WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l6
      0: l0 -> l1 : __const_50^0'=__const_50^post_1, i5^0'=i5^post_1, i^0'=i^post_1, tmp^0'=tmp^post_1, [ __const_50^0<=i5^0 && i^post_1==0 && __const_50^0==__const_50^post_1 && i5^0==i5^post_1 && tmp^0==tmp^post_1 ], cost: 1
      1: l0 -> l2 : __const_50^0'=__const_50^post_2, i5^0'=i5^post_2, i^0'=i^post_2, tmp^0'=tmp^post_2, [ 1+i5^0<=__const_50^0 && i5^post_2==1+i5^0 && __const_50^0==__const_50^post_2 && i^0==i^post_2 && tmp^0==tmp^post_2 ], cost: 1
      3: l1 -> l3 : __const_50^0'=__const_50^post_4, i5^0'=i5^post_4, i^0'=i^post_4, tmp^0'=tmp^post_4, [ __const_50^0==__const_50^post_4 && i^0==i^post_4 && i5^0==i5^post_4 && tmp^0==tmp^post_4 ], cost: 1
      2: l2 -> l0 : __const_50^0'=__const_50^post_3, i5^0'=i5^post_3, i^0'=i^post_3, tmp^0'=tmp^post_3, [ __const_50^0==__const_50^post_3 && i^0==i^post_3 && i5^0==i5^post_3 && tmp^0==tmp^post_3 ], cost: 1
      4: l3 -> l4 : __const_50^0'=__const_50^post_5, i5^0'=i5^post_5, i^0'=i^post_5, tmp^0'=tmp^post_5, [ __const_50^0<=i^0 && __const_50^0==__const_50^post_5 && i^0==i^post_5 && i5^0==i5^post_5 && tmp^0==tmp^post_5 ], cost: 1
      5: l3 -> l1 : __const_50^0'=__const_50^post_6, i5^0'=i5^post_6, i^0'=i^post_6, tmp^0'=tmp^post_6, [ 1+i^0<=__const_50^0 && i^post_6==1+i^0 && __const_50^0==__const_50^post_6 && i5^0==i5^post_6 && tmp^0==tmp^post_6 ], cost: 1
      6: l5 -> l2 : __const_50^0'=__const_50^post_7, i5^0'=i5^post_7, i^0'=i^post_7, tmp^0'=tmp^post_7, [ i^post_7==0 && tmp^post_7==tmp^post_7 && i5^1_1==0 && i5^post_7==0 && __const_50^0==__const_50^post_7 ], cost: 1
      7: l6 -> l5 : __const_50^0'=__const_50^post_8, i5^0'=i5^post_8, i^0'=i^post_8, tmp^0'=tmp^post_8, [ __const_50^0==__const_50^post_8 && i^0==i^post_8 && i5^0==i5^post_8 && tmp^0==tmp^post_8 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      7: l6 -> l5 : __const_50^0'=__const_50^post_8, i5^0'=i5^post_8, i^0'=i^post_8, tmp^0'=tmp^post_8, [ __const_50^0==__const_50^post_8 && i^0==i^post_8 && i5^0==i5^post_8 && tmp^0==tmp^post_8 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l6
      0: l0 -> l1 : __const_50^0'=__const_50^post_1, i5^0'=i5^post_1, i^0'=i^post_1, tmp^0'=tmp^post_1, [ __const_50^0<=i5^0 && i^post_1==0 && __const_50^0==__const_50^post_1 && i5^0==i5^post_1 && tmp^0==tmp^post_1 ], cost: 1
      1: l0 -> l2 : __const_50^0'=__const_50^post_2, i5^0'=i5^post_2, i^0'=i^post_2, tmp^0'=tmp^post_2, [ 1+i5^0<=__const_50^0 && i5^post_2==1+i5^0 && __const_50^0==__const_50^post_2 && i^0==i^post_2 && tmp^0==tmp^post_2 ], cost: 1
      3: l1 -> l3 : __const_50^0'=__const_50^post_4, i5^0'=i5^post_4, i^0'=i^post_4, tmp^0'=tmp^post_4, [ __const_50^0==__const_50^post_4 && i^0==i^post_4 && i5^0==i5^post_4 && tmp^0==tmp^post_4 ], cost: 1
      2: l2 -> l0 : __const_50^0'=__const_50^post_3, i5^0'=i5^post_3, i^0'=i^post_3, tmp^0'=tmp^post_3, [ __const_50^0==__const_50^post_3 && i^0==i^post_3 && i5^0==i5^post_3 && tmp^0==tmp^post_3 ], cost: 1
      5: l3 -> l1 : __const_50^0'=__const_50^post_6, i5^0'=i5^post_6, i^0'=i^post_6, tmp^0'=tmp^post_6, [ 1+i^0<=__const_50^0 && i^post_6==1+i^0 && __const_50^0==__const_50^post_6 && i5^0==i5^post_6 && tmp^0==tmp^post_6 ], cost: 1
      6: l5 -> l2 : __const_50^0'=__const_50^post_7, i5^0'=i5^post_7, i^0'=i^post_7, tmp^0'=tmp^post_7, [ i^post_7==0 && tmp^post_7==tmp^post_7 && i5^1_1==0 && i5^post_7==0 && __const_50^0==__const_50^post_7 ], cost: 1
      7: l6 -> l5 : __const_50^0'=__const_50^post_8, i5^0'=i5^post_8, i^0'=i^post_8, tmp^0'=tmp^post_8, [ __const_50^0==__const_50^post_8 && i^0==i^post_8 && i5^0==i5^post_8 && tmp^0==tmp^post_8 ], cost: 1

Simplified all rules, resulting in:
   Start location: l6
      0: l0 -> l1 : i^0'=0, [ __const_50^0<=i5^0 ], cost: 1
      1: l0 -> l2 : i5^0'=1+i5^0, [ 1+i5^0<=__const_50^0 ], cost: 1
      3: l1 -> l3 : [], cost: 1
      2: l2 -> l0 : [], cost: 1
      5: l3 -> l1 : i^0'=1+i^0, [ 1+i^0<=__const_50^0 ], cost: 1
      6: l5 -> l2 : i5^0'=0, i^0'=0, tmp^0'=tmp^post_7, [], cost: 1
      7: l6 -> l5 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l6
      0: l0 -> l1 : i^0'=0, [ __const_50^0<=i5^0 ], cost: 1
      1: l0 -> l2 : i5^0'=1+i5^0, [ 1+i5^0<=__const_50^0 ], cost: 1
      9: l1 -> l1 : i^0'=1+i^0, [ 1+i^0<=__const_50^0 ], cost: 2
      2: l2 -> l0 : [], cost: 1
      8: l6 -> l2 : i5^0'=0, i^0'=0, tmp^0'=tmp^post_7, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      9: l1 -> l1 : i^0'=1+i^0, [ 1+i^0<=__const_50^0 ], cost: 2

   Accelerated rule 9 with metering function -i^0+__const_50^0, yielding the new rule 10.
   Removing the simple loops: 9.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
      0: l0 -> l1 : i^0'=0, [ __const_50^0<=i5^0 ], cost: 1
      1: l0 -> l2 : i5^0'=1+i5^0, [ 1+i5^0<=__const_50^0 ], cost: 1
     10: l1 -> l1 : i^0'=__const_50^0, [ 1+i^0<=__const_50^0 ], cost: -2*i^0+2*__const_50^0
      2: l2 -> l0 : [], cost: 1
      8: l6 -> l2 : i5^0'=0, i^0'=0, tmp^0'=tmp^post_7, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
      0: l0 -> l1 : i^0'=0, [ __const_50^0<=i5^0 ], cost: 1
      1: l0 -> l2 : i5^0'=1+i5^0, [ 1+i5^0<=__const_50^0 ], cost: 1
     11: l0 -> l1 : i^0'=__const_50^0, [ __const_50^0<=i5^0 && 1<=__const_50^0 ], cost: 1+2*__const_50^0
      2: l2 -> l0 : [], cost: 1
      8: l6 -> l2 : i5^0'=0, i^0'=0, tmp^0'=tmp^post_7, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l6
      1: l0 -> l2 : i5^0'=1+i5^0, [ 1+i5^0<=__const_50^0 ], cost: 1
     11: l0 -> l1 : i^0'=__const_50^0, [ __const_50^0<=i5^0 && 1<=__const_50^0 ], cost: 1+2*__const_50^0
      2: l2 -> l0 : [], cost: 1
      8: l6 -> l2 : i5^0'=0, i^0'=0, tmp^0'=tmp^post_7, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l6
     12: l2 -> l2 : i5^0'=1+i5^0, [ 1+i5^0<=__const_50^0 ], cost: 2
     13: l2 -> l1 : i^0'=__const_50^0, [ __const_50^0<=i5^0 && 1<=__const_50^0 ], cost: 2+2*__const_50^0
      8: l6 -> l2 : i5^0'=0, i^0'=0, tmp^0'=tmp^post_7, [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
     12: l2 -> l2 : i5^0'=1+i5^0, [ 1+i5^0<=__const_50^0 ], cost: 2

   Accelerated rule 12 with metering function __const_50^0-i5^0, yielding the new rule 14.
   Removing the simple loops: 12.

Accelerated all simple loops using metering functions (where possible):
   Start location: l6
     13: l2 -> l1 : i^0'=__const_50^0, [ __const_50^0<=i5^0 && 1<=__const_50^0 ], cost: 2+2*__const_50^0
     14: l2 -> l2 : i5^0'=__const_50^0, [ 1+i5^0<=__const_50^0 ], cost: 2*__const_50^0-2*i5^0
      8: l6 -> l2 : i5^0'=0, i^0'=0, tmp^0'=tmp^post_7, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l6
     13: l2 -> l1 : i^0'=__const_50^0, [ __const_50^0<=i5^0 && 1<=__const_50^0 ], cost: 2+2*__const_50^0
      8: l6 -> l2 : i5^0'=0, i^0'=0, tmp^0'=tmp^post_7, [], cost: 2
     15: l6 -> l2 : i5^0'=__const_50^0, i^0'=0, tmp^0'=tmp^post_7, [ 1<=__const_50^0 ], cost: 2+2*__const_50^0

Eliminated locations (on tree-shaped paths):
   Start location: l6
     16: l6 -> l1 : i5^0'=__const_50^0, i^0'=__const_50^0, tmp^0'=tmp^post_7, [ 1<=__const_50^0 ], cost: 4+4*__const_50^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l6
     16: l6 -> l1 : i5^0'=__const_50^0, i^0'=__const_50^0, tmp^0'=tmp^post_7, [ 1<=__const_50^0 ], cost: 4+4*__const_50^0

Computing asymptotic complexity for rule 16
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      4+4*__const_50^0 (+), __const_50^0 (+/+!) [not solved]

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

      applying transformation rule (C) using substitution {__const_50^0==n}
      resulting limit problem:
      [solved]

   Solution:
      __const_50^0 / n
   Resulting cost 4+4*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: 4+4*n
   Rule cost:   4+4*__const_50^0
   Rule guard:  [ 1<=__const_50^0 ]

WORST_CASE(Omega(n^1),?)