WORST_CASE(Omega(0),?)

Initial ITS
Start location: l6
   0: l0 -> l1 : j^0'=j^post0, j^0-j^post0 == 0, cost: 1
   1: l0 -> l1 : j^0'=j^post1, -j^post1+j^0 == 0, cost: 1
   5: l1 -> l4 : j^0'=j^post5, -j^post5+j^0 == 0, cost: 1
   2: l2 -> l0 : j^0'=j^post2, (-j^post2+j^0 == 0 /\ 2-j^0 <= 0), cost: 1
   3: l2 -> l3 : j^0'=j^post3, (-1-j^0+j^post3 == 0 /\ -1+j^0 <= 0), cost: 1
   4: l3 -> l2 : j^0'=j^post4, -j^post4+j^0 == 0, cost: 1
   6: l5 -> l3 : j^0'=j^post6, j^post6 == 0, cost: 1
   7: l6 -> l5 : j^0'=j^post7, j^0-j^post7 == 0, cost: 1


Removed unreachable rules and leafs
Start location: l6
   3: l2 -> l3 : j^0'=j^post3, (-1-j^0+j^post3 == 0 /\ -1+j^0 <= 0), cost: 1
   4: l3 -> l2 : j^0'=j^post4, -j^post4+j^0 == 0, cost: 1
   6: l5 -> l3 : j^0'=j^post6, j^post6 == 0, cost: 1
   7: l6 -> l5 : j^0'=j^post7, j^0-j^post7 == 0, cost: 1


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

Applied preprocessing
Original rule:
l3 -> l2 : j^0'=j^post4, -j^post4+j^0 == 0, cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l3 : j^0'=j^post6, j^post6 == 0, cost: 1
New rule:
l5 -> l3 : j^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l6 -> l5 : j^0'=j^post7, j^0-j^post7 == 0, cost: 1
New rule:
l6 -> l5 : TRUE, cost: 1

Simplified rules
Start location: l6
   8: l2 -> l3 : j^0'=1+j^0, -1+j^0 <= 0, cost: 1
   9: l3 -> l2 : TRUE, cost: 1
  10: l5 -> l3 : j^0'=0, TRUE, cost: 1
  11: l6 -> l5 : TRUE, cost: 1


Eliminating location l5 by chaining:

Applied chaining
First rule:
l6 -> l5 : TRUE, cost: 1
Second rule:
l5 -> l3 : j^0'=0, TRUE, cost: 1
New rule:
l6 -> l3 : j^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminating location l2 by chaining:

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

Applied deletion
Removed the following rules: 8 9

Eliminated locations on linear paths
Start location: l6
  13: l3 -> l3 : j^0'=1+j^0, -1+j^0 <= 0, cost: 2
  12: l6 -> l3 : j^0'=0, TRUE, cost: 2


Applied acceleration
Original rule:
l3 -> l3 : j^0'=1+j^0, -1+j^0 <= 0, cost: 2
New rule:
l3 -> l3 : j^0'=n+j^0, (n >= 0 /\ 2-n-j^0 >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_oJJJDI.txt

Applied instantiation
Original rule:
l3 -> l3 : j^0'=n+j^0, (n >= 0 /\ 2-n-j^0 >= 0), cost: 2*n
New rule:
l3 -> l3 : j^0'=2, (0 >= 0 /\ 2-j^0 >= 0), cost: 4-2*j^0

Applied simplification
Original rule:
l3 -> l3 : j^0'=2, (0 >= 0 /\ 2-j^0 >= 0), cost: 4-2*j^0
New rule:
l3 -> l3 : j^0'=2, -2+j^0 <= 0, cost: 4-2*j^0

Applied deletion
Removed the following rules: 13

Accelerated simple loops
Start location: l6
  15: l3 -> l3 : j^0'=2, -2+j^0 <= 0, cost: 4-2*j^0
  12: l6 -> l3 : j^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l6 -> l3 : j^0'=0, TRUE, cost: 2
Second rule:
l3 -> l3 : j^0'=2, -2+j^0 <= 0, cost: 4-2*j^0
New rule:
l6 -> l3 : j^0'=2, -2 <= 0, cost: 6

Applied deletion
Removed the following rules: 15

Chained accelerated rules with incoming rules
Start location: l6
  12: l6 -> l3 : j^0'=0, TRUE, cost: 2
  16: l6 -> l3 : j^0'=2, -2 <= 0, cost: 6


Removed unreachable locations and irrelevant leafs
Start location: l6
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0