WORST_CASE(Omega(0),?)

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


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

Applied preprocessing
Original rule:
l2 -> l1 : y^0'=y^post1, x^0'=x^post1, z^0'=z^post1, (-1-x^0+x^post1 == 0 /\ z^0-z^post1 == 0 /\ y^0-y^post1 == 0 /\ -y^0+z^0 <= 0), cost: 1
New rule:
l2 -> l1 : x^0'=1+x^0, -y^0+z^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l3 : y^0'=y^post2, x^0'=x^post2, z^0'=z^post2, (z^0-z^post2 == 0 /\ 1+y^0-z^0 <= 0 /\ -1-y^0+y^post2 == 0 /\ -x^post2+x^0 == 0), cost: 1
New rule:
l2 -> l3 : y^0'=1+y^0, 1+y^0-z^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : 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:
l3 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l1 -> l2 : y^0'=y^post4, x^0'=x^post4, z^0'=z^post4, (-x^post4+x^0 == 0 /\ 1-y^0+x^0 <= 0 /\ -z^post4+z^0 == 0 /\ -y^post4+y^0 == 0), cost: 1
New rule:
l1 -> l2 : 1-y^0+x^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l0 : y^0'=y^post5, x^0'=x^post5, z^0'=z^post5, (-x^post5+x^0 == 0 /\ -z^post5+z^0 == 0 /\ -y^post5+y^0 == 0), cost: 1
New rule:
l4 -> l0 : TRUE, cost: 1

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


Eliminating location l0 by chaining:

Applied chaining
First rule:
l4 -> l0 : TRUE, cost: 1
Second rule:
l0 -> l1 : TRUE, cost: 1
New rule:
l4 -> l1 : TRUE, cost: 2

Applied deletion
Removed the following rules: 6 11

Eliminating location l3 by chaining:

Applied chaining
First rule:
l2 -> l3 : y^0'=1+y^0, 1+y^0-z^0 <= 0, cost: 1
Second rule:
l3 -> l2 : TRUE, cost: 1
New rule:
l2 -> l2 : y^0'=1+y^0, 1+y^0-z^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 8 9

Eliminated locations on linear paths
Start location: l4
  10: l1 -> l2 : 1-y^0+x^0 <= 0, cost: 1
   7: l2 -> l1 : x^0'=1+x^0, -y^0+z^0 <= 0, cost: 1
  13: l2 -> l2 : y^0'=1+y^0, 1+y^0-z^0 <= 0, cost: 2
  12: l4 -> l1 : TRUE, cost: 2


Applied acceleration
Original rule:
l2 -> l2 : y^0'=1+y^0, 1+y^0-z^0 <= 0, cost: 2
New rule:
l2 -> l2 : y^0'=y^0+n, (-y^0+z^0-n >= 0 /\ n >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_APHOko.txt

Applied instantiation
Original rule:
l2 -> l2 : y^0'=y^0+n, (-y^0+z^0-n >= 0 /\ n >= 0), cost: 2*n
New rule:
l2 -> l2 : y^0'=z^0, (0 >= 0 /\ -y^0+z^0 >= 0), cost: -2*y^0+2*z^0

Applied simplification
Original rule:
l2 -> l2 : y^0'=z^0, (0 >= 0 /\ -y^0+z^0 >= 0), cost: -2*y^0+2*z^0
New rule:
l2 -> l2 : y^0'=z^0, -y^0+z^0 >= 0, cost: -2*y^0+2*z^0

Applied deletion
Removed the following rules: 13

Accelerated simple loops
Start location: l4
  10: l1 -> l2 : 1-y^0+x^0 <= 0, cost: 1
   7: l2 -> l1 : x^0'=1+x^0, -y^0+z^0 <= 0, cost: 1
  15: l2 -> l2 : y^0'=z^0, -y^0+z^0 >= 0, cost: -2*y^0+2*z^0
  12: l4 -> l1 : TRUE, cost: 2


Applied chaining
First rule:
l1 -> l2 : 1-y^0+x^0 <= 0, cost: 1
Second rule:
l2 -> l2 : y^0'=z^0, -y^0+z^0 >= 0, cost: -2*y^0+2*z^0
New rule:
l1 -> l2 : y^0'=z^0, (1-y^0+x^0 <= 0 /\ -y^0+z^0 >= 0), cost: 1-2*y^0+2*z^0

Applied deletion
Removed the following rules: 15

Chained accelerated rules with incoming rules
Start location: l4
  10: l1 -> l2 : 1-y^0+x^0 <= 0, cost: 1
  16: l1 -> l2 : y^0'=z^0, (1-y^0+x^0 <= 0 /\ -y^0+z^0 >= 0), cost: 1-2*y^0+2*z^0
   7: l2 -> l1 : x^0'=1+x^0, -y^0+z^0 <= 0, cost: 1
  12: l4 -> l1 : TRUE, cost: 2


Eliminating location l2 by chaining:

Applied chaining
First rule:
l1 -> l2 : 1-y^0+x^0 <= 0, cost: 1
Second rule:
l2 -> l1 : x^0'=1+x^0, -y^0+z^0 <= 0, cost: 1
New rule:
l1 -> l1 : x^0'=1+x^0, (1-y^0+x^0 <= 0 /\ -y^0+z^0 <= 0), cost: 2

Applied chaining
First rule:
l1 -> l2 : y^0'=z^0, (1-y^0+x^0 <= 0 /\ -y^0+z^0 >= 0), cost: 1-2*y^0+2*z^0
Second rule:
l2 -> l1 : x^0'=1+x^0, -y^0+z^0 <= 0, cost: 1
New rule:
l1 -> l1 : y^0'=z^0, x^0'=1+x^0, (0 <= 0 /\ 1-y^0+x^0 <= 0 /\ -y^0+z^0 >= 0), cost: 2-2*y^0+2*z^0

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

Applied deletion
Removed the following rules: 7 10 16

Eliminated locations on tree-shaped paths
Start location: l4
  17: l1 -> l1 : x^0'=1+x^0, (1-y^0+x^0 <= 0 /\ -y^0+z^0 <= 0), cost: 2
  18: l1 -> l1 : y^0'=z^0, x^0'=1+x^0, (1-y^0+x^0 <= 0 /\ -y^0+z^0 >= 0), cost: 2-2*y^0+2*z^0
  12: l4 -> l1 : TRUE, cost: 2


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

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

Applied acceleration
Original rule:
l1 -> l1 : y^0'=z^0, x^0'=1+x^0, (1-y^0+x^0 <= 0 /\ -y^0+z^0 >= 0), cost: 2-2*y^0+2*z^0
New rule:
l1 -> l1 : y^0'=z^0, x^0'=x^0+n1, (-x^0-n1+z^0 >= 0 /\ -1+n1 >= 0 /\ -y^0+z^0 >= 0 /\ -1+y^0-x^0 >= 0), cost: 2*n1
Sub-proof via acceration calculus written to file:///tmp/tmpnam_NkdnhE.txt

Applied instantiation
Original rule:
l1 -> l1 : y^0'=z^0, x^0'=x^0+n1, (-x^0-n1+z^0 >= 0 /\ -1+n1 >= 0 /\ -y^0+z^0 >= 0 /\ -1+y^0-x^0 >= 0), cost: 2*n1
New rule:
l1 -> l1 : y^0'=z^0, x^0'=z^0, (0 >= 0 /\ -1-x^0+z^0 >= 0 /\ -y^0+z^0 >= 0 /\ -1+y^0-x^0 >= 0), cost: -2*x^0+2*z^0

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

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

Applied deletion
Removed the following rules: 17 18

Accelerated simple loops
Start location: l4
  21: l1 -> l1 : x^0'=y^0, (y^0-x^0 >= 0 /\ y^0-z^0 >= 0), cost: 2*y^0-2*x^0
  22: l1 -> l1 : y^0'=z^0, x^0'=z^0, (-y^0+z^0 >= 0 /\ -1+y^0-x^0 >= 0), cost: -2*x^0+2*z^0
  12: l4 -> l1 : TRUE, cost: 2


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

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

Applied deletion
Removed the following rules: 21 22

Chained accelerated rules with incoming rules
Start location: l4
  12: l4 -> l1 : TRUE, cost: 2
  23: l4 -> l1 : x^0'=y^0, (y^0-x^0 >= 0 /\ y^0-z^0 >= 0), cost: 2+2*y^0-2*x^0
  24: l4 -> l1 : y^0'=z^0, x^0'=z^0, (-y^0+z^0 >= 0 /\ -1+y^0-x^0 >= 0), cost: 2-2*x^0+2*z^0


Removed unreachable locations and irrelevant leafs
Start location: l4
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0