WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l6
      0: l0 -> l1 : __const_20^0'=__const_20^post_1, i^0'=i^post_1, [ __const_20^0==__const_20^post_1 && i^0==i^post_1 ], cost: 1
      1: l2 -> l0 : __const_20^0'=__const_20^post_2, i^0'=i^post_2, [ __const_20^0<=i^0 && __const_20^0==__const_20^post_2 && i^0==i^post_2 ], cost: 1
      2: l2 -> l3 : __const_20^0'=__const_20^post_3, i^0'=i^post_3, [ 1+i^0<=__const_20^0 && i^post_3==1+i^0 && __const_20^0==__const_20^post_3 ], cost: 1
      5: l3 -> l2 : __const_20^0'=__const_20^post_6, i^0'=i^post_6, [ __const_20^0==__const_20^post_6 && i^0==i^post_6 ], cost: 1
      3: l4 -> l0 : __const_20^0'=__const_20^post_4, i^0'=i^post_4, [ i^0<=0 && __const_20^0==__const_20^post_4 && i^0==i^post_4 ], cost: 1
      4: l4 -> l3 : __const_20^0'=__const_20^post_5, i^0'=i^post_5, [ 1<=i^0 && __const_20^0==__const_20^post_5 && i^0==i^post_5 ], cost: 1
      6: l5 -> l4 : __const_20^0'=__const_20^post_7, i^0'=i^post_7, [ i^1_1==0 && i^post_7==i^post_7 && __const_20^0==__const_20^post_7 ], cost: 1
      7: l6 -> l5 : __const_20^0'=__const_20^post_8, i^0'=i^post_8, [ __const_20^0==__const_20^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 : __const_20^0'=__const_20^post_8, i^0'=i^post_8, [ __const_20^0==__const_20^post_8 && i^0==i^post_8 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l6
      2: l2 -> l3 : __const_20^0'=__const_20^post_3, i^0'=i^post_3, [ 1+i^0<=__const_20^0 && i^post_3==1+i^0 && __const_20^0==__const_20^post_3 ], cost: 1
      5: l3 -> l2 : __const_20^0'=__const_20^post_6, i^0'=i^post_6, [ __const_20^0==__const_20^post_6 && i^0==i^post_6 ], cost: 1
      4: l4 -> l3 : __const_20^0'=__const_20^post_5, i^0'=i^post_5, [ 1<=i^0 && __const_20^0==__const_20^post_5 && i^0==i^post_5 ], cost: 1
      6: l5 -> l4 : __const_20^0'=__const_20^post_7, i^0'=i^post_7, [ i^1_1==0 && i^post_7==i^post_7 && __const_20^0==__const_20^post_7 ], cost: 1
      7: l6 -> l5 : __const_20^0'=__const_20^post_8, i^0'=i^post_8, [ __const_20^0==__const_20^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<=__const_20^0 ], 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<=__const_20^0 ], 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<=__const_20^0 ], cost: 2

   Accelerated rule 10 with metering function __const_20^0-i^0, yielding the new rule 11.
   Removing the simple loops: 10.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
     11: l3 -> l3 : i^0'=__const_20^0, [ 1+i^0<=__const_20^0 ], cost: 2*__const_20^0-2*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'=__const_20^0, [ 1<=i^post_7 && 1+i^post_7<=__const_20^0 ], cost: 3-2*i^post_7+2*__const_20^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
     12: l6 -> l3 : i^0'=__const_20^0, [ 1<=i^post_7 && 1+i^post_7<=__const_20^0 ], cost: 3-2*i^post_7+2*__const_20^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l6
     12: l6 -> l3 : i^0'=__const_20^0, [ 1<=i^post_7 && 1+i^post_7<=__const_20^0 ], cost: 3-2*i^post_7+2*__const_20^0

Computing asymptotic complexity for rule 12
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      i^post_7 (+/+!), -i^post_7+__const_20^0 (+/+!), 3-2*i^post_7+2*__const_20^0 (+) [not solved]

      removing all constraints (solved by SMT)
      resulting limit problem: [solved]

      applying transformation rule (C) using substitution {i^post_7==n,__const_20^0==2*n}
      resulting limit problem:
      [solved]

   Solution:
      i^post_7 / n
      __const_20^0 / 2*n
   Resulting cost 3+2*n has complexity: Poly(n^1)

Found new complexity Poly(n^1).

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Poly(n^1)
   Cpx degree:  1
   Solved cost: 3+2*n
   Rule cost:   3-2*i^post_7+2*__const_20^0
   Rule guard:  [ 1<=i^post_7 && 1+i^post_7<=__const_20^0 ]

WORST_CASE(Omega(n^1),?)