WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l4
      0: l0 -> l1 : Result_4^0'=Result_4^post_1, x_5^0'=x_5^post_1, [ Result_4^0==Result_4^post_1 && x_5^0==x_5^post_1 ], cost: 1
      1: l1 -> l2 : Result_4^0'=Result_4^post_2, x_5^0'=x_5^post_2, [ x_5^post_2==-1+x_5^0 && x_5^post_2<=0 && Result_4^post_2==Result_4^post_2 ], cost: 1
      2: l1 -> l3 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, [ x_5^post_3==-1+x_5^0 && 0<=-1+x_5^post_3 && Result_4^0==Result_4^post_3 ], cost: 1
      3: l3 -> l1 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, [ Result_4^0==Result_4^post_4 && x_5^0==x_5^post_4 ], cost: 1
      4: l4 -> l0 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ Result_4^0==Result_4^post_5 && x_5^0==x_5^post_5 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      4: l4 -> l0 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ Result_4^0==Result_4^post_5 && x_5^0==x_5^post_5 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l4
      0: l0 -> l1 : Result_4^0'=Result_4^post_1, x_5^0'=x_5^post_1, [ Result_4^0==Result_4^post_1 && x_5^0==x_5^post_1 ], cost: 1
      2: l1 -> l3 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, [ x_5^post_3==-1+x_5^0 && 0<=-1+x_5^post_3 && Result_4^0==Result_4^post_3 ], cost: 1
      3: l3 -> l1 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, [ Result_4^0==Result_4^post_4 && x_5^0==x_5^post_4 ], cost: 1
      4: l4 -> l0 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ Result_4^0==Result_4^post_5 && x_5^0==x_5^post_5 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      0: l0 -> l1 : [], cost: 1
      2: l1 -> l3 : x_5^0'=-1+x_5^0, [ 0<=-2+x_5^0 ], cost: 1
      3: l3 -> l1 : [], cost: 1
      4: l4 -> l0 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      6: l1 -> l1 : x_5^0'=-1+x_5^0, [ 0<=-2+x_5^0 ], cost: 2
      5: l4 -> l1 : [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      6: l1 -> l1 : x_5^0'=-1+x_5^0, [ 0<=-2+x_5^0 ], cost: 2

   Accelerated rule 6 with metering function -1+x_5^0, yielding the new rule 7.
   Removing the simple loops: 6.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
      7: l1 -> l1 : x_5^0'=1, [ 0<=-2+x_5^0 ], cost: -2+2*x_5^0
      5: l4 -> l1 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      5: l4 -> l1 : [], cost: 2
      8: l4 -> l1 : x_5^0'=1, [ 0<=-2+x_5^0 ], cost: 2*x_5^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
      8: l4 -> l1 : x_5^0'=1, [ 0<=-2+x_5^0 ], cost: 2*x_5^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
      8: l4 -> l1 : x_5^0'=1, [ 0<=-2+x_5^0 ], cost: 2*x_5^0

Computing asymptotic complexity for rule 8
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      -1+x_5^0 (+/+!), 2*x_5^0 (+) [not solved]

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

      applying transformation rule (C) using substitution {x_5^0==n}
      resulting limit problem:
      [solved]

   Solution:
      x_5^0 / n
   Resulting cost 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: 2*n
   Rule cost:   2*x_5^0
   Rule guard:  [ 0<=-2+x_5^0 ]

WORST_CASE(Omega(n^1),?)