WORST_CASE(Omega(0),?)

Initial ITS
Start location: l3
   0: l0 -> l1 : c^0'=c^post0, s^0'=s^post0, p^0'=p^post0, (c^0-c^post0 == 0 /\ p^post0-s^0 == 0 /\ 1-c^0+p^0 <= 0 /\ -1-s^0+s^post0 == 0), cost: 1
   1: l1 -> l0 : c^0'=c^post1, s^0'=s^post1, p^0'=p^post1, (s^0-s^post1 == 0 /\ c^0-c^post1 == 0 /\ p^0-p^post1 == 0), cost: 1
   2: l2 -> l0 : c^0'=c^post2, s^0'=s^post2, p^0'=p^post2, (-1+s^post2 == 0 /\ -1+p^post2 == 0 /\ c^0-c^post2 == 0), cost: 1
   3: l3 -> l2 : c^0'=c^post3, s^0'=s^post3, p^0'=p^post3, (p^0-p^post3 == 0 /\ c^0-c^post3 == 0 /\ s^0-s^post3 == 0), cost: 1


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

Applied preprocessing
Original rule:
l1 -> l0 : c^0'=c^post1, s^0'=s^post1, p^0'=p^post1, (s^0-s^post1 == 0 /\ c^0-c^post1 == 0 /\ p^0-p^post1 == 0), cost: 1
New rule:
l1 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : c^0'=c^post2, s^0'=s^post2, p^0'=p^post2, (-1+s^post2 == 0 /\ -1+p^post2 == 0 /\ c^0-c^post2 == 0), cost: 1
New rule:
l2 -> l0 : s^0'=1, p^0'=1, TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : c^0'=c^post3, s^0'=s^post3, p^0'=p^post3, (p^0-p^post3 == 0 /\ c^0-c^post3 == 0 /\ s^0-s^post3 == 0), cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Simplified rules
Start location: l3
   4: l0 -> l1 : s^0'=1+s^0, p^0'=s^0, 1-c^0+p^0 <= 0, cost: 1
   5: l1 -> l0 : TRUE, cost: 1
   6: l2 -> l0 : s^0'=1, p^0'=1, TRUE, cost: 1
   7: l3 -> l2 : TRUE, cost: 1


Eliminating location l2 by chaining:

Applied chaining
First rule:
l3 -> l2 : TRUE, cost: 1
Second rule:
l2 -> l0 : s^0'=1, p^0'=1, TRUE, cost: 1
New rule:
l3 -> l0 : s^0'=1, p^0'=1, TRUE, cost: 2

Applied deletion
Removed the following rules: 6 7

Eliminating location l1 by chaining:

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

Applied deletion
Removed the following rules: 4 5

Eliminated locations on linear paths
Start location: l3
   9: l0 -> l0 : s^0'=1+s^0, p^0'=s^0, 1-c^0+p^0 <= 0, cost: 2
   8: l3 -> l0 : s^0'=1, p^0'=1, TRUE, cost: 2


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

Applied instantiation
Original rule:
l0 -> l0 : s^0'=n0+s^0, p^0'=-1+n0+s^0, (-1+c^0-p^0 >= 0 /\ -1+n0 >= 0 /\ 1+c^0-n0-s^0 >= 0), cost: 2*n0
New rule:
l0 -> l0 : s^0'=1+c^0, p^0'=c^0, (0 >= 0 /\ -1+c^0-p^0 >= 0 /\ c^0-s^0 >= 0), cost: 2+2*c^0-2*s^0

Applied simplification
Original rule:
l0 -> l0 : s^0'=1+c^0, p^0'=c^0, (0 >= 0 /\ -1+c^0-p^0 >= 0 /\ c^0-s^0 >= 0), cost: 2+2*c^0-2*s^0
New rule:
l0 -> l0 : s^0'=1+c^0, p^0'=c^0, (-1+c^0-p^0 >= 0 /\ c^0-s^0 >= 0), cost: 2+2*c^0-2*s^0

Applied deletion
Removed the following rules: 9

Accelerated simple loops
Start location: l3
  11: l0 -> l0 : s^0'=1+c^0, p^0'=c^0, (-1+c^0-p^0 >= 0 /\ c^0-s^0 >= 0), cost: 2+2*c^0-2*s^0
   8: l3 -> l0 : s^0'=1, p^0'=1, TRUE, cost: 2


Applied chaining
First rule:
l3 -> l0 : s^0'=1, p^0'=1, TRUE, cost: 2
Second rule:
l0 -> l0 : s^0'=1+c^0, p^0'=c^0, (-1+c^0-p^0 >= 0 /\ c^0-s^0 >= 0), cost: 2+2*c^0-2*s^0
New rule:
l3 -> l0 : s^0'=1+c^0, p^0'=c^0, -2+c^0 >= 0, cost: 2+2*c^0

Applied deletion
Removed the following rules: 11

Chained accelerated rules with incoming rules
Start location: l3
   8: l3 -> l0 : s^0'=1, p^0'=1, TRUE, cost: 2
  12: l3 -> l0 : s^0'=1+c^0, p^0'=c^0, -2+c^0 >= 0, cost: 2+2*c^0


Removed unreachable locations and irrelevant leafs
Start location: l3
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0