WORST_CASE(Omega(0),?)

Initial ITS
Start location: l4
   0: l0 -> l1 : e^0'=e^post0, n^0'=n^post0, (1-e^0 <= 0 /\ -11-n^0+n^post0 == 0 /\ -100+n^0 <= 0 /\ -1-e^0+e^post0 == 0), cost: 1
   2: l0 -> l2 : e^0'=e^post2, n^0'=n^post2, (10+n^post2-n^0 == 0 /\ 101-n^0 <= 0 /\ 1-e^0 <= 0 /\ 1-e^0+e^post2 == 0), cost: 1
   1: l1 -> l0 : e^0'=e^post1, n^0'=n^post1, (-n^post1+n^0 == 0 /\ e^0-e^post1 == 0), cost: 1
   3: l2 -> l0 : e^0'=e^post3, n^0'=n^post3, (e^0-e^post3 == 0 /\ n^0-n^post3 == 0), cost: 1
   4: l3 -> l0 : e^0'=e^post4, n^0'=n^post4, (0 == 0 /\ -1+e^post4 == 0), cost: 1
   5: l4 -> l3 : e^0'=e^post5, n^0'=n^post5, (n^0-n^post5 == 0 /\ e^0-e^post5 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : e^0'=e^post0, n^0'=n^post0, (1-e^0 <= 0 /\ -11-n^0+n^post0 == 0 /\ -100+n^0 <= 0 /\ -1-e^0+e^post0 == 0), cost: 1
New rule:
l0 -> l1 : e^0'=1+e^0, n^0'=11+n^0, (-1+e^0 >= 0 /\ -100+n^0 <= 0), cost: 1

Applied preprocessing
Original rule:
l1 -> l0 : e^0'=e^post1, n^0'=n^post1, (-n^post1+n^0 == 0 /\ e^0-e^post1 == 0), cost: 1
New rule:
l1 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l0 -> l2 : e^0'=e^post2, n^0'=n^post2, (10+n^post2-n^0 == 0 /\ 101-n^0 <= 0 /\ 1-e^0 <= 0 /\ 1-e^0+e^post2 == 0), cost: 1
New rule:
l0 -> l2 : e^0'=-1+e^0, n^0'=-10+n^0, (-1+e^0 >= 0 /\ -101+n^0 >= 0), cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : e^0'=e^post3, n^0'=n^post3, (e^0-e^post3 == 0 /\ n^0-n^post3 == 0), cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l3 -> l0 : e^0'=e^post4, n^0'=n^post4, (0 == 0 /\ -1+e^post4 == 0), cost: 1
New rule:
l3 -> l0 : e^0'=1, n^0'=n^post4, 0 == 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : e^0'=e^post5, n^0'=n^post5, (n^0-n^post5 == 0 /\ e^0-e^post5 == 0), cost: 1
New rule:
l4 -> l3 : TRUE, cost: 1

Simplified rules
Start location: l4
   6: l0 -> l1 : e^0'=1+e^0, n^0'=11+n^0, (-1+e^0 >= 0 /\ -100+n^0 <= 0), cost: 1
   8: l0 -> l2 : e^0'=-1+e^0, n^0'=-10+n^0, (-1+e^0 >= 0 /\ -101+n^0 >= 0), cost: 1
   7: l1 -> l0 : TRUE, cost: 1
   9: l2 -> l0 : TRUE, cost: 1
  10: l3 -> l0 : e^0'=1, n^0'=n^post4, 0 == 0, cost: 1
  11: l4 -> l3 : TRUE, cost: 1


Eliminating location l3 by chaining:

Applied chaining
First rule:
l4 -> l3 : TRUE, cost: 1
Second rule:
l3 -> l0 : e^0'=1, n^0'=n^post4, 0 == 0, cost: 1
New rule:
l4 -> l0 : e^0'=1, n^0'=n^post4, 0 == 0, cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminating location l1 by chaining:

Applied chaining
First rule:
l0 -> l1 : e^0'=1+e^0, n^0'=11+n^0, (-1+e^0 >= 0 /\ -100+n^0 <= 0), cost: 1
Second rule:
l1 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : e^0'=1+e^0, n^0'=11+n^0, (-1+e^0 >= 0 /\ -100+n^0 <= 0), cost: 2

Applied deletion
Removed the following rules: 6 7

Eliminating location l2 by chaining:

Applied chaining
First rule:
l0 -> l2 : e^0'=-1+e^0, n^0'=-10+n^0, (-1+e^0 >= 0 /\ -101+n^0 >= 0), cost: 1
Second rule:
l2 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : e^0'=-1+e^0, n^0'=-10+n^0, (-1+e^0 >= 0 /\ -101+n^0 >= 0), cost: 2

Applied deletion
Removed the following rules: 8 9

Eliminated locations on linear paths
Start location: l4
  13: l0 -> l0 : e^0'=1+e^0, n^0'=11+n^0, (-1+e^0 >= 0 /\ -100+n^0 <= 0), cost: 2
  14: l0 -> l0 : e^0'=-1+e^0, n^0'=-10+n^0, (-1+e^0 >= 0 /\ -101+n^0 >= 0), cost: 2
  12: l4 -> l0 : e^0'=1, n^0'=n^post4, 0 == 0, cost: 2


Applied acceleration
Original rule:
l0 -> l0 : e^0'=1+e^0, n^0'=11+n^0, (-1+e^0 >= 0 /\ -100+n^0 <= 0), cost: 2
New rule:
l0 -> l0 : e^0'=e^0+n1, n^0'=11*n1+n^0, (111-11*n1-n^0 >= 0 /\ -1+e^0 >= 0 /\ n1 >= 0), cost: 2*n1

Applied acceleration
Original rule:
l0 -> l0 : e^0'=-1+e^0, n^0'=-10+n^0, (-1+e^0 >= 0 /\ -101+n^0 >= 0), cost: 2
New rule:
l0 -> l0 : e^0'=e^0-n3, n^0'=-10*n3+n^0, (-91-10*n3+n^0 >= 0 /\ e^0-n3 >= 0 /\ n3 >= 0), cost: 2*n3

Applied instantiation
Original rule:
l0 -> l0 : e^0'=e^0-n3, n^0'=-10*n3+n^0, (-91-10*n3+n^0 >= 0 /\ e^0-n3 >= 0 /\ n3 >= 0), cost: 2*n3
New rule:
l0 -> l0 : e^0'=0, n^0'=-10*e^0+n^0, (0 >= 0 /\ e^0 >= 0 /\ -91-10*e^0+n^0 >= 0), cost: 2*e^0

Applied simplification
Original rule:
l0 -> l0 : e^0'=0, n^0'=-10*e^0+n^0, (0 >= 0 /\ e^0 >= 0 /\ -91-10*e^0+n^0 >= 0), cost: 2*e^0
New rule:
l0 -> l0 : e^0'=0, n^0'=-10*e^0+n^0, (e^0 >= 0 /\ -91-10*e^0+n^0 >= 0), cost: 2*e^0

Applied deletion
Removed the following rules: 13 14

Accelerated simple loops
Start location: l4
  15: l0 -> l0 : e^0'=e^0+n1, n^0'=11*n1+n^0, (111-11*n1-n^0 >= 0 /\ -1+e^0 >= 0 /\ n1 >= 0), cost: 2*n1
  17: l0 -> l0 : e^0'=0, n^0'=-10*e^0+n^0, (e^0 >= 0 /\ -91-10*e^0+n^0 >= 0), cost: 2*e^0
  12: l4 -> l0 : e^0'=1, n^0'=n^post4, 0 == 0, cost: 2


Applied chaining
First rule:
l4 -> l0 : e^0'=1, n^0'=n^post4, 0 == 0, cost: 2
Second rule:
l0 -> l0 : e^0'=e^0+n1, n^0'=11*n1+n^0, (111-11*n1-n^0 >= 0 /\ -1+e^0 >= 0 /\ n1 >= 0), cost: 2*n1
New rule:
l4 -> l0 : e^0'=1+n1, n^0'=n^post4+11*n1, (111-n^post4-11*n1 >= 0 /\ n1 >= 0), cost: 2+2*n1

Applied chaining
First rule:
l4 -> l0 : e^0'=1, n^0'=n^post4, 0 == 0, cost: 2
Second rule:
l0 -> l0 : e^0'=0, n^0'=-10*e^0+n^0, (e^0 >= 0 /\ -91-10*e^0+n^0 >= 0), cost: 2*e^0
New rule:
l4 -> l0 : e^0'=0, n^0'=-10+n^post4, -101+n^post4 >= 0, cost: 4

Applied deletion
Removed the following rules: 15 17

Chained accelerated rules with incoming rules
Start location: l4
  12: l4 -> l0 : e^0'=1, n^0'=n^post4, 0 == 0, cost: 2
  18: l4 -> l0 : e^0'=1+n1, n^0'=n^post4+11*n1, (111-n^post4-11*n1 >= 0 /\ n1 >= 0), cost: 2+2*n1
  19: l4 -> l0 : e^0'=0, n^0'=-10+n^post4, -101+n^post4 >= 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