NO

Initial ITS

Start location: [1]
Program variables: a b i j k l m
   0: [1] -> [2] : i'=0, T, cost: 1
   1: [2] -> [3] : -100+i < 0, cost: 1
  26: [2] -> [23] : -100+i >= 0, cost: 1
   2: [3] -> [4] : a'=2+i, T, cost: 1
   3: [4] -> [5] : j'=0, T, cost: 1
   4: [5] -> [6] : -a+j < 0, cost: 1
  23: [5] -> [21] : -a+j >= 0, cost: 1
   5: [6] -> [7] : k'=3+j+i, T, cost: 1
   6: [7] -> [8] : k >= 0, cost: 1
  20: [7] -> [19] : k < 0, cost: 1
   7: [8] -> [9] : b'=4+j+i+k, T, cost: 1
   8: [9] -> [10] : l'=0, T, cost: 1
   9: [10] -> [11] : -b+l < 0, cost: 1
  17: [10] -> [17] : -b+l >= 0, cost: 1
  10: [11] -> [12] : m'=1000+l+j+i+k, T, cost: 1
  11: [12] -> [13] : m >= 0, cost: 1
  14: [12] -> [15] : m < 0, cost: 1
  12: [13] -> [14] : m'=m, T, cost: 1
  13: [14] -> [12] : T, cost: 1
  15: [15] -> [16] : l'=1+l, T, cost: 1
  16: [16] -> [10] : T, cost: 1
  18: [17] -> [18] : k'=-1+k, T, cost: 1
  19: [18] -> [7] : T, cost: 1
  21: [19] -> [20] : j'=1+j, T, cost: 1
  22: [20] -> [5] : T, cost: 1
  24: [21] -> [22] : i'=1+i, T, cost: 1
  25: [22] -> [2] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: a b i j k l m
   0: [1] -> [2] : i'=0, T, cost: 1
  26: [2] -> [23] : -100+i >= 0, cost: 1
  28: [2] -> [5] : a'=2+i, j'=0, -100+i < 0, cost: 1
  29: [5] -> [7] : k'=3+j+i, -a+j < 0, cost: 1
  31: [5] -> [2] : i'=1+i, -a+j >= 0, cost: 1
  34: [7] -> [10] : b'=4+j+i+k, l'=0, k >= 0, cost: 1
  35: [7] -> [5] : j'=1+j, k < 0, cost: 1
  36: [10] -> [12] : m'=1000+l+j+i+k, -b+l < 0, cost: 1
  38: [10] -> [7] : k'=-1+k, -b+l >= 0, cost: 1
  41: [12] -> [12] : m'=m, m >= 0, cost: 1
  42: [12] -> [10] : l'=1+l, m < 0, cost: 1

	Eliminating location [3] by chaining:

	Applied chaining

	First rule:
	[2] -> [3] : -100+i < 0, cost: 1
	Second rule:
	[3] -> [4] : a'=2+i, T, cost: 1
	New rule:
	[2] -> [4] : a'=2+i, -100+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 1 2
	
	Eliminating location [4] by chaining:

	Applied chaining

	First rule:
	[2] -> [4] : a'=2+i, -100+i < 0, cost: 1
	Second rule:
	[4] -> [5] : j'=0, T, cost: 1
	New rule:
	[2] -> [5] : a'=2+i, j'=0, -100+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 3 27
	
	Eliminating location [6] by chaining:

	Applied chaining

	First rule:
	[5] -> [6] : -a+j < 0, cost: 1
	Second rule:
	[6] -> [7] : k'=3+j+i, T, cost: 1
	New rule:
	[5] -> [7] : k'=3+j+i, -a+j < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 4 5
	
	Eliminating location [21] by chaining:

	Applied chaining

	First rule:
	[5] -> [21] : -a+j >= 0, cost: 1
	Second rule:
	[21] -> [22] : i'=1+i, T, cost: 1
	New rule:
	[5] -> [22] : i'=1+i, -a+j >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 23 24
	
	Eliminating location [22] by chaining:

	Applied chaining

	First rule:
	[5] -> [22] : i'=1+i, -a+j >= 0, cost: 1
	Second rule:
	[22] -> [2] : T, cost: 1
	New rule:
	[5] -> [2] : i'=1+i, -a+j >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 25 30
	
	Eliminating location [8] by chaining:

	Applied chaining

	First rule:
	[7] -> [8] : k >= 0, cost: 1
	Second rule:
	[8] -> [9] : b'=4+j+i+k, T, cost: 1
	New rule:
	[7] -> [9] : b'=4+j+i+k, k >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 6 7
	
	Eliminating location [19] by chaining:

	Applied chaining

	First rule:
	[7] -> [19] : k < 0, cost: 1
	Second rule:
	[19] -> [20] : j'=1+j, T, cost: 1
	New rule:
	[7] -> [20] : j'=1+j, k < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 20 21
	
	Eliminating location [9] by chaining:

	Applied chaining

	First rule:
	[7] -> [9] : b'=4+j+i+k, k >= 0, cost: 1
	Second rule:
	[9] -> [10] : l'=0, T, cost: 1
	New rule:
	[7] -> [10] : b'=4+j+i+k, l'=0, k >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 8 32
	
	Eliminating location [20] by chaining:

	Applied chaining

	First rule:
	[7] -> [20] : j'=1+j, k < 0, cost: 1
	Second rule:
	[20] -> [5] : T, cost: 1
	New rule:
	[7] -> [5] : j'=1+j, k < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 22 33
	
	Eliminating location [11] by chaining:

	Applied chaining

	First rule:
	[10] -> [11] : -b+l < 0, cost: 1
	Second rule:
	[11] -> [12] : m'=1000+l+j+i+k, T, cost: 1
	New rule:
	[10] -> [12] : m'=1000+l+j+i+k, -b+l < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 9 10
	
	Eliminating location [17] by chaining:

	Applied chaining

	First rule:
	[10] -> [17] : -b+l >= 0, cost: 1
	Second rule:
	[17] -> [18] : k'=-1+k, T, cost: 1
	New rule:
	[10] -> [18] : k'=-1+k, -b+l >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 17 18
	
	Eliminating location [18] by chaining:

	Applied chaining

	First rule:
	[10] -> [18] : k'=-1+k, -b+l >= 0, cost: 1
	Second rule:
	[18] -> [7] : T, cost: 1
	New rule:
	[10] -> [7] : k'=-1+k, -b+l >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 19 37
	
	Eliminating location [13] by chaining:

	Applied chaining

	First rule:
	[12] -> [13] : m >= 0, cost: 1
	Second rule:
	[13] -> [14] : m'=m, T, cost: 1
	New rule:
	[12] -> [14] : m'=m, m >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 11 12
	
	Eliminating location [15] by chaining:

	Applied chaining

	First rule:
	[12] -> [15] : m < 0, cost: 1
	Second rule:
	[15] -> [16] : l'=1+l, T, cost: 1
	New rule:
	[12] -> [16] : l'=1+l, m < 0, cost: 1
	
	Applied deletion

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

	Applied chaining

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

	Removed the following rules: 13 39
	
	Eliminating location [16] by chaining:

	Applied chaining

	First rule:
	[12] -> [16] : l'=1+l, m < 0, cost: 1
	Second rule:
	[16] -> [10] : T, cost: 1
	New rule:
	[12] -> [10] : l'=1+l, m < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 16 40

Simplified Transitions

Start location: [1]
Program variables: a b i j k l m
   0: [1] -> [2] : i'=0, T, cost: 1
  26: [2] -> [23] : -100+i >= 0, cost: 1
  28: [2] -> [5] : a'=2+i, j'=0, -100+i < 0, cost: 1
  29: [5] -> [7] : k'=3+j+i, -a+j < 0, cost: 1
  31: [5] -> [2] : i'=1+i, -a+j >= 0, cost: 1
  34: [7] -> [10] : b'=4+j+i+k, l'=0, k >= 0, cost: 1
  35: [7] -> [5] : j'=1+j, k < 0, cost: 1
  36: [10] -> [12] : m'=1000+l+j+i+k, -b+l < 0, cost: 1
  38: [10] -> [7] : k'=-1+k, -b+l >= 0, cost: 1
  42: [12] -> [10] : l'=1+l, m < 0, cost: 1
  43: [12] -> [12] : m >= 0, cost: 1

	Removed Trivial Updates

	Original rule:
	[12] -> [12] : m'=m, m >= 0, cost: 1
	New rule:
	[12] -> [12] : m >= 0, cost: 1

Step with 0

	Trace

	0[T]
	
	Blocked

	[{}, {}]

Step with 28

	Trace

	0[T], 28[(-100+i < 0)]
	
	Blocked

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

Step with 29

	Trace

	0[T], 28[(-100+i < 0)], 29[(-a+j < 0)]
	
	Blocked

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

Step with 34

	Trace

	0[T], 28[(-100+i < 0)], 29[(-a+j < 0)], 34[(k >= 0)]
	
	Blocked

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

Step with 36

	Trace

	0[T], 28[(-100+i < 0)], 29[(-a+j < 0)], 34[(k >= 0)], 36[(-b+l < 0)]
	
	Blocked

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

Step with 43

	Trace

	0[T], 28[(-100+i < 0)], 29[(-a+j < 0)], 34[(k >= 0)], 36[(-b+l < 0)], 43[(m >= 0)]
	
	Blocked

	[{}, {26[T]}, {}, {}, {}, {42[T]}, {}]

Nonterm

Start location: [1]
Program variables: a b i j k l m
   0: [1] -> [2] : i'=0, T, cost: 1
  26: [2] -> [23] : -100+i >= 0, cost: 1
  28: [2] -> [5] : a'=2+i, j'=0, -100+i < 0, cost: 1
  29: [5] -> [7] : k'=3+j+i, -a+j < 0, cost: 1
  31: [5] -> [2] : i'=1+i, -a+j >= 0, cost: 1
  34: [7] -> [10] : b'=4+j+i+k, l'=0, k >= 0, cost: 1
  35: [7] -> [5] : j'=1+j, k < 0, cost: 1
  36: [10] -> [12] : m'=1000+l+j+i+k, -b+l < 0, cost: 1
  38: [10] -> [7] : k'=-1+k, -b+l >= 0, cost: 1
  42: [12] -> [10] : l'=1+l, m < 0, cost: 1
  43: [12] -> [12] : m >= 0, cost: 1
  44: [12] -> LoAT_sink : (-1+n >= 0 /\ m >= 0), cost: NONTERM

	Certificate of Non-Termination

	Original rule:
	[12] -> [12] : (m >= 0), cost: 1
	New rule:
	[12] -> LoAT_sink : (-1+n >= 0 /\ m >= 0), cost: NONTERM

		m >= 0 [0]: monotonic increase yields m >= 0
		
		Replacement map: {m >= 0 -> m >= 0}

Step with 44

	Trace

	0[T], 28[(-100+i < 0)], 29[(-a+j < 0)], 34[(k >= 0)], 36[(-b+l < 0)], 44[(-1+n >= 0 /\ m >= 0)]
	
	Blocked

	[{}, {26[T]}, {}, {}, {}, {42[T]}, {44[T]}]

Refute

	Counterexample

	[ a=0 b=0 i=0 j=0 k=0 l=0 m=0 ] 0 [ a=2 b=0 i=0 j=0 k=0 l=0 m=0 ] 28 [ a=2 b=0 i=0 j=0 k=3 l=0 m=0 ] 29 [ a=2 b=7 i=0 j=0 k=3 l=0 m=0 ] 34 [ a=2 b=7 i=0 j=0 k=3 l=0 m=1003 ] 36 [ a=0 b=0 i=i j=0 k=0 l=0 m=0 ] 44
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b