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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     10: __init -> f1 : arg1'=arg1P_11, arg2'=arg2P_11, [], cost: 1

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

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, [], cost: 1
      7: f2 -> f3 : [ arg1>=0 ], cost: 1
      1: f3 -> f4 : arg2'=1, [], cost: 1
      3: f4 -> f5 : [ arg1>arg2 ], cost: 1
      5: f4 -> f7 : [ arg1<=arg2 ], cost: 1
      2: f5 -> f6 : arg2'=2*arg2, [], cost: 1
      4: f6 -> f4 : [], cost: 1
      6: f7 -> f8 : arg1'=-1+arg1, [], cost: 1
      8: f8 -> f2 : [], cost: 1
     10: __init -> f1 : arg1'=arg1P_11, arg2'=arg2P_11, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     12: f2 -> f4 : arg2'=1, [ arg1>=0 ], cost: 2
     15: f4 -> f4 : arg2'=2*arg2, [ arg1>arg2 ], cost: 3
     16: f4 -> f2 : arg1'=-1+arg1, [ arg1<=arg2 ], cost: 3
     11: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_11, [], cost: 2

Accelerating simple loops of location 3.
   Accelerating the following rules:
     15: f4 -> f4 : arg2'=2*arg2, [ arg1>arg2 ], cost: 3

[test] deduced invariant 1-arg2<=0
   Accelerated rule 15 with non-termination, yielding the new rule 17.
   Accelerated rule 15 with backward acceleration, yielding the new rule 18.
[accelerate] Nesting with 1 inner and 1 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     12: f2 -> f4 : arg2'=1, [ arg1>=0 ], cost: 2
     15: f4 -> f4 : arg2'=2*arg2, [ arg1>arg2 ], cost: 3
     16: f4 -> f2 : arg1'=-1+arg1, [ arg1<=arg2 ], cost: 3
     17: f4 -> [10] : [ arg1>arg2 && arg2==0 && arg1==1 ], cost: NONTERM
     18: f4 -> f4 : arg2'=2^k*arg2, [ 1-arg2<=0 && k>=0 && arg1>arg2*2^(-1+k) ], cost: 3*k
     11: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_11, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: __init
     12: f2 -> f4 : arg2'=1, [ arg1>=0 ], cost: 2
     19: f2 -> f4 : arg2'=2, [ arg1>1 ], cost: 5
     20: f2 -> f4 : arg2'=2^k, [ arg1>=0 && k>=0 && arg1>2^(-1+k) ], cost: 2+3*k
     16: f4 -> f2 : arg1'=-1+arg1, [ arg1<=arg2 ], cost: 3
     11: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_11, [], cost: 2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     12: f2 -> f4 : arg2'=1, [ arg1>=0 ], cost: 2
     19: f2 -> f4 : arg2'=2, [ arg1>1 ], cost: 5
     20: f2 -> f4 : arg2'=2^k, [ arg1>=0 && k>=0 && arg1>2^(-1+k) ], cost: 2+3*k
     16: f4 -> f2 : arg1'=-1+arg1, [ arg1<=arg2 ], cost: 3
     11: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_11, [], cost: 2

Eliminated locations (on tree-shaped paths):
   Start location: __init
     21: f2 -> f2 : arg1'=-1+arg1, arg2'=1, [ arg1>=0 && arg1<=1 ], cost: 5
     22: f2 -> f2 : arg1'=-1+arg1, arg2'=2, [ arg1>1 && arg1<=2 ], cost: 8
     23: f2 -> f2 : arg1'=-1+arg1, arg2'=2^k, [ arg1>=0 && k>=0 && arg1>2^(-1+k) && arg1<=2^k ], cost: 5+3*k
     11: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_11, [], cost: 2

Accelerating simple loops of location 1.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     21: f2 -> f2 : arg1'=-1+arg1, arg2'=1, [ arg1>=0 && arg1<=1 ], cost: 5
     22: f2 -> f2 : arg1'=-1+arg1, arg2'=2, [ 2-arg1==0 ], cost: 8
     23: f2 -> f2 : arg1'=-1+arg1, arg2'=2^k, [ arg1>=0 && k>=0 && arg1>2^(-1+k) && arg1<=2^k ], cost: 5+3*k

   Accelerated rule 21 with backward acceleration, yielding the new rule 24.
   Failed to prove monotonicity of the guard of rule 22.
   Failed to prove monotonicity of the guard of rule 23.
[accelerate] Nesting with 3 inner and 3 outer candidates
   Removing the simple loops: 21.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     22: f2 -> f2 : arg1'=-1+arg1, arg2'=2, [ 2-arg1==0 ], cost: 8
     23: f2 -> f2 : arg1'=-1+arg1, arg2'=2^k, [ arg1>=0 && k>=0 && arg1>2^(-1+k) && arg1<=2^k ], cost: 5+3*k
     24: f2 -> f2 : arg1'=-1, arg2'=1, [ arg1<=1 && 1+arg1>=1 ], cost: 5+5*arg1
     11: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_11, [], cost: 2

Chained accelerated rules (with incoming rules):
   Start location: __init
     11: __init -> f2 : arg1'=arg1P_1, arg2'=arg2P_11, [], cost: 2
     25: __init -> f2 : arg1'=1, arg2'=2, [], cost: 10
     26: __init -> f2 : arg1'=-1+arg1P_1, arg2'=2^k, [ arg1P_1>=0 && k>=0 && arg1P_1>2^(-1+k) && arg1P_1<=2^k ], cost: 7+3*k
     27: __init -> f2 : arg1'=-1, arg2'=1, [ arg1P_1<=1 && 1+arg1P_1>=1 ], cost: 7+5*arg1P_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     26: __init -> f2 : arg1'=-1+arg1P_1, arg2'=2^k, [ arg1P_1>=0 && k>=0 && arg1P_1>2^(-1+k) && arg1P_1<=2^k ], cost: 7+3*k
     27: __init -> f2 : arg1'=-1, arg2'=1, [ arg1P_1<=1 && 1+arg1P_1>=1 ], cost: 7+5*arg1P_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     26: __init -> f2 : arg1'=-1+arg1P_1, arg2'=2^k, [ arg1P_1>=0 && k>=0 && arg1P_1>2^(-1+k) && arg1P_1<=2^k ], cost: 7+3*k
     27: __init -> f2 : arg1'=-1, arg2'=1, [ arg1P_1<=1 && 1+arg1P_1>=1 ], cost: 7+5*arg1P_1

Computing asymptotic complexity for rule 27
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 26
   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),?)