WORST_CASE(Omega(0),?)

Initial ITS
Start location: l4
   0: l0 -> l1 : i^0'=i^post0, __const_20^0'=__const_20^post0, j^0'=j^post0, (__const_20^0-j^0 <= 0 /\ j^0-j^post0 == 0 /\ __const_20^0-__const_20^post0 == 0 /\ i^0-i^post0 == 0), cost: 1
   1: l0 -> l2 : i^0'=i^post1, __const_20^0'=__const_20^post1, j^0'=j^post1, (j^0-j^post1 == 0 /\ 1-__const_20^0+j^0 <= 0 /\ __const_20^0-__const_20^post1 == 0 /\ i^0-i^post1 == 0), cost: 1
   2: l2 -> l0 : i^0'=i^post2, __const_20^0'=__const_20^post2, j^0'=j^post2, (-2-j^0+j^post2 == 0 /\ -__const_20^post2+__const_20^0 == 0 /\ -2+i^post2-j^post2 == 0), cost: 1
   3: l3 -> l2 : i^0'=i^post3, __const_20^0'=__const_20^post3, j^0'=j^post3, (-__const_20^post3+__const_20^0 == 0 /\ -i^post3+i^0 == 0 /\ j^post3 == 0), cost: 1
   4: l4 -> l3 : i^0'=i^post4, __const_20^0'=__const_20^post4, j^0'=j^post4, (-__const_20^post4+__const_20^0 == 0 /\ -j^post4+j^0 == 0 /\ -i^post4+i^0 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l4
   1: l0 -> l2 : i^0'=i^post1, __const_20^0'=__const_20^post1, j^0'=j^post1, (j^0-j^post1 == 0 /\ 1-__const_20^0+j^0 <= 0 /\ __const_20^0-__const_20^post1 == 0 /\ i^0-i^post1 == 0), cost: 1
   2: l2 -> l0 : i^0'=i^post2, __const_20^0'=__const_20^post2, j^0'=j^post2, (-2-j^0+j^post2 == 0 /\ -__const_20^post2+__const_20^0 == 0 /\ -2+i^post2-j^post2 == 0), cost: 1
   3: l3 -> l2 : i^0'=i^post3, __const_20^0'=__const_20^post3, j^0'=j^post3, (-__const_20^post3+__const_20^0 == 0 /\ -i^post3+i^0 == 0 /\ j^post3 == 0), cost: 1
   4: l4 -> l3 : i^0'=i^post4, __const_20^0'=__const_20^post4, j^0'=j^post4, (-__const_20^post4+__const_20^0 == 0 /\ -j^post4+j^0 == 0 /\ -i^post4+i^0 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l2 : i^0'=i^post1, __const_20^0'=__const_20^post1, j^0'=j^post1, (j^0-j^post1 == 0 /\ 1-__const_20^0+j^0 <= 0 /\ __const_20^0-__const_20^post1 == 0 /\ i^0-i^post1 == 0), cost: 1
New rule:
l0 -> l2 : 1-__const_20^0+j^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : i^0'=i^post2, __const_20^0'=__const_20^post2, j^0'=j^post2, (-2-j^0+j^post2 == 0 /\ -__const_20^post2+__const_20^0 == 0 /\ -2+i^post2-j^post2 == 0), cost: 1
New rule:
l2 -> l0 : i^0'=4+j^0, j^0'=2+j^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : i^0'=i^post3, __const_20^0'=__const_20^post3, j^0'=j^post3, (-__const_20^post3+__const_20^0 == 0 /\ -i^post3+i^0 == 0 /\ j^post3 == 0), cost: 1
New rule:
l3 -> l2 : j^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : i^0'=i^post4, __const_20^0'=__const_20^post4, j^0'=j^post4, (-__const_20^post4+__const_20^0 == 0 /\ -j^post4+j^0 == 0 /\ -i^post4+i^0 == 0), cost: 1
New rule:
l4 -> l3 : TRUE, cost: 1

Simplified rules
Start location: l4
   5: l0 -> l2 : 1-__const_20^0+j^0 <= 0, cost: 1
   6: l2 -> l0 : i^0'=4+j^0, j^0'=2+j^0, TRUE, cost: 1
   7: l3 -> l2 : j^0'=0, TRUE, cost: 1
   8: l4 -> l3 : TRUE, cost: 1


Eliminating location l3 by chaining:

Applied chaining
First rule:
l4 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l2 : j^0'=0, TRUE, cost: 1
New rule:
l4 -> l2 : j^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 7 8

Eliminating location l0 by chaining:

Applied chaining
First rule:
l2 -> l0 : i^0'=4+j^0, j^0'=2+j^0, TRUE, cost: 1
Second rule:
l0 -> l2 : 1-__const_20^0+j^0 <= 0, cost: 1
New rule:
l2 -> l2 : i^0'=4+j^0, j^0'=2+j^0, 3-__const_20^0+j^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 5 6

Eliminated locations on linear paths
Start location: l4
  10: l2 -> l2 : i^0'=4+j^0, j^0'=2+j^0, 3-__const_20^0+j^0 <= 0, cost: 2
   9: l4 -> l2 : j^0'=0, TRUE, cost: 2


Applied acceleration
Original rule:
l2 -> l2 : i^0'=4+j^0, j^0'=2+j^0, 3-__const_20^0+j^0 <= 0, cost: 2
New rule:
l2 -> l2 : i^0'=2+2*n+j^0, j^0'=2*n+j^0, (-1-2*n+__const_20^0-j^0 >= 0 /\ -1+n >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_OkjABM.txt

Applied deletion
Removed the following rules: 10

Accelerated simple loops
Start location: l4
  11: l2 -> l2 : i^0'=2+2*n+j^0, j^0'=2*n+j^0, (-1-2*n+__const_20^0-j^0 >= 0 /\ -1+n >= 0), cost: 2*n
   9: l4 -> l2 : j^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l4 -> l2 : j^0'=0, TRUE, cost: 2
Second rule:
l2 -> l2 : i^0'=2+2*n+j^0, j^0'=2*n+j^0, (-1-2*n+__const_20^0-j^0 >= 0 /\ -1+n >= 0), cost: 2*n
New rule:
l4 -> l2 : i^0'=2+2*n, j^0'=2*n, (-1-2*n+__const_20^0 >= 0 /\ -1+n >= 0), cost: 2+2*n

Applied deletion
Removed the following rules: 11

Chained accelerated rules with incoming rules
Start location: l4
   9: l4 -> l2 : j^0'=0, TRUE, cost: 2
  12: l4 -> l2 : i^0'=2+2*n, j^0'=2*n, (-1-2*n+__const_20^0 >= 0 /\ -1+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