WORST_CASE(Omega(n^1),?)

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

Initial linear ITS problem
   Start location: l5
      0: l0 -> l1 : Result_4^0'=Result_4^post_1, x_5^0'=x_5^post_1, y_6^0'=y_6^post_1, [ -20+x_5^0<=0 && Result_4^post_1==Result_4^post_1 && x_5^0==x_5^post_1 && y_6^0==y_6^post_1 ], cost: 1
      1: l0 -> l2 : Result_4^0'=Result_4^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ 0<=-21+x_5^0 && Result_4^0==Result_4^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1
      3: l2 -> l0 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ -30+y_6^0<=0 && x_5^post_4==-1+x_5^0 && Result_4^0==Result_4^post_4 && y_6^0==y_6^post_4 ], cost: 1
      4: l2 -> l4 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ 0<=-31+y_6^0 && y_6^post_5==-1+y_6^0 && Result_4^0==Result_4^post_5 && x_5^0==x_5^post_5 ], cost: 1
      2: l3 -> l0 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1
      5: l4 -> l2 : Result_4^0'=Result_4^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ Result_4^0==Result_4^post_6 && x_5^0==x_5^post_6 && y_6^0==y_6^post_6 ], cost: 1
      6: l5 -> l3 : Result_4^0'=Result_4^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ Result_4^0==Result_4^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      6: l5 -> l3 : Result_4^0'=Result_4^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ Result_4^0==Result_4^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1

Removed unreachable and leaf rules:
   Start location: l5
      1: l0 -> l2 : Result_4^0'=Result_4^post_2, x_5^0'=x_5^post_2, y_6^0'=y_6^post_2, [ 0<=-21+x_5^0 && Result_4^0==Result_4^post_2 && x_5^0==x_5^post_2 && y_6^0==y_6^post_2 ], cost: 1
      3: l2 -> l0 : Result_4^0'=Result_4^post_4, x_5^0'=x_5^post_4, y_6^0'=y_6^post_4, [ -30+y_6^0<=0 && x_5^post_4==-1+x_5^0 && Result_4^0==Result_4^post_4 && y_6^0==y_6^post_4 ], cost: 1
      4: l2 -> l4 : Result_4^0'=Result_4^post_5, x_5^0'=x_5^post_5, y_6^0'=y_6^post_5, [ 0<=-31+y_6^0 && y_6^post_5==-1+y_6^0 && Result_4^0==Result_4^post_5 && x_5^0==x_5^post_5 ], cost: 1
      2: l3 -> l0 : Result_4^0'=Result_4^post_3, x_5^0'=x_5^post_3, y_6^0'=y_6^post_3, [ Result_4^0==Result_4^post_3 && x_5^0==x_5^post_3 && y_6^0==y_6^post_3 ], cost: 1
      5: l4 -> l2 : Result_4^0'=Result_4^post_6, x_5^0'=x_5^post_6, y_6^0'=y_6^post_6, [ Result_4^0==Result_4^post_6 && x_5^0==x_5^post_6 && y_6^0==y_6^post_6 ], cost: 1
      6: l5 -> l3 : Result_4^0'=Result_4^post_7, x_5^0'=x_5^post_7, y_6^0'=y_6^post_7, [ Result_4^0==Result_4^post_7 && x_5^0==x_5^post_7 && y_6^0==y_6^post_7 ], cost: 1

Simplified all rules, resulting in:
   Start location: l5
      1: l0 -> l2 : [ 0<=-21+x_5^0 ], cost: 1
      3: l2 -> l0 : x_5^0'=-1+x_5^0, [ -30+y_6^0<=0 ], cost: 1
      4: l2 -> l4 : y_6^0'=-1+y_6^0, [ 0<=-31+y_6^0 ], cost: 1
      2: l3 -> l0 : [], cost: 1
      5: l4 -> l2 : [], cost: 1
      6: l5 -> l3 : [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: l5
      1: l0 -> l2 : [ 0<=-21+x_5^0 ], cost: 1
      3: l2 -> l0 : x_5^0'=-1+x_5^0, [ -30+y_6^0<=0 ], cost: 1
      8: l2 -> l2 : y_6^0'=-1+y_6^0, [ 0<=-31+y_6^0 ], cost: 2
      7: l5 -> l0 : [], cost: 2

Accelerating simple loops of location 2.
   Accelerating the following rules:
      8: l2 -> l2 : y_6^0'=-1+y_6^0, [ 0<=-31+y_6^0 ], cost: 2

   Accelerated rule 8 with metering function -30+y_6^0, yielding the new rule 9.
   Removing the simple loops: 8.

Accelerated all simple loops using metering functions (where possible):
   Start location: l5
      1: l0 -> l2 : [ 0<=-21+x_5^0 ], cost: 1
      3: l2 -> l0 : x_5^0'=-1+x_5^0, [ -30+y_6^0<=0 ], cost: 1
      9: l2 -> l2 : y_6^0'=30, [ 0<=-31+y_6^0 ], cost: -60+2*y_6^0
      7: l5 -> l0 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l5
      1: l0 -> l2 : [ 0<=-21+x_5^0 ], cost: 1
     10: l0 -> l2 : y_6^0'=30, [ 0<=-21+x_5^0 && 0<=-31+y_6^0 ], cost: -59+2*y_6^0
      3: l2 -> l0 : x_5^0'=-1+x_5^0, [ -30+y_6^0<=0 ], cost: 1
      7: l5 -> l0 : [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: l5
     11: l0 -> l0 : x_5^0'=-1+x_5^0, [ 0<=-21+x_5^0 && -30+y_6^0<=0 ], cost: 2
     12: l0 -> l0 : x_5^0'=-1+x_5^0, y_6^0'=30, [ 0<=-21+x_5^0 && 0<=-31+y_6^0 ], cost: -58+2*y_6^0
      7: l5 -> l0 : [], cost: 2

Accelerating simple loops of location 0.
   Accelerating the following rules:
     11: l0 -> l0 : x_5^0'=-1+x_5^0, [ 0<=-21+x_5^0 && -30+y_6^0<=0 ], cost: 2
     12: l0 -> l0 : x_5^0'=-1+x_5^0, y_6^0'=30, [ 0<=-21+x_5^0 && 0<=-31+y_6^0 ], cost: -58+2*y_6^0

   Accelerated rule 11 with metering function -20+x_5^0, yielding the new rule 13.
   Found no metering function for rule 12.
   Removing the simple loops: 11.

Accelerated all simple loops using metering functions (where possible):
   Start location: l5
     12: l0 -> l0 : x_5^0'=-1+x_5^0, y_6^0'=30, [ 0<=-21+x_5^0 && 0<=-31+y_6^0 ], cost: -58+2*y_6^0
     13: l0 -> l0 : x_5^0'=20, [ 0<=-21+x_5^0 && -30+y_6^0<=0 ], cost: -40+2*x_5^0
      7: l5 -> l0 : [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: l5
      7: l5 -> l0 : [], cost: 2
     14: l5 -> l0 : x_5^0'=-1+x_5^0, y_6^0'=30, [ 0<=-21+x_5^0 && 0<=-31+y_6^0 ], cost: -56+2*y_6^0
     15: l5 -> l0 : x_5^0'=20, [ 0<=-21+x_5^0 && -30+y_6^0<=0 ], cost: -38+2*x_5^0

Removed unreachable locations (and leaf rules with constant cost):
   Start location: l5
     14: l5 -> l0 : x_5^0'=-1+x_5^0, y_6^0'=30, [ 0<=-21+x_5^0 && 0<=-31+y_6^0 ], cost: -56+2*y_6^0
     15: l5 -> l0 : x_5^0'=20, [ 0<=-21+x_5^0 && -30+y_6^0<=0 ], cost: -38+2*x_5^0

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: l5
     14: l5 -> l0 : x_5^0'=-1+x_5^0, y_6^0'=30, [ 0<=-21+x_5^0 && 0<=-31+y_6^0 ], cost: -56+2*y_6^0
     15: l5 -> l0 : x_5^0'=20, [ 0<=-21+x_5^0 && -30+y_6^0<=0 ], cost: -38+2*x_5^0

Computing asymptotic complexity for rule 14
   Solved the limit problem by the following transformations:
      Created initial limit problem:
      -56+2*y_6^0 (+), -30+y_6^0 (+/+!), -20+x_5^0 (+/+!) [not solved]

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

      applying transformation rule (C) using substitution {y_6^0==n,x_5^0==n}
      resulting limit problem:
      [solved]

   Solution:
      y_6^0 / n
      x_5^0 / n
   Resulting cost -56+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: -56+2*n
   Rule cost:   -56+2*y_6^0
   Rule guard:  [ 0<=-21+x_5^0 && 0<=-31+y_6^0 ]

WORST_CASE(Omega(n^1),?)