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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, [], cost: 1

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

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      1: f2 -> f3 : arg2'=arg2P_2, [], cost: 1
      8: f3 -> f4 : [ arg1>=0 ], cost: 1
      2: f4 -> f5 : arg2'=1, [], cost: 1
      4: f5 -> f6 : [ arg2<arg1 ], cost: 1
      6: f5 -> f8 : [ arg2>=arg1 ], cost: 1
      3: f6 -> f7 : arg2'=2*arg2, [], cost: 1
      5: f7 -> f5 : [], cost: 1
      7: f8 -> f9 : arg1'=-1+arg1, [], cost: 1
      9: f9 -> f3 : [], cost: 1
     11: __init -> f1 : arg1'=arg1P_12, arg2'=arg2P_12, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     14: f3 -> f5 : arg2'=1, [ arg1>=0 ], cost: 2
     17: f5 -> f5 : arg2'=2*arg2, [ arg2<arg1 ], cost: 3
     18: f5 -> f3 : arg1'=-1+arg1, [ arg2>=arg1 ], cost: 3
     13: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Accelerating simple loops of location 4.
   Accelerating the following rules:
     17: f5 -> f5 : arg2'=2*arg2, [ arg2<arg1 ], cost: 3

[test] deduced invariant 1-arg2<=0
   Accelerated rule 17 with non-termination, yielding the new rule 19.
   Accelerated rule 17 with backward acceleration, yielding the new rule 20.
[accelerate] Nesting with 1 inner and 1 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     14: f3 -> f5 : arg2'=1, [ arg1>=0 ], cost: 2
     17: f5 -> f5 : arg2'=2*arg2, [ arg2<arg1 ], cost: 3
     18: f5 -> f3 : arg1'=-1+arg1, [ arg2>=arg1 ], cost: 3
     19: f5 -> [11] : [ arg2<arg1 && arg2==0 && arg1==1 ], cost: NONTERM
     20: f5 -> f5 : arg2'=arg2*2^k, [ 1-arg2<=0 && k>=0 && arg2*2^(-1+k)<arg1 ], cost: 3*k
     13: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     14: f3 -> f5 : arg2'=1, [ arg1>=0 ], cost: 2
     21: f3 -> f5 : arg2'=2, [ 1<arg1 ], cost: 5
     22: f3 -> f5 : arg2'=2^k, [ arg1>=0 && k>=0 && 2^(-1+k)<arg1 ], cost: 2+3*k
     18: f5 -> f3 : arg1'=-1+arg1, [ arg2>=arg1 ], cost: 3
     13: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     14: f3 -> f5 : arg2'=1, [ arg1>=0 ], cost: 2
     21: f3 -> f5 : arg2'=2, [ 1<arg1 ], cost: 5
     22: f3 -> f5 : arg2'=2^k, [ arg1>=0 && k>=0 && 2^(-1+k)<arg1 ], cost: 2+3*k
     18: f5 -> f3 : arg1'=-1+arg1, [ arg2>=arg1 ], cost: 3
     13: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     23: f3 -> f3 : arg1'=-1+arg1, arg2'=1, [ arg1>=0 && 1>=arg1 ], cost: 5
     24: f3 -> f3 : arg1'=-1+arg1, arg2'=2, [ 1<arg1 && 2>=arg1 ], cost: 8
     25: f3 -> f3 : arg1'=-1+arg1, arg2'=2^k, [ arg1>=0 && k>=0 && 2^(-1+k)<arg1 && 2^k>=arg1 ], cost: 5+3*k
     13: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Accelerating simple loops of location 2.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     23: f3 -> f3 : arg1'=-1+arg1, arg2'=1, [ arg1>=0 && 1>=arg1 ], cost: 5
     24: f3 -> f3 : arg1'=-1+arg1, arg2'=2, [ 2-arg1==0 ], cost: 8
     25: f3 -> f3 : arg1'=-1+arg1, arg2'=2^k, [ arg1>=0 && k>=0 && 2^(-1+k)<arg1 && 2^k>=arg1 ], cost: 5+3*k

   Accelerated rule 23 with backward acceleration, yielding the new rule 26.
   Failed to prove monotonicity of the guard of rule 24.
   Failed to prove monotonicity of the guard of rule 25.
[accelerate] Nesting with 3 inner and 3 outer candidates
   Removing the simple loops: 23.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     24: f3 -> f3 : arg1'=-1+arg1, arg2'=2, [ 2-arg1==0 ], cost: 8
     25: f3 -> f3 : arg1'=-1+arg1, arg2'=2^k, [ arg1>=0 && k>=0 && 2^(-1+k)<arg1 && 2^k>=arg1 ], cost: 5+3*k
     26: f3 -> f3 : arg1'=-1, arg2'=1, [ 1>=arg1 && 1+arg1>=1 ], cost: 5+5*arg1
     13: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     13: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3
     27: __init -> f3 : arg1'=1, arg2'=2, [], cost: 11
     28: __init -> f3 : arg1'=-1+arg1P_1, arg2'=2^k, [ arg1P_1>=0 && k>=0 && 2^(-1+k)<arg1P_1 && 2^k>=arg1P_1 ], cost: 8+3*k
     29: __init -> f3 : arg1'=-1, arg2'=1, [ 1>=arg1P_1 && 1+arg1P_1>=1 ], cost: 8+5*arg1P_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     28: __init -> f3 : arg1'=-1+arg1P_1, arg2'=2^k, [ arg1P_1>=0 && k>=0 && 2^(-1+k)<arg1P_1 && 2^k>=arg1P_1 ], cost: 8+3*k
     29: __init -> f3 : arg1'=-1, arg2'=1, [ 1>=arg1P_1 && 1+arg1P_1>=1 ], cost: 8+5*arg1P_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     28: __init -> f3 : arg1'=-1+arg1P_1, arg2'=2^k, [ arg1P_1>=0 && k>=0 && 2^(-1+k)<arg1P_1 && 2^k>=arg1P_1 ], cost: 8+3*k
     29: __init -> f3 : arg1'=-1, arg2'=1, [ 1>=arg1P_1 && 1+arg1P_1>=1 ], cost: 8+5*arg1P_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),?)