WORST_CASE(Omega(0),?)

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


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


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

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

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

Applied preprocessing
Original rule:
l1 -> l3 : guard^0'=guard^post4, j^0'=j^post4, i^0'=i^post4, n^0'=n^post4, (guard^0-guard^post4 == 0 /\ -n^post4+n^0 == 0 /\ -i^post4+i^0 == 0 /\ -j^post4+j^0 == 0), cost: 1
New rule:
l1 -> l3 : TRUE, cost: 1

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

Applied preprocessing
Original rule:
l6 -> l5 : guard^0'=guard^post6, j^0'=j^post6, i^0'=i^post6, n^0'=n^post6, (n^0-n^post6 == 0 /\ guard^0-guard^post6 == 0 /\ -1-j^0+j^post6 == 0 /\ -i^post6+i^0 == 0), cost: 1
New rule:
l6 -> l5 : j^0'=1+j^0, TRUE, cost: 1

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

Applied preprocessing
Original rule:
l2 -> l6 : guard^0'=guard^post8, j^0'=j^post8, i^0'=i^post8, n^0'=n^post8, (guard^0 <= 0 /\ -guard^0 <= 0 /\ -n^post8+n^0 == 0 /\ -i^post8+i^0 == 0 /\ guard^0-guard^post8 == 0 /\ j^0-j^post8 == 0), cost: 1
New rule:
l2 -> l6 : guard^0 == 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l7 : guard^0'=guard^post9, j^0'=j^post9, i^0'=i^post9, n^0'=n^post9, (-j^post9+j^0 == 0 /\ guard^0-guard^post9 == 0 /\ 1-guard^0 <= 0 /\ -n^post9+n^0 == 0 /\ -i^post9+i^0 == 0), cost: 1
New rule:
l2 -> l7 : -1+guard^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l7 : guard^0'=guard^post10, j^0'=j^post10, i^0'=i^post10, n^0'=n^post10, (-n^post10+n^0 == 0 /\ 1+guard^0 <= 0 /\ guard^0-guard^post10 == 0 /\ -i^post10+i^0 == 0 /\ j^0-j^post10 == 0), cost: 1
New rule:
l2 -> l7 : 1+guard^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l8 -> l1 : guard^0'=guard^post11, j^0'=j^post11, i^0'=i^post11, n^0'=n^post11, (-n^post11+n^0 == 0 /\ guard^0-guard^post11 == 0 /\ i^post11 == 0 /\ j^0-j^post11 == 0), cost: 1
New rule:
l8 -> l1 : i^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l9 -> l8 : guard^0'=guard^post12, j^0'=j^post12, i^0'=i^post12, n^0'=n^post12, (i^0-i^post12 == 0 /\ guard^0-guard^post12 == 0 /\ -n^post12+n^0 == 0 /\ j^0-j^post12 == 0), cost: 1
New rule:
l9 -> l8 : TRUE, cost: 1

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


Eliminating location l8 by chaining:

Applied chaining
First rule:
l9 -> l8 : TRUE, cost: 1
Second rule:
l8 -> l1 : i^0'=0, TRUE, cost: 1
New rule:
l9 -> l1 : i^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 23 24

Eliminating location l3 by chaining:

Applied chaining
First rule:
l1 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l5 : j^0'=1+i^0, 1+i^0-n^0 <= 0, cost: 1
New rule:
l1 -> l5 : j^0'=1+i^0, 1+i^0-n^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 15 16

Eliminated locations on linear paths
Start location: l9
  13: l0 -> l1 : i^0'=1+i^0, -j^0+n^0 <= 0, cost: 1
  14: l0 -> l2 : guard^0'=guard^post1, 1+j^0-n^0 <= 0, cost: 1
  26: l1 -> l5 : j^0'=1+i^0, 1+i^0-n^0 <= 0, cost: 2
  20: l2 -> l6 : guard^0 == 0, cost: 1
  21: l2 -> l7 : -1+guard^0 >= 0, cost: 1
  22: l2 -> l7 : 1+guard^0 <= 0, cost: 1
  17: l5 -> l0 : TRUE, cost: 1
  18: l6 -> l5 : j^0'=1+j^0, TRUE, cost: 1
  19: l7 -> l6 : j^0'=-1+j^0, n^0'=-1+n^0, TRUE, cost: 1
  25: l9 -> l1 : 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'=1+i^0, -j^0+n^0 <= 0, cost: 1
New rule:
l5 -> l1 : i^0'=1+i^0, -j^0+n^0 <= 0, cost: 2

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

Applied deletion
Removed the following rules: 13 14 17

Eliminating location l7 by chaining:

Applied chaining
First rule:
l2 -> l7 : -1+guard^0 >= 0, cost: 1
Second rule:
l7 -> l6 : j^0'=-1+j^0, n^0'=-1+n^0, TRUE, cost: 1
New rule:
l2 -> l6 : j^0'=-1+j^0, n^0'=-1+n^0, -1+guard^0 >= 0, cost: 2

Applied chaining
First rule:
l2 -> l7 : 1+guard^0 <= 0, cost: 1
Second rule:
l7 -> l6 : j^0'=-1+j^0, n^0'=-1+n^0, TRUE, cost: 1
New rule:
l2 -> l6 : j^0'=-1+j^0, n^0'=-1+n^0, 1+guard^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 19 21 22

Eliminated locations on tree-shaped paths
Start location: l9
  26: l1 -> l5 : j^0'=1+i^0, 1+i^0-n^0 <= 0, cost: 2
  20: l2 -> l6 : guard^0 == 0, cost: 1
  29: l2 -> l6 : j^0'=-1+j^0, n^0'=-1+n^0, -1+guard^0 >= 0, cost: 2
  30: l2 -> l6 : j^0'=-1+j^0, n^0'=-1+n^0, 1+guard^0 <= 0, cost: 2
  27: l5 -> l1 : i^0'=1+i^0, -j^0+n^0 <= 0, cost: 2
  28: l5 -> l2 : guard^0'=guard^post1, 1+j^0-n^0 <= 0, cost: 2
  18: l6 -> l5 : j^0'=1+j^0, TRUE, cost: 1
  25: l9 -> l1 : i^0'=0, TRUE, cost: 2


Applied merging
first rule:
l2 -> l6 : j^0'=-1+j^0, n^0'=-1+n^0, -1+guard^0 >= 0, cost: 2
second rule:
l2 -> l6 : j^0'=-1+j^0, n^0'=-1+n^0, 1+guard^0 <= 0, cost: 2
new rule:
l2 -> l6 : j^0'=-1+j^0, n^0'=-1+n^0, (-1+guard^0 >= 0 \/ 1+guard^0 <= 0), cost: 2

Merged rules
Start location: l9
  26: l1 -> l5 : j^0'=1+i^0, 1+i^0-n^0 <= 0, cost: 2
  20: l2 -> l6 : guard^0 == 0, cost: 1
  31: l2 -> l6 : j^0'=-1+j^0, n^0'=-1+n^0, (-1+guard^0 >= 0 \/ 1+guard^0 <= 0), cost: 2
  27: l5 -> l1 : i^0'=1+i^0, -j^0+n^0 <= 0, cost: 2
  28: l5 -> l2 : guard^0'=guard^post1, 1+j^0-n^0 <= 0, cost: 2
  18: l6 -> l5 : j^0'=1+j^0, TRUE, cost: 1
  25: l9 -> l1 : i^0'=0, TRUE, cost: 2


Eliminating location l2 by chaining:

Applied chaining
First rule:
l5 -> l2 : guard^0'=guard^post1, 1+j^0-n^0 <= 0, cost: 2
Second rule:
l2 -> l6 : guard^0 == 0, cost: 1
New rule:
l5 -> l6 : guard^0'=guard^post1, (1+j^0-n^0 <= 0 /\ guard^post1 == 0), cost: 3

Applied chaining
First rule:
l5 -> l2 : guard^0'=guard^post1, 1+j^0-n^0 <= 0, cost: 2
Second rule:
l2 -> l6 : j^0'=-1+j^0, n^0'=-1+n^0, (-1+guard^0 >= 0 \/ 1+guard^0 <= 0), cost: 2
New rule:
l5 -> l6 : guard^0'=guard^post1, j^0'=-1+j^0, n^0'=-1+n^0, (1+j^0-n^0 <= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: 4

Applied deletion
Removed the following rules: 20 28 31

Eliminated locations on tree-shaped paths
Start location: l9
  26: l1 -> l5 : j^0'=1+i^0, 1+i^0-n^0 <= 0, cost: 2
  27: l5 -> l1 : i^0'=1+i^0, -j^0+n^0 <= 0, cost: 2
  32: l5 -> l6 : guard^0'=guard^post1, (1+j^0-n^0 <= 0 /\ guard^post1 == 0), cost: 3
  33: l5 -> l6 : guard^0'=guard^post1, j^0'=-1+j^0, n^0'=-1+n^0, (1+j^0-n^0 <= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: 4
  18: l6 -> l5 : j^0'=1+j^0, TRUE, cost: 1
  25: l9 -> l1 : i^0'=0, TRUE, cost: 2


Eliminating location l6 by chaining:

Applied chaining
First rule:
l5 -> l6 : guard^0'=guard^post1, (1+j^0-n^0 <= 0 /\ guard^post1 == 0), cost: 3
Second rule:
l6 -> l5 : j^0'=1+j^0, TRUE, cost: 1
New rule:
l5 -> l5 : guard^0'=guard^post1, j^0'=1+j^0, (1+j^0-n^0 <= 0 /\ guard^post1 == 0), cost: 4

Applied chaining
First rule:
l5 -> l6 : guard^0'=guard^post1, j^0'=-1+j^0, n^0'=-1+n^0, (1+j^0-n^0 <= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: 4
Second rule:
l6 -> l5 : j^0'=1+j^0, TRUE, cost: 1
New rule:
l5 -> l5 : guard^0'=guard^post1, j^0'=j^0, n^0'=-1+n^0, (1+j^0-n^0 <= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: 5

Applied deletion
Removed the following rules: 18 32 33

Eliminated locations on tree-shaped paths
Start location: l9
  26: l1 -> l5 : j^0'=1+i^0, 1+i^0-n^0 <= 0, cost: 2
  27: l5 -> l1 : i^0'=1+i^0, -j^0+n^0 <= 0, cost: 2
  34: l5 -> l5 : guard^0'=guard^post1, j^0'=1+j^0, (1+j^0-n^0 <= 0 /\ guard^post1 == 0), cost: 4
  35: l5 -> l5 : guard^0'=guard^post1, j^0'=j^0, n^0'=-1+n^0, (1+j^0-n^0 <= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: 5
  25: l9 -> l1 : i^0'=0, TRUE, cost: 2


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

Applied simplification
Original rule:
l5 -> l5 : guard^0'=guard^post1, j^0'=j^0, n^0'=-1+n^0, (1+j^0-n^0 <= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: 5
New rule:
l5 -> l5 : guard^0'=guard^post1, n^0'=-1+n^0, (1+j^0-n^0 <= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: 5

Simplified simple loops
Start location: l9
  26: l1 -> l5 : j^0'=1+i^0, 1+i^0-n^0 <= 0, cost: 2
  27: l5 -> l1 : i^0'=1+i^0, -j^0+n^0 <= 0, cost: 2
  36: l5 -> l5 : guard^0'=0, j^0'=1+j^0, 1+j^0-n^0 <= 0, cost: 4
  37: l5 -> l5 : guard^0'=guard^post1, n^0'=-1+n^0, (1+j^0-n^0 <= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: 5
  25: l9 -> l1 : i^0'=0, TRUE, cost: 2


Applied acceleration
Original rule:
l5 -> l5 : guard^0'=0, j^0'=1+j^0, 1+j^0-n^0 <= 0, cost: 4
New rule:
l5 -> l5 : guard^0'=0, j^0'=j^0+n1, (-1+n1 >= 0 /\ -j^0+n^0-n1 >= 0), cost: 4*n1

Applied instantiation
Original rule:
l5 -> l5 : guard^0'=0, j^0'=j^0+n1, (-1+n1 >= 0 /\ -j^0+n^0-n1 >= 0), cost: 4*n1
New rule:
l5 -> l5 : guard^0'=0, j^0'=n^0, (0 >= 0 /\ -1-j^0+n^0 >= 0), cost: -4*j^0+4*n^0

Applied acceleration
Original rule:
l5 -> l5 : guard^0'=guard^post1, n^0'=-1+n^0, (1+j^0-n^0 <= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: 5
New rule:
l5 -> l5 : guard^0'=guard^post1, n^0'=-n3+n^0, (-j^0-n3+n^0 >= 0 /\ -1+n3 >= 0 /\ (-1-guard^post1 >= 0 \/ -1+guard^post1 >= 0)), cost: 5*n3

Applied instantiation
Original rule:
l5 -> l5 : guard^0'=guard^post1, n^0'=-n3+n^0, (-j^0-n3+n^0 >= 0 /\ -1+n3 >= 0 /\ (-1-guard^post1 >= 0 \/ -1+guard^post1 >= 0)), cost: 5*n3
New rule:
l5 -> l5 : guard^0'=guard^post1, n^0'=j^0, (0 >= 0 /\ -1-j^0+n^0 >= 0 /\ (-1-guard^post1 >= 0 \/ -1+guard^post1 >= 0)), cost: -5*j^0+5*n^0

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

Applied simplification
Original rule:
l5 -> l5 : guard^0'=guard^post1, n^0'=j^0, (0 >= 0 /\ -1-j^0+n^0 >= 0 /\ (-1-guard^post1 >= 0 \/ -1+guard^post1 >= 0)), cost: -5*j^0+5*n^0
New rule:
l5 -> l5 : guard^0'=guard^post1, n^0'=j^0, (-1-j^0+n^0 >= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: -5*j^0+5*n^0

Applied deletion
Removed the following rules: 36 37

Accelerated simple loops
Start location: l9
  26: l1 -> l5 : j^0'=1+i^0, 1+i^0-n^0 <= 0, cost: 2
  27: l5 -> l1 : i^0'=1+i^0, -j^0+n^0 <= 0, cost: 2
  40: l5 -> l5 : guard^0'=0, j^0'=n^0, -1-j^0+n^0 >= 0, cost: -4*j^0+4*n^0
  41: l5 -> l5 : guard^0'=guard^post1, n^0'=j^0, (-1-j^0+n^0 >= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: -5*j^0+5*n^0
  25: l9 -> l1 : i^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l1 -> l5 : j^0'=1+i^0, 1+i^0-n^0 <= 0, cost: 2
Second rule:
l5 -> l5 : guard^0'=0, j^0'=n^0, -1-j^0+n^0 >= 0, cost: -4*j^0+4*n^0
New rule:
l1 -> l5 : guard^0'=0, j^0'=n^0, -2-i^0+n^0 >= 0, cost: -2-4*i^0+4*n^0

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

Applied deletion
Removed the following rules: 40 41

Chained accelerated rules with incoming rules
Start location: l9
  26: l1 -> l5 : j^0'=1+i^0, 1+i^0-n^0 <= 0, cost: 2
  42: l1 -> l5 : guard^0'=0, j^0'=n^0, -2-i^0+n^0 >= 0, cost: -2-4*i^0+4*n^0
  43: l1 -> l5 : guard^0'=guard^post1, j^0'=1+i^0, n^0'=1+i^0, (-2-i^0+n^0 >= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: -3-5*i^0+5*n^0
  27: l5 -> l1 : i^0'=1+i^0, -j^0+n^0 <= 0, cost: 2
  25: l9 -> l1 : i^0'=0, TRUE, cost: 2


Eliminating location l5 by chaining:

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

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

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

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

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

Applied deletion
Removed the following rules: 26 27 42 43

Eliminated locations on tree-shaped paths
Start location: l9
  44: l1 -> l1 : j^0'=1+i^0, i^0'=1+i^0, (1+i^0-n^0 <= 0 /\ -1-i^0+n^0 <= 0), cost: 4
  45: l1 -> l1 : guard^0'=0, j^0'=n^0, i^0'=1+i^0, -2-i^0+n^0 >= 0, cost: -4*i^0+4*n^0
  46: l1 -> l1 : guard^0'=guard^post1, j^0'=1+i^0, i^0'=1+i^0, n^0'=1+i^0, (-2-i^0+n^0 >= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: -1-5*i^0+5*n^0
  25: l9 -> l1 : i^0'=0, TRUE, cost: 2


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

Simplified simple loops
Start location: l9
  45: l1 -> l1 : guard^0'=0, j^0'=n^0, i^0'=1+i^0, -2-i^0+n^0 >= 0, cost: -4*i^0+4*n^0
  46: l1 -> l1 : guard^0'=guard^post1, j^0'=1+i^0, i^0'=1+i^0, n^0'=1+i^0, (-2-i^0+n^0 >= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: -1-5*i^0+5*n^0
  47: l1 -> l1 : j^0'=1+i^0, i^0'=1+i^0, 1+i^0-n^0 == 0, cost: 4
  25: l9 -> l1 : i^0'=0, TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : guard^0'=0, j^0'=n^0, i^0'=1+i^0, -2-i^0+n^0 >= 0, cost: -4*i^0+4*n^0
New rule:
l1 -> l1 : guard^0'=0, j^0'=n^0, i^0'=i^0+n14, (-1-i^0+n^0-n14 >= 0 /\ -1+n14 >= 0), cost: -2*n14^2-4*i^0*n14+4*n^0*n14+2*n14

Applied instantiation
Original rule:
l1 -> l1 : guard^0'=0, j^0'=n^0, i^0'=i^0+n14, (-1-i^0+n^0-n14 >= 0 /\ -1+n14 >= 0), cost: -2*n14^2-4*i^0*n14+4*n^0*n14+2*n14
New rule:
l1 -> l1 : guard^0'=0, j^0'=n^0, i^0'=-1+n^0, (0 >= 0 /\ -2-i^0+n^0 >= 0), cost: -2-4*(1+i^0-n^0)*n^0-2*i^0+2*n^0-2*(1+i^0-n^0)^2+4*(1+i^0-n^0)*i^0

Applied acceleration
Original rule:
l1 -> l1 : j^0'=1+i^0, i^0'=1+i^0, 1+i^0-n^0 == 0, cost: 4
New rule:
l1 -> l1 : j^0'=i^0+n17, i^0'=i^0+n17, (1+i^0-n^0 >= 0 /\ -1-i^0+n^0 >= 0 /\ -i^0-n17+n^0 >= 0 /\ -1+n17 >= 0), cost: 4*n17

Applied instantiation
Original rule:
l1 -> l1 : j^0'=i^0+n17, i^0'=i^0+n17, (1+i^0-n^0 >= 0 /\ -1-i^0+n^0 >= 0 /\ -i^0-n17+n^0 >= 0 /\ -1+n17 >= 0), cost: 4*n17
New rule:
l1 -> l1 : j^0'=n^0, i^0'=n^0, (0 >= 0 /\ 1+i^0-n^0 >= 0 /\ -1-i^0+n^0 >= 0), cost: -4*i^0+4*n^0

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

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

Applied deletion
Removed the following rules: 45 47

Accelerated simple loops
Start location: l9
  46: l1 -> l1 : guard^0'=guard^post1, j^0'=1+i^0, i^0'=1+i^0, n^0'=1+i^0, (-2-i^0+n^0 >= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: -1-5*i^0+5*n^0
  50: l1 -> l1 : guard^0'=0, j^0'=n^0, i^0'=-1+n^0, -2-i^0+n^0 >= 0, cost: -2-4*(1+i^0-n^0)*n^0-2*i^0+2*n^0-2*(1+i^0-n^0)^2+4*(1+i^0-n^0)*i^0
  51: l1 -> l1 : j^0'=n^0, i^0'=n^0, (1+i^0-n^0 >= 0 /\ -1-i^0+n^0 >= 0), cost: -4*i^0+4*n^0
  25: l9 -> l1 : i^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l9 -> l1 : i^0'=0, TRUE, cost: 2
Second rule:
l1 -> l1 : guard^0'=guard^post1, j^0'=1+i^0, i^0'=1+i^0, n^0'=1+i^0, (-2-i^0+n^0 >= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: -1-5*i^0+5*n^0
New rule:
l9 -> l1 : guard^0'=guard^post1, j^0'=1, i^0'=1, n^0'=1, (-2+n^0 >= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: 1+5*n^0

Applied chaining
First rule:
l9 -> l1 : i^0'=0, TRUE, cost: 2
Second rule:
l1 -> l1 : guard^0'=0, j^0'=n^0, i^0'=-1+n^0, -2-i^0+n^0 >= 0, cost: -2-4*(1+i^0-n^0)*n^0-2*i^0+2*n^0-2*(1+i^0-n^0)^2+4*(1+i^0-n^0)*i^0
New rule:
l9 -> l1 : guard^0'=0, j^0'=n^0, i^0'=-1+n^0, -2+n^0 >= 0, cost: -2*(-1+n^0)^2+4*n^0*(-1+n^0)+2*n^0

Applied chaining
First rule:
l9 -> l1 : i^0'=0, TRUE, cost: 2
Second rule:
l1 -> l1 : j^0'=n^0, i^0'=n^0, (1+i^0-n^0 >= 0 /\ -1-i^0+n^0 >= 0), cost: -4*i^0+4*n^0
New rule:
l9 -> l1 : j^0'=n^0, i^0'=n^0, -1+n^0 == 0, cost: 2+4*n^0

Applied deletion
Removed the following rules: 46 50 51

Chained accelerated rules with incoming rules
Start location: l9
  25: l9 -> l1 : i^0'=0, TRUE, cost: 2
  52: l9 -> l1 : guard^0'=guard^post1, j^0'=1, i^0'=1, n^0'=1, (-2+n^0 >= 0 /\ (1+guard^post1 <= 0 \/ -1+guard^post1 >= 0)), cost: 1+5*n^0
  53: l9 -> l1 : guard^0'=0, j^0'=n^0, i^0'=-1+n^0, -2+n^0 >= 0, cost: -2*(-1+n^0)^2+4*n^0*(-1+n^0)+2*n^0
  54: l9 -> l1 : j^0'=n^0, i^0'=n^0, -1+n^0 == 0, cost: 2+4*n^0


Removed unreachable locations and irrelevant leafs
Start location: l9
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0