WORST_CASE(Omega(1),?)

### Pre-processing the ITS problem ###

Initial linear ITS problem
   Start location: l10
      0: l0 -> l1 : b^0'=b^post_1, i^0'=i^post_1, j^0'=j^post_1, n^0'=n^post_1, tmp^0'=tmp^post_1, [ 1+n^0<=i^0 && b^0==b^post_1 && i^0==i^post_1 && j^0==j^post_1 && n^0==n^post_1 && tmp^0==tmp^post_1 ], cost: 1
      1: l0 -> l2 : b^0'=b^post_2, i^0'=i^post_2, j^0'=j^post_2, n^0'=n^post_2, tmp^0'=tmp^post_2, [ i^0<=n^0 && i^post_2==1+i^0 && j^post_2==2+j^0 && b^0==b^post_2 && n^0==n^post_2 && tmp^0==tmp^post_2 ], cost: 1
     11: l1 -> l6 : b^0'=b^post_12, i^0'=i^post_12, j^0'=j^post_12, n^0'=n^post_12, tmp^0'=tmp^post_12, [ 1+b^0<=0 && b^0==b^post_12 && i^0==i^post_12 && j^0==j^post_12 && n^0==n^post_12 && tmp^0==tmp^post_12 ], cost: 1
     12: l1 -> l8 : b^0'=b^post_13, i^0'=i^post_13, j^0'=j^post_13, n^0'=n^post_13, tmp^0'=tmp^post_13, [ 0<=b^0 && b^0==b^post_13 && i^0==i^post_13 && j^0==j^post_13 && n^0==n^post_13 && tmp^0==tmp^post_13 ], cost: 1
      7: l2 -> l0 : b^0'=b^post_8, i^0'=i^post_8, j^0'=j^post_8, n^0'=n^post_8, tmp^0'=tmp^post_8, [ b^0==b^post_8 && i^0==i^post_8 && j^0==j^post_8 && n^0==n^post_8 && tmp^0==tmp^post_8 ], cost: 1
      2: l3 -> l2 : b^0'=b^post_3, i^0'=i^post_3, j^0'=j^post_3, n^0'=n^post_3, tmp^0'=tmp^post_3, [ i^post_3==0 && b^0==b^post_3 && j^0==j^post_3 && n^0==n^post_3 && tmp^0==tmp^post_3 ], cost: 1
      3: l4 -> l3 : b^0'=b^post_4, i^0'=i^post_4, j^0'=j^post_4, n^0'=n^post_4, tmp^0'=tmp^post_4, [ n^post_4==0 && b^0==b^post_4 && i^0==i^post_4 && j^0==j^post_4 && tmp^0==tmp^post_4 ], cost: 1
      4: l5 -> l3 : b^0'=b^post_5, i^0'=i^post_5, j^0'=j^post_5, n^0'=n^post_5, tmp^0'=tmp^post_5, [ tmp^0<=0 && 0<=tmp^0 && n^post_5==1023 && b^0==b^post_5 && i^0==i^post_5 && j^0==j^post_5 && tmp^0==tmp^post_5 ], cost: 1
      5: l5 -> l4 : b^0'=b^post_6, i^0'=i^post_6, j^0'=j^post_6, n^0'=n^post_6, tmp^0'=tmp^post_6, [ 1<=tmp^0 && b^0==b^post_6 && i^0==i^post_6 && j^0==j^post_6 && n^0==n^post_6 && tmp^0==tmp^post_6 ], cost: 1
      6: l5 -> l4 : b^0'=b^post_7, i^0'=i^post_7, j^0'=j^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [ 1+tmp^0<=0 && b^0==b^post_7 && i^0==i^post_7 && j^0==j^post_7 && n^0==n^post_7 && tmp^0==tmp^post_7 ], cost: 1
      8: l6 -> l7 : b^0'=b^post_9, i^0'=i^post_9, j^0'=j^post_9, n^0'=n^post_9, tmp^0'=tmp^post_9, [ b^0==b^post_9 && i^0==i^post_9 && j^0==j^post_9 && n^0==n^post_9 && tmp^0==tmp^post_9 ], cost: 1
      9: l8 -> l6 : b^0'=b^post_10, i^0'=i^post_10, j^0'=j^post_10, n^0'=n^post_10, tmp^0'=tmp^post_10, [ 1023<=b^0 && b^0==b^post_10 && i^0==i^post_10 && j^0==j^post_10 && n^0==n^post_10 && tmp^0==tmp^post_10 ], cost: 1
     10: l8 -> l6 : b^0'=b^post_11, i^0'=i^post_11, j^0'=j^post_11, n^0'=n^post_11, tmp^0'=tmp^post_11, [ 1+b^0<=1023 && b^0==b^post_11 && i^0==i^post_11 && j^0==j^post_11 && n^0==n^post_11 && tmp^0==tmp^post_11 ], cost: 1
     13: l9 -> l5 : b^0'=b^post_14, i^0'=i^post_14, j^0'=j^post_14, n^0'=n^post_14, tmp^0'=tmp^post_14, [ tmp^post_14==tmp^post_14 && b^0==b^post_14 && i^0==i^post_14 && j^0==j^post_14 && n^0==n^post_14 ], cost: 1
     14: l10 -> l9 : b^0'=b^post_15, i^0'=i^post_15, j^0'=j^post_15, n^0'=n^post_15, tmp^0'=tmp^post_15, [ b^0==b^post_15 && i^0==i^post_15 && j^0==j^post_15 && n^0==n^post_15 && tmp^0==tmp^post_15 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     14: l10 -> l9 : b^0'=b^post_15, i^0'=i^post_15, j^0'=j^post_15, n^0'=n^post_15, tmp^0'=tmp^post_15, [ b^0==b^post_15 && i^0==i^post_15 && j^0==j^post_15 && n^0==n^post_15 && tmp^0==tmp^post_15 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l10
      1: l0 -> l2 : b^0'=b^post_2, i^0'=i^post_2, j^0'=j^post_2, n^0'=n^post_2, tmp^0'=tmp^post_2, [ i^0<=n^0 && i^post_2==1+i^0 && j^post_2==2+j^0 && b^0==b^post_2 && n^0==n^post_2 && tmp^0==tmp^post_2 ], cost: 1
      7: l2 -> l0 : b^0'=b^post_8, i^0'=i^post_8, j^0'=j^post_8, n^0'=n^post_8, tmp^0'=tmp^post_8, [ b^0==b^post_8 && i^0==i^post_8 && j^0==j^post_8 && n^0==n^post_8 && tmp^0==tmp^post_8 ], cost: 1
      2: l3 -> l2 : b^0'=b^post_3, i^0'=i^post_3, j^0'=j^post_3, n^0'=n^post_3, tmp^0'=tmp^post_3, [ i^post_3==0 && b^0==b^post_3 && j^0==j^post_3 && n^0==n^post_3 && tmp^0==tmp^post_3 ], cost: 1
      3: l4 -> l3 : b^0'=b^post_4, i^0'=i^post_4, j^0'=j^post_4, n^0'=n^post_4, tmp^0'=tmp^post_4, [ n^post_4==0 && b^0==b^post_4 && i^0==i^post_4 && j^0==j^post_4 && tmp^0==tmp^post_4 ], cost: 1
      4: l5 -> l3 : b^0'=b^post_5, i^0'=i^post_5, j^0'=j^post_5, n^0'=n^post_5, tmp^0'=tmp^post_5, [ tmp^0<=0 && 0<=tmp^0 && n^post_5==1023 && b^0==b^post_5 && i^0==i^post_5 && j^0==j^post_5 && tmp^0==tmp^post_5 ], cost: 1
      5: l5 -> l4 : b^0'=b^post_6, i^0'=i^post_6, j^0'=j^post_6, n^0'=n^post_6, tmp^0'=tmp^post_6, [ 1<=tmp^0 && b^0==b^post_6 && i^0==i^post_6 && j^0==j^post_6 && n^0==n^post_6 && tmp^0==tmp^post_6 ], cost: 1
      6: l5 -> l4 : b^0'=b^post_7, i^0'=i^post_7, j^0'=j^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [ 1+tmp^0<=0 && b^0==b^post_7 && i^0==i^post_7 && j^0==j^post_7 && n^0==n^post_7 && tmp^0==tmp^post_7 ], cost: 1
     13: l9 -> l5 : b^0'=b^post_14, i^0'=i^post_14, j^0'=j^post_14, n^0'=n^post_14, tmp^0'=tmp^post_14, [ tmp^post_14==tmp^post_14 && b^0==b^post_14 && i^0==i^post_14 && j^0==j^post_14 && n^0==n^post_14 ], cost: 1
     14: l10 -> l9 : b^0'=b^post_15, i^0'=i^post_15, j^0'=j^post_15, n^0'=n^post_15, tmp^0'=tmp^post_15, [ b^0==b^post_15 && i^0==i^post_15 && j^0==j^post_15 && n^0==n^post_15 && tmp^0==tmp^post_15 ], cost: 1

Simplified all rules, resulting in:
   Start location: l10
      1: l0 -> l2 : i^0'=1+i^0, j^0'=2+j^0, [ i^0<=n^0 ], cost: 1
      7: l2 -> l0 : [], cost: 1
      2: l3 -> l2 : i^0'=0, [], cost: 1
      3: l4 -> l3 : n^0'=0, [], cost: 1
      4: l5 -> l3 : n^0'=1023, [ tmp^0==0 ], cost: 1
      5: l5 -> l4 : [ 1<=tmp^0 ], cost: 1
      6: l5 -> l4 : [ 1+tmp^0<=0 ], cost: 1
     13: l9 -> l5 : tmp^0'=tmp^post_14, [], cost: 1
     14: l10 -> l9 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l10
     16: l2 -> l2 : i^0'=1+i^0, j^0'=2+j^0, [ i^0<=n^0 ], cost: 2
      2: l3 -> l2 : i^0'=0, [], cost: 1
      3: l4 -> l3 : n^0'=0, [], cost: 1
      4: l5 -> l3 : n^0'=1023, [ tmp^0==0 ], cost: 1
      5: l5 -> l4 : [ 1<=tmp^0 ], cost: 1
      6: l5 -> l4 : [ 1+tmp^0<=0 ], cost: 1
     15: l10 -> l5 : tmp^0'=tmp^post_14, [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
     16: l2 -> l2 : i^0'=1+i^0, j^0'=2+j^0, [ i^0<=n^0 ], cost: 2

   Accelerated rule 16 with backward acceleration, yielding the new rule 17.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 16.

Accelerated all simple loops using metering functions (where possible):
   Start location: l10
     17: l2 -> l2 : i^0'=1+n^0, j^0'=2-2*i^0+j^0+2*n^0, [ 1-i^0+n^0>=0 ], cost: 2-2*i^0+2*n^0
      2: l3 -> l2 : i^0'=0, [], cost: 1
      3: l4 -> l3 : n^0'=0, [], cost: 1
      4: l5 -> l3 : n^0'=1023, [ tmp^0==0 ], cost: 1
      5: l5 -> l4 : [ 1<=tmp^0 ], cost: 1
      6: l5 -> l4 : [ 1+tmp^0<=0 ], cost: 1
     15: l10 -> l5 : tmp^0'=tmp^post_14, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l10
      2: l3 -> l2 : i^0'=0, [], cost: 1
     18: l3 -> l2 : i^0'=1+n^0, j^0'=2+j^0+2*n^0, [ 1+n^0>=0 ], cost: 3+2*n^0
      3: l4 -> l3 : n^0'=0, [], cost: 1
      4: l5 -> l3 : n^0'=1023, [ tmp^0==0 ], cost: 1
      5: l5 -> l4 : [ 1<=tmp^0 ], cost: 1
      6: l5 -> l4 : [ 1+tmp^0<=0 ], cost: 1
     15: l10 -> l5 : tmp^0'=tmp^post_14, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l10
     18: l3 -> l2 : i^0'=1+n^0, j^0'=2+j^0+2*n^0, [ 1+n^0>=0 ], cost: 3+2*n^0
      3: l4 -> l3 : n^0'=0, [], cost: 1
      4: l5 -> l3 : n^0'=1023, [ tmp^0==0 ], cost: 1
      5: l5 -> l4 : [ 1<=tmp^0 ], cost: 1
      6: l5 -> l4 : [ 1+tmp^0<=0 ], cost: 1
     15: l10 -> l5 : tmp^0'=tmp^post_14, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l10
     18: l3 -> l2 : i^0'=1+n^0, j^0'=2+j^0+2*n^0, [ 1+n^0>=0 ], cost: 3+2*n^0
      3: l4 -> l3 : n^0'=0, [], cost: 1
     19: l10 -> l3 : n^0'=1023, tmp^0'=tmp^post_14, [ tmp^post_14==0 ], cost: 3
     20: l10 -> l4 : tmp^0'=tmp^post_14, [ 1<=tmp^post_14 ], cost: 3
     21: l10 -> l4 : tmp^0'=tmp^post_14, [ 1+tmp^post_14<=0 ], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: l10
     18: l3 -> l2 : i^0'=1+n^0, j^0'=2+j^0+2*n^0, [ 1+n^0>=0 ], cost: 3+2*n^0
     19: l10 -> l3 : n^0'=1023, tmp^0'=tmp^post_14, [ tmp^post_14==0 ], cost: 3
     22: l10 -> l3 : n^0'=0, tmp^0'=tmp^post_14, [ 1<=tmp^post_14 ], cost: 4
     23: l10 -> l3 : n^0'=0, tmp^0'=tmp^post_14, [ 1+tmp^post_14<=0 ], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: l10
     24: l10 -> l2 : i^0'=1024, j^0'=2048+j^0, n^0'=1023, tmp^0'=tmp^post_14, [ tmp^post_14==0 ], cost: 2052
     25: l10 -> l2 : i^0'=1, j^0'=2+j^0, n^0'=0, tmp^0'=tmp^post_14, [ 1<=tmp^post_14 ], cost: 7
     26: l10 -> l2 : i^0'=1, j^0'=2+j^0, n^0'=0, tmp^0'=tmp^post_14, [ 1+tmp^post_14<=0 ], cost: 7

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l10
     24: l10 -> l2 : i^0'=1024, j^0'=2048+j^0, n^0'=1023, tmp^0'=tmp^post_14, [ tmp^post_14==0 ], cost: 2052
     25: l10 -> l2 : i^0'=1, j^0'=2+j^0, n^0'=0, tmp^0'=tmp^post_14, [ 1<=tmp^post_14 ], cost: 7
     26: l10 -> l2 : i^0'=1, j^0'=2+j^0, n^0'=0, tmp^0'=tmp^post_14, [ 1+tmp^post_14<=0 ], cost: 7

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Constant
   Cpx degree:  0
   Solved cost: 1
   Rule cost:   1
   Rule guard:  [ b^0==b^post_15 && i^0==i^post_15 && j^0==j^post_15 && n^0==n^post_15 && tmp^0==tmp^post_15 ]

WORST_CASE(Omega(1),?)