WORST_CASE(Omega(0),?)

Initial ITS
Start location: l9
   0: l0 -> l1 : y^0'=y^post0, x^0'=x^post0, z^0'=z^post0, (z^0-z^post0 == 0 /\ 1-x^0+x^post0 == 0 /\ 1-x^0 <= 0 /\ y^0-y^post0 == 0), cost: 1
   1: l1 -> l0 : y^0'=y^post1, x^0'=x^post1, z^0'=z^post1, (z^0-z^post1 == 0 /\ x^0-x^post1 == 0 /\ y^0-y^post1 == 0), cost: 1
   2: l2 -> l0 : y^0'=y^post2, x^0'=x^post2, z^0'=z^post2, (z^0-z^post2 == 0 /\ y^0 <= 0 /\ y^0-y^post2 == 0 /\ -x^post2+x^0 == 0), cost: 1
   3: l2 -> l3 : y^0'=y^post3, x^0'=x^post3, z^0'=z^post3, (-x^post3+x^0 == 0 /\ -z^post3+z^0 == 0 /\ 1+y^post3-y^0 == 0 /\ 1-y^0 <= 0), cost: 1
   4: l3 -> l2 : y^0'=y^post4, x^0'=x^post4, z^0'=z^post4, (-x^post4+x^0 == 0 /\ -z^post4+z^0 == 0 /\ -y^post4+y^0 == 0), cost: 1
   5: l4 -> l2 : y^0'=y^post5, x^0'=x^post5, z^0'=z^post5, (-x^post5+x^0 == 0 /\ -z^post5+z^0 == 0 /\ -x^0+z^0 <= 0 /\ -y^post5+y^0 == 0), cost: 1
   6: l4 -> l5 : y^0'=y^post6, x^0'=x^post6, z^0'=z^post6, (1+x^0-z^0 <= 0 /\ y^0-y^post6 == 0 /\ -z^post6+z^0 == 0 /\ -1+x^post6-x^0 == 0), cost: 1
   7: l5 -> l4 : y^0'=y^post7, x^0'=x^post7, z^0'=z^post7, (-z^post7+z^0 == 0 /\ -x^post7+x^0 == 0 /\ y^0-y^post7 == 0), cost: 1
   8: l6 -> l4 : y^0'=y^post8, x^0'=x^post8, z^0'=z^post8, (x^0-x^post8 == 0 /\ -z^post8+z^0 == 0 /\ y^0-y^post8 == 0 /\ y^0-z^0 <= 0), cost: 1
   9: l6 -> l7 : y^0'=y^post9, x^0'=x^post9, z^0'=z^post9, (1-y^0+y^post9 == 0 /\ x^0-x^post9 == 0 /\ -z^post9+z^0 == 0 /\ 1-y^0+z^0 <= 0), cost: 1
  10: l7 -> l6 : y^0'=y^post10, x^0'=x^post10, z^0'=z^post10, (x^0-x^post10 == 0 /\ y^0-y^post10 == 0 /\ -z^post10+z^0 == 0), cost: 1
  11: l8 -> l6 : y^0'=y^post11, x^0'=x^post11, z^0'=z^post11, (y^0-y^post11 == 0 /\ -z^post11+z^0 == 0 /\ x^post11 == 0), cost: 1
  12: l9 -> l8 : y^0'=y^post12, x^0'=x^post12, z^0'=z^post12, (x^0-x^post12 == 0 /\ -z^post12+z^0 == 0 /\ y^0-y^post12 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : y^0'=y^post0, x^0'=x^post0, z^0'=z^post0, (z^0-z^post0 == 0 /\ 1-x^0+x^post0 == 0 /\ 1-x^0 <= 0 /\ y^0-y^post0 == 0), cost: 1
New rule:
l0 -> l1 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l0 : y^0'=y^post1, x^0'=x^post1, z^0'=z^post1, (z^0-z^post1 == 0 /\ x^0-x^post1 == 0 /\ y^0-y^post1 == 0), cost: 1
New rule:
l1 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : y^0'=y^post2, x^0'=x^post2, z^0'=z^post2, (z^0-z^post2 == 0 /\ y^0 <= 0 /\ y^0-y^post2 == 0 /\ -x^post2+x^0 == 0), cost: 1
New rule:
l2 -> l0 : y^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l3 : y^0'=y^post3, x^0'=x^post3, z^0'=z^post3, (-x^post3+x^0 == 0 /\ -z^post3+z^0 == 0 /\ 1+y^post3-y^0 == 0 /\ 1-y^0 <= 0), cost: 1
New rule:
l2 -> l3 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : y^0'=y^post4, x^0'=x^post4, z^0'=z^post4, (-x^post4+x^0 == 0 /\ -z^post4+z^0 == 0 /\ -y^post4+y^0 == 0), cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l2 : y^0'=y^post5, x^0'=x^post5, z^0'=z^post5, (-x^post5+x^0 == 0 /\ -z^post5+z^0 == 0 /\ -x^0+z^0 <= 0 /\ -y^post5+y^0 == 0), cost: 1
New rule:
l4 -> l2 : -x^0+z^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l5 : y^0'=y^post6, x^0'=x^post6, z^0'=z^post6, (1+x^0-z^0 <= 0 /\ y^0-y^post6 == 0 /\ -z^post6+z^0 == 0 /\ -1+x^post6-x^0 == 0), cost: 1
New rule:
l4 -> l5 : x^0'=1+x^0, 1+x^0-z^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l5 -> l4 : y^0'=y^post7, x^0'=x^post7, z^0'=z^post7, (-z^post7+z^0 == 0 /\ -x^post7+x^0 == 0 /\ y^0-y^post7 == 0), cost: 1
New rule:
l5 -> l4 : TRUE, cost: 1

Applied preprocessing
Original rule:
l6 -> l4 : y^0'=y^post8, x^0'=x^post8, z^0'=z^post8, (x^0-x^post8 == 0 /\ -z^post8+z^0 == 0 /\ y^0-y^post8 == 0 /\ y^0-z^0 <= 0), cost: 1
New rule:
l6 -> l4 : y^0-z^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l6 -> l7 : y^0'=y^post9, x^0'=x^post9, z^0'=z^post9, (1-y^0+y^post9 == 0 /\ x^0-x^post9 == 0 /\ -z^post9+z^0 == 0 /\ 1-y^0+z^0 <= 0), cost: 1
New rule:
l6 -> l7 : y^0'=-1+y^0, 1-y^0+z^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l7 -> l6 : y^0'=y^post10, x^0'=x^post10, z^0'=z^post10, (x^0-x^post10 == 0 /\ y^0-y^post10 == 0 /\ -z^post10+z^0 == 0), cost: 1
New rule:
l7 -> l6 : TRUE, cost: 1

Applied preprocessing
Original rule:
l8 -> l6 : y^0'=y^post11, x^0'=x^post11, z^0'=z^post11, (y^0-y^post11 == 0 /\ -z^post11+z^0 == 0 /\ x^post11 == 0), cost: 1
New rule:
l8 -> l6 : x^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l9 -> l8 : y^0'=y^post12, x^0'=x^post12, z^0'=z^post12, (x^0-x^post12 == 0 /\ -z^post12+z^0 == 0 /\ y^0-y^post12 == 0), cost: 1
New rule:
l9 -> l8 : TRUE, cost: 1

Simplified rules
Start location: l9
  13: l0 -> l1 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 1
  14: l1 -> l0 : TRUE, cost: 1
  15: l2 -> l0 : y^0 <= 0, cost: 1
  16: l2 -> l3 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 1
  17: l3 -> l2 : TRUE, cost: 1
  18: l4 -> l2 : -x^0+z^0 <= 0, cost: 1
  19: l4 -> l5 : x^0'=1+x^0, 1+x^0-z^0 <= 0, cost: 1
  20: l5 -> l4 : TRUE, cost: 1
  21: l6 -> l4 : y^0-z^0 <= 0, cost: 1
  22: l6 -> l7 : y^0'=-1+y^0, 1-y^0+z^0 <= 0, cost: 1
  23: l7 -> l6 : TRUE, cost: 1
  24: l8 -> l6 : x^0'=0, TRUE, cost: 1
  25: l9 -> l8 : TRUE, cost: 1


Eliminating location l8 by chaining:

Applied chaining
First rule:
l9 -> l8 : TRUE, cost: 1
Second rule:
l8 -> l6 : x^0'=0, TRUE, cost: 1
New rule:
l9 -> l6 : x^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 24 25

Eliminating location l7 by chaining:

Applied chaining
First rule:
l6 -> l7 : y^0'=-1+y^0, 1-y^0+z^0 <= 0, cost: 1
Second rule:
l7 -> l6 : TRUE, cost: 1
New rule:
l6 -> l6 : y^0'=-1+y^0, 1-y^0+z^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 22 23

Eliminating location l5 by chaining:

Applied chaining
First rule:
l4 -> l5 : x^0'=1+x^0, 1+x^0-z^0 <= 0, cost: 1
Second rule:
l5 -> l4 : TRUE, cost: 1
New rule:
l4 -> l4 : x^0'=1+x^0, 1+x^0-z^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 19 20

Eliminating location l3 by chaining:

Applied chaining
First rule:
l2 -> l3 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 1
Second rule:
l3 -> l2 : TRUE, cost: 1
New rule:
l2 -> l2 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 16 17

Eliminating location l1 by chaining:

Applied chaining
First rule:
l0 -> l1 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 1
Second rule:
l1 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 13 14

Eliminated locations on linear paths
Start location: l9
  30: l0 -> l0 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
  15: l2 -> l0 : y^0 <= 0, cost: 1
  29: l2 -> l2 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 2
  18: l4 -> l2 : -x^0+z^0 <= 0, cost: 1
  28: l4 -> l4 : x^0'=1+x^0, 1+x^0-z^0 <= 0, cost: 2
  21: l6 -> l4 : y^0-z^0 <= 0, cost: 1
  27: l6 -> l6 : y^0'=-1+y^0, 1-y^0+z^0 <= 0, cost: 2
  26: l9 -> l6 : x^0'=0, TRUE, cost: 2


Applied acceleration
Original rule:
l0 -> l0 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
New rule:
l0 -> l0 : x^0'=-n+x^0, (-n+x^0 >= 0 /\ n >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_jaElFP.txt

Applied instantiation
Original rule:
l0 -> l0 : x^0'=-n+x^0, (-n+x^0 >= 0 /\ n >= 0), cost: 2*n
New rule:
l0 -> l0 : x^0'=0, (0 >= 0 /\ x^0 >= 0), cost: 2*x^0

Applied simplification
Original rule:
l0 -> l0 : x^0'=0, (0 >= 0 /\ x^0 >= 0), cost: 2*x^0
New rule:
l0 -> l0 : x^0'=0, x^0 >= 0, cost: 2*x^0

Applied deletion
Removed the following rules: 30

Applied acceleration
Original rule:
l2 -> l2 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 2
New rule:
l2 -> l2 : y^0'=y^0-n0, (n0 >= 0 /\ y^0-n0 >= 0), cost: 2*n0
Sub-proof via acceration calculus written to file:///tmp/tmpnam_pkfDcN.txt

Applied instantiation
Original rule:
l2 -> l2 : y^0'=y^0-n0, (n0 >= 0 /\ y^0-n0 >= 0), cost: 2*n0
New rule:
l2 -> l2 : y^0'=0, (0 >= 0 /\ y^0 >= 0), cost: 2*y^0

Applied simplification
Original rule:
l2 -> l2 : y^0'=0, (0 >= 0 /\ y^0 >= 0), cost: 2*y^0
New rule:
l2 -> l2 : y^0'=0, y^0 >= 0, cost: 2*y^0

Applied deletion
Removed the following rules: 29

Applied acceleration
Original rule:
l4 -> l4 : x^0'=1+x^0, 1+x^0-z^0 <= 0, cost: 2
New rule:
l4 -> l4 : x^0'=n1+x^0, (-n1-x^0+z^0 >= 0 /\ n1 >= 0), cost: 2*n1
Sub-proof via acceration calculus written to file:///tmp/tmpnam_fOJigG.txt

Applied instantiation
Original rule:
l4 -> l4 : x^0'=n1+x^0, (-n1-x^0+z^0 >= 0 /\ n1 >= 0), cost: 2*n1
New rule:
l4 -> l4 : x^0'=z^0, (0 >= 0 /\ -x^0+z^0 >= 0), cost: -2*x^0+2*z^0

Applied simplification
Original rule:
l4 -> l4 : x^0'=z^0, (0 >= 0 /\ -x^0+z^0 >= 0), cost: -2*x^0+2*z^0
New rule:
l4 -> l4 : x^0'=z^0, -x^0+z^0 >= 0, cost: -2*x^0+2*z^0

Applied deletion
Removed the following rules: 28

Applied acceleration
Original rule:
l6 -> l6 : y^0'=-1+y^0, 1-y^0+z^0 <= 0, cost: 2
New rule:
l6 -> l6 : y^0'=y^0-n2, (y^0-z^0-n2 >= 0 /\ n2 >= 0), cost: 2*n2
Sub-proof via acceration calculus written to file:///tmp/tmpnam_fLJfkG.txt

Applied instantiation
Original rule:
l6 -> l6 : y^0'=y^0-n2, (y^0-z^0-n2 >= 0 /\ n2 >= 0), cost: 2*n2
New rule:
l6 -> l6 : y^0'=z^0, (0 >= 0 /\ y^0-z^0 >= 0), cost: 2*y^0-2*z^0

Applied simplification
Original rule:
l6 -> l6 : y^0'=z^0, (0 >= 0 /\ y^0-z^0 >= 0), cost: 2*y^0-2*z^0
New rule:
l6 -> l6 : y^0'=z^0, y^0-z^0 >= 0, cost: 2*y^0-2*z^0

Applied deletion
Removed the following rules: 27

Accelerated simple loops
Start location: l9
  32: l0 -> l0 : x^0'=0, x^0 >= 0, cost: 2*x^0
  15: l2 -> l0 : y^0 <= 0, cost: 1
  34: l2 -> l2 : y^0'=0, y^0 >= 0, cost: 2*y^0
  18: l4 -> l2 : -x^0+z^0 <= 0, cost: 1
  36: l4 -> l4 : x^0'=z^0, -x^0+z^0 >= 0, cost: -2*x^0+2*z^0
  21: l6 -> l4 : y^0-z^0 <= 0, cost: 1
  38: l6 -> l6 : y^0'=z^0, y^0-z^0 >= 0, cost: 2*y^0-2*z^0
  26: l9 -> l6 : x^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l2 -> l0 : y^0 <= 0, cost: 1
Second rule:
l0 -> l0 : x^0'=0, x^0 >= 0, cost: 2*x^0
New rule:
l2 -> l0 : x^0'=0, (y^0 <= 0 /\ x^0 >= 0), cost: 1+2*x^0

Applied deletion
Removed the following rules: 32

Applied chaining
First rule:
l4 -> l2 : -x^0+z^0 <= 0, cost: 1
Second rule:
l2 -> l2 : y^0'=0, y^0 >= 0, cost: 2*y^0
New rule:
l4 -> l2 : y^0'=0, (y^0 >= 0 /\ -x^0+z^0 <= 0), cost: 1+2*y^0

Applied deletion
Removed the following rules: 34

Applied chaining
First rule:
l6 -> l4 : y^0-z^0 <= 0, cost: 1
Second rule:
l4 -> l4 : x^0'=z^0, -x^0+z^0 >= 0, cost: -2*x^0+2*z^0
New rule:
l6 -> l4 : x^0'=z^0, (-x^0+z^0 >= 0 /\ y^0-z^0 <= 0), cost: 1-2*x^0+2*z^0

Applied deletion
Removed the following rules: 36

Applied chaining
First rule:
l9 -> l6 : x^0'=0, TRUE, cost: 2
Second rule:
l6 -> l6 : y^0'=z^0, y^0-z^0 >= 0, cost: 2*y^0-2*z^0
New rule:
l9 -> l6 : y^0'=z^0, x^0'=0, y^0-z^0 >= 0, cost: 2+2*y^0-2*z^0

Applied deletion
Removed the following rules: 38

Chained accelerated rules with incoming rules
Start location: l9
  15: l2 -> l0 : y^0 <= 0, cost: 1
  39: l2 -> l0 : x^0'=0, (y^0 <= 0 /\ x^0 >= 0), cost: 1+2*x^0
  18: l4 -> l2 : -x^0+z^0 <= 0, cost: 1
  40: l4 -> l2 : y^0'=0, (y^0 >= 0 /\ -x^0+z^0 <= 0), cost: 1+2*y^0
  21: l6 -> l4 : y^0-z^0 <= 0, cost: 1
  41: l6 -> l4 : x^0'=z^0, (-x^0+z^0 >= 0 /\ y^0-z^0 <= 0), cost: 1-2*x^0+2*z^0
  26: l9 -> l6 : x^0'=0, TRUE, cost: 2
  42: l9 -> l6 : y^0'=z^0, x^0'=0, y^0-z^0 >= 0, cost: 2+2*y^0-2*z^0


Removed unreachable locations and irrelevant leafs
Start location: l9
  <empty>


Computing asymptotic complexity

Proved the following lower bound
Complexity:  Unknown
Cpx degree: ?

Solved cost: 0
Rule cost:   0