WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      8: f2 -> f3 : arg1'=arg1P_9, [ arg1<255 && arg1==arg1P_9 ], cost: 1
     10: f2 -> f9 : arg1'=arg1P_11, [ arg1>=255 && arg1==arg1P_11 ], cost: 1
      1: f4 -> f7 : arg1'=arg1P_2, [ arg1P_2==1+arg1 ], cost: 1
      6: f7 -> f6 : arg1'=arg1P_7, [ arg1==arg1P_7 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, [ arg1P_3==2+arg1 ], cost: 1
      7: f8 -> f6 : arg1'=arg1P_8, [ arg1==arg1P_8 ], cost: 1
      3: f3 -> f4 : arg1'=arg1P_4, [ x3_1<0 && arg1==arg1P_4 ], cost: 1
      4: f3 -> f4 : arg1'=arg1P_5, [ x14_1>0 && arg1==arg1P_5 ], cost: 1
      5: f3 -> f5 : arg1'=arg1P_6, [ x5_1==0 && arg1==arg1P_6 ], cost: 1
      9: f6 -> f2 : arg1'=arg1P_10, [ arg1==arg1P_10 ], cost: 1
     11: __init -> f1 : arg1'=arg1P_12, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     11: __init -> f1 : arg1'=arg1P_12, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      8: f2 -> f3 : arg1'=arg1P_9, [ arg1<255 && arg1==arg1P_9 ], cost: 1
      1: f4 -> f7 : arg1'=arg1P_2, [ arg1P_2==1+arg1 ], cost: 1
      6: f7 -> f6 : arg1'=arg1P_7, [ arg1==arg1P_7 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, [ arg1P_3==2+arg1 ], cost: 1
      7: f8 -> f6 : arg1'=arg1P_8, [ arg1==arg1P_8 ], cost: 1
      3: f3 -> f4 : arg1'=arg1P_4, [ x3_1<0 && arg1==arg1P_4 ], cost: 1
      4: f3 -> f4 : arg1'=arg1P_5, [ x14_1>0 && arg1==arg1P_5 ], cost: 1
      5: f3 -> f5 : arg1'=arg1P_6, [ x5_1==0 && arg1==arg1P_6 ], cost: 1
      9: f6 -> f2 : arg1'=arg1P_10, [ arg1==arg1P_10 ], cost: 1
     11: __init -> f1 : arg1'=arg1P_12, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      8: f2 -> f3 : [ arg1<255 ], cost: 1
      1: f4 -> f7 : arg1'=1+arg1, [], cost: 1
      6: f7 -> f6 : [], cost: 1
      2: f5 -> f8 : arg1'=2+arg1, [], cost: 1
      7: f8 -> f6 : [], cost: 1
      4: f3 -> f4 : [], cost: 1
      5: f3 -> f5 : [], cost: 1
      9: f6 -> f2 : [], cost: 1
     11: __init -> f1 : arg1'=arg1P_12, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
      8: f2 -> f3 : [ arg1<255 ], cost: 1
     15: f3 -> f6 : arg1'=1+arg1, [], cost: 3
     16: f3 -> f6 : arg1'=2+arg1, [], cost: 3
      9: f6 -> f2 : [], cost: 1
     12: __init -> f2 : arg1'=arg1P_1, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
     17: f2 -> f6 : arg1'=1+arg1, [ arg1<255 ], cost: 4
     18: f2 -> f6 : arg1'=2+arg1, [ arg1<255 ], cost: 4
      9: f6 -> f2 : [], cost: 1
     12: __init -> f2 : arg1'=arg1P_1, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
     19: f2 -> f2 : arg1'=1+arg1, [ arg1<255 ], cost: 5
     20: f2 -> f2 : arg1'=2+arg1, [ arg1<255 ], cost: 5
     12: __init -> f2 : arg1'=arg1P_1, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     19: f2 -> f2 : arg1'=1+arg1, [ arg1<255 ], cost: 5
     20: f2 -> f2 : arg1'=2+arg1, [ arg1<255 ], cost: 5

   Accelerated rule 19 with backward acceleration, yielding the new rule 21.
   Accelerated rule 20 with backward acceleration, yielding the new rule 22.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 19 20.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     21: f2 -> f2 : arg1'=255, [ 255-arg1>=0 ], cost: 1275-5*arg1
     22: f2 -> f2 : arg1'=2*k_1+arg1, [ k_1>=0 && -2+2*k_1+arg1<255 ], cost: 5*k_1
     12: __init -> f2 : arg1'=arg1P_1, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: __init
     12: __init -> f2 : arg1'=arg1P_1, [], cost: 2
     23: __init -> f2 : arg1'=255, [ 255-arg1P_1>=0 ], cost: 1277-5*arg1P_1
     24: __init -> f2 : arg1'=arg1P_1+2*k_1, [ k_1>=0 && -2+arg1P_1+2*k_1<255 ], cost: 2+5*k_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     23: __init -> f2 : arg1'=255, [ 255-arg1P_1>=0 ], cost: 1277-5*arg1P_1
     24: __init -> f2 : arg1'=arg1P_1+2*k_1, [ k_1>=0 && -2+arg1P_1+2*k_1<255 ], cost: 2+5*k_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     23: __init -> f2 : arg1'=255, [ 255-arg1P_1>=0 ], cost: 1277-5*arg1P_1
     24: __init -> f2 : arg1'=arg1P_1+2*k_1, [ k_1>=0 && -2+arg1P_1+2*k_1<255 ], cost: 2+5*k_1

Computing asymptotic complexity for rule 23
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 24
   Resulting cost 0 has complexity: Unknown

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Constant
   Cpx degree:  0
   Solved cost: 1
   Rule cost:   1
   Rule guard:  []

WORST_CASE(Omega(1),?)