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, arg3'=arg3P_1, [ arg1==arg1P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg2==arg2P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ 0==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
     10: f4 -> f5 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2>=0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     12: f4 -> f12 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg2<0 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
      3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && 1==arg3P_4 ], cost: 1
      6: f6 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg2>arg3 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      8: f6 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg2<=arg3 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      4: f7 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3P_5==2*arg3 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f8 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1P_6==1+arg1 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      7: f9 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      9: f10 -> f11 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2P_10==-1+arg2 && arg1==arg1P_10 && arg3==arg3P_10 ], cost: 1
     11: f11 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_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, arg3'=arg3P_14, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg1==arg1P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg2==arg2P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ 0==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
     10: f4 -> f5 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2>=0 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
      3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1==arg1P_4 && arg2==arg2P_4 && 1==arg3P_4 ], cost: 1
      6: f6 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg2>arg3 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      8: f6 -> f10 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg2<=arg3 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      4: f7 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg3P_5==2*arg3 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f8 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1P_6==1+arg1 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      7: f9 -> f6 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      9: f10 -> f11 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2P_10==-1+arg2 && arg1==arg1P_10 && arg3==arg3P_10 ], cost: 1
     11: f11 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg2'=arg2P_1, [], cost: 1
      1: f2 -> f3 : arg3'=arg3P_2, [], cost: 1
      2: f3 -> f4 : arg1'=0, [], cost: 1
     10: f4 -> f5 : [ arg2>=0 ], cost: 1
      3: f5 -> f6 : arg3'=1, [], cost: 1
      6: f6 -> f7 : [ arg2>arg3 ], cost: 1
      8: f6 -> f10 : [ arg2<=arg3 ], cost: 1
      4: f7 -> f8 : arg3'=2*arg3, [], cost: 1
      5: f8 -> f9 : arg1'=1+arg1, [], cost: 1
      7: f9 -> f6 : [], cost: 1
      9: f10 -> f11 : arg2'=-1+arg2, [], cost: 1
     11: f11 -> f4 : [], cost: 1
     13: __init -> f1 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     17: f4 -> f6 : arg3'=1, [ arg2>=0 ], cost: 2
     21: f6 -> f4 : arg2'=-1+arg2, [ arg2<=arg3 ], cost: 3
     22: f6 -> f6 : arg1'=1+arg1, arg3'=2*arg3, [ arg2>arg3 ], cost: 4
     16: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Accelerating simple loops of location 5.
   Accelerating the following rules:
     22: f6 -> f6 : arg1'=1+arg1, arg3'=2*arg3, [ arg2>arg3 ], cost: 4

[test] deduced invariant -arg3<=0
   Accelerated rule 22 with non-termination, yielding the new rule 23.
   Accelerated rule 22 with non-termination, yielding the new rule 24.
   Accelerated rule 22 with backward acceleration, yielding the new rule 25.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Also removing duplicate rules: 23.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     17: f4 -> f6 : arg3'=1, [ arg2>=0 ], cost: 2
     21: f6 -> f4 : arg2'=-1+arg2, [ arg2<=arg3 ], cost: 3
     22: f6 -> f6 : arg1'=1+arg1, arg3'=2*arg3, [ arg2>arg3 ], cost: 4
     24: f6 -> [13] : [ arg2>arg3 && arg2==1 && arg3==0 ], cost: NONTERM
     25: f6 -> f6 : arg1'=k+arg1, arg3'=arg3*2^k, [ -arg3<=0 && k>=0 && arg2>2^(-1+k)*arg3 ], cost: 4*k
     16: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     17: f4 -> f6 : arg3'=1, [ arg2>=0 ], cost: 2
     26: f4 -> f6 : arg1'=1+arg1, arg3'=2, [ arg2>1 ], cost: 6
     27: f4 -> f6 : arg1'=k+arg1, arg3'=2^k, [ arg2>=0 && k>=0 && arg2>2^(-1+k) ], cost: 2+4*k
     21: f6 -> f4 : arg2'=-1+arg2, [ arg2<=arg3 ], cost: 3
     16: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     17: f4 -> f6 : arg3'=1, [ arg2>=0 ], cost: 2
     26: f4 -> f6 : arg1'=1+arg1, arg3'=2, [ arg2>1 ], cost: 6
     27: f4 -> f6 : arg1'=k+arg1, arg3'=2^k, [ arg2>=0 && k>=0 && arg2>2^(-1+k) ], cost: 2+4*k
     21: f6 -> f4 : arg2'=-1+arg2, [ arg2<=arg3 ], cost: 3
     16: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     28: f4 -> f4 : arg2'=-1+arg2, arg3'=1, [ arg2>=0 && arg2<=1 ], cost: 5
     29: f4 -> f4 : arg1'=1+arg1, arg2'=-1+arg2, arg3'=2, [ arg2>1 && arg2<=2 ], cost: 9
     30: f4 -> f4 : arg1'=k+arg1, arg2'=-1+arg2, arg3'=2^k, [ arg2>=0 && k>=0 && arg2>2^(-1+k) && arg2<=2^k ], cost: 5+4*k
     16: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Accelerating simple loops of location 3.
   Simplified some of the simple loops (and removed duplicate rules).
   Accelerating the following rules:
     28: f4 -> f4 : arg2'=-1+arg2, arg3'=1, [ arg2>=0 && arg2<=1 ], cost: 5
     29: f4 -> f4 : arg1'=1+arg1, arg2'=-1+arg2, arg3'=2, [ 2-arg2==0 ], cost: 9
     30: f4 -> f4 : arg1'=k+arg1, arg2'=-1+arg2, arg3'=2^k, [ arg2>=0 && k>=0 && arg2>2^(-1+k) && arg2<=2^k ], cost: 5+4*k

   Accelerated rule 28 with backward acceleration, yielding the new rule 31.
   Failed to prove monotonicity of the guard of rule 29.
   Failed to prove monotonicity of the guard of rule 30.
[accelerate] Nesting with 3 inner and 3 outer candidates
   Removing the simple loops: 28.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     29: f4 -> f4 : arg1'=1+arg1, arg2'=-1+arg2, arg3'=2, [ 2-arg2==0 ], cost: 9
     30: f4 -> f4 : arg1'=k+arg1, arg2'=-1+arg2, arg3'=2^k, [ arg2>=0 && k>=0 && arg2>2^(-1+k) && arg2<=2^k ], cost: 5+4*k
     31: f4 -> f4 : arg2'=-1, arg3'=1, [ arg2<=1 && 1+arg2>=1 ], cost: 5+5*arg2
     16: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     16: __init -> f4 : arg1'=0, arg2'=arg2P_1, arg3'=arg3P_2, [], cost: 4
     32: __init -> f4 : arg1'=1, arg2'=1, arg3'=2, [], cost: 13
     33: __init -> f4 : arg1'=k, arg2'=-1+arg2P_1, arg3'=2^k, [ arg2P_1>=0 && k>=0 && arg2P_1>2^(-1+k) && arg2P_1<=2^k ], cost: 9+4*k
     34: __init -> f4 : arg1'=0, arg2'=-1, arg3'=1, [ arg2P_1<=1 && 1+arg2P_1>=1 ], cost: 9+5*arg2P_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     33: __init -> f4 : arg1'=k, arg2'=-1+arg2P_1, arg3'=2^k, [ arg2P_1>=0 && k>=0 && arg2P_1>2^(-1+k) && arg2P_1<=2^k ], cost: 9+4*k
     34: __init -> f4 : arg1'=0, arg2'=-1, arg3'=1, [ arg2P_1<=1 && 1+arg2P_1>=1 ], cost: 9+5*arg2P_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     33: __init -> f4 : arg1'=k, arg2'=-1+arg2P_1, arg3'=2^k, [ arg2P_1>=0 && k>=0 && arg2P_1>2^(-1+k) && arg2P_1<=2^k ], cost: 9+4*k
     34: __init -> f4 : arg1'=0, arg2'=-1, arg3'=1, [ arg2P_1<=1 && 1+arg2P_1>=1 ], cost: 9+5*arg2P_1

Computing asymptotic complexity for rule 34
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 33
   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),?)