WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg1==arg1P_1 && arg3==arg3P_1 && arg4==arg4P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1==arg1P_2 && arg2==arg2P_2 && arg4==arg4P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
      3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ 0==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && arg4==arg4P_4 ], cost: 1
     11: f5 -> f6 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2<arg3 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1
     13: f5 -> f13 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg2>=arg3 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1
      4: f7 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg2P_5==1+arg2 && arg1==arg1P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1
      8: f10 -> f9 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1
      5: f8 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg4P_6==1+arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      9: f11 -> f9 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1
      6: f6 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg2<arg4 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      7: f6 -> f8 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg2>=arg4 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
     10: f9 -> f12 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg1P_11==1+arg1 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1
     12: f12 -> f5 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 ], cost: 1
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, arg4'=arg4P_1, [ arg1==arg1P_1 && arg3==arg3P_1 && arg4==arg4P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, arg4'=arg4P_2, [ arg1==arg1P_2 && arg2==arg2P_2 && arg4==arg4P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, arg4'=arg4P_3, [ arg1==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
      3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ 0==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 && arg4==arg4P_4 ], cost: 1
     11: f5 -> f6 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg2<arg3 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1
      4: f7 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg2P_5==1+arg2 && arg1==arg1P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1
      8: f10 -> f9 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, arg4'=arg4P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 && arg4==arg4P_9 ], cost: 1
      5: f8 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg4P_6==1+arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      9: f11 -> f9 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1
      6: f6 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg2<arg4 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      7: f6 -> f8 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg2>=arg4 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
     10: f9 -> f12 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg1P_11==1+arg1 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1
     12: f12 -> f5 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 ], cost: 1
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg2'=arg2P_1, [], cost: 1
      1: f2 -> f3 : arg3'=arg3P_2, [], cost: 1
      2: f3 -> f4 : arg4'=arg4P_3, [], cost: 1
      3: f4 -> f5 : arg1'=0, [], cost: 1
     11: f5 -> f6 : [ arg2<arg3 ], cost: 1
      4: f7 -> f10 : arg2'=1+arg2, [], cost: 1
      8: f10 -> f9 : [], cost: 1
      5: f8 -> f11 : arg4'=1+arg4, [], cost: 1
      9: f11 -> f9 : [], cost: 1
      6: f6 -> f7 : [ arg2<arg4 ], cost: 1
      7: f6 -> f8 : [ arg2>=arg4 ], cost: 1
     10: f9 -> f12 : arg1'=1+arg1, [], cost: 1
     12: f12 -> f5 : [], cost: 1
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     11: f5 -> f6 : [ arg2<arg3 ], cost: 1
     21: f6 -> f9 : arg2'=1+arg2, [ arg2<arg4 ], cost: 3
     22: f6 -> f9 : arg4'=1+arg4, [ arg2>=arg4 ], cost: 3
     23: f9 -> f5 : arg1'=1+arg1, [], cost: 2
     18: __init -> f5 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, arg4'=arg4P_3, [], cost: 5

Eliminated locations (on tree-shaped paths):
   Start location: __init
     24: f5 -> f9 : arg2'=1+arg2, [ arg2<arg3 && arg2<arg4 ], cost: 4
     25: f5 -> f9 : arg4'=1+arg4, [ arg2<arg3 && arg2>=arg4 ], cost: 4
     23: f9 -> f5 : arg1'=1+arg1, [], cost: 2
     18: __init -> f5 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, arg4'=arg4P_3, [], cost: 5

Eliminated locations (on tree-shaped paths):
   Start location: __init
     26: f5 -> f5 : arg1'=1+arg1, arg2'=1+arg2, [ arg2<arg3 && arg2<arg4 ], cost: 6
     27: f5 -> f5 : arg1'=1+arg1, arg4'=1+arg4, [ arg2<arg3 && arg2>=arg4 ], cost: 6
     18: __init -> f5 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, arg4'=arg4P_3, [], cost: 5

Accelerating simple loops of location 4.
   Accelerating the following rules:
     26: f5 -> f5 : arg1'=1+arg1, arg2'=1+arg2, [ arg2<arg3 && arg2<arg4 ], cost: 6
     27: f5 -> f5 : arg1'=1+arg1, arg4'=1+arg4, [ arg2<arg3 && arg2>=arg4 ], cost: 6

   Accelerated rule 26 with backward acceleration, yielding the new rule 28.
   Accelerated rule 26 with backward acceleration, yielding the new rule 29.
   Accelerated rule 27 with backward acceleration, yielding the new rule 30.
[accelerate] Nesting with 3 inner and 2 outer candidates
   Removing the simple loops: 26 27.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     28: f5 -> f5 : arg1'=-arg2+arg3+arg1, arg2'=arg3, [ -arg2+arg3>=0 && -1+arg3<arg4 ], cost: -6*arg2+6*arg3
     29: f5 -> f5 : arg1'=-arg2+arg4+arg1, arg2'=arg4, [ -arg2+arg4>=0 && -1+arg4<arg3 ], cost: -6*arg2+6*arg4
     30: f5 -> f5 : arg1'=1+arg2-arg4+arg1, arg4'=1+arg2, [ arg2<arg3 && 1+arg2-arg4>=0 ], cost: 6+6*arg2-6*arg4
     18: __init -> f5 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, arg4'=arg4P_3, [], cost: 5

Chained accelerated rules (with incoming rules):
   Start location: __init
     18: __init -> f5 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, arg4'=arg4P_3, [], cost: 5
     31: __init -> f5 : arg1'=arg3P_2-arg2P_1, arg2'=arg3P_2, arg3'=arg3P_2, arg4'=arg4P_3, [ arg3P_2-arg2P_1>=0 && -1+arg3P_2<arg4P_3 ], cost: 5+6*arg3P_2-6*arg2P_1
     32: __init -> f5 : arg1'=arg4P_3-arg2P_1, arg2'=arg4P_3, arg3'=arg3P_2, arg4'=arg4P_3, [ arg4P_3-arg2P_1>=0 && -1+arg4P_3<arg3P_2 ], cost: 5+6*arg4P_3-6*arg2P_1
     33: __init -> f5 : arg1'=1-arg4P_3+arg2P_1, arg2'=arg2P_1, arg3'=arg3P_2, arg4'=1+arg2P_1, [ arg2P_1<arg3P_2 && 1-arg4P_3+arg2P_1>=0 ], cost: 11-6*arg4P_3+6*arg2P_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     31: __init -> f5 : arg1'=arg3P_2-arg2P_1, arg2'=arg3P_2, arg3'=arg3P_2, arg4'=arg4P_3, [ arg3P_2-arg2P_1>=0 && -1+arg3P_2<arg4P_3 ], cost: 5+6*arg3P_2-6*arg2P_1
     32: __init -> f5 : arg1'=arg4P_3-arg2P_1, arg2'=arg4P_3, arg3'=arg3P_2, arg4'=arg4P_3, [ arg4P_3-arg2P_1>=0 && -1+arg4P_3<arg3P_2 ], cost: 5+6*arg4P_3-6*arg2P_1
     33: __init -> f5 : arg1'=1-arg4P_3+arg2P_1, arg2'=arg2P_1, arg3'=arg3P_2, arg4'=1+arg2P_1, [ arg2P_1<arg3P_2 && 1-arg4P_3+arg2P_1>=0 ], cost: 11-6*arg4P_3+6*arg2P_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     31: __init -> f5 : arg1'=arg3P_2-arg2P_1, arg2'=arg3P_2, arg3'=arg3P_2, arg4'=arg4P_3, [ arg3P_2-arg2P_1>=0 && -1+arg3P_2<arg4P_3 ], cost: 5+6*arg3P_2-6*arg2P_1
     32: __init -> f5 : arg1'=arg4P_3-arg2P_1, arg2'=arg4P_3, arg3'=arg3P_2, arg4'=arg4P_3, [ arg4P_3-arg2P_1>=0 && -1+arg4P_3<arg3P_2 ], cost: 5+6*arg4P_3-6*arg2P_1
     33: __init -> f5 : arg1'=1-arg4P_3+arg2P_1, arg2'=arg2P_1, arg3'=arg3P_2, arg4'=1+arg2P_1, [ arg2P_1<arg3P_2 && 1-arg4P_3+arg2P_1>=0 ], cost: 11-6*arg4P_3+6*arg2P_1

Computing asymptotic complexity for rule 31
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 32
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 33
   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),?)