WORST_CASE(Omega(1),?)

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

Initial linear ITS problem
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [ 3==arg1P_1 ], cost: 1
     12: f2 -> f3 : arg1'=arg1P_13, [ arg1>=3 && arg1==arg1P_13 ], cost: 1
     14: f2 -> f13 : arg1'=arg1P_15, [ arg1<3 && arg1==arg1P_15 ], cost: 1
      1: f4 -> f7 : arg1'=arg1P_2, [ arg1P_2==3+arg1 ], cost: 1
     10: f7 -> f6 : arg1'=arg1P_11, [ arg1==arg1P_11 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, [ arg1P_3==-2+arg1 ], cost: 1
      6: f11 -> f10 : arg1'=arg1P_7, [ arg1==arg1P_7 ], cost: 1
      3: f9 -> f12 : arg1'=arg1P_4, [ arg1P_4==1+arg1 ], cost: 1
      7: f12 -> f10 : arg1'=arg1P_8, [ arg1==arg1P_8 ], cost: 1
      4: f5 -> f8 : arg1'=arg1P_5, [ arg1>10 && arg1==arg1P_5 ], cost: 1
      5: f5 -> f9 : arg1'=arg1P_6, [ arg1<=10 && arg1==arg1P_6 ], cost: 1
     11: f10 -> f6 : arg1'=arg1P_12, [ arg1==arg1P_12 ], cost: 1
      8: f3 -> f4 : arg1'=arg1P_9, [ arg1>5 && arg1==arg1P_9 ], cost: 1
      9: f3 -> f5 : arg1'=arg1P_10, [ arg1<=5 && arg1==arg1P_10 ], cost: 1
     13: f6 -> f2 : arg1'=arg1P_14, [ arg1==arg1P_14 ], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     15: __init -> f1 : arg1'=arg1P_16, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [ 3==arg1P_1 ], cost: 1
     12: f2 -> f3 : arg1'=arg1P_13, [ arg1>=3 && arg1==arg1P_13 ], cost: 1
      1: f4 -> f7 : arg1'=arg1P_2, [ arg1P_2==3+arg1 ], cost: 1
     10: f7 -> f6 : arg1'=arg1P_11, [ arg1==arg1P_11 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, [ arg1P_3==-2+arg1 ], cost: 1
      6: f11 -> f10 : arg1'=arg1P_7, [ arg1==arg1P_7 ], cost: 1
      3: f9 -> f12 : arg1'=arg1P_4, [ arg1P_4==1+arg1 ], cost: 1
      7: f12 -> f10 : arg1'=arg1P_8, [ arg1==arg1P_8 ], cost: 1
      4: f5 -> f8 : arg1'=arg1P_5, [ arg1>10 && arg1==arg1P_5 ], cost: 1
      5: f5 -> f9 : arg1'=arg1P_6, [ arg1<=10 && arg1==arg1P_6 ], cost: 1
     11: f10 -> f6 : arg1'=arg1P_12, [ arg1==arg1P_12 ], cost: 1
      8: f3 -> f4 : arg1'=arg1P_9, [ arg1>5 && arg1==arg1P_9 ], cost: 1
      9: f3 -> f5 : arg1'=arg1P_10, [ arg1<=5 && arg1==arg1P_10 ], cost: 1
     13: f6 -> f2 : arg1'=arg1P_14, [ arg1==arg1P_14 ], cost: 1
     15: __init -> f1 : arg1'=arg1P_16, [], cost: 1

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

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     12: f2 -> f3 : [ arg1>=3 ], cost: 1
     21: f5 -> f10 : arg1'=-2+arg1, [ arg1>10 ], cost: 3
     22: f5 -> f10 : arg1'=1+arg1, [ arg1<=10 ], cost: 3
     11: f10 -> f6 : [], cost: 1
      9: f3 -> f5 : [ arg1<=5 ], cost: 1
     18: f3 -> f6 : arg1'=3+arg1, [ arg1>5 ], cost: 3
     13: f6 -> f2 : [], cost: 1
     16: __init -> f2 : arg1'=3, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
     23: f2 -> f5 : [ arg1>=3 && arg1<=5 ], cost: 2
     24: f2 -> f6 : arg1'=3+arg1, [ arg1>5 ], cost: 4
     25: f5 -> f6 : arg1'=-2+arg1, [ arg1>10 ], cost: 4
     26: f5 -> f6 : arg1'=1+arg1, [ arg1<=10 ], cost: 4
     13: f6 -> f2 : [], cost: 1
     16: __init -> f2 : arg1'=3, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
     28: f2 -> f2 : arg1'=3+arg1, [ arg1>5 ], cost: 5
     29: f2 -> f2 : arg1'=1+arg1, [ arg1>=3 && arg1<=5 ], cost: 7
     16: __init -> f2 : arg1'=3, [], cost: 2

Accelerating simple loops of location 1.
   Accelerating the following rules:
     28: f2 -> f2 : arg1'=3+arg1, [ arg1>5 ], cost: 5
     29: f2 -> f2 : arg1'=1+arg1, [ arg1>=3 && arg1<=5 ], cost: 7

   Accelerated rule 28 with non-termination, yielding the new rule 30.
   Accelerated rule 29 with backward acceleration, yielding the new rule 31.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 28 29.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     30: f2 -> [14] : [ arg1>5 ], cost: NONTERM
     31: f2 -> f2 : arg1'=6, [ arg1>=3 && 6-arg1>=0 ], cost: 42-7*arg1
     16: __init -> f2 : arg1'=3, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: __init
     16: __init -> f2 : arg1'=3, [], cost: 2
     32: __init -> f2 : arg1'=6, [], cost: 23

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     <empty>

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     <empty>

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),?)