WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l3
      0: l0 -> l1 : __const_200^0'=__const_200^post_1, x^0'=x^post_1, [ x^post_1==-1+x^0 && 1+__const_200^0<=x^post_1 && __const_200^0==__const_200^post_1 ], cost: 1
      1: l1 -> l0 : __const_200^0'=__const_200^post_2, x^0'=x^post_2, [ __const_200^0==__const_200^post_2 && x^0==x^post_2 ], cost: 1
      2: l2 -> l0 : __const_200^0'=__const_200^post_3, x^0'=x^post_3, [ __const_200^0==__const_200^post_3 && x^0==x^post_3 ], cost: 1
      3: l3 -> l2 : __const_200^0'=__const_200^post_4, x^0'=x^post_4, [ __const_200^0==__const_200^post_4 && x^0==x^post_4 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      3: l3 -> l2 : __const_200^0'=__const_200^post_4, x^0'=x^post_4, [ __const_200^0==__const_200^post_4 && x^0==x^post_4 ], cost: 1

Simplified all rules, resulting in:
   Start location: l3
      0: l0 -> l1 : x^0'=-1+x^0, [ 1+__const_200^0<=-1+x^0 ], cost: 1
      1: l1 -> l0 : [], cost: 1
      2: l2 -> l0 : [], cost: 1
      3: l3 -> l2 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l3
      5: l0 -> l0 : x^0'=-1+x^0, [ 1+__const_200^0<=-1+x^0 ], cost: 2
      4: l3 -> l0 : [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
      5: l0 -> l0 : x^0'=-1+x^0, [ 1+__const_200^0<=-1+x^0 ], cost: 2

   Accelerated rule 5 with metering function -1-__const_200^0+x^0, yielding the new rule 6.
   Removing the simple loops: 5.

Accelerated all simple loops using metering functions (where possible):
   Start location: l3
      6: l0 -> l0 : x^0'=1+__const_200^0, [ 1+__const_200^0<=-1+x^0 ], cost: -2-2*__const_200^0+2*x^0
      4: l3 -> l0 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l3
      4: l3 -> l0 : [], cost: 2
      7: l3 -> l0 : x^0'=1+__const_200^0, [ 1+__const_200^0<=-1+x^0 ], cost: -2*__const_200^0+2*x^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l3
      7: l3 -> l0 : x^0'=1+__const_200^0, [ 1+__const_200^0<=-1+x^0 ], cost: -2*__const_200^0+2*x^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l3
      7: l3 -> l0 : x^0'=1+__const_200^0, [ 1+__const_200^0<=-1+x^0 ], cost: -2*__const_200^0+2*x^0

Computing asymptotic complexity for rule 7
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      -2*__const_200^0+2*x^0 (+), -1-__const_200^0+x^0 (+/+!) [not solved]

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

      applying transformation rule (C) using substitution {__const_200^0==0,x^0==n}
      resulting limit problem:
      [solved]

   Solution:
      __const_200^0 / 0
      x^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*__const_200^0+2*x^0
   Rule guard:  [ 1+__const_200^0<=-1+x^0 ]

WORST_CASE(Omega(n^1),?)