WORST_CASE(Omega(0),?)

Initial ITS
Start location: l4
   0: l0 -> l1 : x_13^0'=x_13^post0, t_16^0'=t_16^post0, y_21^0'=y_21^post0, temp0_14^0'=temp0_14^post0, result_11^0'=result_11^post0, y_15^0'=y_15^post0, t_22^0'=t_22^post0, (x_13^0-x_13^post0 == 0 /\ -t_16^post0+t_16^0 == 0 /\ -t_22^post0+t_22^0 == 0 /\ -y_15^post0+y_15^0 == 0 /\ -result_11^post0+result_11^0 == 0 /\ temp0_14^0-temp0_14^post0 == 0 /\ y_21^0-y_21^post0 == 0), cost: 1
   1: l1 -> l2 : x_13^0'=x_13^post1, t_16^0'=t_16^post1, y_21^0'=y_21^post1, temp0_14^0'=temp0_14^post1, result_11^0'=result_11^post1, y_15^0'=y_15^post1, t_22^0'=t_22^post1, (y_21^0-y_21^post1 == 0 /\ x_13^0-x_13^post1 == 0 /\ y_15^0 <= 0 /\ t_16^0-t_16^post1 == 0 /\ result_11^post1-temp0_14^0 == 0 /\ 1-x_13^0 <= 0 /\ -t_22^post1+t_22^0 == 0 /\ temp0_14^0-temp0_14^post1 == 0 /\ -y_15^post1+y_15^0 == 0), cost: 1
   2: l1 -> l2 : x_13^0'=x_13^post2, t_16^0'=t_16^post2, y_21^0'=y_21^post2, temp0_14^0'=temp0_14^post2, result_11^0'=result_11^post2, y_15^0'=y_15^post2, t_22^0'=t_22^post2, (0 == 0 /\ x_13^0 <= 0 /\ t_16^0-t_16^post2 == 0 /\ t_22^0-t_22^post2 == 0 /\ x_13^post2 <= 0 /\ -temp0_14^0+result_11^post2 == 0 /\ -y_15^post2+y_15^0 == 0 /\ y_21^0-y_21^post2 == 0 /\ -temp0_14^post2+temp0_14^0 == 0), cost: 1
   3: l1 -> l3 : x_13^0'=x_13^post3, t_16^0'=t_16^post3, y_21^0'=y_21^post3, temp0_14^0'=temp0_14^post3, result_11^0'=result_11^post3, y_15^0'=y_15^post3, t_22^0'=t_22^post3, (0 == 0 /\ 1+t_16^post3-y_15^post3 <= 0 /\ -temp0_14^post3+temp0_14^0 == 0 /\ 1-y_21^post3 <= 0 /\ 2-y_15^10+x_13^post3 == 0 /\ 1-t_22^post3+x_13^post3 <= 0 /\ -2-t_16^post3+y_21^post3 <= 0 /\ 2+t_16^post3-y_21^post3 <= 0 /\ 2-y_15^0+x_13^10 == 0 /\ -1+y_15^10-t_16^10 == 0 /\ 1-t_22^post3 <= 0 /\ -result_11^post3+result_11^0 == 0 /\ -1-t_16^post3+y_15^post3 <= 0 /\ -1-t_16^post3+y_15^post3 == 0 /\ t_16^post3-x_13^10 == 0 /\ -x_13^0+t_16^10 == 0 /\ 1-y_15^0 <= 0 /\ -1+t_22^post3-x_13^post3 <= 0 /\ 1-x_13^0 <= 0), cost: 1
   4: l3 -> l1 : x_13^0'=x_13^post4, t_16^0'=t_16^post4, y_21^0'=y_21^post4, temp0_14^0'=temp0_14^post4, result_11^0'=result_11^post4, y_15^0'=y_15^post4, t_22^0'=t_22^post4, (t_16^0-t_16^post4 == 0 /\ -y_15^post4+y_15^0 == 0 /\ x_13^0-x_13^post4 == 0 /\ -result_11^post4+result_11^0 == 0 /\ t_22^0-t_22^post4 == 0 /\ y_21^0-y_21^post4 == 0 /\ -temp0_14^post4+temp0_14^0 == 0), cost: 1
   5: l4 -> l0 : x_13^0'=x_13^post5, t_16^0'=t_16^post5, y_21^0'=y_21^post5, temp0_14^0'=temp0_14^post5, result_11^0'=result_11^post5, y_15^0'=y_15^post5, t_22^0'=t_22^post5, (-t_22^post5+t_22^0 == 0 /\ result_11^0-result_11^post5 == 0 /\ t_16^0-t_16^post5 == 0 /\ x_13^0-x_13^post5 == 0 /\ y_15^0-y_15^post5 == 0 /\ -y_21^post5+y_21^0 == 0 /\ temp0_14^0-temp0_14^post5 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l4
   0: l0 -> l1 : x_13^0'=x_13^post0, t_16^0'=t_16^post0, y_21^0'=y_21^post0, temp0_14^0'=temp0_14^post0, result_11^0'=result_11^post0, y_15^0'=y_15^post0, t_22^0'=t_22^post0, (x_13^0-x_13^post0 == 0 /\ -t_16^post0+t_16^0 == 0 /\ -t_22^post0+t_22^0 == 0 /\ -y_15^post0+y_15^0 == 0 /\ -result_11^post0+result_11^0 == 0 /\ temp0_14^0-temp0_14^post0 == 0 /\ y_21^0-y_21^post0 == 0), cost: 1
   3: l1 -> l3 : x_13^0'=x_13^post3, t_16^0'=t_16^post3, y_21^0'=y_21^post3, temp0_14^0'=temp0_14^post3, result_11^0'=result_11^post3, y_15^0'=y_15^post3, t_22^0'=t_22^post3, (0 == 0 /\ 1+t_16^post3-y_15^post3 <= 0 /\ -temp0_14^post3+temp0_14^0 == 0 /\ 1-y_21^post3 <= 0 /\ 2-y_15^10+x_13^post3 == 0 /\ 1-t_22^post3+x_13^post3 <= 0 /\ -2-t_16^post3+y_21^post3 <= 0 /\ 2+t_16^post3-y_21^post3 <= 0 /\ 2-y_15^0+x_13^10 == 0 /\ -1+y_15^10-t_16^10 == 0 /\ 1-t_22^post3 <= 0 /\ -result_11^post3+result_11^0 == 0 /\ -1-t_16^post3+y_15^post3 <= 0 /\ -1-t_16^post3+y_15^post3 == 0 /\ t_16^post3-x_13^10 == 0 /\ -x_13^0+t_16^10 == 0 /\ 1-y_15^0 <= 0 /\ -1+t_22^post3-x_13^post3 <= 0 /\ 1-x_13^0 <= 0), cost: 1
   4: l3 -> l1 : x_13^0'=x_13^post4, t_16^0'=t_16^post4, y_21^0'=y_21^post4, temp0_14^0'=temp0_14^post4, result_11^0'=result_11^post4, y_15^0'=y_15^post4, t_22^0'=t_22^post4, (t_16^0-t_16^post4 == 0 /\ -y_15^post4+y_15^0 == 0 /\ x_13^0-x_13^post4 == 0 /\ -result_11^post4+result_11^0 == 0 /\ t_22^0-t_22^post4 == 0 /\ y_21^0-y_21^post4 == 0 /\ -temp0_14^post4+temp0_14^0 == 0), cost: 1
   5: l4 -> l0 : x_13^0'=x_13^post5, t_16^0'=t_16^post5, y_21^0'=y_21^post5, temp0_14^0'=temp0_14^post5, result_11^0'=result_11^post5, y_15^0'=y_15^post5, t_22^0'=t_22^post5, (-t_22^post5+t_22^0 == 0 /\ result_11^0-result_11^post5 == 0 /\ t_16^0-t_16^post5 == 0 /\ x_13^0-x_13^post5 == 0 /\ y_15^0-y_15^post5 == 0 /\ -y_21^post5+y_21^0 == 0 /\ temp0_14^0-temp0_14^post5 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : x_13^0'=x_13^post0, t_16^0'=t_16^post0, y_21^0'=y_21^post0, temp0_14^0'=temp0_14^post0, result_11^0'=result_11^post0, y_15^0'=y_15^post0, t_22^0'=t_22^post0, (x_13^0-x_13^post0 == 0 /\ -t_16^post0+t_16^0 == 0 /\ -t_22^post0+t_22^0 == 0 /\ -y_15^post0+y_15^0 == 0 /\ -result_11^post0+result_11^0 == 0 /\ temp0_14^0-temp0_14^post0 == 0 /\ y_21^0-y_21^post0 == 0), cost: 1
New rule:
l0 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l1 -> l3 : x_13^0'=x_13^post3, t_16^0'=t_16^post3, y_21^0'=y_21^post3, temp0_14^0'=temp0_14^post3, result_11^0'=result_11^post3, y_15^0'=y_15^post3, t_22^0'=t_22^post3, (0 == 0 /\ 1+t_16^post3-y_15^post3 <= 0 /\ -temp0_14^post3+temp0_14^0 == 0 /\ 1-y_21^post3 <= 0 /\ 2-y_15^10+x_13^post3 == 0 /\ 1-t_22^post3+x_13^post3 <= 0 /\ -2-t_16^post3+y_21^post3 <= 0 /\ 2+t_16^post3-y_21^post3 <= 0 /\ 2-y_15^0+x_13^10 == 0 /\ -1+y_15^10-t_16^10 == 0 /\ 1-t_22^post3 <= 0 /\ -result_11^post3+result_11^0 == 0 /\ -1-t_16^post3+y_15^post3 <= 0 /\ -1-t_16^post3+y_15^post3 == 0 /\ t_16^post3-x_13^10 == 0 /\ -x_13^0+t_16^10 == 0 /\ 1-y_15^0 <= 0 /\ -1+t_22^post3-x_13^post3 <= 0 /\ 1-x_13^0 <= 0), cost: 1
New rule:
l1 -> l3 : x_13^0'=-1+x_13^0, t_16^0'=-2+y_15^0, y_21^0'=y_15^0, y_15^0'=-1+y_15^0, t_22^0'=x_13^0, (-1+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 1

Applied preprocessing
Original rule:
l3 -> l1 : x_13^0'=x_13^post4, t_16^0'=t_16^post4, y_21^0'=y_21^post4, temp0_14^0'=temp0_14^post4, result_11^0'=result_11^post4, y_15^0'=y_15^post4, t_22^0'=t_22^post4, (t_16^0-t_16^post4 == 0 /\ -y_15^post4+y_15^0 == 0 /\ x_13^0-x_13^post4 == 0 /\ -result_11^post4+result_11^0 == 0 /\ t_22^0-t_22^post4 == 0 /\ y_21^0-y_21^post4 == 0 /\ -temp0_14^post4+temp0_14^0 == 0), cost: 1
New rule:
l3 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l0 : x_13^0'=x_13^post5, t_16^0'=t_16^post5, y_21^0'=y_21^post5, temp0_14^0'=temp0_14^post5, result_11^0'=result_11^post5, y_15^0'=y_15^post5, t_22^0'=t_22^post5, (-t_22^post5+t_22^0 == 0 /\ result_11^0-result_11^post5 == 0 /\ t_16^0-t_16^post5 == 0 /\ x_13^0-x_13^post5 == 0 /\ y_15^0-y_15^post5 == 0 /\ -y_21^post5+y_21^0 == 0 /\ temp0_14^0-temp0_14^post5 == 0), cost: 1
New rule:
l4 -> l0 : TRUE, cost: 1

Simplified rules
Start location: l4
   6: l0 -> l1 : TRUE, cost: 1
   7: l1 -> l3 : x_13^0'=-1+x_13^0, t_16^0'=-2+y_15^0, y_21^0'=y_15^0, y_15^0'=-1+y_15^0, t_22^0'=x_13^0, (-1+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 1
   8: l3 -> l1 : TRUE, cost: 1
   9: 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 9

Eliminating location l3 by chaining:

Applied chaining
First rule:
l1 -> l3 : x_13^0'=-1+x_13^0, t_16^0'=-2+y_15^0, y_21^0'=y_15^0, y_15^0'=-1+y_15^0, t_22^0'=x_13^0, (-1+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 1
Second rule:
l3 -> l1 : TRUE, cost: 1
New rule:
l1 -> l1 : x_13^0'=-1+x_13^0, t_16^0'=-2+y_15^0, y_21^0'=y_15^0, y_15^0'=-1+y_15^0, t_22^0'=x_13^0, (-1+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 2

Applied deletion
Removed the following rules: 7 8

Eliminated locations on linear paths
Start location: l4
  11: l1 -> l1 : x_13^0'=-1+x_13^0, t_16^0'=-2+y_15^0, y_21^0'=y_15^0, y_15^0'=-1+y_15^0, t_22^0'=x_13^0, (-1+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 2
  10: l4 -> l1 : TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : x_13^0'=-1+x_13^0, t_16^0'=-2+y_15^0, y_21^0'=y_15^0, y_15^0'=-1+y_15^0, t_22^0'=x_13^0, (-1+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 2
New rule:
l1 -> l1 : x_13^0'=x_13^0-n, t_16^0'=-1-n+y_15^0, y_21^0'=1-n+y_15^0, y_15^0'=-n+y_15^0, t_22^0'=1+x_13^0-n, (x_13^0-n >= 0 /\ -1+n >= 0 /\ -n+y_15^0 >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_kkaeNg.txt

Applied instantiation
Original rule:
l1 -> l1 : x_13^0'=x_13^0-n, t_16^0'=-1-n+y_15^0, y_21^0'=1-n+y_15^0, y_15^0'=-n+y_15^0, t_22^0'=1+x_13^0-n, (x_13^0-n >= 0 /\ -1+n >= 0 /\ -n+y_15^0 >= 0), cost: 2*n
New rule:
l1 -> l1 : x_13^0'=0, t_16^0'=-1-x_13^0+y_15^0, y_21^0'=1-x_13^0+y_15^0, y_15^0'=-x_13^0+y_15^0, t_22^0'=1, (0 >= 0 /\ -x_13^0+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 2*x_13^0

Applied instantiation
Original rule:
l1 -> l1 : x_13^0'=x_13^0-n, t_16^0'=-1-n+y_15^0, y_21^0'=1-n+y_15^0, y_15^0'=-n+y_15^0, t_22^0'=1+x_13^0-n, (x_13^0-n >= 0 /\ -1+n >= 0 /\ -n+y_15^0 >= 0), cost: 2*n
New rule:
l1 -> l1 : x_13^0'=x_13^0-y_15^0, t_16^0'=-1, y_21^0'=1, y_15^0'=0, t_22^0'=1+x_13^0-y_15^0, (0 >= 0 /\ -1+y_15^0 >= 0 /\ x_13^0-y_15^0 >= 0), cost: 2*y_15^0

Applied simplification
Original rule:
l1 -> l1 : x_13^0'=0, t_16^0'=-1-x_13^0+y_15^0, y_21^0'=1-x_13^0+y_15^0, y_15^0'=-x_13^0+y_15^0, t_22^0'=1, (0 >= 0 /\ -x_13^0+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 2*x_13^0
New rule:
l1 -> l1 : x_13^0'=0, t_16^0'=-1-x_13^0+y_15^0, y_21^0'=1-x_13^0+y_15^0, y_15^0'=-x_13^0+y_15^0, t_22^0'=1, (-x_13^0+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 2*x_13^0

Applied simplification
Original rule:
l1 -> l1 : x_13^0'=x_13^0-y_15^0, t_16^0'=-1, y_21^0'=1, y_15^0'=0, t_22^0'=1+x_13^0-y_15^0, (0 >= 0 /\ -1+y_15^0 >= 0 /\ x_13^0-y_15^0 >= 0), cost: 2*y_15^0
New rule:
l1 -> l1 : x_13^0'=x_13^0-y_15^0, t_16^0'=-1, y_21^0'=1, y_15^0'=0, t_22^0'=1+x_13^0-y_15^0, (-1+y_15^0 >= 0 /\ x_13^0-y_15^0 >= 0), cost: 2*y_15^0

Applied deletion
Removed the following rules: 11

Accelerated simple loops
Start location: l4
  14: l1 -> l1 : x_13^0'=0, t_16^0'=-1-x_13^0+y_15^0, y_21^0'=1-x_13^0+y_15^0, y_15^0'=-x_13^0+y_15^0, t_22^0'=1, (-x_13^0+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 2*x_13^0
  15: l1 -> l1 : x_13^0'=x_13^0-y_15^0, t_16^0'=-1, y_21^0'=1, y_15^0'=0, t_22^0'=1+x_13^0-y_15^0, (-1+y_15^0 >= 0 /\ x_13^0-y_15^0 >= 0), cost: 2*y_15^0
  10: l4 -> l1 : TRUE, cost: 2


Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : x_13^0'=0, t_16^0'=-1-x_13^0+y_15^0, y_21^0'=1-x_13^0+y_15^0, y_15^0'=-x_13^0+y_15^0, t_22^0'=1, (-x_13^0+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 2*x_13^0
New rule:
l4 -> l1 : x_13^0'=0, t_16^0'=-1-x_13^0+y_15^0, y_21^0'=1-x_13^0+y_15^0, y_15^0'=-x_13^0+y_15^0, t_22^0'=1, (-x_13^0+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 2+2*x_13^0

Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : x_13^0'=x_13^0-y_15^0, t_16^0'=-1, y_21^0'=1, y_15^0'=0, t_22^0'=1+x_13^0-y_15^0, (-1+y_15^0 >= 0 /\ x_13^0-y_15^0 >= 0), cost: 2*y_15^0
New rule:
l4 -> l1 : x_13^0'=x_13^0-y_15^0, t_16^0'=-1, y_21^0'=1, y_15^0'=0, t_22^0'=1+x_13^0-y_15^0, (-1+y_15^0 >= 0 /\ x_13^0-y_15^0 >= 0), cost: 2+2*y_15^0

Applied deletion
Removed the following rules: 14 15

Chained accelerated rules with incoming rules
Start location: l4
  10: l4 -> l1 : TRUE, cost: 2
  16: l4 -> l1 : x_13^0'=0, t_16^0'=-1-x_13^0+y_15^0, y_21^0'=1-x_13^0+y_15^0, y_15^0'=-x_13^0+y_15^0, t_22^0'=1, (-x_13^0+y_15^0 >= 0 /\ -1+x_13^0 >= 0), cost: 2+2*x_13^0
  17: l4 -> l1 : x_13^0'=x_13^0-y_15^0, t_16^0'=-1, y_21^0'=1, y_15^0'=0, t_22^0'=1+x_13^0-y_15^0, (-1+y_15^0 >= 0 /\ x_13^0-y_15^0 >= 0), cost: 2+2*y_15^0


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