WORST_CASE(Omega(0),?)

Initial ITS
Start location: l10
   0: l0 -> l1 : i^0'=i^post0, k^0'=k^post0, tmp___0^0'=tmp___0^post0, j^0'=j^post0, tmp^0'=tmp^post0, (0 == 0 /\ i^post0 == 0 /\ -100+k^0 <= 0 /\ -tmp^post0+tmp^0 == 0 /\ -j^post0+j^0 == 0 /\ k^0-k^post0 == 0), cost: 1
   1: l0 -> l2 : i^0'=i^post1, k^0'=k^post1, tmp___0^0'=tmp___0^post1, j^0'=j^post1, tmp^0'=tmp^post1, (-tmp___0^post1+tmp___0^0 == 0 /\ 101-k^0 <= 0 /\ i^0-i^post1 == 0 /\ j^0-j^post1 == 0 /\ -tmp^post1+tmp^0 == 0 /\ -k^post1+k^0 == 0), cost: 1
   4: l1 -> l4 : i^0'=i^post4, k^0'=k^post4, tmp___0^0'=tmp___0^post4, j^0'=j^post4, tmp^0'=tmp^post4, (-tmp^post4+tmp^0 == 0 /\ -tmp___0^post4+tmp___0^0 == 0 /\ -j^post4+j^0 == 0 /\ i^0-i^post4 == 0 /\ k^0-k^post4 == 0), cost: 1
   2: l3 -> l0 : i^0'=i^post2, k^0'=k^post2, tmp___0^0'=tmp___0^post2, j^0'=j^post2, tmp^0'=tmp^post2, (i^0-i^post2 == 0 /\ -j^post2+j^0 == 0 /\ -tmp___0^post2+tmp___0^0 == 0 /\ 1-k^0 <= 0 /\ k^0-k^post2 == 0 /\ -tmp^post2+tmp^0 == 0), cost: 1
   3: l3 -> l2 : i^0'=i^post3, k^0'=k^post3, tmp___0^0'=tmp___0^post3, j^0'=j^post3, tmp^0'=tmp^post3, (-tmp^post3+tmp^0 == 0 /\ k^0 <= 0 /\ tmp___0^0-tmp___0^post3 == 0 /\ j^0-j^post3 == 0 /\ k^0-k^post3 == 0 /\ i^0-i^post3 == 0), cost: 1
  11: l4 -> l7 : i^0'=i^post11, k^0'=k^post11, tmp___0^0'=tmp___0^post11, j^0'=j^post11, tmp^0'=tmp^post11, (tmp___0^0-tmp___0^post11 == 0 /\ i^0-k^0 <= 0 /\ -tmp^post11+tmp^0 == 0 /\ i^0-i^post11 == 0 /\ -i^0+k^0 <= 0 /\ k^0-k^post11 == 0 /\ -j^post11+j^0 == 0), cost: 1
  12: l4 -> l8 : i^0'=i^post12, k^0'=k^post12, tmp___0^0'=tmp___0^post12, j^0'=j^post12, tmp^0'=tmp^post12, (-tmp___0^post12+tmp___0^0 == 0 /\ tmp^0-tmp^post12 == 0 /\ i^0-i^post12 == 0 /\ 1-i^0+k^0 <= 0 /\ j^0-j^post12 == 0 /\ -k^post12+k^0 == 0), cost: 1
  13: l4 -> l8 : i^0'=i^post13, k^0'=k^post13, tmp___0^0'=tmp___0^post13, j^0'=j^post13, tmp^0'=tmp^post13, (-tmp^post13+tmp^0 == 0 /\ k^0-k^post13 == 0 /\ -j^post13+j^0 == 0 /\ i^0-i^post13 == 0 /\ 1+i^0-k^0 <= 0 /\ tmp___0^0-tmp___0^post13 == 0), cost: 1
   5: l5 -> l2 : i^0'=i^post5, k^0'=k^post5, tmp___0^0'=tmp___0^post5, j^0'=j^post5, tmp^0'=tmp^post5, (-tmp^post5+tmp^0 == 0 /\ tmp___0^0-tmp___0^post5 == 0 /\ i^0-i^post5 == 0 /\ -j^post5+j^0 == 0 /\ i^0-j^0 <= 0 /\ k^0-k^post5 == 0), cost: 1
   6: l5 -> l6 : i^0'=i^post6, k^0'=k^post6, tmp___0^0'=tmp___0^post6, j^0'=j^post6, tmp^0'=tmp^post6, (tmp^0-tmp^post6 == 0 /\ -1+j^post6-j^0 == 0 /\ -tmp___0^post6+tmp___0^0 == 0 /\ 1-i^0+j^0 <= 0 /\ i^0-i^post6 == 0 /\ k^0-k^post6 == 0), cost: 1
   8: l6 -> l5 : i^0'=i^post8, k^0'=k^post8, tmp___0^0'=tmp___0^post8, j^0'=j^post8, tmp^0'=tmp^post8, (-tmp^post8+tmp^0 == 0 /\ i^0-i^post8 == 0 /\ -j^post8+j^0 == 0 /\ k^0-k^post8 == 0 /\ -tmp___0^post8+tmp___0^0 == 0), cost: 1
   7: l7 -> l6 : i^0'=i^post7, k^0'=k^post7, tmp___0^0'=tmp___0^post7, j^0'=j^post7, tmp^0'=tmp^post7, (k^0-k^post7 == 0 /\ j^post7 == 0 /\ tmp___0^0-tmp___0^post7 == 0 /\ -tmp^post7+tmp^0 == 0 /\ 1-i^0+i^post7 == 0), cost: 1
   9: l8 -> l1 : i^0'=i^post9, k^0'=k^post9, tmp___0^0'=tmp___0^post9, j^0'=j^post9, tmp^0'=tmp^post9, (-1-i^0+i^post9 == 0 /\ -tmp^post9+tmp^0 == 0 /\ tmp___0^0-tmp___0^post9 == 0 /\ -j^post9+j^0 == 0 /\ k^0-k^post9 == 0), cost: 1
  10: l8 -> l7 : i^0'=i^post10, k^0'=k^post10, tmp___0^0'=tmp___0^post10, j^0'=j^post10, tmp^0'=tmp^post10, (tmp^0-tmp^post10 == 0 /\ -tmp___0^post10+tmp___0^0 == 0 /\ -j^post10+j^0 == 0 /\ i^0-i^post10 == 0 /\ k^0-k^post10 == 0), cost: 1
  14: l9 -> l3 : i^0'=i^post14, k^0'=k^post14, tmp___0^0'=tmp___0^post14, j^0'=j^post14, tmp^0'=tmp^post14, (0 == 0 /\ k^post14-tmp^post14 == 0 /\ i^0-i^post14 == 0 /\ j^0-j^post14 == 0 /\ -tmp___0^post14+tmp___0^0 == 0), cost: 1
  15: l10 -> l9 : i^0'=i^post15, k^0'=k^post15, tmp___0^0'=tmp___0^post15, j^0'=j^post15, tmp^0'=tmp^post15, (-tmp^post15+tmp^0 == 0 /\ -tmp___0^post15+tmp___0^0 == 0 /\ -j^post15+j^0 == 0 /\ i^0-i^post15 == 0 /\ k^0-k^post15 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l10
   0: l0 -> l1 : i^0'=i^post0, k^0'=k^post0, tmp___0^0'=tmp___0^post0, j^0'=j^post0, tmp^0'=tmp^post0, (0 == 0 /\ i^post0 == 0 /\ -100+k^0 <= 0 /\ -tmp^post0+tmp^0 == 0 /\ -j^post0+j^0 == 0 /\ k^0-k^post0 == 0), cost: 1
   4: l1 -> l4 : i^0'=i^post4, k^0'=k^post4, tmp___0^0'=tmp___0^post4, j^0'=j^post4, tmp^0'=tmp^post4, (-tmp^post4+tmp^0 == 0 /\ -tmp___0^post4+tmp___0^0 == 0 /\ -j^post4+j^0 == 0 /\ i^0-i^post4 == 0 /\ k^0-k^post4 == 0), cost: 1
   2: l3 -> l0 : i^0'=i^post2, k^0'=k^post2, tmp___0^0'=tmp___0^post2, j^0'=j^post2, tmp^0'=tmp^post2, (i^0-i^post2 == 0 /\ -j^post2+j^0 == 0 /\ -tmp___0^post2+tmp___0^0 == 0 /\ 1-k^0 <= 0 /\ k^0-k^post2 == 0 /\ -tmp^post2+tmp^0 == 0), cost: 1
  11: l4 -> l7 : i^0'=i^post11, k^0'=k^post11, tmp___0^0'=tmp___0^post11, j^0'=j^post11, tmp^0'=tmp^post11, (tmp___0^0-tmp___0^post11 == 0 /\ i^0-k^0 <= 0 /\ -tmp^post11+tmp^0 == 0 /\ i^0-i^post11 == 0 /\ -i^0+k^0 <= 0 /\ k^0-k^post11 == 0 /\ -j^post11+j^0 == 0), cost: 1
  12: l4 -> l8 : i^0'=i^post12, k^0'=k^post12, tmp___0^0'=tmp___0^post12, j^0'=j^post12, tmp^0'=tmp^post12, (-tmp___0^post12+tmp___0^0 == 0 /\ tmp^0-tmp^post12 == 0 /\ i^0-i^post12 == 0 /\ 1-i^0+k^0 <= 0 /\ j^0-j^post12 == 0 /\ -k^post12+k^0 == 0), cost: 1
  13: l4 -> l8 : i^0'=i^post13, k^0'=k^post13, tmp___0^0'=tmp___0^post13, j^0'=j^post13, tmp^0'=tmp^post13, (-tmp^post13+tmp^0 == 0 /\ k^0-k^post13 == 0 /\ -j^post13+j^0 == 0 /\ i^0-i^post13 == 0 /\ 1+i^0-k^0 <= 0 /\ tmp___0^0-tmp___0^post13 == 0), cost: 1
   6: l5 -> l6 : i^0'=i^post6, k^0'=k^post6, tmp___0^0'=tmp___0^post6, j^0'=j^post6, tmp^0'=tmp^post6, (tmp^0-tmp^post6 == 0 /\ -1+j^post6-j^0 == 0 /\ -tmp___0^post6+tmp___0^0 == 0 /\ 1-i^0+j^0 <= 0 /\ i^0-i^post6 == 0 /\ k^0-k^post6 == 0), cost: 1
   8: l6 -> l5 : i^0'=i^post8, k^0'=k^post8, tmp___0^0'=tmp___0^post8, j^0'=j^post8, tmp^0'=tmp^post8, (-tmp^post8+tmp^0 == 0 /\ i^0-i^post8 == 0 /\ -j^post8+j^0 == 0 /\ k^0-k^post8 == 0 /\ -tmp___0^post8+tmp___0^0 == 0), cost: 1
   7: l7 -> l6 : i^0'=i^post7, k^0'=k^post7, tmp___0^0'=tmp___0^post7, j^0'=j^post7, tmp^0'=tmp^post7, (k^0-k^post7 == 0 /\ j^post7 == 0 /\ tmp___0^0-tmp___0^post7 == 0 /\ -tmp^post7+tmp^0 == 0 /\ 1-i^0+i^post7 == 0), cost: 1
   9: l8 -> l1 : i^0'=i^post9, k^0'=k^post9, tmp___0^0'=tmp___0^post9, j^0'=j^post9, tmp^0'=tmp^post9, (-1-i^0+i^post9 == 0 /\ -tmp^post9+tmp^0 == 0 /\ tmp___0^0-tmp___0^post9 == 0 /\ -j^post9+j^0 == 0 /\ k^0-k^post9 == 0), cost: 1
  10: l8 -> l7 : i^0'=i^post10, k^0'=k^post10, tmp___0^0'=tmp___0^post10, j^0'=j^post10, tmp^0'=tmp^post10, (tmp^0-tmp^post10 == 0 /\ -tmp___0^post10+tmp___0^0 == 0 /\ -j^post10+j^0 == 0 /\ i^0-i^post10 == 0 /\ k^0-k^post10 == 0), cost: 1
  14: l9 -> l3 : i^0'=i^post14, k^0'=k^post14, tmp___0^0'=tmp___0^post14, j^0'=j^post14, tmp^0'=tmp^post14, (0 == 0 /\ k^post14-tmp^post14 == 0 /\ i^0-i^post14 == 0 /\ j^0-j^post14 == 0 /\ -tmp___0^post14+tmp___0^0 == 0), cost: 1
  15: l10 -> l9 : i^0'=i^post15, k^0'=k^post15, tmp___0^0'=tmp___0^post15, j^0'=j^post15, tmp^0'=tmp^post15, (-tmp^post15+tmp^0 == 0 /\ -tmp___0^post15+tmp___0^0 == 0 /\ -j^post15+j^0 == 0 /\ i^0-i^post15 == 0 /\ k^0-k^post15 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : i^0'=i^post0, k^0'=k^post0, tmp___0^0'=tmp___0^post0, j^0'=j^post0, tmp^0'=tmp^post0, (0 == 0 /\ i^post0 == 0 /\ -100+k^0 <= 0 /\ -tmp^post0+tmp^0 == 0 /\ -j^post0+j^0 == 0 /\ k^0-k^post0 == 0), cost: 1
New rule:
l0 -> l1 : i^0'=0, tmp___0^0'=tmp___0^post0, -100+k^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l0 : i^0'=i^post2, k^0'=k^post2, tmp___0^0'=tmp___0^post2, j^0'=j^post2, tmp^0'=tmp^post2, (i^0-i^post2 == 0 /\ -j^post2+j^0 == 0 /\ -tmp___0^post2+tmp___0^0 == 0 /\ 1-k^0 <= 0 /\ k^0-k^post2 == 0 /\ -tmp^post2+tmp^0 == 0), cost: 1
New rule:
l3 -> l0 : -1+k^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l4 : i^0'=i^post4, k^0'=k^post4, tmp___0^0'=tmp___0^post4, j^0'=j^post4, tmp^0'=tmp^post4, (-tmp^post4+tmp^0 == 0 /\ -tmp___0^post4+tmp___0^0 == 0 /\ -j^post4+j^0 == 0 /\ i^0-i^post4 == 0 /\ k^0-k^post4 == 0), cost: 1
New rule:
l1 -> l4 : TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l6 : i^0'=i^post6, k^0'=k^post6, tmp___0^0'=tmp___0^post6, j^0'=j^post6, tmp^0'=tmp^post6, (tmp^0-tmp^post6 == 0 /\ -1+j^post6-j^0 == 0 /\ -tmp___0^post6+tmp___0^0 == 0 /\ 1-i^0+j^0 <= 0 /\ i^0-i^post6 == 0 /\ k^0-k^post6 == 0), cost: 1
New rule:
l5 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l7 -> l6 : i^0'=i^post7, k^0'=k^post7, tmp___0^0'=tmp___0^post7, j^0'=j^post7, tmp^0'=tmp^post7, (k^0-k^post7 == 0 /\ j^post7 == 0 /\ tmp___0^0-tmp___0^post7 == 0 /\ -tmp^post7+tmp^0 == 0 /\ 1-i^0+i^post7 == 0), cost: 1
New rule:
l7 -> l6 : i^0'=-1+i^0, j^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l6 -> l5 : i^0'=i^post8, k^0'=k^post8, tmp___0^0'=tmp___0^post8, j^0'=j^post8, tmp^0'=tmp^post8, (-tmp^post8+tmp^0 == 0 /\ i^0-i^post8 == 0 /\ -j^post8+j^0 == 0 /\ k^0-k^post8 == 0 /\ -tmp___0^post8+tmp___0^0 == 0), cost: 1
New rule:
l6 -> l5 : TRUE, cost: 1

Applied preprocessing
Original rule:
l8 -> l1 : i^0'=i^post9, k^0'=k^post9, tmp___0^0'=tmp___0^post9, j^0'=j^post9, tmp^0'=tmp^post9, (-1-i^0+i^post9 == 0 /\ -tmp^post9+tmp^0 == 0 /\ tmp___0^0-tmp___0^post9 == 0 /\ -j^post9+j^0 == 0 /\ k^0-k^post9 == 0), cost: 1
New rule:
l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l8 -> l7 : i^0'=i^post10, k^0'=k^post10, tmp___0^0'=tmp___0^post10, j^0'=j^post10, tmp^0'=tmp^post10, (tmp^0-tmp^post10 == 0 /\ -tmp___0^post10+tmp___0^0 == 0 /\ -j^post10+j^0 == 0 /\ i^0-i^post10 == 0 /\ k^0-k^post10 == 0), cost: 1
New rule:
l8 -> l7 : TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l7 : i^0'=i^post11, k^0'=k^post11, tmp___0^0'=tmp___0^post11, j^0'=j^post11, tmp^0'=tmp^post11, (tmp___0^0-tmp___0^post11 == 0 /\ i^0-k^0 <= 0 /\ -tmp^post11+tmp^0 == 0 /\ i^0-i^post11 == 0 /\ -i^0+k^0 <= 0 /\ k^0-k^post11 == 0 /\ -j^post11+j^0 == 0), cost: 1
New rule:
l4 -> l7 : i^0-k^0 == 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l8 : i^0'=i^post12, k^0'=k^post12, tmp___0^0'=tmp___0^post12, j^0'=j^post12, tmp^0'=tmp^post12, (-tmp___0^post12+tmp___0^0 == 0 /\ tmp^0-tmp^post12 == 0 /\ i^0-i^post12 == 0 /\ 1-i^0+k^0 <= 0 /\ j^0-j^post12 == 0 /\ -k^post12+k^0 == 0), cost: 1
New rule:
l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l8 : i^0'=i^post13, k^0'=k^post13, tmp___0^0'=tmp___0^post13, j^0'=j^post13, tmp^0'=tmp^post13, (-tmp^post13+tmp^0 == 0 /\ k^0-k^post13 == 0 /\ -j^post13+j^0 == 0 /\ i^0-i^post13 == 0 /\ 1+i^0-k^0 <= 0 /\ tmp___0^0-tmp___0^post13 == 0), cost: 1
New rule:
l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l9 -> l3 : i^0'=i^post14, k^0'=k^post14, tmp___0^0'=tmp___0^post14, j^0'=j^post14, tmp^0'=tmp^post14, (0 == 0 /\ k^post14-tmp^post14 == 0 /\ i^0-i^post14 == 0 /\ j^0-j^post14 == 0 /\ -tmp___0^post14+tmp___0^0 == 0), cost: 1
New rule:
l9 -> l3 : k^0'=tmp^post14, tmp^0'=tmp^post14, 0 == 0, cost: 1

Applied preprocessing
Original rule:
l10 -> l9 : i^0'=i^post15, k^0'=k^post15, tmp___0^0'=tmp___0^post15, j^0'=j^post15, tmp^0'=tmp^post15, (-tmp^post15+tmp^0 == 0 /\ -tmp___0^post15+tmp___0^0 == 0 /\ -j^post15+j^0 == 0 /\ i^0-i^post15 == 0 /\ k^0-k^post15 == 0), cost: 1
New rule:
l10 -> l9 : TRUE, cost: 1

Simplified rules
Start location: l10
  16: l0 -> l1 : i^0'=0, tmp___0^0'=tmp___0^post0, -100+k^0 <= 0, cost: 1
  18: l1 -> l4 : TRUE, cost: 1
  17: l3 -> l0 : -1+k^0 >= 0, cost: 1
  24: l4 -> l7 : i^0-k^0 == 0, cost: 1
  25: l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1
  26: l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1
  19: l5 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 1
  21: l6 -> l5 : TRUE, cost: 1
  20: l7 -> l6 : i^0'=-1+i^0, j^0'=0, TRUE, cost: 1
  22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1
  23: l8 -> l7 : TRUE, cost: 1
  27: l9 -> l3 : k^0'=tmp^post14, tmp^0'=tmp^post14, 0 == 0, 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 -> l3 : k^0'=tmp^post14, tmp^0'=tmp^post14, 0 == 0, cost: 1
New rule:
l10 -> l3 : k^0'=tmp^post14, tmp^0'=tmp^post14, 0 == 0, cost: 2

Applied deletion
Removed the following rules: 27 28

Eliminating location l3 by chaining:

Applied chaining
First rule:
l10 -> l3 : k^0'=tmp^post14, tmp^0'=tmp^post14, 0 == 0, cost: 2
Second rule:
l3 -> l0 : -1+k^0 >= 0, cost: 1
New rule:
l10 -> l0 : k^0'=tmp^post14, tmp^0'=tmp^post14, (0 == 0 /\ -1+tmp^post14 >= 0), cost: 3

Applied simplification
Original rule:
l10 -> l0 : k^0'=tmp^post14, tmp^0'=tmp^post14, (0 == 0 /\ -1+tmp^post14 >= 0), cost: 3
New rule:
l10 -> l0 : k^0'=tmp^post14, tmp^0'=tmp^post14, -1+tmp^post14 >= 0, cost: 3

Applied deletion
Removed the following rules: 17 29

Eliminating location l0 by chaining:

Applied chaining
First rule:
l10 -> l0 : k^0'=tmp^post14, tmp^0'=tmp^post14, -1+tmp^post14 >= 0, cost: 3
Second rule:
l0 -> l1 : i^0'=0, tmp___0^0'=tmp___0^post0, -100+k^0 <= 0, cost: 1
New rule:
l10 -> l1 : i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4

Applied deletion
Removed the following rules: 16 30

Eliminating location l5 by chaining:

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

Applied deletion
Removed the following rules: 19 21

Eliminated locations on linear paths
Start location: l10
  18: l1 -> l4 : TRUE, cost: 1
  24: l4 -> l7 : i^0-k^0 == 0, cost: 1
  25: l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1
  26: l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1
  32: l6 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 2
  20: l7 -> l6 : i^0'=-1+i^0, j^0'=0, TRUE, cost: 1
  22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1
  23: l8 -> l7 : TRUE, cost: 1
  31: l10 -> l1 : i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4


Applied acceleration
Original rule:
l6 -> l6 : j^0'=1+j^0, 1-i^0+j^0 <= 0, cost: 2
New rule:
l6 -> l6 : j^0'=j^0+n0, (i^0-j^0-n0 >= 0 /\ n0 >= 0), cost: 2*n0

Applied instantiation
Original rule:
l6 -> l6 : j^0'=j^0+n0, (i^0-j^0-n0 >= 0 /\ n0 >= 0), cost: 2*n0
New rule:
l6 -> l6 : j^0'=i^0, (0 >= 0 /\ i^0-j^0 >= 0), cost: 2*i^0-2*j^0

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

Applied deletion
Removed the following rules: 32

Accelerated simple loops
Start location: l10
  18: l1 -> l4 : TRUE, cost: 1
  24: l4 -> l7 : i^0-k^0 == 0, cost: 1
  25: l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1
  26: l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1
  34: l6 -> l6 : j^0'=i^0, i^0-j^0 >= 0, cost: 2*i^0-2*j^0
  20: l7 -> l6 : i^0'=-1+i^0, j^0'=0, TRUE, cost: 1
  22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1
  23: l8 -> l7 : TRUE, cost: 1
  31: l10 -> l1 : i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4


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

Applied deletion
Removed the following rules: 34

Chained accelerated rules with incoming rules
Start location: l10
  18: l1 -> l4 : TRUE, cost: 1
  24: l4 -> l7 : i^0-k^0 == 0, cost: 1
  25: l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1
  26: l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1
  20: l7 -> l6 : i^0'=-1+i^0, j^0'=0, TRUE, cost: 1
  35: l7 -> l6 : i^0'=-1+i^0, j^0'=-1+i^0, -1+i^0 >= 0, cost: -1+2*i^0
  22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1
  23: l8 -> l7 : TRUE, cost: 1
  31: l10 -> l1 : i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4


Removed unreachable locations and irrelevant leafs
Start location: l10
  18: l1 -> l4 : TRUE, cost: 1
  25: l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1
  26: l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1
  22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1
  31: l10 -> l1 : i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4


Eliminating location l4 by chaining:

Applied chaining
First rule:
l1 -> l4 : TRUE, cost: 1
Second rule:
l4 -> l8 : 1-i^0+k^0 <= 0, cost: 1
New rule:
l1 -> l8 : 1-i^0+k^0 <= 0, cost: 2

Applied chaining
First rule:
l1 -> l4 : TRUE, cost: 1
Second rule:
l4 -> l8 : 1+i^0-k^0 <= 0, cost: 1
New rule:
l1 -> l8 : 1+i^0-k^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 18 25 26

Eliminated locations on tree-shaped paths
Start location: l10
  36: l1 -> l8 : 1-i^0+k^0 <= 0, cost: 2
  37: l1 -> l8 : 1+i^0-k^0 <= 0, cost: 2
  22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1
  31: l10 -> l1 : i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4


Applied merging
first rule:
l1 -> l8 : 1-i^0+k^0 <= 0, cost: 2
second rule:
l1 -> l8 : 1+i^0-k^0 <= 0, cost: 2
new rule:
l1 -> l8 : (1+i^0-k^0 <= 0 \/ 1-i^0+k^0 <= 0), cost: 2

Merged rules
Start location: l10
  38: l1 -> l8 : (1+i^0-k^0 <= 0 \/ 1-i^0+k^0 <= 0), cost: 2
  22: l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1
  31: l10 -> l1 : i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4


Eliminating location l8 by chaining:

Applied chaining
First rule:
l1 -> l8 : (1+i^0-k^0 <= 0 \/ 1-i^0+k^0 <= 0), cost: 2
Second rule:
l8 -> l1 : i^0'=1+i^0, TRUE, cost: 1
New rule:
l1 -> l1 : i^0'=1+i^0, (1+i^0-k^0 <= 0 \/ 1-i^0+k^0 <= 0), cost: 3

Applied deletion
Removed the following rules: 22 38

Eliminated locations on linear paths
Start location: l10
  39: l1 -> l1 : i^0'=1+i^0, (1+i^0-k^0 <= 0 \/ 1-i^0+k^0 <= 0), cost: 3
  31: l10 -> l1 : i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4


Applied nonterm
Original rule:
l1 -> l1 : i^0'=1+i^0, (1+i^0-k^0 <= 0 \/ 1-i^0+k^0 <= 0), cost: 3
New rule:
l1 -> [12] : -1+i^0-k^0 >= 0, cost: NONTERM

Applied acceleration
Original rule:
l1 -> l1 : i^0'=1+i^0, (1+i^0-k^0 <= 0 \/ 1-i^0+k^0 <= 0), cost: 3
New rule:
l1 -> l1 : i^0'=i^0+n3, (n3 >= 0 /\ (-1+i^0-k^0 >= 0 \/ -i^0+k^0-n3 >= 0)), cost: 3*n3

Applied instantiation
Original rule:
l1 -> l1 : i^0'=i^0+n3, (n3 >= 0 /\ (-1+i^0-k^0 >= 0 \/ -i^0+k^0-n3 >= 0)), cost: 3*n3
New rule:
l1 -> l1 : i^0'=k^0, (-i^0+k^0 >= 0 /\ (0 >= 0 \/ -1+i^0-k^0 >= 0)), cost: -3*i^0+3*k^0

Applied simplification
Original rule:
l1 -> l1 : i^0'=k^0, (-i^0+k^0 >= 0 /\ (0 >= 0 \/ -1+i^0-k^0 >= 0)), cost: -3*i^0+3*k^0
New rule:
l1 -> l1 : i^0'=k^0, -i^0+k^0 >= 0, cost: -3*i^0+3*k^0

Applied deletion
Removed the following rules: 39

Accelerated simple loops
Start location: l10
  40: l1 -> [12] : -1+i^0-k^0 >= 0, cost: NONTERM
  42: l1 -> l1 : i^0'=k^0, -i^0+k^0 >= 0, cost: -3*i^0+3*k^0
  31: l10 -> l1 : i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4


Applied chaining
First rule:
l10 -> l1 : i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4
Second rule:
l1 -> l1 : i^0'=k^0, -i^0+k^0 >= 0, cost: -3*i^0+3*k^0
New rule:
l10 -> l1 : i^0'=tmp^post14, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4+3*tmp^post14

Applied deletion
Removed the following rules: 40 42

Chained accelerated rules with incoming rules
Start location: l10
  31: l10 -> l1 : i^0'=0, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4
  43: l10 -> l1 : i^0'=tmp^post14, k^0'=tmp^post14, tmp___0^0'=tmp___0^post0, tmp^0'=tmp^post14, (-100+tmp^post14 <= 0 /\ -1+tmp^post14 >= 0), cost: 4+3*tmp^post14


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