WORST_CASE(Omega(0),?)

Initial ITS
Start location: l4
   0: l0 -> l1 : st_14^0'=st_14^post0, y_15^0'=y_15^post0, rt_11^0'=rt_11^post0, x_13^0'=x_13^post0, (y_15^0-y_15^post0 == 0 /\ st_14^0-st_14^post0 == 0 /\ x_13^0-x_13^post0 == 0 /\ rt_11^0-rt_11^post0 == 0), cost: 1
   1: l1 -> l2 : st_14^0'=st_14^post1, y_15^0'=y_15^post1, rt_11^0'=rt_11^post1, x_13^0'=x_13^post1, (y_15^0-y_15^post1 == 0 /\ st_14^0-st_14^post1 == 0 /\ -st_14^0+rt_11^post1 == 0 /\ x_13^0 <= 0 /\ -x_13^post1+x_13^0 == 0), cost: 1
   2: l1 -> l3 : st_14^0'=st_14^post2, y_15^0'=y_15^post2, rt_11^0'=rt_11^post2, x_13^0'=x_13^post2, (1+y_15^post2-y_15^0 == 0 /\ st_14^0-st_14^post2 == 0 /\ 1-x_13^0 <= 0 /\ -rt_11^post2+rt_11^0 == 0 /\ x_13^post2-y_15^0-x_13^0 == 0), cost: 1
   3: l3 -> l1 : st_14^0'=st_14^post3, y_15^0'=y_15^post3, rt_11^0'=rt_11^post3, x_13^0'=x_13^post3, (-rt_11^post3+rt_11^0 == 0 /\ -x_13^post3+x_13^0 == 0 /\ -y_15^post3+y_15^0 == 0 /\ st_14^0-st_14^post3 == 0), cost: 1
   4: l4 -> l0 : st_14^0'=st_14^post4, y_15^0'=y_15^post4, rt_11^0'=rt_11^post4, x_13^0'=x_13^post4, (-rt_11^post4+rt_11^0 == 0 /\ -x_13^post4+x_13^0 == 0 /\ -y_15^post4+y_15^0 == 0 /\ -st_14^post4+st_14^0 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l4
   0: l0 -> l1 : st_14^0'=st_14^post0, y_15^0'=y_15^post0, rt_11^0'=rt_11^post0, x_13^0'=x_13^post0, (y_15^0-y_15^post0 == 0 /\ st_14^0-st_14^post0 == 0 /\ x_13^0-x_13^post0 == 0 /\ rt_11^0-rt_11^post0 == 0), cost: 1
   2: l1 -> l3 : st_14^0'=st_14^post2, y_15^0'=y_15^post2, rt_11^0'=rt_11^post2, x_13^0'=x_13^post2, (1+y_15^post2-y_15^0 == 0 /\ st_14^0-st_14^post2 == 0 /\ 1-x_13^0 <= 0 /\ -rt_11^post2+rt_11^0 == 0 /\ x_13^post2-y_15^0-x_13^0 == 0), cost: 1
   3: l3 -> l1 : st_14^0'=st_14^post3, y_15^0'=y_15^post3, rt_11^0'=rt_11^post3, x_13^0'=x_13^post3, (-rt_11^post3+rt_11^0 == 0 /\ -x_13^post3+x_13^0 == 0 /\ -y_15^post3+y_15^0 == 0 /\ st_14^0-st_14^post3 == 0), cost: 1
   4: l4 -> l0 : st_14^0'=st_14^post4, y_15^0'=y_15^post4, rt_11^0'=rt_11^post4, x_13^0'=x_13^post4, (-rt_11^post4+rt_11^0 == 0 /\ -x_13^post4+x_13^0 == 0 /\ -y_15^post4+y_15^0 == 0 /\ -st_14^post4+st_14^0 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : st_14^0'=st_14^post0, y_15^0'=y_15^post0, rt_11^0'=rt_11^post0, x_13^0'=x_13^post0, (y_15^0-y_15^post0 == 0 /\ st_14^0-st_14^post0 == 0 /\ x_13^0-x_13^post0 == 0 /\ rt_11^0-rt_11^post0 == 0), cost: 1
New rule:
l0 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l1 -> l3 : st_14^0'=st_14^post2, y_15^0'=y_15^post2, rt_11^0'=rt_11^post2, x_13^0'=x_13^post2, (1+y_15^post2-y_15^0 == 0 /\ st_14^0-st_14^post2 == 0 /\ 1-x_13^0 <= 0 /\ -rt_11^post2+rt_11^0 == 0 /\ x_13^post2-y_15^0-x_13^0 == 0), cost: 1
New rule:
l1 -> l3 : y_15^0'=-1+y_15^0, x_13^0'=y_15^0+x_13^0, -1+x_13^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l1 : st_14^0'=st_14^post3, y_15^0'=y_15^post3, rt_11^0'=rt_11^post3, x_13^0'=x_13^post3, (-rt_11^post3+rt_11^0 == 0 /\ -x_13^post3+x_13^0 == 0 /\ -y_15^post3+y_15^0 == 0 /\ st_14^0-st_14^post3 == 0), cost: 1
New rule:
l3 -> l1 : TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l0 : st_14^0'=st_14^post4, y_15^0'=y_15^post4, rt_11^0'=rt_11^post4, x_13^0'=x_13^post4, (-rt_11^post4+rt_11^0 == 0 /\ -x_13^post4+x_13^0 == 0 /\ -y_15^post4+y_15^0 == 0 /\ -st_14^post4+st_14^0 == 0), cost: 1
New rule:
l4 -> l0 : TRUE, cost: 1

Simplified rules
Start location: l4
   5: l0 -> l1 : TRUE, cost: 1
   6: l1 -> l3 : y_15^0'=-1+y_15^0, x_13^0'=y_15^0+x_13^0, -1+x_13^0 >= 0, cost: 1
   7: l3 -> l1 : TRUE, cost: 1
   8: 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: 5 8

Eliminating location l3 by chaining:

Applied chaining
First rule:
l1 -> l3 : y_15^0'=-1+y_15^0, x_13^0'=y_15^0+x_13^0, -1+x_13^0 >= 0, cost: 1
Second rule:
l3 -> l1 : TRUE, cost: 1
New rule:
l1 -> l1 : y_15^0'=-1+y_15^0, x_13^0'=y_15^0+x_13^0, -1+x_13^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 6 7

Eliminated locations on linear paths
Start location: l4
  10: l1 -> l1 : y_15^0'=-1+y_15^0, x_13^0'=y_15^0+x_13^0, -1+x_13^0 >= 0, cost: 2
   9: l4 -> l1 : TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : y_15^0'=-1+y_15^0, x_13^0'=y_15^0+x_13^0, -1+x_13^0 >= 0, cost: 2
New rule:
l1 -> l1 : y_15^0'=y_15^0-n, x_13^0'=-1/2*n^2+1/2*n+x_13^0+y_15^0*n, (-3/2-1/2*(-1+n)^2+1/2*n+x_13^0+y_15^0*(-1+n) >= 0 /\ -1+x_13^0 >= 0 /\ n >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_jnBCnN.txt

Applied deletion
Removed the following rules: 10

Accelerated simple loops
Start location: l4
  11: l1 -> l1 : y_15^0'=y_15^0-n, x_13^0'=-1/2*n^2+1/2*n+x_13^0+y_15^0*n, (-3/2-1/2*(-1+n)^2+1/2*n+x_13^0+y_15^0*(-1+n) >= 0 /\ -1+x_13^0 >= 0 /\ n >= 0), cost: 2*n
   9: l4 -> l1 : TRUE, cost: 2


Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : y_15^0'=y_15^0-n, x_13^0'=-1/2*n^2+1/2*n+x_13^0+y_15^0*n, (-3/2-1/2*(-1+n)^2+1/2*n+x_13^0+y_15^0*(-1+n) >= 0 /\ -1+x_13^0 >= 0 /\ n >= 0), cost: 2*n
New rule:
l4 -> l1 : y_15^0'=y_15^0-n, x_13^0'=-1/2*n^2+1/2*n+x_13^0+y_15^0*n, (-3/2-1/2*(-1+n)^2+1/2*n+x_13^0+y_15^0*(-1+n) >= 0 /\ -1+x_13^0 >= 0 /\ n >= 0), cost: 2+2*n

Applied deletion
Removed the following rules: 11

Chained accelerated rules with incoming rules
Start location: l4
   9: l4 -> l1 : TRUE, cost: 2
  12: l4 -> l1 : y_15^0'=y_15^0-n, x_13^0'=-1/2*n^2+1/2*n+x_13^0+y_15^0*n, (-3/2-1/2*(-1+n)^2+1/2*n+x_13^0+y_15^0*(-1+n) >= 0 /\ -1+x_13^0 >= 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