WORST_CASE(Omega(0),?)

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


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

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

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

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

Simplified rules
Start location: l3
   4: l0 -> l1 : x^0'=x^0-i^0-y^0, z^0'=i^0+y^0, i^0'=1+i^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 : x^0'=x^0-i^0-y^0, z^0'=i^0+y^0, i^0'=1+i^0, -1+x^0 >= 0, cost: 1
Second rule:
l1 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : x^0'=x^0-i^0-y^0, z^0'=i^0+y^0, i^0'=1+i^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 : x^0'=x^0-i^0-y^0, z^0'=i^0+y^0, i^0'=1+i^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 : x^0'=x^0-i^0-y^0, z^0'=i^0+y^0, i^0'=1+i^0, -1+x^0 >= 0, cost: 2
New rule:
l0 -> l0 : x^0'=x^0-1/2*n^2-n*y^0+1/2*n-n*i^0, z^0'=-1+n+i^0+y^0, i^0'=n+i^0, (-1+n >= 0 /\ -3/2+x^0-(-1+n)*i^0+1/2*n-1/2*(-1+n)^2-(-1+n)*y^0 >= 0 /\ -1+x^0 >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_ElglAj.txt

Applied deletion
Removed the following rules: 9

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

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 : x^0'=x^0-1/2*n^2-y^post2*n+1/2*n, z^0'=-1+y^post2+n, i^0'=n, y^0'=y^post2, (-1+n >= 0 /\ -3/2+x^0+1/2*n-(-1+n)*y^post2-1/2*(-1+n)^2 >= 0 /\ -1+x^0 >= 0), cost: 2+2*n


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