WORST_CASE(Omega(0),?)

Initial ITS
Start location: l7
   0: l0 -> l1 : __const_42^0'=__const_42^post0, i1^0'=i1^post0, (__const_42^0-__const_42^post0 == 0 /\ -1-i1^0+i1^post0 == 0), cost: 1
   7: l1 -> l4 : __const_42^0'=__const_42^post7, i1^0'=i1^post7, (__const_42^0-__const_42^post7 == 0 /\ -i1^post7+i1^0 == 0), cost: 1
   1: l2 -> l0 : __const_42^0'=__const_42^post1, i1^0'=i1^post1, (-i1^post1+i1^0 == 0 /\ __const_42^0-__const_42^post1 == 0), cost: 1
   2: l3 -> l2 : __const_42^0'=__const_42^post2, i1^0'=i1^post2, (-i1^post2+i1^0 == 0 /\ __const_42^0-__const_42^post2 == 0), cost: 1
   3: l3 -> l0 : __const_42^0'=__const_42^post3, i1^0'=i1^post3, (__const_42^0-__const_42^post3 == 0 /\ i1^0-i1^post3 == 0), cost: 1
   4: l3 -> l2 : __const_42^0'=__const_42^post4, i1^0'=i1^post4, (__const_42^0-__const_42^post4 == 0 /\ -i1^post4+i1^0 == 0), cost: 1
   5: l4 -> l5 : __const_42^0'=__const_42^post5, i1^0'=i1^post5, (i1^0-i1^post5 == 0 /\ __const_42^0-__const_42^post5 == 0 /\ __const_42^0-i1^0 <= 0), cost: 1
   6: l4 -> l3 : __const_42^0'=__const_42^post6, i1^0'=i1^post6, (-i1^post6+i1^0 == 0 /\ 1-__const_42^0+i1^0 <= 0 /\ __const_42^0-__const_42^post6 == 0), cost: 1
   8: l6 -> l1 : __const_42^0'=__const_42^post8, i1^0'=i1^post8, (__const_42^0-__const_42^post8 == 0 /\ i1^post8 == 0), cost: 1
   9: l7 -> l6 : __const_42^0'=__const_42^post9, i1^0'=i1^post9, (-i1^post9+i1^0 == 0 /\ __const_42^0-__const_42^post9 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l7
   0: l0 -> l1 : __const_42^0'=__const_42^post0, i1^0'=i1^post0, (__const_42^0-__const_42^post0 == 0 /\ -1-i1^0+i1^post0 == 0), cost: 1
   7: l1 -> l4 : __const_42^0'=__const_42^post7, i1^0'=i1^post7, (__const_42^0-__const_42^post7 == 0 /\ -i1^post7+i1^0 == 0), cost: 1
   1: l2 -> l0 : __const_42^0'=__const_42^post1, i1^0'=i1^post1, (-i1^post1+i1^0 == 0 /\ __const_42^0-__const_42^post1 == 0), cost: 1
   2: l3 -> l2 : __const_42^0'=__const_42^post2, i1^0'=i1^post2, (-i1^post2+i1^0 == 0 /\ __const_42^0-__const_42^post2 == 0), cost: 1
   3: l3 -> l0 : __const_42^0'=__const_42^post3, i1^0'=i1^post3, (__const_42^0-__const_42^post3 == 0 /\ i1^0-i1^post3 == 0), cost: 1
   4: l3 -> l2 : __const_42^0'=__const_42^post4, i1^0'=i1^post4, (__const_42^0-__const_42^post4 == 0 /\ -i1^post4+i1^0 == 0), cost: 1
   6: l4 -> l3 : __const_42^0'=__const_42^post6, i1^0'=i1^post6, (-i1^post6+i1^0 == 0 /\ 1-__const_42^0+i1^0 <= 0 /\ __const_42^0-__const_42^post6 == 0), cost: 1
   8: l6 -> l1 : __const_42^0'=__const_42^post8, i1^0'=i1^post8, (__const_42^0-__const_42^post8 == 0 /\ i1^post8 == 0), cost: 1
   9: l7 -> l6 : __const_42^0'=__const_42^post9, i1^0'=i1^post9, (-i1^post9+i1^0 == 0 /\ __const_42^0-__const_42^post9 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : __const_42^0'=__const_42^post0, i1^0'=i1^post0, (__const_42^0-__const_42^post0 == 0 /\ -1-i1^0+i1^post0 == 0), cost: 1
New rule:
l0 -> l1 : i1^0'=1+i1^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : __const_42^0'=__const_42^post1, i1^0'=i1^post1, (-i1^post1+i1^0 == 0 /\ __const_42^0-__const_42^post1 == 0), cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : __const_42^0'=__const_42^post2, i1^0'=i1^post2, (-i1^post2+i1^0 == 0 /\ __const_42^0-__const_42^post2 == 0), cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l0 : __const_42^0'=__const_42^post3, i1^0'=i1^post3, (__const_42^0-__const_42^post3 == 0 /\ i1^0-i1^post3 == 0), cost: 1
New rule:
l3 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : __const_42^0'=__const_42^post4, i1^0'=i1^post4, (__const_42^0-__const_42^post4 == 0 /\ -i1^post4+i1^0 == 0), cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : __const_42^0'=__const_42^post6, i1^0'=i1^post6, (-i1^post6+i1^0 == 0 /\ 1-__const_42^0+i1^0 <= 0 /\ __const_42^0-__const_42^post6 == 0), cost: 1
New rule:
l4 -> l3 : 1-__const_42^0+i1^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l4 : __const_42^0'=__const_42^post7, i1^0'=i1^post7, (__const_42^0-__const_42^post7 == 0 /\ -i1^post7+i1^0 == 0), cost: 1
New rule:
l1 -> l4 : TRUE, cost: 1

Applied preprocessing
Original rule:
l6 -> l1 : __const_42^0'=__const_42^post8, i1^0'=i1^post8, (__const_42^0-__const_42^post8 == 0 /\ i1^post8 == 0), cost: 1
New rule:
l6 -> l1 : i1^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l7 -> l6 : __const_42^0'=__const_42^post9, i1^0'=i1^post9, (-i1^post9+i1^0 == 0 /\ __const_42^0-__const_42^post9 == 0), cost: 1
New rule:
l7 -> l6 : TRUE, cost: 1

Applied deletion
Removed the following rules: 12

Simplified rules
Start location: l7
  10: l0 -> l1 : i1^0'=1+i1^0, TRUE, cost: 1
  16: l1 -> l4 : TRUE, cost: 1
  11: l2 -> l0 : TRUE, cost: 1
  13: l3 -> l0 : TRUE, cost: 1
  14: l3 -> l2 : TRUE, cost: 1
  15: l4 -> l3 : 1-__const_42^0+i1^0 <= 0, cost: 1
  17: l6 -> l1 : i1^0'=0, TRUE, cost: 1
  18: l7 -> l6 : TRUE, cost: 1


Eliminating location l6 by chaining:

Applied chaining
First rule:
l7 -> l6 : TRUE, cost: 1
Second rule:
l6 -> l1 : i1^0'=0, TRUE, cost: 1
New rule:
l7 -> l1 : i1^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 17 18

Eliminating location l4 by chaining:

Applied chaining
First rule:
l1 -> l4 : TRUE, cost: 1
Second rule:
l4 -> l3 : 1-__const_42^0+i1^0 <= 0, cost: 1
New rule:
l1 -> l3 : 1-__const_42^0+i1^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 15 16

Eliminating location l2 by chaining:

Applied chaining
First rule:
l3 -> l2 : TRUE, cost: 1
Second rule:
l2 -> l0 : TRUE, cost: 1
New rule:
l3 -> l0 : TRUE, cost: 2

Applied deletion
Removed the following rules: 11 14

Eliminated locations on linear paths
Start location: l7
  10: l0 -> l1 : i1^0'=1+i1^0, TRUE, cost: 1
  20: l1 -> l3 : 1-__const_42^0+i1^0 <= 0, cost: 2
  13: l3 -> l0 : TRUE, cost: 1
  21: l3 -> l0 : TRUE, cost: 2
  19: l7 -> l1 : i1^0'=0, TRUE, cost: 2


Eliminating location l3 by chaining:

Applied chaining
First rule:
l1 -> l3 : 1-__const_42^0+i1^0 <= 0, cost: 2
Second rule:
l3 -> l0 : TRUE, cost: 1
New rule:
l1 -> l0 : 1-__const_42^0+i1^0 <= 0, cost: 3

Applied chaining
First rule:
l1 -> l3 : 1-__const_42^0+i1^0 <= 0, cost: 2
Second rule:
l3 -> l0 : TRUE, cost: 2
New rule:
l1 -> l0 : 1-__const_42^0+i1^0 <= 0, cost: 4

Applied deletion
Removed the following rules: 13 20 21

Eliminated locations on tree-shaped paths
Start location: l7
  10: l0 -> l1 : i1^0'=1+i1^0, TRUE, cost: 1
  22: l1 -> l0 : 1-__const_42^0+i1^0 <= 0, cost: 3
  23: l1 -> l0 : 1-__const_42^0+i1^0 <= 0, cost: 4
  19: l7 -> l1 : i1^0'=0, TRUE, cost: 2


Eliminating location l0 by chaining:

Applied chaining
First rule:
l1 -> l0 : 1-__const_42^0+i1^0 <= 0, cost: 3
Second rule:
l0 -> l1 : i1^0'=1+i1^0, TRUE, cost: 1
New rule:
l1 -> l1 : i1^0'=1+i1^0, 1-__const_42^0+i1^0 <= 0, cost: 4

Applied chaining
First rule:
l1 -> l0 : 1-__const_42^0+i1^0 <= 0, cost: 4
Second rule:
l0 -> l1 : i1^0'=1+i1^0, TRUE, cost: 1
New rule:
l1 -> l1 : i1^0'=1+i1^0, 1-__const_42^0+i1^0 <= 0, cost: 5

Applied deletion
Removed the following rules: 10 22 23

Eliminated locations on tree-shaped paths
Start location: l7
  24: l1 -> l1 : i1^0'=1+i1^0, 1-__const_42^0+i1^0 <= 0, cost: 4
  25: l1 -> l1 : i1^0'=1+i1^0, 1-__const_42^0+i1^0 <= 0, cost: 5
  19: l7 -> l1 : i1^0'=0, TRUE, cost: 2


Applied deletion
Removed the following rules: 24

Applied acceleration
Original rule:
l1 -> l1 : i1^0'=1+i1^0, 1-__const_42^0+i1^0 <= 0, cost: 5
New rule:
l1 -> l1 : i1^0'=n0+i1^0, (n0 >= 0 /\ __const_42^0-n0-i1^0 >= 0), cost: 5*n0

Applied instantiation
Original rule:
l1 -> l1 : i1^0'=n0+i1^0, (n0 >= 0 /\ __const_42^0-n0-i1^0 >= 0), cost: 5*n0
New rule:
l1 -> l1 : i1^0'=__const_42^0, (0 >= 0 /\ __const_42^0-i1^0 >= 0), cost: 5*__const_42^0-5*i1^0

Applied simplification
Original rule:
l1 -> l1 : i1^0'=__const_42^0, (0 >= 0 /\ __const_42^0-i1^0 >= 0), cost: 5*__const_42^0-5*i1^0
New rule:
l1 -> l1 : i1^0'=__const_42^0, __const_42^0-i1^0 >= 0, cost: 5*__const_42^0-5*i1^0

Applied deletion
Removed the following rules: 25

Accelerated simple loops
Start location: l7
  27: l1 -> l1 : i1^0'=__const_42^0, __const_42^0-i1^0 >= 0, cost: 5*__const_42^0-5*i1^0
  19: l7 -> l1 : i1^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l7 -> l1 : i1^0'=0, TRUE, cost: 2
Second rule:
l1 -> l1 : i1^0'=__const_42^0, __const_42^0-i1^0 >= 0, cost: 5*__const_42^0-5*i1^0
New rule:
l7 -> l1 : i1^0'=__const_42^0, __const_42^0 >= 0, cost: 2+5*__const_42^0

Applied deletion
Removed the following rules: 27

Chained accelerated rules with incoming rules
Start location: l7
  19: l7 -> l1 : i1^0'=0, TRUE, cost: 2
  28: l7 -> l1 : i1^0'=__const_42^0, __const_42^0 >= 0, cost: 2+5*__const_42^0


Removed unreachable locations and irrelevant leafs
Start location: l7
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0