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, [ arg1==arg1P_1 && arg2==arg2P_1 && 0==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ 0==arg1P_2 && arg2==arg2P_2 && arg3==arg3P_2 ], cost: 1
     10: f3 -> f4 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1<10 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     12: f3 -> f12 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg1>=10 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && 3==arg2P_3 && arg3==arg3P_3 ], cost: 1
      6: f5 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg2<12 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      8: f5 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg2>=12 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      3: f6 -> f7 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_4==-1+arg2 && arg1==arg1P_4 && arg3==arg3P_4 ], cost: 1
      4: f7 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3P_5==1+arg3 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f8 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg2P_6==2+arg2 && arg1==arg1P_6 && arg3==arg3P_6 ], cost: 1
      7: f9 -> f5 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      9: f10 -> f11 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1P_10==1+arg1 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     11: f11 -> f3 : 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, [ arg1==arg1P_1 && arg2==arg2P_1 && 0==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ 0==arg1P_2 && arg2==arg2P_2 && arg3==arg3P_2 ], cost: 1
     10: f3 -> f4 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1<10 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && 3==arg2P_3 && arg3==arg3P_3 ], cost: 1
      6: f5 -> f6 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg2<12 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      8: f5 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg2>=12 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      3: f6 -> f7 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg2P_4==-1+arg2 && arg1==arg1P_4 && arg3==arg3P_4 ], cost: 1
      4: f7 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3P_5==1+arg3 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f8 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg2P_6==2+arg2 && arg1==arg1P_6 && arg3==arg3P_6 ], cost: 1
      7: f9 -> f5 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      9: f10 -> f11 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1P_10==1+arg1 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     11: f11 -> f3 : 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 : arg3'=0, [], cost: 1
      1: f2 -> f3 : arg1'=0, [], cost: 1
     10: f3 -> f4 : [ arg1<10 ], cost: 1
      2: f4 -> f5 : arg2'=3, [], cost: 1
      6: f5 -> f6 : [ arg2<12 ], cost: 1
      8: f5 -> f10 : [ arg2>=12 ], cost: 1
      3: f6 -> f7 : arg2'=-1+arg2, [], cost: 1
      4: f7 -> f8 : arg3'=1+arg3, [], cost: 1
      5: f8 -> f9 : arg2'=2+arg2, [], cost: 1
      7: f9 -> f5 : [], cost: 1
      9: f10 -> f11 : arg1'=1+arg1, [], cost: 1
     11: f11 -> f3 : [], 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
     16: f3 -> f5 : arg2'=3, [ arg1<10 ], cost: 2
     20: f5 -> f3 : arg1'=1+arg1, [ arg2>=12 ], cost: 3
     22: f5 -> f5 : arg2'=1+arg2, arg3'=1+arg3, [ arg2<12 ], cost: 5
     15: __init -> f3 : arg1'=0, arg2'=arg2P_14, arg3'=0, [], cost: 3

Accelerating simple loops of location 4.
   Accelerating the following rules:
     22: f5 -> f5 : arg2'=1+arg2, arg3'=1+arg3, [ arg2<12 ], cost: 5

   Accelerated rule 22 with backward acceleration, yielding the new rule 23.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 22.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     16: f3 -> f5 : arg2'=3, [ arg1<10 ], cost: 2
     20: f5 -> f3 : arg1'=1+arg1, [ arg2>=12 ], cost: 3
     23: f5 -> f5 : arg2'=12, arg3'=12-arg2+arg3, [ 12-arg2>=0 ], cost: 60-5*arg2
     15: __init -> f3 : arg1'=0, arg2'=arg2P_14, arg3'=0, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     16: f3 -> f5 : arg2'=3, [ arg1<10 ], cost: 2
     24: f3 -> f5 : arg2'=12, arg3'=9+arg3, [ arg1<10 ], cost: 47
     20: f5 -> f3 : arg1'=1+arg1, [ arg2>=12 ], cost: 3
     15: __init -> f3 : arg1'=0, arg2'=arg2P_14, arg3'=0, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     25: f3 -> f3 : arg1'=1+arg1, arg2'=12, arg3'=9+arg3, [ arg1<10 ], cost: 50
     15: __init -> f3 : arg1'=0, arg2'=arg2P_14, arg3'=0, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     25: f3 -> f3 : arg1'=1+arg1, arg2'=12, arg3'=9+arg3, [ arg1<10 ], cost: 50

   Accelerated rule 25 with backward acceleration, yielding the new rule 26.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 25.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     26: f3 -> f3 : arg1'=10, arg2'=12, arg3'=90+arg3-9*arg1, [ 10-arg1>=1 ], cost: 500-50*arg1
     15: __init -> f3 : arg1'=0, arg2'=arg2P_14, arg3'=0, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     15: __init -> f3 : arg1'=0, arg2'=arg2P_14, arg3'=0, [], cost: 3
     27: __init -> f3 : arg1'=10, arg2'=12, arg3'=90, [], cost: 503

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),?)