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, [ 1==arg1P_1 && arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1
     10: f3 -> f4 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1>0 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     12: f3 -> f12 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1<=0 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==-10+arg2 && arg1==arg1P_3 ], cost: 1
      3: f8 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1P_4==-1+arg1 && arg2==arg2P_4 ], cost: 1
      8: f9 -> f7 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      4: f6 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2P_5==11+arg2 && arg1==arg1P_5 ], cost: 1
      5: f10 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1P_6==1+arg1 && arg2==arg2P_6 ], cost: 1
      9: f11 -> f7 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
      6: f4 -> f5 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2>100 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      7: f4 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg2<=100 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
     11: f7 -> f3 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_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, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ 1==arg1P_1 && arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1
     10: f3 -> f4 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1>0 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
      2: f5 -> f8 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg2P_3==-10+arg2 && arg1==arg1P_3 ], cost: 1
      3: f8 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1P_4==-1+arg1 && arg2==arg2P_4 ], cost: 1
      8: f9 -> f7 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      4: f6 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg2P_5==11+arg2 && arg1==arg1P_5 ], cost: 1
      5: f10 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1P_6==1+arg1 && arg2==arg2P_6 ], cost: 1
      9: f11 -> f7 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
      6: f4 -> f5 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg2>100 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      7: f4 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg2<=100 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
     11: f7 -> f3 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=1, [], cost: 1
      1: f2 -> f3 : arg2'=arg2P_2, [], cost: 1
     10: f3 -> f4 : [ arg1>0 ], cost: 1
      2: f5 -> f8 : arg2'=-10+arg2, [], cost: 1
      3: f8 -> f9 : arg1'=-1+arg1, [], cost: 1
      8: f9 -> f7 : [], cost: 1
      4: f6 -> f10 : arg2'=11+arg2, [], cost: 1
      5: f10 -> f11 : arg1'=1+arg1, [], cost: 1
      9: f11 -> f7 : [], cost: 1
      6: f4 -> f5 : [ arg2>100 ], cost: 1
      7: f4 -> f6 : [ arg2<=100 ], cost: 1
     11: f7 -> f3 : [], cost: 1
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     10: f3 -> f4 : [ arg1>0 ], cost: 1
     20: f4 -> f7 : arg1'=-1+arg1, arg2'=-10+arg2, [ arg2>100 ], cost: 4
     21: f4 -> f7 : arg1'=1+arg1, arg2'=11+arg2, [ arg2<=100 ], cost: 4
     11: f7 -> f3 : [], cost: 1
     15: __init -> f3 : arg1'=1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     22: f3 -> f7 : arg1'=-1+arg1, arg2'=-10+arg2, [ arg1>0 && arg2>100 ], cost: 5
     23: f3 -> f7 : arg1'=1+arg1, arg2'=11+arg2, [ arg1>0 && arg2<=100 ], cost: 5
     11: f7 -> f3 : [], cost: 1
     15: __init -> f3 : arg1'=1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     24: f3 -> f3 : arg1'=-1+arg1, arg2'=-10+arg2, [ arg1>0 && arg2>100 ], cost: 6
     25: f3 -> f3 : arg1'=1+arg1, arg2'=11+arg2, [ arg1>0 && arg2<=100 ], cost: 6
     15: __init -> f3 : arg1'=1, arg2'=arg2P_2, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     24: f3 -> f3 : arg1'=-1+arg1, arg2'=-10+arg2, [ arg1>0 && arg2>100 ], cost: 6
     25: f3 -> f3 : arg1'=1+arg1, arg2'=11+arg2, [ arg1>0 && arg2<=100 ], cost: 6

   Accelerated rule 24 with backward acceleration, yielding the new rule 26.
   Accelerated rule 25 with backward acceleration, yielding the new rule 27.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 24 25.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     26: f3 -> f3 : arg1'=-k+arg1, arg2'=-10*k+arg2, [ k>=0 && 1-k+arg1>0 && 10-10*k+arg2>100 ], cost: 6*k
     27: f3 -> f3 : arg1'=k_1+arg1, arg2'=11*k_1+arg2, [ arg1>0 && k_1>=0 && -11+11*k_1+arg2<=100 ], cost: 6*k_1
     15: __init -> f3 : arg1'=1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     15: __init -> f3 : arg1'=1, arg2'=arg2P_2, [], cost: 3
     28: __init -> f3 : arg1'=1-k, arg2'=-10*k+arg2P_2, [ k>=0 && 2-k>0 && 10-10*k+arg2P_2>100 ], cost: 3+6*k
     29: __init -> f3 : arg1'=1+k_1, arg2'=arg2P_2+11*k_1, [ k_1>=0 && -11+arg2P_2+11*k_1<=100 ], cost: 3+6*k_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     28: __init -> f3 : arg1'=1-k, arg2'=-10*k+arg2P_2, [ k>=0 && 2-k>0 && 10-10*k+arg2P_2>100 ], cost: 3+6*k
     29: __init -> f3 : arg1'=1+k_1, arg2'=arg2P_2+11*k_1, [ k_1>=0 && -11+arg2P_2+11*k_1<=100 ], cost: 3+6*k_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     28: __init -> f3 : arg1'=1-k, arg2'=-10*k+arg2P_2, [ k>=0 && 2-k>0 && 10-10*k+arg2P_2>100 ], cost: 3+6*k
     29: __init -> f3 : arg1'=1+k_1, arg2'=arg2P_2+11*k_1, [ k_1>=0 && -11+arg2P_2+11*k_1<=100 ], cost: 3+6*k_1

Computing asymptotic complexity for rule 29
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 28
   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),?)