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, [ 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, [ 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, [ 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 : [ 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, [ 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, [ arg1>=0 && arg1<=arg3 ], cost: 4

[test] deduced pseudo-invariant -arg2-arg1<=0, also trying arg2+arg1<=-1
   Accelerated rule 15 with backward acceleration, yielding the new rule 16.
   Accelerated rule 15 with backward acceleration, yielding the new rule 17.
[accelerate] Nesting with 2 inner and 1 outer candidates

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     15: f4 -> f4 : arg1'=arg2+2*arg1, arg2'=1+arg2, [ arg1>=0 && arg1<=arg3 ], cost: 4
     16: f4 -> f4 : arg1'=-1-arg2+2^k+2^k*arg1+arg2*2^k-k, arg2'=arg2+k, [ arg1>=0 && -arg2-arg1<=0 && k>=0 && 2^(-1+k)-arg2+2^(-1+k)*arg1+2^(-1+k)*arg2-k<=arg3 ], cost: 4*k
     17: f4 -> f4 : arg1'=-1-1/2*2^k_1*arg2-1/2*2^k_1-1/2*2^k_1*arg1+arg1*2^(1/2*2^k_1*arg2+1/2*2^k_1-arg2+1/2*2^k_1*arg1)+2^(1/2*2^k_1*arg2+1/2*2^k_1-arg2+1/2*2^k_1*arg1)+arg2*2^(1/2*2^k_1*arg2+1/2*2^k_1-arg2+1/2*2^k_1*arg1), arg2'=1/2*2^k_1*arg2+1/2*2^k_1+1/2*2^k_1*arg1, [ arg1<=arg3 && arg2+arg1<=-1 && 1/2*2^k_1*arg2+1/2*2^k_1-arg2+1/2*2^k_1*arg1>=0 && -1/2*2^k_1*arg2-1/2*2^k_1+2^(-1+1/2*2^k_1*arg2+1/2*2^k_1-arg2+1/2*2^k_1*arg1)+arg2*2^(-1+1/2*2^k_1*arg2+1/2*2^k_1-arg2+1/2*2^k_1*arg1)-1/2*2^k_1*arg1+2^(-1+1/2*2^k_1*arg2+1/2*2^k_1-arg2+1/2*2^k_1*arg1)*arg1>=0 ], cost: 2*2^k_1*arg2+2*2^k_1-4*arg2+2*2^k_1*arg1
     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
     18: __init -> f4 : arg1'=2*arg1P_1+arg2P_2, arg2'=1+arg2P_2, arg3'=arg3P_3, [ arg1P_1>=0 && arg1P_1<=arg3P_3 ], cost: 8
     19: __init -> f4 : arg1'=-1+2^k+2^k*arg1P_1-arg2P_2-k+2^k*arg2P_2, arg2'=arg2P_2+k, arg3'=arg3P_3, [ arg1P_1>=0 && -arg1P_1-arg2P_2<=0 && k>=0 && 2^(-1+k)+2^(-1+k)*arg1P_1-arg2P_2+2^(-1+k)*arg2P_2-k<=arg3P_3 ], cost: 4+4*k
     20: __init -> f4 : arg1'=-1-1/2*2^k_1*arg2P_2-1/2*2^k_1+2^(1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)+2^(1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)*arg1P_1-1/2*2^k_1*arg1P_1+2^(1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)*arg2P_2, arg2'=1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1, arg3'=arg3P_3, [ arg1P_1<=arg3P_3 && arg1P_1+arg2P_2<=-1 && 1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2>=0 && -1/2*2^k_1*arg2P_2-1/2*2^k_1+arg1P_1*2^(-1+1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)+2^(-1+1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)-1/2*2^k_1*arg1P_1+2^(-1+1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)*arg2P_2>=0 ], cost: 4+2*2^k_1*arg2P_2+2*2^k_1+2*2^k_1*arg1P_1-4*arg2P_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     19: __init -> f4 : arg1'=-1+2^k+2^k*arg1P_1-arg2P_2-k+2^k*arg2P_2, arg2'=arg2P_2+k, arg3'=arg3P_3, [ arg1P_1>=0 && -arg1P_1-arg2P_2<=0 && k>=0 && 2^(-1+k)+2^(-1+k)*arg1P_1-arg2P_2+2^(-1+k)*arg2P_2-k<=arg3P_3 ], cost: 4+4*k
     20: __init -> f4 : arg1'=-1-1/2*2^k_1*arg2P_2-1/2*2^k_1+2^(1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)+2^(1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)*arg1P_1-1/2*2^k_1*arg1P_1+2^(1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)*arg2P_2, arg2'=1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1, arg3'=arg3P_3, [ arg1P_1<=arg3P_3 && arg1P_1+arg2P_2<=-1 && 1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2>=0 && -1/2*2^k_1*arg2P_2-1/2*2^k_1+arg1P_1*2^(-1+1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)+2^(-1+1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)-1/2*2^k_1*arg1P_1+2^(-1+1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)*arg2P_2>=0 ], cost: 4+2*2^k_1*arg2P_2+2*2^k_1+2*2^k_1*arg1P_1-4*arg2P_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     19: __init -> f4 : arg1'=-1+2^k+2^k*arg1P_1-arg2P_2-k+2^k*arg2P_2, arg2'=arg2P_2+k, arg3'=arg3P_3, [ arg1P_1>=0 && -arg1P_1-arg2P_2<=0 && k>=0 && 2^(-1+k)+2^(-1+k)*arg1P_1-arg2P_2+2^(-1+k)*arg2P_2-k<=arg3P_3 ], cost: 4+4*k
     20: __init -> f4 : arg1'=-1-1/2*2^k_1*arg2P_2-1/2*2^k_1+2^(1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)+2^(1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)*arg1P_1-1/2*2^k_1*arg1P_1+2^(1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)*arg2P_2, arg2'=1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1, arg3'=arg3P_3, [ arg1P_1<=arg3P_3 && arg1P_1+arg2P_2<=-1 && 1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2>=0 && -1/2*2^k_1*arg2P_2-1/2*2^k_1+arg1P_1*2^(-1+1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)+2^(-1+1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)-1/2*2^k_1*arg1P_1+2^(-1+1/2*2^k_1*arg2P_2+1/2*2^k_1+1/2*2^k_1*arg1P_1-arg2P_2)*arg2P_2>=0 ], cost: 4+2*2^k_1*arg2P_2+2*2^k_1+2*2^k_1*arg1P_1-4*arg2P_2

Computing asymptotic complexity for rule 20
   Resulting cost 0 has complexity: Unknown

Computing asymptotic complexity for rule 19
   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),?)