WORST_CASE(Omega(0),?)

Initial ITS
Start location: l5
   0: l0 -> l2 : Result_4^0'=Result_4^post0, w_8^0'=w_8^post0, y_6^0'=y_6^post0, k_7^0'=k_7^post0, x_5^0'=x_5^post0, (-1-y_6^0+y_6^post0 == 0 /\ -1+x_5^post0-x_5^0 == 0 /\ 2+x_5^0 <= 0 /\ Result_4^0-Result_4^post0 == 0 /\ -k_7^post0+k_7^0 == 0 /\ w_8^0-w_8^post0 == 0), cost: 1
   4: l0 -> l3 : Result_4^0'=Result_4^post4, w_8^0'=w_8^post4, y_6^0'=y_6^post4, k_7^0'=k_7^post4, x_5^0'=x_5^post4, (0 == 0 /\ -1-x_5^0 <= 0 /\ -x_5^post4+x_5^0 == 0 /\ -y_6^post4+y_6^0 == 0 /\ -k_7^post4+k_7^0 == 0 /\ w_8^0-w_8^post4 == 0), cost: 1
   1: l2 -> l1 : Result_4^0'=Result_4^post1, w_8^0'=w_8^post1, y_6^0'=y_6^post1, k_7^0'=k_7^post1, x_5^0'=x_5^post1, (-y_6^post1+y_6^0 == 0 /\ 1+y_6^0 <= 0 /\ Result_4^0-Result_4^post1 == 0 /\ k_7^0-k_7^post1 == 0 /\ -x_5^post1+x_5^0 == 0 /\ -w_8^post1+w_8^0 == 0), cost: 1
   2: l2 -> l1 : Result_4^0'=Result_4^post2, w_8^0'=w_8^post2, y_6^0'=y_6^post2, k_7^0'=k_7^post2, x_5^0'=x_5^post2, (Result_4^0-Result_4^post2 == 0 /\ -k_7^post2+k_7^0 == 0 /\ -y_6^post2+y_6^0 == 0 /\ w_8^0-w_8^post2 == 0 /\ 1-y_6^0 <= 0 /\ -x_5^post2+x_5^0 == 0), cost: 1
   3: l1 -> l0 : Result_4^0'=Result_4^post3, w_8^0'=w_8^post3, y_6^0'=y_6^post3, k_7^0'=k_7^post3, x_5^0'=x_5^post3, (-x_5^post3+x_5^0 == 0 /\ y_6^0-y_6^post3 == 0 /\ k_7^0-k_7^post3 == 0 /\ w_8^0-w_8^post3 == 0 /\ Result_4^0-Result_4^post3 == 0), cost: 1
   5: l4 -> l0 : Result_4^0'=Result_4^post5, w_8^0'=w_8^post5, y_6^0'=y_6^post5, k_7^0'=k_7^post5, x_5^0'=x_5^post5, (2-k_7^0 <= 0 /\ 2-w_8^0 <= 0 /\ -x_5^post5+x_5^0 == 0 /\ y_6^0-y_6^post5 == 0 /\ Result_4^0-Result_4^post5 == 0 /\ -k_7^post5+k_7^0 == 0 /\ w_8^0-w_8^post5 == 0), cost: 1
   6: l4 -> l3 : Result_4^0'=Result_4^post6, w_8^0'=w_8^post6, y_6^0'=y_6^post6, k_7^0'=k_7^post6, x_5^0'=x_5^post6, (0 == 0 /\ x_5^0-x_5^post6 == 0 /\ -y_6^post6+y_6^0 == 0 /\ -1+k_7^0 <= 0 /\ w_8^0-w_8^post6 == 0 /\ -k_7^post6+k_7^0 == 0), cost: 1
   7: l5 -> l4 : Result_4^0'=Result_4^post7, w_8^0'=w_8^post7, y_6^0'=y_6^post7, k_7^0'=k_7^post7, x_5^0'=x_5^post7, (-k_7^post7+k_7^0 == 0 /\ w_8^0-w_8^post7 == 0 /\ Result_4^0-Result_4^post7 == 0 /\ y_6^0-y_6^post7 == 0 /\ -x_5^post7+x_5^0 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l5
   0: l0 -> l2 : Result_4^0'=Result_4^post0, w_8^0'=w_8^post0, y_6^0'=y_6^post0, k_7^0'=k_7^post0, x_5^0'=x_5^post0, (-1-y_6^0+y_6^post0 == 0 /\ -1+x_5^post0-x_5^0 == 0 /\ 2+x_5^0 <= 0 /\ Result_4^0-Result_4^post0 == 0 /\ -k_7^post0+k_7^0 == 0 /\ w_8^0-w_8^post0 == 0), cost: 1
   1: l2 -> l1 : Result_4^0'=Result_4^post1, w_8^0'=w_8^post1, y_6^0'=y_6^post1, k_7^0'=k_7^post1, x_5^0'=x_5^post1, (-y_6^post1+y_6^0 == 0 /\ 1+y_6^0 <= 0 /\ Result_4^0-Result_4^post1 == 0 /\ k_7^0-k_7^post1 == 0 /\ -x_5^post1+x_5^0 == 0 /\ -w_8^post1+w_8^0 == 0), cost: 1
   2: l2 -> l1 : Result_4^0'=Result_4^post2, w_8^0'=w_8^post2, y_6^0'=y_6^post2, k_7^0'=k_7^post2, x_5^0'=x_5^post2, (Result_4^0-Result_4^post2 == 0 /\ -k_7^post2+k_7^0 == 0 /\ -y_6^post2+y_6^0 == 0 /\ w_8^0-w_8^post2 == 0 /\ 1-y_6^0 <= 0 /\ -x_5^post2+x_5^0 == 0), cost: 1
   3: l1 -> l0 : Result_4^0'=Result_4^post3, w_8^0'=w_8^post3, y_6^0'=y_6^post3, k_7^0'=k_7^post3, x_5^0'=x_5^post3, (-x_5^post3+x_5^0 == 0 /\ y_6^0-y_6^post3 == 0 /\ k_7^0-k_7^post3 == 0 /\ w_8^0-w_8^post3 == 0 /\ Result_4^0-Result_4^post3 == 0), cost: 1
   5: l4 -> l0 : Result_4^0'=Result_4^post5, w_8^0'=w_8^post5, y_6^0'=y_6^post5, k_7^0'=k_7^post5, x_5^0'=x_5^post5, (2-k_7^0 <= 0 /\ 2-w_8^0 <= 0 /\ -x_5^post5+x_5^0 == 0 /\ y_6^0-y_6^post5 == 0 /\ Result_4^0-Result_4^post5 == 0 /\ -k_7^post5+k_7^0 == 0 /\ w_8^0-w_8^post5 == 0), cost: 1
   7: l5 -> l4 : Result_4^0'=Result_4^post7, w_8^0'=w_8^post7, y_6^0'=y_6^post7, k_7^0'=k_7^post7, x_5^0'=x_5^post7, (-k_7^post7+k_7^0 == 0 /\ w_8^0-w_8^post7 == 0 /\ Result_4^0-Result_4^post7 == 0 /\ y_6^0-y_6^post7 == 0 /\ -x_5^post7+x_5^0 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l2 : Result_4^0'=Result_4^post0, w_8^0'=w_8^post0, y_6^0'=y_6^post0, k_7^0'=k_7^post0, x_5^0'=x_5^post0, (-1-y_6^0+y_6^post0 == 0 /\ -1+x_5^post0-x_5^0 == 0 /\ 2+x_5^0 <= 0 /\ Result_4^0-Result_4^post0 == 0 /\ -k_7^post0+k_7^0 == 0 /\ w_8^0-w_8^post0 == 0), cost: 1
New rule:
l0 -> l2 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, 2+x_5^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l1 : Result_4^0'=Result_4^post1, w_8^0'=w_8^post1, y_6^0'=y_6^post1, k_7^0'=k_7^post1, x_5^0'=x_5^post1, (-y_6^post1+y_6^0 == 0 /\ 1+y_6^0 <= 0 /\ Result_4^0-Result_4^post1 == 0 /\ k_7^0-k_7^post1 == 0 /\ -x_5^post1+x_5^0 == 0 /\ -w_8^post1+w_8^0 == 0), cost: 1
New rule:
l2 -> l1 : 1+y_6^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l1 : Result_4^0'=Result_4^post2, w_8^0'=w_8^post2, y_6^0'=y_6^post2, k_7^0'=k_7^post2, x_5^0'=x_5^post2, (Result_4^0-Result_4^post2 == 0 /\ -k_7^post2+k_7^0 == 0 /\ -y_6^post2+y_6^0 == 0 /\ w_8^0-w_8^post2 == 0 /\ 1-y_6^0 <= 0 /\ -x_5^post2+x_5^0 == 0), cost: 1
New rule:
l2 -> l1 : -1+y_6^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l0 : Result_4^0'=Result_4^post3, w_8^0'=w_8^post3, y_6^0'=y_6^post3, k_7^0'=k_7^post3, x_5^0'=x_5^post3, (-x_5^post3+x_5^0 == 0 /\ y_6^0-y_6^post3 == 0 /\ k_7^0-k_7^post3 == 0 /\ w_8^0-w_8^post3 == 0 /\ Result_4^0-Result_4^post3 == 0), cost: 1
New rule:
l1 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l0 : Result_4^0'=Result_4^post5, w_8^0'=w_8^post5, y_6^0'=y_6^post5, k_7^0'=k_7^post5, x_5^0'=x_5^post5, (2-k_7^0 <= 0 /\ 2-w_8^0 <= 0 /\ -x_5^post5+x_5^0 == 0 /\ y_6^0-y_6^post5 == 0 /\ Result_4^0-Result_4^post5 == 0 /\ -k_7^post5+k_7^0 == 0 /\ w_8^0-w_8^post5 == 0), cost: 1
New rule:
l4 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 1

Applied preprocessing
Original rule:
l5 -> l4 : Result_4^0'=Result_4^post7, w_8^0'=w_8^post7, y_6^0'=y_6^post7, k_7^0'=k_7^post7, x_5^0'=x_5^post7, (-k_7^post7+k_7^0 == 0 /\ w_8^0-w_8^post7 == 0 /\ Result_4^0-Result_4^post7 == 0 /\ y_6^0-y_6^post7 == 0 /\ -x_5^post7+x_5^0 == 0), cost: 1
New rule:
l5 -> l4 : TRUE, cost: 1

Simplified rules
Start location: l5
   8: l0 -> l2 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, 2+x_5^0 <= 0, cost: 1
   9: l2 -> l1 : 1+y_6^0 <= 0, cost: 1
  10: l2 -> l1 : -1+y_6^0 >= 0, cost: 1
  11: l1 -> l0 : TRUE, cost: 1
  12: l4 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 1
  13: l5 -> l4 : TRUE, cost: 1


Eliminating location l4 by chaining:

Applied chaining
First rule:
l5 -> l4 : TRUE, cost: 1
Second rule:
l4 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 1
New rule:
l5 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 2

Applied deletion
Removed the following rules: 12 13

Eliminated locations on linear paths
Start location: l5
   8: l0 -> l2 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, 2+x_5^0 <= 0, cost: 1
   9: l2 -> l1 : 1+y_6^0 <= 0, cost: 1
  10: l2 -> l1 : -1+y_6^0 >= 0, cost: 1
  11: l1 -> l0 : TRUE, cost: 1
  14: l5 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 2


Eliminating location l2 by chaining:

Applied chaining
First rule:
l0 -> l2 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, 2+x_5^0 <= 0, cost: 1
Second rule:
l2 -> l1 : 1+y_6^0 <= 0, cost: 1
New rule:
l0 -> l1 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, (2+y_6^0 <= 0 /\ 2+x_5^0 <= 0), cost: 2

Applied chaining
First rule:
l0 -> l2 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, 2+x_5^0 <= 0, cost: 1
Second rule:
l2 -> l1 : -1+y_6^0 >= 0, cost: 1
New rule:
l0 -> l1 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, (2+x_5^0 <= 0 /\ y_6^0 >= 0), cost: 2

Applied deletion
Removed the following rules: 8 9 10

Eliminated locations on tree-shaped paths
Start location: l5
  15: l0 -> l1 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, (2+y_6^0 <= 0 /\ 2+x_5^0 <= 0), cost: 2
  16: l0 -> l1 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, (2+x_5^0 <= 0 /\ y_6^0 >= 0), cost: 2
  11: l1 -> l0 : TRUE, cost: 1
  14: l5 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 2


Applied merging
first rule:
l0 -> l1 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, (2+y_6^0 <= 0 /\ 2+x_5^0 <= 0), cost: 2
second rule:
l0 -> l1 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, (2+x_5^0 <= 0 /\ y_6^0 >= 0), cost: 2
new rule:
l0 -> l1 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, ((2+x_5^0 <= 0 /\ y_6^0 >= 0) \/ (2+y_6^0 <= 0 /\ 2+x_5^0 <= 0)), cost: 2

Merged rules
Start location: l5
  17: l0 -> l1 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, ((2+x_5^0 <= 0 /\ y_6^0 >= 0) \/ (2+y_6^0 <= 0 /\ 2+x_5^0 <= 0)), cost: 2
  11: l1 -> l0 : TRUE, cost: 1
  14: l5 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 2


Eliminating location l1 by chaining:

Applied chaining
First rule:
l0 -> l1 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, ((2+x_5^0 <= 0 /\ y_6^0 >= 0) \/ (2+y_6^0 <= 0 /\ 2+x_5^0 <= 0)), cost: 2
Second rule:
l1 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, ((2+x_5^0 <= 0 /\ y_6^0 >= 0) \/ (2+y_6^0 <= 0 /\ 2+x_5^0 <= 0)), cost: 3

Applied deletion
Removed the following rules: 11 17

Eliminated locations on linear paths
Start location: l5
  18: l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, ((2+x_5^0 <= 0 /\ y_6^0 >= 0) \/ (2+y_6^0 <= 0 /\ 2+x_5^0 <= 0)), cost: 3
  14: l5 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 2


Applied simplification
Original rule:
l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, ((2+x_5^0 <= 0 /\ y_6^0 >= 0) \/ (2+y_6^0 <= 0 /\ 2+x_5^0 <= 0)), cost: 3
New rule:
l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, ((2+y_6^0 <= 0 /\ 2+x_5^0 <= 0) \/ (2+x_5^0 <= 0 /\ y_6^0 >= 0)), cost: 3

Simplified simple loops
Start location: l5
  19: l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, ((2+y_6^0 <= 0 /\ 2+x_5^0 <= 0) \/ (2+x_5^0 <= 0 /\ y_6^0 >= 0)), cost: 3
  14: l5 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 2


Applied acceleration
Original rule:
l0 -> l0 : y_6^0'=1+y_6^0, x_5^0'=1+x_5^0, ((2+y_6^0 <= 0 /\ 2+x_5^0 <= 0) \/ (2+x_5^0 <= 0 /\ y_6^0 >= 0)), cost: 3
New rule:
l0 -> l0 : y_6^0'=n0+y_6^0, x_5^0'=n0+x_5^0, (n0 >= 0 /\ ((-1-n0-x_5^0 >= 0 /\ y_6^0 >= 0) \/ (-1-n0-y_6^0 >= 0 /\ -1-n0-x_5^0 >= 0))), cost: 3*n0

Applied instantiation
Original rule:
l0 -> l0 : y_6^0'=n0+y_6^0, x_5^0'=n0+x_5^0, (n0 >= 0 /\ ((-1-n0-x_5^0 >= 0 /\ y_6^0 >= 0) \/ (-1-n0-y_6^0 >= 0 /\ -1-n0-x_5^0 >= 0))), cost: 3*n0
New rule:
l0 -> l0 : y_6^0'=-1+y_6^0-x_5^0, x_5^0'=-1, (-1-x_5^0 >= 0 /\ ((0 >= 0 /\ y_6^0 >= 0) \/ (0 >= 0 /\ -y_6^0+x_5^0 >= 0))), cost: -3-3*x_5^0

Applied instantiation
Original rule:
l0 -> l0 : y_6^0'=n0+y_6^0, x_5^0'=n0+x_5^0, (n0 >= 0 /\ ((-1-n0-x_5^0 >= 0 /\ y_6^0 >= 0) \/ (-1-n0-y_6^0 >= 0 /\ -1-n0-x_5^0 >= 0))), cost: 3*n0
New rule:
l0 -> l0 : y_6^0'=-1, x_5^0'=-1-y_6^0+x_5^0, (-1-y_6^0 >= 0 /\ ((0 >= 0 /\ y_6^0-x_5^0 >= 0) \/ (y_6^0 >= 0 /\ y_6^0-x_5^0 >= 0))), cost: -3-3*y_6^0

Applied simplification
Original rule:
l0 -> l0 : y_6^0'=-1+y_6^0-x_5^0, x_5^0'=-1, (-1-x_5^0 >= 0 /\ ((0 >= 0 /\ y_6^0 >= 0) \/ (0 >= 0 /\ -y_6^0+x_5^0 >= 0))), cost: -3-3*x_5^0
New rule:
l0 -> l0 : y_6^0'=-1+y_6^0-x_5^0, x_5^0'=-1, (1+x_5^0 <= 0 /\ ((0 >= 0 /\ -y_6^0+x_5^0 >= 0) \/ y_6^0 >= 0)), cost: -3-3*x_5^0

Applied simplification
Original rule:
l0 -> l0 : y_6^0'=-1, x_5^0'=-1-y_6^0+x_5^0, (-1-y_6^0 >= 0 /\ ((0 >= 0 /\ y_6^0-x_5^0 >= 0) \/ (y_6^0 >= 0 /\ y_6^0-x_5^0 >= 0))), cost: -3-3*y_6^0
New rule:
l0 -> l0 : y_6^0'=-1, x_5^0'=-1-y_6^0+x_5^0, (1+y_6^0 <= 0 /\ y_6^0-x_5^0 >= 0), cost: -3-3*y_6^0

Applied deletion
Removed the following rules: 19

Accelerated simple loops
Start location: l5
  22: l0 -> l0 : y_6^0'=-1+y_6^0-x_5^0, x_5^0'=-1, (1+x_5^0 <= 0 /\ ((0 >= 0 /\ -y_6^0+x_5^0 >= 0) \/ y_6^0 >= 0)), cost: -3-3*x_5^0
  23: l0 -> l0 : y_6^0'=-1, x_5^0'=-1-y_6^0+x_5^0, (1+y_6^0 <= 0 /\ y_6^0-x_5^0 >= 0), cost: -3-3*y_6^0
  14: l5 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 2


Applied chaining
First rule:
l5 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 2
Second rule:
l0 -> l0 : y_6^0'=-1+y_6^0-x_5^0, x_5^0'=-1, (1+x_5^0 <= 0 /\ ((0 >= 0 /\ -y_6^0+x_5^0 >= 0) \/ y_6^0 >= 0)), cost: -3-3*x_5^0
New rule:
l5 -> l0 : y_6^0'=-1+y_6^0-x_5^0, x_5^0'=-1, (1+x_5^0 <= 0 /\ -2+k_7^0 >= 0 /\ -2+w_8^0 >= 0 /\ (y_6^0 >= 0 \/ -y_6^0+x_5^0 >= 0)), cost: -1-3*x_5^0

Applied chaining
First rule:
l5 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 2
Second rule:
l0 -> l0 : y_6^0'=-1, x_5^0'=-1-y_6^0+x_5^0, (1+y_6^0 <= 0 /\ y_6^0-x_5^0 >= 0), cost: -3-3*y_6^0
New rule:
l5 -> l0 : y_6^0'=-1, x_5^0'=-1-y_6^0+x_5^0, (1+y_6^0 <= 0 /\ -2+k_7^0 >= 0 /\ y_6^0-x_5^0 >= 0 /\ -2+w_8^0 >= 0), cost: -1-3*y_6^0

Applied deletion
Removed the following rules: 22 23

Chained accelerated rules with incoming rules
Start location: l5
  14: l5 -> l0 : (-2+k_7^0 >= 0 /\ -2+w_8^0 >= 0), cost: 2
  24: l5 -> l0 : y_6^0'=-1+y_6^0-x_5^0, x_5^0'=-1, (1+x_5^0 <= 0 /\ -2+k_7^0 >= 0 /\ -2+w_8^0 >= 0 /\ (y_6^0 >= 0 \/ -y_6^0+x_5^0 >= 0)), cost: -1-3*x_5^0
  25: l5 -> l0 : y_6^0'=-1, x_5^0'=-1-y_6^0+x_5^0, (1+y_6^0 <= 0 /\ -2+k_7^0 >= 0 /\ y_6^0-x_5^0 >= 0 /\ -2+w_8^0 >= 0), cost: -1-3*y_6^0


Removed unreachable locations and irrelevant leafs
Start location: l5
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0