WORST_CASE(Omega(1),?)

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

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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     10: __init -> f1 : arg1'=arg1P_11, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      6: f2 -> f3 : arg1'=arg1P_7, [ arg1>0 && arg1==arg1P_7 ], cost: 1
      1: f6 -> f7 : arg1'=arg1P_2, [ arg1P_2==-2+arg1 ], cost: 1
      4: f7 -> f3 : arg1'=arg1P_5, [ arg1==arg1P_5 ], cost: 1
      2: f3 -> f6 : arg1'=arg1P_3, [ arg1<0 && arg1==arg1P_3 ], cost: 1
      3: f3 -> f6 : arg1'=arg1P_4, [ arg1>0 && arg1==arg1P_4 ], cost: 1
     10: __init -> f1 : arg1'=arg1P_11, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      6: f2 -> f3 : [ arg1>0 ], cost: 1
      1: f6 -> f7 : arg1'=-2+arg1, [], cost: 1
      4: f7 -> f3 : [], cost: 1
      2: f3 -> f6 : [ arg1<0 ], cost: 1
      3: f3 -> f6 : [ arg1>0 ], cost: 1
     10: __init -> f1 : arg1'=arg1P_11, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     13: f6 -> f3 : arg1'=-2+arg1, [], cost: 2
      2: f3 -> f6 : [ arg1<0 ], cost: 1
      3: f3 -> f6 : [ arg1>0 ], cost: 1
     12: __init -> f3 : arg1'=arg1P_1, [ arg1P_1>0 ], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     14: f3 -> f3 : arg1'=-2+arg1, [ arg1<0 ], cost: 3
     15: f3 -> f3 : arg1'=-2+arg1, [ arg1>0 ], cost: 3
     12: __init -> f3 : arg1'=arg1P_1, [ arg1P_1>0 ], cost: 3

Accelerating simple loops of location 4.
   Accelerating the following rules:
     14: f3 -> f3 : arg1'=-2+arg1, [ arg1<0 ], cost: 3
     15: f3 -> f3 : arg1'=-2+arg1, [ arg1>0 ], cost: 3

   Accelerated rule 14 with non-termination, yielding the new rule 16.
   Accelerated rule 15 with backward acceleration, yielding the new rule 17.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 14 15.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     16: f3 -> [9] : [ arg1<0 ], cost: NONTERM
     17: f3 -> f3 : arg1'=arg1-2*k, [ k>=0 && 2+arg1-2*k>0 ], cost: 3*k
     12: __init -> f3 : arg1'=arg1P_1, [ arg1P_1>0 ], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     12: __init -> f3 : arg1'=arg1P_1, [ arg1P_1>0 ], cost: 3
     18: __init -> f3 : arg1'=arg1P_1-2*k, [ arg1P_1>0 && k>=0 && 2+arg1P_1-2*k>0 ], cost: 3+3*k

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     18: __init -> f3 : arg1'=arg1P_1-2*k, [ arg1P_1>0 && k>=0 && 2+arg1P_1-2*k>0 ], cost: 3+3*k

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     18: __init -> f3 : arg1'=arg1P_1-2*k, [ arg1P_1>0 && k>=0 && 2+arg1P_1-2*k>0 ], cost: 3+3*k

Computing asymptotic complexity for rule 18
   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),?)