WORST_CASE(Omega(0),?)

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


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

Applied preprocessing
Original rule:
l1 -> l0 : p^0'=p^post1, c^0'=c^post1, s^0'=s^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 : p^0'=p^post2, c^0'=c^post2, s^0'=s^post2, (-1+s^post2 == 0 /\ -1+p^post2 == 0 /\ -c^post2+c^0 == 0), cost: 1
New rule:
l2 -> l0 : p^0'=1, s^0'=1, TRUE, cost: 1

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

Simplified rules
Start location: l3
   4: l0 -> l1 : p^0'=s^0, s^0'=1+s^0, 1+p^0-c^0 <= 0, cost: 1
   5: l1 -> l0 : TRUE, cost: 1
   6: l2 -> l0 : p^0'=1, s^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 : p^0'=1, s^0'=1, TRUE, cost: 1
New rule:
l3 -> l0 : p^0'=1, s^0'=1, TRUE, cost: 2

Applied deletion
Removed the following rules: 6 7

Eliminating location l1 by chaining:

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

Applied deletion
Removed the following rules: 4 5

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


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

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

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


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