WORST_CASE(Omega(0),?)

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


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

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

Applied preprocessing
Original rule:
l1 -> l2 : x^0'=x^post2, y^0'=y^post2, (1-y^0 <= 0 /\ x^0-x^post2 == 0 /\ 1+y^post2-y^0 == 0), cost: 1
New rule:
l1 -> l2 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l1 : x^0'=x^post3, y^0'=y^post3, (x^0-x^post3 == 0 /\ y^0-y^post3 == 0), cost: 1
New rule:
l2 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l0 : x^0'=x^post4, y^0'=y^post4, (x^0-x^post4 == 0 /\ -y^post4+y^0 == 0), cost: 1
New rule:
l3 -> l0 : TRUE, cost: 1

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

Simplified rules
Start location: l4
   6: l0 -> l1 : y^0'=x^0, -1+x^0 >= 0, cost: 1
   7: l1 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, y^0 <= 0, cost: 1
   8: l1 -> l2 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 1
   9: l2 -> l1 : TRUE, cost: 1
  10: l3 -> l0 : TRUE, cost: 1
  11: l4 -> l3 : TRUE, cost: 1


Eliminating location l3 by chaining:

Applied chaining
First rule:
l4 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l0 : TRUE, cost: 1
New rule:
l4 -> l0 : TRUE, cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminating location l2 by chaining:

Applied chaining
First rule:
l1 -> l2 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 1
Second rule:
l2 -> l1 : TRUE, cost: 1
New rule:
l1 -> l1 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 8 9

Eliminated locations on linear paths
Start location: l4
   6: l0 -> l1 : y^0'=x^0, -1+x^0 >= 0, cost: 1
   7: l1 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, y^0 <= 0, cost: 1
  13: l1 -> l1 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 2
  12: l4 -> l0 : TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : y^0'=-1+y^0, -1+y^0 >= 0, cost: 2
New rule:
l1 -> l1 : y^0'=-n0+y^0, (n0 >= 0 /\ -n0+y^0 >= 0), cost: 2*n0

Applied instantiation
Original rule:
l1 -> l1 : y^0'=-n0+y^0, (n0 >= 0 /\ -n0+y^0 >= 0), cost: 2*n0
New rule:
l1 -> l1 : y^0'=0, (0 >= 0 /\ y^0 >= 0), cost: 2*y^0

Applied simplification
Original rule:
l1 -> l1 : y^0'=0, (0 >= 0 /\ y^0 >= 0), cost: 2*y^0
New rule:
l1 -> l1 : y^0'=0, y^0 >= 0, cost: 2*y^0

Applied deletion
Removed the following rules: 13

Accelerated simple loops
Start location: l4
   6: l0 -> l1 : y^0'=x^0, -1+x^0 >= 0, cost: 1
   7: l1 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, y^0 <= 0, cost: 1
  15: l1 -> l1 : y^0'=0, y^0 >= 0, cost: 2*y^0
  12: l4 -> l0 : TRUE, cost: 2


Applied chaining
First rule:
l0 -> l1 : y^0'=x^0, -1+x^0 >= 0, cost: 1
Second rule:
l1 -> l1 : y^0'=0, y^0 >= 0, cost: 2*y^0
New rule:
l0 -> l1 : y^0'=0, -1+x^0 >= 0, cost: 1+2*x^0

Applied deletion
Removed the following rules: 15

Chained accelerated rules with incoming rules
Start location: l4
   6: l0 -> l1 : y^0'=x^0, -1+x^0 >= 0, cost: 1
  16: l0 -> l1 : y^0'=0, -1+x^0 >= 0, cost: 1+2*x^0
   7: l1 -> l0 : x^0'=-1+x^0, y^0'=1+y^0, y^0 <= 0, cost: 1
  12: l4 -> l0 : TRUE, cost: 2


Eliminating location l1 by chaining:

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

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

Applied deletion
Removed the following rules: 6 7 16

Eliminated locations on tree-shaped paths
Start location: l4
  17: l0 -> l0 : x^0'=-1+x^0, y^0'=1, -1+x^0 >= 0, cost: 2+2*x^0
  12: l4 -> l0 : TRUE, cost: 2


Applied acceleration
Original rule:
l0 -> l0 : x^0'=-1+x^0, y^0'=1, -1+x^0 >= 0, cost: 2+2*x^0
New rule:
l0 -> l0 : x^0'=x^0-n3, y^0'=1, (x^0-n3 >= 0 /\ -1+n3 >= 0), cost: -n3^2+3*n3+2*x^0*n3

Applied instantiation
Original rule:
l0 -> l0 : x^0'=x^0-n3, y^0'=1, (x^0-n3 >= 0 /\ -1+n3 >= 0), cost: -n3^2+3*n3+2*x^0*n3
New rule:
l0 -> l0 : x^0'=0, y^0'=1, (0 >= 0 /\ -1+x^0 >= 0), cost: 3*x^0+x^0^2

Applied simplification
Original rule:
l0 -> l0 : x^0'=0, y^0'=1, (0 >= 0 /\ -1+x^0 >= 0), cost: 3*x^0+x^0^2
New rule:
l0 -> l0 : x^0'=0, y^0'=1, -1+x^0 >= 0, cost: 3*x^0+x^0^2

Applied deletion
Removed the following rules: 17

Accelerated simple loops
Start location: l4
  19: l0 -> l0 : x^0'=0, y^0'=1, -1+x^0 >= 0, cost: 3*x^0+x^0^2
  12: l4 -> l0 : TRUE, cost: 2


Applied chaining
First rule:
l4 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=0, y^0'=1, -1+x^0 >= 0, cost: 3*x^0+x^0^2
New rule:
l4 -> l0 : x^0'=0, y^0'=1, -1+x^0 >= 0, cost: 2+3*x^0+x^0^2

Applied deletion
Removed the following rules: 19

Chained accelerated rules with incoming rules
Start location: l4
  12: l4 -> l0 : TRUE, cost: 2
  20: l4 -> l0 : x^0'=0, y^0'=1, -1+x^0 >= 0, cost: 2+3*x^0+x^0^2


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