WORST_CASE(Omega(0),?)

Initial ITS
Start location: l10
   0: l0 -> l1 : i^0'=i^post0, n^0'=n^post0, j^0'=j^post0, tmp^0'=tmp^post0, (-tmp^post0+tmp^0 == 0 /\ j^0-j^post0 == 0 /\ i^0-i^post0 == 0 /\ -i^0+n^0 <= 0 /\ n^0-n^post0 == 0), cost: 1
   1: l0 -> l2 : i^0'=i^post1, n^0'=n^post1, j^0'=j^post1, tmp^0'=tmp^post1, (0 == 0 /\ -j^post1+j^0 == 0 /\ i^0-i^post1 == 0 /\ 1+i^0-n^0 <= 0 /\ -n^post1+n^0 == 0), cost: 1
   6: l1 -> l7 : i^0'=i^post6, n^0'=n^post6, j^0'=j^post6, tmp^0'=tmp^post6, (n^0-n^post6 == 0 /\ tmp^0-tmp^post6 == 0 /\ i^0-i^post6 == 0 /\ -j^post6+j^0 == 0), cost: 1
  10: l2 -> l1 : i^0'=i^post10, n^0'=n^post10, j^0'=j^post10, tmp^0'=tmp^post10, (-tmp^post10+tmp^0 == 0 /\ i^0-i^post10 == 0 /\ -j^post10+j^0 == 0 /\ tmp^0 <= 0 /\ -tmp^0 <= 0 /\ n^0-n^post10 == 0), cost: 1
  11: l2 -> l8 : i^0'=i^post11, n^0'=n^post11, j^0'=j^post11, tmp^0'=tmp^post11, (j^0-j^post11 == 0 /\ -tmp^post11+tmp^0 == 0 /\ i^0-i^post11 == 0 /\ n^0-n^post11 == 0 /\ 1-tmp^0 <= 0), cost: 1
  12: l2 -> l8 : i^0'=i^post12, n^0'=n^post12, j^0'=j^post12, tmp^0'=tmp^post12, (j^0-j^post12 == 0 /\ i^0-i^post12 == 0 /\ 1+tmp^0 <= 0 /\ -tmp^post12+tmp^0 == 0 /\ n^0-n^post12 == 0), cost: 1
   2: l3 -> l4 : i^0'=i^post2, n^0'=n^post2, j^0'=j^post2, tmp^0'=tmp^post2, (-j^post2+j^0 == 0 /\ n^0-n^post2 == 0 /\ -i^0+n^0 <= 0 /\ -tmp^post2+tmp^0 == 0 /\ i^0-i^post2 == 0), cost: 1
   3: l3 -> l5 : i^0'=i^post3, n^0'=n^post3, j^0'=j^post3, tmp^0'=tmp^post3, (-1-i^0+i^post3 == 0 /\ n^0-n^post3 == 0 /\ 1+i^0-n^0 <= 0 /\ j^post3 == 0 /\ -tmp^post3+tmp^0 == 0), cost: 1
   5: l5 -> l0 : i^0'=i^post5, n^0'=n^post5, j^0'=j^post5, tmp^0'=tmp^post5, (i^0-i^post5 == 0 /\ n^0-n^post5 == 0 /\ -tmp^post5+tmp^0 == 0 /\ -j^post5+j^0 == 0), cost: 1
   4: l6 -> l3 : i^0'=i^post4, n^0'=n^post4, j^0'=j^post4, tmp^0'=tmp^post4, (i^0-i^post4 == 0 /\ -tmp^post4+tmp^0 == 0 /\ -j^post4+j^0 == 0 /\ -n^post4+n^0 == 0), cost: 1
   7: l7 -> l6 : i^0'=i^post7, n^0'=n^post7, j^0'=j^post7, tmp^0'=tmp^post7, (i^0-i^post7 == 0 /\ j^0-j^post7 == 0 /\ n^0-n^post7 == 0 /\ -tmp^post7+tmp^0 == 0 /\ j^0 <= 0), cost: 1
   8: l7 -> l6 : i^0'=i^post8, n^0'=n^post8, j^0'=j^post8, tmp^0'=tmp^post8, (-tmp^post8+tmp^0 == 0 /\ 1-j^0 <= 0 /\ -j^post8+j^0 == 0 /\ n^0-n^post8 == 0 /\ 1-i^0+i^post8 == 0), cost: 1
   9: l8 -> l5 : i^0'=i^post9, n^0'=n^post9, j^0'=j^post9, tmp^0'=tmp^post9, (-1+j^post9-j^0 == 0 /\ -n^post9+n^0 == 0 /\ -tmp^post9+tmp^0 == 0 /\ -1-i^0+i^post9 == 0), cost: 1
  13: l9 -> l6 : i^0'=i^post13, n^0'=n^post13, j^0'=j^post13, tmp^0'=tmp^post13, (-tmp^post13+tmp^0 == 0 /\ -j^post13+j^0 == 0 /\ i^post13 == 0 /\ n^0-n^post13 == 0), cost: 1
  14: l10 -> l9 : i^0'=i^post14, n^0'=n^post14, j^0'=j^post14, tmp^0'=tmp^post14, (-tmp^post14+tmp^0 == 0 /\ i^0-i^post14 == 0 /\ -n^post14+n^0 == 0 /\ -j^post14+j^0 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l10
   0: l0 -> l1 : i^0'=i^post0, n^0'=n^post0, j^0'=j^post0, tmp^0'=tmp^post0, (-tmp^post0+tmp^0 == 0 /\ j^0-j^post0 == 0 /\ i^0-i^post0 == 0 /\ -i^0+n^0 <= 0 /\ n^0-n^post0 == 0), cost: 1
   1: l0 -> l2 : i^0'=i^post1, n^0'=n^post1, j^0'=j^post1, tmp^0'=tmp^post1, (0 == 0 /\ -j^post1+j^0 == 0 /\ i^0-i^post1 == 0 /\ 1+i^0-n^0 <= 0 /\ -n^post1+n^0 == 0), cost: 1
   6: l1 -> l7 : i^0'=i^post6, n^0'=n^post6, j^0'=j^post6, tmp^0'=tmp^post6, (n^0-n^post6 == 0 /\ tmp^0-tmp^post6 == 0 /\ i^0-i^post6 == 0 /\ -j^post6+j^0 == 0), cost: 1
  10: l2 -> l1 : i^0'=i^post10, n^0'=n^post10, j^0'=j^post10, tmp^0'=tmp^post10, (-tmp^post10+tmp^0 == 0 /\ i^0-i^post10 == 0 /\ -j^post10+j^0 == 0 /\ tmp^0 <= 0 /\ -tmp^0 <= 0 /\ n^0-n^post10 == 0), cost: 1
  11: l2 -> l8 : i^0'=i^post11, n^0'=n^post11, j^0'=j^post11, tmp^0'=tmp^post11, (j^0-j^post11 == 0 /\ -tmp^post11+tmp^0 == 0 /\ i^0-i^post11 == 0 /\ n^0-n^post11 == 0 /\ 1-tmp^0 <= 0), cost: 1
  12: l2 -> l8 : i^0'=i^post12, n^0'=n^post12, j^0'=j^post12, tmp^0'=tmp^post12, (j^0-j^post12 == 0 /\ i^0-i^post12 == 0 /\ 1+tmp^0 <= 0 /\ -tmp^post12+tmp^0 == 0 /\ n^0-n^post12 == 0), cost: 1
   3: l3 -> l5 : i^0'=i^post3, n^0'=n^post3, j^0'=j^post3, tmp^0'=tmp^post3, (-1-i^0+i^post3 == 0 /\ n^0-n^post3 == 0 /\ 1+i^0-n^0 <= 0 /\ j^post3 == 0 /\ -tmp^post3+tmp^0 == 0), cost: 1
   5: l5 -> l0 : i^0'=i^post5, n^0'=n^post5, j^0'=j^post5, tmp^0'=tmp^post5, (i^0-i^post5 == 0 /\ n^0-n^post5 == 0 /\ -tmp^post5+tmp^0 == 0 /\ -j^post5+j^0 == 0), cost: 1
   4: l6 -> l3 : i^0'=i^post4, n^0'=n^post4, j^0'=j^post4, tmp^0'=tmp^post4, (i^0-i^post4 == 0 /\ -tmp^post4+tmp^0 == 0 /\ -j^post4+j^0 == 0 /\ -n^post4+n^0 == 0), cost: 1
   7: l7 -> l6 : i^0'=i^post7, n^0'=n^post7, j^0'=j^post7, tmp^0'=tmp^post7, (i^0-i^post7 == 0 /\ j^0-j^post7 == 0 /\ n^0-n^post7 == 0 /\ -tmp^post7+tmp^0 == 0 /\ j^0 <= 0), cost: 1
   8: l7 -> l6 : i^0'=i^post8, n^0'=n^post8, j^0'=j^post8, tmp^0'=tmp^post8, (-tmp^post8+tmp^0 == 0 /\ 1-j^0 <= 0 /\ -j^post8+j^0 == 0 /\ n^0-n^post8 == 0 /\ 1-i^0+i^post8 == 0), cost: 1
   9: l8 -> l5 : i^0'=i^post9, n^0'=n^post9, j^0'=j^post9, tmp^0'=tmp^post9, (-1+j^post9-j^0 == 0 /\ -n^post9+n^0 == 0 /\ -tmp^post9+tmp^0 == 0 /\ -1-i^0+i^post9 == 0), cost: 1
  13: l9 -> l6 : i^0'=i^post13, n^0'=n^post13, j^0'=j^post13, tmp^0'=tmp^post13, (-tmp^post13+tmp^0 == 0 /\ -j^post13+j^0 == 0 /\ i^post13 == 0 /\ n^0-n^post13 == 0), cost: 1
  14: l10 -> l9 : i^0'=i^post14, n^0'=n^post14, j^0'=j^post14, tmp^0'=tmp^post14, (-tmp^post14+tmp^0 == 0 /\ i^0-i^post14 == 0 /\ -n^post14+n^0 == 0 /\ -j^post14+j^0 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : i^0'=i^post0, n^0'=n^post0, j^0'=j^post0, tmp^0'=tmp^post0, (-tmp^post0+tmp^0 == 0 /\ j^0-j^post0 == 0 /\ i^0-i^post0 == 0 /\ -i^0+n^0 <= 0 /\ n^0-n^post0 == 0), cost: 1
New rule:
l0 -> l1 : -i^0+n^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l0 -> l2 : i^0'=i^post1, n^0'=n^post1, j^0'=j^post1, tmp^0'=tmp^post1, (0 == 0 /\ -j^post1+j^0 == 0 /\ i^0-i^post1 == 0 /\ 1+i^0-n^0 <= 0 /\ -n^post1+n^0 == 0), cost: 1
New rule:
l0 -> l2 : tmp^0'=tmp^post1, 1+i^0-n^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l5 : i^0'=i^post3, n^0'=n^post3, j^0'=j^post3, tmp^0'=tmp^post3, (-1-i^0+i^post3 == 0 /\ n^0-n^post3 == 0 /\ 1+i^0-n^0 <= 0 /\ j^post3 == 0 /\ -tmp^post3+tmp^0 == 0), cost: 1
New rule:
l3 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l6 -> l3 : i^0'=i^post4, n^0'=n^post4, j^0'=j^post4, tmp^0'=tmp^post4, (i^0-i^post4 == 0 /\ -tmp^post4+tmp^0 == 0 /\ -j^post4+j^0 == 0 /\ -n^post4+n^0 == 0), cost: 1
New rule:
l6 -> l3 : TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l0 : i^0'=i^post5, n^0'=n^post5, j^0'=j^post5, tmp^0'=tmp^post5, (i^0-i^post5 == 0 /\ n^0-n^post5 == 0 /\ -tmp^post5+tmp^0 == 0 /\ -j^post5+j^0 == 0), cost: 1
New rule:
l5 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l1 -> l7 : i^0'=i^post6, n^0'=n^post6, j^0'=j^post6, tmp^0'=tmp^post6, (n^0-n^post6 == 0 /\ tmp^0-tmp^post6 == 0 /\ i^0-i^post6 == 0 /\ -j^post6+j^0 == 0), cost: 1
New rule:
l1 -> l7 : TRUE, cost: 1

Applied preprocessing
Original rule:
l7 -> l6 : i^0'=i^post7, n^0'=n^post7, j^0'=j^post7, tmp^0'=tmp^post7, (i^0-i^post7 == 0 /\ j^0-j^post7 == 0 /\ n^0-n^post7 == 0 /\ -tmp^post7+tmp^0 == 0 /\ j^0 <= 0), cost: 1
New rule:
l7 -> l6 : j^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l7 -> l6 : i^0'=i^post8, n^0'=n^post8, j^0'=j^post8, tmp^0'=tmp^post8, (-tmp^post8+tmp^0 == 0 /\ 1-j^0 <= 0 /\ -j^post8+j^0 == 0 /\ n^0-n^post8 == 0 /\ 1-i^0+i^post8 == 0), cost: 1
New rule:
l7 -> l6 : i^0'=-1+i^0, -1+j^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l8 -> l5 : i^0'=i^post9, n^0'=n^post9, j^0'=j^post9, tmp^0'=tmp^post9, (-1+j^post9-j^0 == 0 /\ -n^post9+n^0 == 0 /\ -tmp^post9+tmp^0 == 0 /\ -1-i^0+i^post9 == 0), cost: 1
New rule:
l8 -> l5 : i^0'=1+i^0, j^0'=1+j^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l1 : i^0'=i^post10, n^0'=n^post10, j^0'=j^post10, tmp^0'=tmp^post10, (-tmp^post10+tmp^0 == 0 /\ i^0-i^post10 == 0 /\ -j^post10+j^0 == 0 /\ tmp^0 <= 0 /\ -tmp^0 <= 0 /\ n^0-n^post10 == 0), cost: 1
New rule:
l2 -> l1 : tmp^0 == 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l8 : i^0'=i^post11, n^0'=n^post11, j^0'=j^post11, tmp^0'=tmp^post11, (j^0-j^post11 == 0 /\ -tmp^post11+tmp^0 == 0 /\ i^0-i^post11 == 0 /\ n^0-n^post11 == 0 /\ 1-tmp^0 <= 0), cost: 1
New rule:
l2 -> l8 : -1+tmp^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l8 : i^0'=i^post12, n^0'=n^post12, j^0'=j^post12, tmp^0'=tmp^post12, (j^0-j^post12 == 0 /\ i^0-i^post12 == 0 /\ 1+tmp^0 <= 0 /\ -tmp^post12+tmp^0 == 0 /\ n^0-n^post12 == 0), cost: 1
New rule:
l2 -> l8 : 1+tmp^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l9 -> l6 : i^0'=i^post13, n^0'=n^post13, j^0'=j^post13, tmp^0'=tmp^post13, (-tmp^post13+tmp^0 == 0 /\ -j^post13+j^0 == 0 /\ i^post13 == 0 /\ n^0-n^post13 == 0), cost: 1
New rule:
l9 -> l6 : i^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l10 -> l9 : i^0'=i^post14, n^0'=n^post14, j^0'=j^post14, tmp^0'=tmp^post14, (-tmp^post14+tmp^0 == 0 /\ i^0-i^post14 == 0 /\ -n^post14+n^0 == 0 /\ -j^post14+j^0 == 0), cost: 1
New rule:
l10 -> l9 : TRUE, cost: 1

Simplified rules
Start location: l10
  15: l0 -> l1 : -i^0+n^0 <= 0, cost: 1
  16: l0 -> l2 : tmp^0'=tmp^post1, 1+i^0-n^0 <= 0, cost: 1
  20: l1 -> l7 : TRUE, cost: 1
  24: l2 -> l1 : tmp^0 == 0, cost: 1
  25: l2 -> l8 : -1+tmp^0 >= 0, cost: 1
  26: l2 -> l8 : 1+tmp^0 <= 0, cost: 1
  17: l3 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 1
  19: l5 -> l0 : TRUE, cost: 1
  18: l6 -> l3 : TRUE, cost: 1
  21: l7 -> l6 : j^0 <= 0, cost: 1
  22: l7 -> l6 : i^0'=-1+i^0, -1+j^0 >= 0, cost: 1
  23: l8 -> l5 : i^0'=1+i^0, j^0'=1+j^0, TRUE, cost: 1
  27: l9 -> l6 : i^0'=0, TRUE, cost: 1
  28: l10 -> l9 : TRUE, cost: 1


Eliminating location l9 by chaining:

Applied chaining
First rule:
l10 -> l9 : TRUE, cost: 1
Second rule:
l9 -> l6 : i^0'=0, TRUE, cost: 1
New rule:
l10 -> l6 : i^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 27 28

Eliminating location l3 by chaining:

Applied chaining
First rule:
l6 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 1
New rule:
l6 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 17 18

Eliminated locations on linear paths
Start location: l10
  15: l0 -> l1 : -i^0+n^0 <= 0, cost: 1
  16: l0 -> l2 : tmp^0'=tmp^post1, 1+i^0-n^0 <= 0, cost: 1
  20: l1 -> l7 : TRUE, cost: 1
  24: l2 -> l1 : tmp^0 == 0, cost: 1
  25: l2 -> l8 : -1+tmp^0 >= 0, cost: 1
  26: l2 -> l8 : 1+tmp^0 <= 0, cost: 1
  19: l5 -> l0 : TRUE, cost: 1
  30: l6 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 2
  21: l7 -> l6 : j^0 <= 0, cost: 1
  22: l7 -> l6 : i^0'=-1+i^0, -1+j^0 >= 0, cost: 1
  23: l8 -> l5 : i^0'=1+i^0, j^0'=1+j^0, TRUE, cost: 1
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2


Eliminating location l0 by chaining:

Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 1
Second rule:
l0 -> l1 : -i^0+n^0 <= 0, cost: 1
New rule:
l5 -> l1 : -i^0+n^0 <= 0, cost: 2

Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 1
Second rule:
l0 -> l2 : tmp^0'=tmp^post1, 1+i^0-n^0 <= 0, cost: 1
New rule:
l5 -> l2 : tmp^0'=tmp^post1, 1+i^0-n^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 15 16 19

Eliminating location l7 by chaining:

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

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

Applied deletion
Removed the following rules: 20 21 22

Eliminating location l8 by chaining:

Applied chaining
First rule:
l2 -> l8 : -1+tmp^0 >= 0, cost: 1
Second rule:
l8 -> l5 : i^0'=1+i^0, j^0'=1+j^0, TRUE, cost: 1
New rule:
l2 -> l5 : i^0'=1+i^0, j^0'=1+j^0, -1+tmp^0 >= 0, cost: 2

Applied chaining
First rule:
l2 -> l8 : 1+tmp^0 <= 0, cost: 1
Second rule:
l8 -> l5 : i^0'=1+i^0, j^0'=1+j^0, TRUE, cost: 1
New rule:
l2 -> l5 : i^0'=1+i^0, j^0'=1+j^0, 1+tmp^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 23 25 26

Eliminated locations on tree-shaped paths
Start location: l10
  33: l1 -> l6 : j^0 <= 0, cost: 2
  34: l1 -> l6 : i^0'=-1+i^0, -1+j^0 >= 0, cost: 2
  24: l2 -> l1 : tmp^0 == 0, cost: 1
  35: l2 -> l5 : i^0'=1+i^0, j^0'=1+j^0, -1+tmp^0 >= 0, cost: 2
  36: l2 -> l5 : i^0'=1+i^0, j^0'=1+j^0, 1+tmp^0 <= 0, cost: 2
  31: l5 -> l1 : -i^0+n^0 <= 0, cost: 2
  32: l5 -> l2 : tmp^0'=tmp^post1, 1+i^0-n^0 <= 0, cost: 2
  30: l6 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 2
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2


Applied merging
first rule:
l2 -> l5 : i^0'=1+i^0, j^0'=1+j^0, -1+tmp^0 >= 0, cost: 2
second rule:
l2 -> l5 : i^0'=1+i^0, j^0'=1+j^0, 1+tmp^0 <= 0, cost: 2
new rule:
l2 -> l5 : i^0'=1+i^0, j^0'=1+j^0, (1+tmp^0 <= 0 \/ -1+tmp^0 >= 0), cost: 2

Merged rules
Start location: l10
  33: l1 -> l6 : j^0 <= 0, cost: 2
  34: l1 -> l6 : i^0'=-1+i^0, -1+j^0 >= 0, cost: 2
  24: l2 -> l1 : tmp^0 == 0, cost: 1
  37: l2 -> l5 : i^0'=1+i^0, j^0'=1+j^0, (1+tmp^0 <= 0 \/ -1+tmp^0 >= 0), cost: 2
  31: l5 -> l1 : -i^0+n^0 <= 0, cost: 2
  32: l5 -> l2 : tmp^0'=tmp^post1, 1+i^0-n^0 <= 0, cost: 2
  30: l6 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 2
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2


Eliminating location l2 by chaining:

Applied chaining
First rule:
l5 -> l2 : tmp^0'=tmp^post1, 1+i^0-n^0 <= 0, cost: 2
Second rule:
l2 -> l1 : tmp^0 == 0, cost: 1
New rule:
l5 -> l1 : tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 1+i^0-n^0 <= 0), cost: 3

Applied chaining
First rule:
l5 -> l2 : tmp^0'=tmp^post1, 1+i^0-n^0 <= 0, cost: 2
Second rule:
l2 -> l5 : i^0'=1+i^0, j^0'=1+j^0, (1+tmp^0 <= 0 \/ -1+tmp^0 >= 0), cost: 2
New rule:
l5 -> l5 : i^0'=1+i^0, j^0'=1+j^0, tmp^0'=tmp^post1, (1+i^0-n^0 <= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: 4

Applied deletion
Removed the following rules: 24 32 37

Eliminated locations on tree-shaped paths
Start location: l10
  33: l1 -> l6 : j^0 <= 0, cost: 2
  34: l1 -> l6 : i^0'=-1+i^0, -1+j^0 >= 0, cost: 2
  31: l5 -> l1 : -i^0+n^0 <= 0, cost: 2
  38: l5 -> l1 : tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 1+i^0-n^0 <= 0), cost: 3
  39: l5 -> l5 : i^0'=1+i^0, j^0'=1+j^0, tmp^0'=tmp^post1, (1+i^0-n^0 <= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: 4
  30: l6 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 2
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2


Applied acceleration
Original rule:
l5 -> l5 : i^0'=1+i^0, j^0'=1+j^0, tmp^0'=tmp^post1, (1+i^0-n^0 <= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: 4
New rule:
l5 -> l5 : i^0'=i^0+n0, j^0'=j^0+n0, tmp^0'=tmp^post1, (-1+n0 >= 0 /\ -i^0+n^0-n0 >= 0 /\ (-1-tmp^post1 >= 0 \/ -1+tmp^post1 >= 0)), cost: 4*n0

Applied instantiation
Original rule:
l5 -> l5 : i^0'=i^0+n0, j^0'=j^0+n0, tmp^0'=tmp^post1, (-1+n0 >= 0 /\ -i^0+n^0-n0 >= 0 /\ (-1-tmp^post1 >= 0 \/ -1+tmp^post1 >= 0)), cost: 4*n0
New rule:
l5 -> l5 : i^0'=n^0, j^0'=-i^0+n^0+j^0, tmp^0'=tmp^post1, (0 >= 0 /\ -1-i^0+n^0 >= 0 /\ (-1-tmp^post1 >= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0

Applied simplification
Original rule:
l5 -> l5 : i^0'=n^0, j^0'=-i^0+n^0+j^0, tmp^0'=tmp^post1, (0 >= 0 /\ -1-i^0+n^0 >= 0 /\ (-1-tmp^post1 >= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0
New rule:
l5 -> l5 : i^0'=n^0, j^0'=-i^0+n^0+j^0, tmp^0'=tmp^post1, (-1-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0

Applied deletion
Removed the following rules: 39

Accelerated simple loops
Start location: l10
  33: l1 -> l6 : j^0 <= 0, cost: 2
  34: l1 -> l6 : i^0'=-1+i^0, -1+j^0 >= 0, cost: 2
  31: l5 -> l1 : -i^0+n^0 <= 0, cost: 2
  38: l5 -> l1 : tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 1+i^0-n^0 <= 0), cost: 3
  41: l5 -> l5 : i^0'=n^0, j^0'=-i^0+n^0+j^0, tmp^0'=tmp^post1, (-1-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0
  30: l6 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 2
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l6 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 2
Second rule:
l5 -> l5 : i^0'=n^0, j^0'=-i^0+n^0+j^0, tmp^0'=tmp^post1, (-1-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0
New rule:
l6 -> l5 : i^0'=n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -2-4*i^0+4*n^0

Applied deletion
Removed the following rules: 41

Chained accelerated rules with incoming rules
Start location: l10
  33: l1 -> l6 : j^0 <= 0, cost: 2
  34: l1 -> l6 : i^0'=-1+i^0, -1+j^0 >= 0, cost: 2
  31: l5 -> l1 : -i^0+n^0 <= 0, cost: 2
  38: l5 -> l1 : tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 1+i^0-n^0 <= 0), cost: 3
  30: l6 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 2
  42: l6 -> l5 : i^0'=n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -2-4*i^0+4*n^0
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2


Eliminating location l5 by chaining:

Applied chaining
First rule:
l6 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 2
Second rule:
l5 -> l1 : -i^0+n^0 <= 0, cost: 2
New rule:
l6 -> l1 : i^0'=1+i^0, j^0'=0, (-1-i^0+n^0 <= 0 /\ 1+i^0-n^0 <= 0), cost: 4

Applied chaining
First rule:
l6 -> l5 : i^0'=1+i^0, j^0'=0, 1+i^0-n^0 <= 0, cost: 2
Second rule:
l5 -> l1 : tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 1+i^0-n^0 <= 0), cost: 3
New rule:
l6 -> l1 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 1+i^0-n^0 <= 0 /\ 2+i^0-n^0 <= 0), cost: 5

Applied simplification
Original rule:
l6 -> l1 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 1+i^0-n^0 <= 0 /\ 2+i^0-n^0 <= 0), cost: 5
New rule:
l6 -> l1 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 2+i^0-n^0 <= 0), cost: 5

Applied chaining
First rule:
l6 -> l5 : i^0'=n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -2-4*i^0+4*n^0
Second rule:
l5 -> l1 : -i^0+n^0 <= 0, cost: 2
New rule:
l6 -> l1 : i^0'=n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (0 <= 0 /\ -2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0

Applied simplification
Original rule:
l6 -> l1 : i^0'=n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (0 <= 0 /\ -2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0
New rule:
l6 -> l1 : i^0'=n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0

Applied partial deletion
Original rule:
l6 -> l5 : i^0'=n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -2-4*i^0+4*n^0
New rule:
l6 -> [12] : (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -2-4*i^0+4*n^0

Applied deletion
Removed the following rules: 30 31 38 42

Eliminated locations on tree-shaped paths
Start location: l10
  33: l1 -> l6 : j^0 <= 0, cost: 2
  34: l1 -> l6 : i^0'=-1+i^0, -1+j^0 >= 0, cost: 2
  43: l6 -> l1 : i^0'=1+i^0, j^0'=0, (-1-i^0+n^0 <= 0 /\ 1+i^0-n^0 <= 0), cost: 4
  44: l6 -> l1 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 2+i^0-n^0 <= 0), cost: 5
  45: l6 -> l1 : i^0'=n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0
  46: l6 -> [12] : (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -2-4*i^0+4*n^0
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2


Applied pruning (of leafs and parallel rules):
Start location: l10
  33: l1 -> l6 : j^0 <= 0, cost: 2
  34: l1 -> l6 : i^0'=-1+i^0, -1+j^0 >= 0, cost: 2
  43: l6 -> l1 : i^0'=1+i^0, j^0'=0, (-1-i^0+n^0 <= 0 /\ 1+i^0-n^0 <= 0), cost: 4
  44: l6 -> l1 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 2+i^0-n^0 <= 0), cost: 5
  45: l6 -> l1 : i^0'=n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2


Eliminating location l1 by chaining:

Applied chaining
First rule:
l6 -> l1 : i^0'=1+i^0, j^0'=0, (-1-i^0+n^0 <= 0 /\ 1+i^0-n^0 <= 0), cost: 4
Second rule:
l1 -> l6 : j^0 <= 0, cost: 2
New rule:
l6 -> l6 : i^0'=1+i^0, j^0'=0, (0 <= 0 /\ -1-i^0+n^0 <= 0 /\ 1+i^0-n^0 <= 0), cost: 6

Applied simplification
Original rule:
l6 -> l6 : i^0'=1+i^0, j^0'=0, (0 <= 0 /\ -1-i^0+n^0 <= 0 /\ 1+i^0-n^0 <= 0), cost: 6
New rule:
l6 -> l6 : i^0'=1+i^0, j^0'=0, (-1-i^0+n^0 <= 0 /\ 1+i^0-n^0 <= 0), cost: 6

Applied chaining
First rule:
l6 -> l1 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 2+i^0-n^0 <= 0), cost: 5
Second rule:
l1 -> l6 : j^0 <= 0, cost: 2
New rule:
l6 -> l6 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post1, (0 <= 0 /\ tmp^post1 == 0 /\ 2+i^0-n^0 <= 0), cost: 7

Applied simplification
Original rule:
l6 -> l6 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post1, (0 <= 0 /\ tmp^post1 == 0 /\ 2+i^0-n^0 <= 0), cost: 7
New rule:
l6 -> l6 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 2+i^0-n^0 <= 0), cost: 7

Applied chaining
First rule:
l6 -> l1 : i^0'=n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0
Second rule:
l1 -> l6 : i^0'=-1+i^0, -1+j^0 >= 0, cost: 2
New rule:
l6 -> l6 : i^0'=-1+n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: 2-4*i^0+4*n^0

Applied partial deletion
Original rule:
l6 -> l1 : i^0'=n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0
New rule:
l6 -> [13] : (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0

Applied deletion
Removed the following rules: 33 34 43 44 45

Eliminated locations on tree-shaped paths
Start location: l10
  47: l6 -> l6 : i^0'=1+i^0, j^0'=0, (-1-i^0+n^0 <= 0 /\ 1+i^0-n^0 <= 0), cost: 6
  48: l6 -> l6 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 2+i^0-n^0 <= 0), cost: 7
  49: l6 -> l6 : i^0'=-1+n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: 2-4*i^0+4*n^0
  50: l6 -> [13] : (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: -4*i^0+4*n^0
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2


Applied pruning (of leafs and parallel rules):
Start location: l10
  47: l6 -> l6 : i^0'=1+i^0, j^0'=0, (-1-i^0+n^0 <= 0 /\ 1+i^0-n^0 <= 0), cost: 6
  48: l6 -> l6 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 2+i^0-n^0 <= 0), cost: 7
  49: l6 -> l6 : i^0'=-1+n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: 2-4*i^0+4*n^0
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2


Applied simplification
Original rule:
l6 -> l6 : i^0'=1+i^0, j^0'=0, (-1-i^0+n^0 <= 0 /\ 1+i^0-n^0 <= 0), cost: 6
New rule:
l6 -> l6 : i^0'=1+i^0, j^0'=0, -1-i^0+n^0 == 0, cost: 6

Applied simplification
Original rule:
l6 -> l6 : i^0'=1+i^0, j^0'=0, tmp^0'=tmp^post1, (tmp^post1 == 0 /\ 2+i^0-n^0 <= 0), cost: 7
New rule:
l6 -> l6 : i^0'=1+i^0, j^0'=0, tmp^0'=0, 2+i^0-n^0 <= 0, cost: 7

Simplified simple loops
Start location: l10
  49: l6 -> l6 : i^0'=-1+n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: 2-4*i^0+4*n^0
  51: l6 -> l6 : i^0'=1+i^0, j^0'=0, -1-i^0+n^0 == 0, cost: 6
  52: l6 -> l6 : i^0'=1+i^0, j^0'=0, tmp^0'=0, 2+i^0-n^0 <= 0, cost: 7
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2


Applied acceleration
Original rule:
l6 -> l6 : i^0'=1+i^0, j^0'=0, -1-i^0+n^0 == 0, cost: 6
New rule:
l6 -> l6 : i^0'=i^0+n5, j^0'=0, (-1+n5 >= 0 /\ -1-i^0+n^0 >= 0 /\ -i^0-n5+n^0 >= 0 /\ 1+i^0-n^0 >= 0), cost: 6*n5

Applied instantiation
Original rule:
l6 -> l6 : i^0'=i^0+n5, j^0'=0, (-1+n5 >= 0 /\ -1-i^0+n^0 >= 0 /\ -i^0-n5+n^0 >= 0 /\ 1+i^0-n^0 >= 0), cost: 6*n5
New rule:
l6 -> l6 : i^0'=n^0, j^0'=0, (0 >= 0 /\ -1-i^0+n^0 >= 0 /\ 1+i^0-n^0 >= 0), cost: -6*i^0+6*n^0

Applied acceleration
Original rule:
l6 -> l6 : i^0'=1+i^0, j^0'=0, tmp^0'=0, 2+i^0-n^0 <= 0, cost: 7
New rule:
l6 -> l6 : i^0'=i^0+n7, j^0'=0, tmp^0'=0, (-1-i^0+n^0-n7 >= 0 /\ -1+n7 >= 0), cost: 7*n7

Applied instantiation
Original rule:
l6 -> l6 : i^0'=i^0+n7, j^0'=0, tmp^0'=0, (-1-i^0+n^0-n7 >= 0 /\ -1+n7 >= 0), cost: 7*n7
New rule:
l6 -> l6 : i^0'=-1+n^0, j^0'=0, tmp^0'=0, (0 >= 0 /\ -2-i^0+n^0 >= 0), cost: -7-7*i^0+7*n^0

Applied simplification
Original rule:
l6 -> l6 : i^0'=n^0, j^0'=0, (0 >= 0 /\ -1-i^0+n^0 >= 0 /\ 1+i^0-n^0 >= 0), cost: -6*i^0+6*n^0
New rule:
l6 -> l6 : i^0'=n^0, j^0'=0, (-1-i^0+n^0 >= 0 /\ 1+i^0-n^0 >= 0), cost: -6*i^0+6*n^0

Applied simplification
Original rule:
l6 -> l6 : i^0'=-1+n^0, j^0'=0, tmp^0'=0, (0 >= 0 /\ -2-i^0+n^0 >= 0), cost: -7-7*i^0+7*n^0
New rule:
l6 -> l6 : i^0'=-1+n^0, j^0'=0, tmp^0'=0, -2-i^0+n^0 >= 0, cost: -7-7*i^0+7*n^0

Applied deletion
Removed the following rules: 51 52

Accelerated simple loops
Start location: l10
  49: l6 -> l6 : i^0'=-1+n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: 2-4*i^0+4*n^0
  55: l6 -> l6 : i^0'=n^0, j^0'=0, (-1-i^0+n^0 >= 0 /\ 1+i^0-n^0 >= 0), cost: -6*i^0+6*n^0
  56: l6 -> l6 : i^0'=-1+n^0, j^0'=0, tmp^0'=0, -2-i^0+n^0 >= 0, cost: -7-7*i^0+7*n^0
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l10 -> l6 : i^0'=0, TRUE, cost: 2
Second rule:
l6 -> l6 : i^0'=-1+n^0, j^0'=-1-i^0+n^0, tmp^0'=tmp^post1, (-2-i^0+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: 2-4*i^0+4*n^0
New rule:
l10 -> l6 : i^0'=-1+n^0, j^0'=-1+n^0, tmp^0'=tmp^post1, (-2+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: 4+4*n^0

Applied chaining
First rule:
l10 -> l6 : i^0'=0, TRUE, cost: 2
Second rule:
l6 -> l6 : i^0'=n^0, j^0'=0, (-1-i^0+n^0 >= 0 /\ 1+i^0-n^0 >= 0), cost: -6*i^0+6*n^0
New rule:
l10 -> l6 : i^0'=n^0, j^0'=0, -1+n^0 == 0, cost: 2+6*n^0

Applied chaining
First rule:
l10 -> l6 : i^0'=0, TRUE, cost: 2
Second rule:
l6 -> l6 : i^0'=-1+n^0, j^0'=0, tmp^0'=0, -2-i^0+n^0 >= 0, cost: -7-7*i^0+7*n^0
New rule:
l10 -> l6 : i^0'=-1+n^0, j^0'=0, tmp^0'=0, -2+n^0 >= 0, cost: -5+7*n^0

Applied deletion
Removed the following rules: 49 55 56

Chained accelerated rules with incoming rules
Start location: l10
  29: l10 -> l6 : i^0'=0, TRUE, cost: 2
  57: l10 -> l6 : i^0'=-1+n^0, j^0'=-1+n^0, tmp^0'=tmp^post1, (-2+n^0 >= 0 /\ (1+tmp^post1 <= 0 \/ -1+tmp^post1 >= 0)), cost: 4+4*n^0
  58: l10 -> l6 : i^0'=n^0, j^0'=0, -1+n^0 == 0, cost: 2+6*n^0
  59: l10 -> l6 : i^0'=-1+n^0, j^0'=0, tmp^0'=0, -2+n^0 >= 0, cost: -5+7*n^0


Removed unreachable locations and irrelevant leafs
Start location: l10
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0