WORST_CASE(Omega(0),?)

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


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

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

Applied preprocessing
Original rule:
l1 -> l0 : y^0'=y^post2, x^0'=x^post2, z^0'=z^post2, (z^0-z^post2 == 0 /\ y^0-y^post2 == 0 /\ y^0-z^0 <= 0 /\ -x^0 <= 0 /\ -x^post2+x^0 == 0), cost: 1
New rule:
l1 -> l0 : (x^0 >= 0 /\ y^0-z^0 <= 0), cost: 1

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

Applied preprocessing
Original rule:
l3 -> l2 : y^0'=y^post4, x^0'=x^post4, z^0'=z^post4, (-x^post4+x^0 == 0 /\ -z^post4+z^0 == 0 /\ -y^post4+y^0 == 0), cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Simplified rules
Start location: l3
   5: l0 -> l1 : y^0'=-1+y^0, z^0'=-1+y^0+z^0, TRUE, cost: 1
   6: l0 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, TRUE, cost: 1
   7: l1 -> l0 : (x^0 >= 0 /\ y^0-z^0 <= 0), cost: 1
   8: l2 -> l1 : TRUE, cost: 1
   9: l3 -> l2 : TRUE, cost: 1


Eliminating location l2 by chaining:

Applied chaining
First rule:
l3 -> l2 : TRUE, cost: 1
Second rule:
l2 -> l1 : TRUE, cost: 1
New rule:
l3 -> l1 : TRUE, cost: 2

Applied deletion
Removed the following rules: 8 9

Eliminated locations on linear paths
Start location: l3
   5: l0 -> l1 : y^0'=-1+y^0, z^0'=-1+y^0+z^0, TRUE, cost: 1
   6: l0 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, TRUE, cost: 1
   7: l1 -> l0 : (x^0 >= 0 /\ y^0-z^0 <= 0), cost: 1
  10: l3 -> l1 : TRUE, cost: 2


Eliminating location l0 by chaining:

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

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

Applied deletion
Removed the following rules: 5 6 7

Eliminated locations on tree-shaped paths
Start location: l3
  11: l1 -> l1 : y^0'=-1+y^0, z^0'=-1+y^0+z^0, (x^0 >= 0 /\ y^0-z^0 <= 0), cost: 2
  12: l1 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, (x^0 >= 0 /\ y^0-z^0 <= 0), cost: 2
  10: l3 -> l1 : TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : y^0'=-1+y^0, z^0'=-1+y^0+z^0, (x^0 >= 0 /\ y^0-z^0 <= 0), cost: 2
New rule:
l1 -> l1 : y^0'=-n+y^0, z^0'=-1/2*n+n*y^0+z^0-1/2*n^2, (n >= 0 /\ x^0 >= 0 /\ -1/2+1/2*n-y^0-1/2*(-1+n)^2+y^0*(-1+n)+z^0 >= 0 /\ -y^0+z^0 >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_aEHHik.txt

Applied acceleration
Original rule:
l1 -> l1 : y^0'=-1+y^0, x^0'=-1+x^0, (x^0 >= 0 /\ y^0-z^0 <= 0), cost: 2
New rule:
l1 -> l1 : y^0'=y^0-n0, x^0'=x^0-n0, (n0 >= 0 /\ -y^0+z^0 >= 0 /\ 1+x^0-n0 >= 0), cost: 2*n0
Sub-proof via acceration calculus written to file:///tmp/tmpnam_ijdNba.txt

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

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

Applied deletion
Removed the following rules: 11 12

Accelerated simple loops
Start location: l3
  13: l1 -> l1 : y^0'=-n+y^0, z^0'=-1/2*n+n*y^0+z^0-1/2*n^2, (n >= 0 /\ x^0 >= 0 /\ -1/2+1/2*n-y^0-1/2*(-1+n)^2+y^0*(-1+n)+z^0 >= 0 /\ -y^0+z^0 >= 0), cost: 2*n
  15: l1 -> l1 : y^0'=-1+y^0-x^0, x^0'=-1, (1+x^0 >= 0 /\ -y^0+z^0 >= 0), cost: 2+2*x^0
  10: l3 -> l1 : TRUE, cost: 2


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

Applied chaining
First rule:
l3 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : y^0'=-1+y^0-x^0, x^0'=-1, (1+x^0 >= 0 /\ -y^0+z^0 >= 0), cost: 2+2*x^0
New rule:
l3 -> l1 : y^0'=-1+y^0-x^0, x^0'=-1, (1+x^0 >= 0 /\ -y^0+z^0 >= 0), cost: 4+2*x^0

Applied deletion
Removed the following rules: 13 15

Chained accelerated rules with incoming rules
Start location: l3
  10: l3 -> l1 : TRUE, cost: 2
  16: l3 -> l1 : y^0'=-n+y^0, z^0'=-1/2*n+n*y^0+z^0-1/2*n^2, (n >= 0 /\ x^0 >= 0 /\ -1/2+1/2*n-y^0-1/2*(-1+n)^2+y^0*(-1+n)+z^0 >= 0 /\ -y^0+z^0 >= 0), cost: 2+2*n
  17: l3 -> l1 : y^0'=-1+y^0-x^0, x^0'=-1, (1+x^0 >= 0 /\ -y^0+z^0 >= 0), cost: 4+2*x^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