WORST_CASE(Omega(0),?)

Initial ITS
Start location: l4
   0: l0 -> l1 : i4^0'=i4^post0, Fold6^0'=Fold6^post0, ret_fib9^0'=ret_fib9^post0, ans8^0'=ans8^post0, Fnew5^0'=Fnew5^post0, tmp^0'=tmp^post0, n3^0'=n3^post0, a^0'=a^post0, temp7^0'=temp7^post0, (-Fnew5^0+ans8^post0 == 0 /\ ret_fib9^post0-ans8^post0 == 0 /\ Fnew5^0-Fnew5^post0 == 0 /\ tmp^post0-ret_fib9^post0 == 0 /\ -temp7^post0+temp7^0 == 0 /\ i4^0-i4^post0 == 0 /\ Fold6^0-Fold6^post0 == 0 /\ -a^post0+a^0 == 0 /\ -n3^post0+n3^0 == 0 /\ 1-i4^0+n3^0 <= 0), cost: 1
   1: l0 -> l2 : i4^0'=i4^post1, Fold6^0'=Fold6^post1, ret_fib9^0'=ret_fib9^post1, ans8^0'=ans8^post1, Fnew5^0'=Fnew5^post1, tmp^0'=tmp^post1, n3^0'=n3^post1, a^0'=a^post1, temp7^0'=temp7^post1, (-Fold6^0+Fnew5^post1-Fnew5^0 == 0 /\ Fold6^post1-temp7^post1 == 0 /\ -a^post1+a^0 == 0 /\ -n3^post1+n3^0 == 0 /\ -Fnew5^0+temp7^post1 == 0 /\ ret_fib9^0-ret_fib9^post1 == 0 /\ -tmp^post1+tmp^0 == 0 /\ ans8^0-ans8^post1 == 0 /\ i4^0-n3^0 <= 0 /\ -1-i4^0+i4^post1 == 0), cost: 1
   2: l2 -> l0 : i4^0'=i4^post2, Fold6^0'=Fold6^post2, ret_fib9^0'=ret_fib9^post2, ans8^0'=ans8^post2, Fnew5^0'=Fnew5^post2, tmp^0'=tmp^post2, n3^0'=n3^post2, a^0'=a^post2, temp7^0'=temp7^post2, (Fold6^0-Fold6^post2 == 0 /\ a^0-a^post2 == 0 /\ -temp7^post2+temp7^0 == 0 /\ ans8^0-ans8^post2 == 0 /\ -tmp^post2+tmp^0 == 0 /\ i4^0-i4^post2 == 0 /\ ret_fib9^0-ret_fib9^post2 == 0 /\ n3^0-n3^post2 == 0 /\ -Fnew5^post2+Fnew5^0 == 0), cost: 1
   3: l3 -> l2 : i4^0'=i4^post3, Fold6^0'=Fold6^post3, ret_fib9^0'=ret_fib9^post3, ans8^0'=ans8^post3, Fnew5^0'=Fnew5^post3, tmp^0'=tmp^post3, n3^0'=n3^post3, a^0'=a^post3, temp7^0'=temp7^post3, (-1+Fnew5^post3 == 0 /\ -temp7^post3+temp7^0 == 0 /\ -ans8^post3+ans8^0 == 0 /\ -30+a^post3 == 0 /\ Fold6^post3 == 0 /\ -a^post3+n3^post3 == 0 /\ -ret_fib9^post3+ret_fib9^0 == 0 /\ -2+i4^post3 == 0 /\ -tmp^post3+tmp^0 == 0), cost: 1
   4: l4 -> l3 : i4^0'=i4^post4, Fold6^0'=Fold6^post4, ret_fib9^0'=ret_fib9^post4, ans8^0'=ans8^post4, Fnew5^0'=Fnew5^post4, tmp^0'=tmp^post4, n3^0'=n3^post4, a^0'=a^post4, temp7^0'=temp7^post4, (i4^0-i4^post4 == 0 /\ -n3^post4+n3^0 == 0 /\ -ret_fib9^post4+ret_fib9^0 == 0 /\ tmp^0-tmp^post4 == 0 /\ -ans8^post4+ans8^0 == 0 /\ -a^post4+a^0 == 0 /\ -temp7^post4+temp7^0 == 0 /\ Fnew5^0-Fnew5^post4 == 0 /\ Fold6^0-Fold6^post4 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l4
   1: l0 -> l2 : i4^0'=i4^post1, Fold6^0'=Fold6^post1, ret_fib9^0'=ret_fib9^post1, ans8^0'=ans8^post1, Fnew5^0'=Fnew5^post1, tmp^0'=tmp^post1, n3^0'=n3^post1, a^0'=a^post1, temp7^0'=temp7^post1, (-Fold6^0+Fnew5^post1-Fnew5^0 == 0 /\ Fold6^post1-temp7^post1 == 0 /\ -a^post1+a^0 == 0 /\ -n3^post1+n3^0 == 0 /\ -Fnew5^0+temp7^post1 == 0 /\ ret_fib9^0-ret_fib9^post1 == 0 /\ -tmp^post1+tmp^0 == 0 /\ ans8^0-ans8^post1 == 0 /\ i4^0-n3^0 <= 0 /\ -1-i4^0+i4^post1 == 0), cost: 1
   2: l2 -> l0 : i4^0'=i4^post2, Fold6^0'=Fold6^post2, ret_fib9^0'=ret_fib9^post2, ans8^0'=ans8^post2, Fnew5^0'=Fnew5^post2, tmp^0'=tmp^post2, n3^0'=n3^post2, a^0'=a^post2, temp7^0'=temp7^post2, (Fold6^0-Fold6^post2 == 0 /\ a^0-a^post2 == 0 /\ -temp7^post2+temp7^0 == 0 /\ ans8^0-ans8^post2 == 0 /\ -tmp^post2+tmp^0 == 0 /\ i4^0-i4^post2 == 0 /\ ret_fib9^0-ret_fib9^post2 == 0 /\ n3^0-n3^post2 == 0 /\ -Fnew5^post2+Fnew5^0 == 0), cost: 1
   3: l3 -> l2 : i4^0'=i4^post3, Fold6^0'=Fold6^post3, ret_fib9^0'=ret_fib9^post3, ans8^0'=ans8^post3, Fnew5^0'=Fnew5^post3, tmp^0'=tmp^post3, n3^0'=n3^post3, a^0'=a^post3, temp7^0'=temp7^post3, (-1+Fnew5^post3 == 0 /\ -temp7^post3+temp7^0 == 0 /\ -ans8^post3+ans8^0 == 0 /\ -30+a^post3 == 0 /\ Fold6^post3 == 0 /\ -a^post3+n3^post3 == 0 /\ -ret_fib9^post3+ret_fib9^0 == 0 /\ -2+i4^post3 == 0 /\ -tmp^post3+tmp^0 == 0), cost: 1
   4: l4 -> l3 : i4^0'=i4^post4, Fold6^0'=Fold6^post4, ret_fib9^0'=ret_fib9^post4, ans8^0'=ans8^post4, Fnew5^0'=Fnew5^post4, tmp^0'=tmp^post4, n3^0'=n3^post4, a^0'=a^post4, temp7^0'=temp7^post4, (i4^0-i4^post4 == 0 /\ -n3^post4+n3^0 == 0 /\ -ret_fib9^post4+ret_fib9^0 == 0 /\ tmp^0-tmp^post4 == 0 /\ -ans8^post4+ans8^0 == 0 /\ -a^post4+a^0 == 0 /\ -temp7^post4+temp7^0 == 0 /\ Fnew5^0-Fnew5^post4 == 0 /\ Fold6^0-Fold6^post4 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l2 : i4^0'=i4^post1, Fold6^0'=Fold6^post1, ret_fib9^0'=ret_fib9^post1, ans8^0'=ans8^post1, Fnew5^0'=Fnew5^post1, tmp^0'=tmp^post1, n3^0'=n3^post1, a^0'=a^post1, temp7^0'=temp7^post1, (-Fold6^0+Fnew5^post1-Fnew5^0 == 0 /\ Fold6^post1-temp7^post1 == 0 /\ -a^post1+a^0 == 0 /\ -n3^post1+n3^0 == 0 /\ -Fnew5^0+temp7^post1 == 0 /\ ret_fib9^0-ret_fib9^post1 == 0 /\ -tmp^post1+tmp^0 == 0 /\ ans8^0-ans8^post1 == 0 /\ i4^0-n3^0 <= 0 /\ -1-i4^0+i4^post1 == 0), cost: 1
New rule:
l0 -> l2 : i4^0'=1+i4^0, Fold6^0'=Fnew5^0, Fnew5^0'=Fold6^0+Fnew5^0, temp7^0'=Fnew5^0, i4^0-n3^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : i4^0'=i4^post2, Fold6^0'=Fold6^post2, ret_fib9^0'=ret_fib9^post2, ans8^0'=ans8^post2, Fnew5^0'=Fnew5^post2, tmp^0'=tmp^post2, n3^0'=n3^post2, a^0'=a^post2, temp7^0'=temp7^post2, (Fold6^0-Fold6^post2 == 0 /\ a^0-a^post2 == 0 /\ -temp7^post2+temp7^0 == 0 /\ ans8^0-ans8^post2 == 0 /\ -tmp^post2+tmp^0 == 0 /\ i4^0-i4^post2 == 0 /\ ret_fib9^0-ret_fib9^post2 == 0 /\ n3^0-n3^post2 == 0 /\ -Fnew5^post2+Fnew5^0 == 0), cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : i4^0'=i4^post3, Fold6^0'=Fold6^post3, ret_fib9^0'=ret_fib9^post3, ans8^0'=ans8^post3, Fnew5^0'=Fnew5^post3, tmp^0'=tmp^post3, n3^0'=n3^post3, a^0'=a^post3, temp7^0'=temp7^post3, (-1+Fnew5^post3 == 0 /\ -temp7^post3+temp7^0 == 0 /\ -ans8^post3+ans8^0 == 0 /\ -30+a^post3 == 0 /\ Fold6^post3 == 0 /\ -a^post3+n3^post3 == 0 /\ -ret_fib9^post3+ret_fib9^0 == 0 /\ -2+i4^post3 == 0 /\ -tmp^post3+tmp^0 == 0), cost: 1
New rule:
l3 -> l2 : i4^0'=2, Fold6^0'=0, Fnew5^0'=1, n3^0'=30, a^0'=30, TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : i4^0'=i4^post4, Fold6^0'=Fold6^post4, ret_fib9^0'=ret_fib9^post4, ans8^0'=ans8^post4, Fnew5^0'=Fnew5^post4, tmp^0'=tmp^post4, n3^0'=n3^post4, a^0'=a^post4, temp7^0'=temp7^post4, (i4^0-i4^post4 == 0 /\ -n3^post4+n3^0 == 0 /\ -ret_fib9^post4+ret_fib9^0 == 0 /\ tmp^0-tmp^post4 == 0 /\ -ans8^post4+ans8^0 == 0 /\ -a^post4+a^0 == 0 /\ -temp7^post4+temp7^0 == 0 /\ Fnew5^0-Fnew5^post4 == 0 /\ Fold6^0-Fold6^post4 == 0), cost: 1
New rule:
l4 -> l3 : TRUE, cost: 1

Simplified rules
Start location: l4
   5: l0 -> l2 : i4^0'=1+i4^0, Fold6^0'=Fnew5^0, Fnew5^0'=Fold6^0+Fnew5^0, temp7^0'=Fnew5^0, i4^0-n3^0 <= 0, cost: 1
   6: l2 -> l0 : TRUE, cost: 1
   7: l3 -> l2 : i4^0'=2, Fold6^0'=0, Fnew5^0'=1, n3^0'=30, a^0'=30, 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 : i4^0'=2, Fold6^0'=0, Fnew5^0'=1, n3^0'=30, a^0'=30, TRUE, cost: 1
New rule:
l4 -> l2 : i4^0'=2, Fold6^0'=0, Fnew5^0'=1, n3^0'=30, a^0'=30, TRUE, 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 : i4^0'=1+i4^0, Fold6^0'=Fnew5^0, Fnew5^0'=Fold6^0+Fnew5^0, temp7^0'=Fnew5^0, i4^0-n3^0 <= 0, cost: 1
New rule:
l2 -> l2 : i4^0'=1+i4^0, Fold6^0'=Fnew5^0, Fnew5^0'=Fold6^0+Fnew5^0, temp7^0'=Fnew5^0, i4^0-n3^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 5 6

Eliminated locations on linear paths
Start location: l4
  10: l2 -> l2 : i4^0'=1+i4^0, Fold6^0'=Fnew5^0, Fnew5^0'=Fold6^0+Fnew5^0, temp7^0'=Fnew5^0, i4^0-n3^0 <= 0, cost: 2
   9: l4 -> l2 : i4^0'=2, Fold6^0'=0, Fnew5^0'=1, n3^0'=30, a^0'=30, TRUE, cost: 2


Accelerated simple loops
Start location: l4
  10: l2 -> l2 : i4^0'=1+i4^0, Fold6^0'=Fnew5^0, Fnew5^0'=Fold6^0+Fnew5^0, temp7^0'=Fnew5^0, i4^0-n3^0 <= 0, cost: 2
   9: l4 -> l2 : i4^0'=2, Fold6^0'=0, Fnew5^0'=1, n3^0'=30, a^0'=30, TRUE, cost: 2


Applied chaining
First rule:
l4 -> l2 : i4^0'=2, Fold6^0'=0, Fnew5^0'=1, n3^0'=30, a^0'=30, TRUE, cost: 2
Second rule:
l2 -> l2 : i4^0'=1+i4^0, Fold6^0'=Fnew5^0, Fnew5^0'=Fold6^0+Fnew5^0, temp7^0'=Fnew5^0, i4^0-n3^0 <= 0, cost: 2
New rule:
l4 -> l2 : i4^0'=3, Fold6^0'=1, Fnew5^0'=1, n3^0'=30, a^0'=30, temp7^0'=1, -28 <= 0, cost: 4

Applied deletion
Removed the following rules: 10

Chained accelerated rules with incoming rules
Start location: l4
   9: l4 -> l2 : i4^0'=2, Fold6^0'=0, Fnew5^0'=1, n3^0'=30, a^0'=30, TRUE, cost: 2
  11: l4 -> l2 : i4^0'=3, Fold6^0'=1, Fnew5^0'=1, n3^0'=30, a^0'=30, temp7^0'=1, -28 <= 0, cost: 4


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