NO

Initial ITS

Start location: [1]
Program variables: i j t
   0: [1] -> [2] : i'=nondet, T, cost: 1
   1: [2] -> [3] : j'=nondet1, T, cost: 1
   2: [3] -> [4] : t'=0, T, cost: 1
   3: [4] -> [5] : ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1
   8: [4] -> [9] : ((i <= 0 /\ i >= 0) \/ (j <= 0 /\ j >= 0)), cost: 1
   4: [5] -> [6] : t'=i, T, cost: 1
   5: [6] -> [7] : i'=j, T, cost: 1
   6: [7] -> [8] : j'=t, T, cost: 1
   7: [8] -> [4] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: i j t
  10: [1] -> [4] : i'=nondet, j'=nondet1, t'=0, T, cost: 1
   8: [4] -> [9] : ((i <= 0 /\ i >= 0) \/ (j <= 0 /\ j >= 0)), cost: 1
  14: [4] -> [4] : i'=j, j'=i, t'=i, ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1

	Eliminating location [2] by chaining:

	Applied chaining

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

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

	Applied chaining

	First rule:
	[1] -> [3] : i'=nondet, j'=nondet1, T, cost: 1
	Second rule:
	[3] -> [4] : t'=0, T, cost: 1
	New rule:
	[1] -> [4] : i'=nondet, j'=nondet1, t'=0, T, cost: 1
	
	Applied deletion

	Removed the following rules: 2 9
	
	Eliminating location [5] by chaining:

	Applied chaining

	First rule:
	[4] -> [5] : ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1
	Second rule:
	[5] -> [6] : t'=i, T, cost: 1
	New rule:
	[4] -> [6] : t'=i, ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1
	
	Applied deletion

	Removed the following rules: 3 4
	
	Eliminating location [6] by chaining:

	Applied chaining

	First rule:
	[4] -> [6] : t'=i, ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1
	Second rule:
	[6] -> [7] : i'=j, T, cost: 1
	New rule:
	[4] -> [7] : i'=j, t'=i, ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1
	
	Applied deletion

	Removed the following rules: 5 11
	
	Eliminating location [7] by chaining:

	Applied chaining

	First rule:
	[4] -> [7] : i'=j, t'=i, ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1
	Second rule:
	[7] -> [8] : j'=t, T, cost: 1
	New rule:
	[4] -> [8] : i'=j, j'=i, t'=i, ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1
	
	Applied deletion

	Removed the following rules: 6 12
	
	Eliminating location [8] by chaining:

	Applied chaining

	First rule:
	[4] -> [8] : i'=j, j'=i, t'=i, ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1
	Second rule:
	[8] -> [4] : T, cost: 1
	New rule:
	[4] -> [4] : i'=j, j'=i, t'=i, ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1
	
	Applied deletion

	Removed the following rules: 7 13

Unrolled Loops

Start location: [1]
Program variables: i j t
  10: [1] -> [4] : i'=nondet, j'=nondet1, t'=0, T, cost: 1
   8: [4] -> [9] : ((i <= 0 /\ i >= 0) \/ (j <= 0 /\ j >= 0)), cost: 1
  14: [4] -> [4] : i'=j, j'=i, t'=i, ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1
  15: [4] -> [4] : t'=j, ((j < 0 \/ j > 0) /\ (i < 0 \/ i > 0)), cost: 1

	Unrolling

	Original rule:
	[4] -> [4] : i'=j, j'=i, t'=i, ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1
	New rule:
	[4] -> [4] : i'=i, j'=j, t'=j, ((j < 0 \/ j > 0) /\ (i < 0 \/ i > 0)), cost: 1
	
	Removed Trivial Updates

	Original rule:
	[4] -> [4] : i'=i, j'=j, t'=j, ((j < 0 \/ j > 0) /\ (i < 0 \/ i > 0)), cost: 1
	New rule:
	[4] -> [4] : t'=j, ((j < 0 \/ j > 0) /\ (i < 0 \/ i > 0)), cost: 1

Step with 10

	Trace

	10[T]
	
	Blocked

	[{}, {}]

Step with 8

	Trace

	10[T], 8[(i <= 0 /\ i >= 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	10[T]
	
	Blocked

	[{}, {8[(i <= 0 /\ i >= 0)]}]

Step with 8

	Trace

	10[T], 8[(j <= 0 /\ j >= 0)]
	
	Blocked

	[{}, {8[(i <= 0 /\ i >= 0)]}, {}]

Backtrack

	Trace

	10[T]
	
	Blocked

	[{}, {8[(j <= 0 /\ j >= 0 /\ i <= 0 /\ i >= 0)]}]

Step with 14

	Trace

	10[T], 14[(j > 0 /\ i < 0)]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Step with 14

	Trace

	10[T], 14[(j > 0 /\ i < 0)], 14[(j < 0 /\ i > 0)]
	
	Blocked

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

Acceleration Failed

marked recursive suffix as redundant

Nonterm

Start location: [1]
Program variables: i j t
  10: [1] -> [4] : i'=nondet, j'=nondet1, t'=0, T, cost: 1
   8: [4] -> [9] : ((i <= 0 /\ i >= 0) \/ (j <= 0 /\ j >= 0)), cost: 1
  14: [4] -> [4] : i'=j, j'=i, t'=i, ((i < 0 \/ i > 0) /\ (j < 0 \/ j > 0)), cost: 1
  15: [4] -> [4] : t'=j, ((j < 0 \/ j > 0) /\ (i < 0 \/ i > 0)), cost: 1
  16: [4] -> LoAT_sink : (-1+n >= 0 /\ j > 0 /\ -i > 0), cost: NONTERM

	Certificate of Non-Termination

	Original rule:
	[4] -> [4] : t'=j, (j > 0 /\ i < 0), cost: 1
	New rule:
	[4] -> LoAT_sink : (-1+n >= 0 /\ j > 0 /\ -i > 0), cost: NONTERM

		j > 0 [0]: monotonic increase yields j > 0
		
		-i > 0 [0]: monotonic increase yields -i > 0
		
		Replacement map: {j > 0 -> j > 0, -i > 0 -> -i > 0}

Step with 16

	Trace

	10[T], 16[(-1+n >= 0 /\ j > 0 /\ -i > 0)]
	
	Blocked

	[{}, {8[T]}, {16[T]}]

Refute

	Counterexample

	[ i=-1 j=1 t=0 ] 10 [ i=i j=j t=t ] 16
	
NO

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b