WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l5
      0: l0 -> l1 : __const_127^0'=__const_127^post_1, __const_36^0'=__const_36^post_1, counter^0'=counter^post_1, y^0'=y^post_1, z^0'=z^post_1, [ __const_36^0<=counter^0 && __const_127^0==__const_127^post_1 && __const_36^0==__const_36^post_1 && counter^0==counter^post_1 && y^0==y^post_1 && z^0==z^post_1 ], cost: 1
      1: l0 -> l2 : __const_127^0'=__const_127^post_2, __const_36^0'=__const_36^post_2, counter^0'=counter^post_2, y^0'=y^post_2, z^0'=z^post_2, [ 1+counter^0<=__const_36^0 && z^post_2==1+z^0 && counter^post_2==1+counter^0 && __const_127^0==__const_127^post_2 && __const_36^0==__const_36^post_2 && y^0==y^post_2 ], cost: 1
      4: l2 -> l0 : __const_127^0'=__const_127^post_5, __const_36^0'=__const_36^post_5, counter^0'=counter^post_5, y^0'=y^post_5, z^0'=z^post_5, [ __const_127^0==__const_127^post_5 && __const_36^0==__const_36^post_5 && counter^0==counter^post_5 && y^0==y^post_5 && z^0==z^post_5 ], cost: 1
      2: l3 -> l2 : __const_127^0'=__const_127^post_3, __const_36^0'=__const_36^post_3, counter^0'=counter^post_3, y^0'=y^post_3, z^0'=z^post_3, [ y^0<=__const_127^0 && z^post_3==z^post_3 && __const_127^0==__const_127^post_3 && __const_36^0==__const_36^post_3 && counter^0==counter^post_3 && y^0==y^post_3 ], cost: 1
      3: l3 -> l1 : __const_127^0'=__const_127^post_4, __const_36^0'=__const_36^post_4, counter^0'=counter^post_4, y^0'=y^post_4, z^0'=z^post_4, [ 1+__const_127^0<=y^0 && __const_127^0==__const_127^post_4 && __const_36^0==__const_36^post_4 && counter^0==counter^post_4 && y^0==y^post_4 && z^0==z^post_4 ], cost: 1
      5: l4 -> l3 : __const_127^0'=__const_127^post_6, __const_36^0'=__const_36^post_6, counter^0'=counter^post_6, y^0'=y^post_6, z^0'=z^post_6, [ counter^post_6==0 && __const_127^0==__const_127^post_6 && __const_36^0==__const_36^post_6 && y^0==y^post_6 && z^0==z^post_6 ], cost: 1
      6: l5 -> l4 : __const_127^0'=__const_127^post_7, __const_36^0'=__const_36^post_7, counter^0'=counter^post_7, y^0'=y^post_7, z^0'=z^post_7, [ __const_127^0==__const_127^post_7 && __const_36^0==__const_36^post_7 && counter^0==counter^post_7 && y^0==y^post_7 && z^0==z^post_7 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      6: l5 -> l4 : __const_127^0'=__const_127^post_7, __const_36^0'=__const_36^post_7, counter^0'=counter^post_7, y^0'=y^post_7, z^0'=z^post_7, [ __const_127^0==__const_127^post_7 && __const_36^0==__const_36^post_7 && counter^0==counter^post_7 && y^0==y^post_7 && z^0==z^post_7 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l5
      1: l0 -> l2 : __const_127^0'=__const_127^post_2, __const_36^0'=__const_36^post_2, counter^0'=counter^post_2, y^0'=y^post_2, z^0'=z^post_2, [ 1+counter^0<=__const_36^0 && z^post_2==1+z^0 && counter^post_2==1+counter^0 && __const_127^0==__const_127^post_2 && __const_36^0==__const_36^post_2 && y^0==y^post_2 ], cost: 1
      4: l2 -> l0 : __const_127^0'=__const_127^post_5, __const_36^0'=__const_36^post_5, counter^0'=counter^post_5, y^0'=y^post_5, z^0'=z^post_5, [ __const_127^0==__const_127^post_5 && __const_36^0==__const_36^post_5 && counter^0==counter^post_5 && y^0==y^post_5 && z^0==z^post_5 ], cost: 1
      2: l3 -> l2 : __const_127^0'=__const_127^post_3, __const_36^0'=__const_36^post_3, counter^0'=counter^post_3, y^0'=y^post_3, z^0'=z^post_3, [ y^0<=__const_127^0 && z^post_3==z^post_3 && __const_127^0==__const_127^post_3 && __const_36^0==__const_36^post_3 && counter^0==counter^post_3 && y^0==y^post_3 ], cost: 1
      5: l4 -> l3 : __const_127^0'=__const_127^post_6, __const_36^0'=__const_36^post_6, counter^0'=counter^post_6, y^0'=y^post_6, z^0'=z^post_6, [ counter^post_6==0 && __const_127^0==__const_127^post_6 && __const_36^0==__const_36^post_6 && y^0==y^post_6 && z^0==z^post_6 ], cost: 1
      6: l5 -> l4 : __const_127^0'=__const_127^post_7, __const_36^0'=__const_36^post_7, counter^0'=counter^post_7, y^0'=y^post_7, z^0'=z^post_7, [ __const_127^0==__const_127^post_7 && __const_36^0==__const_36^post_7 && counter^0==counter^post_7 && y^0==y^post_7 && z^0==z^post_7 ], cost: 1

Simplified all rules, resulting in:
   Start location: l5
      1: l0 -> l2 : counter^0'=1+counter^0, z^0'=1+z^0, [ 1+counter^0<=__const_36^0 ], cost: 1
      4: l2 -> l0 : [], cost: 1
      2: l3 -> l2 : z^0'=z^post_3, [ y^0<=__const_127^0 ], cost: 1
      5: l4 -> l3 : counter^0'=0, [], cost: 1
      6: l5 -> l4 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l5
      9: l2 -> l2 : counter^0'=1+counter^0, z^0'=1+z^0, [ 1+counter^0<=__const_36^0 ], cost: 2
      8: l5 -> l2 : counter^0'=0, z^0'=z^post_3, [ y^0<=__const_127^0 ], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
      9: l2 -> l2 : counter^0'=1+counter^0, z^0'=1+z^0, [ 1+counter^0<=__const_36^0 ], cost: 2

   Accelerated rule 9 with metering function -counter^0+__const_36^0, yielding the new rule 10.
   Removing the simple loops: 9.

Accelerated all simple loops using metering functions (where possible):
   Start location: l5
     10: l2 -> l2 : counter^0'=__const_36^0, z^0'=-counter^0+z^0+__const_36^0, [ 1+counter^0<=__const_36^0 ], cost: -2*counter^0+2*__const_36^0
      8: l5 -> l2 : counter^0'=0, z^0'=z^post_3, [ y^0<=__const_127^0 ], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: l5
      8: l5 -> l2 : counter^0'=0, z^0'=z^post_3, [ y^0<=__const_127^0 ], cost: 3
     11: l5 -> l2 : counter^0'=__const_36^0, z^0'=z^post_3+__const_36^0, [ y^0<=__const_127^0 && 1<=__const_36^0 ], cost: 3+2*__const_36^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l5
     11: l5 -> l2 : counter^0'=__const_36^0, z^0'=z^post_3+__const_36^0, [ y^0<=__const_127^0 && 1<=__const_36^0 ], cost: 3+2*__const_36^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l5
     11: l5 -> l2 : counter^0'=__const_36^0, z^0'=z^post_3+__const_36^0, [ y^0<=__const_127^0 && 1<=__const_36^0 ], cost: 3+2*__const_36^0

Computing asymptotic complexity for rule 11
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      3+2*__const_36^0 (+), __const_36^0 (+/+!), 1-y^0+__const_127^0 (+/+!) [not solved]

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

      applying transformation rule (C) using substitution {y^0==0,__const_127^0==n,__const_36^0==n}
      resulting limit problem:
      [solved]

   Solution:
      y^0 / 0
      __const_127^0 / n
      __const_36^0 / 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*__const_36^0
   Rule guard:  [ y^0<=__const_127^0 && 1<=__const_36^0 ]

WORST_CASE(Omega(n^1),?)