WORST_CASE(Omega(0),?)

Initial ITS
Start location: l4
   0: l0 -> l1 : tmp^0'=tmp^post0, i^0'=i^post0, (50-i^0 <= 0 /\ -i^post0+i^0 == 0 /\ -tmp^post0+tmp^0 == 0), cost: 1
   1: l0 -> l2 : tmp^0'=tmp^post1, i^0'=i^post1, (tmp^0-tmp^post1 == 0 /\ -1-i^0+i^post1 == 0 /\ -49+i^0 <= 0), cost: 1
   2: l2 -> l0 : tmp^0'=tmp^post2, i^0'=i^post2, (i^0-i^post2 == 0 /\ tmp^0-tmp^post2 == 0), cost: 1
   3: l3 -> l2 : tmp^0'=tmp^post3, i^0'=i^post3, (0 == 0 /\ i^10 == 0 /\ i^post3 == 0), cost: 1
   4: l4 -> l3 : tmp^0'=tmp^post4, i^0'=i^post4, (i^0-i^post4 == 0 /\ tmp^0-tmp^post4 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l4
   1: l0 -> l2 : tmp^0'=tmp^post1, i^0'=i^post1, (tmp^0-tmp^post1 == 0 /\ -1-i^0+i^post1 == 0 /\ -49+i^0 <= 0), cost: 1
   2: l2 -> l0 : tmp^0'=tmp^post2, i^0'=i^post2, (i^0-i^post2 == 0 /\ tmp^0-tmp^post2 == 0), cost: 1
   3: l3 -> l2 : tmp^0'=tmp^post3, i^0'=i^post3, (0 == 0 /\ i^10 == 0 /\ i^post3 == 0), cost: 1
   4: l4 -> l3 : tmp^0'=tmp^post4, i^0'=i^post4, (i^0-i^post4 == 0 /\ tmp^0-tmp^post4 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l2 : tmp^0'=tmp^post1, i^0'=i^post1, (tmp^0-tmp^post1 == 0 /\ -1-i^0+i^post1 == 0 /\ -49+i^0 <= 0), cost: 1
New rule:
l0 -> l2 : i^0'=1+i^0, -49+i^0 <= 0, cost: 1

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

Applied preprocessing
Original rule:
l3 -> l2 : tmp^0'=tmp^post3, i^0'=i^post3, (0 == 0 /\ i^10 == 0 /\ i^post3 == 0), cost: 1
New rule:
l3 -> l2 : tmp^0'=tmp^post3, i^0'=0, 0 == 0, cost: 1

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

Simplified rules
Start location: l4
   5: l0 -> l2 : i^0'=1+i^0, -49+i^0 <= 0, cost: 1
   6: l2 -> l0 : TRUE, cost: 1
   7: l3 -> l2 : tmp^0'=tmp^post3, i^0'=0, 0 == 0, 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 : tmp^0'=tmp^post3, i^0'=0, 0 == 0, cost: 1
New rule:
l4 -> l2 : tmp^0'=tmp^post3, i^0'=0, 0 == 0, cost: 2

Applied deletion
Removed the following rules: 7 8

Eliminating location l0 by chaining:

Applied chaining
First rule:
l2 -> l0 : TRUE, cost: 1
Second rule:
l0 -> l2 : i^0'=1+i^0, -49+i^0 <= 0, cost: 1
New rule:
l2 -> l2 : i^0'=1+i^0, -49+i^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'=1+i^0, -49+i^0 <= 0, cost: 2
   9: l4 -> l2 : tmp^0'=tmp^post3, i^0'=0, 0 == 0, cost: 2


Applied acceleration
Original rule:
l2 -> l2 : i^0'=1+i^0, -49+i^0 <= 0, cost: 2
New rule:
l2 -> l2 : i^0'=n+i^0, (n >= 0 /\ 50-n-i^0 >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_iIELfm.txt

Applied instantiation
Original rule:
l2 -> l2 : i^0'=n+i^0, (n >= 0 /\ 50-n-i^0 >= 0), cost: 2*n
New rule:
l2 -> l2 : i^0'=50, (0 >= 0 /\ 50-i^0 >= 0), cost: 100-2*i^0

Applied simplification
Original rule:
l2 -> l2 : i^0'=50, (0 >= 0 /\ 50-i^0 >= 0), cost: 100-2*i^0
New rule:
l2 -> l2 : i^0'=50, -50+i^0 <= 0, cost: 100-2*i^0

Applied deletion
Removed the following rules: 10

Accelerated simple loops
Start location: l4
  12: l2 -> l2 : i^0'=50, -50+i^0 <= 0, cost: 100-2*i^0
   9: l4 -> l2 : tmp^0'=tmp^post3, i^0'=0, 0 == 0, cost: 2


Applied chaining
First rule:
l4 -> l2 : tmp^0'=tmp^post3, i^0'=0, 0 == 0, cost: 2
Second rule:
l2 -> l2 : i^0'=50, -50+i^0 <= 0, cost: 100-2*i^0
New rule:
l4 -> l2 : tmp^0'=tmp^post3, i^0'=50, (0 == 0 /\ -50 <= 0), cost: 102

Applied deletion
Removed the following rules: 12

Chained accelerated rules with incoming rules
Start location: l4
   9: l4 -> l2 : tmp^0'=tmp^post3, i^0'=0, 0 == 0, cost: 2
  13: l4 -> l2 : tmp^0'=tmp^post3, i^0'=50, (0 == 0 /\ -50 <= 0), cost: 102


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