WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_Load -> f57_0_collatz_LE : arg1'=arg1P_1, arg2'=arg2P_1, [ arg1>0 && arg2>-1 && arg2==arg1P_1 ], cost: 1
      1: f57_0_collatz_LE -> f57_0_collatz_LE\' : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1>1 && arg1>x5_1 && arg1-2*x6_1==0 && arg1==arg1P_2 ], cost: 1
      3: f57_0_collatz_LE -> f57_0_collatz_LE\' : arg1'=arg1P_4, arg2'=arg2P_4, [ -2*x11_1+arg1==1 && 3*arg1>0 && arg1>1 && arg1==arg1P_4 ], cost: 1
      2: f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>1 && -2*x9_1+arg1==0 && arg1>arg1P_3 && arg1-2*arg1P_3>=0 && arg1-2*arg1P_3<2 && -2*x9_1+arg1<2 && -2*x9_1+arg1>=0 ], cost: 1
      4: f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=arg1P_5, arg2'=arg2P_5, [ -2*x13_1+arg1==1 && arg1>1 && 3*arg1>0 && -2*x13_1+arg1<2 && -2*x13_1+arg1>=0 && 1+3*arg1==arg1P_5 ], cost: 1
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1_0_main_Load -> f57_0_collatz_LE : arg1'=arg2, arg2'=arg2P_1, [ arg1>0 && arg2>-1 ], cost: 1
      1: f57_0_collatz_LE -> f57_0_collatz_LE\' : arg2'=arg2P_2, [ arg1>1 && arg1-2*x6_1==0 ], cost: 1
      3: f57_0_collatz_LE -> f57_0_collatz_LE\' : arg2'=arg2P_4, [ -2*x11_1+arg1==1 && arg1>1 ], cost: 1
      2: f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ -2*x9_1+arg1==0 && arg1>arg1P_3 && arg1-2*arg1P_3>=0 && arg1-2*arg1P_3<2 ], cost: 1
      4: f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P_5, [ -2*x13_1+arg1==1 && arg1>1 ], cost: 1
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
      1: f57_0_collatz_LE -> f57_0_collatz_LE\' : arg2'=arg2P_2, [ arg1>1 && arg1-2*x6_1==0 ], cost: 1
      3: f57_0_collatz_LE -> f57_0_collatz_LE\' : arg2'=arg2P_4, [ -2*x11_1+arg1==1 && arg1>1 ], cost: 1
      2: f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ -2*x9_1+arg1==0 && arg1>arg1P_3 && arg1-2*arg1P_3>=0 && arg1-2*arg1P_3<2 ], cost: 1
      4: f57_0_collatz_LE\' -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P_5, [ -2*x13_1+arg1==1 && arg1>1 ], cost: 1
      6: __init -> f57_0_collatz_LE : arg1'=arg2P_6, arg2'=arg2P_1, [ arg1P_6>0 && arg2P_6>-1 ], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
      7: f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>1 && arg1-2*x6_1==0 && -2*x9_1+arg1==0 && arg1>arg1P_3 && arg1-2*arg1P_3>=0 && arg1-2*arg1P_3<2 ], cost: 2
      8: f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P_5, [ -2*x11_1+arg1==1 && arg1>1 && -2*x13_1+arg1==1 ], cost: 2
      6: __init -> f57_0_collatz_LE : arg1'=arg2P_6, arg2'=arg2P_1, [ arg1P_6>0 && arg2P_6>-1 ], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
      7: f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>1 && arg1-2*x6_1==0 && -2*x9_1+arg1==0 && arg1>arg1P_3 && arg1-2*arg1P_3>=0 && arg1-2*arg1P_3<2 ], cost: 2
      8: f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P_5, [ -2*x11_1+arg1==1 && arg1>1 && -2*x13_1+arg1==1 ], cost: 2

   Failed to prove monotonicity of the guard of rule 7.
   Failed to prove monotonicity of the guard of rule 8.
[accelerate] Nesting with 2 inner and 2 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      7: f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1>1 && arg1-2*x6_1==0 && -2*x9_1+arg1==0 && arg1>arg1P_3 && arg1-2*arg1P_3>=0 && arg1-2*arg1P_3<2 ], cost: 2
      8: f57_0_collatz_LE -> f57_0_collatz_LE : arg1'=1+3*arg1, arg2'=arg2P_5, [ -2*x11_1+arg1==1 && arg1>1 && -2*x13_1+arg1==1 ], cost: 2
      6: __init -> f57_0_collatz_LE : arg1'=arg2P_6, arg2'=arg2P_1, [ arg1P_6>0 && arg2P_6>-1 ], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: __init
      6: __init -> f57_0_collatz_LE : arg1'=arg2P_6, arg2'=arg2P_1, [ arg1P_6>0 && arg2P_6>-1 ], cost: 2
      9: __init -> f57_0_collatz_LE : arg1'=arg1P_3, arg2'=arg2P_3, [ 2*x6_1>1 && 2*x6_1>arg1P_3 && -2*arg1P_3+2*x6_1>=0 && -2*arg1P_3+2*x6_1<2 ], cost: 4
     10: __init -> f57_0_collatz_LE : arg1'=4+6*x11_1, arg2'=arg2P_5, [ 1+2*x11_1>1 ], cost: 4

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     <empty>

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),?)