unknown

Initial ITS

Start location: [1]
Program variables: x
   0: [1] -> [2] : x'=0, T, cost: 1
   1: [2] -> [3] : x >= 0, cost: 1
   4: [2] -> [5] : x < 0, cost: 1
   2: [3] -> [4] : x'=-1+x, T, cost: 1
   3: [4] -> [2] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: x
   0: [1] -> [2] : x'=0, T, cost: 1
   4: [2] -> [5] : x < 0, cost: 1
   6: [2] -> [2] : x'=-1+x, x >= 0, cost: 1

	Eliminating location [3] by chaining:

	Applied chaining

	First rule:
	[2] -> [3] : x >= 0, cost: 1
	Second rule:
	[3] -> [4] : x'=-1+x, T, cost: 1
	New rule:
	[2] -> [4] : x'=-1+x, x >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 1 2
	
	Eliminating location [4] by chaining:

	Applied chaining

	First rule:
	[2] -> [4] : x'=-1+x, x >= 0, cost: 1
	Second rule:
	[4] -> [2] : T, cost: 1
	New rule:
	[2] -> [2] : x'=-1+x, x >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 3 5

Step with 0

	Trace

	0[T]
	
	Blocked

	[{}, {}]

Step with 6

	Trace

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

	[{}, {4[T]}, {}]

Accelerate

Start location: [1]
Program variables: x
   0: [1] -> [2] : x'=0, T, cost: 1
   4: [2] -> [5] : x < 0, cost: 1
   6: [2] -> [2] : x'=-1+x, x >= 0, cost: 1
   7: [2] -> [2] : x'=-n+x, (1-n+x >= 0 /\ -1+n >= 0), cost: 1

	Loop Acceleration

	Original rule:
	[2] -> [2] : x'=-1+x, (x >= 0), cost: 1
	New rule:
	[2] -> [2] : x'=-n+x, (1-n+x >= 0 /\ -1+n >= 0), cost: 1

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

	Trace

	0[T], 7[(1-n+x >= 0 /\ -1+n >= 0)]
	
	Blocked

	[{}, {4[T]}, {6[T], 7[T]}]

Step with 4

	Trace

	0[T], 7[(1-n+x >= 0 /\ -1+n >= 0)], 4[(x < 0)]
	
	Blocked

	[{}, {4[T]}, {6[T], 7[T]}, {}]

Backtrack

	Trace

	0[T], 7[(1-n+x >= 0 /\ -1+n >= 0)]
	
	Blocked

	[{}, {4[T]}, {4[T], 6[T], 7[T]}]

Backtrack

	Trace

	0[T]
	
	Blocked

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

Step with 6

	Trace

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

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

Covered

	Trace

	0[T]
	
	Blocked

	[{}, {4[T], 6[T], 7[T]}]

Backtrack

	Trace

	Blocked

	[{0[T]}]

Accept

unknown

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b