WORST_CASE(Omega(0),?)

Initial ITS
Start location: l7
   0: l0 -> l1 : y^0'=y^post0, __const_99^0'=__const_99^post0, x^0'=x^post0, Result^0'=Result^post0, __disjvr_0^0'=__disjvr_0^post0, (0 == 0 /\ -__disjvr_0^post0+__disjvr_0^0 == 0 /\ -x^0 <= 0 /\ y^0-y^post0 == 0 /\ -__const_99^post0+__const_99^0 == 0 /\ x^0-x^post0 == 0), cost: 1
   1: l0 -> l3 : y^0'=y^post1, __const_99^0'=__const_99^post1, x^0'=x^post1, Result^0'=Result^post1, __disjvr_0^0'=__disjvr_0^post1, (-Result^post1+Result^0 == 0 /\ -x^post1+x^0 == 0 /\ -__disjvr_0^post1+__disjvr_0^0 == 0 /\ __const_99^0-__const_99^post1 == 0 /\ y^0-y^post1 == 0 /\ 1+x^0 <= 0), cost: 1
   5: l0 -> l5 : y^0'=y^post5, __const_99^0'=__const_99^post5, x^0'=x^post5, Result^0'=Result^post5, __disjvr_0^0'=__disjvr_0^post5, (-1-y^0+y^post5 == 0 /\ __const_99^0+x^post5-x^0 == 0 /\ 1+y^0 <= 0 /\ -1-y^0 <= 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0 /\ -Result^post5+Result^0 == 0 /\ 1+x^0 <= 0 /\ __const_99^0-__const_99^post5 == 0), cost: 1
   2: l3 -> l4 : y^0'=y^post2, __const_99^0'=__const_99^post2, x^0'=x^post2, Result^0'=Result^post2, __disjvr_0^0'=__disjvr_0^post2, (y^0-y^post2 == 0 /\ -__const_99^post2+__const_99^0 == 0 /\ -__disjvr_0^post2+__disjvr_0^0 == 0 /\ Result^0-Result^post2 == 0 /\ __disjvr_0^post2-__disjvr_0^0 == 0 /\ x^0-x^post2 == 0), cost: 1
   3: l4 -> l2 : y^0'=y^post3, __const_99^0'=__const_99^post3, x^0'=x^post3, Result^0'=Result^post3, __disjvr_0^0'=__disjvr_0^post3, (-__disjvr_0^post3+__disjvr_0^0 == 0 /\ -1-x^0+x^post3 == 0 /\ __const_99^0-__const_99^post3 == 0 /\ -1-y^0+y^post3 == 0 /\ -Result^post3+Result^0 == 0), cost: 1
   4: l2 -> l0 : y^0'=y^post4, __const_99^0'=__const_99^post4, x^0'=x^post4, Result^0'=Result^post4, __disjvr_0^0'=__disjvr_0^post4, (Result^0-Result^post4 == 0 /\ x^0-x^post4 == 0 /\ -__disjvr_0^post4+__disjvr_0^0 == 0 /\ __const_99^0-__const_99^post4 == 0 /\ y^0-y^post4 == 0), cost: 1
   6: l5 -> l0 : y^0'=y^post6, __const_99^0'=__const_99^post6, x^0'=x^post6, Result^0'=Result^post6, __disjvr_0^0'=__disjvr_0^post6, (-__disjvr_0^post6+__disjvr_0^0 == 0 /\ x^0-x^post6 == 0 /\ y^0-y^post6 == 0 /\ -Result^post6+Result^0 == 0 /\ __const_99^0-__const_99^post6 == 0), cost: 1
   7: l6 -> l0 : y^0'=y^post7, __const_99^0'=__const_99^post7, x^0'=x^post7, Result^0'=Result^post7, __disjvr_0^0'=__disjvr_0^post7, (-x^post7+x^0 == 0 /\ __disjvr_0^0-__disjvr_0^post7 == 0 /\ Result^0-Result^post7 == 0 /\ __const_99^0-__const_99^post7 == 0 /\ y^0-y^post7 == 0), cost: 1
   8: l7 -> l6 : y^0'=y^post8, __const_99^0'=__const_99^post8, x^0'=x^post8, Result^0'=Result^post8, __disjvr_0^0'=__disjvr_0^post8, (-__disjvr_0^post8+__disjvr_0^0 == 0 /\ x^0-x^post8 == 0 /\ y^0-y^post8 == 0 /\ -Result^post8+Result^0 == 0 /\ __const_99^0-__const_99^post8 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l7
   1: l0 -> l3 : y^0'=y^post1, __const_99^0'=__const_99^post1, x^0'=x^post1, Result^0'=Result^post1, __disjvr_0^0'=__disjvr_0^post1, (-Result^post1+Result^0 == 0 /\ -x^post1+x^0 == 0 /\ -__disjvr_0^post1+__disjvr_0^0 == 0 /\ __const_99^0-__const_99^post1 == 0 /\ y^0-y^post1 == 0 /\ 1+x^0 <= 0), cost: 1
   5: l0 -> l5 : y^0'=y^post5, __const_99^0'=__const_99^post5, x^0'=x^post5, Result^0'=Result^post5, __disjvr_0^0'=__disjvr_0^post5, (-1-y^0+y^post5 == 0 /\ __const_99^0+x^post5-x^0 == 0 /\ 1+y^0 <= 0 /\ -1-y^0 <= 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0 /\ -Result^post5+Result^0 == 0 /\ 1+x^0 <= 0 /\ __const_99^0-__const_99^post5 == 0), cost: 1
   2: l3 -> l4 : y^0'=y^post2, __const_99^0'=__const_99^post2, x^0'=x^post2, Result^0'=Result^post2, __disjvr_0^0'=__disjvr_0^post2, (y^0-y^post2 == 0 /\ -__const_99^post2+__const_99^0 == 0 /\ -__disjvr_0^post2+__disjvr_0^0 == 0 /\ Result^0-Result^post2 == 0 /\ __disjvr_0^post2-__disjvr_0^0 == 0 /\ x^0-x^post2 == 0), cost: 1
   3: l4 -> l2 : y^0'=y^post3, __const_99^0'=__const_99^post3, x^0'=x^post3, Result^0'=Result^post3, __disjvr_0^0'=__disjvr_0^post3, (-__disjvr_0^post3+__disjvr_0^0 == 0 /\ -1-x^0+x^post3 == 0 /\ __const_99^0-__const_99^post3 == 0 /\ -1-y^0+y^post3 == 0 /\ -Result^post3+Result^0 == 0), cost: 1
   4: l2 -> l0 : y^0'=y^post4, __const_99^0'=__const_99^post4, x^0'=x^post4, Result^0'=Result^post4, __disjvr_0^0'=__disjvr_0^post4, (Result^0-Result^post4 == 0 /\ x^0-x^post4 == 0 /\ -__disjvr_0^post4+__disjvr_0^0 == 0 /\ __const_99^0-__const_99^post4 == 0 /\ y^0-y^post4 == 0), cost: 1
   6: l5 -> l0 : y^0'=y^post6, __const_99^0'=__const_99^post6, x^0'=x^post6, Result^0'=Result^post6, __disjvr_0^0'=__disjvr_0^post6, (-__disjvr_0^post6+__disjvr_0^0 == 0 /\ x^0-x^post6 == 0 /\ y^0-y^post6 == 0 /\ -Result^post6+Result^0 == 0 /\ __const_99^0-__const_99^post6 == 0), cost: 1
   7: l6 -> l0 : y^0'=y^post7, __const_99^0'=__const_99^post7, x^0'=x^post7, Result^0'=Result^post7, __disjvr_0^0'=__disjvr_0^post7, (-x^post7+x^0 == 0 /\ __disjvr_0^0-__disjvr_0^post7 == 0 /\ Result^0-Result^post7 == 0 /\ __const_99^0-__const_99^post7 == 0 /\ y^0-y^post7 == 0), cost: 1
   8: l7 -> l6 : y^0'=y^post8, __const_99^0'=__const_99^post8, x^0'=x^post8, Result^0'=Result^post8, __disjvr_0^0'=__disjvr_0^post8, (-__disjvr_0^post8+__disjvr_0^0 == 0 /\ x^0-x^post8 == 0 /\ y^0-y^post8 == 0 /\ -Result^post8+Result^0 == 0 /\ __const_99^0-__const_99^post8 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l3 : y^0'=y^post1, __const_99^0'=__const_99^post1, x^0'=x^post1, Result^0'=Result^post1, __disjvr_0^0'=__disjvr_0^post1, (-Result^post1+Result^0 == 0 /\ -x^post1+x^0 == 0 /\ -__disjvr_0^post1+__disjvr_0^0 == 0 /\ __const_99^0-__const_99^post1 == 0 /\ y^0-y^post1 == 0 /\ 1+x^0 <= 0), cost: 1
New rule:
l0 -> l3 : 1+x^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l4 : y^0'=y^post2, __const_99^0'=__const_99^post2, x^0'=x^post2, Result^0'=Result^post2, __disjvr_0^0'=__disjvr_0^post2, (y^0-y^post2 == 0 /\ -__const_99^post2+__const_99^0 == 0 /\ -__disjvr_0^post2+__disjvr_0^0 == 0 /\ Result^0-Result^post2 == 0 /\ __disjvr_0^post2-__disjvr_0^0 == 0 /\ x^0-x^post2 == 0), cost: 1
New rule:
l3 -> l4 : 0 == 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l2 : y^0'=y^post3, __const_99^0'=__const_99^post3, x^0'=x^post3, Result^0'=Result^post3, __disjvr_0^0'=__disjvr_0^post3, (-__disjvr_0^post3+__disjvr_0^0 == 0 /\ -1-x^0+x^post3 == 0 /\ __const_99^0-__const_99^post3 == 0 /\ -1-y^0+y^post3 == 0 /\ -Result^post3+Result^0 == 0), cost: 1
New rule:
l4 -> l2 : y^0'=1+y^0, x^0'=1+x^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : y^0'=y^post4, __const_99^0'=__const_99^post4, x^0'=x^post4, Result^0'=Result^post4, __disjvr_0^0'=__disjvr_0^post4, (Result^0-Result^post4 == 0 /\ x^0-x^post4 == 0 /\ -__disjvr_0^post4+__disjvr_0^0 == 0 /\ __const_99^0-__const_99^post4 == 0 /\ y^0-y^post4 == 0), cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l0 -> l5 : y^0'=y^post5, __const_99^0'=__const_99^post5, x^0'=x^post5, Result^0'=Result^post5, __disjvr_0^0'=__disjvr_0^post5, (-1-y^0+y^post5 == 0 /\ __const_99^0+x^post5-x^0 == 0 /\ 1+y^0 <= 0 /\ -1-y^0 <= 0 /\ __disjvr_0^0-__disjvr_0^post5 == 0 /\ -Result^post5+Result^0 == 0 /\ 1+x^0 <= 0 /\ __const_99^0-__const_99^post5 == 0), cost: 1
New rule:
l0 -> l5 : y^0'=1+y^0, x^0'=-__const_99^0+x^0, (1+y^0 == 0 /\ 1+x^0 <= 0), cost: 1

Applied preprocessing
Original rule:
l5 -> l0 : y^0'=y^post6, __const_99^0'=__const_99^post6, x^0'=x^post6, Result^0'=Result^post6, __disjvr_0^0'=__disjvr_0^post6, (-__disjvr_0^post6+__disjvr_0^0 == 0 /\ x^0-x^post6 == 0 /\ y^0-y^post6 == 0 /\ -Result^post6+Result^0 == 0 /\ __const_99^0-__const_99^post6 == 0), cost: 1
New rule:
l5 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l6 -> l0 : y^0'=y^post7, __const_99^0'=__const_99^post7, x^0'=x^post7, Result^0'=Result^post7, __disjvr_0^0'=__disjvr_0^post7, (-x^post7+x^0 == 0 /\ __disjvr_0^0-__disjvr_0^post7 == 0 /\ Result^0-Result^post7 == 0 /\ __const_99^0-__const_99^post7 == 0 /\ y^0-y^post7 == 0), cost: 1
New rule:
l6 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l7 -> l6 : y^0'=y^post8, __const_99^0'=__const_99^post8, x^0'=x^post8, Result^0'=Result^post8, __disjvr_0^0'=__disjvr_0^post8, (-__disjvr_0^post8+__disjvr_0^0 == 0 /\ x^0-x^post8 == 0 /\ y^0-y^post8 == 0 /\ -Result^post8+Result^0 == 0 /\ __const_99^0-__const_99^post8 == 0), cost: 1
New rule:
l7 -> l6 : TRUE, cost: 1

Simplified rules
Start location: l7
   9: l0 -> l3 : 1+x^0 <= 0, cost: 1
  13: l0 -> l5 : y^0'=1+y^0, x^0'=-__const_99^0+x^0, (1+y^0 == 0 /\ 1+x^0 <= 0), cost: 1
  10: l3 -> l4 : 0 == 0, cost: 1
  11: l4 -> l2 : y^0'=1+y^0, x^0'=1+x^0, TRUE, cost: 1
  12: l2 -> l0 : TRUE, cost: 1
  14: l5 -> l0 : TRUE, cost: 1
  15: l6 -> l0 : TRUE, cost: 1
  16: l7 -> l6 : TRUE, cost: 1


Eliminating location l6 by chaining:

Applied chaining
First rule:
l7 -> l6 : TRUE, cost: 1
Second rule:
l6 -> l0 : TRUE, cost: 1
New rule:
l7 -> l0 : TRUE, cost: 2

Applied deletion
Removed the following rules: 15 16

Eliminating location l3 by chaining:

Applied chaining
First rule:
l0 -> l3 : 1+x^0 <= 0, cost: 1
Second rule:
l3 -> l4 : 0 == 0, cost: 1
New rule:
l0 -> l4 : (0 == 0 /\ 1+x^0 <= 0), cost: 2

Applied simplification
Original rule:
l0 -> l4 : (0 == 0 /\ 1+x^0 <= 0), cost: 2
New rule:
l0 -> l4 : 1+x^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 9 10

Eliminating location l5 by chaining:

Applied chaining
First rule:
l0 -> l5 : y^0'=1+y^0, x^0'=-__const_99^0+x^0, (1+y^0 == 0 /\ 1+x^0 <= 0), cost: 1
Second rule:
l5 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : y^0'=1+y^0, x^0'=-__const_99^0+x^0, (1+y^0 == 0 /\ 1+x^0 <= 0), cost: 2

Applied deletion
Removed the following rules: 13 14

Eliminating location l4 by chaining:

Applied chaining
First rule:
l0 -> l4 : 1+x^0 <= 0, cost: 2
Second rule:
l4 -> l2 : y^0'=1+y^0, x^0'=1+x^0, TRUE, cost: 1
New rule:
l0 -> l2 : y^0'=1+y^0, x^0'=1+x^0, 1+x^0 <= 0, cost: 3

Applied deletion
Removed the following rules: 11 18

Eliminating location l2 by chaining:

Applied chaining
First rule:
l0 -> l2 : y^0'=1+y^0, x^0'=1+x^0, 1+x^0 <= 0, cost: 3
Second rule:
l2 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : y^0'=1+y^0, x^0'=1+x^0, 1+x^0 <= 0, cost: 4

Applied deletion
Removed the following rules: 12 20

Eliminated locations on linear paths
Start location: l7
  19: l0 -> l0 : y^0'=1+y^0, x^0'=-__const_99^0+x^0, (1+y^0 == 0 /\ 1+x^0 <= 0), cost: 2
  21: l0 -> l0 : y^0'=1+y^0, x^0'=1+x^0, 1+x^0 <= 0, cost: 4
  17: l7 -> l0 : TRUE, cost: 2


Applied acceleration
Original rule:
l0 -> l0 : y^0'=1+y^0, x^0'=1+x^0, 1+x^0 <= 0, cost: 4
New rule:
l0 -> l0 : y^0'=y^0+n0, x^0'=x^0+n0, (n0 >= 0 /\ -x^0-n0 >= 0), cost: 4*n0
Sub-proof via acceration calculus written to file:///tmp/tmpnam_JCGBdJ.txt

Applied instantiation
Original rule:
l0 -> l0 : y^0'=y^0+n0, x^0'=x^0+n0, (n0 >= 0 /\ -x^0-n0 >= 0), cost: 4*n0
New rule:
l0 -> l0 : y^0'=y^0-x^0, x^0'=0, (0 >= 0 /\ -x^0 >= 0), cost: -4*x^0

Applied simplification
Original rule:
l0 -> l0 : y^0'=y^0-x^0, x^0'=0, (0 >= 0 /\ -x^0 >= 0), cost: -4*x^0
New rule:
l0 -> l0 : y^0'=y^0-x^0, x^0'=0, x^0 <= 0, cost: -4*x^0

Applied deletion
Removed the following rules: 21

Accelerated simple loops
Start location: l7
  19: l0 -> l0 : y^0'=1+y^0, x^0'=-__const_99^0+x^0, (1+y^0 == 0 /\ 1+x^0 <= 0), cost: 2
  23: l0 -> l0 : y^0'=y^0-x^0, x^0'=0, x^0 <= 0, cost: -4*x^0
  17: l7 -> l0 : TRUE, cost: 2


Applied chaining
First rule:
l7 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : y^0'=1+y^0, x^0'=-__const_99^0+x^0, (1+y^0 == 0 /\ 1+x^0 <= 0), cost: 2
New rule:
l7 -> l0 : y^0'=1+y^0, x^0'=-__const_99^0+x^0, (1+y^0 == 0 /\ 1+x^0 <= 0), cost: 4

Applied chaining
First rule:
l7 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : y^0'=y^0-x^0, x^0'=0, x^0 <= 0, cost: -4*x^0
New rule:
l7 -> l0 : y^0'=y^0-x^0, x^0'=0, x^0 <= 0, cost: 2-4*x^0

Applied deletion
Removed the following rules: 19 23

Chained accelerated rules with incoming rules
Start location: l7
  17: l7 -> l0 : TRUE, cost: 2
  24: l7 -> l0 : y^0'=1+y^0, x^0'=-__const_99^0+x^0, (1+y^0 == 0 /\ 1+x^0 <= 0), cost: 4
  25: l7 -> l0 : y^0'=y^0-x^0, x^0'=0, x^0 <= 0, cost: 2-4*x^0


Removed unreachable locations and irrelevant leafs
Start location: l7
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0