WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1_0_main_Load -> f248_0_mod_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2P_1>-1 && arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f248_0_mod_LT -> f319_0_minus_EQ : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg2<=arg1 && arg2>0 && arg2==arg1P_2 && arg1==arg2P_2 && arg2==arg3P_2 && arg2==arg4P_2 ], cost: 1
      2: f319_0_minus_EQ -> f248_0_mod_LT : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ 0==arg3 && 0==arg4 && arg2==arg1P_3 && arg1==arg2P_3 ], cost: 1
      3: f319_0_minus_EQ -> f319_0_minus_EQ : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg3<0 && arg3<1 && arg3==arg4 && arg1==arg1P_4 && 1+arg2==arg2P_4 && 1+arg3==arg3P_4 && 1+arg3==arg4P_4 ], cost: 1
      4: f319_0_minus_EQ -> f319_0_minus_EQ : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg3>0 && arg3<1 && arg3==arg4 && arg1==arg1P_5 && 1+arg2==arg2P_5 && 1+arg3==arg3P_5 && 1+arg3==arg4P_5 ], cost: 1
      5: f319_0_minus_EQ -> f319_0_minus_EQ : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3>0 && arg3==arg4 && arg1==arg1P_6 && -1+arg2==arg2P_6 && -1+arg3==arg3P_6 && -1+arg3==arg4P_6 ], cost: 1
      6: __init -> f1_0_main_Load : 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_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [], cost: 1

Removed rules with unsatisfiable guard:
   Start location: __init
      0: f1_0_main_Load -> f248_0_mod_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2P_1>-1 && arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f248_0_mod_LT -> f319_0_minus_EQ : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg2<=arg1 && arg2>0 && arg2==arg1P_2 && arg1==arg2P_2 && arg2==arg3P_2 && arg2==arg4P_2 ], cost: 1
      2: f319_0_minus_EQ -> f248_0_mod_LT : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ 0==arg3 && 0==arg4 && arg2==arg1P_3 && arg1==arg2P_3 ], cost: 1
      3: f319_0_minus_EQ -> f319_0_minus_EQ : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg3<0 && arg3<1 && arg3==arg4 && arg1==arg1P_4 && 1+arg2==arg2P_4 && 1+arg3==arg3P_4 && 1+arg3==arg4P_4 ], cost: 1
      5: f319_0_minus_EQ -> f319_0_minus_EQ : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3>0 && arg3==arg4 && arg1==arg1P_6 && -1+arg2==arg2P_6 && -1+arg3==arg3P_6 && -1+arg3==arg4P_6 ], cost: 1
      6: __init -> f1_0_main_Load : 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_Load -> f248_0_mod_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2P_1>-1 && arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f248_0_mod_LT -> f319_0_minus_EQ : arg1'=arg2, arg2'=arg1, arg3'=arg2, arg4'=arg2, [ arg2<=arg1 && arg2>0 ], cost: 1
      2: f319_0_minus_EQ -> f248_0_mod_LT : arg1'=arg2, arg2'=arg1, arg3'=arg3P_3, arg4'=arg4P_3, [ 0==arg3 && 0==arg4 ], cost: 1
      3: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=1+arg2, arg3'=1+arg3, arg4'=1+arg3, [ arg3<0 && arg3==arg4 ], cost: 1
      5: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=-1+arg2, arg3'=-1+arg3, arg4'=-1+arg3, [ arg3>0 && arg3==arg4 ], cost: 1
      6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [], cost: 1

### Simplification by acceleration and chaining ###

Accelerating simple loops of location 2.
   Accelerating the following rules:
      3: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=1+arg2, arg3'=1+arg3, arg4'=1+arg3, [ arg3<0 && arg3==arg4 ], cost: 1
      5: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=-1+arg2, arg3'=-1+arg3, arg4'=-1+arg3, [ arg3>0 && arg3==arg4 ], cost: 1

   Accelerated rule 3 with backward acceleration, yielding the new rule 7.
   Accelerated rule 5 with backward acceleration, yielding the new rule 8.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 3 5.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
      0: f1_0_main_Load -> f248_0_mod_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2P_1>-1 && arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f248_0_mod_LT -> f319_0_minus_EQ : arg1'=arg2, arg2'=arg1, arg3'=arg2, arg4'=arg2, [ arg2<=arg1 && arg2>0 ], cost: 1
      2: f319_0_minus_EQ -> f248_0_mod_LT : arg1'=arg2, arg2'=arg1, arg3'=arg3P_3, arg4'=arg4P_3, [ 0==arg3 && 0==arg4 ], cost: 1
      7: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-arg3, arg3'=0, arg4'=0, [ arg3==arg4 && -arg3>=1 ], cost: -arg3
      8: f319_0_minus_EQ -> f319_0_minus_EQ : arg2'=arg2-arg3, arg3'=0, arg4'=0, [ arg3==arg4 && arg3>=1 ], cost: arg3
      6: __init -> f1_0_main_Load : 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_Load -> f248_0_mod_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2P_1>-1 && arg2>1 && arg1P_1>-1 && arg1>0 ], cost: 1
      1: f248_0_mod_LT -> f319_0_minus_EQ : arg1'=arg2, arg2'=arg1, arg3'=arg2, arg4'=arg2, [ arg2<=arg1 && arg2>0 ], cost: 1
      9: f248_0_mod_LT -> f319_0_minus_EQ : arg1'=arg2, arg2'=-arg2+arg1, arg3'=0, arg4'=0, [ arg2<=arg1 && arg2>0 ], cost: 1+arg2
      2: f319_0_minus_EQ -> f248_0_mod_LT : arg1'=arg2, arg2'=arg1, arg3'=arg3P_3, arg4'=arg4P_3, [ 0==arg3 && 0==arg4 ], cost: 1
      6: __init -> f1_0_main_Load : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [], cost: 1

Eliminated locations (on linear paths):
   Start location: __init
      1: f248_0_mod_LT -> f319_0_minus_EQ : arg1'=arg2, arg2'=arg1, arg3'=arg2, arg4'=arg2, [ arg2<=arg1 && arg2>0 ], cost: 1
      9: f248_0_mod_LT -> f319_0_minus_EQ : arg1'=arg2, arg2'=-arg2+arg1, arg3'=0, arg4'=0, [ arg2<=arg1 && arg2>0 ], cost: 1+arg2
      2: f319_0_minus_EQ -> f248_0_mod_LT : arg1'=arg2, arg2'=arg1, arg3'=arg3P_3, arg4'=arg4P_3, [ 0==arg3 && 0==arg4 ], cost: 1
     10: __init -> f248_0_mod_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2P_1>-1 && arg2P_7>1 && arg1P_1>-1 && arg1P_7>0 ], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
     11: f248_0_mod_LT -> f248_0_mod_LT : arg1'=-arg2+arg1, arg2'=arg2, arg3'=arg3P_3, arg4'=arg4P_3, [ arg2<=arg1 && arg2>0 ], cost: 2+arg2
     10: __init -> f248_0_mod_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2P_1>-1 && arg2P_7>1 && arg1P_1>-1 && arg1P_7>0 ], cost: 2

Accelerating simple loops of location 1.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     11: f248_0_mod_LT -> f248_0_mod_LT : arg1'=-arg2+arg1, arg3'=arg3P_3, arg4'=arg4P_3, [ arg2<=arg1 && arg2>0 ], cost: 2+arg2

   Accelerated rule 11 with backward acceleration, yielding the new rule 12.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 11.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     12: f248_0_mod_LT -> f248_0_mod_LT : arg1'=-k_2*arg2+arg1, arg3'=arg3P_3, arg4'=arg4P_3, [ arg2>0 && k_2>=1 && arg2<=-arg2*(-1+k_2)+arg1 ], cost: 2*k_2+k_2*arg2
     10: __init -> f248_0_mod_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2P_1>-1 && arg2P_7>1 && arg1P_1>-1 && arg1P_7>0 ], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: __init
     10: __init -> f248_0_mod_LT : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg2P_1>-1 && arg2P_7>1 && arg1P_1>-1 && arg1P_7>0 ], cost: 2
     13: __init -> f248_0_mod_LT : arg1'=-k_2*arg2P_1+arg1P_1, arg2'=arg2P_1, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1P_1>-1 && arg2P_1>0 && k_2>=1 && arg2P_1<=-(-1+k_2)*arg2P_1+arg1P_1 ], cost: 2+2*k_2+k_2*arg2P_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     13: __init -> f248_0_mod_LT : arg1'=-k_2*arg2P_1+arg1P_1, arg2'=arg2P_1, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1P_1>-1 && arg2P_1>0 && k_2>=1 && arg2P_1<=-(-1+k_2)*arg2P_1+arg1P_1 ], cost: 2+2*k_2+k_2*arg2P_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     13: __init -> f248_0_mod_LT : arg1'=-k_2*arg2P_1+arg1P_1, arg2'=arg2P_1, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1P_1>-1 && arg2P_1>0 && k_2>=1 && arg2P_1<=-(-1+k_2)*arg2P_1+arg1P_1 ], cost: 2+2*k_2+k_2*arg2P_1

Computing asymptotic complexity for rule 13
   Simplified the guard:
     13: __init -> f248_0_mod_LT : arg1'=-k_2*arg2P_1+arg1P_1, arg2'=arg2P_1, arg3'=arg3P_3, arg4'=arg4P_3, [ arg2P_1>0 && k_2>=1 && arg2P_1<=-(-1+k_2)*arg2P_1+arg1P_1 ], cost: 2+2*k_2+k_2*arg2P_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),?)