WORST_CASE(Omega(0),?)

Initial ITS
Start location: l10
   0: l0 -> l1 : tmp^0'=tmp^post0, i^0'=i^post0, n^0'=n^post0, b^0'=b^post0, j^0'=j^post0, (-j^post0+j^0 == 0 /\ tmp^0-tmp^post0 == 0 /\ b^0-b^post0 == 0 /\ -i^post0+i^0 == 0 /\ 1-i^0+n^0 <= 0 /\ n^0-n^post0 == 0), cost: 1
   1: l0 -> l2 : tmp^0'=tmp^post1, i^0'=i^post1, n^0'=n^post1, b^0'=b^post1, j^0'=j^post1, (-b^post1+b^0 == 0 /\ -n^post1+n^0 == 0 /\ -2+j^post1-j^0 == 0 /\ tmp^0-tmp^post1 == 0 /\ -1-i^0+i^post1 == 0 /\ i^0-n^0 <= 0), cost: 1
  11: l1 -> l6 : tmp^0'=tmp^post11, i^0'=i^post11, n^0'=n^post11, b^0'=b^post11, j^0'=j^post11, (-i^post11+i^0 == 0 /\ -j^post11+j^0 == 0 /\ 1+b^0 <= 0 /\ b^0-b^post11 == 0 /\ n^0-n^post11 == 0 /\ tmp^0-tmp^post11 == 0), cost: 1
  12: l1 -> l8 : tmp^0'=tmp^post12, i^0'=i^post12, n^0'=n^post12, b^0'=b^post12, j^0'=j^post12, (-n^post12+n^0 == 0 /\ i^0-i^post12 == 0 /\ tmp^0-tmp^post12 == 0 /\ -b^post12+b^0 == 0 /\ -b^0 <= 0 /\ -j^post12+j^0 == 0), cost: 1
   7: l2 -> l0 : tmp^0'=tmp^post7, i^0'=i^post7, n^0'=n^post7, b^0'=b^post7, j^0'=j^post7, (-n^post7+n^0 == 0 /\ j^0-j^post7 == 0 /\ b^0-b^post7 == 0 /\ i^0-i^post7 == 0 /\ tmp^0-tmp^post7 == 0), cost: 1
   2: l3 -> l2 : tmp^0'=tmp^post2, i^0'=i^post2, n^0'=n^post2, b^0'=b^post2, j^0'=j^post2, (tmp^0-tmp^post2 == 0 /\ -j^post2+j^0 == 0 /\ i^post2 == 0 /\ b^0-b^post2 == 0 /\ n^0-n^post2 == 0), cost: 1
   3: l4 -> l3 : tmp^0'=tmp^post3, i^0'=i^post3, n^0'=n^post3, b^0'=b^post3, j^0'=j^post3, (tmp^0-tmp^post3 == 0 /\ -j^post3+j^0 == 0 /\ i^0-i^post3 == 0 /\ -b^post3+b^0 == 0 /\ n^post3 == 0), cost: 1
   4: l5 -> l3 : tmp^0'=tmp^post4, i^0'=i^post4, n^0'=n^post4, b^0'=b^post4, j^0'=j^post4, (tmp^0 <= 0 /\ b^0-b^post4 == 0 /\ -j^post4+j^0 == 0 /\ i^0-i^post4 == 0 /\ tmp^0-tmp^post4 == 0 /\ -tmp^0 <= 0 /\ -1023+n^post4 == 0), cost: 1
   5: l5 -> l4 : tmp^0'=tmp^post5, i^0'=i^post5, n^0'=n^post5, b^0'=b^post5, j^0'=j^post5, (j^0-j^post5 == 0 /\ tmp^0-tmp^post5 == 0 /\ -n^post5+n^0 == 0 /\ -b^post5+b^0 == 0 /\ 1-tmp^0 <= 0 /\ i^0-i^post5 == 0), cost: 1
   6: l5 -> l4 : tmp^0'=tmp^post6, i^0'=i^post6, n^0'=n^post6, b^0'=b^post6, j^0'=j^post6, (1+tmp^0 <= 0 /\ -j^post6+j^0 == 0 /\ n^0-n^post6 == 0 /\ tmp^0-tmp^post6 == 0 /\ -b^post6+b^0 == 0 /\ i^0-i^post6 == 0), cost: 1
   8: l6 -> l7 : tmp^0'=tmp^post8, i^0'=i^post8, n^0'=n^post8, b^0'=b^post8, j^0'=j^post8, (-j^post8+j^0 == 0 /\ n^0-n^post8 == 0 /\ tmp^0-tmp^post8 == 0 /\ -b^post8+b^0 == 0 /\ i^0-i^post8 == 0), cost: 1
   9: l8 -> l6 : tmp^0'=tmp^post9, i^0'=i^post9, n^0'=n^post9, b^0'=b^post9, j^0'=j^post9, (-n^post9+n^0 == 0 /\ 1023-b^0 <= 0 /\ j^0-j^post9 == 0 /\ b^0-b^post9 == 0 /\ i^0-i^post9 == 0 /\ tmp^0-tmp^post9 == 0), cost: 1
  10: l8 -> l6 : tmp^0'=tmp^post10, i^0'=i^post10, n^0'=n^post10, b^0'=b^post10, j^0'=j^post10, (-1022+b^0 <= 0 /\ -b^post10+b^0 == 0 /\ n^0-n^post10 == 0 /\ tmp^0-tmp^post10 == 0 /\ i^0-i^post10 == 0 /\ -j^post10+j^0 == 0), cost: 1
  13: l9 -> l5 : tmp^0'=tmp^post13, i^0'=i^post13, n^0'=n^post13, b^0'=b^post13, j^0'=j^post13, (0 == 0 /\ b^0-b^post13 == 0 /\ n^0-n^post13 == 0 /\ i^0-i^post13 == 0 /\ -j^post13+j^0 == 0), cost: 1
  14: l10 -> l9 : tmp^0'=tmp^post14, i^0'=i^post14, n^0'=n^post14, b^0'=b^post14, j^0'=j^post14, (-j^post14+j^0 == 0 /\ tmp^0-tmp^post14 == 0 /\ i^0-i^post14 == 0 /\ n^0-n^post14 == 0 /\ -b^post14+b^0 == 0), cost: 1


Removed unreachable rules and leafs
Start location: l10
   1: l0 -> l2 : tmp^0'=tmp^post1, i^0'=i^post1, n^0'=n^post1, b^0'=b^post1, j^0'=j^post1, (-b^post1+b^0 == 0 /\ -n^post1+n^0 == 0 /\ -2+j^post1-j^0 == 0 /\ tmp^0-tmp^post1 == 0 /\ -1-i^0+i^post1 == 0 /\ i^0-n^0 <= 0), cost: 1
   7: l2 -> l0 : tmp^0'=tmp^post7, i^0'=i^post7, n^0'=n^post7, b^0'=b^post7, j^0'=j^post7, (-n^post7+n^0 == 0 /\ j^0-j^post7 == 0 /\ b^0-b^post7 == 0 /\ i^0-i^post7 == 0 /\ tmp^0-tmp^post7 == 0), cost: 1
   2: l3 -> l2 : tmp^0'=tmp^post2, i^0'=i^post2, n^0'=n^post2, b^0'=b^post2, j^0'=j^post2, (tmp^0-tmp^post2 == 0 /\ -j^post2+j^0 == 0 /\ i^post2 == 0 /\ b^0-b^post2 == 0 /\ n^0-n^post2 == 0), cost: 1
   3: l4 -> l3 : tmp^0'=tmp^post3, i^0'=i^post3, n^0'=n^post3, b^0'=b^post3, j^0'=j^post3, (tmp^0-tmp^post3 == 0 /\ -j^post3+j^0 == 0 /\ i^0-i^post3 == 0 /\ -b^post3+b^0 == 0 /\ n^post3 == 0), cost: 1
   4: l5 -> l3 : tmp^0'=tmp^post4, i^0'=i^post4, n^0'=n^post4, b^0'=b^post4, j^0'=j^post4, (tmp^0 <= 0 /\ b^0-b^post4 == 0 /\ -j^post4+j^0 == 0 /\ i^0-i^post4 == 0 /\ tmp^0-tmp^post4 == 0 /\ -tmp^0 <= 0 /\ -1023+n^post4 == 0), cost: 1
   5: l5 -> l4 : tmp^0'=tmp^post5, i^0'=i^post5, n^0'=n^post5, b^0'=b^post5, j^0'=j^post5, (j^0-j^post5 == 0 /\ tmp^0-tmp^post5 == 0 /\ -n^post5+n^0 == 0 /\ -b^post5+b^0 == 0 /\ 1-tmp^0 <= 0 /\ i^0-i^post5 == 0), cost: 1
   6: l5 -> l4 : tmp^0'=tmp^post6, i^0'=i^post6, n^0'=n^post6, b^0'=b^post6, j^0'=j^post6, (1+tmp^0 <= 0 /\ -j^post6+j^0 == 0 /\ n^0-n^post6 == 0 /\ tmp^0-tmp^post6 == 0 /\ -b^post6+b^0 == 0 /\ i^0-i^post6 == 0), cost: 1
  13: l9 -> l5 : tmp^0'=tmp^post13, i^0'=i^post13, n^0'=n^post13, b^0'=b^post13, j^0'=j^post13, (0 == 0 /\ b^0-b^post13 == 0 /\ n^0-n^post13 == 0 /\ i^0-i^post13 == 0 /\ -j^post13+j^0 == 0), cost: 1
  14: l10 -> l9 : tmp^0'=tmp^post14, i^0'=i^post14, n^0'=n^post14, b^0'=b^post14, j^0'=j^post14, (-j^post14+j^0 == 0 /\ tmp^0-tmp^post14 == 0 /\ i^0-i^post14 == 0 /\ n^0-n^post14 == 0 /\ -b^post14+b^0 == 0), cost: 1


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

Applied preprocessing
Original rule:
l3 -> l2 : tmp^0'=tmp^post2, i^0'=i^post2, n^0'=n^post2, b^0'=b^post2, j^0'=j^post2, (tmp^0-tmp^post2 == 0 /\ -j^post2+j^0 == 0 /\ i^post2 == 0 /\ b^0-b^post2 == 0 /\ n^0-n^post2 == 0), cost: 1
New rule:
l3 -> l2 : i^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l4 -> l3 : tmp^0'=tmp^post3, i^0'=i^post3, n^0'=n^post3, b^0'=b^post3, j^0'=j^post3, (tmp^0-tmp^post3 == 0 /\ -j^post3+j^0 == 0 /\ i^0-i^post3 == 0 /\ -b^post3+b^0 == 0 /\ n^post3 == 0), cost: 1
New rule:
l4 -> l3 : n^0'=0, TRUE, cost: 1

Applied preprocessing
Original rule:
l5 -> l3 : tmp^0'=tmp^post4, i^0'=i^post4, n^0'=n^post4, b^0'=b^post4, j^0'=j^post4, (tmp^0 <= 0 /\ b^0-b^post4 == 0 /\ -j^post4+j^0 == 0 /\ i^0-i^post4 == 0 /\ tmp^0-tmp^post4 == 0 /\ -tmp^0 <= 0 /\ -1023+n^post4 == 0), cost: 1
New rule:
l5 -> l3 : n^0'=1023, tmp^0 == 0, cost: 1

Applied preprocessing
Original rule:
l5 -> l4 : tmp^0'=tmp^post5, i^0'=i^post5, n^0'=n^post5, b^0'=b^post5, j^0'=j^post5, (j^0-j^post5 == 0 /\ tmp^0-tmp^post5 == 0 /\ -n^post5+n^0 == 0 /\ -b^post5+b^0 == 0 /\ 1-tmp^0 <= 0 /\ i^0-i^post5 == 0), cost: 1
New rule:
l5 -> l4 : -1+tmp^0 >= 0, cost: 1

Applied preprocessing
Original rule:
l5 -> l4 : tmp^0'=tmp^post6, i^0'=i^post6, n^0'=n^post6, b^0'=b^post6, j^0'=j^post6, (1+tmp^0 <= 0 /\ -j^post6+j^0 == 0 /\ n^0-n^post6 == 0 /\ tmp^0-tmp^post6 == 0 /\ -b^post6+b^0 == 0 /\ i^0-i^post6 == 0), cost: 1
New rule:
l5 -> l4 : 1+tmp^0 <= 0, cost: 1

Applied preprocessing
Original rule:
l2 -> l0 : tmp^0'=tmp^post7, i^0'=i^post7, n^0'=n^post7, b^0'=b^post7, j^0'=j^post7, (-n^post7+n^0 == 0 /\ j^0-j^post7 == 0 /\ b^0-b^post7 == 0 /\ i^0-i^post7 == 0 /\ tmp^0-tmp^post7 == 0), cost: 1
New rule:
l2 -> l0 : TRUE, cost: 1

Applied preprocessing
Original rule:
l9 -> l5 : tmp^0'=tmp^post13, i^0'=i^post13, n^0'=n^post13, b^0'=b^post13, j^0'=j^post13, (0 == 0 /\ b^0-b^post13 == 0 /\ n^0-n^post13 == 0 /\ i^0-i^post13 == 0 /\ -j^post13+j^0 == 0), cost: 1
New rule:
l9 -> l5 : tmp^0'=tmp^post13, 0 == 0, cost: 1

Applied preprocessing
Original rule:
l10 -> l9 : tmp^0'=tmp^post14, i^0'=i^post14, n^0'=n^post14, b^0'=b^post14, j^0'=j^post14, (-j^post14+j^0 == 0 /\ tmp^0-tmp^post14 == 0 /\ i^0-i^post14 == 0 /\ n^0-n^post14 == 0 /\ -b^post14+b^0 == 0), cost: 1
New rule:
l10 -> l9 : TRUE, cost: 1

Simplified rules
Start location: l10
  15: l0 -> l2 : i^0'=1+i^0, j^0'=2+j^0, i^0-n^0 <= 0, cost: 1
  21: l2 -> l0 : TRUE, cost: 1
  16: l3 -> l2 : i^0'=0, TRUE, cost: 1
  17: l4 -> l3 : n^0'=0, TRUE, cost: 1
  18: l5 -> l3 : n^0'=1023, tmp^0 == 0, cost: 1
  19: l5 -> l4 : -1+tmp^0 >= 0, cost: 1
  20: l5 -> l4 : 1+tmp^0 <= 0, cost: 1
  22: l9 -> l5 : tmp^0'=tmp^post13, 0 == 0, cost: 1
  23: l10 -> l9 : TRUE, cost: 1


Eliminating location l9 by chaining:

Applied chaining
First rule:
l10 -> l9 : TRUE, cost: 1
Second rule:
l9 -> l5 : tmp^0'=tmp^post13, 0 == 0, cost: 1
New rule:
l10 -> l5 : tmp^0'=tmp^post13, 0 == 0, cost: 2

Applied deletion
Removed the following rules: 22 23

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, i^0-n^0 <= 0, cost: 1
New rule:
l2 -> l2 : i^0'=1+i^0, j^0'=2+j^0, i^0-n^0 <= 0, cost: 2

Applied deletion
Removed the following rules: 15 21

Eliminated locations on linear paths
Start location: l10
  25: l2 -> l2 : i^0'=1+i^0, j^0'=2+j^0, i^0-n^0 <= 0, cost: 2
  16: l3 -> l2 : i^0'=0, TRUE, cost: 1
  17: l4 -> l3 : n^0'=0, TRUE, cost: 1
  18: l5 -> l3 : n^0'=1023, tmp^0 == 0, cost: 1
  19: l5 -> l4 : -1+tmp^0 >= 0, cost: 1
  20: l5 -> l4 : 1+tmp^0 <= 0, cost: 1
  24: l10 -> l5 : tmp^0'=tmp^post13, 0 == 0, cost: 2


Applied acceleration
Original rule:
l2 -> l2 : i^0'=1+i^0, j^0'=2+j^0, i^0-n^0 <= 0, cost: 2
New rule:
l2 -> l2 : i^0'=i^0+n, j^0'=j^0+2*n, (1-i^0+n^0-n >= 0 /\ n >= 0), cost: 2*n
Sub-proof via acceration calculus written to file:///tmp/tmpnam_IBcGnd.txt

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

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

Applied deletion
Removed the following rules: 25

Accelerated simple loops
Start location: l10
  27: l2 -> l2 : i^0'=1+n^0, j^0'=2-2*i^0+2*n^0+j^0, 1-i^0+n^0 >= 0, cost: 2-2*i^0+2*n^0
  16: l3 -> l2 : i^0'=0, TRUE, cost: 1
  17: l4 -> l3 : n^0'=0, TRUE, cost: 1
  18: l5 -> l3 : n^0'=1023, tmp^0 == 0, cost: 1
  19: l5 -> l4 : -1+tmp^0 >= 0, cost: 1
  20: l5 -> l4 : 1+tmp^0 <= 0, cost: 1
  24: l10 -> l5 : tmp^0'=tmp^post13, 0 == 0, cost: 2


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

Applied deletion
Removed the following rules: 27

Chained accelerated rules with incoming rules
Start location: l10
  16: l3 -> l2 : i^0'=0, TRUE, cost: 1
  28: l3 -> l2 : i^0'=1+n^0, j^0'=2+2*n^0+j^0, 1+n^0 >= 0, cost: 3+2*n^0
  17: l4 -> l3 : n^0'=0, TRUE, cost: 1
  18: l5 -> l3 : n^0'=1023, tmp^0 == 0, cost: 1
  19: l5 -> l4 : -1+tmp^0 >= 0, cost: 1
  20: l5 -> l4 : 1+tmp^0 <= 0, cost: 1
  24: l10 -> l5 : tmp^0'=tmp^post13, 0 == 0, cost: 2


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