unknown

Initial ITS

Start location: [1]
Program variables: x y
   0: [1] -> [2] : x'=nondet, T, cost: 1
   1: [2] -> [3] : y'=nondet1, T, cost: 1
   2: [3] -> [5] : x > 0, cost: 1
   8: [3] -> [4] : x <= 0, cost: 1
   3: [5] -> [6] : -y+x > 0, cost: 1
   6: [5] -> [8] : -y+x <= 0, cost: 1
   4: [6] -> [7] : y'=y+x, T, cost: 1
   5: [7] -> [5] : T, cost: 1
   7: [8] -> [4] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: x y
   9: [1] -> [3] : x'=nondet, y'=nondet1, T, cost: 1
   2: [3] -> [5] : x > 0, cost: 1
   8: [3] -> [4] : x <= 0, cost: 1
  11: [5] -> [4] : -y+x <= 0, cost: 1
  12: [5] -> [5] : y'=y+x, -y+x > 0, cost: 1

	Eliminating location [2] by chaining:

	Applied chaining

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

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

	Applied chaining

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

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

	Applied chaining

	First rule:
	[5] -> [8] : -y+x <= 0, cost: 1
	Second rule:
	[8] -> [4] : T, cost: 1
	New rule:
	[5] -> [4] : -y+x <= 0, cost: 1
	
	Applied deletion

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

	Applied chaining

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

	Removed the following rules: 5 10

Step with 9

	Trace

	9[T]
	
	Blocked

	[{}, {}]

Step with 2

	Trace

	9[T], 2[(x > 0)]
	
	Blocked

	[{}, {}, {}]

Step with 11

	Trace

	9[T], 2[(x > 0)], 11[(-y+x <= 0)]
	
	Blocked

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

Backtrack

	Trace

	9[T], 2[(x > 0)]
	
	Blocked

	[{}, {}, {11[T]}]

Step with 12

	Trace

	9[T], 2[(x > 0)], 12[(-y+x > 0)]
	
	Blocked

	[{}, {}, {11[T]}, {}]

Accelerate

Start location: [1]
Program variables: x y
   9: [1] -> [3] : x'=nondet, y'=nondet1, T, cost: 1
   2: [3] -> [5] : x > 0, cost: 1
   8: [3] -> [4] : x <= 0, cost: 1
  11: [5] -> [4] : -y+x <= 0, cost: 1
  12: [5] -> [5] : y'=y+x, -y+x > 0, cost: 1
  13: [5] -> LoAT_sink : (-y+x > 0 /\ x <= 0), cost: NONTERM
  14: [5] -> [5] : y'=n*x+y, (-1+n >= 0 /\ -y+x > 0 /\ -(-1+n)*x-y+x > 0), cost: 1

	Certificate of Non-Termination

	Original rule:
	[5] -> [5] : y'=y+x, (-y+x > 0), cost: 1
	New rule:
	[5] -> LoAT_sink : (-y+x > 0 /\ x <= 0), cost: NONTERM

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

	Loop Acceleration

	Original rule:
	[5] -> [5] : y'=y+x, (-y+x > 0), cost: 1
	New rule:
	[5] -> [5] : y'=n*x+y, (-1+n >= 0 /\ -y+x > 0 /\ -(-1+n)*x-y+x > 0), cost: 1

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

	Trace

	9[T], 2[(x > 0)], 14[(-1+n >= 0 /\ -y+x > 0 /\ -(-1+n)*x-y+x > 0)]
	
	Blocked

	[{}, {}, {11[T]}, {12[T], 14[T]}]

Step with 11

	Trace

	9[T], 2[(x > 0)], 14[(-1+n >= 0 /\ -y+x > 0 /\ -(-1+n)*x-y+x > 0)], 11[(-y+x <= 0)]
	
	Blocked

	[{}, {}, {11[T]}, {12[T], 13[T], 14[T]}, {}]

Backtrack

	Trace

	9[T], 2[(x > 0)], 14[(-1+n >= 0 /\ -y+x > 0 /\ -(-1+n)*x-y+x > 0)]
	
	Blocked

	[{}, {}, {11[T]}, {11[T], 12[T], 13[T], 14[T]}]

Backtrack

	Trace

	9[T], 2[(x > 0)]
	
	Blocked

	[{}, {}, {11[T], 14[T]}]

Step with 12

	Trace

	9[T], 2[(x > 0)], 12[(-y+x > 0)]
	
	Blocked

	[{}, {}, {11[T], 14[T]}, {}]

Covered

	Trace

	9[T], 2[(x > 0)]
	
	Blocked

	[{}, {}, {11[T], 12[T], 14[T]}]

Backtrack

	Trace

	9[T]
	
	Blocked

	[{}, {2[T]}]

Step with 8

	Trace

	9[T], 8[(x <= 0)]
	
	Blocked

	[{}, {2[T]}, {}]

Backtrack

	Trace

	9[T]
	
	Blocked

	[{}, {2[T], 8[T]}]

Backtrack

	Trace

	Blocked

	[{9[T]}]

Accept

unknown

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b