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 && arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg3==arg3P_2 ], cost: 1
     12: f3 -> f4 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg2>0 && arg3>arg2 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
     13: f3 -> f5 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg2<=0 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     14: f3 -> f5 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg3<=arg2 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
      2: f4 -> f7 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg3==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
      9: f7 -> f8 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1>0 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
     11: f7 -> f14 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1<=0 && arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
      3: f9 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==-1+arg1 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
      7: f12 -> f11 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      4: f10 -> f13 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_5==-arg2+arg1 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      8: f13 -> f11 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      5: f8 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1<arg2 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f8 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1>=arg2 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
     10: f11 -> f7 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     15: f14 -> f6 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1
     16: f5 -> f6 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [ arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 ], cost: 1
     17: __init -> f1 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     17: __init -> f1 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], 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 && arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, arg3'=arg3P_2, [ arg1==arg1P_2 && arg3==arg3P_2 ], cost: 1
     12: f3 -> f4 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg2>0 && arg3>arg2 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
      2: f4 -> f7 : arg1'=arg1P_3, arg2'=arg2P_3, arg3'=arg3P_3, [ arg3==arg1P_3 && arg2==arg2P_3 && arg3==arg3P_3 ], cost: 1
      9: f7 -> f8 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg1>0 && arg1==arg1P_10 && arg2==arg2P_10 && arg3==arg3P_10 ], cost: 1
      3: f9 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==-1+arg1 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
      7: f12 -> f11 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      4: f10 -> f13 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_5==-arg2+arg1 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      8: f13 -> f11 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      5: f8 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg1<arg2 && arg1==arg1P_6 && arg2==arg2P_6 && arg3==arg3P_6 ], cost: 1
      6: f8 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg1>=arg2 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
     10: f11 -> f7 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     17: __init -> f1 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], cost: 1

Simplified all rules, resulting in:
   Start location: __init
      0: f1 -> f2 : arg3'=arg3P_1, [], cost: 1
      1: f2 -> f3 : arg2'=arg2P_2, [], cost: 1
     12: f3 -> f4 : [ arg2>0 && arg3>arg2 ], cost: 1
      2: f4 -> f7 : arg1'=arg3, [], cost: 1
      9: f7 -> f8 : [ arg1>0 ], cost: 1
      3: f9 -> f12 : arg1'=-1+arg1, [], cost: 1
      7: f12 -> f11 : [], cost: 1
      4: f10 -> f13 : arg1'=-arg2+arg1, [], cost: 1
      8: f13 -> f11 : [], cost: 1
      5: f8 -> f9 : [ arg1<arg2 ], cost: 1
      6: f8 -> f10 : [ arg1>=arg2 ], cost: 1
     10: f11 -> f7 : [], cost: 1
     17: __init -> f1 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
      9: f7 -> f8 : [ arg1>0 ], cost: 1
     24: f8 -> f11 : arg1'=-1+arg1, [ arg1<arg2 ], cost: 3
     25: f8 -> f11 : arg1'=-arg2+arg1, [ arg1>=arg2 ], cost: 3
     10: f11 -> f7 : [], cost: 1
     21: __init -> f7 : arg1'=arg3P_1, arg2'=arg2P_2, arg3'=arg3P_1, [ arg2P_2>0 && arg3P_1>arg2P_2 ], cost: 5

Eliminated locations (on tree-shaped paths):
   Start location: __init
     26: f7 -> f11 : arg1'=-1+arg1, [ arg1>0 && arg1<arg2 ], cost: 4
     27: f7 -> f11 : arg1'=-arg2+arg1, [ arg1>0 && arg1>=arg2 ], cost: 4
     10: f11 -> f7 : [], cost: 1
     21: __init -> f7 : arg1'=arg3P_1, arg2'=arg2P_2, arg3'=arg3P_1, [ arg2P_2>0 && arg3P_1>arg2P_2 ], cost: 5

Eliminated locations (on tree-shaped paths):
   Start location: __init
     28: f7 -> f7 : arg1'=-1+arg1, [ arg1>0 && arg1<arg2 ], cost: 5
     29: f7 -> f7 : arg1'=-arg2+arg1, [ arg1>0 && arg1>=arg2 ], cost: 5
     21: __init -> f7 : arg1'=arg3P_1, arg2'=arg2P_2, arg3'=arg3P_1, [ arg2P_2>0 && arg3P_1>arg2P_2 ], cost: 5

Accelerating simple loops of location 4.
   Accelerating the following rules:
     28: f7 -> f7 : arg1'=-1+arg1, [ arg1>0 && arg1<arg2 ], cost: 5
     29: f7 -> f7 : arg1'=-arg2+arg1, [ arg1>0 && arg1>=arg2 ], cost: 5

   Accelerated rule 28 with backward acceleration, yielding the new rule 30.
[test] deduced invariant 1-2*arg2<=0
   Accelerated rule 29 with non-termination, yielding the new rule 31.
   Accelerated rule 29 with backward acceleration, yielding the new rule 32.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 28.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     29: f7 -> f7 : arg1'=-arg2+arg1, [ arg1>0 && arg1>=arg2 ], cost: 5
     30: f7 -> f7 : arg1'=0, [ arg1<arg2 && arg1>=0 ], cost: 5*arg1
     31: f7 -> [15] : [ arg1>=arg2 && arg2==0 && arg1==1 ], cost: NONTERM
     32: f7 -> f7 : arg1'=-arg2*k_2+arg1, [ 1-2*arg2<=0 && k_2>=0 && -arg2*(-1+k_2)+arg1>0 && -arg2*(-1+k_2)+arg1>=arg2 ], cost: 5*k_2
     21: __init -> f7 : arg1'=arg3P_1, arg2'=arg2P_2, arg3'=arg3P_1, [ arg2P_2>0 && arg3P_1>arg2P_2 ], cost: 5

Chained accelerated rules (with incoming rules):
   Start location: __init
     21: __init -> f7 : arg1'=arg3P_1, arg2'=arg2P_2, arg3'=arg3P_1, [ arg2P_2>0 && arg3P_1>arg2P_2 ], cost: 5
     33: __init -> f7 : arg1'=arg3P_1-arg2P_2, arg2'=arg2P_2, arg3'=arg3P_1, [ arg2P_2>0 && arg3P_1>arg2P_2 && arg3P_1>0 ], cost: 10
     34: __init -> f7 : arg1'=arg3P_1-k_2*arg2P_2, arg2'=arg2P_2, arg3'=arg3P_1, [ arg2P_2>0 && arg3P_1>arg2P_2 && 1-2*arg2P_2<=0 && k_2>=0 && arg3P_1-arg2P_2*(-1+k_2)>0 && arg3P_1-arg2P_2*(-1+k_2)>=arg2P_2 ], cost: 5+5*k_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     34: __init -> f7 : arg1'=arg3P_1-k_2*arg2P_2, arg2'=arg2P_2, arg3'=arg3P_1, [ arg2P_2>0 && arg3P_1>arg2P_2 && 1-2*arg2P_2<=0 && k_2>=0 && arg3P_1-arg2P_2*(-1+k_2)>0 && arg3P_1-arg2P_2*(-1+k_2)>=arg2P_2 ], cost: 5+5*k_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     34: __init -> f7 : arg1'=arg3P_1-k_2*arg2P_2, arg2'=arg2P_2, arg3'=arg3P_1, [ arg2P_2>0 && arg3P_1>arg2P_2 && 1-2*arg2P_2<=0 && k_2>=0 && arg3P_1-arg2P_2*(-1+k_2)>0 && arg3P_1-arg2P_2*(-1+k_2)>=arg2P_2 ], cost: 5+5*k_2

Computing asymptotic complexity for rule 34
   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),?)