WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_New -> f83_0_doSum_NONNULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, arg6'=arg6P_1, [ arg1P_1>3 ], cost: 1
      1: f83_0_doSum_NONNULL -> f160_0_factorial_GT : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, arg5'=arg5P_2, arg6'=arg6P_2, [ arg1P_2<=arg1 && 1+arg6P_2<=arg1 && arg1>0 && arg1P_2>0 && arg6P_2>-1 && 2+arg5P_2<=arg1 && 1==arg2P_2 && 1==arg3P_2 && 1==arg4P_2 ], cost: 1
      2: f160_0_factorial_GT -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ arg2>0 && arg5<arg3 && arg1>=1+arg1P_3 && arg6>=arg1P_3 && arg1>0 && arg6>-1 && arg1P_3>-1 && 2+arg5<=arg1 && arg3==arg4 ], cost: 1
      3: f160_0_factorial_GT -> f160_0_factorial_GT : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, arg5'=arg5P_4, arg6'=arg6P_4, [ arg5>=arg3 && arg3>0 && arg2>0 && arg1P_4<=arg1 && 1+arg6P_4<=arg1 && arg6P_4<=arg6 && arg1>0 && arg6>-1 && arg1P_4>0 && arg6P_4>-1 && 2+arg5<=arg1 && arg3==arg4 && arg2*arg3==arg2P_4 && 1+arg3==arg3P_4 && 1+arg3==arg4P_4 && arg5==arg5P_4 ], cost: 1
      4: __init -> f1_0_main_New : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      4: __init -> f1_0_main_New : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1_0_main_New -> f83_0_doSum_NONNULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, arg6'=arg6P_1, [ arg1P_1>3 ], cost: 1
      1: f83_0_doSum_NONNULL -> f160_0_factorial_GT : arg1'=arg1P_2, arg2'=1, arg3'=1, arg4'=1, arg5'=arg5P_2, arg6'=arg6P_2, [ arg1P_2<=arg1 && 1+arg6P_2<=arg1 && arg1>0 && arg1P_2>0 && arg6P_2>-1 && 2+arg5P_2<=arg1 ], cost: 1
      2: f160_0_factorial_GT -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ arg2>0 && arg5<arg3 && arg1>=1+arg1P_3 && arg6>=arg1P_3 && arg1>0 && arg6>-1 && arg1P_3>-1 && 2+arg5<=arg1 && arg3==arg4 ], cost: 1
      3: f160_0_factorial_GT -> f160_0_factorial_GT : arg1'=arg1P_4, arg2'=arg2*arg3, arg3'=1+arg3, arg4'=1+arg3, arg6'=arg6P_4, [ arg5>=arg3 && arg3>0 && arg2>0 && arg1P_4<=arg1 && 1+arg6P_4<=arg1 && arg6P_4<=arg6 && arg1>0 && arg6>-1 && arg1P_4>0 && arg6P_4>-1 && 2+arg5<=arg1 && arg3==arg4 ], cost: 1
      4: __init -> f1_0_main_New : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [], cost: 1

### Simplification by acceleration and chaining ###

Accelerating simple loops of location 2.
   Accelerating the following rules:
      3: f160_0_factorial_GT -> f160_0_factorial_GT : arg1'=arg1P_4, arg2'=arg2*arg3, arg3'=1+arg3, arg4'=1+arg3, arg6'=arg6P_4, [ arg5>=arg3 && arg3>0 && arg2>0 && arg1P_4<=arg1 && 1+arg6P_4<=arg1 && arg6P_4<=arg6 && arg1>0 && arg6>-1 && arg1P_4>0 && arg6P_4>-1 && 2+arg5<=arg1 && arg3==arg4 ], cost: 1

   Found no closed form for 3.
[accelerate] Nesting with 0 inner and 1 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      0: f1_0_main_New -> f83_0_doSum_NONNULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, arg6'=arg6P_1, [ arg1P_1>3 ], cost: 1
      1: f83_0_doSum_NONNULL -> f160_0_factorial_GT : arg1'=arg1P_2, arg2'=1, arg3'=1, arg4'=1, arg5'=arg5P_2, arg6'=arg6P_2, [ arg1P_2<=arg1 && 1+arg6P_2<=arg1 && arg1>0 && arg1P_2>0 && arg6P_2>-1 && 2+arg5P_2<=arg1 ], cost: 1
      2: f160_0_factorial_GT -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ arg2>0 && arg5<arg3 && arg1>=1+arg1P_3 && arg6>=arg1P_3 && arg1>0 && arg6>-1 && arg1P_3>-1 && 2+arg5<=arg1 && arg3==arg4 ], cost: 1
      3: f160_0_factorial_GT -> f160_0_factorial_GT : arg1'=arg1P_4, arg2'=arg2*arg3, arg3'=1+arg3, arg4'=1+arg3, arg6'=arg6P_4, [ arg5>=arg3 && arg3>0 && arg2>0 && arg1P_4<=arg1 && 1+arg6P_4<=arg1 && arg6P_4<=arg6 && arg1>0 && arg6>-1 && arg1P_4>0 && arg6P_4>-1 && 2+arg5<=arg1 && arg3==arg4 ], cost: 1
      4: __init -> f1_0_main_New : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [], cost: 1

Chained accelerated rules (with incoming rules):
   Start location: __init
      0: f1_0_main_New -> f83_0_doSum_NONNULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, arg6'=arg6P_1, [ arg1P_1>3 ], cost: 1
      1: f83_0_doSum_NONNULL -> f160_0_factorial_GT : arg1'=arg1P_2, arg2'=1, arg3'=1, arg4'=1, arg5'=arg5P_2, arg6'=arg6P_2, [ arg1P_2<=arg1 && 1+arg6P_2<=arg1 && arg1>0 && arg1P_2>0 && arg6P_2>-1 && 2+arg5P_2<=arg1 ], cost: 1
      5: f83_0_doSum_NONNULL -> f160_0_factorial_GT : arg1'=arg1P_4, arg2'=1, arg3'=2, arg4'=2, arg5'=arg5P_2, arg6'=arg6P_4, [ arg1>0 && 2+arg5P_2<=arg1 && arg5P_2>=1 && arg1P_4>0 && arg6P_4>-1 && arg1P_4<=arg1 && 1+arg6P_4<=arg1 ], cost: 2
      2: f160_0_factorial_GT -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ arg2>0 && arg5<arg3 && arg1>=1+arg1P_3 && arg6>=arg1P_3 && arg1>0 && arg6>-1 && arg1P_3>-1 && 2+arg5<=arg1 && arg3==arg4 ], cost: 1
      4: __init -> f1_0_main_New : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, arg5'=arg5P_5, arg6'=arg6P_5, [], cost: 1

Eliminated locations (on linear paths):
   Start location: __init
      1: f83_0_doSum_NONNULL -> f160_0_factorial_GT : arg1'=arg1P_2, arg2'=1, arg3'=1, arg4'=1, arg5'=arg5P_2, arg6'=arg6P_2, [ arg1P_2<=arg1 && 1+arg6P_2<=arg1 && arg1>0 && arg1P_2>0 && arg6P_2>-1 && 2+arg5P_2<=arg1 ], cost: 1
      5: f83_0_doSum_NONNULL -> f160_0_factorial_GT : arg1'=arg1P_4, arg2'=1, arg3'=2, arg4'=2, arg5'=arg5P_2, arg6'=arg6P_4, [ arg1>0 && 2+arg5P_2<=arg1 && arg5P_2>=1 && arg1P_4>0 && arg6P_4>-1 && arg1P_4<=arg1 && 1+arg6P_4<=arg1 ], cost: 2
      2: f160_0_factorial_GT -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ arg2>0 && arg5<arg3 && arg1>=1+arg1P_3 && arg6>=arg1P_3 && arg1>0 && arg6>-1 && arg1P_3>-1 && 2+arg5<=arg1 && arg3==arg4 ], cost: 1
      6: __init -> f83_0_doSum_NONNULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, arg6'=arg6P_1, [ arg1P_1>3 ], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
      7: f83_0_doSum_NONNULL -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ arg1P_2<=arg1 && 1+arg6P_2<=arg1 && arg1>0 && arg1P_2>0 && arg6P_2>-1 && 2+arg5P_2<=arg1 && arg5P_2<1 && arg1P_2>=1+arg1P_3 && arg6P_2>=arg1P_3 && arg1P_3>-1 && 2+arg5P_2<=arg1P_2 ], cost: 2
      8: f83_0_doSum_NONNULL -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ arg1>0 && 2+arg5P_2<=arg1 && arg5P_2>=1 && arg1P_4>0 && arg6P_4>-1 && arg1P_4<=arg1 && 1+arg6P_4<=arg1 && arg5P_2<2 && arg1P_4>=1+arg1P_3 && arg6P_4>=arg1P_3 && arg1P_3>-1 && 2+arg5P_2<=arg1P_4 ], cost: 3
      6: __init -> f83_0_doSum_NONNULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, arg6'=arg6P_1, [ arg1P_1>3 ], cost: 2

Accelerating simple loops of location 1.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
      7: f83_0_doSum_NONNULL -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ arg1>0 && arg1P_3>-1 && 1+arg1P_3<=arg1 ], cost: 2
      8: f83_0_doSum_NONNULL -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ 3<=arg1 && arg1P_3>-1 && 1+arg1P_3<=arg1 ], cost: 3

   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: f83_0_doSum_NONNULL -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ arg1>0 && arg1P_3>-1 && 1+arg1P_3<=arg1 ], cost: 2
      8: f83_0_doSum_NONNULL -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ 3<=arg1 && arg1P_3>-1 && 1+arg1P_3<=arg1 ], cost: 3
      6: __init -> f83_0_doSum_NONNULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, arg6'=arg6P_1, [ arg1P_1>3 ], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: __init
      6: __init -> f83_0_doSum_NONNULL : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, arg5'=arg5P_1, arg6'=arg6P_1, [ arg1P_1>3 ], cost: 2
      9: __init -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ arg1P_3>-1 ], cost: 4
     10: __init -> f83_0_doSum_NONNULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, arg5'=arg5P_3, arg6'=arg6P_3, [ arg1P_3>-1 ], cost: 5

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),?)