WORST_CASE(Omega(0),?)

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


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

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

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

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

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

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

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

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

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

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

Simplified rules
Start location: l4
  10: l0 -> l1 : x^0'=1+x^0, (1-y^0+x^0 <= 0 /\ -y^0-x^0 <= 0), cost: 1
  11: l0 -> l1 : y^0'=1+y^0, (-y^0+x^0 <= 0 /\ 1+y^0+x^0 <= 0), cost: 1
  12: l0 -> l1 : x^0'=-1+x^0, (1+y^0-x^0 <= 0 /\ -1+y^0+x^0 <= 0), cost: 1
  13: l0 -> l1 : y^0'=-1+y^0, (y^0-x^0 <= 0 /\ 2-y^0-x^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, (1-y^0+x^0 <= 0 /\ -y^0-x^0 <= 0), cost: 1
  11: l0 -> l1 : y^0'=1+y^0, (-y^0+x^0 <= 0 /\ 1+y^0+x^0 <= 0), cost: 1
  12: l0 -> l1 : x^0'=-1+x^0, (1+y^0-x^0 <= 0 /\ -1+y^0+x^0 <= 0), cost: 1
  13: l0 -> l1 : y^0'=-1+y^0, (y^0-x^0 <= 0 /\ 2-y^0-x^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+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+y^0 >= 0 /\ -1+x^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, (1-y^0+x^0 <= 0 /\ -y^0-x^0 <= 0), cost: 1
  11: l0 -> l1 : y^0'=1+y^0, (-y^0+x^0 <= 0 /\ 1+y^0+x^0 <= 0), cost: 1
  12: l0 -> l1 : x^0'=-1+x^0, (1+y^0-x^0 <= 0 /\ -1+y^0+x^0 <= 0), cost: 1
  13: l0 -> l1 : y^0'=-1+y^0, (y^0-x^0 <= 0 /\ 2-y^0-x^0 <= 0), cost: 1
  21: l1 -> l0 : (1+x^0 <= 0 /\ 1+y^0 <= 0), cost: 2
  22: l1 -> l0 : (1+x^0 <= 0 /\ -1+y^0 >= 0), cost: 2
  23: l1 -> l0 : (1+y^0 <= 0 /\ -1+x^0 >= 0), cost: 2
  24: l1 -> l0 : (-1+y^0 >= 0 /\ -1+x^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, (-y^0+x^0 <= 0 /\ 1+y^0+x^0 <= 0), cost: 1
New rule:
l1 -> l1 : y^0'=1+y^0, (1+x^0 <= 0 /\ 1+y^0 <= 0 /\ -y^0+x^0 <= 0 /\ 1+y^0+x^0 <= 0), cost: 3

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

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

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

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

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

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

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

Applied simplification
Original rule:
l1 -> l1 : y^0'=-1+y^0, (y^0-x^0 <= 0 /\ -1+y^0 >= 0 /\ 2-y^0-x^0 <= 0 /\ -1+x^0 >= 0), cost: 3
New rule:
l1 -> l1 : y^0'=-1+y^0, (y^0-x^0 <= 0 /\ -1+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 /\ -y^0+x^0 <= 0), cost: 3
  26: l1 -> l1 : x^0'=-1+x^0, (1+x^0 <= 0 /\ 1+y^0-x^0 <= 0), cost: 3
  27: l1 -> l1 : x^0'=1+x^0, (1+x^0 <= 0 /\ -y^0-x^0 <= 0), cost: 3
  28: l1 -> l1 : y^0'=1+y^0, (-1+y^0 >= 0 /\ 1+y^0+x^0 <= 0), cost: 3
  29: l1 -> l1 : x^0'=-1+x^0, (-1+y^0+x^0 <= 0 /\ 1+y^0 <= 0 /\ -1+x^0 >= 0), cost: 3
  30: l1 -> l1 : y^0'=-1+y^0, (1+y^0 <= 0 /\ 2-y^0-x^0 <= 0), cost: 3
  31: l1 -> l1 : x^0'=1+x^0, (1-y^0+x^0 <= 0 /\ -1+x^0 >= 0), cost: 3
  32: l1 -> l1 : y^0'=-1+y^0, (y^0-x^0 <= 0 /\ -1+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 /\ -y^0+x^0 <= 0), cost: 3
New rule:
l1 -> l1 : y^0'=y^0+n, (y^0-x^0 >= 0 /\ n >= 0 /\ -y^0-n >= 0), cost: 3*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_aLElDL.txt

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

Applied acceleration
Original rule:
l1 -> l1 : x^0'=-1+x^0, (1+x^0 <= 0 /\ 1+y^0-x^0 <= 0), cost: 3
New rule:
l1 -> l1 : x^0'=x^0-n0, (-1-x^0 >= 0 /\ -y^0+x^0-n0 >= 0 /\ n0 >= 0), cost: 3*n0
Sub-proof via acceration calculus written to file:///tmp/tmpnam_fGDCpF.txt

Applied instantiation
Original rule:
l1 -> l1 : x^0'=x^0-n0, (-1-x^0 >= 0 /\ -y^0+x^0-n0 >= 0 /\ n0 >= 0), cost: 3*n0
New rule:
l1 -> l1 : x^0'=y^0, (0 >= 0 /\ -1-x^0 >= 0 /\ -y^0+x^0 >= 0), cost: -3*y^0+3*x^0

Applied acceleration
Original rule:
l1 -> l1 : x^0'=1+x^0, (1+x^0 <= 0 /\ -y^0-x^0 <= 0), cost: 3
New rule:
l1 -> l1 : x^0'=x^0+n1, (-x^0-n1 >= 0 /\ n1 >= 0 /\ y^0+x^0 >= 0), cost: 3*n1
Sub-proof via acceration calculus written to file:///tmp/tmpnam_AcGcfO.txt

Applied instantiation
Original rule:
l1 -> l1 : x^0'=x^0+n1, (-x^0-n1 >= 0 /\ n1 >= 0 /\ y^0+x^0 >= 0), cost: 3*n1
New rule:
l1 -> l1 : x^0'=0, (0 >= 0 /\ -x^0 >= 0 /\ y^0+x^0 >= 0), cost: -3*x^0

Applied acceleration
Original rule:
l1 -> l1 : y^0'=1+y^0, (-1+y^0 >= 0 /\ 1+y^0+x^0 <= 0), cost: 3
New rule:
l1 -> l1 : y^0'=n2+y^0, (n2 >= 0 /\ -n2-y^0-x^0 >= 0 /\ -1+y^0 >= 0), cost: 3*n2
Sub-proof via acceration calculus written to file:///tmp/tmpnam_cMgEOP.txt

Applied instantiation
Original rule:
l1 -> l1 : y^0'=n2+y^0, (n2 >= 0 /\ -n2-y^0-x^0 >= 0 /\ -1+y^0 >= 0), cost: 3*n2
New rule:
l1 -> l1 : y^0'=-x^0, (0 >= 0 /\ -1+y^0 >= 0 /\ -y^0-x^0 >= 0), cost: -3*y^0-3*x^0

Applied acceleration
Original rule:
l1 -> l1 : x^0'=-1+x^0, (-1+y^0+x^0 <= 0 /\ 1+y^0 <= 0 /\ -1+x^0 >= 0), cost: 3
New rule:
l1 -> l1 : x^0'=-n3+x^0, (-1-y^0 >= 0 /\ n3 >= 0 /\ -n3+x^0 >= 0 /\ 1-y^0-x^0 >= 0), cost: 3*n3
Sub-proof via acceration calculus written to file:///tmp/tmpnam_CfLcoe.txt

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

Applied acceleration
Original rule:
l1 -> l1 : y^0'=-1+y^0, (1+y^0 <= 0 /\ 2-y^0-x^0 <= 0), cost: 3
New rule:
l1 -> l1 : y^0'=y^0-n4, (-1-y^0 >= 0 /\ -1+y^0-n4+x^0 >= 0 /\ n4 >= 0), cost: 3*n4
Sub-proof via acceration calculus written to file:///tmp/tmpnam_LHAhaD.txt

Applied instantiation
Original rule:
l1 -> l1 : y^0'=y^0-n4, (-1-y^0 >= 0 /\ -1+y^0-n4+x^0 >= 0 /\ n4 >= 0), cost: 3*n4
New rule:
l1 -> l1 : y^0'=1-x^0, (0 >= 0 /\ -1+y^0+x^0 >= 0 /\ -1-y^0 >= 0), cost: -3+3*y^0+3*x^0

Applied acceleration
Original rule:
l1 -> l1 : x^0'=1+x^0, (1-y^0+x^0 <= 0 /\ -1+x^0 >= 0), cost: 3
New rule:
l1 -> l1 : x^0'=n5+x^0, (n5 >= 0 /\ y^0-n5-x^0 >= 0 /\ -1+x^0 >= 0), cost: 3*n5
Sub-proof via acceration calculus written to file:///tmp/tmpnam_ONaeND.txt

Applied instantiation
Original rule:
l1 -> l1 : x^0'=n5+x^0, (n5 >= 0 /\ y^0-n5-x^0 >= 0 /\ -1+x^0 >= 0), cost: 3*n5
New rule:
l1 -> l1 : x^0'=y^0, (0 >= 0 /\ y^0-x^0 >= 0 /\ -1+x^0 >= 0), cost: 3*y^0-3*x^0

Applied acceleration
Original rule:
l1 -> l1 : y^0'=-1+y^0, (y^0-x^0 <= 0 /\ -1+y^0 >= 0), cost: 3
New rule:
l1 -> l1 : y^0'=y^0-n6, (-y^0+x^0 >= 0 /\ y^0-n6 >= 0 /\ n6 >= 0), cost: 3*n6
Sub-proof via acceration calculus written to file:///tmp/tmpnam_NIonip.txt

Applied instantiation
Original rule:
l1 -> l1 : y^0'=y^0-n6, (-y^0+x^0 >= 0 /\ y^0-n6 >= 0 /\ n6 >= 0), cost: 3*n6
New rule:
l1 -> l1 : y^0'=0, (0 >= 0 /\ y^0 >= 0 /\ -y^0+x^0 >= 0), cost: 3*y^0

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

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

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

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

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

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

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

Applied simplification
Original rule:
l1 -> l1 : y^0'=0, (0 >= 0 /\ y^0 >= 0 /\ -y^0+x^0 >= 0), cost: 3*y^0
New rule:
l1 -> l1 : y^0'=0, (y^0 >= 0 /\ -y^0+x^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, (y^0 <= 0 /\ y^0-x^0 >= 0), cost: -3*y^0
  42: l1 -> l1 : x^0'=y^0, (1+x^0 <= 0 /\ -y^0+x^0 >= 0), cost: -3*y^0+3*x^0
  43: l1 -> l1 : x^0'=0, (x^0 <= 0 /\ y^0+x^0 >= 0), cost: -3*x^0
  44: l1 -> l1 : y^0'=-x^0, (-1+y^0 >= 0 /\ -y^0-x^0 >= 0), cost: -3*y^0-3*x^0
  45: l1 -> l1 : x^0'=0, (1+y^0 <= 0 /\ x^0 >= 0 /\ 1-y^0-x^0 >= 0), cost: 3*x^0
  46: l1 -> l1 : y^0'=1-x^0, (-1+y^0+x^0 >= 0 /\ 1+y^0 <= 0), cost: -3+3*y^0+3*x^0
  47: l1 -> l1 : x^0'=y^0, (y^0-x^0 >= 0 /\ -1+x^0 >= 0), cost: 3*y^0-3*x^0
  48: l1 -> l1 : y^0'=0, (y^0 >= 0 /\ -y^0+x^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, (y^0 <= 0 /\ y^0-x^0 >= 0), cost: -3*y^0
New rule:
l4 -> l1 : y^0'=0, (y^0 <= 0 /\ y^0-x^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 /\ -y^0+x^0 >= 0), cost: -3*y^0+3*x^0
New rule:
l4 -> l1 : x^0'=y^0, (1+x^0 <= 0 /\ -y^0+x^0 >= 0), cost: 2-3*y^0+3*x^0

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

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

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

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

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