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, [ 0==arg1P_1 && arg2==arg2P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && 100==arg2P_2 && arg3==arg3P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1
     10: f4 -> f5 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1<40 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     12: f4 -> f11 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1>=40 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], 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
      8: f9 -> f8 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      4: f7 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_5==2+arg1 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      9: f10 -> f8 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
      5: f5 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg3==0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f5 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg3<0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      7: f5 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg3>0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
     11: f8 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ 0==arg1P_1 && arg2==arg2P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && 100==arg2P_2 && arg3==arg3P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1
     10: f4 -> f5 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1<40 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], 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
      8: f9 -> f8 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      4: f7 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_5==2+arg1 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      9: f10 -> f8 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
      5: f5 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg3==0 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f5 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg3<0 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      7: f5 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg3>0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
     11: f8 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=0, [], cost: 1
      1: f2 -> f3 : arg2'=100, [], cost: 1
      2: f3 -> f4 : arg3'=arg3P_3, [], cost: 1
     10: f4 -> f5 : [ arg1<40 ], cost: 1
      3: f6 -> f9 : arg1'=1+arg1, [], cost: 1
      8: f9 -> f8 : [], cost: 1
      4: f7 -> f10 : arg1'=2+arg1, [], cost: 1
      9: f10 -> f8 : [], cost: 1
      5: f5 -> f6 : [ arg3==0 ], cost: 1
      6: f5 -> f7 : [ arg3<0 ], cost: 1
      7: f5 -> f7 : [ arg3>0 ], cost: 1
     11: f8 -> f4 : [], cost: 1
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     10: f4 -> f5 : [ arg1<40 ], cost: 1
     19: f7 -> f8 : arg1'=2+arg1, [], cost: 2
      6: f5 -> f7 : [ arg3<0 ], cost: 1
      7: f5 -> f7 : [ arg3>0 ], cost: 1
     18: f5 -> f8 : arg1'=1+arg1, [ arg3==0 ], cost: 3
     11: f8 -> f4 : [], cost: 1
     16: __init -> f4 : arg1'=0, arg2'=100, arg3'=arg3P_3, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     20: f4 -> f7 : [ arg1<40 && arg3<0 ], cost: 2
     21: f4 -> f7 : [ arg1<40 && arg3>0 ], cost: 2
     22: f4 -> f8 : arg1'=1+arg1, [ arg1<40 && arg3==0 ], cost: 4
     19: f7 -> f8 : arg1'=2+arg1, [], cost: 2
     11: f8 -> f4 : [], cost: 1
     16: __init -> f4 : arg1'=0, arg2'=100, arg3'=arg3P_3, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     25: f4 -> f4 : arg1'=1+arg1, [ arg1<40 && arg3==0 ], cost: 5
     26: f4 -> f4 : arg1'=2+arg1, [ arg1<40 && arg3<0 ], cost: 5
     27: f4 -> f4 : arg1'=2+arg1, [ arg1<40 && arg3>0 ], cost: 5
     16: __init -> f4 : arg1'=0, arg2'=100, arg3'=arg3P_3, [], cost: 4

Accelerating simple loops of location 3.
   Accelerating the following rules:
     25: f4 -> f4 : arg1'=1+arg1, [ arg1<40 && arg3==0 ], cost: 5
     26: f4 -> f4 : arg1'=2+arg1, [ arg1<40 && arg3<0 ], cost: 5
     27: f4 -> f4 : arg1'=2+arg1, [ arg1<40 && arg3>0 ], cost: 5

   Accelerated rule 25 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 3 outer candidates
   Removing the simple loops: 25 26 27.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     28: f4 -> f4 : arg1'=40, [ arg3==0 && 40-arg1>=0 ], cost: 200-5*arg1
     29: f4 -> f4 : arg1'=2*k_1+arg1, [ arg3<0 && k_1>=0 && -2+2*k_1+arg1<40 ], cost: 5*k_1
     30: f4 -> f4 : arg1'=2*k_2+arg1, [ arg3>0 && k_2>=0 && -2+2*k_2+arg1<40 ], cost: 5*k_2
     16: __init -> f4 : arg1'=0, arg2'=100, arg3'=arg3P_3, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     16: __init -> f4 : arg1'=0, arg2'=100, arg3'=arg3P_3, [], cost: 4
     31: __init -> f4 : arg1'=40, arg2'=100, arg3'=0, [], cost: 204
     32: __init -> f4 : arg1'=2*k_1, arg2'=100, arg3'=arg3P_3, [ arg3P_3<0 && k_1>=0 && -2+2*k_1<40 ], cost: 4+5*k_1
     33: __init -> f4 : arg1'=2*k_2, arg2'=100, arg3'=arg3P_3, [ arg3P_3>0 && k_2>=0 && -2+2*k_2<40 ], cost: 4+5*k_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     32: __init -> f4 : arg1'=2*k_1, arg2'=100, arg3'=arg3P_3, [ arg3P_3<0 && k_1>=0 && -2+2*k_1<40 ], cost: 4+5*k_1
     33: __init -> f4 : arg1'=2*k_2, arg2'=100, arg3'=arg3P_3, [ arg3P_3>0 && k_2>=0 && -2+2*k_2<40 ], cost: 4+5*k_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     32: __init -> f4 : arg1'=2*k_1, arg2'=100, arg3'=arg3P_3, [ arg3P_3<0 && k_1>=0 && -2+2*k_1<40 ], cost: 4+5*k_1
     33: __init -> f4 : arg1'=2*k_2, arg2'=100, arg3'=arg3P_3, [ arg3P_3>0 && k_2>=0 && -2+2*k_2<40 ], cost: 4+5*k_2

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),?)