WORST_CASE(Omega(0),?)

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


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


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

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

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

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

Simplified rules
Start location: l4
   5: l0 -> l1 : TRUE, cost: 1
   6: l1 -> l3 : x_13^0'=x_13^0+y_15^0, y_15^0'=-1+y_15^0, -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 : x_13^0'=x_13^0+y_15^0, y_15^0'=-1+y_15^0, -1+x_13^0 >= 0, cost: 1
Second rule:
l3 -> l1 : TRUE, cost: 1
New rule:
l1 -> l1 : x_13^0'=x_13^0+y_15^0, y_15^0'=-1+y_15^0, -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 : x_13^0'=x_13^0+y_15^0, y_15^0'=-1+y_15^0, -1+x_13^0 >= 0, cost: 2
   9: l4 -> l1 : TRUE, cost: 2


Applied acceleration
Original rule:
l1 -> l1 : x_13^0'=x_13^0+y_15^0, y_15^0'=-1+y_15^0, -1+x_13^0 >= 0, cost: 2
New rule:
l1 -> l1 : x_13^0'=-1/2*n0^2+x_13^0+1/2*n0+n0*y_15^0, y_15^0'=-n0+y_15^0, (-1+x_13^0 >= 0 /\ n0 >= 0 /\ -3/2-1/2*(-1+n0)^2+x_13^0+1/2*n0+(-1+n0)*y_15^0 >= 0), cost: 2*n0

Applied deletion
Removed the following rules: 10

Accelerated simple loops
Start location: l4
  11: l1 -> l1 : x_13^0'=-1/2*n0^2+x_13^0+1/2*n0+n0*y_15^0, y_15^0'=-n0+y_15^0, (-1+x_13^0 >= 0 /\ n0 >= 0 /\ -3/2-1/2*(-1+n0)^2+x_13^0+1/2*n0+(-1+n0)*y_15^0 >= 0), cost: 2*n0
   9: l4 -> l1 : TRUE, cost: 2


Applied chaining
First rule:
l4 -> l1 : TRUE, cost: 2
Second rule:
l1 -> l1 : x_13^0'=-1/2*n0^2+x_13^0+1/2*n0+n0*y_15^0, y_15^0'=-n0+y_15^0, (-1+x_13^0 >= 0 /\ n0 >= 0 /\ -3/2-1/2*(-1+n0)^2+x_13^0+1/2*n0+(-1+n0)*y_15^0 >= 0), cost: 2*n0
New rule:
l4 -> l1 : x_13^0'=-1/2*n0^2+x_13^0+1/2*n0+n0*y_15^0, y_15^0'=-n0+y_15^0, (-1+x_13^0 >= 0 /\ n0 >= 0 /\ -3/2-1/2*(-1+n0)^2+x_13^0+1/2*n0+(-1+n0)*y_15^0 >= 0), cost: 2+2*n0

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 : x_13^0'=-1/2*n0^2+x_13^0+1/2*n0+n0*y_15^0, y_15^0'=-n0+y_15^0, (-1+x_13^0 >= 0 /\ n0 >= 0 /\ -3/2-1/2*(-1+n0)^2+x_13^0+1/2*n0+(-1+n0)*y_15^0 >= 0), cost: 2+2*n0


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