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, [ arg2==arg2P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg3==arg3P_2 ], cost: 1
     11: f3 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1>0 && arg2>0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     13: f3 -> f13 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1<=0 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     14: f3 -> f13 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg2<=0 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1
      7: f5 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg3<42 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      8: f5 -> f7 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg3>=42 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==-1+arg1 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
      4: f9 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f10 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1==arg1P_6 && arg3==arg2P_6 && arg3==arg3P_6 ], cost: 1
      9: f11 -> f8 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
      6: f7 -> f12 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg2P_7==-1+arg2 && arg1==arg1P_7 && arg3==arg3P_7 ], cost: 1
     10: f12 -> f8 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     12: f8 -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_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, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2==arg2P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg3==arg3P_2 ], cost: 1
     11: f3 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1>0 && arg2>0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1
      7: f5 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg3<42 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      8: f5 -> f7 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg3>=42 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==-1+arg1 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
      4: f9 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f10 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1==arg1P_6 && arg3==arg2P_6 && arg3==arg3P_6 ], cost: 1
      9: f11 -> f8 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
      6: f7 -> f12 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg2P_7==-1+arg2 && arg1==arg1P_7 && arg3==arg3P_7 ], cost: 1
     10: f12 -> f8 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     12: f8 -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      1: f2 -> f3 : arg2'=arg2P_2, [], cost: 1
     11: f3 -> f4 : [ arg1>0 && arg2>0 ], cost: 1
      2: f4 -> f5 : arg3'=arg3P_3, [], cost: 1
      7: f5 -> f6 : [ arg3<42 ], cost: 1
      8: f5 -> f7 : [ arg3>=42 ], cost: 1
      3: f6 -> f9 : arg1'=-1+arg1, [], cost: 1
      4: f9 -> f10 : arg3'=arg3P_5, [], cost: 1
      5: f10 -> f11 : arg2'=arg3, [], cost: 1
      9: f11 -> f8 : [], cost: 1
      6: f7 -> f12 : arg2'=-1+arg2, [], cost: 1
     10: f12 -> f8 : [], cost: 1
     12: f8 -> f3 : [], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     18: f3 -> f5 : arg3'=arg3P_3, [ arg1>0 && arg2>0 ], cost: 2
     22: f5 -> f8 : arg2'=-1+arg2, [ arg3>=42 ], cost: 3
     24: f5 -> f8 : arg1'=-1+arg1, arg2'=arg3P_5, arg3'=arg3P_5, [ arg3<42 ], cost: 5
     12: f8 -> f3 : [], cost: 1
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     25: f3 -> f8 : arg2'=-1+arg2, arg3'=arg3P_3, [ arg1>0 && arg2>0 && arg3P_3>=42 ], cost: 5
     26: f3 -> f8 : arg1'=-1+arg1, arg2'=arg3P_5, arg3'=arg3P_5, [ arg1>0 && arg2>0 && arg3P_3<42 ], cost: 7
     12: f8 -> f3 : [], cost: 1
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     27: f3 -> f3 : arg2'=-1+arg2, arg3'=arg3P_3, [ arg1>0 && arg2>0 && arg3P_3>=42 ], cost: 6
     28: f3 -> f3 : arg1'=-1+arg1, arg2'=arg3P_5, arg3'=arg3P_5, [ arg1>0 && arg2>0 && arg3P_3<42 ], cost: 8
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, [], cost: 3

Accelerating simple loops of location 2.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     27: f3 -> f3 : arg2'=-1+arg2, arg3'=arg3P_3, [ arg1>0 && arg2>0 && arg3P_3>=42 ], cost: 6
     28: f3 -> f3 : arg1'=-1+arg1, arg2'=arg3P_5, arg3'=arg3P_5, [ arg1>0 && arg2>0 ], cost: 8

   Accelerated rule 27 with backward acceleration, yielding the new rule 29.
[test] deduced pseudo-invariant -arg2+arg3P_5<=0, also trying arg2-arg3P_5<=-1
   Accelerated rule 28 with backward acceleration, yielding the new rule 30.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 27.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     28: f3 -> f3 : arg1'=-1+arg1, arg2'=arg3P_5, arg3'=arg3P_5, [ arg1>0 && arg2>0 ], cost: 8
     29: f3 -> f3 : arg2'=0, arg3'=arg3P_3, [ arg1>0 && arg3P_3>=42 && arg2>=1 ], cost: 6*arg2
     30: f3 -> f3 : arg1'=0, arg2'=arg3P_5, arg3'=arg3P_5, [ -arg2+arg3P_5<=0 && arg1>=1 && arg3P_5>0 ], cost: 8*arg1
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     17: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_16, [], cost: 3
     31: __init -> f3 : arg1'=-1+arg1P_1, arg2'=arg3P_5, arg3'=arg3P_5, [ arg1P_1>0 ], cost: 11
     32: __init -> f3 : arg1'=arg1P_1, arg2'=0, arg3'=arg3P_3, [ arg1P_1>0 && arg3P_3>=42 && arg2P_2>=1 ], cost: 3+6*arg2P_2
     33: __init -> f3 : arg1'=0, arg2'=arg3P_5, arg3'=arg3P_5, [ arg1P_1>=1 && arg3P_5>0 ], cost: 3+8*arg1P_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     32: __init -> f3 : arg1'=arg1P_1, arg2'=0, arg3'=arg3P_3, [ arg1P_1>0 && arg3P_3>=42 && arg2P_2>=1 ], cost: 3+6*arg2P_2
     33: __init -> f3 : arg1'=0, arg2'=arg3P_5, arg3'=arg3P_5, [ arg1P_1>=1 && arg3P_5>0 ], cost: 3+8*arg1P_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     32: __init -> f3 : arg1'=arg1P_1, arg2'=0, arg3'=arg3P_3, [ arg1P_1>0 && arg3P_3>=42 && arg2P_2>=1 ], cost: 3+6*arg2P_2
     33: __init -> f3 : arg1'=0, arg2'=arg3P_5, arg3'=arg3P_5, [ arg1P_1>=1 && arg3P_5>0 ], cost: 3+8*arg1P_1

Computing asymptotic complexity for rule 33
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 32
   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),?)