WORST_CASE(Omega(0),?)

Initial ITS
Start location: l7
   0: l0 -> l1 : i^0'=i^post0, x^0'=x^post0, j^0'=j^post0, (i^0-i^post0 == 0 /\ x^0-x^post0 == 0 /\ -j^post0+j^0 == 0 /\ -i^0+x^0 <= 0), cost: 1
   1: l0 -> l2 : i^0'=i^post1, x^0'=x^post1, j^0'=j^post1, (-2-j^0+j^post1 == 0 /\ x^0-x^post1 == 0 /\ 1+i^0-x^0 <= 0 /\ -1-i^0+i^post1 == 0), cost: 1
   6: l1 -> l5 : i^0'=i^post6, x^0'=x^post6, j^0'=j^post6, (j^0-j^post6 == 0 /\ 1-2*x^0+j^0 <= 0 /\ i^0-i^post6 == 0 /\ x^0-x^post6 == 0), cost: 1
   7: l1 -> l5 : i^0'=i^post7, x^0'=x^post7, j^0'=j^post7, (2*x^0-j^0 <= 0 /\ x^0-x^post7 == 0 /\ j^0-j^post7 == 0 /\ i^0-i^post7 == 0), cost: 1
   4: l2 -> l0 : i^0'=i^post4, x^0'=x^post4, j^0'=j^post4, (x^0-x^post4 == 0 /\ j^0-j^post4 == 0 /\ i^0-i^post4 == 0), cost: 1
   2: l3 -> l2 : i^0'=i^post2, x^0'=x^post2, j^0'=j^post2, (i^post2 == 0 /\ x^0-x^post2 == 0 /\ 2-x^0 <= 0 /\ j^0-j^post2 == 0), cost: 1
   3: l3 -> l4 : i^0'=i^post3, x^0'=x^post3, j^0'=j^post3, (j^0-j^post3 == 0 /\ -1+x^0 <= 0 /\ i^0-i^post3 == 0 /\ x^0-x^post3 == 0), cost: 1
   5: l5 -> l4 : i^0'=i^post5, x^0'=x^post5, j^0'=j^post5, (i^0-i^post5 == 0 /\ x^0-x^post5 == 0 /\ j^0-j^post5 == 0), cost: 1
   8: l6 -> l3 : i^0'=i^post8, x^0'=x^post8, j^0'=j^post8, (i^0-i^post8 == 0 /\ -10+x^post8 == 0 /\ j^post8 == 0), cost: 1
   9: l7 -> l6 : i^0'=i^post9, x^0'=x^post9, j^0'=j^post9, (i^0-i^post9 == 0 /\ x^0-x^post9 == 0 /\ -j^post9+j^0 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l7
   1: l0 -> l2 : i^0'=i^post1, x^0'=x^post1, j^0'=j^post1, (-2-j^0+j^post1 == 0 /\ x^0-x^post1 == 0 /\ 1+i^0-x^0 <= 0 /\ -1-i^0+i^post1 == 0), cost: 1
   4: l2 -> l0 : i^0'=i^post4, x^0'=x^post4, j^0'=j^post4, (x^0-x^post4 == 0 /\ j^0-j^post4 == 0 /\ i^0-i^post4 == 0), cost: 1
   2: l3 -> l2 : i^0'=i^post2, x^0'=x^post2, j^0'=j^post2, (i^post2 == 0 /\ x^0-x^post2 == 0 /\ 2-x^0 <= 0 /\ j^0-j^post2 == 0), cost: 1
   8: l6 -> l3 : i^0'=i^post8, x^0'=x^post8, j^0'=j^post8, (i^0-i^post8 == 0 /\ -10+x^post8 == 0 /\ j^post8 == 0), cost: 1
   9: l7 -> l6 : i^0'=i^post9, x^0'=x^post9, j^0'=j^post9, (i^0-i^post9 == 0 /\ x^0-x^post9 == 0 /\ -j^post9+j^0 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l2 : i^0'=i^post1, x^0'=x^post1, j^0'=j^post1, (-2-j^0+j^post1 == 0 /\ x^0-x^post1 == 0 /\ 1+i^0-x^0 <= 0 /\ -1-i^0+i^post1 == 0), cost: 1
New rule:
l0 -> l2 : i^0'=1+i^0, j^0'=2+j^0, 1+i^0-x^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l3 -> l2 : i^0'=i^post2, x^0'=x^post2, j^0'=j^post2, (i^post2 == 0 /\ x^0-x^post2 == 0 /\ 2-x^0 <= 0 /\ j^0-j^post2 == 0), cost: 1
New rule:
l3 -> l2 : i^0'=0, -2+x^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : i^0'=i^post4, x^0'=x^post4, j^0'=j^post4, (x^0-x^post4 == 0 /\ j^0-j^post4 == 0 /\ i^0-i^post4 == 0), cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l6 -> l3 : i^0'=i^post8, x^0'=x^post8, j^0'=j^post8, (i^0-i^post8 == 0 /\ -10+x^post8 == 0 /\ j^post8 == 0), cost: 1
New rule:
l6 -> l3 : x^0'=10, j^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l7 -> l6 : i^0'=i^post9, x^0'=x^post9, j^0'=j^post9, (i^0-i^post9 == 0 /\ x^0-x^post9 == 0 /\ -j^post9+j^0 == 0), cost: 1
New rule:
l7 -> l6 : TRUE, cost: 1

Simplified rules
Start location: l7
  10: l0 -> l2 : i^0'=1+i^0, j^0'=2+j^0, 1+i^0-x^0 <= 0, cost: 1
  12: l2 -> l0 : TRUE, cost: 1
  11: l3 -> l2 : i^0'=0, -2+x^0 >= 0, cost: 1
  13: l6 -> l3 : x^0'=10, j^0'=0, TRUE, cost: 1
  14: l7 -> l6 : TRUE, cost: 1


Eliminating location l6 by chaining:

Applied chaining
First rule:
l7 -> l6 : TRUE, cost: 1
Second rule:
l6 -> l3 : x^0'=10, j^0'=0, TRUE, cost: 1
New rule:
l7 -> l3 : x^0'=10, j^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 13 14

Eliminating location l3 by chaining:

Applied chaining
First rule:
l7 -> l3 : x^0'=10, j^0'=0, TRUE, cost: 2
Second rule:
l3 -> l2 : i^0'=0, -2+x^0 >= 0, cost: 1
New rule:
l7 -> l2 : i^0'=0, x^0'=10, j^0'=0, 8 >= 0, cost: 3

Applied deletion
Removed the following rules: 11 15

Eliminating location l0 by chaining:

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

Applied deletion
Removed the following rules: 10 12

Eliminated locations on linear paths
Start location: l7
  17: l2 -> l2 : i^0'=1+i^0, j^0'=2+j^0, 1+i^0-x^0 <= 0, cost: 2
  16: l7 -> l2 : i^0'=0, x^0'=10, j^0'=0, 8 >= 0, cost: 3


Applied acceleration
Original rule:
l2 -> l2 : i^0'=1+i^0, j^0'=2+j^0, 1+i^0-x^0 <= 0, cost: 2
New rule:
l2 -> l2 : i^0'=i^0+n0, j^0'=j^0+2*n0, (n0 >= 0 /\ -i^0+x^0-n0 >= 0), cost: 2*n0

Applied instantiation
Original rule:
l2 -> l2 : i^0'=i^0+n0, j^0'=j^0+2*n0, (n0 >= 0 /\ -i^0+x^0-n0 >= 0), cost: 2*n0
New rule:
l2 -> l2 : i^0'=x^0, j^0'=-2*i^0+2*x^0+j^0, (0 >= 0 /\ -i^0+x^0 >= 0), cost: -2*i^0+2*x^0

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

Applied deletion
Removed the following rules: 17

Accelerated simple loops
Start location: l7
  19: l2 -> l2 : i^0'=x^0, j^0'=-2*i^0+2*x^0+j^0, -i^0+x^0 >= 0, cost: -2*i^0+2*x^0
  16: l7 -> l2 : i^0'=0, x^0'=10, j^0'=0, 8 >= 0, cost: 3


Applied chaining
First rule:
l7 -> l2 : i^0'=0, x^0'=10, j^0'=0, 8 >= 0, cost: 3
Second rule:
l2 -> l2 : i^0'=x^0, j^0'=-2*i^0+2*x^0+j^0, -i^0+x^0 >= 0, cost: -2*i^0+2*x^0
New rule:
l7 -> l2 : i^0'=10, x^0'=10, j^0'=20, (8 >= 0 /\ 10 >= 0), cost: 23

Applied deletion
Removed the following rules: 19

Chained accelerated rules with incoming rules
Start location: l7
  16: l7 -> l2 : i^0'=0, x^0'=10, j^0'=0, 8 >= 0, cost: 3
  20: l7 -> l2 : i^0'=10, x^0'=10, j^0'=20, (8 >= 0 /\ 10 >= 0), cost: 23


Removed unreachable locations and irrelevant leafs
Start location: l7
  <empty>


Computing asymptotic complexity

Proved the following lower bound
Complexity:  Unknown
Cpx degree: ?

Solved cost: 0
Rule cost:   0