WORST_CASE(Omega(0),?)

Initial ITS
Start location: l4
   0: l0 -> l1 : x^0'=x^post0, __const_10^0'=__const_10^post0, y^0'=y^post0, (y^0-y^post0 == 0 /\ 1-x^0+__const_10^0 <= 0 /\ __const_10^0-__const_10^post0 == 0 /\ x^0-x^post0 == 0), cost: 1
   1: l0 -> l2 : x^0'=x^post1, __const_10^0'=__const_10^post1, y^0'=y^post1, (x^0-__const_10^0 <= 0 /\ -1-x^0+x^post1 == 0 /\ __const_10^0-__const_10^post1 == 0 /\ x^0-__const_10^0+y^post1 == 0), cost: 1
   2: l2 -> l0 : x^0'=x^post2, __const_10^0'=__const_10^post2, y^0'=y^post2, (y^0-y^post2 == 0 /\ x^0-x^post2 == 0 /\ -__const_10^post2+__const_10^0 == 0), cost: 1
   3: l3 -> l2 : x^0'=x^post3, __const_10^0'=__const_10^post3, y^0'=y^post3, (-__const_10^post3+__const_10^0 == 0 /\ -y^post3+y^0 == 0 /\ -1+x^post3 == 0), cost: 1
   4: l4 -> l3 : x^0'=x^post4, __const_10^0'=__const_10^post4, y^0'=y^post4, (-__const_10^post4+__const_10^0 == 0 /\ -y^post4+y^0 == 0 /\ -x^post4+x^0 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l4
   1: l0 -> l2 : x^0'=x^post1, __const_10^0'=__const_10^post1, y^0'=y^post1, (x^0-__const_10^0 <= 0 /\ -1-x^0+x^post1 == 0 /\ __const_10^0-__const_10^post1 == 0 /\ x^0-__const_10^0+y^post1 == 0), cost: 1
   2: l2 -> l0 : x^0'=x^post2, __const_10^0'=__const_10^post2, y^0'=y^post2, (y^0-y^post2 == 0 /\ x^0-x^post2 == 0 /\ -__const_10^post2+__const_10^0 == 0), cost: 1
   3: l3 -> l2 : x^0'=x^post3, __const_10^0'=__const_10^post3, y^0'=y^post3, (-__const_10^post3+__const_10^0 == 0 /\ -y^post3+y^0 == 0 /\ -1+x^post3 == 0), cost: 1
   4: l4 -> l3 : x^0'=x^post4, __const_10^0'=__const_10^post4, y^0'=y^post4, (-__const_10^post4+__const_10^0 == 0 /\ -y^post4+y^0 == 0 /\ -x^post4+x^0 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l2 : x^0'=x^post1, __const_10^0'=__const_10^post1, y^0'=y^post1, (x^0-__const_10^0 <= 0 /\ -1-x^0+x^post1 == 0 /\ __const_10^0-__const_10^post1 == 0 /\ x^0-__const_10^0+y^post1 == 0), cost: 1
New rule:
l0 -> l2 : x^0'=1+x^0, y^0'=-x^0+__const_10^0, x^0-__const_10^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : x^0'=x^post2, __const_10^0'=__const_10^post2, y^0'=y^post2, (y^0-y^post2 == 0 /\ x^0-x^post2 == 0 /\ -__const_10^post2+__const_10^0 == 0), cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : x^0'=x^post3, __const_10^0'=__const_10^post3, y^0'=y^post3, (-__const_10^post3+__const_10^0 == 0 /\ -y^post3+y^0 == 0 /\ -1+x^post3 == 0), cost: 1
New rule:
l3 -> l2 : x^0'=1, TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : x^0'=x^post4, __const_10^0'=__const_10^post4, y^0'=y^post4, (-__const_10^post4+__const_10^0 == 0 /\ -y^post4+y^0 == 0 /\ -x^post4+x^0 == 0), cost: 1
New rule:
l4 -> l3 : TRUE, cost: 1

Simplified rules
Start location: l4
   5: l0 -> l2 : x^0'=1+x^0, y^0'=-x^0+__const_10^0, x^0-__const_10^0 <= 0, cost: 1
   6: l2 -> l0 : TRUE, cost: 1
   7: l3 -> l2 : x^0'=1, TRUE, cost: 1
   8: l4 -> l3 : TRUE, cost: 1


Eliminating location l3 by chaining:

Applied chaining
First rule:
l4 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l2 : x^0'=1, TRUE, cost: 1
New rule:
l4 -> l2 : x^0'=1, TRUE, cost: 2

Applied deletion
Removed the following rules: 7 8

Eliminating location l0 by chaining:

Applied chaining
First rule:
l2 -> l0 : TRUE, cost: 1
Second rule:
l0 -> l2 : x^0'=1+x^0, y^0'=-x^0+__const_10^0, x^0-__const_10^0 <= 0, cost: 1
New rule:
l2 -> l2 : x^0'=1+x^0, y^0'=-x^0+__const_10^0, x^0-__const_10^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 5 6

Eliminated locations on linear paths
Start location: l4
  10: l2 -> l2 : x^0'=1+x^0, y^0'=-x^0+__const_10^0, x^0-__const_10^0 <= 0, cost: 2
   9: l4 -> l2 : x^0'=1, TRUE, cost: 2


Applied acceleration
Original rule:
l2 -> l2 : x^0'=1+x^0, y^0'=-x^0+__const_10^0, x^0-__const_10^0 <= 0, cost: 2
New rule:
l2 -> l2 : x^0'=n+x^0, y^0'=1-n-x^0+__const_10^0, (1-n-x^0+__const_10^0 >= 0 /\ -1+n >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_dfGaGB.txt

Applied instantiation
Original rule:
l2 -> l2 : x^0'=n+x^0, y^0'=1-n-x^0+__const_10^0, (1-n-x^0+__const_10^0 >= 0 /\ -1+n >= 0), cost: 2*n
New rule:
l2 -> l2 : x^0'=1+__const_10^0, y^0'=0, (0 >= 0 /\ -x^0+__const_10^0 >= 0), cost: 2-2*x^0+2*__const_10^0

Applied simplification
Original rule:
l2 -> l2 : x^0'=1+__const_10^0, y^0'=0, (0 >= 0 /\ -x^0+__const_10^0 >= 0), cost: 2-2*x^0+2*__const_10^0
New rule:
l2 -> l2 : x^0'=1+__const_10^0, y^0'=0, -x^0+__const_10^0 >= 0, cost: 2-2*x^0+2*__const_10^0

Applied deletion
Removed the following rules: 10

Accelerated simple loops
Start location: l4
  12: l2 -> l2 : x^0'=1+__const_10^0, y^0'=0, -x^0+__const_10^0 >= 0, cost: 2-2*x^0+2*__const_10^0
   9: l4 -> l2 : x^0'=1, TRUE, cost: 2


Applied chaining
First rule:
l4 -> l2 : x^0'=1, TRUE, cost: 2
Second rule:
l2 -> l2 : x^0'=1+__const_10^0, y^0'=0, -x^0+__const_10^0 >= 0, cost: 2-2*x^0+2*__const_10^0
New rule:
l4 -> l2 : x^0'=1+__const_10^0, y^0'=0, -1+__const_10^0 >= 0, cost: 2+2*__const_10^0

Applied deletion
Removed the following rules: 12

Chained accelerated rules with incoming rules
Start location: l4
   9: l4 -> l2 : x^0'=1, TRUE, cost: 2
  13: l4 -> l2 : x^0'=1+__const_10^0, y^0'=0, -1+__const_10^0 >= 0, cost: 2+2*__const_10^0


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