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

Chained Linear Paths

Start location: [1]
Program variables: x y
  10: [1] -> [3] : x'=nondet, y'=nondet1, T, cost: 1
   9: [3] -> [9] : x < 0, cost: 1
  11: [3] -> [5] : x'=y+x, x >= 0, cost: 1
   7: [5] -> [6] : y < 0, cost: 1
  13: [5] -> [6] : y'=-1+y, y >= 0, cost: 1
   8: [6] -> [3] : 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] : 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 [7] by chaining:

	Applied chaining

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

	Removed the following rules: 4 5
	
	Eliminating location [8] by chaining:

	Applied chaining

	First rule:
	[5] -> [8] : y'=-1+y, y >= 0, cost: 1
	Second rule:
	[8] -> [6] : T, cost: 1
	New rule:
	[5] -> [6] : y'=-1+y, y >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 6 12

Step with 10

	Trace

	10[T]
	
	Blocked

	[{}, {}]

Step with 9

	Trace

	10[T], 9[(x < 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	10[T]
	
	Blocked

	[{}, {9[T]}]

Step with 11

	Trace

	10[T], 11[(x >= 0)]
	
	Blocked

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

Step with 7

	Trace

	10[T], 11[(x >= 0)], 7[(y < 0)]
	
	Blocked

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

Step with 8

	Trace

	10[T], 11[(x >= 0)], 7[(y < 0)], 8[T]
	
	Blocked

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

Accelerate

Start location: [1]
Program variables: x y
  10: [1] -> [3] : x'=nondet, y'=nondet1, T, cost: 1
   9: [3] -> [9] : x < 0, cost: 1
  11: [3] -> [5] : x'=y+x, x >= 0, cost: 1
  14: [3] -> [3] : x'=n*y+x, ((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0), cost: 1
   7: [5] -> [6] : y < 0, cost: 1
  13: [5] -> [6] : y'=-1+y, y >= 0, cost: 1
   8: [6] -> [3] : T, cost: 1

	Loop Acceleration

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

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

	Trace

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

	[{}, {9[T]}, {14[T]}]

Step with 9

	Trace

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

	[{}, {9[T]}, {14[T]}, {}]

Backtrack

	Trace

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

	[{}, {9[T]}, {9[T], 14[T]}]

Step with 11

	Trace

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

	[{}, {9[T]}, {9[T], 14[T]}, {}]

Step with 7

	Trace

	10[T], 14[((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0)], 11[(x >= 0)], 7[(y < 0)]
	
	Blocked

	[{}, {9[T]}, {9[T], 14[T]}, {}, {}]

Step with 8

	Trace

	10[T], 14[((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0)], 11[(x >= 0)], 7[(y < 0)], 8[T]
	
	Blocked

	[{}, {9[T]}, {9[T], 14[T]}, {}, {}, {}]

Covered

	Trace

	10[T], 14[((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0)], 11[(x >= 0)], 7[(y < 0)]
	
	Blocked

	[{}, {9[T]}, {9[T], 14[T]}, {}, {8[T]}]

Backtrack

	Trace

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

	[{}, {9[T]}, {9[T], 14[T]}, {7[T]}]

Backtrack

	Trace

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

	[{}, {9[T]}, {9[T], 11[T], 14[T]}]

Backtrack

	Trace

	10[T]
	
	Blocked

	[{}, {9[T], 14[T]}]

Step with 11

	Trace

	10[T], 11[(x >= 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {}]

Step with 7

	Trace

	10[T], 11[(x >= 0)], 7[(y < 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {}, {}]

Step with 8

	Trace

	10[T], 11[(x >= 0)], 7[(y < 0)], 8[T]
	
	Blocked

	[{}, {9[T], 14[T]}, {}, {}, {}]

Covered

	Trace

	10[T], 11[(x >= 0)], 7[(y < 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {}, {8[T]}]

Backtrack

	Trace

	10[T], 11[(x >= 0)]
	
	Blocked

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

Step with 13

	Trace

	10[T], 11[(x >= 0)], 13[(y >= 0)]
	
	Blocked

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

Step with 8

	Trace

	10[T], 11[(x >= 0)], 13[(y >= 0)], 8[T]
	
	Blocked

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

Accelerate

Start location: [1]
Program variables: x y
  10: [1] -> [3] : x'=nondet, y'=nondet1, T, cost: 1
   9: [3] -> [9] : x < 0, cost: 1
  11: [3] -> [5] : x'=y+x, x >= 0, cost: 1
  14: [3] -> [3] : x'=n*y+x, ((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0), cost: 1
  15: [3] -> [3] : x'=-1/2*n2^2+y*n2+x+1/2*n2, y'=y-n2, (1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0), cost: 1
   7: [5] -> [6] : y < 0, cost: 1
  13: [5] -> [6] : y'=-1+y, y >= 0, cost: 1
   8: [6] -> [3] : T, cost: 1

	Loop Acceleration

	Original rule:
	[3] -> [3] : x'=y+x, y'=-1+y, (y >= 0 /\ x >= 0), cost: 1
	New rule:
	[3] -> [3] : x'=-1/2*n2^2+y*n2+x+1/2*n2, y'=y-n2, (1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0), cost: 1

		y >= 0 [0]: montonic decrease yields 1+y-n2 >= 0
		
		y >= 0 [1]: eventual increase yields (1 <= 0 /\ y >= 0)
		
		x >= 0 [0]: monotonic increase yields x >= 0, dependencies: y >= 0
		
		Replacement map: {y >= 0 -> 1+y-n2 >= 0, x >= 0 -> x >= 0}

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {15[T]}]

Step with 11

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 11[(x >= 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 15[T]}, {}]

Step with 13

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 11[(x >= 0)], 13[(y >= 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 15[T]}, {}, {}]

Step with 8

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 11[(x >= 0)], 13[(y >= 0)], 8[T]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 15[T]}, {}, {}, {}]

Covered

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 11[(x >= 0)], 13[(y >= 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 15[T]}, {}, {8[T]}]

Backtrack

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 11[(x >= 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 15[T]}, {13[T]}]

Step with 7

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 11[(x >= 0)], 7[(y < 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 15[T]}, {13[T]}, {}]

Step with 8

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 11[(x >= 0)], 7[(y < 0)], 8[T]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 15[T]}, {13[T]}, {}, {}]

Covered

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 11[(x >= 0)], 7[(y < 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 15[T]}, {13[T]}, {8[T]}]

Backtrack

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 11[(x >= 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 15[T]}, {7[T], 13[T]}]

Backtrack

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 11[T], 15[T]}]

Step with 14

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 14[((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 11[T], 15[T]}, {14[T]}]

Acceleration Failed

marked recursive suffix as redundant

Step with 9

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 14[((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0)], 9[(x < 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 11[T], 15[T]}, {14[T], 15[T]}, {}]

Backtrack

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 14[((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 11[T], 15[T]}, {9[T], 14[T], 15[T]}]

Step with 11

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 14[((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0)], 11[(x >= 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 11[T], 15[T]}, {9[T], 14[T], 15[T]}, {}]

Step with 7

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 14[((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0)], 11[(x >= 0)], 7[(y < 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 11[T], 15[T]}, {9[T], 14[T], 15[T]}, {}, {}]

Step with 8

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 14[((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0)], 11[(x >= 0)], 7[(y < 0)], 8[T]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 11[T], 15[T]}, {9[T], 14[T], 15[T]}, {}, {}, {}]

Covered

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 14[((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0)], 11[(x >= 0)], 7[(y < 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 11[T], 15[T]}, {9[T], 14[T], 15[T]}, {}, {8[T]}]

Backtrack

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 14[((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0)], 11[(x >= 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 11[T], 15[T]}, {9[T], 14[T], 15[T]}, {7[T]}]

Backtrack

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)], 14[((-1+n)*y+x >= 0 /\ -1+n >= 0 /\ -y > 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 11[T], 15[T]}, {9[T], 11[T], 14[T], 15[T]}]

Backtrack

	Trace

	10[T], 15[(1+y-n2 >= 0 /\ -1+n2 >= 0 /\ x >= 0)]
	
	Blocked

	[{}, {9[T], 14[T]}, {9[T], 11[T], 14[T], 15[T]}]

Backtrack

	Trace

	10[T]
	
	Blocked

	[{}, {9[T], 14[T], 15[T]}]

Step with 11

	Trace

	10[T], 11[(x >= 0)]
	
	Blocked

	[{}, {9[T], 14[T], 15[T]}, {}]

Step with 7

	Trace

	10[T], 11[(x >= 0)], 7[(y < 0)]
	
	Blocked

	[{}, {9[T], 14[T], 15[T]}, {}, {}]

Step with 8

	Trace

	10[T], 11[(x >= 0)], 7[(y < 0)], 8[T]
	
	Blocked

	[{}, {9[T], 14[T], 15[T]}, {}, {}, {}]

Covered

	Trace

	10[T], 11[(x >= 0)], 7[(y < 0)]
	
	Blocked

	[{}, {9[T], 14[T], 15[T]}, {}, {8[T]}]

Backtrack

	Trace

	10[T], 11[(x >= 0)]
	
	Blocked

	[{}, {9[T], 14[T], 15[T]}, {7[T]}]

Step with 13

	Trace

	10[T], 11[(x >= 0)], 13[(y >= 0)]
	
	Blocked

	[{}, {9[T], 14[T], 15[T]}, {7[T]}, {}]

Step with 8

	Trace

	10[T], 11[(x >= 0)], 13[(y >= 0)], 8[T]
	
	Blocked

	[{}, {9[T], 14[T], 15[T]}, {7[T]}, {}, {}]

Covered

	Trace

	10[T], 11[(x >= 0)], 13[(y >= 0)]
	
	Blocked

	[{}, {9[T], 14[T], 15[T]}, {7[T]}, {8[T]}]

Backtrack

	Trace

	10[T], 11[(x >= 0)]
	
	Blocked

	[{}, {9[T], 14[T], 15[T]}, {7[T], 13[T]}]

Backtrack

	Trace

	10[T]
	
	Blocked

	[{}, {9[T], 11[T], 14[T], 15[T]}]

Backtrack

	Trace

	Blocked

	[{10[T]}]

Accept

unknown

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b