WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: l6
      0: l0 -> l1 : i^0'=i^post_1, [ i^0==i^post_1 ], cost: 1
      1: l2 -> l0 : i^0'=i^post_2, [ 20<=i^0 && i^0==i^post_2 ], cost: 1
      2: l2 -> l3 : i^0'=i^post_3, [ 1+i^0<=20 && i^post_3==1+i^0 ], cost: 1
      5: l3 -> l2 : i^0'=i^post_6, [ i^0==i^post_6 ], cost: 1
      3: l4 -> l0 : i^0'=i^post_4, [ i^0<=0 && i^0==i^post_4 ], cost: 1
      4: l4 -> l3 : i^0'=i^post_5, [ 1<=i^0 && i^0==i^post_5 ], cost: 1
      6: l5 -> l4 : i^0'=i^post_7, [ i^1_1==0 && i^post_7==i^post_7 ], cost: 1
      7: l6 -> l5 : i^0'=i^post_8, [ i^0==i^post_8 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      7: l6 -> l5 : i^0'=i^post_8, [ i^0==i^post_8 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l6
      2: l2 -> l3 : i^0'=i^post_3, [ 1+i^0<=20 && i^post_3==1+i^0 ], cost: 1
      5: l3 -> l2 : i^0'=i^post_6, [ i^0==i^post_6 ], cost: 1
      4: l4 -> l3 : i^0'=i^post_5, [ 1<=i^0 && i^0==i^post_5 ], cost: 1
      6: l5 -> l4 : i^0'=i^post_7, [ i^1_1==0 && i^post_7==i^post_7 ], cost: 1
      7: l6 -> l5 : i^0'=i^post_8, [ i^0==i^post_8 ], cost: 1

Simplified all rules, resulting in:
   Start location: l6
      2: l2 -> l3 : i^0'=1+i^0, [ 1+i^0<=20 ], cost: 1
      5: l3 -> l2 : [], cost: 1
      4: l4 -> l3 : [ 1<=i^0 ], cost: 1
      6: l5 -> l4 : i^0'=i^post_7, [], cost: 1
      7: l6 -> l5 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l6
     10: l3 -> l3 : i^0'=1+i^0, [ 1+i^0<=20 ], cost: 2
      9: l6 -> l3 : i^0'=i^post_7, [ 1<=i^post_7 ], cost: 3

Accelerating simple loops of location 3.
   Accelerating the following rules:
     10: l3 -> l3 : i^0'=1+i^0, [ 1+i^0<=20 ], cost: 2

   Accelerated rule 10 with backward acceleration, yielding the new rule 11.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 10.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
     11: l3 -> l3 : i^0'=20, [ 20-i^0>=0 ], cost: 40-2*i^0
      9: l6 -> l3 : i^0'=i^post_7, [ 1<=i^post_7 ], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: l6
      9: l6 -> l3 : i^0'=i^post_7, [ 1<=i^post_7 ], cost: 3
     12: l6 -> l3 : i^0'=20, [ 1<=i^post_7 && 20-i^post_7>=0 ], cost: 43-2*i^post_7

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
     12: l6 -> l3 : i^0'=20, [ 1<=i^post_7 && 20-i^post_7>=0 ], cost: 43-2*i^post_7

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l6
     12: l6 -> l3 : i^0'=20, [ 1<=i^post_7 && 20-i^post_7>=0 ], cost: 43-2*i^post_7

Computing asymptotic complexity for rule 12
   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:  [ i^0==i^post_8 ]

WORST_CASE(Omega(1),?)