WORST_CASE(Omega(0),?)

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


Applied preprocessing
Original rule:
l0 -> l2 : x^0'=x^post0, 1-x^0+x^post0 == 0, cost: 1
New rule:
l0 -> l2 : x^0'=-1+x^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l2 -> l1 : x^0'=x^post1, (1-x^0 <= 0 /\ x^0-x^post1 == 0), cost: 1
New rule:
l2 -> l1 : -1+x^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l1 : x^0'=x^post2, (x^0-x^post2 == 0 /\ 1+x^0 <= 0), cost: 1
New rule:
l2 -> l1 : 1+x^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l1 -> l0 : x^0'=x^post3, x^0-x^post3 == 0, cost: 1
New rule:
l1 -> l0 : TRUE, cost: 1

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

Applied preprocessing
Original rule:
l4 -> l3 : x^0'=x^post5, x^0-x^post5 == 0, cost: 1
New rule:
l4 -> l3 : TRUE, cost: 1

Simplified rules
Start location: l4
   6: l0 -> l2 : x^0'=-1+x^0, TRUE, cost: 1
   7: l2 -> l1 : -1+x^0 >= 0, cost: 1
   8: l2 -> l1 : 1+x^0 <= 0, cost: 1
   9: l1 -> l0 : TRUE, cost: 1
  10: l3 -> l0 : -1+x^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 : -1+x^0 >= 0, cost: 1
New rule:
l4 -> l0 : -1+x^0 >= 0, cost: 2

Applied deletion
Removed the following rules: 10 11

Eliminated locations on linear paths
Start location: l4
   6: l0 -> l2 : x^0'=-1+x^0, TRUE, cost: 1
   7: l2 -> l1 : -1+x^0 >= 0, cost: 1
   8: l2 -> l1 : 1+x^0 <= 0, cost: 1
   9: l1 -> l0 : TRUE, cost: 1
  12: l4 -> l0 : -1+x^0 >= 0, cost: 2


Eliminating location l2 by chaining:

Applied chaining
First rule:
l0 -> l2 : x^0'=-1+x^0, TRUE, cost: 1
Second rule:
l2 -> l1 : -1+x^0 >= 0, cost: 1
New rule:
l0 -> l1 : x^0'=-1+x^0, -2+x^0 >= 0, cost: 2

Applied chaining
First rule:
l0 -> l2 : x^0'=-1+x^0, TRUE, cost: 1
Second rule:
l2 -> l1 : 1+x^0 <= 0, cost: 1
New rule:
l0 -> l1 : x^0'=-1+x^0, x^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 6 7 8

Eliminated locations on tree-shaped paths
Start location: l4
  13: l0 -> l1 : x^0'=-1+x^0, -2+x^0 >= 0, cost: 2
  14: l0 -> l1 : x^0'=-1+x^0, x^0 <= 0, cost: 2
   9: l1 -> l0 : TRUE, cost: 1
  12: l4 -> l0 : -1+x^0 >= 0, cost: 2


Applied merging
first rule:
l0 -> l1 : x^0'=-1+x^0, -2+x^0 >= 0, cost: 2
second rule:
l0 -> l1 : x^0'=-1+x^0, x^0 <= 0, cost: 2
new rule:
l0 -> l1 : x^0'=-1+x^0, (x^0 <= 0 \/ -2+x^0 >= 0), cost: 2

Merged rules
Start location: l4
  15: l0 -> l1 : x^0'=-1+x^0, (x^0 <= 0 \/ -2+x^0 >= 0), cost: 2
   9: l1 -> l0 : TRUE, cost: 1
  12: l4 -> l0 : -1+x^0 >= 0, cost: 2


Eliminating location l1 by chaining:

Applied chaining
First rule:
l0 -> l1 : x^0'=-1+x^0, (x^0 <= 0 \/ -2+x^0 >= 0), cost: 2
Second rule:
l1 -> l0 : TRUE, cost: 1
New rule:
l0 -> l0 : x^0'=-1+x^0, (x^0 <= 0 \/ -2+x^0 >= 0), cost: 3

Applied deletion
Removed the following rules: 9 15

Eliminated locations on linear paths
Start location: l4
  16: l0 -> l0 : x^0'=-1+x^0, (x^0 <= 0 \/ -2+x^0 >= 0), cost: 3
  12: l4 -> l0 : -1+x^0 >= 0, cost: 2


Applied nonterm
Original rule:
l0 -> l0 : x^0'=-1+x^0, (x^0 <= 0 \/ -2+x^0 >= 0), cost: 3
New rule:
l0 -> [5] : -x^0 >= 0, cost: NONTERM

Applied acceleration
Original rule:
l0 -> l0 : x^0'=-1+x^0, (x^0 <= 0 \/ -2+x^0 >= 0), cost: 3
New rule:
l0 -> l0 : x^0'=x^0-n0, (n0 >= 0 /\ (-1+x^0-n0 >= 0 \/ -x^0 >= 0)), cost: 3*n0

Applied instantiation
Original rule:
l0 -> l0 : x^0'=x^0-n0, (n0 >= 0 /\ (-1+x^0-n0 >= 0 \/ -x^0 >= 0)), cost: 3*n0
New rule:
l0 -> l0 : x^0'=1, (-1+x^0 >= 0 /\ (0 >= 0 \/ -x^0 >= 0)), cost: -3+3*x^0

Applied simplification
Original rule:
l0 -> [5] : -x^0 >= 0, cost: NONTERM
New rule:
l0 -> [5] : x^0 <= 0, cost: NONTERM

Applied simplification
Original rule:
l0 -> l0 : x^0'=1, (-1+x^0 >= 0 /\ (0 >= 0 \/ -x^0 >= 0)), cost: -3+3*x^0
New rule:
l0 -> l0 : x^0'=1, -1+x^0 >= 0, cost: -3+3*x^0

Applied deletion
Removed the following rules: 16

Accelerated simple loops
Start location: l4
  19: l0 -> [5] : x^0 <= 0, cost: NONTERM
  20: l0 -> l0 : x^0'=1, -1+x^0 >= 0, cost: -3+3*x^0
  12: l4 -> l0 : -1+x^0 >= 0, cost: 2


Applied chaining
First rule:
l4 -> l0 : -1+x^0 >= 0, cost: 2
Second rule:
l0 -> l0 : x^0'=1, -1+x^0 >= 0, cost: -3+3*x^0
New rule:
l4 -> l0 : x^0'=1, -1+x^0 >= 0, cost: -1+3*x^0

Applied deletion
Removed the following rules: 19 20

Chained accelerated rules with incoming rules
Start location: l4
  12: l4 -> l0 : -1+x^0 >= 0, cost: 2
  21: l4 -> l0 : x^0'=1, -1+x^0 >= 0, cost: -1+3*x^0


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