WORST_CASE(Omega(0),?)

Initial ITS
Start location: l4
   0: l0 -> l1 : x^0'=x^post0, y^0'=y^post0, (y^0-y^post0 == 0 /\ -x^0-y^0 <= 0 /\ -1-x^0+x^post0 == 0 /\ 1+x^0-y^0 <= 0), cost: 1
   1: l0 -> l1 : x^0'=x^post1, y^0'=y^post1, (1+x^0+y^0 <= 0 /\ -1+y^post1-y^0 == 0 /\ x^0-y^0 <= 0 /\ x^0-x^post1 == 0), cost: 1
   2: l0 -> l1 : x^0'=x^post2, y^0'=y^post2, (1-x^0+y^0 <= 0 /\ -y^post2+y^0 == 0 /\ -1+x^0+y^0 <= 0 /\ 1-x^0+x^post2 == 0), cost: 1
   3: l0 -> l1 : x^0'=x^post3, y^0'=y^post3, (2-x^0-y^0 <= 0 /\ x^0-x^post3 == 0 /\ 1-y^0+y^post3 == 0 /\ -x^0+y^0 <= 0), cost: 1
   4: l1 -> l2 : x^0'=x^post4, y^0'=y^post4, (x^0-x^post4 == 0 /\ 1+x^0 <= 0 /\ -y^post4+y^0 == 0), cost: 1
   5: l1 -> l2 : x^0'=x^post5, y^0'=y^post5, (1-x^0 <= 0 /\ y^0-y^post5 == 0 /\ x^0-x^post5 == 0), cost: 1
   6: l2 -> l0 : x^0'=x^post6, y^0'=y^post6, (-y^post6+y^0 == 0 /\ 1+y^0 <= 0 /\ x^0-x^post6 == 0), cost: 1
   7: l2 -> l0 : x^0'=x^post7, y^0'=y^post7, (x^0-x^post7 == 0 /\ 1-y^0 <= 0 /\ -y^post7+y^0 == 0), cost: 1
   8: l3 -> l1 : x^0'=x^post8, y^0'=y^post8, (x^0-x^post8 == 0 /\ y^0-y^post8 == 0), cost: 1
   9: l4 -> l3 : x^0'=x^post9, y^0'=y^post9, (-y^post9+y^0 == 0 /\ x^0-x^post9 == 0), cost: 1


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

Applied preprocessing
Original rule:
l0 -> l1 : x^0'=x^post1, y^0'=y^post1, (1+x^0+y^0 <= 0 /\ -1+y^post1-y^0 == 0 /\ x^0-y^0 <= 0 /\ x^0-x^post1 == 0), cost: 1
New rule:
l0 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ x^0-y^0 <= 0), cost: 1

Applied preprocessing
Original rule:
l0 -> l1 : x^0'=x^post2, y^0'=y^post2, (1-x^0+y^0 <= 0 /\ -y^post2+y^0 == 0 /\ -1+x^0+y^0 <= 0 /\ 1-x^0+x^post2 == 0), cost: 1
New rule:
l0 -> l1 : x^0'=-1+x^0, (1-x^0+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 1

Applied preprocessing
Original rule:
l0 -> l1 : x^0'=x^post3, y^0'=y^post3, (2-x^0-y^0 <= 0 /\ x^0-x^post3 == 0 /\ 1-y^0+y^post3 == 0 /\ -x^0+y^0 <= 0), cost: 1
New rule:
l0 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ -x^0+y^0 <= 0), cost: 1

Applied preprocessing
Original rule:
l1 -> l2 : x^0'=x^post4, y^0'=y^post4, (x^0-x^post4 == 0 /\ 1+x^0 <= 0 /\ -y^post4+y^0 == 0), cost: 1
New rule:
l1 -> l2 : 1+x^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l2 : x^0'=x^post5, y^0'=y^post5, (1-x^0 <= 0 /\ y^0-y^post5 == 0 /\ x^0-x^post5 == 0), cost: 1
New rule:
l1 -> l2 : -1+x^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : x^0'=x^post6, y^0'=y^post6, (-y^post6+y^0 == 0 /\ 1+y^0 <= 0 /\ x^0-x^post6 == 0), cost: 1
New rule:
l2 -> l0 : 1+y^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : x^0'=x^post7, y^0'=y^post7, (x^0-x^post7 == 0 /\ 1-y^0 <= 0 /\ -y^post7+y^0 == 0), cost: 1
New rule:
l2 -> l0 : -1+y^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l1 : x^0'=x^post8, y^0'=y^post8, (x^0-x^post8 == 0 /\ y^0-y^post8 == 0), cost: 1
New rule:
l3 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : x^0'=x^post9, y^0'=y^post9, (-y^post9+y^0 == 0 /\ x^0-x^post9 == 0), cost: 1
New rule:
l4 -> l3 : TRUE, cost: 1

Simplified rules
Start location: l4
  10: l0 -> l1 : x^0'=1+x^0, (-x^0-y^0 <= 0 /\ 1+x^0-y^0 <= 0), cost: 1
  11: l0 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ x^0-y^0 <= 0), cost: 1
  12: l0 -> l1 : x^0'=-1+x^0, (1-x^0+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 1
  13: l0 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ -x^0+y^0 <= 0), cost: 1
  14: l1 -> l2 : 1+x^0 <= 0, cost: 1
  15: l1 -> l2 : -1+x^0 >= 0, cost: 1
  16: l2 -> l0 : 1+y^0 <= 0, cost: 1
  17: l2 -> l0 : -1+y^0 >= 0, cost: 1
  18: l3 -> l1 : TRUE, cost: 1
  19: l4 -> l3 : TRUE, cost: 1


Eliminating location l3 by chaining:

Applied chaining
First rule:
l4 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l1 : TRUE, cost: 1
New rule:
l4 -> l1 : TRUE, cost: 2

Applied deletion
Removed the following rules: 18 19

Eliminated locations on linear paths
Start location: l4
  10: l0 -> l1 : x^0'=1+x^0, (-x^0-y^0 <= 0 /\ 1+x^0-y^0 <= 0), cost: 1
  11: l0 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ x^0-y^0 <= 0), cost: 1
  12: l0 -> l1 : x^0'=-1+x^0, (1-x^0+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 1
  13: l0 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ -x^0+y^0 <= 0), cost: 1
  14: l1 -> l2 : 1+x^0 <= 0, cost: 1
  15: l1 -> l2 : -1+x^0 >= 0, cost: 1
  16: l2 -> l0 : 1+y^0 <= 0, cost: 1
  17: l2 -> l0 : -1+y^0 >= 0, cost: 1
  20: l4 -> l1 : TRUE, cost: 2


Eliminating location l2 by chaining:

Applied chaining
First rule:
l1 -> l2 : 1+x^0 <= 0, cost: 1
Second rule:
l2 -> l0 : 1+y^0 <= 0, cost: 1
New rule:
l1 -> l0 : (1+x^0 <= 0 /\ 1+y^0 <= 0), cost: 2

Applied chaining
First rule:
l1 -> l2 : 1+x^0 <= 0, cost: 1
Second rule:
l2 -> l0 : -1+y^0 >= 0, cost: 1
New rule:
l1 -> l0 : (-1+y^0 >= 0 /\ 1+x^0 <= 0), cost: 2

Applied chaining
First rule:
l1 -> l2 : -1+x^0 >= 0, cost: 1
Second rule:
l2 -> l0 : 1+y^0 <= 0, cost: 1
New rule:
l1 -> l0 : (-1+x^0 >= 0 /\ 1+y^0 <= 0), cost: 2

Applied chaining
First rule:
l1 -> l2 : -1+x^0 >= 0, cost: 1
Second rule:
l2 -> l0 : -1+y^0 >= 0, cost: 1
New rule:
l1 -> l0 : (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2

Applied deletion
Removed the following rules: 14 15 16 17

Eliminated locations on tree-shaped paths
Start location: l4
  10: l0 -> l1 : x^0'=1+x^0, (-x^0-y^0 <= 0 /\ 1+x^0-y^0 <= 0), cost: 1
  11: l0 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ x^0-y^0 <= 0), cost: 1
  12: l0 -> l1 : x^0'=-1+x^0, (1-x^0+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 1
  13: l0 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ -x^0+y^0 <= 0), cost: 1
  21: l1 -> l0 : (1+x^0 <= 0 /\ 1+y^0 <= 0), cost: 2
  22: l1 -> l0 : (-1+y^0 >= 0 /\ 1+x^0 <= 0), cost: 2
  23: l1 -> l0 : (-1+x^0 >= 0 /\ 1+y^0 <= 0), cost: 2
  24: l1 -> l0 : (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
  20: l4 -> l1 : TRUE, cost: 2


Eliminating location l0 by chaining:

Applied chaining
First rule:
l1 -> l0 : (1+x^0 <= 0 /\ 1+y^0 <= 0), cost: 2
Second rule:
l0 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ x^0-y^0 <= 0), cost: 1
New rule:
l1 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ 1+x^0 <= 0 /\ 1+y^0 <= 0 /\ x^0-y^0 <= 0), cost: 3

Applied simplification
Original rule:
l1 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ 1+x^0 <= 0 /\ 1+y^0 <= 0 /\ x^0-y^0 <= 0), cost: 3
New rule:
l1 -> l1 : y^0'=1+y^0, (1+y^0 <= 0 /\ x^0-y^0 <= 0), cost: 3

Applied chaining
First rule:
l1 -> l0 : (1+x^0 <= 0 /\ 1+y^0 <= 0), cost: 2
Second rule:
l0 -> l1 : x^0'=-1+x^0, (1-x^0+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 1
New rule:
l1 -> l1 : x^0'=-1+x^0, (1-x^0+y^0 <= 0 /\ 1+x^0 <= 0 /\ 1+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 3

Applied simplification
Original rule:
l1 -> l1 : x^0'=-1+x^0, (1-x^0+y^0 <= 0 /\ 1+x^0 <= 0 /\ 1+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 3
New rule:
l1 -> l1 : x^0'=-1+x^0, (1-x^0+y^0 <= 0 /\ 1+x^0 <= 0), cost: 3

Applied chaining
First rule:
l1 -> l0 : (-1+y^0 >= 0 /\ 1+x^0 <= 0), cost: 2
Second rule:
l0 -> l1 : x^0'=1+x^0, (-x^0-y^0 <= 0 /\ 1+x^0-y^0 <= 0), cost: 1
New rule:
l1 -> l1 : x^0'=1+x^0, (-x^0-y^0 <= 0 /\ -1+y^0 >= 0 /\ 1+x^0 <= 0 /\ 1+x^0-y^0 <= 0), cost: 3

Applied simplification
Original rule:
l1 -> l1 : x^0'=1+x^0, (-x^0-y^0 <= 0 /\ -1+y^0 >= 0 /\ 1+x^0 <= 0 /\ 1+x^0-y^0 <= 0), cost: 3
New rule:
l1 -> l1 : x^0'=1+x^0, (-x^0-y^0 <= 0 /\ 1+x^0 <= 0), cost: 3

Applied chaining
First rule:
l1 -> l0 : (-1+y^0 >= 0 /\ 1+x^0 <= 0), cost: 2
Second rule:
l0 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ x^0-y^0 <= 0), cost: 1
New rule:
l1 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ -1+y^0 >= 0 /\ 1+x^0 <= 0 /\ x^0-y^0 <= 0), cost: 3

Applied simplification
Original rule:
l1 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ -1+y^0 >= 0 /\ 1+x^0 <= 0 /\ x^0-y^0 <= 0), cost: 3
New rule:
l1 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ -1+y^0 >= 0), cost: 3

Applied chaining
First rule:
l1 -> l0 : (-1+x^0 >= 0 /\ 1+y^0 <= 0), cost: 2
Second rule:
l0 -> l1 : x^0'=-1+x^0, (1-x^0+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 1
New rule:
l1 -> l1 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ 1-x^0+y^0 <= 0 /\ 1+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 3

Applied simplification
Original rule:
l1 -> l1 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ 1-x^0+y^0 <= 0 /\ 1+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 3
New rule:
l1 -> l1 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ 1+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 3

Applied chaining
First rule:
l1 -> l0 : (-1+x^0 >= 0 /\ 1+y^0 <= 0), cost: 2
Second rule:
l0 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ -x^0+y^0 <= 0), cost: 1
New rule:
l1 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ -1+x^0 >= 0 /\ -x^0+y^0 <= 0 /\ 1+y^0 <= 0), cost: 3

Applied simplification
Original rule:
l1 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ -1+x^0 >= 0 /\ -x^0+y^0 <= 0 /\ 1+y^0 <= 0), cost: 3
New rule:
l1 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ 1+y^0 <= 0), cost: 3

Applied chaining
First rule:
l1 -> l0 : (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
Second rule:
l0 -> l1 : x^0'=1+x^0, (-x^0-y^0 <= 0 /\ 1+x^0-y^0 <= 0), cost: 1
New rule:
l1 -> l1 : x^0'=1+x^0, (-1+x^0 >= 0 /\ -x^0-y^0 <= 0 /\ -1+y^0 >= 0 /\ 1+x^0-y^0 <= 0), cost: 3

Applied simplification
Original rule:
l1 -> l1 : x^0'=1+x^0, (-1+x^0 >= 0 /\ -x^0-y^0 <= 0 /\ -1+y^0 >= 0 /\ 1+x^0-y^0 <= 0), cost: 3
New rule:
l1 -> l1 : x^0'=1+x^0, (-1+x^0 >= 0 /\ 1+x^0-y^0 <= 0), cost: 3

Applied chaining
First rule:
l1 -> l0 : (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
Second rule:
l0 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ -x^0+y^0 <= 0), cost: 1
New rule:
l1 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ -1+x^0 >= 0 /\ -1+y^0 >= 0 /\ -x^0+y^0 <= 0), cost: 3

Applied simplification
Original rule:
l1 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ -1+x^0 >= 0 /\ -1+y^0 >= 0 /\ -x^0+y^0 <= 0), cost: 3
New rule:
l1 -> l1 : y^0'=-1+y^0, (-1+y^0 >= 0 /\ -x^0+y^0 <= 0), cost: 3

Applied deletion
Removed the following rules: 10 11 12 13 21 22 23 24

Eliminated locations on tree-shaped paths
Start location: l4
  25: l1 -> l1 : y^0'=1+y^0, (1+y^0 <= 0 /\ x^0-y^0 <= 0), cost: 3
  26: l1 -> l1 : x^0'=-1+x^0, (1-x^0+y^0 <= 0 /\ 1+x^0 <= 0), cost: 3
  27: l1 -> l1 : x^0'=1+x^0, (-x^0-y^0 <= 0 /\ 1+x^0 <= 0), cost: 3
  28: l1 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ -1+y^0 >= 0), cost: 3
  29: l1 -> l1 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ 1+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 3
  30: l1 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ 1+y^0 <= 0), cost: 3
  31: l1 -> l1 : x^0'=1+x^0, (-1+x^0 >= 0 /\ 1+x^0-y^0 <= 0), cost: 3
  32: l1 -> l1 : y^0'=-1+y^0, (-1+y^0 >= 0 /\ -x^0+y^0 <= 0), cost: 3
  20: l4 -> l1 : TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : y^0'=1+y^0, (1+y^0 <= 0 /\ x^0-y^0 <= 0), cost: 3
New rule:
l1 -> l1 : y^0'=n7+y^0, (n7 >= 0 /\ -n7-y^0 >= 0 /\ -x^0+y^0 >= 0), cost: 3*n7

Applied instantiation
Original rule:
l1 -> l1 : y^0'=n7+y^0, (n7 >= 0 /\ -n7-y^0 >= 0 /\ -x^0+y^0 >= 0), cost: 3*n7
New rule:
l1 -> l1 : y^0'=0, (0 >= 0 /\ -y^0 >= 0 /\ -x^0+y^0 >= 0), cost: -3*y^0

Applied acceleration
Original rule:
l1 -> l1 : x^0'=-1+x^0, (1-x^0+y^0 <= 0 /\ 1+x^0 <= 0), cost: 3
New rule:
l1 -> l1 : x^0'=x^0-n9, (-1-x^0 >= 0 /\ n9 >= 0 /\ x^0-y^0-n9 >= 0), cost: 3*n9

Applied instantiation
Original rule:
l1 -> l1 : x^0'=x^0-n9, (-1-x^0 >= 0 /\ n9 >= 0 /\ x^0-y^0-n9 >= 0), cost: 3*n9
New rule:
l1 -> l1 : x^0'=y^0, (0 >= 0 /\ -1-x^0 >= 0 /\ x^0-y^0 >= 0), cost: 3*x^0-3*y^0

Applied acceleration
Original rule:
l1 -> l1 : x^0'=1+x^0, (-x^0-y^0 <= 0 /\ 1+x^0 <= 0), cost: 3
New rule:
l1 -> l1 : x^0'=x^0+n11, (x^0+y^0 >= 0 /\ n11 >= 0 /\ -x^0-n11 >= 0), cost: 3*n11

Applied instantiation
Original rule:
l1 -> l1 : x^0'=x^0+n11, (x^0+y^0 >= 0 /\ n11 >= 0 /\ -x^0-n11 >= 0), cost: 3*n11
New rule:
l1 -> l1 : x^0'=0, (0 >= 0 /\ x^0+y^0 >= 0 /\ -x^0 >= 0), cost: -3*x^0

Applied acceleration
Original rule:
l1 -> l1 : y^0'=1+y^0, (1+x^0+y^0 <= 0 /\ -1+y^0 >= 0), cost: 3
New rule:
l1 -> l1 : y^0'=n13+y^0, (-x^0-n13-y^0 >= 0 /\ -1+y^0 >= 0 /\ n13 >= 0), cost: 3*n13

Applied instantiation
Original rule:
l1 -> l1 : y^0'=n13+y^0, (-x^0-n13-y^0 >= 0 /\ -1+y^0 >= 0 /\ n13 >= 0), cost: 3*n13
New rule:
l1 -> l1 : y^0'=-x^0, (0 >= 0 /\ -x^0-y^0 >= 0 /\ -1+y^0 >= 0), cost: -3*x^0-3*y^0

Applied acceleration
Original rule:
l1 -> l1 : x^0'=-1+x^0, (-1+x^0 >= 0 /\ 1+y^0 <= 0 /\ -1+x^0+y^0 <= 0), cost: 3
New rule:
l1 -> l1 : x^0'=x^0-n15, (x^0-n15 >= 0 /\ 1-x^0-y^0 >= 0 /\ -1-y^0 >= 0 /\ n15 >= 0), cost: 3*n15

Applied instantiation
Original rule:
l1 -> l1 : x^0'=x^0-n15, (x^0-n15 >= 0 /\ 1-x^0-y^0 >= 0 /\ -1-y^0 >= 0 /\ n15 >= 0), cost: 3*n15
New rule:
l1 -> l1 : x^0'=0, (0 >= 0 /\ x^0 >= 0 /\ 1-x^0-y^0 >= 0 /\ -1-y^0 >= 0), cost: 3*x^0

Applied acceleration
Original rule:
l1 -> l1 : y^0'=-1+y^0, (2-x^0-y^0 <= 0 /\ 1+y^0 <= 0), cost: 3
New rule:
l1 -> l1 : y^0'=-n17+y^0, (-1+x^0-n17+y^0 >= 0 /\ n17 >= 0 /\ -1-y^0 >= 0), cost: 3*n17

Applied instantiation
Original rule:
l1 -> l1 : y^0'=-n17+y^0, (-1+x^0-n17+y^0 >= 0 /\ n17 >= 0 /\ -1-y^0 >= 0), cost: 3*n17
New rule:
l1 -> l1 : y^0'=1-x^0, (0 >= 0 /\ -1-y^0 >= 0 /\ -1+x^0+y^0 >= 0), cost: -3+3*x^0+3*y^0

Applied acceleration
Original rule:
l1 -> l1 : x^0'=1+x^0, (-1+x^0 >= 0 /\ 1+x^0-y^0 <= 0), cost: 3
New rule:
l1 -> l1 : x^0'=x^0+n19, (-1+x^0 >= 0 /\ n19 >= 0 /\ -x^0-n19+y^0 >= 0), cost: 3*n19

Applied instantiation
Original rule:
l1 -> l1 : x^0'=x^0+n19, (-1+x^0 >= 0 /\ n19 >= 0 /\ -x^0-n19+y^0 >= 0), cost: 3*n19
New rule:
l1 -> l1 : x^0'=y^0, (0 >= 0 /\ -1+x^0 >= 0 /\ -x^0+y^0 >= 0), cost: -3*x^0+3*y^0

Applied acceleration
Original rule:
l1 -> l1 : y^0'=-1+y^0, (-1+y^0 >= 0 /\ -x^0+y^0 <= 0), cost: 3
New rule:
l1 -> l1 : y^0'=-n21+y^0, (-n21+y^0 >= 0 /\ n21 >= 0 /\ x^0-y^0 >= 0), cost: 3*n21

Applied instantiation
Original rule:
l1 -> l1 : y^0'=-n21+y^0, (-n21+y^0 >= 0 /\ n21 >= 0 /\ x^0-y^0 >= 0), cost: 3*n21
New rule:
l1 -> l1 : y^0'=0, (0 >= 0 /\ y^0 >= 0 /\ x^0-y^0 >= 0), cost: 3*y^0

Applied simplification
Original rule:
l1 -> l1 : y^0'=0, (0 >= 0 /\ -y^0 >= 0 /\ -x^0+y^0 >= 0), cost: -3*y^0
New rule:
l1 -> l1 : y^0'=0, (-x^0+y^0 >= 0 /\ y^0 <= 0), cost: -3*y^0

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

Applied simplification
Original rule:
l1 -> l1 : x^0'=0, (0 >= 0 /\ x^0+y^0 >= 0 /\ -x^0 >= 0), cost: -3*x^0
New rule:
l1 -> l1 : x^0'=0, (x^0 <= 0 /\ x^0+y^0 >= 0), cost: -3*x^0

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

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

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

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

Applied simplification
Original rule:
l1 -> l1 : y^0'=0, (0 >= 0 /\ y^0 >= 0 /\ x^0-y^0 >= 0), cost: 3*y^0
New rule:
l1 -> l1 : y^0'=0, (y^0 >= 0 /\ x^0-y^0 >= 0), cost: 3*y^0

Applied deletion
Removed the following rules: 25 26 27 28 29 30 31 32

Accelerated simple loops
Start location: l4
  41: l1 -> l1 : y^0'=0, (-x^0+y^0 >= 0 /\ y^0 <= 0), cost: -3*y^0
  42: l1 -> l1 : x^0'=y^0, (1+x^0 <= 0 /\ x^0-y^0 >= 0), cost: 3*x^0-3*y^0
  43: l1 -> l1 : x^0'=0, (x^0 <= 0 /\ x^0+y^0 >= 0), cost: -3*x^0
  44: l1 -> l1 : y^0'=-x^0, (-x^0-y^0 >= 0 /\ -1+y^0 >= 0), cost: -3*x^0-3*y^0
  45: l1 -> l1 : x^0'=0, (x^0 >= 0 /\ 1-x^0-y^0 >= 0 /\ -1-y^0 >= 0), cost: 3*x^0
  46: l1 -> l1 : y^0'=1-x^0, (1+y^0 <= 0 /\ -1+x^0+y^0 >= 0), cost: -3+3*x^0+3*y^0
  47: l1 -> l1 : x^0'=y^0, (-1+x^0 >= 0 /\ -x^0+y^0 >= 0), cost: -3*x^0+3*y^0
  48: l1 -> l1 : y^0'=0, (y^0 >= 0 /\ x^0-y^0 >= 0), cost: 3*y^0
  20: l4 -> l1 : TRUE, cost: 2


Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : y^0'=0, (-x^0+y^0 >= 0 /\ y^0 <= 0), cost: -3*y^0
New rule:
l4 -> l1 : y^0'=0, (-x^0+y^0 >= 0 /\ y^0 <= 0), cost: 2-3*y^0

Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : x^0'=y^0, (1+x^0 <= 0 /\ x^0-y^0 >= 0), cost: 3*x^0-3*y^0
New rule:
l4 -> l1 : x^0'=y^0, (1+x^0 <= 0 /\ x^0-y^0 >= 0), cost: 2+3*x^0-3*y^0

Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : x^0'=0, (x^0 <= 0 /\ x^0+y^0 >= 0), cost: -3*x^0
New rule:
l4 -> l1 : x^0'=0, (x^0 <= 0 /\ x^0+y^0 >= 0), cost: 2-3*x^0

Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : y^0'=-x^0, (-x^0-y^0 >= 0 /\ -1+y^0 >= 0), cost: -3*x^0-3*y^0
New rule:
l4 -> l1 : y^0'=-x^0, (-x^0-y^0 >= 0 /\ -1+y^0 >= 0), cost: 2-3*x^0-3*y^0

Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : x^0'=0, (x^0 >= 0 /\ 1-x^0-y^0 >= 0 /\ -1-y^0 >= 0), cost: 3*x^0
New rule:
l4 -> l1 : x^0'=0, (x^0 >= 0 /\ 1-x^0-y^0 >= 0 /\ -1-y^0 >= 0), cost: 2+3*x^0

Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : y^0'=1-x^0, (1+y^0 <= 0 /\ -1+x^0+y^0 >= 0), cost: -3+3*x^0+3*y^0
New rule:
l4 -> l1 : y^0'=1-x^0, (1+y^0 <= 0 /\ -1+x^0+y^0 >= 0), cost: -1+3*x^0+3*y^0

Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : x^0'=y^0, (-1+x^0 >= 0 /\ -x^0+y^0 >= 0), cost: -3*x^0+3*y^0
New rule:
l4 -> l1 : x^0'=y^0, (-1+x^0 >= 0 /\ -x^0+y^0 >= 0), cost: 2-3*x^0+3*y^0

Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : y^0'=0, (y^0 >= 0 /\ x^0-y^0 >= 0), cost: 3*y^0
New rule:
l4 -> l1 : y^0'=0, (y^0 >= 0 /\ x^0-y^0 >= 0), cost: 2+3*y^0

Applied deletion
Removed the following rules: 41 42 43 44 45 46 47 48

Chained accelerated rules with incoming rules
Start location: l4
  20: l4 -> l1 : TRUE, cost: 2
  49: l4 -> l1 : y^0'=0, (-x^0+y^0 >= 0 /\ y^0 <= 0), cost: 2-3*y^0
  50: l4 -> l1 : x^0'=y^0, (1+x^0 <= 0 /\ x^0-y^0 >= 0), cost: 2+3*x^0-3*y^0
  51: l4 -> l1 : x^0'=0, (x^0 <= 0 /\ x^0+y^0 >= 0), cost: 2-3*x^0
  52: l4 -> l1 : y^0'=-x^0, (-x^0-y^0 >= 0 /\ -1+y^0 >= 0), cost: 2-3*x^0-3*y^0
  53: l4 -> l1 : x^0'=0, (x^0 >= 0 /\ 1-x^0-y^0 >= 0 /\ -1-y^0 >= 0), cost: 2+3*x^0
  54: l4 -> l1 : y^0'=1-x^0, (1+y^0 <= 0 /\ -1+x^0+y^0 >= 0), cost: -1+3*x^0+3*y^0
  55: l4 -> l1 : x^0'=y^0, (-1+x^0 >= 0 /\ -x^0+y^0 >= 0), cost: 2-3*x^0+3*y^0
  56: l4 -> l1 : y^0'=0, (y^0 >= 0 /\ x^0-y^0 >= 0), cost: 2+3*y^0


Removed unreachable locations and irrelevant leafs
Start location: l4
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0