WORST_CASE(Omega(n^1),?)

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

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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      5: l4 -> l3 : x^0'=x^post_6, [ x^0==x^post_6 ], cost: 1

Simplified all rules, resulting in:
   Start location: l4
      0: l0 -> l2 : x^0'=-1+x^0, [], cost: 1
      1: l2 -> l1 : [ 1<=x^0 ], cost: 1
      2: l2 -> l1 : [ 1+x^0<=0 ], cost: 1
      3: l1 -> l0 : [], cost: 1
      4: l3 -> l0 : [ 1<=x^0 ], cost: 1
      5: l4 -> l3 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l4
      0: l0 -> l2 : x^0'=-1+x^0, [], cost: 1
      1: l2 -> l1 : [ 1<=x^0 ], cost: 1
      2: l2 -> l1 : [ 1+x^0<=0 ], cost: 1
      3: l1 -> l0 : [], cost: 1
      6: l4 -> l0 : [ 1<=x^0 ], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l4
      7: l0 -> l1 : x^0'=-1+x^0, [ 1<=-1+x^0 ], cost: 2
      8: l0 -> l1 : x^0'=-1+x^0, [ x^0<=0 ], cost: 2
      3: l1 -> l0 : [], cost: 1
      6: l4 -> l0 : [ 1<=x^0 ], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l4
      9: l0 -> l0 : x^0'=-1+x^0, [ 1<=-1+x^0 ], cost: 3
     10: l0 -> l0 : x^0'=-1+x^0, [ x^0<=0 ], cost: 3
      6: l4 -> l0 : [ 1<=x^0 ], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
      9: l0 -> l0 : x^0'=-1+x^0, [ 1<=-1+x^0 ], cost: 3
     10: l0 -> l0 : x^0'=-1+x^0, [ x^0<=0 ], cost: 3

   Accelerated rule 9 with metering function -1+x^0, yielding the new rule 11.
   Accelerated rule 10 with NONTERM, yielding the new rule 12.
   Removing the simple loops: 9 10.

Accelerated all simple loops using metering functions (where possible):
   Start location: l4
     11: l0 -> l0 : x^0'=1, [ 1<=-1+x^0 ], cost: -3+3*x^0
     12: l0 -> [5] : [ x^0<=0 ], cost: NONTERM
      6: l4 -> l0 : [ 1<=x^0 ], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l4
      6: l4 -> l0 : [ 1<=x^0 ], cost: 2
     13: l4 -> l0 : x^0'=1, [ 1<=-1+x^0 ], cost: -1+3*x^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l4
     13: l4 -> l0 : x^0'=1, [ 1<=-1+x^0 ], cost: -1+3*x^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l4
     13: l4 -> l0 : x^0'=1, [ 1<=-1+x^0 ], cost: -1+3*x^0

Computing asymptotic complexity for rule 13
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      -1+x^0 (+/+!), -1+3*x^0 (+) [not solved]

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

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

   Solution:
      x^0 / n
   Resulting cost -1+3*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: -1+3*n
   Rule cost:   -1+3*x^0
   Rule guard:  [ 1<=-1+x^0 ]

WORST_CASE(Omega(n^1),?)