unknown

Initial ITS

Start location: [1]
Program variables: c x
   0: [1] -> [2] : x'=nondet, T, cost: 1
   1: [2] -> [3] : c'=nondet1, T, cost: 1
   2: [3] -> [5] : -2+c >= 0, cost: 1
   9: [3] -> [4] : -2+c < 0, cost: 1
   3: [5] -> [6] : c+x >= 0, cost: 1
   7: [5] -> [9] : c+x < 0, cost: 1
   4: [6] -> [7] : x'=-c+x, T, cost: 1
   5: [7] -> [8] : c'=1+c, T, cost: 1
   6: [8] -> [5] : T, cost: 1
   8: [9] -> [4] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: c x
  10: [1] -> [3] : c'=nondet1, x'=nondet, T, cost: 1
   2: [3] -> [5] : -2+c >= 0, cost: 1
   9: [3] -> [4] : -2+c < 0, cost: 1
  12: [5] -> [4] : c+x < 0, cost: 1
  14: [5] -> [5] : c'=1+c, x'=-c+x, c+x >= 0, cost: 1

	Eliminating location [2] by chaining:

	Applied chaining

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

	Removed the following rules: 0 1
	
	Eliminating location [6] by chaining:

	Applied chaining

	First rule:
	[5] -> [6] : c+x >= 0, cost: 1
	Second rule:
	[6] -> [7] : x'=-c+x, T, cost: 1
	New rule:
	[5] -> [7] : x'=-c+x, c+x >= 0, cost: 1
	
	Applied deletion

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

	Applied chaining

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

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

	Applied chaining

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

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

	Applied chaining

	First rule:
	[5] -> [8] : c'=1+c, x'=-c+x, c+x >= 0, cost: 1
	Second rule:
	[8] -> [5] : T, cost: 1
	New rule:
	[5] -> [5] : c'=1+c, x'=-c+x, c+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[(-2+c >= 0)]
	
	Blocked

	[{}, {}, {}]

Step with 12

	Trace

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

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

Backtrack

	Trace

	10[T], 2[(-2+c >= 0)]
	
	Blocked

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

Step with 14

	Trace

	10[T], 2[(-2+c >= 0)], 14[(c+x >= 0)]
	
	Blocked

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

Accelerate

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

	Loop Acceleration

	Original rule:
	[5] -> [5] : c'=1+c, x'=-c+x, (c+x >= 0), cost: 1
	New rule:
	[5] -> [5] : c'=n+c, x'=-n*c-1/2*n^2+1/2*n+x, (-1+n >= 0 /\ -3/2-1/2*(-1+n)^2-(-1+n)*c+3/2*n+c+x >= 0 /\ c+x >= 0), cost: 1

		c+x >= 0 [0]: eventual decrease yields (-3/2-1/2*(-1+n)^2-(-1+n)*c+3/2*n+c+x >= 0 /\ c+x >= 0)
		
		Replacement map: {c+x >= 0 -> (-3/2-1/2*(-1+n)^2-(-1+n)*c+3/2*n+c+x >= 0 /\ c+x >= 0)}

	Trace

	10[T], 2[(-2+c >= 0)], 15[(-1+n >= 0 /\ -3/2-1/2*(-1+n)^2-(-1+n)*c+3/2*n+c+x >= 0 /\ c+x >= 0)]
	
	Blocked

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

Step with 12

	Trace

	10[T], 2[(-2+c >= 0)], 15[(-1+n >= 0 /\ -3/2-1/2*(-1+n)^2-(-1+n)*c+3/2*n+c+x >= 0 /\ c+x >= 0)], 12[(c+x < 0)]
	
	Blocked

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

Backtrack

	Trace

	10[T], 2[(-2+c >= 0)], 15[(-1+n >= 0 /\ -3/2-1/2*(-1+n)^2-(-1+n)*c+3/2*n+c+x >= 0 /\ c+x >= 0)]
	
	Blocked

	[{}, {}, {12[T]}, {12[T], 14[T], 15[T]}]

Backtrack

	Trace

	10[T], 2[(-2+c >= 0)]
	
	Blocked

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

Step with 14

	Trace

	10[T], 2[(-2+c >= 0)], 14[(c+x >= 0)]
	
	Blocked

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

Covered

	Trace

	10[T], 2[(-2+c >= 0)]
	
	Blocked

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

Backtrack

	Trace

	10[T]
	
	Blocked

	[{}, {2[T]}]

Step with 9

	Trace

	10[T], 9[(-2+c < 0)]
	
	Blocked

	[{}, {2[T]}, {}]

Backtrack

	Trace

	10[T]
	
	Blocked

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

Backtrack

	Trace

	Blocked

	[{10[T]}]

Accept

unknown

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b