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] -> [5] : -1+y+x > 0, cost: 1
   9: [3] -> [4] : -1+y+x <= 0, cost: 1
   3: [5] -> [6] : x > 0, cost: 1
   7: [5] -> [9] : x <= 0, cost: 1
   4: [6] -> [7] : x'=y+2*x, T, cost: 1
   5: [7] -> [8] : y'=-1+y, T, cost: 1
   6: [8] -> [5] : T, cost: 1
   8: [9] -> [4] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: x y
  10: [1] -> [3] : x'=nondet, y'=nondet1, T, cost: 1
   2: [3] -> [5] : -1+y+x > 0, cost: 1
   9: [3] -> [4] : -1+y+x <= 0, cost: 1
  12: [5] -> [4] : x <= 0, cost: 1
  14: [5] -> [5] : x'=y+2*x, y'=-1+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] : x > 0, cost: 1
	Second rule:
	[6] -> [7] : x'=y+2*x, T, cost: 1
	New rule:
	[5] -> [7] : x'=y+2*x, x > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 3 4
	
	Eliminating location [9] by chaining:

	Applied chaining

	First rule:
	[5] -> [9] : x <= 0, cost: 1
	Second rule:
	[9] -> [4] : T, cost: 1
	New rule:
	[5] -> [4] : x <= 0, cost: 1
	
	Applied deletion

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

	Applied chaining

	First rule:
	[5] -> [7] : x'=y+2*x, x > 0, cost: 1
	Second rule:
	[7] -> [8] : y'=-1+y, T, cost: 1
	New rule:
	[5] -> [8] : x'=y+2*x, y'=-1+y, x > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 5 11
	
	Eliminating location [8] by chaining:

	Applied chaining

	First rule:
	[5] -> [8] : x'=y+2*x, y'=-1+y, x > 0, cost: 1
	Second rule:
	[8] -> [5] : T, cost: 1
	New rule:
	[5] -> [5] : x'=y+2*x, y'=-1+y, x > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 6 13

Step with 10

	Trace

	10[T]
	
	Blocked

	[{}, {}]

Step with 2

	Trace

	10[T], 2[(-1+y+x > 0)]
	
	Blocked

	[{}, {}, {}]

Step with 12

	Trace

	10[T], 2[(-1+y+x > 0)], 12[(x <= 0)]
	
	Blocked

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

Backtrack

	Trace

	10[T], 2[(-1+y+x > 0)]
	
	Blocked

	[{}, {}, {12[T]}]

Step with 14

	Trace

	10[T], 2[(-1+y+x > 0)], 14[(x > 0)]
	
	Blocked

	[{}, {}, {12[T]}, {}]

Nonterm

Start location: [1]
Program variables: x y
  10: [1] -> [3] : x'=nondet, y'=nondet1, T, cost: 1
   2: [3] -> [5] : -1+y+x > 0, cost: 1
   9: [3] -> [4] : -1+y+x <= 0, cost: 1
  12: [5] -> [4] : x <= 0, cost: 1
  14: [5] -> [5] : x'=y+2*x, y'=-1+y, x > 0, cost: 1
  15: [5] -> LoAT_sink : (-y-x < 0 /\ x > 0), cost: NONTERM

	Certificate of Non-Termination

	Original rule:
	[5] -> [5] : x'=y+2*x, y'=-1+y, (x > 0), cost: 1
	New rule:
	[5] -> LoAT_sink : (-y-x < 0 /\ x > 0), cost: NONTERM

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

Step with 15

	Trace

	10[T], 2[(-1+y+x > 0)], 15[(-y-x < 0 /\ x > 0)]
	
	Blocked

	[{}, {}, {12[T]}, {15[T]}]

Refute

	Counterexample

	[ x=1 y=1 ] 10 [ x=1 y=1 ] 2 [ x=x y=y ] 15
	
NO

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