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
      7: f5 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg2>arg3 && arg2>arg4 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      9: f5 -> f10 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, arg4'=arg4P_10, [ arg2<=arg3 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 && arg4==arg4P_10 ], cost: 1
     10: f5 -> f10 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, arg4'=arg4P_11, [ arg2<=arg4 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 && arg4==arg4P_11 ], cost: 1
      4: f6 -> f7 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg3P_5==1+arg3 && arg1==arg1P_5 && arg2==arg2P_5 && arg4==arg4P_5 ], cost: 1
      5: f7 -> f8 : 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
      6: f8 -> f9 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg1P_7==1+arg1 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      8: f9 -> f5 : 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
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [], 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
      7: f5 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, arg4'=arg4P_8, [ arg2>arg3 && arg2>arg4 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 && arg4==arg4P_8 ], cost: 1
      4: f6 -> f7 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, arg4'=arg4P_5, [ arg3P_5==1+arg3 && arg1==arg1P_5 && arg2==arg2P_5 && arg4==arg4P_5 ], cost: 1
      5: f7 -> f8 : 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
      6: f8 -> f9 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, arg4'=arg4P_7, [ arg1P_7==1+arg1 && arg2==arg2P_7 && arg3==arg3P_7 && arg4==arg4P_7 ], cost: 1
      8: f9 -> f5 : 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
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [], 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
      7: f5 -> f6 : [ arg2>arg3 && arg2>arg4 ], cost: 1
      4: f6 -> f7 : arg3'=1+arg3, [], cost: 1
      5: f7 -> f8 : arg4'=1+arg4, [], cost: 1
      6: f8 -> f9 : arg1'=1+arg1, [], cost: 1
      8: f9 -> f5 : [], cost: 1
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, arg4'=arg4P_12, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     19: f5 -> f5 : arg1'=1+arg1, arg3'=1+arg3, arg4'=1+arg4, [ arg2>arg3 && arg2>arg4 ], cost: 5
     15: __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:
     19: f5 -> f5 : arg1'=1+arg1, arg3'=1+arg3, arg4'=1+arg4, [ arg2>arg3 && arg2>arg4 ], cost: 5

   Accelerated rule 19 with backward acceleration, yielding the new rule 20.
   Accelerated rule 19 with backward acceleration, yielding the new rule 21.
[accelerate] Nesting with 2 inner and 1 outer candidates
   Removing the simple loops: 19.

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

Chained accelerated rules (with incoming rules):
   Start location: __init
     15: __init -> f5 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, arg4'=arg4P_3, [], cost: 5
     22: __init -> f5 : arg1'=-arg3P_2+arg2P_1, arg2'=arg2P_1, arg3'=arg2P_1, arg4'=-arg3P_2+arg4P_3+arg2P_1, [ -arg3P_2+arg2P_1>=0 && arg2P_1>-1-arg3P_2+arg4P_3+arg2P_1 ], cost: 5-5*arg3P_2+5*arg2P_1
     23: __init -> f5 : arg1'=-arg4P_3+arg2P_1, arg2'=arg2P_1, arg3'=arg3P_2-arg4P_3+arg2P_1, arg4'=arg2P_1, [ -arg4P_3+arg2P_1>=0 && arg2P_1>-1+arg3P_2-arg4P_3+arg2P_1 ], cost: 5-5*arg4P_3+5*arg2P_1

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

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     22: __init -> f5 : arg1'=-arg3P_2+arg2P_1, arg2'=arg2P_1, arg3'=arg2P_1, arg4'=-arg3P_2+arg4P_3+arg2P_1, [ -arg3P_2+arg2P_1>=0 && arg2P_1>-1-arg3P_2+arg4P_3+arg2P_1 ], cost: 5-5*arg3P_2+5*arg2P_1
     23: __init -> f5 : arg1'=-arg4P_3+arg2P_1, arg2'=arg2P_1, arg3'=arg3P_2-arg4P_3+arg2P_1, arg4'=arg2P_1, [ -arg4P_3+arg2P_1>=0 && arg2P_1>-1+arg3P_2-arg4P_3+arg2P_1 ], cost: 5-5*arg4P_3+5*arg2P_1

Computing asymptotic complexity for rule 22
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 23
   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),?)