WORST_CASE(Omega(0),?)

Initial ITS
Start location: l4
   0: l0 -> l1 : c0^0'=c0^post0, wnt^0'=wnt^post0, deltaext^0'=deltaext^post0, (c0^0-c0^post0 == 0 /\ wnt^0-wnt^post0 == 0 /\ 1+deltaext^post0-deltaext^0 == 0 /\ 2+c0^0+wnt^0-2*deltaext^0 <= 0), cost: 1
   2: l0 -> l2 : c0^0'=c0^post2, wnt^0'=wnt^post2, deltaext^0'=deltaext^post2, (wnt^0-wnt^post2 == 0 /\ 1-c0^0-wnt^0+2*deltaext^0 <= 0 /\ c0^0-c0^post2 == 0 /\ -1-deltaext^0+deltaext^post2 == 0), cost: 1
   1: l1 -> l0 : c0^0'=c0^post1, wnt^0'=wnt^post1, deltaext^0'=deltaext^post1, (wnt^0-wnt^post1 == 0 /\ c0^0-c0^post1 == 0 /\ deltaext^0-deltaext^post1 == 0), cost: 1
   3: l2 -> l0 : c0^0'=c0^post3, wnt^0'=wnt^post3, deltaext^0'=deltaext^post3, (deltaext^0-deltaext^post3 == 0 /\ c0^0-c0^post3 == 0 /\ wnt^0-wnt^post3 == 0), cost: 1
   4: l3 -> l0 : c0^0'=c0^post4, wnt^0'=wnt^post4, deltaext^0'=deltaext^post4, (-wnt^0 <= 0 /\ -deltaext^0 <= 0 /\ -2+c0^post4 == 0 /\ -3+deltaext^0 <= 0 /\ wnt^0-wnt^post4 == 0 /\ deltaext^0-deltaext^post4 == 0 /\ -3+wnt^0 <= 0), cost: 1
   5: l4 -> l3 : c0^0'=c0^post5, wnt^0'=wnt^post5, deltaext^0'=deltaext^post5, (c0^0-c0^post5 == 0 /\ wnt^0-wnt^post5 == 0 /\ deltaext^0-deltaext^post5 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : c0^0'=c0^post0, wnt^0'=wnt^post0, deltaext^0'=deltaext^post0, (c0^0-c0^post0 == 0 /\ wnt^0-wnt^post0 == 0 /\ 1+deltaext^post0-deltaext^0 == 0 /\ 2+c0^0+wnt^0-2*deltaext^0 <= 0), cost: 1
New rule:
l0 -> l1 : deltaext^0'=-1+deltaext^0, 2+c0^0+wnt^0-2*deltaext^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l0 : c0^0'=c0^post1, wnt^0'=wnt^post1, deltaext^0'=deltaext^post1, (wnt^0-wnt^post1 == 0 /\ c0^0-c0^post1 == 0 /\ deltaext^0-deltaext^post1 == 0), cost: 1
New rule:
l1 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l0 -> l2 : c0^0'=c0^post2, wnt^0'=wnt^post2, deltaext^0'=deltaext^post2, (wnt^0-wnt^post2 == 0 /\ 1-c0^0-wnt^0+2*deltaext^0 <= 0 /\ c0^0-c0^post2 == 0 /\ -1-deltaext^0+deltaext^post2 == 0), cost: 1
New rule:
l0 -> l2 : deltaext^0'=1+deltaext^0, 1-c0^0-wnt^0+2*deltaext^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : c0^0'=c0^post3, wnt^0'=wnt^post3, deltaext^0'=deltaext^post3, (deltaext^0-deltaext^post3 == 0 /\ c0^0-c0^post3 == 0 /\ wnt^0-wnt^post3 == 0), cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l0 : c0^0'=c0^post4, wnt^0'=wnt^post4, deltaext^0'=deltaext^post4, (-wnt^0 <= 0 /\ -deltaext^0 <= 0 /\ -2+c0^post4 == 0 /\ -3+deltaext^0 <= 0 /\ wnt^0-wnt^post4 == 0 /\ deltaext^0-deltaext^post4 == 0 /\ -3+wnt^0 <= 0), cost: 1
New rule:
l3 -> l0 : c0^0'=2, (wnt^0 >= 0 /\ deltaext^0 >= 0 /\ -3+deltaext^0 <= 0 /\ -3+wnt^0 <= 0), cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : c0^0'=c0^post5, wnt^0'=wnt^post5, deltaext^0'=deltaext^post5, (c0^0-c0^post5 == 0 /\ wnt^0-wnt^post5 == 0 /\ deltaext^0-deltaext^post5 == 0), cost: 1
New rule:
l4 -> l3 : TRUE, cost: 1

Simplified rules
Start location: l4
   6: l0 -> l1 : deltaext^0'=-1+deltaext^0, 2+c0^0+wnt^0-2*deltaext^0 <= 0, cost: 1
   8: l0 -> l2 : deltaext^0'=1+deltaext^0, 1-c0^0-wnt^0+2*deltaext^0 <= 0, cost: 1
   7: l1 -> l0 : TRUE, cost: 1
   9: l2 -> l0 : TRUE, cost: 1
  10: l3 -> l0 : c0^0'=2, (wnt^0 >= 0 /\ deltaext^0 >= 0 /\ -3+deltaext^0 <= 0 /\ -3+wnt^0 <= 0), cost: 1
  11: l4 -> l3 : TRUE, cost: 1


Eliminating location l3 by chaining:

Applied chaining
First rule:
l4 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l0 : c0^0'=2, (wnt^0 >= 0 /\ deltaext^0 >= 0 /\ -3+deltaext^0 <= 0 /\ -3+wnt^0 <= 0), cost: 1
New rule:
l4 -> l0 : c0^0'=2, (wnt^0 >= 0 /\ deltaext^0 >= 0 /\ -3+deltaext^0 <= 0 /\ -3+wnt^0 <= 0), cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminating location l1 by chaining:

Applied chaining
First rule:
l0 -> l1 : deltaext^0'=-1+deltaext^0, 2+c0^0+wnt^0-2*deltaext^0 <= 0, cost: 1
Second rule:
l1 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : deltaext^0'=-1+deltaext^0, 2+c0^0+wnt^0-2*deltaext^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 6 7

Eliminating location l2 by chaining:

Applied chaining
First rule:
l0 -> l2 : deltaext^0'=1+deltaext^0, 1-c0^0-wnt^0+2*deltaext^0 <= 0, cost: 1
Second rule:
l2 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : deltaext^0'=1+deltaext^0, 1-c0^0-wnt^0+2*deltaext^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 8 9

Eliminated locations on linear paths
Start location: l4
  13: l0 -> l0 : deltaext^0'=-1+deltaext^0, 2+c0^0+wnt^0-2*deltaext^0 <= 0, cost: 2
  14: l0 -> l0 : deltaext^0'=1+deltaext^0, 1-c0^0-wnt^0+2*deltaext^0 <= 0, cost: 2
  12: l4 -> l0 : c0^0'=2, (wnt^0 >= 0 /\ deltaext^0 >= 0 /\ -3+deltaext^0 <= 0 /\ -3+wnt^0 <= 0), cost: 2


Applied acceleration
Original rule:
l0 -> l0 : deltaext^0'=-1+deltaext^0, 2+c0^0+wnt^0-2*deltaext^0 <= 0, cost: 2
New rule:
l0 -> l0 : deltaext^0'=deltaext^0-n1, (-c0^0-wnt^0+2*deltaext^0-2*n1 >= 0 /\ n1 >= 0), cost: 2*n1

Applied acceleration
Original rule:
l0 -> l0 : deltaext^0'=1+deltaext^0, 1-c0^0-wnt^0+2*deltaext^0 <= 0, cost: 2
New rule:
l0 -> l0 : deltaext^0'=n3+deltaext^0, (n3 >= 0 /\ 1+c0^0-2*n3+wnt^0-2*deltaext^0 >= 0), cost: 2*n3

Applied deletion
Removed the following rules: 13 14

Accelerated simple loops
Start location: l4
  15: l0 -> l0 : deltaext^0'=deltaext^0-n1, (-c0^0-wnt^0+2*deltaext^0-2*n1 >= 0 /\ n1 >= 0), cost: 2*n1
  16: l0 -> l0 : deltaext^0'=n3+deltaext^0, (n3 >= 0 /\ 1+c0^0-2*n3+wnt^0-2*deltaext^0 >= 0), cost: 2*n3
  12: l4 -> l0 : c0^0'=2, (wnt^0 >= 0 /\ deltaext^0 >= 0 /\ -3+deltaext^0 <= 0 /\ -3+wnt^0 <= 0), cost: 2


Applied chaining
First rule:
l4 -> l0 : c0^0'=2, (wnt^0 >= 0 /\ deltaext^0 >= 0 /\ -3+deltaext^0 <= 0 /\ -3+wnt^0 <= 0), cost: 2
Second rule:
l0 -> l0 : deltaext^0'=deltaext^0-n1, (-c0^0-wnt^0+2*deltaext^0-2*n1 >= 0 /\ n1 >= 0), cost: 2*n1
New rule:
l4 -> l0 : c0^0'=2, deltaext^0'=deltaext^0-n1, (wnt^0 >= 0 /\ -2-wnt^0+2*deltaext^0-2*n1 >= 0 /\ -3+deltaext^0 <= 0 /\ n1 >= 0 /\ -3+wnt^0 <= 0), cost: 2+2*n1

Applied chaining
First rule:
l4 -> l0 : c0^0'=2, (wnt^0 >= 0 /\ deltaext^0 >= 0 /\ -3+deltaext^0 <= 0 /\ -3+wnt^0 <= 0), cost: 2
Second rule:
l0 -> l0 : deltaext^0'=n3+deltaext^0, (n3 >= 0 /\ 1+c0^0-2*n3+wnt^0-2*deltaext^0 >= 0), cost: 2*n3
New rule:
l4 -> l0 : c0^0'=2, deltaext^0'=n3+deltaext^0, (n3 >= 0 /\ wnt^0 >= 0 /\ deltaext^0 >= 0 /\ 3-2*n3+wnt^0-2*deltaext^0 >= 0 /\ -3+wnt^0 <= 0), cost: 2+2*n3

Applied deletion
Removed the following rules: 15 16

Chained accelerated rules with incoming rules
Start location: l4
  12: l4 -> l0 : c0^0'=2, (wnt^0 >= 0 /\ deltaext^0 >= 0 /\ -3+deltaext^0 <= 0 /\ -3+wnt^0 <= 0), cost: 2
  17: l4 -> l0 : c0^0'=2, deltaext^0'=deltaext^0-n1, (wnt^0 >= 0 /\ -2-wnt^0+2*deltaext^0-2*n1 >= 0 /\ -3+deltaext^0 <= 0 /\ n1 >= 0 /\ -3+wnt^0 <= 0), cost: 2+2*n1
  18: l4 -> l0 : c0^0'=2, deltaext^0'=n3+deltaext^0, (n3 >= 0 /\ wnt^0 >= 0 /\ deltaext^0 >= 0 /\ 3-2*n3+wnt^0-2*deltaext^0 >= 0 /\ -3+wnt^0 <= 0), cost: 2+2*n3


Removed unreachable locations and irrelevant leafs
Start location: l4
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0