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, [ 0==arg1P_1 && arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 && 0==arg2P_2 ], cost: 1
      9: f3 -> f4 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg2>=0 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
     11: f3 -> f11 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg2<0 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==1+arg2 && arg1==arg1P_3 ], cost: 1
      6: f8 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==-1+arg2 && arg1==arg1P_4 ], cost: 1
      7: f9 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      4: f4 -> f5 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1<=50 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f4 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1>50 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      8: f7 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1P_9==1+arg1 && arg2==arg2P_9 ], cost: 1
     10: f10 -> f3 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     12: __init -> f1 : arg1'=arg1P_13, arg2'=arg2P_13, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     12: __init -> f1 : arg1'=arg1P_13, arg2'=arg2P_13, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ 0==arg1P_1 && arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 && 0==arg2P_2 ], cost: 1
      9: f3 -> f4 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg2>=0 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==1+arg2 && arg1==arg1P_3 ], cost: 1
      6: f8 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      3: f6 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg2P_4==-1+arg2 && arg1==arg1P_4 ], cost: 1
      7: f9 -> f7 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      4: f4 -> f5 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1<=50 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f4 -> f6 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1>50 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      8: f7 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1P_9==1+arg1 && arg2==arg2P_9 ], cost: 1
     10: f10 -> f3 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     12: __init -> f1 : arg1'=arg1P_13, arg2'=arg2P_13, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=0, [], cost: 1
      1: f2 -> f3 : arg2'=0, [], cost: 1
      9: f3 -> f4 : [ arg2>=0 ], cost: 1
      2: f5 -> f8 : arg2'=1+arg2, [], cost: 1
      6: f8 -> f7 : [], cost: 1
      3: f6 -> f9 : arg2'=-1+arg2, [], cost: 1
      7: f9 -> f7 : [], cost: 1
      4: f4 -> f5 : [ arg1<=50 ], cost: 1
      5: f4 -> f6 : [ arg1>50 ], cost: 1
      8: f7 -> f10 : arg1'=1+arg1, [], cost: 1
     10: f10 -> f3 : [], cost: 1
     12: __init -> f1 : arg1'=arg1P_13, arg2'=arg2P_13, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
      9: f3 -> f4 : [ arg2>=0 ], cost: 1
     17: f4 -> f7 : arg2'=1+arg2, [ arg1<=50 ], cost: 3
     18: f4 -> f7 : arg2'=-1+arg2, [ arg1>50 ], cost: 3
     19: f7 -> f3 : arg1'=1+arg1, [], cost: 2
     14: __init -> f3 : arg1'=0, arg2'=0, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     20: f3 -> f7 : arg2'=1+arg2, [ arg2>=0 && arg1<=50 ], cost: 4
     21: f3 -> f7 : arg2'=-1+arg2, [ arg2>=0 && arg1>50 ], cost: 4
     19: f7 -> f3 : arg1'=1+arg1, [], cost: 2
     14: __init -> f3 : arg1'=0, arg2'=0, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     22: f3 -> f3 : arg1'=1+arg1, arg2'=1+arg2, [ arg2>=0 && arg1<=50 ], cost: 6
     23: f3 -> f3 : arg1'=1+arg1, arg2'=-1+arg2, [ arg2>=0 && arg1>50 ], cost: 6
     14: __init -> f3 : arg1'=0, arg2'=0, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     22: f3 -> f3 : arg1'=1+arg1, arg2'=1+arg2, [ arg2>=0 && arg1<=50 ], cost: 6
     23: f3 -> f3 : arg1'=1+arg1, arg2'=-1+arg2, [ arg2>=0 && arg1>50 ], cost: 6

   Accelerated rule 22 with backward acceleration, yielding the new rule 24.
   Accelerated rule 23 with backward acceleration, yielding the new rule 25.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 22 23.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     24: f3 -> f3 : arg1'=51, arg2'=51+arg2-arg1, [ arg2>=0 && 51-arg1>=0 ], cost: 306-6*arg1
     25: f3 -> f3 : arg1'=1+arg2+arg1, arg2'=-1, [ arg1>50 && 1+arg2>=0 ], cost: 6+6*arg2
     14: __init -> f3 : arg1'=0, arg2'=0, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     14: __init -> f3 : arg1'=0, arg2'=0, [], cost: 3
     26: __init -> f3 : arg1'=51, arg2'=51, [], cost: 309

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),?)