WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l9
      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 -> l3 : Result_4^0'=Result_4^post_2, x_5^0'=x_5^post_2, [ x_5^post_2==-1+x_5^0 && Result_4^0==Result_4^post_2 ], cost: 1
      6: l1 -> l6 : Result_4^0'=Result_4^post_7, x_5^0'=x_5^post_7, [ x_5^post_7==-1+x_5^0 && Result_4^0==Result_4^post_7 ], cost: 1
     10: l1 -> l8 : Result_4^0'=Result_4^post_11, x_5^0'=x_5^post_11, [ x_5^1_1==-1+x_5^0 && x_5^1_1<=13 && 13<=x_5^1_1 && x_5^post_11==x_5^post_11 && -x_5^post_11<=0 && Result_4^0==Result_4^post_11 ], cost: 1
     12: l1 -> l5 : Result_4^0'=Result_4^post_13, x_5^0'=x_5^post_13, [ x_5^1_2==-1+x_5^0 && x_5^1_2<=13 && 13<=x_5^1_2 && x_5^post_13==x_5^post_13 && 0<=-1-x_5^post_13 && Result_4^post_13==Result_4^post_13 ], cost: 1
      2: l3 -> l4 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, [ 1+x_5^0<=13 && Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 ], cost: 1
      3: l3 -> l4 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, [ 14<=x_5^0 && Result_4^0==Result_4^post_4 && x_5^0==x_5^post_4 ], cost: 1
      4: l4 -> l2 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ -x_5^0<=0 && Result_4^0==Result_4^post_5 && x_5^0==x_5^post_5 ], cost: 1
      5: l2 -> l1 : Result_4^0'=Result_4^post_6, x_5^0'=x_5^post_6, [ Result_4^0==Result_4^post_6 && x_5^0==x_5^post_6 ], cost: 1
      7: l6 -> l7 : Result_4^0'=Result_4^post_8, x_5^0'=x_5^post_8, [ 1+x_5^0<=13 && Result_4^0==Result_4^post_8 && x_5^0==x_5^post_8 ], cost: 1
      8: l6 -> l7 : Result_4^0'=Result_4^post_9, x_5^0'=x_5^post_9, [ 14<=x_5^0 && Result_4^0==Result_4^post_9 && x_5^0==x_5^post_9 ], cost: 1
      9: l7 -> l5 : Result_4^0'=Result_4^post_10, x_5^0'=x_5^post_10, [ 0<=-1-x_5^0 && Result_4^post_10==Result_4^post_10 && x_5^0==x_5^post_10 ], cost: 1
     11: l8 -> l1 : Result_4^0'=Result_4^post_12, x_5^0'=x_5^post_12, [ Result_4^0==Result_4^post_12 && x_5^0==x_5^post_12 ], cost: 1
     13: l9 -> l0 : Result_4^0'=Result_4^post_14, x_5^0'=x_5^post_14, [ Result_4^0==Result_4^post_14 && x_5^0==x_5^post_14 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     13: l9 -> l0 : Result_4^0'=Result_4^post_14, x_5^0'=x_5^post_14, [ Result_4^0==Result_4^post_14 && x_5^0==x_5^post_14 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l9
      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 -> l3 : Result_4^0'=Result_4^post_2, x_5^0'=x_5^post_2, [ x_5^post_2==-1+x_5^0 && Result_4^0==Result_4^post_2 ], cost: 1
     10: l1 -> l8 : Result_4^0'=Result_4^post_11, x_5^0'=x_5^post_11, [ x_5^1_1==-1+x_5^0 && x_5^1_1<=13 && 13<=x_5^1_1 && x_5^post_11==x_5^post_11 && -x_5^post_11<=0 && Result_4^0==Result_4^post_11 ], cost: 1
      2: l3 -> l4 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, [ 1+x_5^0<=13 && Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 ], cost: 1
      3: l3 -> l4 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, [ 14<=x_5^0 && Result_4^0==Result_4^post_4 && x_5^0==x_5^post_4 ], cost: 1
      4: l4 -> l2 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, [ -x_5^0<=0 && Result_4^0==Result_4^post_5 && x_5^0==x_5^post_5 ], cost: 1
      5: l2 -> l1 : Result_4^0'=Result_4^post_6, x_5^0'=x_5^post_6, [ Result_4^0==Result_4^post_6 && x_5^0==x_5^post_6 ], cost: 1
     11: l8 -> l1 : Result_4^0'=Result_4^post_12, x_5^0'=x_5^post_12, [ Result_4^0==Result_4^post_12 && x_5^0==x_5^post_12 ], cost: 1
     13: l9 -> l0 : Result_4^0'=Result_4^post_14, x_5^0'=x_5^post_14, [ Result_4^0==Result_4^post_14 && x_5^0==x_5^post_14 ], cost: 1

Simplified all rules, resulting in:
   Start location: l9
      0: l0 -> l1 : [], cost: 1
      1: l1 -> l3 : x_5^0'=-1+x_5^0, [], cost: 1
     10: l1 -> l8 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 1
      2: l3 -> l4 : [ 1+x_5^0<=13 ], cost: 1
      3: l3 -> l4 : [ 14<=x_5^0 ], cost: 1
      4: l4 -> l2 : [ -x_5^0<=0 ], cost: 1
      5: l2 -> l1 : [], cost: 1
     11: l8 -> l1 : [], cost: 1
     13: l9 -> l0 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l9
      1: l1 -> l3 : x_5^0'=-1+x_5^0, [], cost: 1
     15: l1 -> l1 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 2
      2: l3 -> l4 : [ 1+x_5^0<=13 ], cost: 1
      3: l3 -> l4 : [ 14<=x_5^0 ], cost: 1
     16: l4 -> l1 : [ -x_5^0<=0 ], cost: 2
     14: l9 -> l1 : [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     15: l1 -> l1 : x_5^0'=x_5^post_11, [ -14+x_5^0==0 && -x_5^post_11<=0 ], cost: 2

      During metering: Instantiating temporary variables by {x_5^post_11==0}
   Accelerated rule 15 with metering function meter (where 14*meter==-13+x_5^0), yielding the new rule 17.
   Removing the simple loops: 15.

Accelerated all simple loops using metering functions (where possible):
   Start location: l9
      1: l1 -> l3 : x_5^0'=-1+x_5^0, [], cost: 1
     17: l1 -> l1 : x_5^0'=0, [ -14+x_5^0==0 && 14*meter==-13+x_5^0 && meter>=1 ], cost: 2*meter
      2: l3 -> l4 : [ 1+x_5^0<=13 ], cost: 1
      3: l3 -> l4 : [ 14<=x_5^0 ], cost: 1
     16: l4 -> l1 : [ -x_5^0<=0 ], cost: 2
     14: l9 -> l1 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l9
      1: l1 -> l3 : x_5^0'=-1+x_5^0, [], cost: 1
      2: l3 -> l4 : [ 1+x_5^0<=13 ], cost: 1
      3: l3 -> l4 : [ 14<=x_5^0 ], cost: 1
     16: l4 -> l1 : [ -x_5^0<=0 ], cost: 2
     14: l9 -> l1 : [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l9
     18: l1 -> l4 : x_5^0'=-1+x_5^0, [ x_5^0<=13 ], cost: 2
     19: l1 -> l4 : x_5^0'=-1+x_5^0, [ 14<=-1+x_5^0 ], cost: 2
     16: l4 -> l1 : [ -x_5^0<=0 ], cost: 2
     14: l9 -> l1 : [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l9
     20: l1 -> l1 : x_5^0'=-1+x_5^0, [ x_5^0<=13 && 1-x_5^0<=0 ], cost: 4
     21: l1 -> l1 : x_5^0'=-1+x_5^0, [ 14<=-1+x_5^0 ], cost: 4
     14: l9 -> l1 : [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     20: l1 -> l1 : x_5^0'=-1+x_5^0, [ x_5^0<=13 && 1-x_5^0<=0 ], cost: 4
     21: l1 -> l1 : x_5^0'=-1+x_5^0, [ 14<=-1+x_5^0 ], cost: 4

   Accelerated rule 20 with metering function x_5^0, yielding the new rule 22.
   Accelerated rule 21 with metering function -14+x_5^0, yielding the new rule 23.
   Removing the simple loops: 20 21.

Accelerated all simple loops using metering functions (where possible):
   Start location: l9
     22: l1 -> l1 : x_5^0'=0, [ x_5^0<=13 && 1-x_5^0<=0 ], cost: 4*x_5^0
     23: l1 -> l1 : x_5^0'=14, [ 14<=-1+x_5^0 ], cost: -56+4*x_5^0
     14: l9 -> l1 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l9
     14: l9 -> l1 : [], cost: 2
     24: l9 -> l1 : x_5^0'=0, [ x_5^0<=13 && 1-x_5^0<=0 ], cost: 2+4*x_5^0
     25: l9 -> l1 : x_5^0'=14, [ 14<=-1+x_5^0 ], cost: -54+4*x_5^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l9
     24: l9 -> l1 : x_5^0'=0, [ x_5^0<=13 && 1-x_5^0<=0 ], cost: 2+4*x_5^0
     25: l9 -> l1 : x_5^0'=14, [ 14<=-1+x_5^0 ], cost: -54+4*x_5^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l9
     24: l9 -> l1 : x_5^0'=0, [ x_5^0<=13 && 1-x_5^0<=0 ], cost: 2+4*x_5^0
     25: l9 -> l1 : x_5^0'=14, [ 14<=-1+x_5^0 ], cost: -54+4*x_5^0

Computing asymptotic complexity for rule 24
   Could not solve the limit problem.
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 25
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      -14+x_5^0 (+/+!), -54+4*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 -54+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: -54+4*n
   Rule cost:   -54+4*x_5^0
   Rule guard:  [ 14<=-1+x_5^0 ]

WORST_CASE(Omega(n^1),?)