WORST_CASE(Omega(0),?)

Initial ITS
Start location: l5
   0: l0 -> l1 : x_5^0'=x_5^post0, Result_4^0'=Result_4^post0, y_6^0'=y_6^post0, (0 == 0 /\ y_6^0-y_6^post0 == 0 /\ -20+x_5^0 <= 0 /\ x_5^0-x_5^post0 == 0), cost: 1
   1: l0 -> l2 : x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, (21-x_5^0 <= 0 /\ y_6^0-y_6^post1 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ x_5^0-x_5^post1 == 0), cost: 1
   3: l2 -> l0 : x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, (-Result_4^post3+Result_4^0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ 1+x_5^post3-x_5^0 == 0 /\ -30+y_6^0 <= 0), cost: 1
   4: l2 -> l4 : x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, (-Result_4^post4+Result_4^0 == 0 /\ 31-y_6^0 <= 0 /\ -x_5^post4+x_5^0 == 0 /\ 1+y_6^post4-y_6^0 == 0), cost: 1
   2: l3 -> l0 : x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, y_6^0'=y_6^post2, (y_6^0-y_6^post2 == 0 /\ x_5^0-x_5^post2 == 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1
   5: l4 -> l2 : x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, (-Result_4^post5+Result_4^0 == 0 /\ -y_6^post5+y_6^0 == 0 /\ -x_5^post5+x_5^0 == 0), cost: 1
   6: l5 -> l3 : x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, (-Result_4^post6+Result_4^0 == 0 /\ x_5^0-x_5^post6 == 0 /\ -y_6^post6+y_6^0 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l5
   1: l0 -> l2 : x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, (21-x_5^0 <= 0 /\ y_6^0-y_6^post1 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ x_5^0-x_5^post1 == 0), cost: 1
   3: l2 -> l0 : x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, (-Result_4^post3+Result_4^0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ 1+x_5^post3-x_5^0 == 0 /\ -30+y_6^0 <= 0), cost: 1
   4: l2 -> l4 : x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, (-Result_4^post4+Result_4^0 == 0 /\ 31-y_6^0 <= 0 /\ -x_5^post4+x_5^0 == 0 /\ 1+y_6^post4-y_6^0 == 0), cost: 1
   2: l3 -> l0 : x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, y_6^0'=y_6^post2, (y_6^0-y_6^post2 == 0 /\ x_5^0-x_5^post2 == 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1
   5: l4 -> l2 : x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, (-Result_4^post5+Result_4^0 == 0 /\ -y_6^post5+y_6^0 == 0 /\ -x_5^post5+x_5^0 == 0), cost: 1
   6: l5 -> l3 : x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, (-Result_4^post6+Result_4^0 == 0 /\ x_5^0-x_5^post6 == 0 /\ -y_6^post6+y_6^0 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l2 : x_5^0'=x_5^post1, Result_4^0'=Result_4^post1, y_6^0'=y_6^post1, (21-x_5^0 <= 0 /\ y_6^0-y_6^post1 == 0 /\ Result_4^0-Result_4^post1 == 0 /\ x_5^0-x_5^post1 == 0), cost: 1
New rule:
l0 -> l2 : -21+x_5^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l0 : x_5^0'=x_5^post2, Result_4^0'=Result_4^post2, y_6^0'=y_6^post2, (y_6^0-y_6^post2 == 0 /\ x_5^0-x_5^post2 == 0 /\ -Result_4^post2+Result_4^0 == 0), cost: 1
New rule:
l3 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : x_5^0'=x_5^post3, Result_4^0'=Result_4^post3, y_6^0'=y_6^post3, (-Result_4^post3+Result_4^0 == 0 /\ -y_6^post3+y_6^0 == 0 /\ 1+x_5^post3-x_5^0 == 0 /\ -30+y_6^0 <= 0), cost: 1
New rule:
l2 -> l0 : x_5^0'=-1+x_5^0, -30+y_6^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l4 : x_5^0'=x_5^post4, Result_4^0'=Result_4^post4, y_6^0'=y_6^post4, (-Result_4^post4+Result_4^0 == 0 /\ 31-y_6^0 <= 0 /\ -x_5^post4+x_5^0 == 0 /\ 1+y_6^post4-y_6^0 == 0), cost: 1
New rule:
l2 -> l4 : y_6^0'=-1+y_6^0, -31+y_6^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l2 : x_5^0'=x_5^post5, Result_4^0'=Result_4^post5, y_6^0'=y_6^post5, (-Result_4^post5+Result_4^0 == 0 /\ -y_6^post5+y_6^0 == 0 /\ -x_5^post5+x_5^0 == 0), cost: 1
New rule:
l4 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l3 : x_5^0'=x_5^post6, Result_4^0'=Result_4^post6, y_6^0'=y_6^post6, (-Result_4^post6+Result_4^0 == 0 /\ x_5^0-x_5^post6 == 0 /\ -y_6^post6+y_6^0 == 0), cost: 1
New rule:
l5 -> l3 : TRUE, cost: 1

Simplified rules
Start location: l5
   7: l0 -> l2 : -21+x_5^0 >= 0, cost: 1
   9: l2 -> l0 : x_5^0'=-1+x_5^0, -30+y_6^0 <= 0, cost: 1
  10: l2 -> l4 : y_6^0'=-1+y_6^0, -31+y_6^0 >= 0, cost: 1
   8: l3 -> l0 : TRUE, cost: 1
  11: l4 -> l2 : TRUE, cost: 1
  12: l5 -> l3 : TRUE, cost: 1


Eliminating location l3 by chaining:

Applied chaining
First rule:
l5 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l0 : TRUE, cost: 1
New rule:
l5 -> l0 : TRUE, cost: 2

Applied deletion
Removed the following rules: 8 12

Eliminating location l4 by chaining:

Applied chaining
First rule:
l2 -> l4 : y_6^0'=-1+y_6^0, -31+y_6^0 >= 0, cost: 1
Second rule:
l4 -> l2 : TRUE, cost: 1
New rule:
l2 -> l2 : y_6^0'=-1+y_6^0, -31+y_6^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminated locations on linear paths
Start location: l5
   7: l0 -> l2 : -21+x_5^0 >= 0, cost: 1
   9: l2 -> l0 : x_5^0'=-1+x_5^0, -30+y_6^0 <= 0, cost: 1
  14: l2 -> l2 : y_6^0'=-1+y_6^0, -31+y_6^0 >= 0, cost: 2
  13: l5 -> l0 : TRUE, cost: 2


Applied acceleration
Original rule:
l2 -> l2 : y_6^0'=-1+y_6^0, -31+y_6^0 >= 0, cost: 2
New rule:
l2 -> l2 : y_6^0'=-n+y_6^0, (-30-n+y_6^0 >= 0 /\ n >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_pIHJpa.txt

Applied instantiation
Original rule:
l2 -> l2 : y_6^0'=-n+y_6^0, (-30-n+y_6^0 >= 0 /\ n >= 0), cost: 2*n
New rule:
l2 -> l2 : y_6^0'=30, (0 >= 0 /\ -30+y_6^0 >= 0), cost: -60+2*y_6^0

Applied simplification
Original rule:
l2 -> l2 : y_6^0'=30, (0 >= 0 /\ -30+y_6^0 >= 0), cost: -60+2*y_6^0
New rule:
l2 -> l2 : y_6^0'=30, -30+y_6^0 >= 0, cost: -60+2*y_6^0

Applied deletion
Removed the following rules: 14

Accelerated simple loops
Start location: l5
   7: l0 -> l2 : -21+x_5^0 >= 0, cost: 1
   9: l2 -> l0 : x_5^0'=-1+x_5^0, -30+y_6^0 <= 0, cost: 1
  16: l2 -> l2 : y_6^0'=30, -30+y_6^0 >= 0, cost: -60+2*y_6^0
  13: l5 -> l0 : TRUE, cost: 2


Applied chaining
First rule:
l0 -> l2 : -21+x_5^0 >= 0, cost: 1
Second rule:
l2 -> l2 : y_6^0'=30, -30+y_6^0 >= 0, cost: -60+2*y_6^0
New rule:
l0 -> l2 : y_6^0'=30, (-21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -59+2*y_6^0

Applied deletion
Removed the following rules: 16

Chained accelerated rules with incoming rules
Start location: l5
   7: l0 -> l2 : -21+x_5^0 >= 0, cost: 1
  17: l0 -> l2 : y_6^0'=30, (-21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -59+2*y_6^0
   9: l2 -> l0 : x_5^0'=-1+x_5^0, -30+y_6^0 <= 0, cost: 1
  13: l5 -> l0 : TRUE, cost: 2


Eliminating location l2 by chaining:

Applied chaining
First rule:
l0 -> l2 : -21+x_5^0 >= 0, cost: 1
Second rule:
l2 -> l0 : x_5^0'=-1+x_5^0, -30+y_6^0 <= 0, cost: 1
New rule:
l0 -> l0 : x_5^0'=-1+x_5^0, (-21+x_5^0 >= 0 /\ -30+y_6^0 <= 0), cost: 2

Applied chaining
First rule:
l0 -> l2 : y_6^0'=30, (-21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -59+2*y_6^0
Second rule:
l2 -> l0 : x_5^0'=-1+x_5^0, -30+y_6^0 <= 0, cost: 1
New rule:
l0 -> l0 : x_5^0'=-1+x_5^0, y_6^0'=30, (0 <= 0 /\ -21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -58+2*y_6^0

Applied simplification
Original rule:
l0 -> l0 : x_5^0'=-1+x_5^0, y_6^0'=30, (0 <= 0 /\ -21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -58+2*y_6^0
New rule:
l0 -> l0 : x_5^0'=-1+x_5^0, y_6^0'=30, (-21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -58+2*y_6^0

Applied deletion
Removed the following rules: 7 9 17

Eliminated locations on tree-shaped paths
Start location: l5
  18: l0 -> l0 : x_5^0'=-1+x_5^0, (-21+x_5^0 >= 0 /\ -30+y_6^0 <= 0), cost: 2
  19: l0 -> l0 : x_5^0'=-1+x_5^0, y_6^0'=30, (-21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -58+2*y_6^0
  13: l5 -> l0 : TRUE, cost: 2


Applied acceleration
Original rule:
l0 -> l0 : x_5^0'=-1+x_5^0, (-21+x_5^0 >= 0 /\ -30+y_6^0 <= 0), cost: 2
New rule:
l0 -> l0 : x_5^0'=x_5^0-n0, (30-y_6^0 >= 0 /\ n0 >= 0 /\ -20+x_5^0-n0 >= 0), cost: 2*n0
Sub-proof via acceration calculus written to file:///tmp/tmpnam_KkAnAJ.txt

Applied instantiation
Original rule:
l0 -> l0 : x_5^0'=x_5^0-n0, (30-y_6^0 >= 0 /\ n0 >= 0 /\ -20+x_5^0-n0 >= 0), cost: 2*n0
New rule:
l0 -> l0 : x_5^0'=20, (0 >= 0 /\ -20+x_5^0 >= 0 /\ 30-y_6^0 >= 0), cost: -40+2*x_5^0

Applied acceleration
Original rule:
l0 -> l0 : x_5^0'=-1+x_5^0, y_6^0'=30, (-21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -58+2*y_6^0
New rule:
l0 -> l0 : x_5^0'=x_5^0-n1, y_6^0'=30, (-1+n1 >= 0 /\ -30+y_6^0 >= 0 /\ -20+x_5^0-n1 >= 0), cost: 2*n1
Sub-proof via acceration calculus written to file:///tmp/tmpnam_dhljGi.txt

Applied instantiation
Original rule:
l0 -> l0 : x_5^0'=x_5^0-n1, y_6^0'=30, (-1+n1 >= 0 /\ -30+y_6^0 >= 0 /\ -20+x_5^0-n1 >= 0), cost: 2*n1
New rule:
l0 -> l0 : x_5^0'=20, y_6^0'=30, (0 >= 0 /\ -21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -40+2*x_5^0

Applied simplification
Original rule:
l0 -> l0 : x_5^0'=20, (0 >= 0 /\ -20+x_5^0 >= 0 /\ 30-y_6^0 >= 0), cost: -40+2*x_5^0
New rule:
l0 -> l0 : x_5^0'=20, (-20+x_5^0 >= 0 /\ -30+y_6^0 <= 0), cost: -40+2*x_5^0

Applied simplification
Original rule:
l0 -> l0 : x_5^0'=20, y_6^0'=30, (0 >= 0 /\ -21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -40+2*x_5^0
New rule:
l0 -> l0 : x_5^0'=20, y_6^0'=30, (-21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -40+2*x_5^0

Applied deletion
Removed the following rules: 18 19

Accelerated simple loops
Start location: l5
  22: l0 -> l0 : x_5^0'=20, (-20+x_5^0 >= 0 /\ -30+y_6^0 <= 0), cost: -40+2*x_5^0
  23: l0 -> l0 : x_5^0'=20, y_6^0'=30, (-21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -40+2*x_5^0
  13: l5 -> l0 : TRUE, cost: 2


Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x_5^0'=20, (-20+x_5^0 >= 0 /\ -30+y_6^0 <= 0), cost: -40+2*x_5^0
New rule:
l5 -> l0 : x_5^0'=20, (-20+x_5^0 >= 0 /\ -30+y_6^0 <= 0), cost: -38+2*x_5^0

Applied chaining
First rule:
l5 -> l0 : TRUE, cost: 2
Second rule:
l0 -> l0 : x_5^0'=20, y_6^0'=30, (-21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -40+2*x_5^0
New rule:
l5 -> l0 : x_5^0'=20, y_6^0'=30, (-21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -38+2*x_5^0

Applied deletion
Removed the following rules: 22 23

Chained accelerated rules with incoming rules
Start location: l5
  13: l5 -> l0 : TRUE, cost: 2
  24: l5 -> l0 : x_5^0'=20, (-20+x_5^0 >= 0 /\ -30+y_6^0 <= 0), cost: -38+2*x_5^0
  25: l5 -> l0 : x_5^0'=20, y_6^0'=30, (-21+x_5^0 >= 0 /\ -30+y_6^0 >= 0), cost: -38+2*x_5^0


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