unknown

Initial ITS

Start location: [1]
Program variables: n x y
   0: [1] -> [2] : n'=nondet, T, cost: 1
   1: [2] -> [3] : y'=nondet1, T, cost: 1
   2: [3] -> [4] : x'=n, T, cost: 1
   3: [4] -> [6] : x >= 0, cost: 1
  17: [4] -> [5] : x < 0, cost: 1
   4: [6] -> [7] : x >= 0, cost: 1
  15: [6] -> [15] : x < 0, cost: 1
   5: [7] -> [8] : y'=1, T, cost: 1
   6: [8] -> [10] : -x+y < 0, cost: 1
  12: [8] -> [9] : -x+y >= 0, cost: 1
  13: [9] -> [14] : x'=-1+x, T, cost: 1
   7: [10] -> [11] : -x+y < 0, cost: 1
  10: [10] -> [13] : -x+y >= 0, cost: 1
   8: [11] -> [12] : y'=2*y, T, cost: 1
   9: [12] -> [10] : T, cost: 1
  11: [13] -> [9] : T, cost: 1
  14: [14] -> [6] : T, cost: 1
  16: [15] -> [5] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: n x y
  19: [1] -> [4] : n'=nondet, x'=nondet, y'=nondet1, T, cost: 1
   3: [4] -> [6] : x >= 0, cost: 1
  17: [4] -> [5] : x < 0, cost: 1
  20: [6] -> [8] : y'=1, x >= 0, cost: 1
  21: [6] -> [5] : x < 0, cost: 1
   6: [8] -> [10] : -x+y < 0, cost: 1
  12: [8] -> [9] : -x+y >= 0, cost: 1
  22: [9] -> [6] : x'=-1+x, T, cost: 1
  24: [10] -> [9] : -x+y >= 0, cost: 1
  25: [10] -> [10] : y'=2*y, -x+y < 0, cost: 1

	Eliminating location [2] by chaining:

	Applied chaining

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

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

	Applied chaining

	First rule:
	[1] -> [3] : n'=nondet, y'=nondet1, T, cost: 1
	Second rule:
	[3] -> [4] : x'=n, T, cost: 1
	New rule:
	[1] -> [4] : n'=nondet, x'=nondet, y'=nondet1, T, cost: 1
	
	Applied deletion

	Removed the following rules: 2 18
	
	Eliminating location [7] by chaining:

	Applied chaining

	First rule:
	[6] -> [7] : x >= 0, cost: 1
	Second rule:
	[7] -> [8] : y'=1, T, cost: 1
	New rule:
	[6] -> [8] : y'=1, x >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 4 5
	
	Eliminating location [15] by chaining:

	Applied chaining

	First rule:
	[6] -> [15] : x < 0, cost: 1
	Second rule:
	[15] -> [5] : T, cost: 1
	New rule:
	[6] -> [5] : x < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 15 16
	
	Eliminating location [14] by chaining:

	Applied chaining

	First rule:
	[9] -> [14] : x'=-1+x, T, cost: 1
	Second rule:
	[14] -> [6] : T, cost: 1
	New rule:
	[9] -> [6] : x'=-1+x, T, cost: 1
	
	Applied deletion

	Removed the following rules: 13 14
	
	Eliminating location [11] by chaining:

	Applied chaining

	First rule:
	[10] -> [11] : -x+y < 0, cost: 1
	Second rule:
	[11] -> [12] : y'=2*y, T, cost: 1
	New rule:
	[10] -> [12] : y'=2*y, -x+y < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 7 8
	
	Eliminating location [13] by chaining:

	Applied chaining

	First rule:
	[10] -> [13] : -x+y >= 0, cost: 1
	Second rule:
	[13] -> [9] : T, cost: 1
	New rule:
	[10] -> [9] : -x+y >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 10 11
	
	Eliminating location [12] by chaining:

	Applied chaining

	First rule:
	[10] -> [12] : y'=2*y, -x+y < 0, cost: 1
	Second rule:
	[12] -> [10] : T, cost: 1
	New rule:
	[10] -> [10] : y'=2*y, -x+y < 0, cost: 1
	
	Applied deletion

	Removed the following rules: 9 23

Step with 19

	Trace

	19[T]
	
	Blocked

	[{}, {}]

Step with 3

	Trace

	19[T], 3[(x >= 0)]
	
	Blocked

	[{}, {}, {}]

Step with 20

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)]
	
	Blocked

	[{}, {}, {21[T]}, {}]

Step with 6

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)], 6[(-x+y < 0)]
	
	Blocked

	[{}, {}, {21[T]}, {}, {}]

Step with 25

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)], 6[(-x+y < 0)], 25[(-x+y < 0)]
	
	Blocked

	[{}, {}, {21[T]}, {}, {24[T]}, {}]

Accelerate and Drop

Start location: [1]
Program variables: n x y
  19: [1] -> [4] : n'=nondet, x'=nondet, y'=nondet1, T, cost: 1
   3: [4] -> [6] : x >= 0, cost: 1
  17: [4] -> [5] : x < 0, cost: 1
  20: [6] -> [8] : y'=1, x >= 0, cost: 1
  21: [6] -> [5] : x < 0, cost: 1
   6: [8] -> [10] : -x+y < 0, cost: 1
  12: [8] -> [9] : -x+y >= 0, cost: 1
  22: [9] -> [6] : x'=-1+x, T, cost: 1
  24: [10] -> [9] : -x+y >= 0, cost: 1
  25: [10] -> [10] : y'=2*y, -x+y < 0, cost: 1
  26: [10] -> LoAT_sink : (x-y > 0 /\ y <= 0), cost: NONTERM

	Certificate of Non-Termination

	Original rule:
	[10] -> [10] : y'=2*y, (-x+y < 0), cost: 1
	New rule:
	[10] -> LoAT_sink : (x-y > 0 /\ y <= 0), cost: NONTERM

		x-y > 0 [0]: eventual decrease yields (-2^(-1+n6)*y+x > 0 /\ x-y > 0)
		
		x-y > 0 [1]: eventual increase yields (x-y > 0 /\ y <= 0)
		
		Replacement map: {x-y > 0 -> (x-y > 0 /\ y <= 0)}

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)], 6[(-x+y < 0)]
	
	Blocked

	[{}, {}, {21[T]}, {}, {24[T], 25[T]}]

Backtrack

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)]
	
	Blocked

	[{}, {}, {21[T]}, {6[T]}]

Step with 12

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)], 12[(-x+y >= 0)]
	
	Blocked

	[{}, {}, {21[T]}, {6[T]}, {}]

Step with 22

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)], 12[(-x+y >= 0)], 22[T]
	
	Blocked

	[{}, {}, {21[T]}, {6[T]}, {}, {}]

Accelerate

Start location: [1]
Program variables: n x y
  19: [1] -> [4] : n'=nondet, x'=nondet, y'=nondet1, T, cost: 1
   3: [4] -> [6] : x >= 0, cost: 1
  17: [4] -> [5] : x < 0, cost: 1
  20: [6] -> [8] : y'=1, x >= 0, cost: 1
  21: [6] -> [5] : x < 0, cost: 1
  27: [6] -> [6] : x'=x-n9, y'=1, (1+x-n9 >= 0 /\ 1-x >= 0 /\ -1+n9 >= 0), cost: 1
   6: [8] -> [10] : -x+y < 0, cost: 1
  12: [8] -> [9] : -x+y >= 0, cost: 1
  22: [9] -> [6] : x'=-1+x, T, cost: 1
  24: [10] -> [9] : -x+y >= 0, cost: 1
  25: [10] -> [10] : y'=2*y, -x+y < 0, cost: 1
  26: [10] -> LoAT_sink : (x-y > 0 /\ y <= 0), cost: NONTERM

	Loop Acceleration

	Original rule:
	[6] -> [6] : x'=-1+x, y'=1, (x >= 0 /\ 1-x >= 0), cost: 1
	New rule:
	[6] -> [6] : x'=x-n9, y'=1, (1+x-n9 >= 0 /\ 1-x >= 0 /\ -1+n9 >= 0), cost: 1

		x >= 0 [0]: montonic decrease yields 1+x-n9 >= 0
		
		x >= 0 [1]: eventual increase yields (1 <= 0 /\ x >= 0)
		
		1-x >= 0 [0]: monotonic increase yields 1-x >= 0
		
		Replacement map: {x >= 0 -> 1+x-n9 >= 0, 1-x >= 0 -> 1-x >= 0}

	Trace

	19[T], 3[(x >= 0)], 27[(1+x-n9 >= 0 /\ 1-x >= 0 /\ -1+n9 >= 0)]
	
	Blocked

	[{}, {}, {21[T]}, {27[T]}]

Step with 21

	Trace

	19[T], 3[(x >= 0)], 27[(1+x-n9 >= 0 /\ 1-x >= 0 /\ -1+n9 >= 0)], 21[(x < 0)]
	
	Blocked

	[{}, {}, {21[T]}, {27[T]}, {}]

Backtrack

	Trace

	19[T], 3[(x >= 0)], 27[(1+x-n9 >= 0 /\ 1-x >= 0 /\ -1+n9 >= 0)]
	
	Blocked

	[{}, {}, {21[T]}, {21[T], 27[T]}]

Step with 20

	Trace

	19[T], 3[(x >= 0)], 27[(1+x-n9 >= 0 /\ 1-x >= 0 /\ -1+n9 >= 0)], 20[(x >= 0)]
	
	Blocked

	[{}, {}, {21[T]}, {21[T], 27[T]}, {}]

Step with 12

	Trace

	19[T], 3[(x >= 0)], 27[(1+x-n9 >= 0 /\ 1-x >= 0 /\ -1+n9 >= 0)], 20[(x >= 0)], 12[(-x+y >= 0)]
	
	Blocked

	[{}, {}, {21[T]}, {21[T], 27[T]}, {}, {}]

Step with 22

	Trace

	19[T], 3[(x >= 0)], 27[(1+x-n9 >= 0 /\ 1-x >= 0 /\ -1+n9 >= 0)], 20[(x >= 0)], 12[(-x+y >= 0)], 22[T]
	
	Blocked

	[{}, {}, {21[T]}, {21[T], 27[T]}, {}, {}, {}]

Covered

	Trace

	19[T], 3[(x >= 0)], 27[(1+x-n9 >= 0 /\ 1-x >= 0 /\ -1+n9 >= 0)], 20[(x >= 0)], 12[(-x+y >= 0)]
	
	Blocked

	[{}, {}, {21[T]}, {21[T], 27[T]}, {}, {22[T]}]

Backtrack

	Trace

	19[T], 3[(x >= 0)], 27[(1+x-n9 >= 0 /\ 1-x >= 0 /\ -1+n9 >= 0)], 20[(x >= 0)]
	
	Blocked

	[{}, {}, {21[T]}, {21[T], 27[T]}, {12[T]}]

Backtrack

	Trace

	19[T], 3[(x >= 0)], 27[(1+x-n9 >= 0 /\ 1-x >= 0 /\ -1+n9 >= 0)]
	
	Blocked

	[{}, {}, {21[T]}, {20[T], 21[T], 27[T]}]

Backtrack

	Trace

	19[T], 3[(x >= 0)]
	
	Blocked

	[{}, {}, {21[T], 27[T]}]

Step with 20

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)]
	
	Blocked

	[{}, {}, {21[T], 27[T]}, {}]

Step with 12

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)], 12[(-x+y >= 0)]
	
	Blocked

	[{}, {}, {21[T], 27[T]}, {}, {}]

Step with 22

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)], 12[(-x+y >= 0)], 22[T]
	
	Blocked

	[{}, {}, {21[T], 27[T]}, {}, {}, {}]

Covered

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)], 12[(-x+y >= 0)]
	
	Blocked

	[{}, {}, {21[T], 27[T]}, {}, {22[T]}]

Backtrack

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)]
	
	Blocked

	[{}, {}, {21[T], 27[T]}, {12[T]}]

Step with 6

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)], 6[(-x+y < 0)]
	
	Blocked

	[{}, {}, {21[T], 27[T]}, {12[T]}, {}]

Step with 25

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)], 6[(-x+y < 0)], 25[(-x+y < 0)]
	
	Blocked

	[{}, {}, {21[T], 27[T]}, {12[T]}, {24[T], 26[T]}, {}]

Covered

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)], 6[(-x+y < 0)]
	
	Blocked

	[{}, {}, {21[T], 27[T]}, {12[T]}, {24[T], 25[T], 26[T]}]

Backtrack

	Trace

	19[T], 3[(x >= 0)], 20[(x >= 0)]
	
	Blocked

	[{}, {}, {21[T], 27[T]}, {6[T], 12[T]}]

Backtrack

	Trace

	19[T], 3[(x >= 0)]
	
	Blocked

	[{}, {}, {20[T], 21[T], 27[T]}]

Backtrack

	Trace

	19[T]
	
	Blocked

	[{}, {3[T]}]

Step with 17

	Trace

	19[T], 17[(x < 0)]
	
	Blocked

	[{}, {3[T]}, {}]

Backtrack

	Trace

	19[T]
	
	Blocked

	[{}, {3[T], 17[T]}]

Backtrack

	Trace

	Blocked

	[{19[T]}]

Accept

unknown

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b