NO

Initial ITS

Start location: [1]
Program variables: c i
   0: [1] -> [2] : c'=864, T, cost: 1
   1: [2] -> [4] : -10+c <= 0, cost: 1
   8: [2] -> [9] : -10+c > 0, cost: 1
   2: [4] -> [5] : i'=0, T, cost: 1
   3: [5] -> [6] : -100+i < 0, cost: 1
   6: [5] -> [8] : -100+i >= 0, cost: 1
   4: [6] -> [7] : i'=1+i, T, cost: 1
   5: [7] -> [5] : T, cost: 1
   7: [8] -> [3] : T, cost: 1
   9: [9] -> [11] : -50+c <= 0, cost: 1
  16: [9] -> [10] : -50+c > 0, cost: 1
  17: [10] -> [17] : -100+c <= 0, cost: 1
  24: [10] -> [22] : -100+c > 0, cost: 1
  10: [11] -> [12] : i'=0, T, cost: 1
  11: [12] -> [13] : -101+i < 0, cost: 1
  14: [12] -> [15] : -101+i >= 0, cost: 1
  12: [13] -> [14] : i'=1+i, T, cost: 1
  13: [14] -> [12] : T, cost: 1
  15: [15] -> [10] : T, cost: 1
  31: [16] -> [3] : T, cost: 1
  18: [17] -> [18] : i'=0, T, cost: 1
  19: [18] -> [19] : -102+i < 0, cost: 1
  22: [18] -> [21] : -102+i >= 0, cost: 1
  20: [19] -> [20] : i'=1+i, T, cost: 1
  21: [20] -> [18] : T, cost: 1
  23: [21] -> [16] : T, cost: 1
  25: [22] -> [23] : i'=0, T, cost: 1
  26: [23] -> [24] : -103+i < 0, cost: 1
  29: [23] -> [26] : -103+i >= 0, cost: 1
  27: [24] -> [25] : i'=i, T, cost: 1
  28: [25] -> [23] : T, cost: 1
  30: [26] -> [16] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: c i
   0: [1] -> [2] : c'=864, T, cost: 1
   8: [2] -> [9] : -10+c > 0, cost: 1
  32: [2] -> [5] : i'=0, -10+c <= 0, cost: 1
  34: [5] -> [3] : -100+i >= 0, cost: 1
  35: [5] -> [5] : i'=1+i, -100+i < 0, cost: 1
  16: [9] -> [10] : -50+c > 0, cost: 1
  36: [9] -> [12] : i'=0, -50+c <= 0, cost: 1
  37: [10] -> [18] : i'=0, -100+c <= 0, cost: 1
  38: [10] -> [23] : i'=0, -100+c > 0, cost: 1
  46: [12] -> [10] : -101+i >= 0, cost: 1
  47: [12] -> [12] : i'=1+i, -101+i < 0, cost: 1
  31: [16] -> [3] : T, cost: 1
  40: [18] -> [16] : -102+i >= 0, cost: 1
  41: [18] -> [18] : i'=1+i, -102+i < 0, cost: 1
  43: [23] -> [16] : -103+i >= 0, cost: 1
  44: [23] -> [23] : i'=i, -103+i < 0, cost: 1

	Eliminating location [4] by chaining:

	Applied chaining

	First rule:
	[2] -> [4] : -10+c <= 0, cost: 1
	Second rule:
	[4] -> [5] : i'=0, T, cost: 1
	New rule:
	[2] -> [5] : i'=0, -10+c <= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 1 2
	
	Eliminating location [6] by chaining:

	Applied chaining

	First rule:
	[5] -> [6] : -100+i < 0, cost: 1
	Second rule:
	[6] -> [7] : i'=1+i, T, cost: 1
	New rule:
	[5] -> [7] : i'=1+i, -100+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 3 4
	
	Eliminating location [8] by chaining:

	Applied chaining

	First rule:
	[5] -> [8] : -100+i >= 0, cost: 1
	Second rule:
	[8] -> [3] : T, cost: 1
	New rule:
	[5] -> [3] : -100+i >= 0, cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	[5] -> [7] : i'=1+i, -100+i < 0, cost: 1
	Second rule:
	[7] -> [5] : T, cost: 1
	New rule:
	[5] -> [5] : i'=1+i, -100+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 5 33
	
	Eliminating location [11] by chaining:

	Applied chaining

	First rule:
	[9] -> [11] : -50+c <= 0, cost: 1
	Second rule:
	[11] -> [12] : i'=0, T, cost: 1
	New rule:
	[9] -> [12] : i'=0, -50+c <= 0, cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	[10] -> [17] : -100+c <= 0, cost: 1
	Second rule:
	[17] -> [18] : i'=0, T, cost: 1
	New rule:
	[10] -> [18] : i'=0, -100+c <= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 17 18
	
	Eliminating location [22] by chaining:

	Applied chaining

	First rule:
	[10] -> [22] : -100+c > 0, cost: 1
	Second rule:
	[22] -> [23] : i'=0, T, cost: 1
	New rule:
	[10] -> [23] : i'=0, -100+c > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 24 25
	
	Eliminating location [19] by chaining:

	Applied chaining

	First rule:
	[18] -> [19] : -102+i < 0, cost: 1
	Second rule:
	[19] -> [20] : i'=1+i, T, cost: 1
	New rule:
	[18] -> [20] : i'=1+i, -102+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 19 20
	
	Eliminating location [21] by chaining:

	Applied chaining

	First rule:
	[18] -> [21] : -102+i >= 0, cost: 1
	Second rule:
	[21] -> [16] : T, cost: 1
	New rule:
	[18] -> [16] : -102+i >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 22 23
	
	Eliminating location [20] by chaining:

	Applied chaining

	First rule:
	[18] -> [20] : i'=1+i, -102+i < 0, cost: 1
	Second rule:
	[20] -> [18] : T, cost: 1
	New rule:
	[18] -> [18] : i'=1+i, -102+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 21 39
	
	Eliminating location [24] by chaining:

	Applied chaining

	First rule:
	[23] -> [24] : -103+i < 0, cost: 1
	Second rule:
	[24] -> [25] : i'=i, T, cost: 1
	New rule:
	[23] -> [25] : i'=i, -103+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 26 27
	
	Eliminating location [26] by chaining:

	Applied chaining

	First rule:
	[23] -> [26] : -103+i >= 0, cost: 1
	Second rule:
	[26] -> [16] : T, cost: 1
	New rule:
	[23] -> [16] : -103+i >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 29 30
	
	Eliminating location [25] by chaining:

	Applied chaining

	First rule:
	[23] -> [25] : i'=i, -103+i < 0, cost: 1
	Second rule:
	[25] -> [23] : T, cost: 1
	New rule:
	[23] -> [23] : i'=i, -103+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 28 42
	
	Eliminating location [13] by chaining:

	Applied chaining

	First rule:
	[12] -> [13] : -101+i < 0, cost: 1
	Second rule:
	[13] -> [14] : i'=1+i, T, cost: 1
	New rule:
	[12] -> [14] : i'=1+i, -101+i < 0, cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	[12] -> [15] : -101+i >= 0, cost: 1
	Second rule:
	[15] -> [10] : T, cost: 1
	New rule:
	[12] -> [10] : -101+i >= 0, cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	[12] -> [14] : i'=1+i, -101+i < 0, cost: 1
	Second rule:
	[14] -> [12] : T, cost: 1
	New rule:
	[12] -> [12] : i'=1+i, -101+i < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 13 45

Simplified Transitions

Start location: [1]
Program variables: c i
   0: [1] -> [2] : c'=864, T, cost: 1
   8: [2] -> [9] : -10+c > 0, cost: 1
  32: [2] -> [5] : i'=0, -10+c <= 0, cost: 1
  34: [5] -> [3] : -100+i >= 0, cost: 1
  35: [5] -> [5] : i'=1+i, -100+i < 0, cost: 1
  16: [9] -> [10] : -50+c > 0, cost: 1
  36: [9] -> [12] : i'=0, -50+c <= 0, cost: 1
  37: [10] -> [18] : i'=0, -100+c <= 0, cost: 1
  38: [10] -> [23] : i'=0, -100+c > 0, cost: 1
  46: [12] -> [10] : -101+i >= 0, cost: 1
  47: [12] -> [12] : i'=1+i, -101+i < 0, cost: 1
  31: [16] -> [3] : T, cost: 1
  40: [18] -> [16] : -102+i >= 0, cost: 1
  41: [18] -> [18] : i'=1+i, -102+i < 0, cost: 1
  43: [23] -> [16] : -103+i >= 0, cost: 1
  48: [23] -> [23] : -103+i < 0, cost: 1

	Removed Trivial Updates

	Original rule:
	[23] -> [23] : i'=i, -103+i < 0, cost: 1
	New rule:
	[23] -> [23] : -103+i < 0, cost: 1

Step with 0

	Trace

	0[T]
	
	Blocked

	[{}, {}]

Step with 8

	Trace

	0[T], 8[(-10+c > 0)]
	
	Blocked

	[{}, {}, {}]

Step with 16

	Trace

	0[T], 8[(-10+c > 0)], 16[(-50+c > 0)]
	
	Blocked

	[{}, {}, {}, {}]

Step with 38

	Trace

	0[T], 8[(-10+c > 0)], 16[(-50+c > 0)], 38[(-100+c > 0)]
	
	Blocked

	[{}, {}, {}, {37[T]}, {}]

Step with 48

	Trace

	0[T], 8[(-10+c > 0)], 16[(-50+c > 0)], 38[(-100+c > 0)], 48[(-103+i < 0)]
	
	Blocked

	[{}, {}, {}, {37[T]}, {43[T]}, {}]

Nonterm

Start location: [1]
Program variables: c i
   0: [1] -> [2] : c'=864, T, cost: 1
   8: [2] -> [9] : -10+c > 0, cost: 1
  32: [2] -> [5] : i'=0, -10+c <= 0, cost: 1
  34: [5] -> [3] : -100+i >= 0, cost: 1
  35: [5] -> [5] : i'=1+i, -100+i < 0, cost: 1
  16: [9] -> [10] : -50+c > 0, cost: 1
  36: [9] -> [12] : i'=0, -50+c <= 0, cost: 1
  37: [10] -> [18] : i'=0, -100+c <= 0, cost: 1
  38: [10] -> [23] : i'=0, -100+c > 0, cost: 1
  46: [12] -> [10] : -101+i >= 0, cost: 1
  47: [12] -> [12] : i'=1+i, -101+i < 0, cost: 1
  31: [16] -> [3] : T, cost: 1
  40: [18] -> [16] : -102+i >= 0, cost: 1
  41: [18] -> [18] : i'=1+i, -102+i < 0, cost: 1
  43: [23] -> [16] : -103+i >= 0, cost: 1
  48: [23] -> [23] : -103+i < 0, cost: 1
  49: [23] -> LoAT_sink : (103-i > 0 /\ -1+n >= 0), cost: NONTERM

	Certificate of Non-Termination

	Original rule:
	[23] -> [23] : (-103+i < 0), cost: 1
	New rule:
	[23] -> LoAT_sink : (103-i > 0 /\ -1+n >= 0), cost: NONTERM

		103-i > 0 [0]: monotonic increase yields 103-i > 0
		
		Replacement map: {103-i > 0 -> 103-i > 0}

Step with 49

	Trace

	0[T], 8[(-10+c > 0)], 16[(-50+c > 0)], 38[(-100+c > 0)], 49[(103-i > 0 /\ -1+n >= 0)]
	
	Blocked

	[{}, {}, {}, {37[T]}, {43[T]}, {49[T]}]

Refute

	Counterexample

	[ c=864 i=0 ] 0 [ c=864 i=0 ] 8 [ c=864 i=0 ] 16 [ c=864 i=0 ] 38 [ c=c i=0 ] 49
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b