NO

Initial ITS

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

Chained Linear Paths

Start location: [1]
Program variables: oldx x y
   8: [1] -> [3] : x'=nondet, y'=nondet1, T, cost: 1
   7: [3] -> [8] : _|_, cost: 1
  12: [3] -> [3] : oldx'=x, x'=-y, y'=x, T, 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] : T, cost: 1
	Second rule:
	[4] -> [5] : oldx'=x, T, cost: 1
	New rule:
	[3] -> [5] : oldx'=x, T, cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	[3] -> [5] : oldx'=x, T, cost: 1
	Second rule:
	[5] -> [6] : x'=-y, T, cost: 1
	New rule:
	[3] -> [6] : oldx'=x, x'=-y, T, cost: 1
	
	Applied deletion

	Removed the following rules: 4 9
	
	Eliminating location [6] by chaining:

	Applied chaining

	First rule:
	[3] -> [6] : oldx'=x, x'=-y, T, cost: 1
	Second rule:
	[6] -> [7] : y'=oldx, T, cost: 1
	New rule:
	[3] -> [7] : oldx'=x, x'=-y, y'=x, T, cost: 1
	
	Applied deletion

	Removed the following rules: 5 10
	
	Eliminating location [7] by chaining:

	Applied chaining

	First rule:
	[3] -> [7] : oldx'=x, x'=-y, y'=x, T, cost: 1
	Second rule:
	[7] -> [3] : T, cost: 1
	New rule:
	[3] -> [3] : oldx'=x, x'=-y, y'=x, T, cost: 1
	
	Applied deletion

	Removed the following rules: 6 11

Unrolled Loops

Start location: [1]
Program variables: oldx x y
   8: [1] -> [3] : x'=nondet, y'=nondet1, T, cost: 1
   7: [3] -> [8] : _|_, cost: 1
  12: [3] -> [3] : oldx'=x, x'=-y, y'=x, T, cost: 1
  13: [3] -> [3] : oldx'=-y, x'=-x, y'=-y, T, cost: 1

	Unrolling

	Original rule:
	[3] -> [3] : oldx'=x, x'=-y, y'=x, T, cost: 1
	New rule:
	[3] -> [3] : oldx'=-y, x'=-x, y'=-y, T, cost: 1

Step with 8

	Trace

	8[T]
	
	Blocked

	[{}, {}]

Step with 12

	Trace

	8[T], 12[T]
	
	Blocked

	[{}, {7[T]}, {}]

Nonterm

Start location: [1]
Program variables: oldx x y
   8: [1] -> [3] : x'=nondet, y'=nondet1, T, cost: 1
   7: [3] -> [8] : _|_, cost: 1
  12: [3] -> [3] : oldx'=x, x'=-y, y'=x, T, cost: 1
  13: [3] -> [3] : oldx'=-y, x'=-x, y'=-y, T, cost: 1
  14: [3] -> LoAT_sink : -1+n >= 0, cost: NONTERM
  15: [3] -> [3] : oldx'=-y*(-1)^(-1+n), x'=(-1)^n*x, y'=(-1)^n*y, -1+n >= 0, cost: 1

	unrolling

	Original rule:
	[3] -> [3] : oldx'=x, x'=-y, y'=x, T, cost: 1
	New rule:
	[3] -> [3] : oldx'=-y, x'=-x, y'=-y, T, cost: 1
	
	Certificate of Non-Termination

	Original rule:
	[3] -> [3] : oldx'=-y, x'=-x, y'=-y, T, cost: 1
	New rule:
	[3] -> LoAT_sink : -1+n >= 0, cost: NONTERM

		Replacement map: {}

	Loop Acceleration

	Original rule:
	[3] -> [3] : oldx'=-y, x'=-x, y'=-y, T, cost: 1
	New rule:
	[3] -> [3] : oldx'=-y*(-1)^(-1+n), x'=(-1)^n*x, y'=(-1)^n*y, -1+n >= 0, cost: 1

		Replacement map: {}

Step with 14

	Trace

	8[T], 14[-1+n >= 0]
	
	Blocked

	[{}, {7[T]}, {14[T]}]

Refute

	Counterexample

	[ oldx=0 x=0 y=0 ] 8 [ oldx=0 x=x y=y ] 14
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b