WORST_CASE(Omega(0),?)

Initial ITS
Start location: l10
   0: l0 -> l1 : N^0'=N^post0, tmp^0'=tmp^post0, i^0'=i^post0, x^0'=x^post0, (i^0-i^post0 == 0 /\ -2+x^post0-x^0 == 0 /\ N^0-N^post0 == 0 /\ tmp^0-tmp^post0 == 0), cost: 1
   1: l0 -> l1 : N^0'=N^post1, tmp^0'=tmp^post1, i^0'=i^post1, x^0'=x^post1, (-i^post1+i^0 == 0 /\ N^0-N^post1 == 0 /\ -tmp^post1+tmp^0 == 0 /\ -x^post1+x^0 == 0), cost: 1
  13: l1 -> l4 : N^0'=N^post13, tmp^0'=tmp^post13, i^0'=i^post13, x^0'=x^post13, (-1+i^post13-i^0 == 0 /\ -x^post13+x^0 == 0 /\ N^0-N^post13 == 0 /\ tmp^0-tmp^post13 == 0), cost: 1
   2: l2 -> l3 : N^0'=N^post2, tmp^0'=tmp^post2, i^0'=i^post2, x^0'=x^post2, (-i^post2+i^0 == 0 /\ tmp^0-tmp^post2 == 0 /\ N^0-i^0 <= 0 /\ -x^post2+x^0 == 0 /\ N^0-N^post2 == 0), cost: 1
   3: l2 -> l0 : N^0'=N^post3, tmp^0'=tmp^post3, i^0'=i^post3, x^0'=x^post3, (N^0-N^post3 == 0 /\ 1-N^0+i^0 <= 0 /\ tmp^0-tmp^post3 == 0 /\ i^0-i^post3 == 0 /\ -x^post3+x^0 == 0), cost: 1
  10: l3 -> l7 : N^0'=N^post10, tmp^0'=tmp^post10, i^0'=i^post10, x^0'=x^post10, (-x^post10+x^0 == 0 /\ 1+N^0-x^0 <= 0 /\ N^0-N^post10 == 0 /\ -i^post10+i^0 == 0 /\ tmp^0-tmp^post10 == 0), cost: 1
  11: l3 -> l7 : N^0'=N^post11, tmp^0'=tmp^post11, i^0'=i^post11, x^0'=x^post11, (1-N^0+x^0 <= 0 /\ i^0-i^post11 == 0 /\ -x^post11+x^0 == 0 /\ N^0-N^post11 == 0 /\ tmp^0-tmp^post11 == 0), cost: 1
  12: l3 -> l6 : N^0'=N^post12, tmp^0'=tmp^post12, i^0'=i^post12, x^0'=x^post12, (-N^0+x^0 <= 0 /\ i^0-i^post12 == 0 /\ -1+tmp^post12 == 0 /\ N^0-N^post12 == 0 /\ -x^post12+x^0 == 0 /\ N^0-x^0 <= 0), cost: 1
   4: l4 -> l2 : N^0'=N^post4, tmp^0'=tmp^post4, i^0'=i^post4, x^0'=x^post4, (N^0-N^post4 == 0 /\ -x^post4+x^0 == 0 /\ -i^post4+i^0 == 0 /\ -tmp^post4+tmp^0 == 0), cost: 1
   5: l5 -> l6 : N^0'=N^post5, tmp^0'=tmp^post5, i^0'=i^post5, x^0'=x^post5, (N^0-N^post5 == 0 /\ tmp^post5 == 0 /\ -x^post5+x^0 == 0 /\ -i^post5+i^0 == 0), cost: 1
   9: l6 -> l8 : N^0'=N^post9, tmp^0'=tmp^post9, i^0'=i^post9, x^0'=x^post9, (-tmp^post9+tmp^0 == 0 /\ N^0-N^post9 == 0 /\ -x^post9+x^0 == 0 /\ -i^post9+i^0 == 0), cost: 1
   6: l7 -> l5 : N^0'=N^post6, tmp^0'=tmp^post6, i^0'=i^post6, x^0'=x^post6, (tmp^0-tmp^post6 == 0 /\ 2+N^0-x^0 <= 0 /\ x^0-x^post6 == 0 /\ N^0-N^post6 == 0 /\ -i^post6+i^0 == 0), cost: 1
   7: l7 -> l5 : N^0'=N^post7, tmp^0'=tmp^post7, i^0'=i^post7, x^0'=x^post7, (N^0-N^post7 == 0 /\ -N^0+x^0 <= 0 /\ i^0-i^post7 == 0 /\ tmp^0-tmp^post7 == 0 /\ -x^post7+x^0 == 0), cost: 1
   8: l7 -> l6 : N^0'=N^post8, tmp^0'=tmp^post8, i^0'=i^post8, x^0'=x^post8, (1+N^0-x^0 <= 0 /\ -x^post8+x^0 == 0 /\ -i^post8+i^0 == 0 /\ N^0-N^post8 == 0 /\ -1+tmp^post8 == 0 /\ -1-N^0+x^0 <= 0), cost: 1
  14: l9 -> l4 : N^0'=N^post14, tmp^0'=tmp^post14, i^0'=i^post14, x^0'=x^post14, (i^post14 == 0 /\ N^0-N^post14 == 0 /\ -tmp^post14+tmp^0 == 0 /\ x^post14 == 0), cost: 1
  15: l10 -> l9 : N^0'=N^post15, tmp^0'=tmp^post15, i^0'=i^post15, x^0'=x^post15, (-x^post15+x^0 == 0 /\ -i^post15+i^0 == 0 /\ tmp^0-tmp^post15 == 0 /\ N^0-N^post15 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l10
   0: l0 -> l1 : N^0'=N^post0, tmp^0'=tmp^post0, i^0'=i^post0, x^0'=x^post0, (i^0-i^post0 == 0 /\ -2+x^post0-x^0 == 0 /\ N^0-N^post0 == 0 /\ tmp^0-tmp^post0 == 0), cost: 1
   1: l0 -> l1 : N^0'=N^post1, tmp^0'=tmp^post1, i^0'=i^post1, x^0'=x^post1, (-i^post1+i^0 == 0 /\ N^0-N^post1 == 0 /\ -tmp^post1+tmp^0 == 0 /\ -x^post1+x^0 == 0), cost: 1
  13: l1 -> l4 : N^0'=N^post13, tmp^0'=tmp^post13, i^0'=i^post13, x^0'=x^post13, (-1+i^post13-i^0 == 0 /\ -x^post13+x^0 == 0 /\ N^0-N^post13 == 0 /\ tmp^0-tmp^post13 == 0), cost: 1
   3: l2 -> l0 : N^0'=N^post3, tmp^0'=tmp^post3, i^0'=i^post3, x^0'=x^post3, (N^0-N^post3 == 0 /\ 1-N^0+i^0 <= 0 /\ tmp^0-tmp^post3 == 0 /\ i^0-i^post3 == 0 /\ -x^post3+x^0 == 0), cost: 1
   4: l4 -> l2 : N^0'=N^post4, tmp^0'=tmp^post4, i^0'=i^post4, x^0'=x^post4, (N^0-N^post4 == 0 /\ -x^post4+x^0 == 0 /\ -i^post4+i^0 == 0 /\ -tmp^post4+tmp^0 == 0), cost: 1
  14: l9 -> l4 : N^0'=N^post14, tmp^0'=tmp^post14, i^0'=i^post14, x^0'=x^post14, (i^post14 == 0 /\ N^0-N^post14 == 0 /\ -tmp^post14+tmp^0 == 0 /\ x^post14 == 0), cost: 1
  15: l10 -> l9 : N^0'=N^post15, tmp^0'=tmp^post15, i^0'=i^post15, x^0'=x^post15, (-x^post15+x^0 == 0 /\ -i^post15+i^0 == 0 /\ tmp^0-tmp^post15 == 0 /\ N^0-N^post15 == 0), cost: 1


Applied preprocessing
Original rule:
l0 -> l1 : N^0'=N^post0, tmp^0'=tmp^post0, i^0'=i^post0, x^0'=x^post0, (i^0-i^post0 == 0 /\ -2+x^post0-x^0 == 0 /\ N^0-N^post0 == 0 /\ tmp^0-tmp^post0 == 0), cost: 1
New rule:
l0 -> l1 : x^0'=2+x^0, TRUE, cost: 1

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

Applied preprocessing
Original rule:
l2 -> l0 : N^0'=N^post3, tmp^0'=tmp^post3, i^0'=i^post3, x^0'=x^post3, (N^0-N^post3 == 0 /\ 1-N^0+i^0 <= 0 /\ tmp^0-tmp^post3 == 0 /\ i^0-i^post3 == 0 /\ -x^post3+x^0 == 0), cost: 1
New rule:
l2 -> l0 : 1-N^0+i^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l4 -> l2 : N^0'=N^post4, tmp^0'=tmp^post4, i^0'=i^post4, x^0'=x^post4, (N^0-N^post4 == 0 /\ -x^post4+x^0 == 0 /\ -i^post4+i^0 == 0 /\ -tmp^post4+tmp^0 == 0), cost: 1
New rule:
l4 -> l2 : TRUE, cost: 1

Applied preprocessing
Original rule:
l1 -> l4 : N^0'=N^post13, tmp^0'=tmp^post13, i^0'=i^post13, x^0'=x^post13, (-1+i^post13-i^0 == 0 /\ -x^post13+x^0 == 0 /\ N^0-N^post13 == 0 /\ tmp^0-tmp^post13 == 0), cost: 1
New rule:
l1 -> l4 : i^0'=1+i^0, TRUE, cost: 1

Applied preprocessing
Original rule:
l9 -> l4 : N^0'=N^post14, tmp^0'=tmp^post14, i^0'=i^post14, x^0'=x^post14, (i^post14 == 0 /\ N^0-N^post14 == 0 /\ -tmp^post14+tmp^0 == 0 /\ x^post14 == 0), cost: 1
New rule:
l9 -> l4 : i^0'=0, x^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l10 -> l9 : N^0'=N^post15, tmp^0'=tmp^post15, i^0'=i^post15, x^0'=x^post15, (-x^post15+x^0 == 0 /\ -i^post15+i^0 == 0 /\ tmp^0-tmp^post15 == 0 /\ N^0-N^post15 == 0), cost: 1
New rule:
l10 -> l9 : TRUE, cost: 1

Simplified rules
Start location: l10
  16: l0 -> l1 : x^0'=2+x^0, TRUE, cost: 1
  17: l0 -> l1 : TRUE, cost: 1
  20: l1 -> l4 : i^0'=1+i^0, TRUE, cost: 1
  18: l2 -> l0 : 1-N^0+i^0 <= 0, cost: 1
  19: l4 -> l2 : TRUE, cost: 1
  21: l9 -> l4 : i^0'=0, x^0'=0, TRUE, cost: 1
  22: l10 -> l9 : TRUE, cost: 1


Eliminating location l9 by chaining:

Applied chaining
First rule:
l10 -> l9 : TRUE, cost: 1
Second rule:
l9 -> l4 : i^0'=0, x^0'=0, TRUE, cost: 1
New rule:
l10 -> l4 : i^0'=0, x^0'=0, TRUE, cost: 2

Applied deletion
Removed the following rules: 21 22

Eliminating location l2 by chaining:

Applied chaining
First rule:
l4 -> l2 : TRUE, cost: 1
Second rule:
l2 -> l0 : 1-N^0+i^0 <= 0, cost: 1
New rule:
l4 -> l0 : 1-N^0+i^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 18 19

Eliminated locations on linear paths
Start location: l10
  16: l0 -> l1 : x^0'=2+x^0, TRUE, cost: 1
  17: l0 -> l1 : TRUE, cost: 1
  20: l1 -> l4 : i^0'=1+i^0, TRUE, cost: 1
  24: l4 -> l0 : 1-N^0+i^0 <= 0, cost: 2
  23: l10 -> l4 : i^0'=0, x^0'=0, TRUE, cost: 2


Eliminating location l0 by chaining:

Applied chaining
First rule:
l4 -> l0 : 1-N^0+i^0 <= 0, cost: 2
Second rule:
l0 -> l1 : x^0'=2+x^0, TRUE, cost: 1
New rule:
l4 -> l1 : x^0'=2+x^0, 1-N^0+i^0 <= 0, cost: 3

Applied chaining
First rule:
l4 -> l0 : 1-N^0+i^0 <= 0, cost: 2
Second rule:
l0 -> l1 : TRUE, cost: 1
New rule:
l4 -> l1 : 1-N^0+i^0 <= 0, cost: 3

Applied deletion
Removed the following rules: 16 17 24

Eliminated locations on tree-shaped paths
Start location: l10
  20: l1 -> l4 : i^0'=1+i^0, TRUE, cost: 1
  25: l4 -> l1 : x^0'=2+x^0, 1-N^0+i^0 <= 0, cost: 3
  26: l4 -> l1 : 1-N^0+i^0 <= 0, cost: 3
  23: l10 -> l4 : i^0'=0, x^0'=0, TRUE, cost: 2


Eliminating location l1 by chaining:

Applied chaining
First rule:
l4 -> l1 : x^0'=2+x^0, 1-N^0+i^0 <= 0, cost: 3
Second rule:
l1 -> l4 : i^0'=1+i^0, TRUE, cost: 1
New rule:
l4 -> l4 : i^0'=1+i^0, x^0'=2+x^0, 1-N^0+i^0 <= 0, cost: 4

Applied chaining
First rule:
l4 -> l1 : 1-N^0+i^0 <= 0, cost: 3
Second rule:
l1 -> l4 : i^0'=1+i^0, TRUE, cost: 1
New rule:
l4 -> l4 : i^0'=1+i^0, 1-N^0+i^0 <= 0, cost: 4

Applied deletion
Removed the following rules: 20 25 26

Eliminated locations on tree-shaped paths
Start location: l10
  27: l4 -> l4 : i^0'=1+i^0, x^0'=2+x^0, 1-N^0+i^0 <= 0, cost: 4
  28: l4 -> l4 : i^0'=1+i^0, 1-N^0+i^0 <= 0, cost: 4
  23: l10 -> l4 : i^0'=0, x^0'=0, TRUE, cost: 2


Applied acceleration
Original rule:
l4 -> l4 : i^0'=1+i^0, x^0'=2+x^0, 1-N^0+i^0 <= 0, cost: 4
New rule:
l4 -> l4 : i^0'=i^0+n1, x^0'=2*n1+x^0, (n1 >= 0 /\ N^0-i^0-n1 >= 0), cost: 4*n1

Applied instantiation
Original rule:
l4 -> l4 : i^0'=i^0+n1, x^0'=2*n1+x^0, (n1 >= 0 /\ N^0-i^0-n1 >= 0), cost: 4*n1
New rule:
l4 -> l4 : i^0'=N^0, x^0'=2*N^0-2*i^0+x^0, (0 >= 0 /\ N^0-i^0 >= 0), cost: 4*N^0-4*i^0

Applied acceleration
Original rule:
l4 -> l4 : i^0'=1+i^0, 1-N^0+i^0 <= 0, cost: 4
New rule:
l4 -> l4 : i^0'=n3+i^0, (N^0-n3-i^0 >= 0 /\ n3 >= 0), cost: 4*n3

Applied instantiation
Original rule:
l4 -> l4 : i^0'=n3+i^0, (N^0-n3-i^0 >= 0 /\ n3 >= 0), cost: 4*n3
New rule:
l4 -> l4 : i^0'=N^0, (0 >= 0 /\ N^0-i^0 >= 0), cost: 4*N^0-4*i^0

Applied simplification
Original rule:
l4 -> l4 : i^0'=N^0, x^0'=2*N^0-2*i^0+x^0, (0 >= 0 /\ N^0-i^0 >= 0), cost: 4*N^0-4*i^0
New rule:
l4 -> l4 : i^0'=N^0, x^0'=2*N^0-2*i^0+x^0, N^0-i^0 >= 0, cost: 4*N^0-4*i^0

Applied simplification
Original rule:
l4 -> l4 : i^0'=N^0, (0 >= 0 /\ N^0-i^0 >= 0), cost: 4*N^0-4*i^0
New rule:
l4 -> l4 : i^0'=N^0, N^0-i^0 >= 0, cost: 4*N^0-4*i^0

Applied deletion
Removed the following rules: 27 28

Accelerated simple loops
Start location: l10
  31: l4 -> l4 : i^0'=N^0, x^0'=2*N^0-2*i^0+x^0, N^0-i^0 >= 0, cost: 4*N^0-4*i^0
  32: l4 -> l4 : i^0'=N^0, N^0-i^0 >= 0, cost: 4*N^0-4*i^0
  23: l10 -> l4 : i^0'=0, x^0'=0, TRUE, cost: 2


Applied chaining
First rule:
l10 -> l4 : i^0'=0, x^0'=0, TRUE, cost: 2
Second rule:
l4 -> l4 : i^0'=N^0, x^0'=2*N^0-2*i^0+x^0, N^0-i^0 >= 0, cost: 4*N^0-4*i^0
New rule:
l10 -> l4 : i^0'=N^0, x^0'=2*N^0, N^0 >= 0, cost: 2+4*N^0

Applied chaining
First rule:
l10 -> l4 : i^0'=0, x^0'=0, TRUE, cost: 2
Second rule:
l4 -> l4 : i^0'=N^0, N^0-i^0 >= 0, cost: 4*N^0-4*i^0
New rule:
l10 -> l4 : i^0'=N^0, x^0'=0, N^0 >= 0, cost: 2+4*N^0

Applied deletion
Removed the following rules: 31 32

Chained accelerated rules with incoming rules
Start location: l10
  23: l10 -> l4 : i^0'=0, x^0'=0, TRUE, cost: 2
  33: l10 -> l4 : i^0'=N^0, x^0'=2*N^0, N^0 >= 0, cost: 2+4*N^0
  34: l10 -> l4 : i^0'=N^0, x^0'=0, N^0 >= 0, cost: 2+4*N^0


Removed unreachable locations and irrelevant leafs
Start location: l10
  <empty>


Computing asymptotic complexity

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

Solved cost: 0
Rule cost:   0