WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l11
      0: l0 -> l1 : a^0'=a^post_1, b^0'=b^post_1, i^0'=i^post_1, n^0'=n^post_1, tmp^0'=tmp^post_1, [ a^0<=0 && a^0==a^post_1 && b^0==b^post_1 && i^0==i^post_1 && n^0==n^post_1 && tmp^0==tmp^post_1 ], cost: 1
      1: l0 -> l2 : a^0'=a^post_2, b^0'=b^post_2, i^0'=i^post_2, n^0'=n^post_2, tmp^0'=tmp^post_2, [ 1<=a^0 && a^post_2==-1+a^0 && b^post_2==1+b^0 && i^0==i^post_2 && n^0==n^post_2 && tmp^0==tmp^post_2 ], cost: 1
      3: l2 -> l4 : a^0'=a^post_4, b^0'=b^post_4, i^0'=i^post_4, n^0'=n^post_4, tmp^0'=tmp^post_4, [ a^0==a^post_4 && b^0==b^post_4 && i^0==i^post_4 && n^0==n^post_4 && tmp^0==tmp^post_4 ], cost: 1
      2: l3 -> l0 : a^0'=a^post_3, b^0'=b^post_3, i^0'=i^post_3, n^0'=n^post_3, tmp^0'=tmp^post_3, [ a^0==a^post_3 && b^0==b^post_3 && i^0==i^post_3 && n^0==n^post_3 && tmp^0==tmp^post_3 ], cost: 1
     12: l4 -> l3 : a^0'=a^post_13, b^0'=b^post_13, i^0'=i^post_13, n^0'=n^post_13, tmp^0'=tmp^post_13, [ b^0<=0 && a^0==a^post_13 && b^0==b^post_13 && i^0==i^post_13 && n^0==n^post_13 && tmp^0==tmp^post_13 ], cost: 1
     13: l4 -> l6 : a^0'=a^post_14, b^0'=b^post_14, i^0'=i^post_14, n^0'=n^post_14, tmp^0'=tmp^post_14, [ 1<=b^0 && b^post_14==-1+b^0 && i^post_14==-1+a^0 && a^0==a^post_14 && n^0==n^post_14 && tmp^0==tmp^post_14 ], cost: 1
      4: l5 -> l6 : a^0'=a^post_5, b^0'=b^post_5, i^0'=i^post_5, n^0'=n^post_5, tmp^0'=tmp^post_5, [ i^post_5==-1+i^0 && a^0==a^post_5 && b^0==b^post_5 && n^0==n^post_5 && tmp^0==tmp^post_5 ], cost: 1
      5: l6 -> l7 : a^0'=a^post_6, b^0'=b^post_6, i^0'=i^post_6, n^0'=n^post_6, tmp^0'=tmp^post_6, [ a^0==a^post_6 && b^0==b^post_6 && i^0==i^post_6 && n^0==n^post_6 && tmp^0==tmp^post_6 ], cost: 1
     10: l7 -> l2 : a^0'=a^post_11, b^0'=b^post_11, i^0'=i^post_11, n^0'=n^post_11, tmp^0'=tmp^post_11, [ i^0<=0 && a^0==a^post_11 && b^0==b^post_11 && i^0==i^post_11 && n^0==n^post_11 && tmp^0==tmp^post_11 ], cost: 1
     11: l7 -> l9 : a^0'=a^post_12, b^0'=b^post_12, i^0'=i^post_12, n^0'=n^post_12, tmp^0'=tmp^post_12, [ 1<=i^0 && tmp^post_12==tmp^post_12 && a^0==a^post_12 && b^0==b^post_12 && i^0==i^post_12 && n^0==n^post_12 ], cost: 1
      6: l8 -> l5 : a^0'=a^post_7, b^0'=b^post_7, i^0'=i^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [ a^post_7==-1+a^0 && b^post_7==1+b^0 && i^0==i^post_7 && n^0==n^post_7 && tmp^0==tmp^post_7 ], cost: 1
      7: l9 -> l5 : a^0'=a^post_8, b^0'=b^post_8, i^0'=i^post_8, n^0'=n^post_8, tmp^0'=tmp^post_8, [ tmp^0<=0 && 0<=tmp^0 && a^0==a^post_8 && b^0==b^post_8 && i^0==i^post_8 && n^0==n^post_8 && tmp^0==tmp^post_8 ], cost: 1
      8: l9 -> l8 : a^0'=a^post_9, b^0'=b^post_9, i^0'=i^post_9, n^0'=n^post_9, tmp^0'=tmp^post_9, [ 1<=tmp^0 && a^0==a^post_9 && b^0==b^post_9 && i^0==i^post_9 && n^0==n^post_9 && tmp^0==tmp^post_9 ], cost: 1
      9: l9 -> l8 : a^0'=a^post_10, b^0'=b^post_10, i^0'=i^post_10, n^0'=n^post_10, tmp^0'=tmp^post_10, [ 1+tmp^0<=0 && a^0==a^post_10 && b^0==b^post_10 && i^0==i^post_10 && n^0==n^post_10 && tmp^0==tmp^post_10 ], cost: 1
     14: l10 -> l3 : a^0'=a^post_15, b^0'=b^post_15, i^0'=i^post_15, n^0'=n^post_15, tmp^0'=tmp^post_15, [ a^post_15==n^0 && b^post_15==0 && i^0==i^post_15 && n^0==n^post_15 && tmp^0==tmp^post_15 ], cost: 1
     15: l11 -> l10 : a^0'=a^post_16, b^0'=b^post_16, i^0'=i^post_16, n^0'=n^post_16, tmp^0'=tmp^post_16, [ a^0==a^post_16 && b^0==b^post_16 && i^0==i^post_16 && n^0==n^post_16 && tmp^0==tmp^post_16 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     15: l11 -> l10 : a^0'=a^post_16, b^0'=b^post_16, i^0'=i^post_16, n^0'=n^post_16, tmp^0'=tmp^post_16, [ a^0==a^post_16 && b^0==b^post_16 && i^0==i^post_16 && n^0==n^post_16 && tmp^0==tmp^post_16 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l11
      1: l0 -> l2 : a^0'=a^post_2, b^0'=b^post_2, i^0'=i^post_2, n^0'=n^post_2, tmp^0'=tmp^post_2, [ 1<=a^0 && a^post_2==-1+a^0 && b^post_2==1+b^0 && i^0==i^post_2 && n^0==n^post_2 && tmp^0==tmp^post_2 ], cost: 1
      3: l2 -> l4 : a^0'=a^post_4, b^0'=b^post_4, i^0'=i^post_4, n^0'=n^post_4, tmp^0'=tmp^post_4, [ a^0==a^post_4 && b^0==b^post_4 && i^0==i^post_4 && n^0==n^post_4 && tmp^0==tmp^post_4 ], cost: 1
      2: l3 -> l0 : a^0'=a^post_3, b^0'=b^post_3, i^0'=i^post_3, n^0'=n^post_3, tmp^0'=tmp^post_3, [ a^0==a^post_3 && b^0==b^post_3 && i^0==i^post_3 && n^0==n^post_3 && tmp^0==tmp^post_3 ], cost: 1
     12: l4 -> l3 : a^0'=a^post_13, b^0'=b^post_13, i^0'=i^post_13, n^0'=n^post_13, tmp^0'=tmp^post_13, [ b^0<=0 && a^0==a^post_13 && b^0==b^post_13 && i^0==i^post_13 && n^0==n^post_13 && tmp^0==tmp^post_13 ], cost: 1
     13: l4 -> l6 : a^0'=a^post_14, b^0'=b^post_14, i^0'=i^post_14, n^0'=n^post_14, tmp^0'=tmp^post_14, [ 1<=b^0 && b^post_14==-1+b^0 && i^post_14==-1+a^0 && a^0==a^post_14 && n^0==n^post_14 && tmp^0==tmp^post_14 ], cost: 1
      4: l5 -> l6 : a^0'=a^post_5, b^0'=b^post_5, i^0'=i^post_5, n^0'=n^post_5, tmp^0'=tmp^post_5, [ i^post_5==-1+i^0 && a^0==a^post_5 && b^0==b^post_5 && n^0==n^post_5 && tmp^0==tmp^post_5 ], cost: 1
      5: l6 -> l7 : a^0'=a^post_6, b^0'=b^post_6, i^0'=i^post_6, n^0'=n^post_6, tmp^0'=tmp^post_6, [ a^0==a^post_6 && b^0==b^post_6 && i^0==i^post_6 && n^0==n^post_6 && tmp^0==tmp^post_6 ], cost: 1
     10: l7 -> l2 : a^0'=a^post_11, b^0'=b^post_11, i^0'=i^post_11, n^0'=n^post_11, tmp^0'=tmp^post_11, [ i^0<=0 && a^0==a^post_11 && b^0==b^post_11 && i^0==i^post_11 && n^0==n^post_11 && tmp^0==tmp^post_11 ], cost: 1
     11: l7 -> l9 : a^0'=a^post_12, b^0'=b^post_12, i^0'=i^post_12, n^0'=n^post_12, tmp^0'=tmp^post_12, [ 1<=i^0 && tmp^post_12==tmp^post_12 && a^0==a^post_12 && b^0==b^post_12 && i^0==i^post_12 && n^0==n^post_12 ], cost: 1
      6: l8 -> l5 : a^0'=a^post_7, b^0'=b^post_7, i^0'=i^post_7, n^0'=n^post_7, tmp^0'=tmp^post_7, [ a^post_7==-1+a^0 && b^post_7==1+b^0 && i^0==i^post_7 && n^0==n^post_7 && tmp^0==tmp^post_7 ], cost: 1
      7: l9 -> l5 : a^0'=a^post_8, b^0'=b^post_8, i^0'=i^post_8, n^0'=n^post_8, tmp^0'=tmp^post_8, [ tmp^0<=0 && 0<=tmp^0 && a^0==a^post_8 && b^0==b^post_8 && i^0==i^post_8 && n^0==n^post_8 && tmp^0==tmp^post_8 ], cost: 1
      8: l9 -> l8 : a^0'=a^post_9, b^0'=b^post_9, i^0'=i^post_9, n^0'=n^post_9, tmp^0'=tmp^post_9, [ 1<=tmp^0 && a^0==a^post_9 && b^0==b^post_9 && i^0==i^post_9 && n^0==n^post_9 && tmp^0==tmp^post_9 ], cost: 1
      9: l9 -> l8 : a^0'=a^post_10, b^0'=b^post_10, i^0'=i^post_10, n^0'=n^post_10, tmp^0'=tmp^post_10, [ 1+tmp^0<=0 && a^0==a^post_10 && b^0==b^post_10 && i^0==i^post_10 && n^0==n^post_10 && tmp^0==tmp^post_10 ], cost: 1
     14: l10 -> l3 : a^0'=a^post_15, b^0'=b^post_15, i^0'=i^post_15, n^0'=n^post_15, tmp^0'=tmp^post_15, [ a^post_15==n^0 && b^post_15==0 && i^0==i^post_15 && n^0==n^post_15 && tmp^0==tmp^post_15 ], cost: 1
     15: l11 -> l10 : a^0'=a^post_16, b^0'=b^post_16, i^0'=i^post_16, n^0'=n^post_16, tmp^0'=tmp^post_16, [ a^0==a^post_16 && b^0==b^post_16 && i^0==i^post_16 && n^0==n^post_16 && tmp^0==tmp^post_16 ], cost: 1

Simplified all rules, resulting in:
   Start location: l11
      1: l0 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=a^0 ], cost: 1
      3: l2 -> l4 : [], cost: 1
      2: l3 -> l0 : [], cost: 1
     12: l4 -> l3 : [ b^0<=0 ], cost: 1
     13: l4 -> l6 : b^0'=-1+b^0, i^0'=-1+a^0, [ 1<=b^0 ], cost: 1
      4: l5 -> l6 : i^0'=-1+i^0, [], cost: 1
      5: l6 -> l7 : [], cost: 1
     10: l7 -> l2 : [ i^0<=0 ], cost: 1
     11: l7 -> l9 : tmp^0'=tmp^post_12, [ 1<=i^0 ], cost: 1
      6: l8 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, [], cost: 1
      7: l9 -> l5 : [ tmp^0==0 ], cost: 1
      8: l9 -> l8 : [ 1<=tmp^0 ], cost: 1
      9: l9 -> l8 : [ 1+tmp^0<=0 ], cost: 1
     14: l10 -> l3 : a^0'=n^0, b^0'=0, [], cost: 1
     15: l11 -> l10 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l11
      3: l2 -> l4 : [], cost: 1
     17: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=a^0 ], cost: 2
     12: l4 -> l3 : [ b^0<=0 ], cost: 1
     13: l4 -> l6 : b^0'=-1+b^0, i^0'=-1+a^0, [ 1<=b^0 ], cost: 1
      4: l5 -> l6 : i^0'=-1+i^0, [], cost: 1
      5: l6 -> l7 : [], cost: 1
     10: l7 -> l2 : [ i^0<=0 ], cost: 1
     11: l7 -> l9 : tmp^0'=tmp^post_12, [ 1<=i^0 ], cost: 1
      6: l8 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, [], cost: 1
      7: l9 -> l5 : [ tmp^0==0 ], cost: 1
      8: l9 -> l8 : [ 1<=tmp^0 ], cost: 1
      9: l9 -> l8 : [ 1+tmp^0<=0 ], cost: 1
     16: l11 -> l3 : a^0'=n^0, b^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l11
     18: l2 -> l3 : [ b^0<=0 ], cost: 2
     19: l2 -> l6 : b^0'=-1+b^0, i^0'=-1+a^0, [ 1<=b^0 ], cost: 2
     17: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=a^0 ], cost: 2
      4: l5 -> l6 : i^0'=-1+i^0, [], cost: 1
     20: l6 -> l2 : [ i^0<=0 ], cost: 2
     21: l6 -> l9 : tmp^0'=tmp^post_12, [ 1<=i^0 ], cost: 2
      7: l9 -> l5 : [ tmp^0==0 ], cost: 1
     22: l9 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=tmp^0 ], cost: 2
     23: l9 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, [ 1+tmp^0<=0 ], cost: 2
     16: l11 -> l3 : a^0'=n^0, b^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l11
     18: l2 -> l3 : [ b^0<=0 ], cost: 2
     19: l2 -> l6 : b^0'=-1+b^0, i^0'=-1+a^0, [ 1<=b^0 ], cost: 2
     17: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=a^0 ], cost: 2
      4: l5 -> l6 : i^0'=-1+i^0, [], cost: 1
     20: l6 -> l2 : [ i^0<=0 ], cost: 2
     24: l6 -> l5 : tmp^0'=tmp^post_12, [ 1<=i^0 && tmp^post_12==0 ], cost: 3
     25: l6 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, tmp^0'=tmp^post_12, [ 1<=i^0 && 1<=tmp^post_12 ], cost: 4
     26: l6 -> l5 : a^0'=-1+a^0, b^0'=1+b^0, tmp^0'=tmp^post_12, [ 1<=i^0 && 1+tmp^post_12<=0 ], cost: 4
     16: l11 -> l3 : a^0'=n^0, b^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l11
     18: l2 -> l3 : [ b^0<=0 ], cost: 2
     19: l2 -> l6 : b^0'=-1+b^0, i^0'=-1+a^0, [ 1<=b^0 ], cost: 2
     17: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=a^0 ], cost: 2
     20: l6 -> l2 : [ i^0<=0 ], cost: 2
     27: l6 -> l6 : i^0'=-1+i^0, tmp^0'=tmp^post_12, [ 1<=i^0 && tmp^post_12==0 ], cost: 4
     28: l6 -> l6 : a^0'=-1+a^0, b^0'=1+b^0, i^0'=-1+i^0, tmp^0'=tmp^post_12, [ 1<=i^0 && 1<=tmp^post_12 ], cost: 5
     29: l6 -> l6 : a^0'=-1+a^0, b^0'=1+b^0, i^0'=-1+i^0, tmp^0'=tmp^post_12, [ 1<=i^0 && 1+tmp^post_12<=0 ], cost: 5
     16: l11 -> l3 : a^0'=n^0, b^0'=0, [], cost: 2

Accelerating simple loops of location 6.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     27: l6 -> l6 : i^0'=-1+i^0, tmp^0'=0, [ 1<=i^0 ], cost: 4
     28: l6 -> l6 : a^0'=-1+a^0, b^0'=1+b^0, i^0'=-1+i^0, tmp^0'=tmp^post_12, [ 1<=i^0 && 1<=tmp^post_12 ], cost: 5
     29: l6 -> l6 : a^0'=-1+a^0, b^0'=1+b^0, i^0'=-1+i^0, tmp^0'=tmp^post_12, [ 1<=i^0 && 1+tmp^post_12<=0 ], cost: 5

   Accelerated rule 27 with backward acceleration, yielding the new rule 30.
   Accelerated rule 28 with backward acceleration, yielding the new rule 31.
   Accelerated rule 29 with backward acceleration, yielding the new rule 32.
[accelerate] Nesting with 3 inner and 3 outer candidates
   Removing the simple loops: 27 28 29.

Accelerated all simple loops using metering functions (where possible):
   Start location: l11
     18: l2 -> l3 : [ b^0<=0 ], cost: 2
     19: l2 -> l6 : b^0'=-1+b^0, i^0'=-1+a^0, [ 1<=b^0 ], cost: 2
     17: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=a^0 ], cost: 2
     20: l6 -> l2 : [ i^0<=0 ], cost: 2
     30: l6 -> l6 : i^0'=0, tmp^0'=0, [ i^0>=1 ], cost: 4*i^0
     31: l6 -> l6 : a^0'=-i^0+a^0, b^0'=b^0+i^0, i^0'=0, tmp^0'=tmp^post_12, [ 1<=tmp^post_12 && i^0>=1 ], cost: 5*i^0
     32: l6 -> l6 : a^0'=-i^0+a^0, b^0'=b^0+i^0, i^0'=0, tmp^0'=tmp^post_12, [ 1+tmp^post_12<=0 && i^0>=1 ], cost: 5*i^0
     16: l11 -> l3 : a^0'=n^0, b^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l11
     18: l2 -> l3 : [ b^0<=0 ], cost: 2
     19: l2 -> l6 : b^0'=-1+b^0, i^0'=-1+a^0, [ 1<=b^0 ], cost: 2
     33: l2 -> l6 : b^0'=-1+b^0, i^0'=0, tmp^0'=0, [ 1<=b^0 && -1+a^0>=1 ], cost: -2+4*a^0
     34: l2 -> l6 : a^0'=1, b^0'=-2+b^0+a^0, i^0'=0, tmp^0'=tmp^post_12, [ 1<=b^0 && 1<=tmp^post_12 && -1+a^0>=1 ], cost: -3+5*a^0
     35: l2 -> l6 : a^0'=1, b^0'=-2+b^0+a^0, i^0'=0, tmp^0'=tmp^post_12, [ 1<=b^0 && 1+tmp^post_12<=0 && -1+a^0>=1 ], cost: -3+5*a^0
     17: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=a^0 ], cost: 2
     20: l6 -> l2 : [ i^0<=0 ], cost: 2
     16: l11 -> l3 : a^0'=n^0, b^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l11
     18: l2 -> l3 : [ b^0<=0 ], cost: 2
     36: l2 -> l2 : b^0'=-1+b^0, i^0'=-1+a^0, [ 1<=b^0 && -1+a^0<=0 ], cost: 4
     37: l2 -> l2 : b^0'=-1+b^0, i^0'=0, tmp^0'=0, [ 1<=b^0 && -1+a^0>=1 ], cost: 4*a^0
     38: l2 -> l2 : a^0'=1, b^0'=-2+b^0+a^0, i^0'=0, tmp^0'=tmp^post_12, [ 1<=b^0 && 1<=tmp^post_12 && -1+a^0>=1 ], cost: -1+5*a^0
     39: l2 -> l2 : a^0'=1, b^0'=-2+b^0+a^0, i^0'=0, tmp^0'=tmp^post_12, [ 1<=b^0 && 1+tmp^post_12<=0 && -1+a^0>=1 ], cost: -1+5*a^0
     17: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=a^0 ], cost: 2
     16: l11 -> l3 : a^0'=n^0, b^0'=0, [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
     36: l2 -> l2 : b^0'=-1+b^0, i^0'=-1+a^0, [ 1<=b^0 && -1+a^0<=0 ], cost: 4
     37: l2 -> l2 : b^0'=-1+b^0, i^0'=0, tmp^0'=0, [ 1<=b^0 && -1+a^0>=1 ], cost: 4*a^0
     38: l2 -> l2 : a^0'=1, b^0'=-2+b^0+a^0, i^0'=0, tmp^0'=tmp^post_12, [ 1<=b^0 && 1<=tmp^post_12 && -1+a^0>=1 ], cost: -1+5*a^0
     39: l2 -> l2 : a^0'=1, b^0'=-2+b^0+a^0, i^0'=0, tmp^0'=tmp^post_12, [ 1<=b^0 && 1+tmp^post_12<=0 && -1+a^0>=1 ], cost: -1+5*a^0

   Accelerated rule 36 with backward acceleration, yielding the new rule 40.
   Accelerated rule 37 with backward acceleration, yielding the new rule 41.
   Failed to prove monotonicity of the guard of rule 38.
   Failed to prove monotonicity of the guard of rule 39.
[accelerate] Nesting with 4 inner and 4 outer candidates
   Removing the simple loops: 36 37.

Accelerated all simple loops using metering functions (where possible):
   Start location: l11
     18: l2 -> l3 : [ b^0<=0 ], cost: 2
     38: l2 -> l2 : a^0'=1, b^0'=-2+b^0+a^0, i^0'=0, tmp^0'=tmp^post_12, [ 1<=b^0 && 1<=tmp^post_12 && -1+a^0>=1 ], cost: -1+5*a^0
     39: l2 -> l2 : a^0'=1, b^0'=-2+b^0+a^0, i^0'=0, tmp^0'=tmp^post_12, [ 1<=b^0 && 1+tmp^post_12<=0 && -1+a^0>=1 ], cost: -1+5*a^0
     40: l2 -> l2 : b^0'=0, i^0'=-1+a^0, [ -1+a^0<=0 && b^0>=1 ], cost: 4*b^0
     41: l2 -> l2 : b^0'=0, i^0'=0, tmp^0'=0, [ -1+a^0>=1 && b^0>=1 ], cost: 4*b^0*a^0
     17: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=a^0 ], cost: 2
     16: l11 -> l3 : a^0'=n^0, b^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l11
     18: l2 -> l3 : [ b^0<=0 ], cost: 2
     17: l3 -> l2 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=a^0 ], cost: 2
     42: l3 -> l2 : a^0'=1, b^0'=-2+b^0+a^0, i^0'=0, tmp^0'=tmp^post_12, [ 1<=1+b^0 && 1<=tmp^post_12 && -2+a^0>=1 ], cost: -4+5*a^0
     43: l3 -> l2 : a^0'=1, b^0'=-2+b^0+a^0, i^0'=0, tmp^0'=tmp^post_12, [ 1<=1+b^0 && 1+tmp^post_12<=0 && -2+a^0>=1 ], cost: -4+5*a^0
     44: l3 -> l2 : a^0'=-1+a^0, b^0'=0, i^0'=-2+a^0, [ 1<=a^0 && -2+a^0<=0 && 1+b^0>=1 ], cost: 6+4*b^0
     45: l3 -> l2 : a^0'=-1+a^0, b^0'=0, i^0'=0, tmp^0'=0, [ -2+a^0>=1 && 1+b^0>=1 ], cost: 2+4*(-1+a^0)*(1+b^0)
     16: l11 -> l3 : a^0'=n^0, b^0'=0, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l11
     46: l3 -> l3 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=a^0 && 1+b^0<=0 ], cost: 4
     47: l3 -> l3 : a^0'=-1+a^0, b^0'=0, i^0'=-2+a^0, [ 1<=a^0 && -2+a^0<=0 && 1+b^0>=1 ], cost: 8+4*b^0
     48: l3 -> l3 : a^0'=-1+a^0, b^0'=0, i^0'=0, tmp^0'=0, [ -2+a^0>=1 && 1+b^0>=1 ], cost: 4+4*(-1+a^0)*(1+b^0)
     49: l3 -> [14] : [ 1<=1+b^0 && 1<=tmp^post_12 && -2+a^0>=1 ], cost: -4+5*a^0
     50: l3 -> [14] : [ 1<=1+b^0 && 1+tmp^post_12<=0 && -2+a^0>=1 ], cost: -4+5*a^0
     16: l11 -> l3 : a^0'=n^0, b^0'=0, [], cost: 2

Accelerating simple loops of location 3.
   Accelerating the following rules:
     46: l3 -> l3 : a^0'=-1+a^0, b^0'=1+b^0, [ 1<=a^0 && 1+b^0<=0 ], cost: 4
     47: l3 -> l3 : a^0'=-1+a^0, b^0'=0, i^0'=-2+a^0, [ 1<=a^0 && -2+a^0<=0 && 1+b^0>=1 ], cost: 8+4*b^0
     48: l3 -> l3 : a^0'=-1+a^0, b^0'=0, i^0'=0, tmp^0'=0, [ -2+a^0>=1 && 1+b^0>=1 ], cost: 4+4*(-1+a^0)*(1+b^0)

   Accelerated rule 46 with backward acceleration, yielding the new rule 51.
   Accelerated rule 46 with backward acceleration, yielding the new rule 52.
   Accelerated rule 47 with backward acceleration, yielding the new rule 53.
   Accelerated rule 48 with backward acceleration, yielding the new rule 54.
[accelerate] Nesting with 4 inner and 3 outer candidates
   Nested simple loops 48 (outer loop) and 52 (inner loop) with Rule(3 | -b^0>=0, -2+a^0>=1, 1>=1, | -4+4*(-2+a^0)*a^0-2*(-2+a^0)^2+2*a^0 || 3 | 0=2, 1=0, 2=0, 4=0, ), resulting in the new rules: 55, 56.
   Removing the simple loops: 46 47 48.

Accelerated all simple loops using metering functions (where possible):
   Start location: l11
     49: l3 -> [14] : [ 1<=1+b^0 && 1<=tmp^post_12 && -2+a^0>=1 ], cost: -4+5*a^0
     50: l3 -> [14] : [ 1<=1+b^0 && 1+tmp^post_12<=0 && -2+a^0>=1 ], cost: -4+5*a^0
     51: l3 -> l3 : a^0'=0, b^0'=b^0+a^0, [ a^0>=0 && b^0+a^0<=0 ], cost: 4*a^0
     52: l3 -> l3 : a^0'=b^0+a^0, b^0'=0, [ -b^0>=0 && 1<=1+b^0+a^0 ], cost: -4*b^0
     53: l3 -> l3 : a^0'=0, b^0'=0, i^0'=-1, [ -2+a^0<=0 && 1+b^0>=1 && a^0>=1 ], cost: 8*a^0
     54: l3 -> l3 : a^0'=2, b^0'=0, i^0'=0, tmp^0'=0, [ 1+b^0>=1 && -2+a^0>=1 ], cost: -4+4*(-2+a^0)*a^0-2*(-2+a^0)^2+2*a^0
     55: l3 -> l3 : a^0'=2, b^0'=0, i^0'=0, tmp^0'=0, [ -b^0>=0 && -2+a^0>=1 ], cost: -4+4*(-2+a^0)*a^0-2*(-2+a^0)^2+2*a^0
     56: l3 -> l3 : a^0'=2, b^0'=0, i^0'=0, tmp^0'=0, [ 1+b^0>=1 && -3+a^0>=1 ], cost: -2+4*(-3+a^0)*(-1+a^0)+4*(-1+a^0)*(1+b^0)-2*(-3+a^0)^2+2*a^0
     16: l11 -> l3 : a^0'=n^0, b^0'=0, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l11
     49: l3 -> [14] : [ 1<=1+b^0 && 1<=tmp^post_12 && -2+a^0>=1 ], cost: -4+5*a^0
     50: l3 -> [14] : [ 1<=1+b^0 && 1+tmp^post_12<=0 && -2+a^0>=1 ], cost: -4+5*a^0
     16: l11 -> l3 : a^0'=n^0, b^0'=0, [], cost: 2
     57: l11 -> l3 : a^0'=0, b^0'=n^0, [ -n^0==0 ], cost: 2+4*n^0
     58: l11 -> l3 : a^0'=n^0, b^0'=0, [ 1<=1+n^0 ], cost: 2
     59: l11 -> l3 : a^0'=0, b^0'=0, i^0'=-1, [ -2+n^0<=0 && n^0>=1 ], cost: 2+8*n^0
     60: l11 -> l3 : a^0'=2, b^0'=0, i^0'=0, tmp^0'=0, [ -2+n^0>=1 ], cost: -2-2*(-2+n^0)^2+4*(-2+n^0)*n^0+2*n^0
     61: l11 -> l3 : a^0'=2, b^0'=0, i^0'=0, tmp^0'=0, [ -2+n^0>=1 ], cost: -2-2*(-2+n^0)^2+4*(-2+n^0)*n^0+2*n^0
     62: l11 -> l3 : a^0'=2, b^0'=0, i^0'=0, tmp^0'=0, [ -3+n^0>=1 ], cost: -4-2*(-3+n^0)^2+4*(-3+n^0)*(-1+n^0)+6*n^0

Eliminated locations (on tree-shaped paths):
   Start location: l11
     63: l11 -> [14] : a^0'=n^0, b^0'=0, [ 1<=tmp^post_12 && -2+n^0>=1 ], cost: -2+5*n^0
     64: l11 -> [14] : a^0'=n^0, b^0'=0, [ 1+tmp^post_12<=0 && -2+n^0>=1 ], cost: -2+5*n^0
     65: l11 -> [14] : a^0'=n^0, b^0'=0, [ 1<=tmp^post_12 && -2+n^0>=1 ], cost: -2+5*n^0
     66: l11 -> [14] : a^0'=n^0, b^0'=0, [ 1+tmp^post_12<=0 && -2+n^0>=1 ], cost: -2+5*n^0
     67: l11 -> [16] : [ -n^0==0 ], cost: 2+4*n^0
     68: l11 -> [16] : [ -2+n^0<=0 && n^0>=1 ], cost: 2+8*n^0
     69: l11 -> [16] : [ -2+n^0>=1 ], cost: -2-2*(-2+n^0)^2+4*(-2+n^0)*n^0+2*n^0
     70: l11 -> [16] : [ -2+n^0>=1 ], cost: -2-2*(-2+n^0)^2+4*(-2+n^0)*n^0+2*n^0
     71: l11 -> [16] : [ -3+n^0>=1 ], cost: -4-2*(-3+n^0)^2+4*(-3+n^0)*(-1+n^0)+6*n^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l11
     65: l11 -> [14] : a^0'=n^0, b^0'=0, [ 1<=tmp^post_12 && -2+n^0>=1 ], cost: -2+5*n^0
     66: l11 -> [14] : a^0'=n^0, b^0'=0, [ 1+tmp^post_12<=0 && -2+n^0>=1 ], cost: -2+5*n^0
     67: l11 -> [16] : [ -n^0==0 ], cost: 2+4*n^0
     68: l11 -> [16] : [ -2+n^0<=0 && n^0>=1 ], cost: 2+8*n^0
     70: l11 -> [16] : [ -2+n^0>=1 ], cost: -2-2*(-2+n^0)^2+4*(-2+n^0)*n^0+2*n^0
     71: l11 -> [16] : [ -3+n^0>=1 ], cost: -4-2*(-3+n^0)^2+4*(-3+n^0)*(-1+n^0)+6*n^0

Computing asymptotic complexity for rule 70
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 71
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 67
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 65
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 66
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 68
   Resulting cost 0 has complexity: Unknown

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:  [ a^0==a^post_16 && b^0==b^post_16 && i^0==i^post_16 && n^0==n^post_16 && tmp^0==tmp^post_16 ]

WORST_CASE(Omega(1),?)