WORST_CASE(Omega(0),?)

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


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

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

Applied preprocessing
Original rule:
l2 -> l0 : x^0'=x^post2, y^0'=y^post2, (-y^post2+y^0 == 0 /\ x^0-x^post2 == 0), cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : x^0'=x^post3, y^0'=y^post3, (x^0-x^post3 == 0 /\ y^0-y^post3 == 0), cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Simplified rules
Start location: l3
   4: l0 -> l1 : x^0'=1+x^0, -x^0+y^0 == 0, cost: 1
   5: l1 -> l0 : TRUE, cost: 1
   6: l2 -> l0 : TRUE, cost: 1
   7: l3 -> l2 : TRUE, cost: 1


Eliminating location l2 by chaining:

Applied chaining
First rule:
l3 -> l2 : TRUE, cost: 1
Second rule:
l2 -> l0 : TRUE, cost: 1
New rule:
l3 -> l0 : TRUE, cost: 2

Applied deletion
Removed the following rules: 6 7

Eliminating location l1 by chaining:

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

Applied deletion
Removed the following rules: 4 5

Eliminated locations on linear paths
Start location: l3
   9: l0 -> l0 : x^0'=1+x^0, -x^0+y^0 == 0, cost: 2
   8: l3 -> l0 : TRUE, cost: 2


Applied acceleration
Original rule:
l0 -> l0 : x^0'=1+x^0, -x^0+y^0 == 0, cost: 2
New rule:
l0 -> l0 : x^0'=x^0+n0, (1-x^0-n0+y^0 >= 0 /\ n0 >= 0 /\ -x^0+y^0 >= 0 /\ x^0-y^0 >= 0), cost: 2*n0

Applied instantiation
Original rule:
l0 -> l0 : x^0'=x^0+n0, (1-x^0-n0+y^0 >= 0 /\ n0 >= 0 /\ -x^0+y^0 >= 0 /\ x^0-y^0 >= 0), cost: 2*n0
New rule:
l0 -> l0 : x^0'=1+y^0, (0 >= 0 /\ 1-x^0+y^0 >= 0 /\ -x^0+y^0 >= 0 /\ x^0-y^0 >= 0), cost: 2-2*x^0+2*y^0

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

Applied deletion
Removed the following rules: 9

Accelerated simple loops
Start location: l3
  11: l0 -> l0 : x^0'=1+y^0, (-x^0+y^0 >= 0 /\ x^0-y^0 >= 0), cost: 2-2*x^0+2*y^0
   8: l3 -> l0 : TRUE, cost: 2


Applied chaining
First rule:
l3 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x^0'=1+y^0, (-x^0+y^0 >= 0 /\ x^0-y^0 >= 0), cost: 2-2*x^0+2*y^0
New rule:
l3 -> l0 : x^0'=1+y^0, x^0-y^0 == 0, cost: 4-2*x^0+2*y^0

Applied deletion
Removed the following rules: 11

Chained accelerated rules with incoming rules
Start location: l3
   8: l3 -> l0 : TRUE, cost: 2
  12: l3 -> l0 : x^0'=1+y^0, x^0-y^0 == 0, cost: 4-2*x^0+2*y^0


Removed unreachable locations and irrelevant leafs
Start location: l3
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0