WORST_CASE(Omega(0),?)

Initial ITS
Start location: l6
   0: l0 -> l1 : i10^0'=i10^post0, tmp^0'=tmp^post0, n12^0'=n12^post0, n^0'=n^post0, i13^0'=i13^post0, tmp___0^0'=tmp___0^post0, n9^0'=n9^post0, (tmp^0-tmp^post0 == 0 /\ i10^0-i10^post0 == 0 /\ -tmp___0^post0+tmp___0^0 == 0 /\ -n12^post0+n12^0 == 0 /\ -n9^post0+n9^0 == 0 /\ i13^0-i13^post0 == 0 /\ -n^post0+n^0 == 0), cost: 1
   4: l1 -> l4 : i10^0'=i10^post4, tmp^0'=tmp^post4, n12^0'=n12^post4, n^0'=n^post4, i13^0'=i13^post4, tmp___0^0'=tmp___0^post4, n9^0'=n9^post4, (0 == 0 /\ -i10^0+n9^0 <= 0 /\ i13^post4 == 0 /\ -n9^post4+n9^0 == 0 /\ tmp^0-tmp^post4 == 0 /\ i10^0-i10^post4 == 0 /\ n^0-n^post4 == 0 /\ -n^0+n12^post4 == 0), cost: 1
   5: l1 -> l0 : i10^0'=i10^post5, tmp^0'=tmp^post5, n12^0'=n12^post5, n^0'=n^post5, i13^0'=i13^post5, tmp___0^0'=tmp___0^post5, n9^0'=n9^post5, (-n9^post5+n9^0 == 0 /\ -tmp___0^post5+tmp___0^0 == 0 /\ tmp^0-tmp^post5 == 0 /\ 1+i10^0-n9^0 <= 0 /\ -n^post5+n^0 == 0 /\ -1-i10^0+i10^post5 == 0 /\ n12^0-n12^post5 == 0 /\ -i13^post5+i13^0 == 0), cost: 1
   1: l2 -> l3 : i10^0'=i10^post1, tmp^0'=tmp^post1, n12^0'=n12^post1, n^0'=n^post1, i13^0'=i13^post1, tmp___0^0'=tmp___0^post1, n9^0'=n9^post1, (n^0-n^post1 == 0 /\ n12^0-i13^0 <= 0 /\ i13^0-i13^post1 == 0 /\ -n9^post1+n9^0 == 0 /\ tmp^0-tmp^post1 == 0 /\ n12^0-n12^post1 == 0 /\ i10^0-i10^post1 == 0 /\ -tmp___0^post1+tmp___0^0 == 0), cost: 1
   2: l2 -> l4 : i10^0'=i10^post2, tmp^0'=tmp^post2, n12^0'=n12^post2, n^0'=n^post2, i13^0'=i13^post2, tmp___0^0'=tmp___0^post2, n9^0'=n9^post2, (-tmp___0^post2+tmp___0^0 == 0 /\ -n9^post2+n9^0 == 0 /\ -1+i13^post2-i13^0 == 0 /\ i10^0-i10^post2 == 0 /\ 1-n12^0+i13^0 <= 0 /\ n^0-n^post2 == 0 /\ tmp^0-tmp^post2 == 0 /\ n12^0-n12^post2 == 0), cost: 1
   3: l4 -> l2 : i10^0'=i10^post3, tmp^0'=tmp^post3, n12^0'=n12^post3, n^0'=n^post3, i13^0'=i13^post3, tmp___0^0'=tmp___0^post3, n9^0'=n9^post3, (i10^0-i10^post3 == 0 /\ tmp^0-tmp^post3 == 0 /\ n12^0-n12^post3 == 0 /\ -i13^post3+i13^0 == 0 /\ -n9^post3+n9^0 == 0 /\ -tmp___0^post3+tmp___0^0 == 0 /\ n^0-n^post3 == 0), cost: 1
   6: l5 -> l0 : i10^0'=i10^post6, tmp^0'=tmp^post6, n12^0'=n12^post6, n^0'=n^post6, i13^0'=i13^post6, tmp___0^0'=tmp___0^post6, n9^0'=n9^post6, (0 == 0 /\ i10^post6 == 0 /\ -tmp___0^post6+tmp___0^0 == 0 /\ -i13^post6+i13^0 == 0 /\ n12^0-n12^post6 == 0), cost: 1
   7: l6 -> l5 : i10^0'=i10^post7, tmp^0'=tmp^post7, n12^0'=n12^post7, n^0'=n^post7, i13^0'=i13^post7, tmp___0^0'=tmp___0^post7, n9^0'=n9^post7, (-n^post7+n^0 == 0 /\ i10^0-i10^post7 == 0 /\ -n9^post7+n9^0 == 0 /\ tmp___0^0-tmp___0^post7 == 0 /\ i13^0-i13^post7 == 0 /\ -n12^post7+n12^0 == 0 /\ tmp^0-tmp^post7 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l6
   0: l0 -> l1 : i10^0'=i10^post0, tmp^0'=tmp^post0, n12^0'=n12^post0, n^0'=n^post0, i13^0'=i13^post0, tmp___0^0'=tmp___0^post0, n9^0'=n9^post0, (tmp^0-tmp^post0 == 0 /\ i10^0-i10^post0 == 0 /\ -tmp___0^post0+tmp___0^0 == 0 /\ -n12^post0+n12^0 == 0 /\ -n9^post0+n9^0 == 0 /\ i13^0-i13^post0 == 0 /\ -n^post0+n^0 == 0), cost: 1
   4: l1 -> l4 : i10^0'=i10^post4, tmp^0'=tmp^post4, n12^0'=n12^post4, n^0'=n^post4, i13^0'=i13^post4, tmp___0^0'=tmp___0^post4, n9^0'=n9^post4, (0 == 0 /\ -i10^0+n9^0 <= 0 /\ i13^post4 == 0 /\ -n9^post4+n9^0 == 0 /\ tmp^0-tmp^post4 == 0 /\ i10^0-i10^post4 == 0 /\ n^0-n^post4 == 0 /\ -n^0+n12^post4 == 0), cost: 1
   5: l1 -> l0 : i10^0'=i10^post5, tmp^0'=tmp^post5, n12^0'=n12^post5, n^0'=n^post5, i13^0'=i13^post5, tmp___0^0'=tmp___0^post5, n9^0'=n9^post5, (-n9^post5+n9^0 == 0 /\ -tmp___0^post5+tmp___0^0 == 0 /\ tmp^0-tmp^post5 == 0 /\ 1+i10^0-n9^0 <= 0 /\ -n^post5+n^0 == 0 /\ -1-i10^0+i10^post5 == 0 /\ n12^0-n12^post5 == 0 /\ -i13^post5+i13^0 == 0), cost: 1
   2: l2 -> l4 : i10^0'=i10^post2, tmp^0'=tmp^post2, n12^0'=n12^post2, n^0'=n^post2, i13^0'=i13^post2, tmp___0^0'=tmp___0^post2, n9^0'=n9^post2, (-tmp___0^post2+tmp___0^0 == 0 /\ -n9^post2+n9^0 == 0 /\ -1+i13^post2-i13^0 == 0 /\ i10^0-i10^post2 == 0 /\ 1-n12^0+i13^0 <= 0 /\ n^0-n^post2 == 0 /\ tmp^0-tmp^post2 == 0 /\ n12^0-n12^post2 == 0), cost: 1
   3: l4 -> l2 : i10^0'=i10^post3, tmp^0'=tmp^post3, n12^0'=n12^post3, n^0'=n^post3, i13^0'=i13^post3, tmp___0^0'=tmp___0^post3, n9^0'=n9^post3, (i10^0-i10^post3 == 0 /\ tmp^0-tmp^post3 == 0 /\ n12^0-n12^post3 == 0 /\ -i13^post3+i13^0 == 0 /\ -n9^post3+n9^0 == 0 /\ -tmp___0^post3+tmp___0^0 == 0 /\ n^0-n^post3 == 0), cost: 1
   6: l5 -> l0 : i10^0'=i10^post6, tmp^0'=tmp^post6, n12^0'=n12^post6, n^0'=n^post6, i13^0'=i13^post6, tmp___0^0'=tmp___0^post6, n9^0'=n9^post6, (0 == 0 /\ i10^post6 == 0 /\ -tmp___0^post6+tmp___0^0 == 0 /\ -i13^post6+i13^0 == 0 /\ n12^0-n12^post6 == 0), cost: 1
   7: l6 -> l5 : i10^0'=i10^post7, tmp^0'=tmp^post7, n12^0'=n12^post7, n^0'=n^post7, i13^0'=i13^post7, tmp___0^0'=tmp___0^post7, n9^0'=n9^post7, (-n^post7+n^0 == 0 /\ i10^0-i10^post7 == 0 /\ -n9^post7+n9^0 == 0 /\ tmp___0^0-tmp___0^post7 == 0 /\ i13^0-i13^post7 == 0 /\ -n12^post7+n12^0 == 0 /\ tmp^0-tmp^post7 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : i10^0'=i10^post0, tmp^0'=tmp^post0, n12^0'=n12^post0, n^0'=n^post0, i13^0'=i13^post0, tmp___0^0'=tmp___0^post0, n9^0'=n9^post0, (tmp^0-tmp^post0 == 0 /\ i10^0-i10^post0 == 0 /\ -tmp___0^post0+tmp___0^0 == 0 /\ -n12^post0+n12^0 == 0 /\ -n9^post0+n9^0 == 0 /\ i13^0-i13^post0 == 0 /\ -n^post0+n^0 == 0), cost: 1
New rule:
l0 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l4 : i10^0'=i10^post2, tmp^0'=tmp^post2, n12^0'=n12^post2, n^0'=n^post2, i13^0'=i13^post2, tmp___0^0'=tmp___0^post2, n9^0'=n9^post2, (-tmp___0^post2+tmp___0^0 == 0 /\ -n9^post2+n9^0 == 0 /\ -1+i13^post2-i13^0 == 0 /\ i10^0-i10^post2 == 0 /\ 1-n12^0+i13^0 <= 0 /\ n^0-n^post2 == 0 /\ tmp^0-tmp^post2 == 0 /\ n12^0-n12^post2 == 0), cost: 1
New rule:
l2 -> l4 : i13^0'=1+i13^0, 1-n12^0+i13^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l2 : i10^0'=i10^post3, tmp^0'=tmp^post3, n12^0'=n12^post3, n^0'=n^post3, i13^0'=i13^post3, tmp___0^0'=tmp___0^post3, n9^0'=n9^post3, (i10^0-i10^post3 == 0 /\ tmp^0-tmp^post3 == 0 /\ n12^0-n12^post3 == 0 /\ -i13^post3+i13^0 == 0 /\ -n9^post3+n9^0 == 0 /\ -tmp___0^post3+tmp___0^0 == 0 /\ n^0-n^post3 == 0), cost: 1
New rule:
l4 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l1 -> l4 : i10^0'=i10^post4, tmp^0'=tmp^post4, n12^0'=n12^post4, n^0'=n^post4, i13^0'=i13^post4, tmp___0^0'=tmp___0^post4, n9^0'=n9^post4, (0 == 0 /\ -i10^0+n9^0 <= 0 /\ i13^post4 == 0 /\ -n9^post4+n9^0 == 0 /\ tmp^0-tmp^post4 == 0 /\ i10^0-i10^post4 == 0 /\ n^0-n^post4 == 0 /\ -n^0+n12^post4 == 0), cost: 1
New rule:
l1 -> l4 : n12^0'=n^0, i13^0'=0, tmp___0^0'=tmp___0^post4, -i10^0+n9^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l0 : i10^0'=i10^post5, tmp^0'=tmp^post5, n12^0'=n12^post5, n^0'=n^post5, i13^0'=i13^post5, tmp___0^0'=tmp___0^post5, n9^0'=n9^post5, (-n9^post5+n9^0 == 0 /\ -tmp___0^post5+tmp___0^0 == 0 /\ tmp^0-tmp^post5 == 0 /\ 1+i10^0-n9^0 <= 0 /\ -n^post5+n^0 == 0 /\ -1-i10^0+i10^post5 == 0 /\ n12^0-n12^post5 == 0 /\ -i13^post5+i13^0 == 0), cost: 1
New rule:
l1 -> l0 : i10^0'=1+i10^0, 1+i10^0-n9^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l5 -> l0 : i10^0'=i10^post6, tmp^0'=tmp^post6, n12^0'=n12^post6, n^0'=n^post6, i13^0'=i13^post6, tmp___0^0'=tmp___0^post6, n9^0'=n9^post6, (0 == 0 /\ i10^post6 == 0 /\ -tmp___0^post6+tmp___0^0 == 0 /\ -i13^post6+i13^0 == 0 /\ n12^0-n12^post6 == 0), cost: 1
New rule:
l5 -> l0 : i10^0'=0, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, 0 == 0, cost: 1

Applied preprocessing
Original rule:
l6 -> l5 : i10^0'=i10^post7, tmp^0'=tmp^post7, n12^0'=n12^post7, n^0'=n^post7, i13^0'=i13^post7, tmp___0^0'=tmp___0^post7, n9^0'=n9^post7, (-n^post7+n^0 == 0 /\ i10^0-i10^post7 == 0 /\ -n9^post7+n9^0 == 0 /\ tmp___0^0-tmp___0^post7 == 0 /\ i13^0-i13^post7 == 0 /\ -n12^post7+n12^0 == 0 /\ tmp^0-tmp^post7 == 0), cost: 1
New rule:
l6 -> l5 : TRUE, cost: 1

Simplified rules
Start location: l6
   8: l0 -> l1 : TRUE, cost: 1
  11: l1 -> l4 : n12^0'=n^0, i13^0'=0, tmp___0^0'=tmp___0^post4, -i10^0+n9^0 <= 0, cost: 1
  12: l1 -> l0 : i10^0'=1+i10^0, 1+i10^0-n9^0 <= 0, cost: 1
   9: l2 -> l4 : i13^0'=1+i13^0, 1-n12^0+i13^0 <= 0, cost: 1
  10: l4 -> l2 : TRUE, cost: 1
  13: l5 -> l0 : i10^0'=0, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, 0 == 0, cost: 1
  14: l6 -> l5 : TRUE, cost: 1


Eliminating location l5 by chaining:

Applied chaining
First rule:
l6 -> l5 : TRUE, cost: 1
Second rule:
l5 -> l0 : i10^0'=0, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, 0 == 0, cost: 1
New rule:
l6 -> l0 : i10^0'=0, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, 0 == 0, cost: 2

Applied deletion
Removed the following rules: 13 14

Eliminating location l2 by chaining:

Applied chaining
First rule:
l4 -> l2 : TRUE, cost: 1
Second rule:
l2 -> l4 : i13^0'=1+i13^0, 1-n12^0+i13^0 <= 0, cost: 1
New rule:
l4 -> l4 : i13^0'=1+i13^0, 1-n12^0+i13^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 9 10

Eliminated locations on linear paths
Start location: l6
   8: l0 -> l1 : TRUE, cost: 1
  11: l1 -> l4 : n12^0'=n^0, i13^0'=0, tmp___0^0'=tmp___0^post4, -i10^0+n9^0 <= 0, cost: 1
  12: l1 -> l0 : i10^0'=1+i10^0, 1+i10^0-n9^0 <= 0, cost: 1
  16: l4 -> l4 : i13^0'=1+i13^0, 1-n12^0+i13^0 <= 0, cost: 2
  15: l6 -> l0 : i10^0'=0, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, 0 == 0, cost: 2


Applied acceleration
Original rule:
l4 -> l4 : i13^0'=1+i13^0, 1-n12^0+i13^0 <= 0, cost: 2
New rule:
l4 -> l4 : i13^0'=n0+i13^0, (n0 >= 0 /\ n12^0-n0-i13^0 >= 0), cost: 2*n0

Applied instantiation
Original rule:
l4 -> l4 : i13^0'=n0+i13^0, (n0 >= 0 /\ n12^0-n0-i13^0 >= 0), cost: 2*n0
New rule:
l4 -> l4 : i13^0'=n12^0, (0 >= 0 /\ n12^0-i13^0 >= 0), cost: 2*n12^0-2*i13^0

Applied simplification
Original rule:
l4 -> l4 : i13^0'=n12^0, (0 >= 0 /\ n12^0-i13^0 >= 0), cost: 2*n12^0-2*i13^0
New rule:
l4 -> l4 : i13^0'=n12^0, n12^0-i13^0 >= 0, cost: 2*n12^0-2*i13^0

Applied deletion
Removed the following rules: 16

Accelerated simple loops
Start location: l6
   8: l0 -> l1 : TRUE, cost: 1
  11: l1 -> l4 : n12^0'=n^0, i13^0'=0, tmp___0^0'=tmp___0^post4, -i10^0+n9^0 <= 0, cost: 1
  12: l1 -> l0 : i10^0'=1+i10^0, 1+i10^0-n9^0 <= 0, cost: 1
  18: l4 -> l4 : i13^0'=n12^0, n12^0-i13^0 >= 0, cost: 2*n12^0-2*i13^0
  15: l6 -> l0 : i10^0'=0, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, 0 == 0, cost: 2


Applied chaining
First rule:
l1 -> l4 : n12^0'=n^0, i13^0'=0, tmp___0^0'=tmp___0^post4, -i10^0+n9^0 <= 0, cost: 1
Second rule:
l4 -> l4 : i13^0'=n12^0, n12^0-i13^0 >= 0, cost: 2*n12^0-2*i13^0
New rule:
l1 -> l4 : n12^0'=n^0, i13^0'=n^0, tmp___0^0'=tmp___0^post4, (-i10^0+n9^0 <= 0 /\ n^0 >= 0), cost: 1+2*n^0

Applied deletion
Removed the following rules: 18

Chained accelerated rules with incoming rules
Start location: l6
   8: l0 -> l1 : TRUE, cost: 1
  11: l1 -> l4 : n12^0'=n^0, i13^0'=0, tmp___0^0'=tmp___0^post4, -i10^0+n9^0 <= 0, cost: 1
  12: l1 -> l0 : i10^0'=1+i10^0, 1+i10^0-n9^0 <= 0, cost: 1
  19: l1 -> l4 : n12^0'=n^0, i13^0'=n^0, tmp___0^0'=tmp___0^post4, (-i10^0+n9^0 <= 0 /\ n^0 >= 0), cost: 1+2*n^0
  15: l6 -> l0 : i10^0'=0, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, 0 == 0, cost: 2


Removed unreachable locations and irrelevant leafs
Start location: l6
   8: l0 -> l1 : TRUE, cost: 1
  12: l1 -> l0 : i10^0'=1+i10^0, 1+i10^0-n9^0 <= 0, cost: 1
  15: l6 -> l0 : i10^0'=0, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, 0 == 0, cost: 2


Eliminating location l1 by chaining:

Applied chaining
First rule:
l0 -> l1 : TRUE, cost: 1
Second rule:
l1 -> l0 : i10^0'=1+i10^0, 1+i10^0-n9^0 <= 0, cost: 1
New rule:
l0 -> l0 : i10^0'=1+i10^0, 1+i10^0-n9^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 8 12

Eliminated locations on linear paths
Start location: l6
  20: l0 -> l0 : i10^0'=1+i10^0, 1+i10^0-n9^0 <= 0, cost: 2
  15: l6 -> l0 : i10^0'=0, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, 0 == 0, cost: 2


Applied acceleration
Original rule:
l0 -> l0 : i10^0'=1+i10^0, 1+i10^0-n9^0 <= 0, cost: 2
New rule:
l0 -> l0 : i10^0'=i10^0+n3, (-i10^0-n3+n9^0 >= 0 /\ n3 >= 0), cost: 2*n3

Applied instantiation
Original rule:
l0 -> l0 : i10^0'=i10^0+n3, (-i10^0-n3+n9^0 >= 0 /\ n3 >= 0), cost: 2*n3
New rule:
l0 -> l0 : i10^0'=n9^0, (0 >= 0 /\ -i10^0+n9^0 >= 0), cost: -2*i10^0+2*n9^0

Applied simplification
Original rule:
l0 -> l0 : i10^0'=n9^0, (0 >= 0 /\ -i10^0+n9^0 >= 0), cost: -2*i10^0+2*n9^0
New rule:
l0 -> l0 : i10^0'=n9^0, -i10^0+n9^0 >= 0, cost: -2*i10^0+2*n9^0

Applied deletion
Removed the following rules: 20

Accelerated simple loops
Start location: l6
  22: l0 -> l0 : i10^0'=n9^0, -i10^0+n9^0 >= 0, cost: -2*i10^0+2*n9^0
  15: l6 -> l0 : i10^0'=0, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, 0 == 0, cost: 2


Applied chaining
First rule:
l6 -> l0 : i10^0'=0, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, 0 == 0, cost: 2
Second rule:
l0 -> l0 : i10^0'=n9^0, -i10^0+n9^0 >= 0, cost: -2*i10^0+2*n9^0
New rule:
l6 -> l0 : i10^0'=n9^post6, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, n9^post6 >= 0, cost: 2+2*n9^post6

Applied deletion
Removed the following rules: 22

Chained accelerated rules with incoming rules
Start location: l6
  15: l6 -> l0 : i10^0'=0, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, 0 == 0, cost: 2
  23: l6 -> l0 : i10^0'=n9^post6, tmp^0'=tmp^post6, n^0'=n^post6, n9^0'=n9^post6, n9^post6 >= 0, cost: 2+2*n9^post6


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