WORST_CASE(Omega(0),?)

Initial ITS
Start location: l4
   0: l0 -> l1 : st_14^0'=st_14^post0, y_13^0'=y_13^post0, rt_11^0'=rt_11^post0, x_15^0'=x_15^post0, (y_13^0-y_13^post0 == 0 /\ st_14^0-st_14^post0 == 0 /\ -st_14^0+rt_11^post0 == 0 /\ y_13^0 <= 0 /\ x_15^0-x_15^post0 == 0), cost: 1
   1: l0 -> l2 : st_14^0'=st_14^post1, y_13^0'=y_13^post1, rt_11^0'=rt_11^post1, x_15^0'=x_15^post1, (rt_11^0-rt_11^post1 == 0 /\ 1-y_13^0 <= 0 /\ y_13^0-y_13^post1 == 0 /\ st_14^0-st_14^post1 == 0 /\ -x_15^post1+x_15^0 == 0), cost: 1
   2: l2 -> l1 : st_14^0'=st_14^post2, y_13^0'=y_13^post2, rt_11^0'=rt_11^post2, x_15^0'=x_15^post2, (-y_13^post2+y_13^0 == 0 /\ st_14^0-st_14^post2 == 0 /\ rt_11^post2-st_14^0 == 0 /\ -x_15^post2+x_15^0 == 0 /\ x_15^0 <= 0), cost: 1
   3: l2 -> l3 : st_14^0'=st_14^post3, y_13^0'=y_13^post3, rt_11^0'=rt_11^post3, x_15^0'=x_15^post3, (-rt_11^post3+rt_11^0 == 0 /\ -1+y_13^post3-y_13^0 == 0 /\ 1-x_15^0 <= 0 /\ y_13^0+x_15^post3-x_15^0 == 0 /\ st_14^0-st_14^post3 == 0), cost: 1
   4: l3 -> l2 : st_14^0'=st_14^post4, y_13^0'=y_13^post4, rt_11^0'=rt_11^post4, x_15^0'=x_15^post4, (-rt_11^post4+rt_11^0 == 0 /\ -x_15^post4+x_15^0 == 0 /\ -y_13^post4+y_13^0 == 0 /\ -st_14^post4+st_14^0 == 0), cost: 1
   5: l4 -> l0 : st_14^0'=st_14^post5, y_13^0'=y_13^post5, rt_11^0'=rt_11^post5, x_15^0'=x_15^post5, (y_13^0-y_13^post5 == 0 /\ x_15^0-x_15^post5 == 0 /\ st_14^0-st_14^post5 == 0 /\ rt_11^0-rt_11^post5 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l4
   1: l0 -> l2 : st_14^0'=st_14^post1, y_13^0'=y_13^post1, rt_11^0'=rt_11^post1, x_15^0'=x_15^post1, (rt_11^0-rt_11^post1 == 0 /\ 1-y_13^0 <= 0 /\ y_13^0-y_13^post1 == 0 /\ st_14^0-st_14^post1 == 0 /\ -x_15^post1+x_15^0 == 0), cost: 1
   3: l2 -> l3 : st_14^0'=st_14^post3, y_13^0'=y_13^post3, rt_11^0'=rt_11^post3, x_15^0'=x_15^post3, (-rt_11^post3+rt_11^0 == 0 /\ -1+y_13^post3-y_13^0 == 0 /\ 1-x_15^0 <= 0 /\ y_13^0+x_15^post3-x_15^0 == 0 /\ st_14^0-st_14^post3 == 0), cost: 1
   4: l3 -> l2 : st_14^0'=st_14^post4, y_13^0'=y_13^post4, rt_11^0'=rt_11^post4, x_15^0'=x_15^post4, (-rt_11^post4+rt_11^0 == 0 /\ -x_15^post4+x_15^0 == 0 /\ -y_13^post4+y_13^0 == 0 /\ -st_14^post4+st_14^0 == 0), cost: 1
   5: l4 -> l0 : st_14^0'=st_14^post5, y_13^0'=y_13^post5, rt_11^0'=rt_11^post5, x_15^0'=x_15^post5, (y_13^0-y_13^post5 == 0 /\ x_15^0-x_15^post5 == 0 /\ st_14^0-st_14^post5 == 0 /\ rt_11^0-rt_11^post5 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l2 : st_14^0'=st_14^post1, y_13^0'=y_13^post1, rt_11^0'=rt_11^post1, x_15^0'=x_15^post1, (rt_11^0-rt_11^post1 == 0 /\ 1-y_13^0 <= 0 /\ y_13^0-y_13^post1 == 0 /\ st_14^0-st_14^post1 == 0 /\ -x_15^post1+x_15^0 == 0), cost: 1
New rule:
l0 -> l2 : -1+y_13^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l3 : st_14^0'=st_14^post3, y_13^0'=y_13^post3, rt_11^0'=rt_11^post3, x_15^0'=x_15^post3, (-rt_11^post3+rt_11^0 == 0 /\ -1+y_13^post3-y_13^0 == 0 /\ 1-x_15^0 <= 0 /\ y_13^0+x_15^post3-x_15^0 == 0 /\ st_14^0-st_14^post3 == 0), cost: 1
New rule:
l2 -> l3 : y_13^0'=1+y_13^0, x_15^0'=-y_13^0+x_15^0, -1+x_15^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : st_14^0'=st_14^post4, y_13^0'=y_13^post4, rt_11^0'=rt_11^post4, x_15^0'=x_15^post4, (-rt_11^post4+rt_11^0 == 0 /\ -x_15^post4+x_15^0 == 0 /\ -y_13^post4+y_13^0 == 0 /\ -st_14^post4+st_14^0 == 0), cost: 1
New rule:
l3 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l0 : st_14^0'=st_14^post5, y_13^0'=y_13^post5, rt_11^0'=rt_11^post5, x_15^0'=x_15^post5, (y_13^0-y_13^post5 == 0 /\ x_15^0-x_15^post5 == 0 /\ st_14^0-st_14^post5 == 0 /\ rt_11^0-rt_11^post5 == 0), cost: 1
New rule:
l4 -> l0 : TRUE, cost: 1

Simplified rules
Start location: l4
   6: l0 -> l2 : -1+y_13^0 >= 0, cost: 1
   7: l2 -> l3 : y_13^0'=1+y_13^0, x_15^0'=-y_13^0+x_15^0, -1+x_15^0 >= 0, cost: 1
   8: l3 -> l2 : 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 -> l2 : -1+y_13^0 >= 0, cost: 1
New rule:
l4 -> l2 : -1+y_13^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 6 9

Eliminating location l3 by chaining:

Applied chaining
First rule:
l2 -> l3 : y_13^0'=1+y_13^0, x_15^0'=-y_13^0+x_15^0, -1+x_15^0 >= 0, cost: 1
Second rule:
l3 -> l2 : TRUE, cost: 1
New rule:
l2 -> l2 : y_13^0'=1+y_13^0, x_15^0'=-y_13^0+x_15^0, -1+x_15^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 7 8

Eliminated locations on linear paths
Start location: l4
  11: l2 -> l2 : y_13^0'=1+y_13^0, x_15^0'=-y_13^0+x_15^0, -1+x_15^0 >= 0, cost: 2
  10: l4 -> l2 : -1+y_13^0 >= 0, cost: 2


Applied acceleration
Original rule:
l2 -> l2 : y_13^0'=1+y_13^0, x_15^0'=-y_13^0+x_15^0, -1+x_15^0 >= 0, cost: 2
New rule:
l2 -> l2 : y_13^0'=y_13^0+n, x_15^0'=-1/2*n^2-y_13^0*n+x_15^0+1/2*n, (-1+x_15^0 >= 0 /\ -3/2-(-1+n)*y_13^0-1/2*(-1+n)^2+x_15^0+1/2*n >= 0 /\ n >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_CLpMJo.txt

Applied deletion
Removed the following rules: 11

Accelerated simple loops
Start location: l4
  12: l2 -> l2 : y_13^0'=y_13^0+n, x_15^0'=-1/2*n^2-y_13^0*n+x_15^0+1/2*n, (-1+x_15^0 >= 0 /\ -3/2-(-1+n)*y_13^0-1/2*(-1+n)^2+x_15^0+1/2*n >= 0 /\ n >= 0), cost: 2*n
  10: l4 -> l2 : -1+y_13^0 >= 0, cost: 2


Applied chaining
First rule:
l4 -> l2 : -1+y_13^0 >= 0, cost: 2
Second rule:
l2 -> l2 : y_13^0'=y_13^0+n, x_15^0'=-1/2*n^2-y_13^0*n+x_15^0+1/2*n, (-1+x_15^0 >= 0 /\ -3/2-(-1+n)*y_13^0-1/2*(-1+n)^2+x_15^0+1/2*n >= 0 /\ n >= 0), cost: 2*n
New rule:
l4 -> l2 : y_13^0'=y_13^0+n, x_15^0'=-1/2*n^2-y_13^0*n+x_15^0+1/2*n, (-1+y_13^0 >= 0 /\ -1+x_15^0 >= 0 /\ -3/2-(-1+n)*y_13^0-1/2*(-1+n)^2+x_15^0+1/2*n >= 0 /\ n >= 0), cost: 2+2*n

Applied deletion
Removed the following rules: 12

Chained accelerated rules with incoming rules
Start location: l4
  10: l4 -> l2 : -1+y_13^0 >= 0, cost: 2
  13: l4 -> l2 : y_13^0'=y_13^0+n, x_15^0'=-1/2*n^2-y_13^0*n+x_15^0+1/2*n, (-1+y_13^0 >= 0 /\ -1+x_15^0 >= 0 /\ -3/2-(-1+n)*y_13^0-1/2*(-1+n)^2+x_15^0+1/2*n >= 0 /\ n >= 0), cost: 2+2*n


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