WORST_CASE(Omega(0),?)

Initial ITS
Start location: l2
   0: l0 -> l1 : x^0'=x^post0, (1-x^0+x^post0 == 0 /\ 1-x^0 <= 0), cost: 1
   1: l1 -> l0 : x^0'=x^post1, -x^post1+x^0 == 0, cost: 1
   2: l2 -> l0 : x^0'=x^post2, -x^post2+x^0 == 0, cost: 1


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

Applied preprocessing
Original rule:
l1 -> l0 : x^0'=x^post1, -x^post1+x^0 == 0, cost: 1
New rule:
l1 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : x^0'=x^post2, -x^post2+x^0 == 0, cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

Simplified rules
Start location: l2
   3: l0 -> l1 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 1
   4: l1 -> l0 : TRUE, cost: 1
   5: l2 -> l0 : TRUE, cost: 1


Eliminating location l1 by chaining:

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

Applied deletion
Removed the following rules: 3 4

Eliminated locations on linear paths
Start location: l2
   6: l0 -> l0 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
   5: l2 -> l0 : TRUE, cost: 1


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

Applied instantiation
Original rule:
l0 -> l0 : x^0'=x^0-n, (n >= 0 /\ x^0-n >= 0), cost: 2*n
New rule:
l0 -> l0 : x^0'=0, (0 >= 0 /\ x^0 >= 0), cost: 2*x^0

Applied simplification
Original rule:
l0 -> l0 : x^0'=0, (0 >= 0 /\ x^0 >= 0), cost: 2*x^0
New rule:
l0 -> l0 : x^0'=0, x^0 >= 0, cost: 2*x^0

Applied deletion
Removed the following rules: 6

Accelerated simple loops
Start location: l2
   8: l0 -> l0 : x^0'=0, x^0 >= 0, cost: 2*x^0
   5: l2 -> l0 : TRUE, cost: 1


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

Applied deletion
Removed the following rules: 8

Chained accelerated rules with incoming rules
Start location: l2
   5: l2 -> l0 : TRUE, cost: 1
   9: l2 -> l0 : x^0'=0, x^0 >= 0, cost: 1+2*x^0


Removed unreachable locations and irrelevant leafs
Start location: l2
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0