WORST_CASE(Omega(0),?)

Initial ITS
Start location: l6
   0: l0 -> l1 : oldX1^0'=oldX1^post0, oldX0^0'=oldX0^post0, x0^0'=x0^post0, (0 == 0 /\ -oldX1^post0+x0^post0 == 0 /\ oldX0^post0-x0^0 == 0), cost: 1
   1: l0 -> l2 : oldX1^0'=oldX1^post1, oldX0^0'=oldX0^post1, x0^0'=x0^post1, (oldX0^post1-x0^0 == 0 /\ 1-oldX0^post1+x0^post1 == 0 /\ oldX1^0-oldX1^post1 == 0), cost: 1
   5: l2 -> l4 : oldX1^0'=oldX1^post5, oldX0^0'=oldX0^post5, x0^0'=x0^post5, (-oldX0^post5+x0^post5 == 0 /\ -oldX1^post5+oldX1^0 == 0 /\ oldX0^post5-x0^0 == 0), cost: 1
   2: l3 -> l1 : oldX1^0'=oldX1^post2, oldX0^0'=oldX0^post2, x0^0'=x0^post2, (0 == 0 /\ oldX0^post2-x0^0 == 0 /\ -oldX1^post2+x0^post2 == 0), cost: 1
   3: l4 -> l0 : oldX1^0'=oldX1^post3, oldX0^0'=oldX0^post3, x0^0'=x0^post3, (-oldX0^post3 <= 0 /\ -oldX1^post3+oldX1^0 == 0 /\ -oldX0^post3+x0^post3 == 0 /\ oldX0^post3-x0^0 == 0), cost: 1
   4: l4 -> l3 : oldX1^0'=oldX1^post4, oldX0^0'=oldX0^post4, x0^0'=x0^post4, (-oldX0^post4+x0^post4 == 0 /\ oldX0^post4-x0^0 == 0 /\ -oldX1^post4+oldX1^0 == 0 /\ 1+oldX0^post4 <= 0), cost: 1
   6: l5 -> l1 : oldX1^0'=oldX1^post6, oldX0^0'=oldX0^post6, x0^0'=x0^post6, (-oldX0^post6+oldX0^0 == 0 /\ oldX1^0-oldX1^post6 == 0 /\ -x0^post6+x0^0 == 0), cost: 1
   7: l5 -> l0 : oldX1^0'=oldX1^post7, oldX0^0'=oldX0^post7, x0^0'=x0^post7, (-x0^post7+x0^0 == 0 /\ -oldX0^post7+oldX0^0 == 0 /\ oldX1^0-oldX1^post7 == 0), cost: 1
   8: l5 -> l3 : oldX1^0'=oldX1^post8, oldX0^0'=oldX0^post8, x0^0'=x0^post8, (oldX0^0-oldX0^post8 == 0 /\ -x0^post8+x0^0 == 0 /\ oldX1^0-oldX1^post8 == 0), cost: 1
   9: l5 -> l4 : oldX1^0'=oldX1^post9, oldX0^0'=oldX0^post9, x0^0'=x0^post9, (oldX1^0-oldX1^post9 == 0 /\ oldX0^0-oldX0^post9 == 0 /\ -x0^post9+x0^0 == 0), cost: 1
  10: l5 -> l2 : oldX1^0'=oldX1^post10, oldX0^0'=oldX0^post10, x0^0'=x0^post10, (oldX0^0-oldX0^post10 == 0 /\ oldX1^0-oldX1^post10 == 0 /\ -x0^post10+x0^0 == 0), cost: 1
  11: l6 -> l5 : oldX1^0'=oldX1^post11, oldX0^0'=oldX0^post11, x0^0'=x0^post11, (oldX1^0-oldX1^post11 == 0 /\ oldX0^0-oldX0^post11 == 0 /\ -x0^post11+x0^0 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l6
   1: l0 -> l2 : oldX1^0'=oldX1^post1, oldX0^0'=oldX0^post1, x0^0'=x0^post1, (oldX0^post1-x0^0 == 0 /\ 1-oldX0^post1+x0^post1 == 0 /\ oldX1^0-oldX1^post1 == 0), cost: 1
   5: l2 -> l4 : oldX1^0'=oldX1^post5, oldX0^0'=oldX0^post5, x0^0'=x0^post5, (-oldX0^post5+x0^post5 == 0 /\ -oldX1^post5+oldX1^0 == 0 /\ oldX0^post5-x0^0 == 0), cost: 1
   3: l4 -> l0 : oldX1^0'=oldX1^post3, oldX0^0'=oldX0^post3, x0^0'=x0^post3, (-oldX0^post3 <= 0 /\ -oldX1^post3+oldX1^0 == 0 /\ -oldX0^post3+x0^post3 == 0 /\ oldX0^post3-x0^0 == 0), cost: 1
   7: l5 -> l0 : oldX1^0'=oldX1^post7, oldX0^0'=oldX0^post7, x0^0'=x0^post7, (-x0^post7+x0^0 == 0 /\ -oldX0^post7+oldX0^0 == 0 /\ oldX1^0-oldX1^post7 == 0), cost: 1
   9: l5 -> l4 : oldX1^0'=oldX1^post9, oldX0^0'=oldX0^post9, x0^0'=x0^post9, (oldX1^0-oldX1^post9 == 0 /\ oldX0^0-oldX0^post9 == 0 /\ -x0^post9+x0^0 == 0), cost: 1
  10: l5 -> l2 : oldX1^0'=oldX1^post10, oldX0^0'=oldX0^post10, x0^0'=x0^post10, (oldX0^0-oldX0^post10 == 0 /\ oldX1^0-oldX1^post10 == 0 /\ -x0^post10+x0^0 == 0), cost: 1
  11: l6 -> l5 : oldX1^0'=oldX1^post11, oldX0^0'=oldX0^post11, x0^0'=x0^post11, (oldX1^0-oldX1^post11 == 0 /\ oldX0^0-oldX0^post11 == 0 /\ -x0^post11+x0^0 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l2 : oldX1^0'=oldX1^post1, oldX0^0'=oldX0^post1, x0^0'=x0^post1, (oldX0^post1-x0^0 == 0 /\ 1-oldX0^post1+x0^post1 == 0 /\ oldX1^0-oldX1^post1 == 0), cost: 1
New rule:
l0 -> l2 : oldX0^0'=x0^0, x0^0'=-1+x0^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l0 : oldX1^0'=oldX1^post3, oldX0^0'=oldX0^post3, x0^0'=x0^post3, (-oldX0^post3 <= 0 /\ -oldX1^post3+oldX1^0 == 0 /\ -oldX0^post3+x0^post3 == 0 /\ oldX0^post3-x0^0 == 0), cost: 1
New rule:
l4 -> l0 : oldX0^0'=x0^0, x0^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l4 : oldX1^0'=oldX1^post5, oldX0^0'=oldX0^post5, x0^0'=x0^post5, (-oldX0^post5+x0^post5 == 0 /\ -oldX1^post5+oldX1^0 == 0 /\ oldX0^post5-x0^0 == 0), cost: 1
New rule:
l2 -> l4 : oldX0^0'=x0^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l0 : oldX1^0'=oldX1^post7, oldX0^0'=oldX0^post7, x0^0'=x0^post7, (-x0^post7+x0^0 == 0 /\ -oldX0^post7+oldX0^0 == 0 /\ oldX1^0-oldX1^post7 == 0), cost: 1
New rule:
l5 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l4 : oldX1^0'=oldX1^post9, oldX0^0'=oldX0^post9, x0^0'=x0^post9, (oldX1^0-oldX1^post9 == 0 /\ oldX0^0-oldX0^post9 == 0 /\ -x0^post9+x0^0 == 0), cost: 1
New rule:
l5 -> l4 : TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l2 : oldX1^0'=oldX1^post10, oldX0^0'=oldX0^post10, x0^0'=x0^post10, (oldX0^0-oldX0^post10 == 0 /\ oldX1^0-oldX1^post10 == 0 /\ -x0^post10+x0^0 == 0), cost: 1
New rule:
l5 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l6 -> l5 : oldX1^0'=oldX1^post11, oldX0^0'=oldX0^post11, x0^0'=x0^post11, (oldX1^0-oldX1^post11 == 0 /\ oldX0^0-oldX0^post11 == 0 /\ -x0^post11+x0^0 == 0), cost: 1
New rule:
l6 -> l5 : TRUE, cost: 1

Simplified rules
Start location: l6
  12: l0 -> l2 : oldX0^0'=x0^0, x0^0'=-1+x0^0, TRUE, cost: 1
  14: l2 -> l4 : oldX0^0'=x0^0, TRUE, cost: 1
  13: l4 -> l0 : oldX0^0'=x0^0, x0^0 >= 0, cost: 1
  15: l5 -> l0 : TRUE, cost: 1
  16: l5 -> l4 : TRUE, cost: 1
  17: l5 -> l2 : TRUE, cost: 1
  18: l6 -> l5 : TRUE, cost: 1


Eliminating location l5 by chaining:

Applied chaining
First rule:
l6 -> l5 : TRUE, cost: 1
Second rule:
l5 -> l0 : TRUE, cost: 1
New rule:
l6 -> l0 : TRUE, cost: 2

Applied chaining
First rule:
l6 -> l5 : TRUE, cost: 1
Second rule:
l5 -> l4 : TRUE, cost: 1
New rule:
l6 -> l4 : TRUE, cost: 2

Applied chaining
First rule:
l6 -> l5 : TRUE, cost: 1
Second rule:
l5 -> l2 : TRUE, cost: 1
New rule:
l6 -> l2 : TRUE, cost: 2

Applied deletion
Removed the following rules: 15 16 17 18

Eliminated locations on tree-shaped paths
Start location: l6
  12: l0 -> l2 : oldX0^0'=x0^0, x0^0'=-1+x0^0, TRUE, cost: 1
  14: l2 -> l4 : oldX0^0'=x0^0, TRUE, cost: 1
  13: l4 -> l0 : oldX0^0'=x0^0, x0^0 >= 0, cost: 1
  19: l6 -> l0 : TRUE, cost: 2
  20: l6 -> l4 : TRUE, cost: 2
  21: l6 -> l2 : TRUE, cost: 2


Eliminated location l0
Start location: l6
  14: l2 -> l4 : oldX0^0'=x0^0, TRUE, cost: 1
  22: l4 -> l2 : oldX0^0'=x0^0, x0^0'=-1+x0^0, x0^0 >= 0, cost: 2
  20: l6 -> l4 : TRUE, cost: 2
  21: l6 -> l2 : TRUE, cost: 2
  23: l6 -> l2 : oldX0^0'=x0^0, x0^0'=-1+x0^0, TRUE, cost: 3


Eliminated location l2
Start location: l6
  25: l4 -> l4 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, x0^0 >= 0, cost: 3
  20: l6 -> l4 : TRUE, cost: 2
  24: l6 -> l4 : oldX0^0'=x0^0, TRUE, cost: 3
  26: l6 -> l4 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, TRUE, cost: 4


Applied acceleration
Original rule:
l4 -> l4 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, x0^0 >= 0, cost: 3
New rule:
l4 -> l4 : oldX0^0'=-n+x0^0, x0^0'=-n+x0^0, (1-n+x0^0 >= 0 /\ -1+n >= 0), cost: 3*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_mBmaOD.txt

Applied instantiation
Original rule:
l4 -> l4 : oldX0^0'=-n+x0^0, x0^0'=-n+x0^0, (1-n+x0^0 >= 0 /\ -1+n >= 0), cost: 3*n
New rule:
l4 -> l4 : oldX0^0'=-1, x0^0'=-1, (0 >= 0 /\ x0^0 >= 0), cost: 3+3*x0^0

Applied simplification
Original rule:
l4 -> l4 : oldX0^0'=-1, x0^0'=-1, (0 >= 0 /\ x0^0 >= 0), cost: 3+3*x0^0
New rule:
l4 -> l4 : oldX0^0'=-1, x0^0'=-1, x0^0 >= 0, cost: 3+3*x0^0

Applied deletion
Removed the following rules: 25

Accelerated simple loops
Start location: l6
  28: l4 -> l4 : oldX0^0'=-1, x0^0'=-1, x0^0 >= 0, cost: 3+3*x0^0
  20: l6 -> l4 : TRUE, cost: 2
  24: l6 -> l4 : oldX0^0'=x0^0, TRUE, cost: 3
  26: l6 -> l4 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, TRUE, cost: 4


Applied chaining
First rule:
l6 -> l4 : TRUE, cost: 2
Second rule:
l4 -> l4 : oldX0^0'=-1, x0^0'=-1, x0^0 >= 0, cost: 3+3*x0^0
New rule:
l6 -> l4 : oldX0^0'=-1, x0^0'=-1, x0^0 >= 0, cost: 5+3*x0^0

Applied chaining
First rule:
l6 -> l4 : oldX0^0'=x0^0, TRUE, cost: 3
Second rule:
l4 -> l4 : oldX0^0'=-1, x0^0'=-1, x0^0 >= 0, cost: 3+3*x0^0
New rule:
l6 -> l4 : oldX0^0'=-1, x0^0'=-1, x0^0 >= 0, cost: 6+3*x0^0

Applied chaining
First rule:
l6 -> l4 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, TRUE, cost: 4
Second rule:
l4 -> l4 : oldX0^0'=-1, x0^0'=-1, x0^0 >= 0, cost: 3+3*x0^0
New rule:
l6 -> l4 : oldX0^0'=-1, x0^0'=-1, -1+x0^0 >= 0, cost: 4+3*x0^0

Applied deletion
Removed the following rules: 28

Chained accelerated rules with incoming rules
Start location: l6
  20: l6 -> l4 : TRUE, cost: 2
  24: l6 -> l4 : oldX0^0'=x0^0, TRUE, cost: 3
  26: l6 -> l4 : oldX0^0'=-1+x0^0, x0^0'=-1+x0^0, TRUE, cost: 4
  29: l6 -> l4 : oldX0^0'=-1, x0^0'=-1, x0^0 >= 0, cost: 5+3*x0^0
  30: l6 -> l4 : oldX0^0'=-1, x0^0'=-1, x0^0 >= 0, cost: 6+3*x0^0
  31: l6 -> l4 : oldX0^0'=-1, x0^0'=-1, -1+x0^0 >= 0, cost: 4+3*x0^0


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