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, [ 1==arg1P_1 && arg2==arg2P_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 && 0==arg2P_2 && arg3==arg3P_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 && arg4==arg4P_3 ], cost: 1
      3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
     11: f5 -> f6 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1<0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1
     12: f5 -> f6 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg1>0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 ], cost: 1
     14: f5 -> f13 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, arg4'=arg4P_15, [ arg1==0 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 && arg4==arg4P_15 ], cost: 1
      4: f7 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ 0==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1
      7: f10 -> f9 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      5: f6 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3>=arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1
      6: f6 -> f8 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg3<arg4 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      8: f8 -> 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
      9: f9 -> f11 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg3P_10==1+arg3 && arg1==arg1P_10 && arg2==arg2P_10 && arg4==arg4P_10 ], cost: 1
     10: f11 -> f12 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg2P_11==1+arg2 && arg1==arg1P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1
     13: f12 -> f5 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [], 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, [ 1==arg1P_1 && arg2==arg2P_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 && 0==arg2P_2 && arg3==arg3P_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 && arg4==arg4P_3 ], cost: 1
      3: f4 -> f5 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, arg4'=arg4P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
     11: f5 -> f6 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [ arg1<0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 && arg4==arg4P_12 ], cost: 1
     12: f5 -> f6 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, arg4'=arg4P_13, [ arg1>0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 && arg4==arg4P_13 ], cost: 1
      4: f7 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ 0==arg1P_5 && arg2==arg2P_5 && arg3==arg3P_5 && arg4==arg4P_5 ], cost: 1
      7: f10 -> f9 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      5: f6 -> f7 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, arg4'=arg4P_6, [ arg3>=arg4 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 && arg4==arg4P_6 ], cost: 1
      6: f6 -> f8 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg3<arg4 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      8: f8 -> 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
      9: f9 -> f11 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg3P_10==1+arg3 && arg1==arg1P_10 && arg2==arg2P_10 && arg4==arg4P_10 ], cost: 1
     10: f11 -> f12 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg2P_11==1+arg2 && arg1==arg1P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1
     13: f12 -> f5 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, arg4'=arg4P_14, [ arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 && arg4==arg4P_14 ], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=1, [], cost: 1
      1: f2 -> f3 : arg2'=0, [], cost: 1
      2: f3 -> f4 : arg3'=arg3P_3, [], cost: 1
      3: f4 -> f5 : arg4'=arg4P_4, [], cost: 1
     11: f5 -> f6 : [ arg1<0 ], cost: 1
     12: f5 -> f6 : [ arg1>0 ], cost: 1
      4: f7 -> f10 : arg1'=0, [], cost: 1
      7: f10 -> f9 : [], cost: 1
      5: f6 -> f7 : [ arg3>=arg4 ], cost: 1
      6: f6 -> f8 : [ arg3<arg4 ], cost: 1
      8: f8 -> f9 : [], cost: 1
      9: f9 -> f11 : arg3'=1+arg3, [], cost: 1
     10: f11 -> f12 : arg2'=1+arg2, [], cost: 1
     13: f12 -> f5 : [], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, arg4'=arg4P_16, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     11: f5 -> f6 : [ arg1<0 ], cost: 1
     12: f5 -> f6 : [ arg1>0 ], cost: 1
     21: f6 -> f9 : [ arg3<arg4 ], cost: 2
     22: f6 -> f9 : arg1'=0, [ arg3>=arg4 ], cost: 3
     24: f9 -> f5 : arg2'=1+arg2, arg3'=1+arg3, [], cost: 3
     19: __init -> f5 : arg1'=1, arg2'=0, arg3'=arg3P_3, arg4'=arg4P_4, [], cost: 5

Eliminated locations (on tree-shaped paths):
   Start location: __init
     25: f5 -> f9 : [ arg1<0 && arg3<arg4 ], cost: 3
     26: f5 -> f9 : arg1'=0, [ arg1<0 && arg3>=arg4 ], cost: 4
     27: f5 -> f9 : [ arg1>0 && arg3<arg4 ], cost: 3
     28: f5 -> f9 : arg1'=0, [ arg1>0 && arg3>=arg4 ], cost: 4
     24: f9 -> f5 : arg2'=1+arg2, arg3'=1+arg3, [], cost: 3
     19: __init -> f5 : arg1'=1, arg2'=0, arg3'=arg3P_3, arg4'=arg4P_4, [], cost: 5

Eliminated locations (on tree-shaped paths):
   Start location: __init
     29: f5 -> f5 : arg2'=1+arg2, arg3'=1+arg3, [ arg1<0 && arg3<arg4 ], cost: 6
     30: f5 -> f5 : arg1'=0, arg2'=1+arg2, arg3'=1+arg3, [ arg1<0 && arg3>=arg4 ], cost: 7
     31: f5 -> f5 : arg2'=1+arg2, arg3'=1+arg3, [ arg1>0 && arg3<arg4 ], cost: 6
     32: f5 -> f5 : arg1'=0, arg2'=1+arg2, arg3'=1+arg3, [ arg1>0 && arg3>=arg4 ], cost: 7
     19: __init -> f5 : arg1'=1, arg2'=0, arg3'=arg3P_3, arg4'=arg4P_4, [], cost: 5

Accelerating simple loops of location 4.
   Accelerating the following rules:
     29: f5 -> f5 : arg2'=1+arg2, arg3'=1+arg3, [ arg1<0 && arg3<arg4 ], cost: 6
     30: f5 -> f5 : arg1'=0, arg2'=1+arg2, arg3'=1+arg3, [ arg1<0 && arg3>=arg4 ], cost: 7
     31: f5 -> f5 : arg2'=1+arg2, arg3'=1+arg3, [ arg1>0 && arg3<arg4 ], cost: 6
     32: f5 -> f5 : arg1'=0, arg2'=1+arg2, arg3'=1+arg3, [ arg1>0 && arg3>=arg4 ], cost: 7

   Accelerated rule 29 with backward acceleration, yielding the new rule 33.
   Failed to prove monotonicity of the guard of rule 30.
   Accelerated rule 31 with backward acceleration, yielding the new rule 34.
   Failed to prove monotonicity of the guard of rule 32.
[accelerate] Nesting with 4 inner and 4 outer candidates
   Removing the simple loops: 29 31.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     30: f5 -> f5 : arg1'=0, arg2'=1+arg2, arg3'=1+arg3, [ arg1<0 && arg3>=arg4 ], cost: 7
     32: f5 -> f5 : arg1'=0, arg2'=1+arg2, arg3'=1+arg3, [ arg1>0 && arg3>=arg4 ], cost: 7
     33: f5 -> f5 : arg2'=arg2-arg3+arg4, arg3'=arg4, [ arg1<0 && -arg3+arg4>=0 ], cost: -6*arg3+6*arg4
     34: f5 -> f5 : arg2'=arg2-arg3+arg4, arg3'=arg4, [ arg1>0 && -arg3+arg4>=0 ], cost: -6*arg3+6*arg4
     19: __init -> f5 : arg1'=1, arg2'=0, arg3'=arg3P_3, arg4'=arg4P_4, [], cost: 5

Chained accelerated rules (with incoming rules):
   Start location: __init
     19: __init -> f5 : arg1'=1, arg2'=0, arg3'=arg3P_3, arg4'=arg4P_4, [], cost: 5
     35: __init -> f5 : arg1'=0, arg2'=1, arg3'=1+arg3P_3, arg4'=arg4P_4, [ arg3P_3>=arg4P_4 ], cost: 12
     36: __init -> f5 : arg1'=1, arg2'=arg4P_4-arg3P_3, arg3'=arg4P_4, arg4'=arg4P_4, [ arg4P_4-arg3P_3>=0 ], cost: 5+6*arg4P_4-6*arg3P_3

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     36: __init -> f5 : arg1'=1, arg2'=arg4P_4-arg3P_3, arg3'=arg4P_4, arg4'=arg4P_4, [ arg4P_4-arg3P_3>=0 ], cost: 5+6*arg4P_4-6*arg3P_3

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     36: __init -> f5 : arg1'=1, arg2'=arg4P_4-arg3P_3, arg3'=arg4P_4, arg4'=arg4P_4, [ arg4P_4-arg3P_3>=0 ], cost: 5+6*arg4P_4-6*arg3P_3

Computing asymptotic complexity for rule 36
   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),?)