WORST_CASE(Omega(0),?)

Initial ITS
Start location: l5
   0: l0 -> l1 : s_17^0'=s_17^post0, j_15^0'=j_15^post0, s_16^0'=s_16^post0, i_13^0'=i_13^post0, st_14^0'=st_14^post0, rt_11^0'=rt_11^post0, (rt_11^0-rt_11^post0 == 0 /\ -s_16^post0+s_16^0 == 0 /\ -s_16^0+j_15^post0 == 0 /\ -s_17^0+i_13^10 == 0 /\ -st_14^post0+st_14^0 == 0 /\ i_13^post0-j_15^post0 == 0 /\ s_17^0-s_17^post0 == 0), cost: 1
   4: l1 -> l3 : s_17^0'=s_17^post4, j_15^0'=j_15^post4, s_16^0'=s_16^post4, i_13^0'=i_13^post4, st_14^0'=st_14^post4, rt_11^0'=rt_11^post4, (500-i_13^0 <= 0 /\ rt_11^post4-st_14^0 == 0 /\ -st_14^post4+st_14^0 == 0 /\ j_15^0-j_15^post4 == 0 /\ i_13^0-i_13^post4 == 0 /\ s_17^0-s_17^post4 == 0 /\ s_16^0-s_16^post4 == 0), cost: 1
   5: l1 -> l2 : s_17^0'=s_17^post5, j_15^0'=j_15^post5, s_16^0'=s_16^post5, i_13^0'=i_13^post5, st_14^0'=st_14^post5, rt_11^0'=rt_11^post5, (-1-i_13^0+i_13^post5 == 0 /\ -499+i_13^0 <= 0 /\ -s_16^post5+s_16^0 == 0 /\ -rt_11^post5+rt_11^0 == 0 /\ j_15^0-j_15^post5 == 0 /\ s_17^0-s_17^post5 == 0 /\ st_14^0-st_14^post5 == 0), cost: 1
   1: l2 -> l3 : s_17^0'=s_17^post1, j_15^0'=j_15^post1, s_16^0'=s_16^post1, i_13^0'=i_13^post1, st_14^0'=st_14^post1, rt_11^0'=rt_11^post1, (-st_14^0+rt_11^post1 == 0 /\ s_17^0-s_17^post1 == 0 /\ -i_13^post1+i_13^0 == 0 /\ 500-i_13^0 <= 0 /\ s_16^0-s_16^post1 == 0 /\ j_15^0-j_15^post1 == 0 /\ -st_14^post1+st_14^0 == 0), cost: 1
   2: l2 -> l4 : s_17^0'=s_17^post2, j_15^0'=j_15^post2, s_16^0'=s_16^post2, i_13^0'=i_13^post2, st_14^0'=st_14^post2, rt_11^0'=rt_11^post2, (s_17^0-s_17^post2 == 0 /\ s_16^0-s_16^post2 == 0 /\ -499+i_13^0 <= 0 /\ -st_14^post2+st_14^0 == 0 /\ -rt_11^post2+rt_11^0 == 0 /\ j_15^0-j_15^post2 == 0 /\ -1-i_13^0+i_13^post2 == 0), cost: 1
   3: l4 -> l2 : s_17^0'=s_17^post3, j_15^0'=j_15^post3, s_16^0'=s_16^post3, i_13^0'=i_13^post3, st_14^0'=st_14^post3, rt_11^0'=rt_11^post3, (s_16^0-s_16^post3 == 0 /\ s_17^0-s_17^post3 == 0 /\ -st_14^post3+st_14^0 == 0 /\ -rt_11^post3+rt_11^0 == 0 /\ i_13^0-i_13^post3 == 0 /\ -j_15^post3+j_15^0 == 0), cost: 1
   6: l5 -> l0 : s_17^0'=s_17^post6, j_15^0'=j_15^post6, s_16^0'=s_16^post6, i_13^0'=i_13^post6, st_14^0'=st_14^post6, rt_11^0'=rt_11^post6, (-s_16^post6+s_16^0 == 0 /\ j_15^0-j_15^post6 == 0 /\ -st_14^post6+st_14^0 == 0 /\ s_17^0-s_17^post6 == 0 /\ rt_11^0-rt_11^post6 == 0 /\ -i_13^post6+i_13^0 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l5
   0: l0 -> l1 : s_17^0'=s_17^post0, j_15^0'=j_15^post0, s_16^0'=s_16^post0, i_13^0'=i_13^post0, st_14^0'=st_14^post0, rt_11^0'=rt_11^post0, (rt_11^0-rt_11^post0 == 0 /\ -s_16^post0+s_16^0 == 0 /\ -s_16^0+j_15^post0 == 0 /\ -s_17^0+i_13^10 == 0 /\ -st_14^post0+st_14^0 == 0 /\ i_13^post0-j_15^post0 == 0 /\ s_17^0-s_17^post0 == 0), cost: 1
   5: l1 -> l2 : s_17^0'=s_17^post5, j_15^0'=j_15^post5, s_16^0'=s_16^post5, i_13^0'=i_13^post5, st_14^0'=st_14^post5, rt_11^0'=rt_11^post5, (-1-i_13^0+i_13^post5 == 0 /\ -499+i_13^0 <= 0 /\ -s_16^post5+s_16^0 == 0 /\ -rt_11^post5+rt_11^0 == 0 /\ j_15^0-j_15^post5 == 0 /\ s_17^0-s_17^post5 == 0 /\ st_14^0-st_14^post5 == 0), cost: 1
   2: l2 -> l4 : s_17^0'=s_17^post2, j_15^0'=j_15^post2, s_16^0'=s_16^post2, i_13^0'=i_13^post2, st_14^0'=st_14^post2, rt_11^0'=rt_11^post2, (s_17^0-s_17^post2 == 0 /\ s_16^0-s_16^post2 == 0 /\ -499+i_13^0 <= 0 /\ -st_14^post2+st_14^0 == 0 /\ -rt_11^post2+rt_11^0 == 0 /\ j_15^0-j_15^post2 == 0 /\ -1-i_13^0+i_13^post2 == 0), cost: 1
   3: l4 -> l2 : s_17^0'=s_17^post3, j_15^0'=j_15^post3, s_16^0'=s_16^post3, i_13^0'=i_13^post3, st_14^0'=st_14^post3, rt_11^0'=rt_11^post3, (s_16^0-s_16^post3 == 0 /\ s_17^0-s_17^post3 == 0 /\ -st_14^post3+st_14^0 == 0 /\ -rt_11^post3+rt_11^0 == 0 /\ i_13^0-i_13^post3 == 0 /\ -j_15^post3+j_15^0 == 0), cost: 1
   6: l5 -> l0 : s_17^0'=s_17^post6, j_15^0'=j_15^post6, s_16^0'=s_16^post6, i_13^0'=i_13^post6, st_14^0'=st_14^post6, rt_11^0'=rt_11^post6, (-s_16^post6+s_16^0 == 0 /\ j_15^0-j_15^post6 == 0 /\ -st_14^post6+st_14^0 == 0 /\ s_17^0-s_17^post6 == 0 /\ rt_11^0-rt_11^post6 == 0 /\ -i_13^post6+i_13^0 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : s_17^0'=s_17^post0, j_15^0'=j_15^post0, s_16^0'=s_16^post0, i_13^0'=i_13^post0, st_14^0'=st_14^post0, rt_11^0'=rt_11^post0, (rt_11^0-rt_11^post0 == 0 /\ -s_16^post0+s_16^0 == 0 /\ -s_16^0+j_15^post0 == 0 /\ -s_17^0+i_13^10 == 0 /\ -st_14^post0+st_14^0 == 0 /\ i_13^post0-j_15^post0 == 0 /\ s_17^0-s_17^post0 == 0), cost: 1
New rule:
l0 -> l1 : j_15^0'=s_16^0, i_13^0'=s_16^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l4 : s_17^0'=s_17^post2, j_15^0'=j_15^post2, s_16^0'=s_16^post2, i_13^0'=i_13^post2, st_14^0'=st_14^post2, rt_11^0'=rt_11^post2, (s_17^0-s_17^post2 == 0 /\ s_16^0-s_16^post2 == 0 /\ -499+i_13^0 <= 0 /\ -st_14^post2+st_14^0 == 0 /\ -rt_11^post2+rt_11^0 == 0 /\ j_15^0-j_15^post2 == 0 /\ -1-i_13^0+i_13^post2 == 0), cost: 1
New rule:
l2 -> l4 : i_13^0'=1+i_13^0, -499+i_13^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l2 : s_17^0'=s_17^post3, j_15^0'=j_15^post3, s_16^0'=s_16^post3, i_13^0'=i_13^post3, st_14^0'=st_14^post3, rt_11^0'=rt_11^post3, (s_16^0-s_16^post3 == 0 /\ s_17^0-s_17^post3 == 0 /\ -st_14^post3+st_14^0 == 0 /\ -rt_11^post3+rt_11^0 == 0 /\ i_13^0-i_13^post3 == 0 /\ -j_15^post3+j_15^0 == 0), cost: 1
New rule:
l4 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l1 -> l2 : s_17^0'=s_17^post5, j_15^0'=j_15^post5, s_16^0'=s_16^post5, i_13^0'=i_13^post5, st_14^0'=st_14^post5, rt_11^0'=rt_11^post5, (-1-i_13^0+i_13^post5 == 0 /\ -499+i_13^0 <= 0 /\ -s_16^post5+s_16^0 == 0 /\ -rt_11^post5+rt_11^0 == 0 /\ j_15^0-j_15^post5 == 0 /\ s_17^0-s_17^post5 == 0 /\ st_14^0-st_14^post5 == 0), cost: 1
New rule:
l1 -> l2 : i_13^0'=1+i_13^0, -499+i_13^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l5 -> l0 : s_17^0'=s_17^post6, j_15^0'=j_15^post6, s_16^0'=s_16^post6, i_13^0'=i_13^post6, st_14^0'=st_14^post6, rt_11^0'=rt_11^post6, (-s_16^post6+s_16^0 == 0 /\ j_15^0-j_15^post6 == 0 /\ -st_14^post6+st_14^0 == 0 /\ s_17^0-s_17^post6 == 0 /\ rt_11^0-rt_11^post6 == 0 /\ -i_13^post6+i_13^0 == 0), cost: 1
New rule:
l5 -> l0 : TRUE, cost: 1

Simplified rules
Start location: l5
   7: l0 -> l1 : j_15^0'=s_16^0, i_13^0'=s_16^0, TRUE, cost: 1
  10: l1 -> l2 : i_13^0'=1+i_13^0, -499+i_13^0 <= 0, cost: 1
   8: l2 -> l4 : i_13^0'=1+i_13^0, -499+i_13^0 <= 0, cost: 1
   9: l4 -> l2 : TRUE, cost: 1
  11: l5 -> l0 : TRUE, cost: 1


Eliminating location l0 by chaining:

Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 1
Second rule:
l0 -> l1 : j_15^0'=s_16^0, i_13^0'=s_16^0, TRUE, cost: 1
New rule:
l5 -> l1 : j_15^0'=s_16^0, i_13^0'=s_16^0, TRUE, cost: 2

Applied deletion
Removed the following rules: 7 11

Eliminating location l1 by chaining:

Applied chaining
First rule:
l5 -> l1 : j_15^0'=s_16^0, i_13^0'=s_16^0, TRUE, cost: 2
Second rule:
l1 -> l2 : i_13^0'=1+i_13^0, -499+i_13^0 <= 0, cost: 1
New rule:
l5 -> l2 : j_15^0'=s_16^0, i_13^0'=1+s_16^0, -499+s_16^0 <= 0, cost: 3

Applied deletion
Removed the following rules: 10 12

Eliminating location l4 by chaining:

Applied chaining
First rule:
l2 -> l4 : i_13^0'=1+i_13^0, -499+i_13^0 <= 0, cost: 1
Second rule:
l4 -> l2 : TRUE, cost: 1
New rule:
l2 -> l2 : i_13^0'=1+i_13^0, -499+i_13^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 8 9

Eliminated locations on linear paths
Start location: l5
  14: l2 -> l2 : i_13^0'=1+i_13^0, -499+i_13^0 <= 0, cost: 2
  13: l5 -> l2 : j_15^0'=s_16^0, i_13^0'=1+s_16^0, -499+s_16^0 <= 0, cost: 3


Applied acceleration
Original rule:
l2 -> l2 : i_13^0'=1+i_13^0, -499+i_13^0 <= 0, cost: 2
New rule:
l2 -> l2 : i_13^0'=i_13^0+n, (500-i_13^0-n >= 0 /\ n >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_FAmgbo.txt

Applied instantiation
Original rule:
l2 -> l2 : i_13^0'=i_13^0+n, (500-i_13^0-n >= 0 /\ n >= 0), cost: 2*n
New rule:
l2 -> l2 : i_13^0'=500, (0 >= 0 /\ 500-i_13^0 >= 0), cost: 1000-2*i_13^0

Applied simplification
Original rule:
l2 -> l2 : i_13^0'=500, (0 >= 0 /\ 500-i_13^0 >= 0), cost: 1000-2*i_13^0
New rule:
l2 -> l2 : i_13^0'=500, -500+i_13^0 <= 0, cost: 1000-2*i_13^0

Applied deletion
Removed the following rules: 14

Accelerated simple loops
Start location: l5
  16: l2 -> l2 : i_13^0'=500, -500+i_13^0 <= 0, cost: 1000-2*i_13^0
  13: l5 -> l2 : j_15^0'=s_16^0, i_13^0'=1+s_16^0, -499+s_16^0 <= 0, cost: 3


Applied chaining
First rule:
l5 -> l2 : j_15^0'=s_16^0, i_13^0'=1+s_16^0, -499+s_16^0 <= 0, cost: 3
Second rule:
l2 -> l2 : i_13^0'=500, -500+i_13^0 <= 0, cost: 1000-2*i_13^0
New rule:
l5 -> l2 : j_15^0'=s_16^0, i_13^0'=500, -499+s_16^0 <= 0, cost: 1001-2*s_16^0

Applied deletion
Removed the following rules: 16

Chained accelerated rules with incoming rules
Start location: l5
  13: l5 -> l2 : j_15^0'=s_16^0, i_13^0'=1+s_16^0, -499+s_16^0 <= 0, cost: 3
  17: l5 -> l2 : j_15^0'=s_16^0, i_13^0'=500, -499+s_16^0 <= 0, cost: 1001-2*s_16^0


Removed unreachable locations and irrelevant leafs
Start location: l5
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0