WORST_CASE(Omega(0),?)

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


Removed unreachable rules and leafs
Start location: l8
   4: l2 -> l3 : y^0'=y^post4, ox^0'=ox^post4, x^0'=x^post4, c^0'=c^post4, oy^0'=oy^post4, (c^0-c^post4 == 0 /\ -oy^post4+oy^0 == 0 /\ ox^0-ox^post4 == 0 /\ -x^0+x^post4 == 0 /\ y^0-y^post4 == 0), cost: 1
  11: l3 -> l6 : y^0'=y^post11, ox^0'=ox^post11, x^0'=x^post11, c^0'=c^post11, oy^0'=oy^post11, (-ox^post11+ox^0 == 0 /\ -oy^post11+oy^0 == 0 /\ 1-x^0 <= 0 /\ c^0-c^post11 == 0 /\ x^0-x^post11 == 0 /\ y^0-y^post11 == 0 /\ 1-y^0 <= 0), cost: 1
   5: l4 -> l3 : y^0'=y^post5, ox^0'=ox^post5, x^0'=x^post5, c^0'=c^post5, oy^0'=oy^post5, (oy^0-oy^post5 == 0 /\ y^0-y^post5 == 0 /\ c^0 <= 0 /\ -x^post5+x^0 == 0 /\ -c^post5+c^0 == 0 /\ ox^0-ox^post5 == 0), cost: 1
   6: l4 -> l3 : y^0'=y^post6, ox^0'=ox^post6, x^0'=x^post6, c^0'=c^post6, oy^0'=oy^post6, (-y^0+oy^post6 == 0 /\ x^0-x^post6 == 0 /\ y^0-y^post6 == 0 /\ -x^0+ox^post6 == 0 /\ -1+c^post6 == 0), cost: 1
   7: l5 -> l4 : y^0'=y^post7, ox^0'=ox^post7, x^0'=x^post7, c^0'=c^post7, oy^0'=oy^post7, (-x^post7+x^0 == 0 /\ oy^0-oy^post7 == 0 /\ c^0 <= 0 /\ c^0-c^post7 == 0 /\ ox^0-ox^post7 == 0 /\ y^0-y^post7 == 0), cost: 1
   8: l5 -> l2 : y^0'=y^post8, ox^0'=ox^post8, x^0'=x^post8, c^0'=c^post8, oy^0'=oy^post8, (-oy^post8+oy^0 == 0 /\ x^0-x^post8 == 0 /\ y^0-y^post8 == 0 /\ -c^post8+c^0 == 0 /\ ox^0-ox^post8 == 0 /\ 1-c^0 <= 0), cost: 1
   9: l6 -> l5 : y^0'=y^post9, ox^0'=ox^post9, x^0'=x^post9, c^0'=c^post9, oy^0'=oy^post9, (-x^post9+x^0 == 0 /\ oy^0-oy^post9 == 0 /\ c^0-c^post9 == 0 /\ 1-y^0+y^post9 == 0 /\ ox^0-ox^post9 == 0), cost: 1
  10: l6 -> l5 : y^0'=y^post10, ox^0'=ox^post10, x^0'=x^post10, c^0'=c^post10, oy^0'=oy^post10, (-c^post10+c^0 == 0 /\ y^0-y^post10 == 0 /\ ox^0-ox^post10 == 0 /\ -oy^post10+oy^0 == 0 /\ 1-x^0+x^post10 == 0), cost: 1
  12: l7 -> l3 : y^0'=y^post12, ox^0'=ox^post12, x^0'=x^post12, c^0'=c^post12, oy^0'=oy^post12, (-x^post12+x^0 == 0 /\ ox^0-ox^post12 == 0 /\ y^0-y^post12 == 0 /\ c^0 <= 0 /\ -c^post12+c^0 == 0 /\ -oy^post12+oy^0 == 0), cost: 1
  13: l8 -> l7 : y^0'=y^post13, ox^0'=ox^post13, x^0'=x^post13, c^0'=c^post13, oy^0'=oy^post13, (c^0-c^post13 == 0 /\ x^0-x^post13 == 0 /\ ox^0-ox^post13 == 0 /\ y^0-y^post13 == 0 /\ -oy^post13+oy^0 == 0), cost: 1


Applied preprocessing
Original rule:
l2 -> l3 : y^0'=y^post4, ox^0'=ox^post4, x^0'=x^post4, c^0'=c^post4, oy^0'=oy^post4, (c^0-c^post4 == 0 /\ -oy^post4+oy^0 == 0 /\ ox^0-ox^post4 == 0 /\ -x^0+x^post4 == 0 /\ y^0-y^post4 == 0), cost: 1
New rule:
l2 -> l3 : TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : y^0'=y^post5, ox^0'=ox^post5, x^0'=x^post5, c^0'=c^post5, oy^0'=oy^post5, (oy^0-oy^post5 == 0 /\ y^0-y^post5 == 0 /\ c^0 <= 0 /\ -x^post5+x^0 == 0 /\ -c^post5+c^0 == 0 /\ ox^0-ox^post5 == 0), cost: 1
New rule:
l4 -> l3 : c^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : y^0'=y^post6, ox^0'=ox^post6, x^0'=x^post6, c^0'=c^post6, oy^0'=oy^post6, (-y^0+oy^post6 == 0 /\ x^0-x^post6 == 0 /\ y^0-y^post6 == 0 /\ -x^0+ox^post6 == 0 /\ -1+c^post6 == 0), cost: 1
New rule:
l4 -> l3 : ox^0'=x^0, c^0'=1, oy^0'=y^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l4 : y^0'=y^post7, ox^0'=ox^post7, x^0'=x^post7, c^0'=c^post7, oy^0'=oy^post7, (-x^post7+x^0 == 0 /\ oy^0-oy^post7 == 0 /\ c^0 <= 0 /\ c^0-c^post7 == 0 /\ ox^0-ox^post7 == 0 /\ y^0-y^post7 == 0), cost: 1
New rule:
l5 -> l4 : c^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l5 -> l2 : y^0'=y^post8, ox^0'=ox^post8, x^0'=x^post8, c^0'=c^post8, oy^0'=oy^post8, (-oy^post8+oy^0 == 0 /\ x^0-x^post8 == 0 /\ y^0-y^post8 == 0 /\ -c^post8+c^0 == 0 /\ ox^0-ox^post8 == 0 /\ 1-c^0 <= 0), cost: 1
New rule:
l5 -> l2 : -1+c^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l6 -> l5 : y^0'=y^post9, ox^0'=ox^post9, x^0'=x^post9, c^0'=c^post9, oy^0'=oy^post9, (-x^post9+x^0 == 0 /\ oy^0-oy^post9 == 0 /\ c^0-c^post9 == 0 /\ 1-y^0+y^post9 == 0 /\ ox^0-ox^post9 == 0), cost: 1
New rule:
l6 -> l5 : y^0'=-1+y^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l6 -> l5 : y^0'=y^post10, ox^0'=ox^post10, x^0'=x^post10, c^0'=c^post10, oy^0'=oy^post10, (-c^post10+c^0 == 0 /\ y^0-y^post10 == 0 /\ ox^0-ox^post10 == 0 /\ -oy^post10+oy^0 == 0 /\ 1-x^0+x^post10 == 0), cost: 1
New rule:
l6 -> l5 : x^0'=-1+x^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l6 : y^0'=y^post11, ox^0'=ox^post11, x^0'=x^post11, c^0'=c^post11, oy^0'=oy^post11, (-ox^post11+ox^0 == 0 /\ -oy^post11+oy^0 == 0 /\ 1-x^0 <= 0 /\ c^0-c^post11 == 0 /\ x^0-x^post11 == 0 /\ y^0-y^post11 == 0 /\ 1-y^0 <= 0), cost: 1
New rule:
l3 -> l6 : (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 1

Applied preprocessing
Original rule:
l7 -> l3 : y^0'=y^post12, ox^0'=ox^post12, x^0'=x^post12, c^0'=c^post12, oy^0'=oy^post12, (-x^post12+x^0 == 0 /\ ox^0-ox^post12 == 0 /\ y^0-y^post12 == 0 /\ c^0 <= 0 /\ -c^post12+c^0 == 0 /\ -oy^post12+oy^0 == 0), cost: 1
New rule:
l7 -> l3 : c^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l8 -> l7 : y^0'=y^post13, ox^0'=ox^post13, x^0'=x^post13, c^0'=c^post13, oy^0'=oy^post13, (c^0-c^post13 == 0 /\ x^0-x^post13 == 0 /\ ox^0-ox^post13 == 0 /\ y^0-y^post13 == 0 /\ -oy^post13+oy^0 == 0), cost: 1
New rule:
l8 -> l7 : TRUE, cost: 1

Simplified rules
Start location: l8
  14: l2 -> l3 : TRUE, cost: 1
  21: l3 -> l6 : (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 1
  15: l4 -> l3 : c^0 <= 0, cost: 1
  16: l4 -> l3 : ox^0'=x^0, c^0'=1, oy^0'=y^0, TRUE, cost: 1
  17: l5 -> l4 : c^0 <= 0, cost: 1
  18: l5 -> l2 : -1+c^0 >= 0, cost: 1
  19: l6 -> l5 : y^0'=-1+y^0, TRUE, cost: 1
  20: l6 -> l5 : x^0'=-1+x^0, TRUE, cost: 1
  22: l7 -> l3 : c^0 <= 0, cost: 1
  23: l8 -> l7 : TRUE, cost: 1


Eliminating location l7 by chaining:

Applied chaining
First rule:
l8 -> l7 : TRUE, cost: 1
Second rule:
l7 -> l3 : c^0 <= 0, cost: 1
New rule:
l8 -> l3 : c^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 22 23

Eliminating location l2 by chaining:

Applied chaining
First rule:
l5 -> l2 : -1+c^0 >= 0, cost: 1
Second rule:
l2 -> l3 : TRUE, cost: 1
New rule:
l5 -> l3 : -1+c^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 14 18

Eliminated locations on linear paths
Start location: l8
  21: l3 -> l6 : (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 1
  15: l4 -> l3 : c^0 <= 0, cost: 1
  16: l4 -> l3 : ox^0'=x^0, c^0'=1, oy^0'=y^0, TRUE, cost: 1
  17: l5 -> l4 : c^0 <= 0, cost: 1
  25: l5 -> l3 : -1+c^0 >= 0, cost: 2
  19: l6 -> l5 : y^0'=-1+y^0, TRUE, cost: 1
  20: l6 -> l5 : x^0'=-1+x^0, TRUE, cost: 1
  24: l8 -> l3 : c^0 <= 0, cost: 2


Eliminating location l6 by chaining:

Applied chaining
First rule:
l3 -> l6 : (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 1
Second rule:
l6 -> l5 : y^0'=-1+y^0, TRUE, cost: 1
New rule:
l3 -> l5 : y^0'=-1+y^0, (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2

Applied chaining
First rule:
l3 -> l6 : (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 1
Second rule:
l6 -> l5 : x^0'=-1+x^0, TRUE, cost: 1
New rule:
l3 -> l5 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2

Applied deletion
Removed the following rules: 19 20 21

Eliminating location l4 by chaining:

Applied chaining
First rule:
l5 -> l4 : c^0 <= 0, cost: 1
Second rule:
l4 -> l3 : c^0 <= 0, cost: 1
New rule:
l5 -> l3 : c^0 <= 0, cost: 2

Applied chaining
First rule:
l5 -> l4 : c^0 <= 0, cost: 1
Second rule:
l4 -> l3 : ox^0'=x^0, c^0'=1, oy^0'=y^0, TRUE, cost: 1
New rule:
l5 -> l3 : ox^0'=x^0, c^0'=1, oy^0'=y^0, c^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 15 16 17

Eliminated locations on tree-shaped paths
Start location: l8
  26: l3 -> l5 : y^0'=-1+y^0, (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
  27: l3 -> l5 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
  25: l5 -> l3 : -1+c^0 >= 0, cost: 2
  28: l5 -> l3 : c^0 <= 0, cost: 2
  29: l5 -> l3 : ox^0'=x^0, c^0'=1, oy^0'=y^0, c^0 <= 0, cost: 2
  24: l8 -> l3 : c^0 <= 0, cost: 2


Eliminating location l5 by chaining:

Applied chaining
First rule:
l3 -> l5 : y^0'=-1+y^0, (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
Second rule:
l5 -> l3 : -1+c^0 >= 0, cost: 2
New rule:
l3 -> l3 : y^0'=-1+y^0, (-1+x^0 >= 0 /\ -1+c^0 >= 0 /\ -1+y^0 >= 0), cost: 4

Applied chaining
First rule:
l3 -> l5 : y^0'=-1+y^0, (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
Second rule:
l5 -> l3 : c^0 <= 0, cost: 2
New rule:
l3 -> l3 : y^0'=-1+y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4

Applied chaining
First rule:
l3 -> l5 : y^0'=-1+y^0, (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
Second rule:
l5 -> l3 : ox^0'=x^0, c^0'=1, oy^0'=y^0, c^0 <= 0, cost: 2
New rule:
l3 -> l3 : y^0'=-1+y^0, ox^0'=x^0, c^0'=1, oy^0'=-1+y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4

Applied chaining
First rule:
l3 -> l5 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
Second rule:
l5 -> l3 : -1+c^0 >= 0, cost: 2
New rule:
l3 -> l3 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ -1+c^0 >= 0 /\ -1+y^0 >= 0), cost: 4

Applied chaining
First rule:
l3 -> l5 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
Second rule:
l5 -> l3 : c^0 <= 0, cost: 2
New rule:
l3 -> l3 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4

Applied chaining
First rule:
l3 -> l5 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
Second rule:
l5 -> l3 : ox^0'=x^0, c^0'=1, oy^0'=y^0, c^0 <= 0, cost: 2
New rule:
l3 -> l3 : ox^0'=-1+x^0, x^0'=-1+x^0, c^0'=1, oy^0'=y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4

Applied deletion
Removed the following rules: 25 26 27 28 29

Eliminated locations on tree-shaped paths
Start location: l8
  30: l3 -> l3 : y^0'=-1+y^0, (-1+x^0 >= 0 /\ -1+c^0 >= 0 /\ -1+y^0 >= 0), cost: 4
  31: l3 -> l3 : y^0'=-1+y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4
  32: l3 -> l3 : y^0'=-1+y^0, ox^0'=x^0, c^0'=1, oy^0'=-1+y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4
  33: l3 -> l3 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ -1+c^0 >= 0 /\ -1+y^0 >= 0), cost: 4
  34: l3 -> l3 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4
  35: l3 -> l3 : ox^0'=-1+x^0, x^0'=-1+x^0, c^0'=1, oy^0'=y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4
  24: l8 -> l3 : c^0 <= 0, cost: 2


Applied acceleration
Original rule:
l3 -> l3 : y^0'=-1+y^0, (-1+x^0 >= 0 /\ -1+c^0 >= 0 /\ -1+y^0 >= 0), cost: 4
New rule:
l3 -> l3 : y^0'=y^0-n, (-1+x^0 >= 0 /\ y^0-n >= 0 /\ n >= 0 /\ -1+c^0 >= 0), cost: 4*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_BdBgCp.txt

Applied instantiation
Original rule:
l3 -> l3 : y^0'=y^0-n, (-1+x^0 >= 0 /\ y^0-n >= 0 /\ n >= 0 /\ -1+c^0 >= 0), cost: 4*n
New rule:
l3 -> l3 : y^0'=0, (0 >= 0 /\ y^0 >= 0 /\ -1+x^0 >= 0 /\ -1+c^0 >= 0), cost: 4*y^0

Applied acceleration
Original rule:
l3 -> l3 : y^0'=-1+y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4
New rule:
l3 -> l3 : y^0'=y^0-n0, (-1+x^0 >= 0 /\ y^0-n0 >= 0 /\ n0 >= 0 /\ -c^0 >= 0), cost: 4*n0
Sub-proof via acceration calculus written to file:///tmp/tmpnam_GNjiPM.txt

Applied instantiation
Original rule:
l3 -> l3 : y^0'=y^0-n0, (-1+x^0 >= 0 /\ y^0-n0 >= 0 /\ n0 >= 0 /\ -c^0 >= 0), cost: 4*n0
New rule:
l3 -> l3 : y^0'=0, (0 >= 0 /\ y^0 >= 0 /\ -1+x^0 >= 0 /\ -c^0 >= 0), cost: 4*y^0

Applied acceleration
Original rule:
l3 -> l3 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ -1+c^0 >= 0 /\ -1+y^0 >= 0), cost: 4
New rule:
l3 -> l3 : x^0'=-n2+x^0, (n2 >= 0 /\ -n2+x^0 >= 0 /\ -1+c^0 >= 0 /\ -1+y^0 >= 0), cost: 4*n2
Sub-proof via acceration calculus written to file:///tmp/tmpnam_lnnLJh.txt

Applied instantiation
Original rule:
l3 -> l3 : x^0'=-n2+x^0, (n2 >= 0 /\ -n2+x^0 >= 0 /\ -1+c^0 >= 0 /\ -1+y^0 >= 0), cost: 4*n2
New rule:
l3 -> l3 : x^0'=0, (0 >= 0 /\ x^0 >= 0 /\ -1+c^0 >= 0 /\ -1+y^0 >= 0), cost: 4*x^0

Applied acceleration
Original rule:
l3 -> l3 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4
New rule:
l3 -> l3 : x^0'=x^0-n3, (n3 >= 0 /\ -c^0 >= 0 /\ x^0-n3 >= 0 /\ -1+y^0 >= 0), cost: 4*n3
Sub-proof via acceration calculus written to file:///tmp/tmpnam_GJFBdF.txt

Applied instantiation
Original rule:
l3 -> l3 : x^0'=x^0-n3, (n3 >= 0 /\ -c^0 >= 0 /\ x^0-n3 >= 0 /\ -1+y^0 >= 0), cost: 4*n3
New rule:
l3 -> l3 : x^0'=0, (0 >= 0 /\ x^0 >= 0 /\ -c^0 >= 0 /\ -1+y^0 >= 0), cost: 4*x^0

Applied simplification
Original rule:
l3 -> l3 : y^0'=0, (0 >= 0 /\ y^0 >= 0 /\ -1+x^0 >= 0 /\ -1+c^0 >= 0), cost: 4*y^0
New rule:
l3 -> l3 : y^0'=0, (y^0 >= 0 /\ -1+x^0 >= 0 /\ -1+c^0 >= 0), cost: 4*y^0

Applied simplification
Original rule:
l3 -> l3 : y^0'=0, (0 >= 0 /\ y^0 >= 0 /\ -1+x^0 >= 0 /\ -c^0 >= 0), cost: 4*y^0
New rule:
l3 -> l3 : y^0'=0, (y^0 >= 0 /\ -1+x^0 >= 0 /\ c^0 <= 0), cost: 4*y^0

Applied simplification
Original rule:
l3 -> l3 : x^0'=0, (0 >= 0 /\ x^0 >= 0 /\ -1+c^0 >= 0 /\ -1+y^0 >= 0), cost: 4*x^0
New rule:
l3 -> l3 : x^0'=0, (x^0 >= 0 /\ -1+c^0 >= 0 /\ -1+y^0 >= 0), cost: 4*x^0

Applied simplification
Original rule:
l3 -> l3 : x^0'=0, (0 >= 0 /\ x^0 >= 0 /\ -c^0 >= 0 /\ -1+y^0 >= 0), cost: 4*x^0
New rule:
l3 -> l3 : x^0'=0, (x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4*x^0

Applied deletion
Removed the following rules: 30 31 33 34

Accelerated simple loops
Start location: l8
  32: l3 -> l3 : y^0'=-1+y^0, ox^0'=x^0, c^0'=1, oy^0'=-1+y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4
  35: l3 -> l3 : ox^0'=-1+x^0, x^0'=-1+x^0, c^0'=1, oy^0'=y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4
  40: l3 -> l3 : y^0'=0, (y^0 >= 0 /\ -1+x^0 >= 0 /\ -1+c^0 >= 0), cost: 4*y^0
  41: l3 -> l3 : y^0'=0, (y^0 >= 0 /\ -1+x^0 >= 0 /\ c^0 <= 0), cost: 4*y^0
  42: l3 -> l3 : x^0'=0, (x^0 >= 0 /\ -1+c^0 >= 0 /\ -1+y^0 >= 0), cost: 4*x^0
  43: l3 -> l3 : x^0'=0, (x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4*x^0
  24: l8 -> l3 : c^0 <= 0, cost: 2


Applied chaining
First rule:
l8 -> l3 : c^0 <= 0, cost: 2
Second rule:
l3 -> l3 : y^0'=-1+y^0, ox^0'=x^0, c^0'=1, oy^0'=-1+y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4
New rule:
l8 -> l3 : y^0'=-1+y^0, ox^0'=x^0, c^0'=1, oy^0'=-1+y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 6

Applied chaining
First rule:
l8 -> l3 : c^0 <= 0, cost: 2
Second rule:
l3 -> l3 : ox^0'=-1+x^0, x^0'=-1+x^0, c^0'=1, oy^0'=y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4
New rule:
l8 -> l3 : ox^0'=-1+x^0, x^0'=-1+x^0, c^0'=1, oy^0'=y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 6

Applied chaining
First rule:
l8 -> l3 : c^0 <= 0, cost: 2
Second rule:
l3 -> l3 : y^0'=0, (y^0 >= 0 /\ -1+x^0 >= 0 /\ c^0 <= 0), cost: 4*y^0
New rule:
l8 -> l3 : y^0'=0, (y^0 >= 0 /\ -1+x^0 >= 0 /\ c^0 <= 0), cost: 2+4*y^0

Applied chaining
First rule:
l8 -> l3 : c^0 <= 0, cost: 2
Second rule:
l3 -> l3 : x^0'=0, (x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 4*x^0
New rule:
l8 -> l3 : x^0'=0, (x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 2+4*x^0

Applied deletion
Removed the following rules: 32 35 40 41 42 43

Chained accelerated rules with incoming rules
Start location: l8
  24: l8 -> l3 : c^0 <= 0, cost: 2
  44: l8 -> l3 : y^0'=-1+y^0, ox^0'=x^0, c^0'=1, oy^0'=-1+y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 6
  45: l8 -> l3 : ox^0'=-1+x^0, x^0'=-1+x^0, c^0'=1, oy^0'=y^0, (-1+x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 6
  46: l8 -> l3 : y^0'=0, (y^0 >= 0 /\ -1+x^0 >= 0 /\ c^0 <= 0), cost: 2+4*y^0
  47: l8 -> l3 : x^0'=0, (x^0 >= 0 /\ c^0 <= 0 /\ -1+y^0 >= 0), cost: 2+4*x^0


Removed unreachable locations and irrelevant leafs
Start location: l8
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0