i >= 0 /\ 9-n22 >= 0)
		
		10-i >= 0 [3]: eventual increase yields (10-i >= 0 /\ 1+n22-i <= 0)
		
		-1+n22 >= 0 [0]: monotonic increase yields -1+n22 >= 0
		
		11-i > 0 [0]: montonic decrease yields 10-n22 > 0, dependencies: 10-i >= 0
		
		11-i > 0 [1]: eventual increase yields (11-i > 0 /\ 1+n22-i <= 0)
		
		11-i >= 0 [0]: monotonic increase yields 11-i >= 0, dependencies: 10-n22 > 0
		
		11-i >= 0 [1]: montonic decrease yields 10-n22 >= 0, dependencies: 10-i >= 0
		
		11-i >= 0 [2]: eventual increase yields (11-i >= 0 /\ 1+n22-i <= 0)
		
		-10+i >= 0 [0]: eventual decrease yields (-10+i >= 0 /\ -9+n22 >= 0)
		
		-10+i >= 0 [1]: eventual increase yields (-1-n22+i <= 0 /\ -10+i >= 0)
		
		10-n22 > 0 [0]: monotonic increase yields 10-n22 > 0
		
		-1+i >= 0 [0]: monotonic increase yields -1+i >= 0, dependencies: -1+n22 >= 0
		
		i >= 0 [0]: monotonic increase yields i >= 0, dependencies: -1+n22 >= 0
		
		Replacement map: {10-i >= 0 -> 10-i >= 0, -1+n22 >= 0 -> -1+n22 >= 0, 11-i > 0 -> (11-i > 0 /\ 1+n22-i <= 0), 11-i >= 0 -> 11-i >= 0, -10+i >= 0 -> (-1-n22+i <= 0 /\ -10+i >= 0), 10-n22 > 0 -> 10-n22 > 0, -1+i >= 0 -> -1+i >= 0, i >= 0 -> i >= 0}

	Loop Acceleration

	Original rule:
	[3] -> [3] : i'=1+n22, up'=1, (-1+n22 >= 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -10+i <= 0 /\ -10+i == 0 /\ 10-n22 > 0 /\ -1+i >= 0 /\ -i <= 0), cost: 1
	New rule:
	[3] -> [3] : i'=1+n22, up'=1, (-1+n4 >= 0 /\ 10-i >= 0 /\ -1+n22 >= 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ -9+n22 >= 0 /\ 10-n22 > 0 /\ -1+i >= 0 /\ i >= 0), cost: 1

		10-i >= 0 [0]: monotonic increase yields 10-i >= 0, dependencies: 10-n22 > 0
		
		10-i >= 0 [1]: montonic decrease yields 9-n22 >= 0, dependencies: 11-i > 0
		
		10-i >= 0 [2]: eventual decrease yields (10-i >= 0 /\ 9-n22 >= 0)
		
		10-i >= 0 [3]: eventual increase yields (10-i >= 0 /\ 1+n22-i <= 0)
		
		-1+n22 >= 0 [0]: monotonic increase yields -1+n22 >= 0
		
		11-i > 0 [0]: montonic decrease yields 10-n22 > 0, dependencies: 10-i >= 0
		
		11-i > 0 [1]: eventual increase yields (11-i > 0 /\ 1+n22-i <= 0)
		
		11-i >= 0 [0]: monotonic increase yields 11-i >= 0, dependencies: 10-n22 > 0
		
		11-i >= 0 [1]: montonic decrease yields 10-n22 >= 0, dependencies: 10-i >= 0
		
		11-i >= 0 [2]: eventual increase yields (11-i >= 0 /\ 1+n22-i <= 0)
		
		-10+i >= 0 [0]: eventual decrease yields (-10+i >= 0 /\ -9+n22 >= 0)
		
		-10+i >= 0 [1]: eventual increase yields (-1-n22+i <= 0 /\ -10+i >= 0)
		
		10-n22 > 0 [0]: monotonic increase yields 10-n22 > 0
		
		-1+i >= 0 [0]: monotonic increase yields -1+i >= 0, dependencies: -1+n22 >= 0
		
		i >= 0 [0]: monotonic increase yields i >= 0, dependencies: -1+n22 >= 0
		
		Replacement map: {10-i >= 0 -> 10-i >= 0, -1+n22 >= 0 -> -1+n22 >= 0, 11-i > 0 -> 10-n22 > 0, 11-i >= 0 -> 11-i >= 0, -10+i >= 0 -> (-10+i >= 0 /\ -9+n22 >= 0), 10-n22 > 0 -> 10-n22 > 0, -1+i >= 0 -> -1+i >= 0, i >= 0 -> i >= 0}

	made implied equalities explicit

	Original rule:
	[3] -> [3] : i'=1+n22, up'=1, (-1+n4 >= 0 /\ 10-i >= 0 /\ -1+n22 >= 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ -9+n22 >= 0 /\ 10-n22 > 0 /\ -1+i >= 0 /\ i >= 0), cost: 1
	New rule:
	[3] -> [3] : i'=1+n22, up'=1, (-1+n4 >= 0 /\ 10-i >= 0 /\ -1+n22 >= 0 /\ 9-n22 == 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ -10+i == 0 /\ -9+n22 >= 0 /\ 10-n22 > 0 /\ -1+i >= 0 /\ i >= 0), cost: 1
	
	Propagated Equalities

	Original rule:
	[3] -> [3] : i'=1+n22, up'=1, (-1+n4 >= 0 /\ 10-i >= 0 /\ -1+n22 >= 0 /\ 9-n22 == 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ -10+i == 0 /\ -9+n22 >= 0 /\ 10-n22 > 0 /\ -1+i >= 0 /\ i >= 0), cost: 1
	New rule:
	[3] -> [3] : i'=10, up'=1, (0 >= 0 /\ 0 == 0 /\ 8 >= 0 /\ 1 > 0 /\ -1+n4 >= 0 /\ 10-i >= 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ -10+i == 0 /\ -1+i >= 0 /\ i >= 0), cost: 1
	
		propagated equality n22 = 9
		
	Simplified Guard

	Original rule:
	[3] -> [3] : i'=10, up'=1, (0 >= 0 /\ 0 == 0 /\ 8 >= 0 /\ 1 > 0 /\ -1+n4 >= 0 /\ 10-i >= 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ -10+i == 0 /\ -1+i >= 0 /\ i >= 0), cost: 1
	New rule:
	[3] -> [3] : i'=10, up'=1, (-1+n4 >= 0 /\ 10-i >= 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ -10+i == 0 /\ -1+i >= 0 /\ i >= 0), cost: 1
	
	Eliminated Temporary Variables via Transitive Closure

	Original rule:
	[3] -> [3] : i'=10, up'=1, (-1+n4 >= 0 /\ 10-i >= 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ -10+i == 0 /\ -1+i >= 0 /\ i >= 0), cost: 1
	New rule:
	[3] -> [3] : i'=10, up'=1, (10-i >= 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ -10+i == 0 /\ -1+i >= 0 /\ i >= 0), cost: 1

Step with 31

	Trace

	19[T], 31[(10-i >= 0 /\ -1+n22 >= 0 /\ -1-n22+i <= 0 /\ 11-i > 0 /\ 11-i >= 0 /\ -10+i >= 0 /\ 1+n22-i <= 0 /\ 10-n22 > 0 /\ -1+i >= 0 /\ i >= 0)]
	
	Blocked

	[{}, {18[T]}, {31[T]}]

Refute

	Counterexample

	[ i=10 up=0 ] 19 [ i=i up=up ] 31
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b