NO

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

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_New -> f909_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg1P_1<=arg1 && arg2>-1 && -1+arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>1 && 1==arg3P_1 && arg2==arg4P_1 ], cost: 1
      1: f909_0_main_GE -> f1058_0_size_NULL : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg4<=arg3 && arg2>0 && arg1P_2>-1 ], cost: 1
      5: f909_0_main_GE -> f909_0_main_GE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg4>2+arg3 && arg4>1+arg3 && arg4>-1 && arg1P_6<=arg1 && arg1P_6<=arg2 && arg1>0 && arg2>0 && arg1P_6>0 && arg2P_6>6 && 4+arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1
      2: f1058_0_size_NULL -> f1097_0_outputList_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1>-1 && arg1P_3>-1 ], cost: 1
      3: f1058_0_size_NULL -> f1058_0_size_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1>0 && arg1P_4>-1 ], cost: 1
      4: f1097_0_outputList_NULL -> f1097_0_outputList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1>0 && arg1P_5>-1 ], cost: 1
      6: __init -> f1_0_main_New : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      6: __init -> f1_0_main_New : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1_0_main_New -> f909_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=1, arg4'=arg2, [ arg1P_1<=arg1 && arg2>-1 && -1+arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>1 ], cost: 1
      1: f909_0_main_GE -> f1058_0_size_NULL : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg4<=arg3 && arg2>0 && arg1P_2>-1 ], cost: 1
      5: f909_0_main_GE -> f909_0_main_GE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=4+arg3, [ arg4>2+arg3 && arg4>-1 && arg1P_6<=arg1 && arg1P_6<=arg2 && arg1>0 && arg2>0 && arg1P_6>0 && arg2P_6>6 ], cost: 1
      2: f1058_0_size_NULL -> f1097_0_outputList_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1>-1 && arg1P_3>-1 ], cost: 1
      3: f1058_0_size_NULL -> f1058_0_size_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1>0 && arg1P_4>-1 ], cost: 1
      4: f1097_0_outputList_NULL -> f1097_0_outputList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1>0 && arg1P_5>-1 ], cost: 1
      6: __init -> f1_0_main_New : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [], cost: 1

### Simplification by acceleration and chaining ###

Accelerating simple loops of location 1.
   Accelerating the following rules:
      5: f909_0_main_GE -> f909_0_main_GE : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=4+arg3, [ arg4>2+arg3 && arg4>-1 && arg1P_6<=arg1 && arg1P_6<=arg2 && arg1>0 && arg2>0 && arg1P_6>0 && arg2P_6>6 ], cost: 1

      During metering: Instantiating temporary variables by {arg1P_6==1,arg2P_6==7}
   Accelerated rule 5 with metering function meter (where 4*meter==-2-arg3+arg4), yielding the new rule 7.
   Removing the simple loops: 5.

Accelerating simple loops of location 2.
   Accelerating the following rules:
      3: f1058_0_size_NULL -> f1058_0_size_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1>0 && arg1P_4>-1 ], cost: 1

   Accelerated rule 3 with NONTERM (after strengthening guard), yielding the new rule 8.
   Removing the simple loops:.

Accelerating simple loops of location 3.
   Accelerating the following rules:
      4: f1097_0_outputList_NULL -> f1097_0_outputList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1>0 && arg1P_5>-1 ], cost: 1

   Accelerated rule 4 with NONTERM (after strengthening guard), yielding the new rule 9.
   Removing the simple loops:.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      0: f1_0_main_New -> f909_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=1, arg4'=arg2, [ arg1P_1<=arg1 && arg2>-1 && -1+arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>1 ], cost: 1
      1: f909_0_main_GE -> f1058_0_size_NULL : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg4<=arg3 && arg2>0 && arg1P_2>-1 ], cost: 1
      7: f909_0_main_GE -> f909_0_main_GE : arg1'=1, arg2'=7, arg3'=4*meter+arg3, [ arg4>2+arg3 && arg4>-1 && 1<=arg1 && 1<=arg2 && 4*meter==-2-arg3+arg4 && meter>=1 ], cost: meter
      2: f1058_0_size_NULL -> f1097_0_outputList_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1>-1 && arg1P_3>-1 ], cost: 1
      3: f1058_0_size_NULL -> f1058_0_size_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1>0 && arg1P_4>-1 ], cost: 1
      8: f1058_0_size_NULL -> [6] : [ arg1>0 && arg1P_4>0 ], cost: NONTERM
      4: f1097_0_outputList_NULL -> f1097_0_outputList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1>0 && arg1P_5>-1 ], cost: 1
      9: f1097_0_outputList_NULL -> [7] : [ arg1>0 && arg1P_5>0 ], cost: NONTERM
      6: __init -> f1_0_main_New : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [], cost: 1

Chained accelerated rules (with incoming rules):
   Start location: __init
      0: f1_0_main_New -> f909_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=1, arg4'=arg2, [ arg1P_1<=arg1 && arg2>-1 && -1+arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>1 ], cost: 1
     10: f1_0_main_New -> f909_0_main_GE : arg1'=1, arg2'=7, arg3'=1+4*meter, arg4'=arg2, [ arg1>0 && arg2>3 && 4*meter==-3+arg2 && meter>=1 ], cost: 1+meter
      1: f909_0_main_GE -> f1058_0_size_NULL : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg4<=arg3 && arg2>0 && arg1P_2>-1 ], cost: 1
     11: f909_0_main_GE -> f1058_0_size_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1>0 && arg4<=arg3 && arg2>0 && arg1P_4>-1 ], cost: 2
     12: f909_0_main_GE -> [6] : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg4<=arg3 && arg2>0 && arg1P_2>0 ], cost: NONTERM
      2: f1058_0_size_NULL -> f1097_0_outputList_NULL : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1>-1 && arg1P_3>-1 ], cost: 1
     13: f1058_0_size_NULL -> f1097_0_outputList_NULL : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg1>-1 && arg1P_5>-1 ], cost: 2
     14: f1058_0_size_NULL -> [7] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1>-1 && arg1P_3>0 ], cost: NONTERM
      6: __init -> f1_0_main_New : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [], cost: 1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
      0: f1_0_main_New -> f909_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=1, arg4'=arg2, [ arg1P_1<=arg1 && arg2>-1 && -1+arg2P_1<=arg1 && arg1>0 && arg1P_1>0 && arg2P_1>1 ], cost: 1
     10: f1_0_main_New -> f909_0_main_GE : arg1'=1, arg2'=7, arg3'=1+4*meter, arg4'=arg2, [ arg1>0 && arg2>3 && 4*meter==-3+arg2 && meter>=1 ], cost: 1+meter
      1: f909_0_main_GE -> f1058_0_size_NULL : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg4<=arg3 && arg2>0 && arg1P_2>-1 ], cost: 1
     11: f909_0_main_GE -> f1058_0_size_NULL : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1>0 && arg4<=arg3 && arg2>0 && arg1P_4>-1 ], cost: 2
     12: f909_0_main_GE -> [6] : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg4<=arg3 && arg2>0 && arg1P_2>0 ], cost: NONTERM
     14: f1058_0_size_NULL -> [7] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1>-1 && arg1P_3>0 ], cost: NONTERM
      6: __init -> f1_0_main_New : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [], cost: 1

Eliminated locations (on tree-shaped paths):
   Start location: __init
     12: f909_0_main_GE -> [6] : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1>0 && arg4<=arg3 && arg2>0 && arg1P_2>0 ], cost: NONTERM
     17: f909_0_main_GE -> [7] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1>0 && arg4<=arg3 && arg2>0 && arg1P_2>-1 && arg1P_3>0 ], cost: NONTERM
     18: f909_0_main_GE -> [7] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1>0 && arg4<=arg3 && arg2>0 && arg1P_4>-1 && arg1P_3>0 ], cost: NONTERM
     15: __init -> f909_0_main_GE : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=1, arg4'=arg2P_7, [ arg1P_1<=arg1P_7 && arg2P_7>-1 && -1+arg2P_1<=arg1P_7 && arg1P_7>0 && arg1P_1>0 && arg2P_1>1 ], cost: 2
     16: __init -> f909_0_main_GE : arg1'=1, arg2'=7, arg3'=1+4*meter, arg4'=arg2P_7, [ arg1P_7>0 && arg2P_7>3 && 4*meter==-3+arg2P_7 && meter>=1 ], cost: 2+meter

Eliminated locations (on tree-shaped paths):
   Start location: __init
     19: __init -> [6] : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_1<=arg1P_7 && arg2P_7>-1 && -1+arg2P_1<=arg1P_7 && arg1P_7>0 && arg1P_1>0 && arg2P_1>1 && arg2P_7<=1 && arg1P_2>0 ], cost: NONTERM
     20: __init -> [7] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1P_1<=arg1P_7 && arg2P_7>-1 && -1+arg2P_1<=arg1P_7 && arg1P_7>0 && arg1P_1>0 && arg2P_1>1 && arg2P_7<=1 && arg1P_2>-1 && arg1P_3>0 ], cost: NONTERM
     21: __init -> [7] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1P_1<=arg1P_7 && arg2P_7>-1 && -1+arg2P_1<=arg1P_7 && arg1P_7>0 && arg1P_1>0 && arg2P_1>1 && arg2P_7<=1 && arg1P_4>-1 && arg1P_3>0 ], cost: NONTERM
     22: __init -> [8] : [ arg1P_7>0 && arg2P_7>3 && 4*meter==-3+arg2P_7 && meter>=1 ], cost: 2+meter

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     19: __init -> [6] : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1P_1<=arg1P_7 && arg2P_7>-1 && -1+arg2P_1<=arg1P_7 && arg1P_7>0 && arg1P_1>0 && arg2P_1>1 && arg2P_7<=1 && arg1P_2>0 ], cost: NONTERM
     20: __init -> [7] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1P_1<=arg1P_7 && arg2P_7>-1 && -1+arg2P_1<=arg1P_7 && arg1P_7>0 && arg1P_1>0 && arg2P_1>1 && arg2P_7<=1 && arg1P_2>-1 && arg1P_3>0 ], cost: NONTERM
     21: __init -> [7] : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1P_1<=arg1P_7 && arg2P_7>-1 && -1+arg2P_1<=arg1P_7 && arg1P_7>0 && arg1P_1>0 && arg2P_1>1 && arg2P_7<=1 && arg1P_4>-1 && arg1P_3>0 ], cost: NONTERM
     22: __init -> [8] : [ arg1P_7>0 && arg2P_7>3 && 4*meter==-3+arg2P_7 && meter>=1 ], cost: 2+meter

Computing asymptotic complexity for rule 19
   Guard is satisfiable, yielding nontermination
   Resulting cost NONTERM has complexity: Nonterm

Found new complexity Nonterm.

Obtained the following overall complexity (w.r.t. the length of the input n):
   Complexity:  Nonterm
   Cpx degree:  Nonterm
   Solved cost: NONTERM
   Rule cost:   NONTERM
   Rule guard:  [ arg1P_1<=arg1P_7 && arg2P_7>-1 && -1+arg2P_1<=arg1P_7 && arg1P_7>0 && arg1P_1>0 && arg2P_1>1 && arg2P_7<=1 && arg1P_2>0 ]

NO