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, [ arg2==arg2P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg3==arg3P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1
      5: f4 -> f5 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg2+arg1>=0 && arg1<=arg3 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      7: f4 -> f8 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg2+arg1<0 && arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      8: f4 -> f8 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1>arg3 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==arg2+2*arg1 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
      4: f6 -> f7 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2P_5==1+arg2 && arg1==arg1P_5 && arg3==arg3P_5 ], cost: 1
      6: f7 -> f4 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      9: __init -> f1 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
      9: __init -> f1 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, arg3'=arg3P_1, [ arg2==arg2P_1 && arg3==arg3P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg3==arg3P_2 ], cost: 1
      2: f3 -> f4 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg1==arg1P_3 && arg2==arg2P_3 ], cost: 1
      5: f4 -> f5 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg2+arg1>=0 && arg1<=arg3 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==arg2+2*arg1 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
      4: f6 -> f7 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg2P_5==1+arg2 && arg1==arg1P_5 && arg3==arg3P_5 ], cost: 1
      6: f7 -> f4 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      9: __init -> f1 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [], 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
      2: f3 -> f4 : arg3'=arg3P_3, [], cost: 1
      5: f4 -> f5 : [ arg2+arg1>=0 && arg1<=arg3 ], cost: 1
      3: f5 -> f6 : arg1'=arg2+2*arg1, [], cost: 1
      4: f6 -> f7 : arg2'=1+arg2, [], cost: 1
      6: f7 -> f4 : [], cost: 1
      9: __init -> f1 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     15: f4 -> f4 : arg1'=arg2+2*arg1, arg2'=1+arg2, [ arg2+arg1>=0 && arg1<=arg3 ], cost: 4
     12: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4

Accelerating simple loops of location 3.
   Accelerating the following rules:
     15: f4 -> f4 : arg1'=arg2+2*arg1, arg2'=1+arg2, [ arg2+arg1>=0 && arg1<=arg3 ], cost: 4

   Accelerated rule 15 with backward acceleration, yielding the new rule 16.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 15.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     16: f4 -> f4 : arg1'=-1-arg2-k+arg1*2^k+arg2*2^k+2^k, arg2'=arg2+k, [ arg2+arg1>=0 && k>=0 && -arg2+2^(-1+k)*arg1-k+2^(-1+k)+arg2*2^(-1+k)<=arg3 ], cost: 4*k
     12: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     12: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [], cost: 4
     17: __init -> f4 : arg1'=-1-k+arg1P_1*2^k+arg2P_2*2^k-arg2P_2+2^k, arg2'=k+arg2P_2, arg3'=arg3P_3, [ arg1P_1+arg2P_2>=0 && k>=0 && 2^(-1+k)*arg1P_1-k+2^(-1+k)+2^(-1+k)*arg2P_2-arg2P_2<=arg3P_3 ], cost: 4+4*k

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     17: __init -> f4 : arg1'=-1-k+arg1P_1*2^k+arg2P_2*2^k-arg2P_2+2^k, arg2'=k+arg2P_2, arg3'=arg3P_3, [ arg1P_1+arg2P_2>=0 && k>=0 && 2^(-1+k)*arg1P_1-k+2^(-1+k)+2^(-1+k)*arg2P_2-arg2P_2<=arg3P_3 ], cost: 4+4*k

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     17: __init -> f4 : arg1'=-1-k+arg1P_1*2^k+arg2P_2*2^k-arg2P_2+2^k, arg2'=k+arg2P_2, arg3'=arg3P_3, [ arg1P_1+arg2P_2>=0 && k>=0 && 2^(-1+k)*arg1P_1-k+2^(-1+k)+2^(-1+k)*arg2P_2-arg2P_2<=arg3P_3 ], cost: 4+4*k

Computing asymptotic complexity for rule 17
   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),?)