unknown

Initial ITS

Start location: [1]
Program variables: c u v w x y z
   0: [1] -> [2] : x'=nondet, T, cost: 1
   1: [2] -> [3] : y'=nondet1, T, cost: 1
   2: [3] -> [4] : z'=nondet2, T, cost: 1
   3: [4] -> [5] : u'=x, T, cost: 1
   4: [5] -> [6] : v'=y, T, cost: 1
   5: [6] -> [7] : w'=z, T, cost: 1
   6: [7] -> [8] : c'=0, T, cost: 1
   7: [8] -> [9] : -y+x >= 0, cost: 1
  17: [8] -> [17] : -y+x < 0, cost: 1
   8: [9] -> [10] : c'=1+c, T, cost: 1
   9: [10] -> [12] : -1+z > 0, cost: 1
  13: [10] -> [15] : -1+z <= 0, cost: 1
  16: [11] -> [8] : T, cost: 1
  10: [12] -> [13] : z'=-1+z, T, cost: 1
  11: [13] -> [14] : x'=z+x, T, cost: 1
  12: [14] -> [11] : T, cost: 1
  14: [15] -> [16] : y'=1+y, T, cost: 1
  15: [16] -> [11] : T, cost: 1

Chained Linear Paths

Start location: [1]
Program variables: c u v w x y z
  23: [1] -> [8] : c'=0, u'=nondet, v'=nondet1, w'=nondet2, x'=nondet, y'=nondet1, z'=nondet2, T, cost: 1
  17: [8] -> [17] : -y+x < 0, cost: 1
  24: [8] -> [10] : c'=1+c, -y+x >= 0, cost: 1
  28: [10] -> [11] : y'=1+y, -1+z <= 0, cost: 1
  29: [10] -> [11] : x'=-1+z+x, z'=-1+z, -1+z > 0, cost: 1
  16: [11] -> [8] : 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 [3] by chaining:

	Applied chaining

	First rule:
	[1] -> [3] : x'=nondet, y'=nondet1, T, cost: 1
	Second rule:
	[3] -> [4] : z'=nondet2, T, cost: 1
	New rule:
	[1] -> [4] : x'=nondet, y'=nondet1, z'=nondet2, T, cost: 1
	
	Applied deletion

	Removed the following rules: 2 18
	
	Eliminating location [4] by chaining:

	Applied chaining

	First rule:
	[1] -> [4] : x'=nondet, y'=nondet1, z'=nondet2, T, cost: 1
	Second rule:
	[4] -> [5] : u'=x, T, cost: 1
	New rule:
	[1] -> [5] : u'=nondet, x'=nondet, y'=nondet1, z'=nondet2, T, cost: 1
	
	Applied deletion

	Removed the following rules: 3 19
	
	Eliminating location [5] by chaining:

	Applied chaining

	First rule:
	[1] -> [5] : u'=nondet, x'=nondet, y'=nondet1, z'=nondet2, T, cost: 1
	Second rule:
	[5] -> [6] : v'=y, T, cost: 1
	New rule:
	[1] -> [6] : u'=nondet, v'=nondet1, x'=nondet, y'=nondet1, z'=nondet2, T, cost: 1
	
	Applied deletion

	Removed the following rules: 4 20
	
	Eliminating location [6] by chaining:

	Applied chaining

	First rule:
	[1] -> [6] : u'=nondet, v'=nondet1, x'=nondet, y'=nondet1, z'=nondet2, T, cost: 1
	Second rule:
	[6] -> [7] : w'=z, T, cost: 1
	New rule:
	[1] -> [7] : u'=nondet, v'=nondet1, w'=nondet2, x'=nondet, y'=nondet1, z'=nondet2, T, cost: 1
	
	Applied deletion

	Removed the following rules: 5 21
	
	Eliminating location [7] by chaining:

	Applied chaining

	First rule:
	[1] -> [7] : u'=nondet, v'=nondet1, w'=nondet2, x'=nondet, y'=nondet1, z'=nondet2, T, cost: 1
	Second rule:
	[7] -> [8] : c'=0, T, cost: 1
	New rule:
	[1] -> [8] : c'=0, u'=nondet, v'=nondet1, w'=nondet2, x'=nondet, y'=nondet1, z'=nondet2, T, cost: 1
	
	Applied deletion

	Removed the following rules: 6 22
	
	Eliminating location [9] by chaining:

	Applied chaining

	First rule:
	[8] -> [9] : -y+x >= 0, cost: 1
	Second rule:
	[9] -> [10] : c'=1+c, T, cost: 1
	New rule:
	[8] -> [10] : c'=1+c, -y+x >= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 7 8
	
	Eliminating location [12] by chaining:

	Applied chaining

	First rule:
	[10] -> [12] : -1+z > 0, cost: 1
	Second rule:
	[12] -> [13] : z'=-1+z, T, cost: 1
	New rule:
	[10] -> [13] : z'=-1+z, -1+z > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 9 10
	
	Eliminating location [15] by chaining:

	Applied chaining

	First rule:
	[10] -> [15] : -1+z <= 0, cost: 1
	Second rule:
	[15] -> [16] : y'=1+y, T, cost: 1
	New rule:
	[10] -> [16] : y'=1+y, -1+z <= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 13 14
	
	Eliminating location [13] by chaining:

	Applied chaining

	First rule:
	[10] -> [13] : z'=-1+z, -1+z > 0, cost: 1
	Second rule:
	[13] -> [14] : x'=z+x, T, cost: 1
	New rule:
	[10] -> [14] : x'=-1+z+x, z'=-1+z, -1+z > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 11 25
	
	Eliminating location [16] by chaining:

	Applied chaining

	First rule:
	[10] -> [16] : y'=1+y, -1+z <= 0, cost: 1
	Second rule:
	[16] -> [11] : T, cost: 1
	New rule:
	[10] -> [11] : y'=1+y, -1+z <= 0, cost: 1
	
	Applied deletion

	Removed the following rules: 15 26
	
	Eliminating location [14] by chaining:

	Applied chaining

	First rule:
	[10] -> [14] : x'=-1+z+x, z'=-1+z, -1+z > 0, cost: 1
	Second rule:
	[14] -> [11] : T, cost: 1
	New rule:
	[10] -> [11] : x'=-1+z+x, z'=-1+z, -1+z > 0, cost: 1
	
	Applied deletion

	Removed the following rules: 12 27

Step with 23

	Trace

	23[T]
	
	Blocked

	[{}, {}]

Step with 17

	Trace

	23[T], 17[(-y+x < 0)]
	
	Blocked

	[{}, {}, {}]

Backtrack

	Trace

	23[T]
	
	Blocked

	[{}, {17[T]}]

Step with 24

	Trace

	23[T], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T]}, {}]

Step with 28

	Trace

	23[T], 24[(-y+x >= 0)], 28[(-1+z <= 0)]
	
	Blocked

	[{}, {17[T]}, {}, {}]

Step with 16

	Trace

	23[T], 24[(-y+x >= 0)], 28[(-1+z <= 0)], 16[T]
	
	Blocked

	[{}, {17[T]}, {}, {}, {}]

Accelerate

Start location: [1]
Program variables: c u v w x y z
  23: [1] -> [8] : c'=0, u'=nondet, v'=nondet1, w'=nondet2, x'=nondet, y'=nondet1, z'=nondet2, T, cost: 1
  17: [8] -> [17] : -y+x < 0, cost: 1
  24: [8] -> [10] : c'=1+c, -y+x >= 0, cost: 1
  30: [8] -> [8] : c'=n+c, y'=n+y, (1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0), cost: 1
  28: [10] -> [11] : y'=1+y, -1+z <= 0, cost: 1
  29: [10] -> [11] : x'=-1+z+x, z'=-1+z, -1+z > 0, cost: 1
  16: [11] -> [8] : T, cost: 1

	Loop Acceleration

	Original rule:
	[8] -> [8] : c'=1+c, y'=1+y, (-1+z <= 0 /\ -y+x >= 0), cost: 1
	New rule:
	[8] -> [8] : c'=n+c, y'=n+y, (1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0), cost: 1

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

	Trace

	23[T], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)]
	
	Blocked

	[{}, {17[T]}, {30[T]}]

Step with 17

	Trace

	23[T], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)], 17[(-y+x < 0)]
	
	Blocked

	[{}, {17[T]}, {30[T]}, {}]

Backtrack

	Trace

	23[T], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)]
	
	Blocked

	[{}, {17[T]}, {17[T], 30[T]}]

Step with 24

	Trace

	23[T], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T]}, {17[T], 30[T]}, {}]

Step with 28

	Trace

	23[T], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)], 24[(-y+x >= 0)], 28[(-1+z <= 0)]
	
	Blocked

	[{}, {17[T]}, {17[T], 30[T]}, {}, {}]

Step with 16

	Trace

	23[T], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)], 24[(-y+x >= 0)], 28[(-1+z <= 0)], 16[T]
	
	Blocked

	[{}, {17[T]}, {17[T], 30[T]}, {}, {}, {}]

Covered

	Trace

	23[T], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)], 24[(-y+x >= 0)], 28[(-1+z <= 0)]
	
	Blocked

	[{}, {17[T]}, {17[T], 30[T]}, {}, {16[T]}]

Backtrack

	Trace

	23[T], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T]}, {17[T], 30[T]}, {28[T]}]

Backtrack

	Trace

	23[T], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)]
	
	Blocked

	[{}, {17[T]}, {17[T], 24[T], 30[T]}]

Backtrack

	Trace

	23[T]
	
	Blocked

	[{}, {17[T], 30[T]}]

Step with 24

	Trace

	23[T], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {}]

Step with 28

	Trace

	23[T], 24[(-y+x >= 0)], 28[(-1+z <= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {}, {}]

Step with 16

	Trace

	23[T], 24[(-y+x >= 0)], 28[(-1+z <= 0)], 16[T]
	
	Blocked

	[{}, {17[T], 30[T]}, {}, {}, {}]

Covered

	Trace

	23[T], 24[(-y+x >= 0)], 28[(-1+z <= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {}, {16[T]}]

Backtrack

	Trace

	23[T], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {28[T]}]

Step with 29

	Trace

	23[T], 24[(-y+x >= 0)], 29[(-1+z > 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {28[T]}, {}]

Step with 16

	Trace

	23[T], 24[(-y+x >= 0)], 29[(-1+z > 0)], 16[T]
	
	Blocked

	[{}, {17[T], 30[T]}, {28[T]}, {}, {}]

Accelerate

Start location: [1]
Program variables: c u v w x y z
  23: [1] -> [8] : c'=0, u'=nondet, v'=nondet1, w'=nondet2, x'=nondet, y'=nondet1, z'=nondet2, T, cost: 1
  17: [8] -> [17] : -y+x < 0, cost: 1
  24: [8] -> [10] : c'=1+c, -y+x >= 0, cost: 1
  30: [8] -> [8] : c'=n+c, y'=n+y, (1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0), cost: 1
  31: [8] -> [8] : c'=n2+c, x'=-1/2*n2+n2*z-1/2*n2^2+x, z'=-n2+z, (-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0), cost: 1
  28: [10] -> [11] : y'=1+y, -1+z <= 0, cost: 1
  29: [10] -> [11] : x'=-1+z+x, z'=-1+z, -1+z > 0, cost: 1
  16: [11] -> [8] : T, cost: 1

	Loop Acceleration

	Original rule:
	[8] -> [8] : c'=1+c, x'=-1+z+x, z'=-1+z, (-1+z > 0 /\ -y+x >= 0), cost: 1
	New rule:
	[8] -> [8] : c'=n2+c, x'=-1/2*n2+n2*z-1/2*n2^2+x, z'=-n2+z, (-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0), cost: 1

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

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {31[T]}]

Step with 24

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 31[T]}, {}]

Step with 29

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 24[(-y+x >= 0)], 29[(-1+z > 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 31[T]}, {}, {}]

Step with 16

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 24[(-y+x >= 0)], 29[(-1+z > 0)], 16[T]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 31[T]}, {}, {}, {}]

Covered

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 24[(-y+x >= 0)], 29[(-1+z > 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 31[T]}, {}, {16[T]}]

Backtrack

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 31[T]}, {29[T]}]

Step with 28

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 24[(-y+x >= 0)], 28[(-1+z <= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 31[T]}, {29[T]}, {}]

Step with 16

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 24[(-y+x >= 0)], 28[(-1+z <= 0)], 16[T]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 31[T]}, {29[T]}, {}, {}]

Covered

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 24[(-y+x >= 0)], 28[(-1+z <= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 31[T]}, {29[T]}, {16[T]}]

Backtrack

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 31[T]}, {28[T], 29[T]}]

Backtrack

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 24[T], 31[T]}]

Step with 30

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 24[T], 31[T]}, {30[T]}]

Acceleration Failed

marked recursive suffix as redundant

Step with 17

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)], 17[(-y+x < 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 24[T], 31[T]}, {30[T], 31[T]}, {}]

Backtrack

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 24[T], 31[T]}, {17[T], 30[T], 31[T]}]

Step with 24

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 24[T], 31[T]}, {17[T], 30[T], 31[T]}, {}]

Step with 28

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)], 24[(-y+x >= 0)], 28[(-1+z <= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 24[T], 31[T]}, {17[T], 30[T], 31[T]}, {}, {}]

Step with 16

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)], 24[(-y+x >= 0)], 28[(-1+z <= 0)], 16[T]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 24[T], 31[T]}, {17[T], 30[T], 31[T]}, {}, {}, {}]

Covered

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)], 24[(-y+x >= 0)], 28[(-1+z <= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 24[T], 31[T]}, {17[T], 30[T], 31[T]}, {}, {16[T]}]

Backtrack

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 24[T], 31[T]}, {17[T], 30[T], 31[T]}, {28[T]}]

Backtrack

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)], 30[(1-z >= 0 /\ -1+n >= 0 /\ 1-n-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 24[T], 31[T]}, {17[T], 24[T], 30[T], 31[T]}]

Backtrack

	Trace

	23[T], 31[(-y+x >= 0 /\ -1+n2 >= 0 /\ -n2+z > 0)]
	
	Blocked

	[{}, {17[T], 30[T]}, {17[T], 24[T], 30[T], 31[T]}]

Backtrack

	Trace

	23[T]
	
	Blocked

	[{}, {17[T], 30[T], 31[T]}]

Step with 24

	Trace

	23[T], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T], 31[T]}, {}]

Step with 28

	Trace

	23[T], 24[(-y+x >= 0)], 28[(-1+z <= 0)]
	
	Blocked

	[{}, {17[T], 30[T], 31[T]}, {}, {}]

Step with 16

	Trace

	23[T], 24[(-y+x >= 0)], 28[(-1+z <= 0)], 16[T]
	
	Blocked

	[{}, {17[T], 30[T], 31[T]}, {}, {}, {}]

Covered

	Trace

	23[T], 24[(-y+x >= 0)], 28[(-1+z <= 0)]
	
	Blocked

	[{}, {17[T], 30[T], 31[T]}, {}, {16[T]}]

Backtrack

	Trace

	23[T], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T], 31[T]}, {28[T]}]

Step with 29

	Trace

	23[T], 24[(-y+x >= 0)], 29[(-1+z > 0)]
	
	Blocked

	[{}, {17[T], 30[T], 31[T]}, {28[T]}, {}]

Step with 16

	Trace

	23[T], 24[(-y+x >= 0)], 29[(-1+z > 0)], 16[T]
	
	Blocked

	[{}, {17[T], 30[T], 31[T]}, {28[T]}, {}, {}]

Covered

	Trace

	23[T], 24[(-y+x >= 0)], 29[(-1+z > 0)]
	
	Blocked

	[{}, {17[T], 30[T], 31[T]}, {28[T]}, {16[T]}]

Backtrack

	Trace

	23[T], 24[(-y+x >= 0)]
	
	Blocked

	[{}, {17[T], 30[T], 31[T]}, {28[T], 29[T]}]

Backtrack

	Trace

	23[T]
	
	Blocked

	[{}, {17[T], 24[T], 30[T], 31[T]}]

Backtrack

	Trace

	Blocked

	[{23[T]}]

Accept

unknown

Build SHA: a05f16bf13df659c382799650051f91bf6828c7b