WORST_CASE(Omega(0),?)

Initial ITS
Start location: l6
   0: l0 -> l1 : st_14^0'=st_14^post0, i_13^0'=i_13^post0, rt_11^0'=rt_11^post0, a_20^0'=a_20^post0, i_21^0'=i_21^post0, (-i_21^post0+i_21^0 == 0 /\ st_14^0-st_14^post0 == 0 /\ i_13^post0 <= 0 /\ i_13^post0 == 0 /\ a_20^0-a_20^post0 == 0 /\ -i_13^post0 <= 0 /\ rt_11^0-rt_11^post0 == 0), cost: 1
   3: l1 -> l4 : st_14^0'=st_14^post3, i_13^0'=i_13^post3, rt_11^0'=rt_11^post3, a_20^0'=a_20^post3, i_21^0'=i_21^post3, (i_13^0-i_13^post3 == 0 /\ -a_20^post3+a_20^0 == 0 /\ -st_14^0+rt_11^post3 == 0 /\ st_14^0-st_14^post3 == 0 /\ 10-i_13^0 <= 0 /\ -i_21^post3+i_21^0 == 0), cost: 1
   4: l1 -> l5 : st_14^0'=st_14^post4, i_13^0'=i_13^post4, rt_11^0'=rt_11^post4, a_20^0'=a_20^post4, i_21^0'=i_21^post4, (0 == 0 /\ rt_11^0-rt_11^post4 == 0 /\ st_14^0-st_14^post4 == 0 /\ -1-i_13^0+i_13^post4 == 0 /\ -9+i_13^0 <= 0 /\ -1-i_21^post4+i_13^post4 <= 0 /\ -9+i_21^post4 <= 0 /\ a_20^0-a_20^post4 == 0 /\ 1+i_21^post4-i_13^post4 <= 0), cost: 1
   1: l2 -> l1 : st_14^0'=st_14^post1, i_13^0'=i_13^post1, rt_11^0'=rt_11^post1, a_20^0'=a_20^post1, i_21^0'=i_21^post1, (0 == 0 /\ -a_20^post1+i_13^post1 <= 0 /\ -9+i_13^0 <= 0 /\ -2+i_13^post1 <= 0 /\ a_20^post1-i_13^post1 <= 0 /\ rt_11^0-rt_11^post1 == 0 /\ -i_21^post1+i_21^0 == 0 /\ -1-i_13^0+i_13^10 == 0 /\ -st_14^post1+st_14^0 == 0 /\ 2-i_13^post1 <= 0), cost: 1
   2: l3 -> l1 : st_14^0'=st_14^post2, i_13^0'=i_13^post2, rt_11^0'=rt_11^post2, a_20^0'=a_20^post2, i_21^0'=i_21^post2, (st_14^0-st_14^post2 == 0 /\ -1+i_13^post2-i_13^0 == 0 /\ -9+i_13^0 <= 0 /\ i_21^0-i_21^post2 == 0 /\ -rt_11^post2+rt_11^0 == 0 /\ 1-i_13^post2 <= 0 /\ -1+i_13^post2 <= 0 /\ a_20^0-a_20^post2 == 0), cost: 1
   5: l5 -> l1 : st_14^0'=st_14^post5, i_13^0'=i_13^post5, rt_11^0'=rt_11^post5, a_20^0'=a_20^post5, i_21^0'=i_21^post5, (-a_20^post5+a_20^0 == 0 /\ -rt_11^post5+rt_11^0 == 0 /\ st_14^0-st_14^post5 == 0 /\ -i_21^post5+i_21^0 == 0 /\ i_13^0-i_13^post5 == 0), cost: 1
   6: l6 -> l0 : st_14^0'=st_14^post6, i_13^0'=i_13^post6, rt_11^0'=rt_11^post6, a_20^0'=a_20^post6, i_21^0'=i_21^post6, (a_20^0-a_20^post6 == 0 /\ -i_21^post6+i_21^0 == 0 /\ rt_11^0-rt_11^post6 == 0 /\ i_13^0-i_13^post6 == 0 /\ st_14^0-st_14^post6 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l6
   0: l0 -> l1 : st_14^0'=st_14^post0, i_13^0'=i_13^post0, rt_11^0'=rt_11^post0, a_20^0'=a_20^post0, i_21^0'=i_21^post0, (-i_21^post0+i_21^0 == 0 /\ st_14^0-st_14^post0 == 0 /\ i_13^post0 <= 0 /\ i_13^post0 == 0 /\ a_20^0-a_20^post0 == 0 /\ -i_13^post0 <= 0 /\ rt_11^0-rt_11^post0 == 0), cost: 1
   4: l1 -> l5 : st_14^0'=st_14^post4, i_13^0'=i_13^post4, rt_11^0'=rt_11^post4, a_20^0'=a_20^post4, i_21^0'=i_21^post4, (0 == 0 /\ rt_11^0-rt_11^post4 == 0 /\ st_14^0-st_14^post4 == 0 /\ -1-i_13^0+i_13^post4 == 0 /\ -9+i_13^0 <= 0 /\ -1-i_21^post4+i_13^post4 <= 0 /\ -9+i_21^post4 <= 0 /\ a_20^0-a_20^post4 == 0 /\ 1+i_21^post4-i_13^post4 <= 0), cost: 1
   5: l5 -> l1 : st_14^0'=st_14^post5, i_13^0'=i_13^post5, rt_11^0'=rt_11^post5, a_20^0'=a_20^post5, i_21^0'=i_21^post5, (-a_20^post5+a_20^0 == 0 /\ -rt_11^post5+rt_11^0 == 0 /\ st_14^0-st_14^post5 == 0 /\ -i_21^post5+i_21^0 == 0 /\ i_13^0-i_13^post5 == 0), cost: 1
   6: l6 -> l0 : st_14^0'=st_14^post6, i_13^0'=i_13^post6, rt_11^0'=rt_11^post6, a_20^0'=a_20^post6, i_21^0'=i_21^post6, (a_20^0-a_20^post6 == 0 /\ -i_21^post6+i_21^0 == 0 /\ rt_11^0-rt_11^post6 == 0 /\ i_13^0-i_13^post6 == 0 /\ st_14^0-st_14^post6 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : st_14^0'=st_14^post0, i_13^0'=i_13^post0, rt_11^0'=rt_11^post0, a_20^0'=a_20^post0, i_21^0'=i_21^post0, (-i_21^post0+i_21^0 == 0 /\ st_14^0-st_14^post0 == 0 /\ i_13^post0 <= 0 /\ i_13^post0 == 0 /\ a_20^0-a_20^post0 == 0 /\ -i_13^post0 <= 0 /\ rt_11^0-rt_11^post0 == 0), cost: 1
New rule:
l0 -> l1 : i_13^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l1 -> l5 : st_14^0'=st_14^post4, i_13^0'=i_13^post4, rt_11^0'=rt_11^post4, a_20^0'=a_20^post4, i_21^0'=i_21^post4, (0 == 0 /\ rt_11^0-rt_11^post4 == 0 /\ st_14^0-st_14^post4 == 0 /\ -1-i_13^0+i_13^post4 == 0 /\ -9+i_13^0 <= 0 /\ -1-i_21^post4+i_13^post4 <= 0 /\ -9+i_21^post4 <= 0 /\ a_20^0-a_20^post4 == 0 /\ 1+i_21^post4-i_13^post4 <= 0), cost: 1
New rule:
l1 -> l5 : i_13^0'=1+i_13^0, i_21^0'=i_13^0, -9+i_13^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l5 -> l1 : st_14^0'=st_14^post5, i_13^0'=i_13^post5, rt_11^0'=rt_11^post5, a_20^0'=a_20^post5, i_21^0'=i_21^post5, (-a_20^post5+a_20^0 == 0 /\ -rt_11^post5+rt_11^0 == 0 /\ st_14^0-st_14^post5 == 0 /\ -i_21^post5+i_21^0 == 0 /\ i_13^0-i_13^post5 == 0), cost: 1
New rule:
l5 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l6 -> l0 : st_14^0'=st_14^post6, i_13^0'=i_13^post6, rt_11^0'=rt_11^post6, a_20^0'=a_20^post6, i_21^0'=i_21^post6, (a_20^0-a_20^post6 == 0 /\ -i_21^post6+i_21^0 == 0 /\ rt_11^0-rt_11^post6 == 0 /\ i_13^0-i_13^post6 == 0 /\ st_14^0-st_14^post6 == 0), cost: 1
New rule:
l6 -> l0 : TRUE, cost: 1

Simplified rules
Start location: l6
   7: l0 -> l1 : i_13^0'=0, TRUE, cost: 1
   8: l1 -> l5 : i_13^0'=1+i_13^0, i_21^0'=i_13^0, -9+i_13^0 <= 0, cost: 1
   9: l5 -> l1 : TRUE, cost: 1
  10: l6 -> l0 : TRUE, cost: 1


Eliminating location l0 by chaining:

Applied chaining
First rule:
l6 -> l0 : TRUE, cost: 1
Second rule:
l0 -> l1 : i_13^0'=0, TRUE, cost: 1
New rule:
l6 -> l1 : i_13^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 7 10

Eliminating location l5 by chaining:

Applied chaining
First rule:
l1 -> l5 : i_13^0'=1+i_13^0, i_21^0'=i_13^0, -9+i_13^0 <= 0, cost: 1
Second rule:
l5 -> l1 : TRUE, cost: 1
New rule:
l1 -> l1 : i_13^0'=1+i_13^0, i_21^0'=i_13^0, -9+i_13^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 8 9

Eliminated locations on linear paths
Start location: l6
  12: l1 -> l1 : i_13^0'=1+i_13^0, i_21^0'=i_13^0, -9+i_13^0 <= 0, cost: 2
  11: l6 -> l1 : i_13^0'=0, TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : i_13^0'=1+i_13^0, i_21^0'=i_13^0, -9+i_13^0 <= 0, cost: 2
New rule:
l1 -> l1 : i_13^0'=i_13^0+n, i_21^0'=-1+i_13^0+n, (10-i_13^0-n >= 0 /\ -1+n >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_pJHBlC.txt

Applied instantiation
Original rule:
l1 -> l1 : i_13^0'=i_13^0+n, i_21^0'=-1+i_13^0+n, (10-i_13^0-n >= 0 /\ -1+n >= 0), cost: 2*n
New rule:
l1 -> l1 : i_13^0'=10, i_21^0'=9, (0 >= 0 /\ 9-i_13^0 >= 0), cost: 20-2*i_13^0

Applied simplification
Original rule:
l1 -> l1 : i_13^0'=10, i_21^0'=9, (0 >= 0 /\ 9-i_13^0 >= 0), cost: 20-2*i_13^0
New rule:
l1 -> l1 : i_13^0'=10, i_21^0'=9, -9+i_13^0 <= 0, cost: 20-2*i_13^0

Applied deletion
Removed the following rules: 12

Accelerated simple loops
Start location: l6
  14: l1 -> l1 : i_13^0'=10, i_21^0'=9, -9+i_13^0 <= 0, cost: 20-2*i_13^0
  11: l6 -> l1 : i_13^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l6 -> l1 : i_13^0'=0, TRUE, cost: 2
Second rule:
l1 -> l1 : i_13^0'=10, i_21^0'=9, -9+i_13^0 <= 0, cost: 20-2*i_13^0
New rule:
l6 -> l1 : i_13^0'=10, i_21^0'=9, -9 <= 0, cost: 22

Applied deletion
Removed the following rules: 14

Chained accelerated rules with incoming rules
Start location: l6
  11: l6 -> l1 : i_13^0'=0, TRUE, cost: 2
  15: l6 -> l1 : i_13^0'=10, i_21^0'=9, -9 <= 0, cost: 22


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