WORST_CASE(Omega(0),?)

Initial ITS
Start location: l10
   0: l0 -> l1 : i^0'=i^post0, tmp5^0'=tmp5^post0, y4^0'=y4^post0, j^0'=j^post0, x3^0'=x3^post0, (y4^0-y4^post0 == 0 /\ i^0-i^post0 == 0 /\ -x3^post0+x3^0 == 0 /\ -j^post0+j^0 == 0 /\ tmp5^0-tmp5^post0 == 0), cost: 1
  10: l1 -> l4 : i^0'=i^post10, tmp5^0'=tmp5^post10, y4^0'=y4^post10, j^0'=j^post10, x3^0'=x3^post10, (x3^0-x3^post10 == 0 /\ -y4^post10+y4^0 == 0 /\ 1+i^0 <= 0 /\ -j^post10+j^0 == 0 /\ i^0-i^post10 == 0 /\ tmp5^0-tmp5^post10 == 0), cost: 1
  11: l1 -> l6 : i^0'=i^post11, tmp5^0'=tmp5^post11, y4^0'=y4^post11, j^0'=j^post11, x3^0'=x3^post11, (-i^0 <= 0 /\ y4^0-y4^post11 == 0 /\ -x3^post11+x3^0 == 0 /\ i^0-i^post11 == 0 /\ tmp5^0-tmp5^post11 == 0 /\ -j^post11+j^0 == 0), cost: 1
   1: l2 -> l3 : i^0'=i^post1, tmp5^0'=tmp5^post1, y4^0'=y4^post1, j^0'=j^post1, x3^0'=x3^post1, (-y4^post1+y4^0 == 0 /\ i^0-i^post1 == 0 /\ j^0-j^post1 == 0 /\ -x3^post1+x3^0 == 0 /\ -tmp5^post1+tmp5^0 == 0), cost: 1
   2: l4 -> l2 : i^0'=i^post2, tmp5^0'=tmp5^post2, y4^0'=y4^post2, j^0'=j^post2, x3^0'=x3^post2, (i^0-i^post2 == 0 /\ -j^post2+j^0 == 0 /\ -y4^post2+y4^0 == 0 /\ tmp5^0-tmp5^post2 == 0 /\ -x3^post2+x3^0 == 0), cost: 1
   3: l4 -> l2 : i^0'=i^post3, tmp5^0'=tmp5^post3, y4^0'=y4^post3, j^0'=j^post3, x3^0'=x3^post3, (-x3^post3+x3^0 == 0 /\ y4^0-y4^post3 == 0 /\ j^0-j^post3 == 0 /\ tmp5^0-tmp5^post3 == 0 /\ i^0-i^post3 == 0), cost: 1
   4: l5 -> l6 : i^0'=i^post4, tmp5^0'=tmp5^post4, y4^0'=y4^post4, j^0'=j^post4, x3^0'=x3^post4, (-1+j^post4-j^0 == 0 /\ -x3^post4+x3^0 == 0 /\ -y4^post4+y4^0 == 0 /\ i^0-i^post4 == 0 /\ tmp5^0-tmp5^post4 == 0), cost: 1
   5: l6 -> l7 : i^0'=i^post5, tmp5^0'=tmp5^post5, y4^0'=y4^post5, j^0'=j^post5, x3^0'=x3^post5, (-x3^post5+x3^0 == 0 /\ y4^0-y4^post5 == 0 /\ i^0-i^post5 == 0 /\ -j^post5+j^0 == 0 /\ tmp5^0-tmp5^post5 == 0), cost: 1
   8: l7 -> l0 : i^0'=i^post8, tmp5^0'=tmp5^post8, y4^0'=y4^post8, j^0'=j^post8, x3^0'=x3^post8, (-x3^post8+x3^0 == 0 /\ 1-i^0+i^post8 == 0 /\ -j^post8+j^0 == 0 /\ tmp5^0-tmp5^post8 == 0 /\ i^0-j^0 <= 0 /\ -y4^post8+y4^0 == 0), cost: 1
   9: l7 -> l8 : i^0'=i^post9, tmp5^0'=tmp5^post9, y4^0'=y4^post9, j^0'=j^post9, x3^0'=x3^post9, (-x3^post9+x3^0 == 0 /\ y4^0-y4^post9 == 0 /\ -j^post9+j^0 == 0 /\ 1-i^0+j^0 <= 0 /\ i^0-i^post9 == 0 /\ tmp5^0-tmp5^post9 == 0), cost: 1
   6: l8 -> l5 : i^0'=i^post6, tmp5^0'=tmp5^post6, y4^0'=y4^post6, j^0'=j^post6, x3^0'=x3^post6, (0 == 0 /\ -j^0+x3^post6 == 0 /\ -1+y4^post6-j^0 == 0 /\ i^0-i^post6 == 0 /\ -j^post6+j^0 == 0), cost: 1
   7: l8 -> l5 : i^0'=i^post7, tmp5^0'=tmp5^post7, y4^0'=y4^post7, j^0'=j^post7, x3^0'=x3^post7, (-j^post7+j^0 == 0 /\ tmp5^0-tmp5^post7 == 0 /\ i^0-i^post7 == 0 /\ y4^0-y4^post7 == 0 /\ -x3^post7+x3^0 == 0), cost: 1
  12: l9 -> l0 : i^0'=i^post12, tmp5^0'=tmp5^post12, y4^0'=y4^post12, j^0'=j^post12, x3^0'=x3^post12, (-y4^post12+y4^0 == 0 /\ x3^0-x3^post12 == 0 /\ -4+i^post12 == 0 /\ j^post12 == 0 /\ -tmp5^post12+tmp5^0 == 0), cost: 1
  13: l10 -> l9 : i^0'=i^post13, tmp5^0'=tmp5^post13, y4^0'=y4^post13, j^0'=j^post13, x3^0'=x3^post13, (-x3^post13+x3^0 == 0 /\ tmp5^0-tmp5^post13 == 0 /\ -j^post13+j^0 == 0 /\ i^0-i^post13 == 0 /\ y4^0-y4^post13 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l10
   0: l0 -> l1 : i^0'=i^post0, tmp5^0'=tmp5^post0, y4^0'=y4^post0, j^0'=j^post0, x3^0'=x3^post0, (y4^0-y4^post0 == 0 /\ i^0-i^post0 == 0 /\ -x3^post0+x3^0 == 0 /\ -j^post0+j^0 == 0 /\ tmp5^0-tmp5^post0 == 0), cost: 1
  11: l1 -> l6 : i^0'=i^post11, tmp5^0'=tmp5^post11, y4^0'=y4^post11, j^0'=j^post11, x3^0'=x3^post11, (-i^0 <= 0 /\ y4^0-y4^post11 == 0 /\ -x3^post11+x3^0 == 0 /\ i^0-i^post11 == 0 /\ tmp5^0-tmp5^post11 == 0 /\ -j^post11+j^0 == 0), cost: 1
   4: l5 -> l6 : i^0'=i^post4, tmp5^0'=tmp5^post4, y4^0'=y4^post4, j^0'=j^post4, x3^0'=x3^post4, (-1+j^post4-j^0 == 0 /\ -x3^post4+x3^0 == 0 /\ -y4^post4+y4^0 == 0 /\ i^0-i^post4 == 0 /\ tmp5^0-tmp5^post4 == 0), cost: 1
   5: l6 -> l7 : i^0'=i^post5, tmp5^0'=tmp5^post5, y4^0'=y4^post5, j^0'=j^post5, x3^0'=x3^post5, (-x3^post5+x3^0 == 0 /\ y4^0-y4^post5 == 0 /\ i^0-i^post5 == 0 /\ -j^post5+j^0 == 0 /\ tmp5^0-tmp5^post5 == 0), cost: 1
   8: l7 -> l0 : i^0'=i^post8, tmp5^0'=tmp5^post8, y4^0'=y4^post8, j^0'=j^post8, x3^0'=x3^post8, (-x3^post8+x3^0 == 0 /\ 1-i^0+i^post8 == 0 /\ -j^post8+j^0 == 0 /\ tmp5^0-tmp5^post8 == 0 /\ i^0-j^0 <= 0 /\ -y4^post8+y4^0 == 0), cost: 1
   9: l7 -> l8 : i^0'=i^post9, tmp5^0'=tmp5^post9, y4^0'=y4^post9, j^0'=j^post9, x3^0'=x3^post9, (-x3^post9+x3^0 == 0 /\ y4^0-y4^post9 == 0 /\ -j^post9+j^0 == 0 /\ 1-i^0+j^0 <= 0 /\ i^0-i^post9 == 0 /\ tmp5^0-tmp5^post9 == 0), cost: 1
   6: l8 -> l5 : i^0'=i^post6, tmp5^0'=tmp5^post6, y4^0'=y4^post6, j^0'=j^post6, x3^0'=x3^post6, (0 == 0 /\ -j^0+x3^post6 == 0 /\ -1+y4^post6-j^0 == 0 /\ i^0-i^post6 == 0 /\ -j^post6+j^0 == 0), cost: 1
   7: l8 -> l5 : i^0'=i^post7, tmp5^0'=tmp5^post7, y4^0'=y4^post7, j^0'=j^post7, x3^0'=x3^post7, (-j^post7+j^0 == 0 /\ tmp5^0-tmp5^post7 == 0 /\ i^0-i^post7 == 0 /\ y4^0-y4^post7 == 0 /\ -x3^post7+x3^0 == 0), cost: 1
  12: l9 -> l0 : i^0'=i^post12, tmp5^0'=tmp5^post12, y4^0'=y4^post12, j^0'=j^post12, x3^0'=x3^post12, (-y4^post12+y4^0 == 0 /\ x3^0-x3^post12 == 0 /\ -4+i^post12 == 0 /\ j^post12 == 0 /\ -tmp5^post12+tmp5^0 == 0), cost: 1
  13: l10 -> l9 : i^0'=i^post13, tmp5^0'=tmp5^post13, y4^0'=y4^post13, j^0'=j^post13, x3^0'=x3^post13, (-x3^post13+x3^0 == 0 /\ tmp5^0-tmp5^post13 == 0 /\ -j^post13+j^0 == 0 /\ i^0-i^post13 == 0 /\ y4^0-y4^post13 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : i^0'=i^post0, tmp5^0'=tmp5^post0, y4^0'=y4^post0, j^0'=j^post0, x3^0'=x3^post0, (y4^0-y4^post0 == 0 /\ i^0-i^post0 == 0 /\ -x3^post0+x3^0 == 0 /\ -j^post0+j^0 == 0 /\ tmp5^0-tmp5^post0 == 0), cost: 1
New rule:
l0 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l6 : i^0'=i^post4, tmp5^0'=tmp5^post4, y4^0'=y4^post4, j^0'=j^post4, x3^0'=x3^post4, (-1+j^post4-j^0 == 0 /\ -x3^post4+x3^0 == 0 /\ -y4^post4+y4^0 == 0 /\ i^0-i^post4 == 0 /\ tmp5^0-tmp5^post4 == 0), cost: 1
New rule:
l5 -> l6 : j^0'=1+j^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l6 -> l7 : i^0'=i^post5, tmp5^0'=tmp5^post5, y4^0'=y4^post5, j^0'=j^post5, x3^0'=x3^post5, (-x3^post5+x3^0 == 0 /\ y4^0-y4^post5 == 0 /\ i^0-i^post5 == 0 /\ -j^post5+j^0 == 0 /\ tmp5^0-tmp5^post5 == 0), cost: 1
New rule:
l6 -> l7 : TRUE, cost: 1

Applied preprocessing
Original rule:
l8 -> l5 : i^0'=i^post6, tmp5^0'=tmp5^post6, y4^0'=y4^post6, j^0'=j^post6, x3^0'=x3^post6, (0 == 0 /\ -j^0+x3^post6 == 0 /\ -1+y4^post6-j^0 == 0 /\ i^0-i^post6 == 0 /\ -j^post6+j^0 == 0), cost: 1
New rule:
l8 -> l5 : tmp5^0'=tmp5^post6, y4^0'=1+j^0, x3^0'=j^0, 0 == 0, cost: 1

Applied preprocessing
Original rule:
l8 -> l5 : i^0'=i^post7, tmp5^0'=tmp5^post7, y4^0'=y4^post7, j^0'=j^post7, x3^0'=x3^post7, (-j^post7+j^0 == 0 /\ tmp5^0-tmp5^post7 == 0 /\ i^0-i^post7 == 0 /\ y4^0-y4^post7 == 0 /\ -x3^post7+x3^0 == 0), cost: 1
New rule:
l8 -> l5 : TRUE, cost: 1

Applied preprocessing
Original rule:
l7 -> l0 : i^0'=i^post8, tmp5^0'=tmp5^post8, y4^0'=y4^post8, j^0'=j^post8, x3^0'=x3^post8, (-x3^post8+x3^0 == 0 /\ 1-i^0+i^post8 == 0 /\ -j^post8+j^0 == 0 /\ tmp5^0-tmp5^post8 == 0 /\ i^0-j^0 <= 0 /\ -y4^post8+y4^0 == 0), cost: 1
New rule:
l7 -> l0 : i^0'=-1+i^0, i^0-j^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l7 -> l8 : i^0'=i^post9, tmp5^0'=tmp5^post9, y4^0'=y4^post9, j^0'=j^post9, x3^0'=x3^post9, (-x3^post9+x3^0 == 0 /\ y4^0-y4^post9 == 0 /\ -j^post9+j^0 == 0 /\ 1-i^0+j^0 <= 0 /\ i^0-i^post9 == 0 /\ tmp5^0-tmp5^post9 == 0), cost: 1
New rule:
l7 -> l8 : 1-i^0+j^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l6 : i^0'=i^post11, tmp5^0'=tmp5^post11, y4^0'=y4^post11, j^0'=j^post11, x3^0'=x3^post11, (-i^0 <= 0 /\ y4^0-y4^post11 == 0 /\ -x3^post11+x3^0 == 0 /\ i^0-i^post11 == 0 /\ tmp5^0-tmp5^post11 == 0 /\ -j^post11+j^0 == 0), cost: 1
New rule:
l1 -> l6 : i^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l9 -> l0 : i^0'=i^post12, tmp5^0'=tmp5^post12, y4^0'=y4^post12, j^0'=j^post12, x3^0'=x3^post12, (-y4^post12+y4^0 == 0 /\ x3^0-x3^post12 == 0 /\ -4+i^post12 == 0 /\ j^post12 == 0 /\ -tmp5^post12+tmp5^0 == 0), cost: 1
New rule:
l9 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l10 -> l9 : i^0'=i^post13, tmp5^0'=tmp5^post13, y4^0'=y4^post13, j^0'=j^post13, x3^0'=x3^post13, (-x3^post13+x3^0 == 0 /\ tmp5^0-tmp5^post13 == 0 /\ -j^post13+j^0 == 0 /\ i^0-i^post13 == 0 /\ y4^0-y4^post13 == 0), cost: 1
New rule:
l10 -> l9 : TRUE, cost: 1

Simplified rules
Start location: l10
  14: l0 -> l1 : TRUE, cost: 1
  21: l1 -> l6 : i^0 >= 0, cost: 1
  15: l5 -> l6 : j^0'=1+j^0, TRUE, cost: 1
  16: l6 -> l7 : TRUE, cost: 1
  19: l7 -> l0 : i^0'=-1+i^0, i^0-j^0 <= 0, cost: 1
  20: l7 -> l8 : 1-i^0+j^0 <= 0, cost: 1
  17: l8 -> l5 : tmp5^0'=tmp5^post6, y4^0'=1+j^0, x3^0'=j^0, 0 == 0, cost: 1
  18: l8 -> l5 : TRUE, cost: 1
  22: l9 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 1
  23: l10 -> l9 : TRUE, cost: 1


Eliminating location l9 by chaining:

Applied chaining
First rule:
l10 -> l9 : TRUE, cost: 1
Second rule:
l9 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 1
New rule:
l10 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 22 23

Eliminating location l1 by chaining:

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

Applied deletion
Removed the following rules: 14 21

Eliminated locations on linear paths
Start location: l10
  25: l0 -> l6 : i^0 >= 0, cost: 2
  15: l5 -> l6 : j^0'=1+j^0, TRUE, cost: 1
  16: l6 -> l7 : TRUE, cost: 1
  19: l7 -> l0 : i^0'=-1+i^0, i^0-j^0 <= 0, cost: 1
  20: l7 -> l8 : 1-i^0+j^0 <= 0, cost: 1
  17: l8 -> l5 : tmp5^0'=tmp5^post6, y4^0'=1+j^0, x3^0'=j^0, 0 == 0, cost: 1
  18: l8 -> l5 : TRUE, cost: 1
  24: l10 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 2


Eliminating location l7 by chaining:

Applied chaining
First rule:
l6 -> l7 : TRUE, cost: 1
Second rule:
l7 -> l0 : i^0'=-1+i^0, i^0-j^0 <= 0, cost: 1
New rule:
l6 -> l0 : i^0'=-1+i^0, i^0-j^0 <= 0, cost: 2

Applied chaining
First rule:
l6 -> l7 : TRUE, cost: 1
Second rule:
l7 -> l8 : 1-i^0+j^0 <= 0, cost: 1
New rule:
l6 -> l8 : 1-i^0+j^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 16 19 20

Eliminating location l5 by chaining:

Applied chaining
First rule:
l8 -> l5 : tmp5^0'=tmp5^post6, y4^0'=1+j^0, x3^0'=j^0, 0 == 0, cost: 1
Second rule:
l5 -> l6 : j^0'=1+j^0, TRUE, cost: 1
New rule:
l8 -> l6 : tmp5^0'=tmp5^post6, y4^0'=1+j^0, j^0'=1+j^0, x3^0'=j^0, 0 == 0, cost: 2

Applied chaining
First rule:
l8 -> l5 : TRUE, cost: 1
Second rule:
l5 -> l6 : j^0'=1+j^0, TRUE, cost: 1
New rule:
l8 -> l6 : j^0'=1+j^0, TRUE, cost: 2

Applied deletion
Removed the following rules: 15 17 18

Eliminated locations on tree-shaped paths
Start location: l10
  25: l0 -> l6 : i^0 >= 0, cost: 2
  26: l6 -> l0 : i^0'=-1+i^0, i^0-j^0 <= 0, cost: 2
  27: l6 -> l8 : 1-i^0+j^0 <= 0, cost: 2
  28: l8 -> l6 : tmp5^0'=tmp5^post6, y4^0'=1+j^0, j^0'=1+j^0, x3^0'=j^0, 0 == 0, cost: 2
  29: l8 -> l6 : j^0'=1+j^0, TRUE, cost: 2
  24: l10 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 2


Eliminating location l8 by chaining:

Applied chaining
First rule:
l6 -> l8 : 1-i^0+j^0 <= 0, cost: 2
Second rule:
l8 -> l6 : tmp5^0'=tmp5^post6, y4^0'=1+j^0, j^0'=1+j^0, x3^0'=j^0, 0 == 0, cost: 2
New rule:
l6 -> l6 : tmp5^0'=tmp5^post6, y4^0'=1+j^0, j^0'=1+j^0, x3^0'=j^0, (0 == 0 /\ 1-i^0+j^0 <= 0), cost: 4

Applied simplification
Original rule:
l6 -> l6 : tmp5^0'=tmp5^post6, y4^0'=1+j^0, j^0'=1+j^0, x3^0'=j^0, (0 == 0 /\ 1-i^0+j^0 <= 0), cost: 4
New rule:
l6 -> l6 : tmp5^0'=tmp5^post6, y4^0'=1+j^0, j^0'=1+j^0, x3^0'=j^0, 1-i^0+j^0 <= 0, cost: 4

Applied chaining
First rule:
l6 -> l8 : 1-i^0+j^0 <= 0, cost: 2
Second rule:
l8 -> l6 : j^0'=1+j^0, TRUE, cost: 2
New rule:
l6 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 4

Applied deletion
Removed the following rules: 27 28 29

Eliminated locations on tree-shaped paths
Start location: l10
  25: l0 -> l6 : i^0 >= 0, cost: 2
  26: l6 -> l0 : i^0'=-1+i^0, i^0-j^0 <= 0, cost: 2
  30: l6 -> l6 : tmp5^0'=tmp5^post6, y4^0'=1+j^0, j^0'=1+j^0, x3^0'=j^0, 1-i^0+j^0 <= 0, cost: 4
  31: l6 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 4
  24: l10 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 2


Applied acceleration
Original rule:
l6 -> l6 : tmp5^0'=tmp5^post6, y4^0'=1+j^0, j^0'=1+j^0, x3^0'=j^0, 1-i^0+j^0 <= 0, cost: 4
New rule:
l6 -> l6 : tmp5^0'=tmp5^post6, y4^0'=n1+j^0, j^0'=n1+j^0, x3^0'=-1+n1+j^0, (-1+n1 >= 0 /\ i^0-n1-j^0 >= 0), cost: 4*n1

Applied instantiation
Original rule:
l6 -> l6 : tmp5^0'=tmp5^post6, y4^0'=n1+j^0, j^0'=n1+j^0, x3^0'=-1+n1+j^0, (-1+n1 >= 0 /\ i^0-n1-j^0 >= 0), cost: 4*n1
New rule:
l6 -> l6 : tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, (0 >= 0 /\ -1+i^0-j^0 >= 0), cost: 4*i^0-4*j^0

Applied acceleration
Original rule:
l6 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 4
New rule:
l6 -> l6 : j^0'=n3+j^0, (n3 >= 0 /\ i^0-n3-j^0 >= 0), cost: 4*n3

Applied instantiation
Original rule:
l6 -> l6 : j^0'=n3+j^0, (n3 >= 0 /\ i^0-n3-j^0 >= 0), cost: 4*n3
New rule:
l6 -> l6 : j^0'=i^0, (0 >= 0 /\ i^0-j^0 >= 0), cost: 4*i^0-4*j^0

Applied simplification
Original rule:
l6 -> l6 : tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, (0 >= 0 /\ -1+i^0-j^0 >= 0), cost: 4*i^0-4*j^0
New rule:
l6 -> l6 : tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, -1+i^0-j^0 >= 0, cost: 4*i^0-4*j^0

Applied simplification
Original rule:
l6 -> l6 : j^0'=i^0, (0 >= 0 /\ i^0-j^0 >= 0), cost: 4*i^0-4*j^0
New rule:
l6 -> l6 : j^0'=i^0, i^0-j^0 >= 0, cost: 4*i^0-4*j^0

Applied deletion
Removed the following rules: 30 31

Accelerated simple loops
Start location: l10
  25: l0 -> l6 : i^0 >= 0, cost: 2
  26: l6 -> l0 : i^0'=-1+i^0, i^0-j^0 <= 0, cost: 2
  34: l6 -> l6 : tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, -1+i^0-j^0 >= 0, cost: 4*i^0-4*j^0
  35: l6 -> l6 : j^0'=i^0, i^0-j^0 >= 0, cost: 4*i^0-4*j^0
  24: l10 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l0 -> l6 : i^0 >= 0, cost: 2
Second rule:
l6 -> l6 : tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, -1+i^0-j^0 >= 0, cost: 4*i^0-4*j^0
New rule:
l0 -> l6 : tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, (i^0 >= 0 /\ -1+i^0-j^0 >= 0), cost: 2+4*i^0-4*j^0

Applied chaining
First rule:
l0 -> l6 : i^0 >= 0, cost: 2
Second rule:
l6 -> l6 : j^0'=i^0, i^0-j^0 >= 0, cost: 4*i^0-4*j^0
New rule:
l0 -> l6 : j^0'=i^0, (i^0 >= 0 /\ i^0-j^0 >= 0), cost: 2+4*i^0-4*j^0

Applied deletion
Removed the following rules: 34 35

Chained accelerated rules with incoming rules
Start location: l10
  25: l0 -> l6 : i^0 >= 0, cost: 2
  36: l0 -> l6 : tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, (i^0 >= 0 /\ -1+i^0-j^0 >= 0), cost: 2+4*i^0-4*j^0
  37: l0 -> l6 : j^0'=i^0, (i^0 >= 0 /\ i^0-j^0 >= 0), cost: 2+4*i^0-4*j^0
  26: l6 -> l0 : i^0'=-1+i^0, i^0-j^0 <= 0, cost: 2
  24: l10 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 2


Eliminating location l6 by chaining:

Applied chaining
First rule:
l0 -> l6 : i^0 >= 0, cost: 2
Second rule:
l6 -> l0 : i^0'=-1+i^0, i^0-j^0 <= 0, cost: 2
New rule:
l0 -> l0 : i^0'=-1+i^0, (i^0 >= 0 /\ i^0-j^0 <= 0), cost: 4

Applied chaining
First rule:
l0 -> l6 : tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, (i^0 >= 0 /\ -1+i^0-j^0 >= 0), cost: 2+4*i^0-4*j^0
Second rule:
l6 -> l0 : i^0'=-1+i^0, i^0-j^0 <= 0, cost: 2
New rule:
l0 -> l0 : i^0'=-1+i^0, tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, (0 <= 0 /\ i^0 >= 0 /\ -1+i^0-j^0 >= 0), cost: 4+4*i^0-4*j^0

Applied simplification
Original rule:
l0 -> l0 : i^0'=-1+i^0, tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, (0 <= 0 /\ i^0 >= 0 /\ -1+i^0-j^0 >= 0), cost: 4+4*i^0-4*j^0
New rule:
l0 -> l0 : i^0'=-1+i^0, tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, (i^0 >= 0 /\ -1+i^0-j^0 >= 0), cost: 4+4*i^0-4*j^0

Applied chaining
First rule:
l0 -> l6 : j^0'=i^0, (i^0 >= 0 /\ i^0-j^0 >= 0), cost: 2+4*i^0-4*j^0
Second rule:
l6 -> l0 : i^0'=-1+i^0, i^0-j^0 <= 0, cost: 2
New rule:
l0 -> l0 : i^0'=-1+i^0, j^0'=i^0, (0 <= 0 /\ i^0 >= 0 /\ i^0-j^0 >= 0), cost: 4+4*i^0-4*j^0

Applied simplification
Original rule:
l0 -> l0 : i^0'=-1+i^0, j^0'=i^0, (0 <= 0 /\ i^0 >= 0 /\ i^0-j^0 >= 0), cost: 4+4*i^0-4*j^0
New rule:
l0 -> l0 : i^0'=-1+i^0, j^0'=i^0, (i^0 >= 0 /\ i^0-j^0 >= 0), cost: 4+4*i^0-4*j^0

Applied deletion
Removed the following rules: 25 26 36 37

Eliminated locations on tree-shaped paths
Start location: l10
  38: l0 -> l0 : i^0'=-1+i^0, (i^0 >= 0 /\ i^0-j^0 <= 0), cost: 4
  39: l0 -> l0 : i^0'=-1+i^0, tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, (i^0 >= 0 /\ -1+i^0-j^0 >= 0), cost: 4+4*i^0-4*j^0
  40: l0 -> l0 : i^0'=-1+i^0, j^0'=i^0, (i^0 >= 0 /\ i^0-j^0 >= 0), cost: 4+4*i^0-4*j^0
  24: l10 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 2


Applied acceleration
Original rule:
l0 -> l0 : i^0'=-1+i^0, (i^0 >= 0 /\ i^0-j^0 <= 0), cost: 4
New rule:
l0 -> l0 : i^0'=i^0-n14, (n14 >= 0 /\ -i^0+j^0 >= 0 /\ 1+i^0-n14 >= 0), cost: 4*n14

Applied instantiation
Original rule:
l0 -> l0 : i^0'=i^0-n14, (n14 >= 0 /\ -i^0+j^0 >= 0 /\ 1+i^0-n14 >= 0), cost: 4*n14
New rule:
l0 -> l0 : i^0'=-1, (0 >= 0 /\ 1+i^0 >= 0 /\ -i^0+j^0 >= 0), cost: 4+4*i^0

Applied simplification
Original rule:
l0 -> l0 : i^0'=-1, (0 >= 0 /\ 1+i^0 >= 0 /\ -i^0+j^0 >= 0), cost: 4+4*i^0
New rule:
l0 -> l0 : i^0'=-1, (1+i^0 >= 0 /\ -i^0+j^0 >= 0), cost: 4+4*i^0

Applied deletion
Removed the following rules: 38

Accelerated simple loops
Start location: l10
  39: l0 -> l0 : i^0'=-1+i^0, tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, (i^0 >= 0 /\ -1+i^0-j^0 >= 0), cost: 4+4*i^0-4*j^0
  40: l0 -> l0 : i^0'=-1+i^0, j^0'=i^0, (i^0 >= 0 /\ i^0-j^0 >= 0), cost: 4+4*i^0-4*j^0
  42: l0 -> l0 : i^0'=-1, (1+i^0 >= 0 /\ -i^0+j^0 >= 0), cost: 4+4*i^0
  24: l10 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l10 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 2
Second rule:
l0 -> l0 : i^0'=-1+i^0, tmp5^0'=tmp5^post6, y4^0'=i^0, j^0'=i^0, x3^0'=-1+i^0, (i^0 >= 0 /\ -1+i^0-j^0 >= 0), cost: 4+4*i^0-4*j^0
New rule:
l10 -> l0 : i^0'=3, tmp5^0'=tmp5^post6, y4^0'=4, j^0'=4, x3^0'=3, (3 >= 0 /\ 4 >= 0), cost: 22

Applied chaining
First rule:
l10 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 2
Second rule:
l0 -> l0 : i^0'=-1+i^0, j^0'=i^0, (i^0 >= 0 /\ i^0-j^0 >= 0), cost: 4+4*i^0-4*j^0
New rule:
l10 -> l0 : i^0'=3, j^0'=4, 4 >= 0, cost: 22

Applied deletion
Removed the following rules: 39 40 42

Chained accelerated rules with incoming rules
Start location: l10
  24: l10 -> l0 : i^0'=4, j^0'=0, TRUE, cost: 2
  43: l10 -> l0 : i^0'=3, tmp5^0'=tmp5^post6, y4^0'=4, j^0'=4, x3^0'=3, (3 >= 0 /\ 4 >= 0), cost: 22
  44: l10 -> l0 : i^0'=3, j^0'=4, 4 >= 0, cost: 22


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