WORST_CASE(Omega(0),?)

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


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

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

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

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

Simplified rules
Start location: l3
   4: l0 -> l1 : i^0'=1+i^0, x^0'=-i^0-y^0+x^0, z^0'=i^0+y^0, -1+x^0 >= 0, cost: 1
   5: l1 -> l0 : TRUE, cost: 1
   6: l2 -> l0 : i^0'=0, y^0'=y^post2, 0 == 0, 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 : i^0'=0, y^0'=y^post2, 0 == 0, cost: 1
New rule:
l3 -> l0 : i^0'=0, y^0'=y^post2, 0 == 0, cost: 2

Applied deletion
Removed the following rules: 6 7

Eliminating location l1 by chaining:

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

Applied deletion
Removed the following rules: 4 5

Eliminated locations on linear paths
Start location: l3
   9: l0 -> l0 : i^0'=1+i^0, x^0'=-i^0-y^0+x^0, z^0'=i^0+y^0, -1+x^0 >= 0, cost: 2
   8: l3 -> l0 : i^0'=0, y^0'=y^post2, 0 == 0, cost: 2


Applied acceleration
Original rule:
l0 -> l0 : i^0'=1+i^0, x^0'=-i^0-y^0+x^0, z^0'=i^0+y^0, -1+x^0 >= 0, cost: 2
New rule:
l0 -> l0 : i^0'=i^0+n0, x^0'=-i^0*n0+1/2*n0-n0*y^0-1/2*n0^2+x^0, z^0'=-1+i^0+n0+y^0, (-1+n0 >= 0 /\ -1+x^0 >= 0 /\ -3/2+1/2*n0-1/2*(-1+n0)^2-y^0*(-1+n0)+x^0-i^0*(-1+n0) >= 0), cost: 2*n0

Applied deletion
Removed the following rules: 9

Accelerated simple loops
Start location: l3
  10: l0 -> l0 : i^0'=i^0+n0, x^0'=-i^0*n0+1/2*n0-n0*y^0-1/2*n0^2+x^0, z^0'=-1+i^0+n0+y^0, (-1+n0 >= 0 /\ -1+x^0 >= 0 /\ -3/2+1/2*n0-1/2*(-1+n0)^2-y^0*(-1+n0)+x^0-i^0*(-1+n0) >= 0), cost: 2*n0
   8: l3 -> l0 : i^0'=0, y^0'=y^post2, 0 == 0, cost: 2


Applied chaining
First rule:
l3 -> l0 : i^0'=0, y^0'=y^post2, 0 == 0, cost: 2
Second rule:
l0 -> l0 : i^0'=i^0+n0, x^0'=-i^0*n0+1/2*n0-n0*y^0-1/2*n0^2+x^0, z^0'=-1+i^0+n0+y^0, (-1+n0 >= 0 /\ -1+x^0 >= 0 /\ -3/2+1/2*n0-1/2*(-1+n0)^2-y^0*(-1+n0)+x^0-i^0*(-1+n0) >= 0), cost: 2*n0
New rule:
l3 -> l0 : i^0'=n0, y^0'=y^post2, x^0'=1/2*n0-n0*y^post2-1/2*n0^2+x^0, z^0'=-1+n0+y^post2, (-1+n0 >= 0 /\ -1+x^0 >= 0 /\ -3/2+1/2*n0-1/2*(-1+n0)^2+x^0-y^post2*(-1+n0) >= 0), cost: 2+2*n0

Applied deletion
Removed the following rules: 10

Chained accelerated rules with incoming rules
Start location: l3
   8: l3 -> l0 : i^0'=0, y^0'=y^post2, 0 == 0, cost: 2
  11: l3 -> l0 : i^0'=n0, y^0'=y^post2, x^0'=1/2*n0-n0*y^post2-1/2*n0^2+x^0, z^0'=-1+n0+y^post2, (-1+n0 >= 0 /\ -1+x^0 >= 0 /\ -3/2+1/2*n0-1/2*(-1+n0)^2+x^0-y^post2*(-1+n0) >= 0), cost: 2+2*n0


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