WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_Load -> f161_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f161_0_main_LT -> f212_0_main_LE : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>-1 && arg1==arg1P_2 && 1==arg2P_2 ], cost: 1
      2: f212_0_main_LE -> f161_0_main_LT : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2>=arg1 && -1+arg1==arg1P_3 ], cost: 1
      3: f212_0_main_LE -> f212_0_main_LE : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2>0 && arg2<arg1 && arg1==arg1P_4 && 2*arg2==arg2P_4 ], cost: 1
      4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1_0_main_Load -> f161_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f161_0_main_LT -> f212_0_main_LE : arg2'=1, [ arg1>-1 ], cost: 1
      2: f212_0_main_LE -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P_3, [ arg2>=arg1 ], cost: 1
      3: f212_0_main_LE -> f212_0_main_LE : arg2'=2*arg2, [ arg2>0 && arg2<arg1 ], cost: 1
      4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1

### Simplification by acceleration and chaining ###

Accelerating simple loops of location 2.
   Accelerating the following rules:
      3: f212_0_main_LE -> f212_0_main_LE : arg2'=2*arg2, [ arg2>0 && arg2<arg1 ], cost: 1

   Accelerated rule 3 with backward acceleration, yielding the new rule 5.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 3.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      0: f1_0_main_Load -> f161_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f161_0_main_LT -> f212_0_main_LE : arg2'=1, [ arg1>-1 ], cost: 1
      2: f212_0_main_LE -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P_3, [ arg2>=arg1 ], cost: 1
      5: f212_0_main_LE -> f212_0_main_LE : arg2'=arg2*2^k, [ arg2>0 && k>=0 && arg2*2^(-1+k)<arg1 ], cost: k
      4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1

Chained accelerated rules (with incoming rules):
   Start location: __init
      0: f1_0_main_Load -> f161_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2>-1 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f161_0_main_LT -> f212_0_main_LE : arg2'=1, [ arg1>-1 ], cost: 1
      6: f161_0_main_LT -> f212_0_main_LE : arg2'=2^k, [ arg1>-1 && k>=0 && 2^(-1+k)<arg1 ], cost: 1+k
      2: f212_0_main_LE -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P_3, [ arg2>=arg1 ], cost: 1
      4: __init -> f1_0_main_Load : arg1'=arg1P_5, arg2'=arg2P_5, [], cost: 1

Eliminated locations (on linear paths):
   Start location: __init
      1: f161_0_main_LT -> f212_0_main_LE : arg2'=1, [ arg1>-1 ], cost: 1
      6: f161_0_main_LT -> f212_0_main_LE : arg2'=2^k, [ arg1>-1 && k>=0 && 2^(-1+k)<arg1 ], cost: 1+k
      2: f212_0_main_LE -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P_3, [ arg2>=arg1 ], cost: 1
      7: __init -> f161_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_5>-1 && arg1P_1>-1 && arg1P_5>0 ], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
      8: f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>-1 && 1>=arg1 ], cost: 2
      9: f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>-1 && k>=0 && 2^(-1+k)<arg1 && 2^k>=arg1 ], cost: 2+k
      7: __init -> f161_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_5>-1 && arg1P_1>-1 && arg1P_5>0 ], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      8: f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>-1 && 1>=arg1 ], cost: 2
      9: f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>-1 && k>=0 && 2^(-1+k)<arg1 && 2^k>=arg1 ], cost: 2+k

   Accelerated rule 8 with backward acceleration, yielding the new rule 10.
   Failed to prove monotonicity of the guard of rule 9.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 8.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      9: f161_0_main_LT -> f161_0_main_LT : arg1'=-1+arg1, arg2'=arg2P_3, [ arg1>-1 && k>=0 && 2^(-1+k)<arg1 && 2^k>=arg1 ], cost: 2+k
     10: f161_0_main_LT -> f161_0_main_LT : arg1'=-1, arg2'=arg2P_3, [ 1>=arg1 && 1+arg1>=1 ], cost: 2+2*arg1
      7: __init -> f161_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_5>-1 && arg1P_1>-1 && arg1P_5>0 ], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: __init
      7: __init -> f161_0_main_LT : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2P_5>-1 && arg1P_1>-1 && arg1P_5>0 ], cost: 2
     11: __init -> f161_0_main_LT : arg1'=-1+arg1P_1, arg2'=arg2P_3, [ arg1P_1>-1 && k>=0 && 2^(-1+k)<arg1P_1 && 2^k>=arg1P_1 ], cost: 4+k
     12: __init -> f161_0_main_LT : arg1'=-1, arg2'=arg2P_3, [ arg1P_1>-1 && 1>=arg1P_1 ], cost: 4+2*arg1P_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     11: __init -> f161_0_main_LT : arg1'=-1+arg1P_1, arg2'=arg2P_3, [ arg1P_1>-1 && k>=0 && 2^(-1+k)<arg1P_1 && 2^k>=arg1P_1 ], cost: 4+k
     12: __init -> f161_0_main_LT : arg1'=-1, arg2'=arg2P_3, [ arg1P_1>-1 && 1>=arg1P_1 ], cost: 4+2*arg1P_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     11: __init -> f161_0_main_LT : arg1'=-1+arg1P_1, arg2'=arg2P_3, [ arg1P_1>-1 && k>=0 && 2^(-1+k)<arg1P_1 && 2^k>=arg1P_1 ], cost: 4+k
     12: __init -> f161_0_main_LT : arg1'=-1, arg2'=arg2P_3, [ arg1P_1>-1 && 1>=arg1P_1 ], cost: 4+2*arg1P_1

Computing asymptotic complexity for rule 12
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 11
   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),?)