WORST_CASE(Omega(0),?)

Initial ITS
Start location: l5
   0: l0 -> l1 : x^0'=x^post0, y^0'=y^post0, (y^0-y^post0 == 0 /\ x^0-x^post0 == 0), cost: 1
   1: l1 -> l3 : x^0'=x^post1, y^0'=y^post1, (-y^post1+y^0 == 0 /\ 1-x^0 <= 0 /\ x^0-x^post1 == 0), cost: 1
   2: l3 -> l4 : x^0'=x^post2, y^0'=y^post2, (-y^post2+y^0 == 0 /\ x^0-x^post2 == 0 /\ 1+y^0 <= 0), cost: 1
   3: l3 -> l4 : x^0'=x^post3, y^0'=y^post3, (x^0-x^post3 == 0 /\ 1-y^0 <= 0 /\ y^0-y^post3 == 0), cost: 1
   4: l4 -> l2 : x^0'=x^post4, y^0'=y^post4, (-x^0-y^0+x^post4 == 0 /\ -y^post4+y^0 == 0), cost: 1
   5: l2 -> l1 : x^0'=x^post5, y^0'=y^post5, (y^0-y^post5 == 0 /\ x^0-x^post5 == 0), cost: 1
   6: l5 -> l0 : x^0'=x^post6, y^0'=y^post6, (-y^post6+y^0 == 0 /\ x^0-x^post6 == 0), cost: 1


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

Applied preprocessing
Original rule:
l1 -> l3 : x^0'=x^post1, y^0'=y^post1, (-y^post1+y^0 == 0 /\ 1-x^0 <= 0 /\ x^0-x^post1 == 0), cost: 1
New rule:
l1 -> l3 : -1+x^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l4 : x^0'=x^post2, y^0'=y^post2, (-y^post2+y^0 == 0 /\ x^0-x^post2 == 0 /\ 1+y^0 <= 0), cost: 1
New rule:
l3 -> l4 : 1+y^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l4 : x^0'=x^post3, y^0'=y^post3, (x^0-x^post3 == 0 /\ 1-y^0 <= 0 /\ y^0-y^post3 == 0), cost: 1
New rule:
l3 -> l4 : -1+y^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l2 : x^0'=x^post4, y^0'=y^post4, (-x^0-y^0+x^post4 == 0 /\ -y^post4+y^0 == 0), cost: 1
New rule:
l4 -> l2 : x^0'=x^0+y^0, TRUE, cost: 1

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

Applied preprocessing
Original rule:
l5 -> l0 : x^0'=x^post6, y^0'=y^post6, (-y^post6+y^0 == 0 /\ x^0-x^post6 == 0), cost: 1
New rule:
l5 -> l0 : TRUE, cost: 1

Simplified rules
Start location: l5
   7: l0 -> l1 : TRUE, cost: 1
   8: l1 -> l3 : -1+x^0 >= 0, cost: 1
   9: l3 -> l4 : 1+y^0 <= 0, cost: 1
  10: l3 -> l4 : -1+y^0 >= 0, cost: 1
  11: l4 -> l2 : x^0'=x^0+y^0, TRUE, cost: 1
  12: l2 -> l1 : TRUE, cost: 1
  13: l5 -> l0 : TRUE, cost: 1


Eliminating location l0 by chaining:

Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 1
Second rule:
l0 -> l1 : TRUE, cost: 1
New rule:
l5 -> l1 : TRUE, cost: 2

Applied deletion
Removed the following rules: 7 13

Eliminating location l2 by chaining:

Applied chaining
First rule:
l4 -> l2 : x^0'=x^0+y^0, TRUE, cost: 1
Second rule:
l2 -> l1 : TRUE, cost: 1
New rule:
l4 -> l1 : x^0'=x^0+y^0, TRUE, cost: 2

Applied deletion
Removed the following rules: 11 12

Eliminated locations on linear paths
Start location: l5
   8: l1 -> l3 : -1+x^0 >= 0, cost: 1
   9: l3 -> l4 : 1+y^0 <= 0, cost: 1
  10: l3 -> l4 : -1+y^0 >= 0, cost: 1
  15: l4 -> l1 : x^0'=x^0+y^0, TRUE, cost: 2
  14: l5 -> l1 : TRUE, cost: 2


Eliminating location l3 by chaining:

Applied chaining
First rule:
l1 -> l3 : -1+x^0 >= 0, cost: 1
Second rule:
l3 -> l4 : 1+y^0 <= 0, cost: 1
New rule:
l1 -> l4 : (-1+x^0 >= 0 /\ 1+y^0 <= 0), cost: 2

Applied chaining
First rule:
l1 -> l3 : -1+x^0 >= 0, cost: 1
Second rule:
l3 -> l4 : -1+y^0 >= 0, cost: 1
New rule:
l1 -> l4 : (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2

Applied deletion
Removed the following rules: 8 9 10

Eliminated locations on tree-shaped paths
Start location: l5
  16: l1 -> l4 : (-1+x^0 >= 0 /\ 1+y^0 <= 0), cost: 2
  17: l1 -> l4 : (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
  15: l4 -> l1 : x^0'=x^0+y^0, TRUE, cost: 2
  14: l5 -> l1 : TRUE, cost: 2


Applied merging
first rule:
l1 -> l4 : (-1+x^0 >= 0 /\ 1+y^0 <= 0), cost: 2
second rule:
l1 -> l4 : (-1+x^0 >= 0 /\ -1+y^0 >= 0), cost: 2
new rule:
l1 -> l4 : ((-1+x^0 >= 0 /\ 1+y^0 <= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0)), cost: 2

Merged rules
Start location: l5
  18: l1 -> l4 : ((-1+x^0 >= 0 /\ 1+y^0 <= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0)), cost: 2
  15: l4 -> l1 : x^0'=x^0+y^0, TRUE, cost: 2
  14: l5 -> l1 : TRUE, cost: 2


Eliminating location l4 by chaining:

Applied chaining
First rule:
l1 -> l4 : ((-1+x^0 >= 0 /\ 1+y^0 <= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0)), cost: 2
Second rule:
l4 -> l1 : x^0'=x^0+y^0, TRUE, cost: 2
New rule:
l1 -> l1 : x^0'=x^0+y^0, ((-1+x^0 >= 0 /\ 1+y^0 <= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0)), cost: 4

Applied simplification
Original rule:
l1 -> l1 : x^0'=x^0+y^0, ((-1+x^0 >= 0 /\ 1+y^0 <= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0)), cost: 4
New rule:
l1 -> l1 : x^0'=x^0+y^0, ((-1+x^0 >= 0 /\ -1+y^0 >= 0) \/ (-1+x^0 >= 0 /\ 1+y^0 <= 0)), cost: 4

Applied deletion
Removed the following rules: 15 18

Eliminated locations on linear paths
Start location: l5
  19: l1 -> l1 : x^0'=x^0+y^0, ((-1+x^0 >= 0 /\ -1+y^0 >= 0) \/ (-1+x^0 >= 0 /\ 1+y^0 <= 0)), cost: 4
  14: l5 -> l1 : TRUE, cost: 2


Applied simplification
Original rule:
l1 -> l1 : x^0'=x^0+y^0, ((-1+x^0 >= 0 /\ -1+y^0 >= 0) \/ (-1+x^0 >= 0 /\ 1+y^0 <= 0)), cost: 4
New rule:
l1 -> l1 : x^0'=x^0+y^0, ((-1+x^0 >= 0 /\ 1+y^0 <= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0)), cost: 4

Simplified simple loops
Start location: l5
  20: l1 -> l1 : x^0'=x^0+y^0, ((-1+x^0 >= 0 /\ 1+y^0 <= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0)), cost: 4
  14: l5 -> l1 : TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : x^0'=x^0+y^0, ((-1+x^0 >= 0 /\ 1+y^0 <= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0)), cost: 4
New rule:
l1 -> l1 : x^0'=x^0+n0*y^0, (n0 >= 0 /\ ((-1+y^0 >= 0 /\ ((-1+x^0 >= 0 /\ -1+y^0 >= 0) \/ (-1+x^0 >= 0 /\ -1+x^0+y^0*(-1+n0) >= 0))) \/ (-1-y^0 >= 0 /\ ((-1+x^0 >= 0 /\ -1+y^0 >= 0) \/ (-1+x^0 >= 0 /\ -1+x^0+y^0*(-1+n0) >= 0))))), cost: 4*n0

Applied simplification
Original rule:
l1 -> l1 : x^0'=x^0+n0*y^0, (n0 >= 0 /\ ((-1+y^0 >= 0 /\ ((-1+x^0 >= 0 /\ -1+y^0 >= 0) \/ (-1+x^0 >= 0 /\ -1+x^0+y^0*(-1+n0) >= 0))) \/ (-1-y^0 >= 0 /\ ((-1+x^0 >= 0 /\ -1+y^0 >= 0) \/ (-1+x^0 >= 0 /\ -1+x^0+y^0*(-1+n0) >= 0))))), cost: 4*n0
New rule:
l1 -> l1 : x^0'=x^0+n0*y^0, (n0 >= 0 /\ ((-1+x^0 >= 0 /\ -1+y^0 >= 0) \/ (1+y^0 <= 0 /\ ((-1+x^0 >= 0 /\ -1+x^0+y^0*(-1+n0) >= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0))))), cost: 4*n0

Applied deletion
Removed the following rules: 20

Accelerated simple loops
Start location: l5
  22: l1 -> l1 : x^0'=x^0+n0*y^0, (n0 >= 0 /\ ((-1+x^0 >= 0 /\ -1+y^0 >= 0) \/ (1+y^0 <= 0 /\ ((-1+x^0 >= 0 /\ -1+x^0+y^0*(-1+n0) >= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0))))), cost: 4*n0
  14: l5 -> l1 : TRUE, cost: 2


Applied chaining
First rule:
l5 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : x^0'=x^0+n0*y^0, (n0 >= 0 /\ ((-1+x^0 >= 0 /\ -1+y^0 >= 0) \/ (1+y^0 <= 0 /\ ((-1+x^0 >= 0 /\ -1+x^0+y^0*(-1+n0) >= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0))))), cost: 4*n0
New rule:
l5 -> l1 : x^0'=x^0+n0*y^0, (n0 >= 0 /\ ((-1+x^0 >= 0 /\ 1+y^0 <= 0 /\ -1+x^0+y^0*(-1+n0) >= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0))), cost: 2+4*n0

Applied deletion
Removed the following rules: 22

Chained accelerated rules with incoming rules
Start location: l5
  14: l5 -> l1 : TRUE, cost: 2
  23: l5 -> l1 : x^0'=x^0+n0*y^0, (n0 >= 0 /\ ((-1+x^0 >= 0 /\ 1+y^0 <= 0 /\ -1+x^0+y^0*(-1+n0) >= 0) \/ (-1+x^0 >= 0 /\ -1+y^0 >= 0))), cost: 2+4*n0


Removed unreachable locations and irrelevant leafs
Start location: l5
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0