WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_Load -> f172_0_appendNewList_LE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2>0 && arg1P_1>-1 && arg1>0 && 0==arg2P_1 ], cost: 1
      1: f172_0_appendNewList_LE -> f172_0_appendNewList_LE : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2P_2>arg2 && arg1>1 && arg2>0 && -1+arg1==arg1P_2 ], cost: 1
      2: f172_0_appendNewList_LE -> f172_0_appendNewList_LE : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1>1 && -1+arg1==arg1P_3 && 1==arg2P_3 ], cost: 1
      3: f172_0_appendNewList_LE -> f282_0_copy_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4>1 && arg2P_4>3 && arg1<2 && 0==arg3P_4 ], cost: 1
      4: f282_0_copy_NULL -> f282_0_copy_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ -1+arg1P_5<=arg2 && 1+arg2P_5<=arg2 && arg1>1 && arg2>0 && arg1P_5>1 && arg2P_5>-1 && 2+arg3<=arg1 && 2+arg3P_5<=arg2 ], cost: 1
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_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, arg3'=arg3P_6, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1_0_main_Load -> f172_0_appendNewList_LE : arg1'=arg1P_1, arg2'=0, arg3'=arg3P_1, [ arg2>0 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f172_0_appendNewList_LE -> f172_0_appendNewList_LE : arg1'=-1+arg1, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2P_2>arg2 && arg1>1 && arg2>0 ], cost: 1
      2: f172_0_appendNewList_LE -> f172_0_appendNewList_LE : arg1'=-1+arg1, arg2'=1, arg3'=arg3P_3, [ arg1>1 ], cost: 1
      3: f172_0_appendNewList_LE -> f282_0_copy_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=0, [ arg1P_4>1 && arg2P_4>3 && arg1<2 ], cost: 1
      4: f282_0_copy_NULL -> f282_0_copy_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ -1+arg1P_5<=arg2 && 1+arg2P_5<=arg2 && arg1>1 && arg2>0 && arg1P_5>1 && arg2P_5>-1 && 2+arg3<=arg1 && 2+arg3P_5<=arg2 ], cost: 1
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1

### Simplification by acceleration and chaining ###

Accelerating simple loops of location 1.
   Accelerating the following rules:
      1: f172_0_appendNewList_LE -> f172_0_appendNewList_LE : arg1'=-1+arg1, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2P_2>arg2 && arg1>1 && arg2>0 ], cost: 1
      2: f172_0_appendNewList_LE -> f172_0_appendNewList_LE : arg1'=-1+arg1, arg2'=1, arg3'=arg3P_3, [ arg1>1 ], cost: 1

   Failed to prove monotonicity of the guard of rule 1.
   Accelerated rule 2 with backward acceleration, yielding the new rule 6.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Nested simple loops 2 (outer loop) and 1 (inner loop) with Rule(1 | arg2>0, k_1>=1, 1-2*k_1+arg1>1, | 2*k_1 || 1 | 0=-2*k_1+arg1, 1=1, 2=arg3P_3, ), resulting in the new rules: 7, 8.
   Removing the simple loops: 2.

Accelerating simple loops of location 2.
   Accelerating the following rules:
      4: f282_0_copy_NULL -> f282_0_copy_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ -1+arg1P_5<=arg2 && 1+arg2P_5<=arg2 && arg1>1 && arg2>0 && arg1P_5>1 && arg2P_5>-1 && 2+arg3<=arg1 && 2+arg3P_5<=arg2 ], cost: 1

   Failed to prove monotonicity of the guard of rule 4.
[accelerate] Nesting with 1 inner and 1 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      0: f1_0_main_Load -> f172_0_appendNewList_LE : arg1'=arg1P_1, arg2'=0, arg3'=arg3P_1, [ arg2>0 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f172_0_appendNewList_LE -> f172_0_appendNewList_LE : arg1'=-1+arg1, arg2'=arg2P_2, arg3'=arg3P_2, [ arg2P_2>arg2 && arg1>1 && arg2>0 ], cost: 1
      3: f172_0_appendNewList_LE -> f282_0_copy_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=0, [ arg1P_4>1 && arg2P_4>3 && arg1<2 ], cost: 1
      6: f172_0_appendNewList_LE -> f172_0_appendNewList_LE : arg1'=1, arg2'=1, arg3'=arg3P_3, [ -1+arg1>=1 ], cost: -1+arg1
      7: f172_0_appendNewList_LE -> f172_0_appendNewList_LE : arg1'=-2*k_1+arg1, arg2'=1, arg3'=arg3P_3, [ arg2>0 && k_1>=1 && 1-2*k_1+arg1>1 ], cost: 2*k_1
      8: f172_0_appendNewList_LE -> f172_0_appendNewList_LE : arg1'=-1-2*k_1+arg1, arg2'=1, arg3'=arg3P_3, [ arg1>1 && k_1>=1 && -2*k_1+arg1>1 ], cost: 1+2*k_1
      4: f282_0_copy_NULL -> f282_0_copy_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ -1+arg1P_5<=arg2 && 1+arg2P_5<=arg2 && arg1>1 && arg2>0 && arg1P_5>1 && arg2P_5>-1 && 2+arg3<=arg1 && 2+arg3P_5<=arg2 ], cost: 1
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1

Chained accelerated rules (with incoming rules):
   Start location: __init
      0: f1_0_main_Load -> f172_0_appendNewList_LE : arg1'=arg1P_1, arg2'=0, arg3'=arg3P_1, [ arg2>0 && arg1P_1>-1 && arg1>0 ], cost: 1
      9: f1_0_main_Load -> f172_0_appendNewList_LE : arg1'=1, arg2'=1, arg3'=arg3P_3, [ arg2>0 && arg1>0 && -1+arg1P_1>=1 ], cost: arg1P_1
     10: f1_0_main_Load -> f172_0_appendNewList_LE : arg1'=-1+arg1P_1-2*k_1, arg2'=1, arg3'=arg3P_3, [ arg2>0 && arg1>0 && arg1P_1>1 && k_1>=1 && arg1P_1-2*k_1>1 ], cost: 2+2*k_1
      3: f172_0_appendNewList_LE -> f282_0_copy_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=0, [ arg1P_4>1 && arg2P_4>3 && arg1<2 ], cost: 1
     11: f172_0_appendNewList_LE -> f282_0_copy_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1<2 && arg1P_5>1 && arg2P_5>-1 ], cost: 2
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
      9: f1_0_main_Load -> f172_0_appendNewList_LE : arg1'=1, arg2'=1, arg3'=arg3P_3, [ arg2>0 && arg1>0 && -1+arg1P_1>=1 ], cost: arg1P_1
     10: f1_0_main_Load -> f172_0_appendNewList_LE : arg1'=-1+arg1P_1-2*k_1, arg2'=1, arg3'=arg3P_3, [ arg2>0 && arg1>0 && arg1P_1>1 && k_1>=1 && arg1P_1-2*k_1>1 ], cost: 2+2*k_1
      5: __init -> f1_0_main_Load : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [], cost: 1

Eliminated locations (on tree-shaped paths):
   Start location: __init
     12: __init -> f172_0_appendNewList_LE : arg1'=1, arg2'=1, arg3'=arg3P_3, [ arg2P_6>0 && arg1P_6>0 && -1+arg1P_1>=1 ], cost: 1+arg1P_1
     13: __init -> f172_0_appendNewList_LE : arg1'=-1+arg1P_1-2*k_1, arg2'=1, arg3'=arg3P_3, [ arg2P_6>0 && arg1P_6>0 && arg1P_1>1 && k_1>=1 && arg1P_1-2*k_1>1 ], cost: 3+2*k_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     12: __init -> f172_0_appendNewList_LE : arg1'=1, arg2'=1, arg3'=arg3P_3, [ arg2P_6>0 && arg1P_6>0 && -1+arg1P_1>=1 ], cost: 1+arg1P_1
     13: __init -> f172_0_appendNewList_LE : arg1'=-1+arg1P_1-2*k_1, arg2'=1, arg3'=arg3P_3, [ arg2P_6>0 && arg1P_6>0 && arg1P_1>1 && k_1>=1 && arg1P_1-2*k_1>1 ], cost: 3+2*k_1

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

Computing asymptotic complexity for rule 13
   Simplified the guard:
     13: __init -> f172_0_appendNewList_LE : arg1'=-1+arg1P_1-2*k_1, arg2'=1, arg3'=arg3P_3, [ arg2P_6>0 && arg1P_6>0 && k_1>=1 && arg1P_1-2*k_1>1 ], cost: 3+2*k_1
   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),?)