WORST_CASE(Omega(0),?)

Initial ITS
Start location: l5
   0: l0 -> l1 : z^0'=z^post0, __const_36^0'=__const_36^post0, y^0'=y^post0, __const_127^0'=__const_127^post0, counter^0'=counter^post0, (-counter^post0+counter^0 == 0 /\ z^0-z^post0 == 0 /\ __const_127^0-__const_127^post0 == 0 /\ -__const_36^post0+__const_36^0 == 0 /\ __const_36^0-counter^0 <= 0 /\ y^0-y^post0 == 0), cost: 1
   1: l0 -> l2 : z^0'=z^post1, __const_36^0'=__const_36^post1, y^0'=y^post1, __const_127^0'=__const_127^post1, counter^0'=counter^post1, (-__const_127^post1+__const_127^0 == 0 /\ -y^post1+y^0 == 0 /\ __const_36^0-__const_36^post1 == 0 /\ -1+counter^post1-counter^0 == 0 /\ 1-__const_36^0+counter^0 <= 0 /\ -1-z^0+z^post1 == 0), cost: 1
   4: l2 -> l0 : z^0'=z^post4, __const_36^0'=__const_36^post4, y^0'=y^post4, __const_127^0'=__const_127^post4, counter^0'=counter^post4, (__const_127^0-__const_127^post4 == 0 /\ y^0-y^post4 == 0 /\ -counter^post4+counter^0 == 0 /\ __const_36^0-__const_36^post4 == 0 /\ z^0-z^post4 == 0), cost: 1
   2: l3 -> l2 : z^0'=z^post2, __const_36^0'=__const_36^post2, y^0'=y^post2, __const_127^0'=__const_127^post2, counter^0'=counter^post2, (0 == 0 /\ -__const_36^post2+__const_36^0 == 0 /\ -counter^post2+counter^0 == 0 /\ __const_127^0-__const_127^post2 == 0 /\ y^0-__const_127^0 <= 0 /\ y^0-y^post2 == 0), cost: 1
   3: l3 -> l1 : z^0'=z^post3, __const_36^0'=__const_36^post3, y^0'=y^post3, __const_127^0'=__const_127^post3, counter^0'=counter^post3, (z^0-z^post3 == 0 /\ -counter^post3+counter^0 == 0 /\ 1-y^0+__const_127^0 <= 0 /\ __const_36^0-__const_36^post3 == 0 /\ y^0-y^post3 == 0 /\ -__const_127^post3+__const_127^0 == 0), cost: 1
   5: l4 -> l3 : z^0'=z^post5, __const_36^0'=__const_36^post5, y^0'=y^post5, __const_127^0'=__const_127^post5, counter^0'=counter^post5, (z^0-z^post5 == 0 /\ counter^post5 == 0 /\ -y^post5+y^0 == 0 /\ -__const_127^post5+__const_127^0 == 0 /\ __const_36^0-__const_36^post5 == 0), cost: 1
   6: l5 -> l4 : z^0'=z^post6, __const_36^0'=__const_36^post6, y^0'=y^post6, __const_127^0'=__const_127^post6, counter^0'=counter^post6, (-counter^post6+counter^0 == 0 /\ y^0-y^post6 == 0 /\ z^0-z^post6 == 0 /\ -__const_127^post6+__const_127^0 == 0 /\ __const_36^0-__const_36^post6 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l5
   1: l0 -> l2 : z^0'=z^post1, __const_36^0'=__const_36^post1, y^0'=y^post1, __const_127^0'=__const_127^post1, counter^0'=counter^post1, (-__const_127^post1+__const_127^0 == 0 /\ -y^post1+y^0 == 0 /\ __const_36^0-__const_36^post1 == 0 /\ -1+counter^post1-counter^0 == 0 /\ 1-__const_36^0+counter^0 <= 0 /\ -1-z^0+z^post1 == 0), cost: 1
   4: l2 -> l0 : z^0'=z^post4, __const_36^0'=__const_36^post4, y^0'=y^post4, __const_127^0'=__const_127^post4, counter^0'=counter^post4, (__const_127^0-__const_127^post4 == 0 /\ y^0-y^post4 == 0 /\ -counter^post4+counter^0 == 0 /\ __const_36^0-__const_36^post4 == 0 /\ z^0-z^post4 == 0), cost: 1
   2: l3 -> l2 : z^0'=z^post2, __const_36^0'=__const_36^post2, y^0'=y^post2, __const_127^0'=__const_127^post2, counter^0'=counter^post2, (0 == 0 /\ -__const_36^post2+__const_36^0 == 0 /\ -counter^post2+counter^0 == 0 /\ __const_127^0-__const_127^post2 == 0 /\ y^0-__const_127^0 <= 0 /\ y^0-y^post2 == 0), cost: 1
   5: l4 -> l3 : z^0'=z^post5, __const_36^0'=__const_36^post5, y^0'=y^post5, __const_127^0'=__const_127^post5, counter^0'=counter^post5, (z^0-z^post5 == 0 /\ counter^post5 == 0 /\ -y^post5+y^0 == 0 /\ -__const_127^post5+__const_127^0 == 0 /\ __const_36^0-__const_36^post5 == 0), cost: 1
   6: l5 -> l4 : z^0'=z^post6, __const_36^0'=__const_36^post6, y^0'=y^post6, __const_127^0'=__const_127^post6, counter^0'=counter^post6, (-counter^post6+counter^0 == 0 /\ y^0-y^post6 == 0 /\ z^0-z^post6 == 0 /\ -__const_127^post6+__const_127^0 == 0 /\ __const_36^0-__const_36^post6 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l2 : z^0'=z^post1, __const_36^0'=__const_36^post1, y^0'=y^post1, __const_127^0'=__const_127^post1, counter^0'=counter^post1, (-__const_127^post1+__const_127^0 == 0 /\ -y^post1+y^0 == 0 /\ __const_36^0-__const_36^post1 == 0 /\ -1+counter^post1-counter^0 == 0 /\ 1-__const_36^0+counter^0 <= 0 /\ -1-z^0+z^post1 == 0), cost: 1
New rule:
l0 -> l2 : z^0'=1+z^0, counter^0'=1+counter^0, 1-__const_36^0+counter^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : z^0'=z^post2, __const_36^0'=__const_36^post2, y^0'=y^post2, __const_127^0'=__const_127^post2, counter^0'=counter^post2, (0 == 0 /\ -__const_36^post2+__const_36^0 == 0 /\ -counter^post2+counter^0 == 0 /\ __const_127^0-__const_127^post2 == 0 /\ y^0-__const_127^0 <= 0 /\ y^0-y^post2 == 0), cost: 1
New rule:
l3 -> l2 : z^0'=z^post2, y^0-__const_127^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : z^0'=z^post4, __const_36^0'=__const_36^post4, y^0'=y^post4, __const_127^0'=__const_127^post4, counter^0'=counter^post4, (__const_127^0-__const_127^post4 == 0 /\ y^0-y^post4 == 0 /\ -counter^post4+counter^0 == 0 /\ __const_36^0-__const_36^post4 == 0 /\ z^0-z^post4 == 0), cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : z^0'=z^post5, __const_36^0'=__const_36^post5, y^0'=y^post5, __const_127^0'=__const_127^post5, counter^0'=counter^post5, (z^0-z^post5 == 0 /\ counter^post5 == 0 /\ -y^post5+y^0 == 0 /\ -__const_127^post5+__const_127^0 == 0 /\ __const_36^0-__const_36^post5 == 0), cost: 1
New rule:
l4 -> l3 : counter^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l4 : z^0'=z^post6, __const_36^0'=__const_36^post6, y^0'=y^post6, __const_127^0'=__const_127^post6, counter^0'=counter^post6, (-counter^post6+counter^0 == 0 /\ y^0-y^post6 == 0 /\ z^0-z^post6 == 0 /\ -__const_127^post6+__const_127^0 == 0 /\ __const_36^0-__const_36^post6 == 0), cost: 1
New rule:
l5 -> l4 : TRUE, cost: 1

Simplified rules
Start location: l5
   7: l0 -> l2 : z^0'=1+z^0, counter^0'=1+counter^0, 1-__const_36^0+counter^0 <= 0, cost: 1
   9: l2 -> l0 : TRUE, cost: 1
   8: l3 -> l2 : z^0'=z^post2, y^0-__const_127^0 <= 0, cost: 1
  10: l4 -> l3 : counter^0'=0, TRUE, cost: 1
  11: l5 -> l4 : TRUE, cost: 1


Eliminating location l4 by chaining:

Applied chaining
First rule:
l5 -> l4 : TRUE, cost: 1
Second rule:
l4 -> l3 : counter^0'=0, TRUE, cost: 1
New rule:
l5 -> l3 : counter^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminating location l3 by chaining:

Applied chaining
First rule:
l5 -> l3 : counter^0'=0, TRUE, cost: 2
Second rule:
l3 -> l2 : z^0'=z^post2, y^0-__const_127^0 <= 0, cost: 1
New rule:
l5 -> l2 : z^0'=z^post2, counter^0'=0, y^0-__const_127^0 <= 0, cost: 3

Applied deletion
Removed the following rules: 8 12

Eliminating location l0 by chaining:

Applied chaining
First rule:
l2 -> l0 : TRUE, cost: 1
Second rule:
l0 -> l2 : z^0'=1+z^0, counter^0'=1+counter^0, 1-__const_36^0+counter^0 <= 0, cost: 1
New rule:
l2 -> l2 : z^0'=1+z^0, counter^0'=1+counter^0, 1-__const_36^0+counter^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 7 9

Eliminated locations on linear paths
Start location: l5
  14: l2 -> l2 : z^0'=1+z^0, counter^0'=1+counter^0, 1-__const_36^0+counter^0 <= 0, cost: 2
  13: l5 -> l2 : z^0'=z^post2, counter^0'=0, y^0-__const_127^0 <= 0, cost: 3


Applied acceleration
Original rule:
l2 -> l2 : z^0'=1+z^0, counter^0'=1+counter^0, 1-__const_36^0+counter^0 <= 0, cost: 2
New rule:
l2 -> l2 : z^0'=z^0+n, counter^0'=n+counter^0, (__const_36^0-n-counter^0 >= 0 /\ n >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_bhflhB.txt

Applied instantiation
Original rule:
l2 -> l2 : z^0'=z^0+n, counter^0'=n+counter^0, (__const_36^0-n-counter^0 >= 0 /\ n >= 0), cost: 2*n
New rule:
l2 -> l2 : z^0'=z^0+__const_36^0-counter^0, counter^0'=__const_36^0, (0 >= 0 /\ __const_36^0-counter^0 >= 0), cost: 2*__const_36^0-2*counter^0

Applied simplification
Original rule:
l2 -> l2 : z^0'=z^0+__const_36^0-counter^0, counter^0'=__const_36^0, (0 >= 0 /\ __const_36^0-counter^0 >= 0), cost: 2*__const_36^0-2*counter^0
New rule:
l2 -> l2 : z^0'=z^0+__const_36^0-counter^0, counter^0'=__const_36^0, __const_36^0-counter^0 >= 0, cost: 2*__const_36^0-2*counter^0

Applied deletion
Removed the following rules: 14

Accelerated simple loops
Start location: l5
  16: l2 -> l2 : z^0'=z^0+__const_36^0-counter^0, counter^0'=__const_36^0, __const_36^0-counter^0 >= 0, cost: 2*__const_36^0-2*counter^0
  13: l5 -> l2 : z^0'=z^post2, counter^0'=0, y^0-__const_127^0 <= 0, cost: 3


Applied chaining
First rule:
l5 -> l2 : z^0'=z^post2, counter^0'=0, y^0-__const_127^0 <= 0, cost: 3
Second rule:
l2 -> l2 : z^0'=z^0+__const_36^0-counter^0, counter^0'=__const_36^0, __const_36^0-counter^0 >= 0, cost: 2*__const_36^0-2*counter^0
New rule:
l5 -> l2 : z^0'=__const_36^0+z^post2, counter^0'=__const_36^0, (__const_36^0 >= 0 /\ y^0-__const_127^0 <= 0), cost: 3+2*__const_36^0

Applied deletion
Removed the following rules: 16

Chained accelerated rules with incoming rules
Start location: l5
  13: l5 -> l2 : z^0'=z^post2, counter^0'=0, y^0-__const_127^0 <= 0, cost: 3
  17: l5 -> l2 : z^0'=__const_36^0+z^post2, counter^0'=__const_36^0, (__const_36^0 >= 0 /\ y^0-__const_127^0 <= 0), cost: 3+2*__const_36^0


Removed unreachable locations and irrelevant leafs
Start location: l5
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0