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

Accelerating simple loops of location 4.
   Accelerating the following rules:
     18: f5 -> f5 : arg2'=2*arg2, [ arg1>arg2 && arg2>0 ], cost: 3

   Accelerated rule 18 with backward acceleration, yielding the new rule 20.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 18.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     16: f3 -> f5 : arg2'=1, [ arg1>=0 && arg2>0 ], cost: 2
      6: f5 -> f8 : [ arg1<=arg2 ], cost: 1
      7: f5 -> f8 : [ arg2<=0 ], cost: 1
     20: f5 -> f5 : arg2'=arg2*2^k, [ arg2>0 && k>=0 && arg1>arg2*2^(-1+k) ], cost: 3*k
     19: f8 -> f3 : arg1'=-1+arg1, [], cost: 2
     15: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     16: f3 -> f5 : arg2'=1, [ arg1>=0 && arg2>0 ], cost: 2
     21: f3 -> f5 : arg2'=2^k, [ arg1>=0 && arg2>0 && k>=0 && arg1>2^(-1+k) ], cost: 2+3*k
      6: f5 -> f8 : [ arg1<=arg2 ], cost: 1
      7: f5 -> f8 : [ arg2<=0 ], cost: 1
     19: f8 -> f3 : arg1'=-1+arg1, [], cost: 2
     15: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     22: f3 -> f8 : arg2'=1, [ arg1>=0 && arg2>0 && arg1<=1 ], cost: 3
     23: f3 -> f8 : arg2'=2^k, [ arg1>=0 && arg2>0 && k>=0 && arg1>2^(-1+k) && arg1<=2^k ], cost: 3+3*k
     24: f3 -> f8 : arg2'=2^k, [ arg1>=0 && arg2>0 && k>=0 && arg1>2^(-1+k) && 2^k<=0 ], cost: 3+3*k
     19: f8 -> f3 : arg1'=-1+arg1, [], cost: 2
     15: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

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

Accelerating simple loops of location 2.
   Accelerating the following rules:
     25: f3 -> f3 : arg1'=-1+arg1, arg2'=1, [ arg1>=0 && arg2>0 && arg1<=1 ], cost: 5
     26: f3 -> f3 : arg1'=-1+arg1, arg2'=2^k, [ arg1>=0 && arg2>0 && k>=0 && arg1>2^(-1+k) && arg1<=2^k ], cost: 5+3*k
     27: f3 -> f3 : arg1'=-1+arg1, arg2'=2^k, [ arg1>=0 && arg2>0 && k>=0 && arg1>2^(-1+k) && 2^k<=0 ], cost: 5+3*k

   Accelerated rule 25 with backward acceleration, yielding the new rule 28.
   Failed to prove monotonicity of the guard of rule 26.
   Failed to prove monotonicity of the guard of rule 27.
[accelerate] Nesting with 3 inner and 3 outer candidates
   Removing the simple loops: 25.

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

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

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

### Computing asymptotic complexity ###

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

Computing asymptotic complexity for rule 31
   Resulting cost 0 has complexity: Unknown

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

Computing asymptotic complexity for rule 30
   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),?)