WORST_CASE(Omega(0),?)

Initial ITS
Start location: l3
   0: l0 -> l1 : x^0'=x^post0, (-x^10+x^20 == 0 /\ x^30-x^20 == 0 /\ x^0 <= 0 /\ -x^30+x^post0 == 0 /\ -x^0+x^10 == 0), cost: 1
   1: l0 -> l2 : x^0'=x^post1, (-x^0+x^11 == 0 /\ 1+x^post1-x^11 == 0 /\ 1-x^0 <= 0), cost: 1
   2: l2 -> l0 : x^0'=x^post2, -x^0+x^post2 == 0, cost: 1
   3: l3 -> l2 : x^0'=x^post3, x^0-x^post3 == 0, cost: 1


Removed unreachable rules and leafs
Start location: l3
   1: l0 -> l2 : x^0'=x^post1, (-x^0+x^11 == 0 /\ 1+x^post1-x^11 == 0 /\ 1-x^0 <= 0), cost: 1
   2: l2 -> l0 : x^0'=x^post2, -x^0+x^post2 == 0, cost: 1
   3: l3 -> l2 : x^0'=x^post3, x^0-x^post3 == 0, cost: 1


Applied preprocessing
Original rule:
l0 -> l2 : x^0'=x^post1, (-x^0+x^11 == 0 /\ 1+x^post1-x^11 == 0 /\ 1-x^0 <= 0), cost: 1
New rule:
l0 -> l2 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 1

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

Applied preprocessing
Original rule:
l3 -> l2 : x^0'=x^post3, x^0-x^post3 == 0, cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Simplified rules
Start location: l3
   4: l0 -> l2 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 1
   5: l2 -> l0 : TRUE, cost: 1
   6: l3 -> l2 : TRUE, cost: 1


Eliminating location l0 by chaining:

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

Applied deletion
Removed the following rules: 4 5

Eliminated locations on linear paths
Start location: l3
   7: l2 -> l2 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
   6: l3 -> l2 : TRUE, cost: 1


Applied acceleration
Original rule:
l2 -> l2 : x^0'=-1+x^0, -1+x^0 >= 0, cost: 2
New rule:
l2 -> l2 : x^0'=-n+x^0, (-n+x^0 >= 0 /\ n >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_nPDAoj.txt

Applied instantiation
Original rule:
l2 -> l2 : x^0'=-n+x^0, (-n+x^0 >= 0 /\ n >= 0), cost: 2*n
New rule:
l2 -> l2 : x^0'=0, (0 >= 0 /\ x^0 >= 0), cost: 2*x^0

Applied simplification
Original rule:
l2 -> l2 : x^0'=0, (0 >= 0 /\ x^0 >= 0), cost: 2*x^0
New rule:
l2 -> l2 : x^0'=0, x^0 >= 0, cost: 2*x^0

Applied deletion
Removed the following rules: 7

Accelerated simple loops
Start location: l3
   9: l2 -> l2 : x^0'=0, x^0 >= 0, cost: 2*x^0
   6: l3 -> l2 : TRUE, cost: 1


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

Applied deletion
Removed the following rules: 9

Chained accelerated rules with incoming rules
Start location: l3
   6: l3 -> l2 : TRUE, cost: 1
  10: l3 -> l2 : x^0'=0, x^0 >= 0, cost: 1+2*x^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