NO

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] -> [4] : x > 0, cost: 1
   5: [3] -> [6] : x <= 0, cost: 1
   3: [4] -> [5] : x'=y+x, T, cost: 1
   4: [5] -> [3] : T, cost: 1

Chained Linear Paths

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

	Applied chaining

	First rule:
	[3] -> [4] : x > 0, cost: 1
	Second rule:
	[4] -> [5] : x'=y+x, T, cost: 1
	New rule:
	[3] -> [5] : x'=y+x, x > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 2 3
	
	Eliminating location [5] by chaining:

	Applied chaining

	First rule:
	[3] -> [5] : x'=y+x, x > 0, cost: 1
	Second rule:
	[5] -> [3] : T, cost: 1
	New rule:
	[3] -> [3] : x'=y+x, x > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 4 7

Step with 6

	Trace

	6[T]
	
	Blocked

	[{}, {}]

Step with 5

	Trace

	6[T], 5[(x <= 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	6[T]
	
	Blocked

	[{}, {5[T]}]

Step with 8

	Trace

	6[T], 8[(x > 0)]
	
	Blocked

	[{}, {5[T]}, {}]

Nonterm

Start location: [1]
Program variables: x y
   6: [1] -> [3] : x'=nondet, y'=nondet1, T, cost: 1
   5: [3] -> [6] : x <= 0, cost: 1
   8: [3] -> [3] : x'=y+x, x > 0, cost: 1
   9: [3] -> LoAT_sink : (-y <= 0 /\ x > 0), cost: NONTERM
  10: [3] -> [3] : x'=n*y+x, ((-1+n)*y+x > 0 /\ -1+n >= 0 /\ x > 0), cost: 1

	Certificate of Non-Termination

	Original rule:
	[3] -> [3] : x'=y+x, (x > 0), cost: 1
	New rule:
	[3] -> LoAT_sink : (-y <= 0 /\ x > 0), cost: NONTERM

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

	Loop Acceleration

	Original rule:
	[3] -> [3] : x'=y+x, (x > 0), cost: 1
	New rule:
	[3] -> [3] : x'=n*y+x, ((-1+n)*y+x > 0 /\ -1+n >= 0 /\ x > 0), cost: 1

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

Step with 9

	Trace

	6[T], 9[(-y <= 0 /\ x > 0)]
	
	Blocked

	[{}, {5[T]}, {9[T]}]

Refute

	Counterexample

	[ x=1 y=0 ] 6 [ x=x y=y ] 9
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b