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
     13: f4 -> f5 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1<=10000 && arg1>=-10000 && arg2<=10000 && arg3<=10000 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
     14: f4 -> f6 : arg1'=arg1P_15, arg2'=arg2P_15, arg3'=arg3P_15, [ arg3>10000 && arg1==arg1P_15 && arg2==arg2P_15 && arg3==arg3P_15 ], cost: 1
     15: f4 -> f6 : arg1'=arg1P_16, arg2'=arg2P_16, arg3'=arg3P_16, [ arg2>10000 && arg1==arg1P_16 && arg2==arg2P_16 && arg3==arg3P_16 ], cost: 1
     16: f4 -> f6 : arg1'=arg1P_17, arg2'=arg2P_17, arg3'=arg3P_17, [ arg1>10000 && arg1==arg1P_17 && arg2==arg2P_17 && arg3==arg3P_17 ], cost: 1
     17: f4 -> f6 : arg1'=arg1P_18, arg2'=arg2P_18, arg3'=arg3P_18, [ arg1<-10000 && arg1==arg1P_18 && arg2==arg2P_18 && arg3==arg3P_18 ], cost: 1
      3: f8 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==-1+arg1 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
      6: f9 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg2<arg3 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      8: f9 -> f13 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg2>=arg3 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      4: f10 -> f11 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_5==1+arg1 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      5: f11 -> f12 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg3P_6==-1+arg3 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      7: f12 -> f9 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      9: f13 -> f14 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2P_10==arg2+arg1 && arg1==arg1P_10 && arg3==arg3P_10 ], cost: 1
     11: f14 -> f5 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     10: f5 -> f8 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2>=1 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     12: f5 -> f15 : arg1'=arg1P_13, arg2'=arg2P_13, arg3'=arg3P_13, [ arg2<1 && arg1==arg1P_13 && arg2==arg2P_13 && arg3==arg3P_13 ], cost: 1
     18: f15 -> f7 : arg1'=arg1P_19, arg2'=arg2P_19, arg3'=arg3P_19, [ arg1==arg1P_19 && arg2==arg2P_19 && arg3==arg3P_19 ], cost: 1
     19: f6 -> f7 : arg1'=arg1P_20, arg2'=arg2P_20, arg3'=arg3P_20, [ arg1==arg1P_20 && arg2==arg2P_20 && arg3==arg3P_20 ], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, [], 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
     13: f4 -> f5 : arg1'=arg1P_14, arg2'=arg2P_14, arg3'=arg3P_14, [ arg1<=10000 && arg1>=-10000 && arg2<=10000 && arg3<=10000 && arg1==arg1P_14 && arg2==arg2P_14 && arg3==arg3P_14 ], cost: 1
      3: f8 -> f9 : arg1'=arg1P_4, arg2'=arg2P_4, arg3'=arg3P_4, [ arg1P_4==-1+arg1 && arg2==arg2P_4 && arg3==arg3P_4 ], cost: 1
      6: f9 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, arg3'=arg3P_7, [ arg2<arg3 && arg1==arg1P_7 && arg2==arg2P_7 && arg3==arg3P_7 ], cost: 1
      8: f9 -> f13 : arg1'=arg1P_9, arg2'=arg2P_9, arg3'=arg3P_9, [ arg2>=arg3 && arg1==arg1P_9 && arg2==arg2P_9 && arg3==arg3P_9 ], cost: 1
      4: f10 -> f11 : arg1'=arg1P_5, arg2'=arg2P_5, arg3'=arg3P_5, [ arg1P_5==1+arg1 && arg2==arg2P_5 && arg3==arg3P_5 ], cost: 1
      5: f11 -> f12 : arg1'=arg1P_6, arg2'=arg2P_6, arg3'=arg3P_6, [ arg3P_6==-1+arg3 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
      7: f12 -> f9 : arg1'=arg1P_8, arg2'=arg2P_8, arg3'=arg3P_8, [ arg1==arg1P_8 && arg2==arg2P_8 && arg3==arg3P_8 ], cost: 1
      9: f13 -> f14 : arg1'=arg1P_10, arg2'=arg2P_10, arg3'=arg3P_10, [ arg2P_10==arg2+arg1 && arg1==arg1P_10 && arg3==arg3P_10 ], cost: 1
     11: f14 -> f5 : arg1'=arg1P_12, arg2'=arg2P_12, arg3'=arg3P_12, [ arg1==arg1P_12 && arg2==arg2P_12 && arg3==arg3P_12 ], cost: 1
     10: f5 -> f8 : arg1'=arg1P_11, arg2'=arg2P_11, arg3'=arg3P_11, [ arg2>=1 && arg1==arg1P_11 && arg2==arg2P_11 && arg3==arg3P_11 ], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, [], 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
     13: f4 -> f5 : [ arg1<=10000 && arg1>=-10000 && arg2<=10000 && arg3<=10000 ], cost: 1
      3: f8 -> f9 : arg1'=-1+arg1, [], cost: 1
      6: f9 -> f10 : [ arg2<arg3 ], cost: 1
      8: f9 -> f13 : [ arg2>=arg3 ], cost: 1
      4: f10 -> f11 : arg1'=1+arg1, [], cost: 1
      5: f11 -> f12 : arg3'=-1+arg3, [], cost: 1
      7: f12 -> f9 : [], cost: 1
      9: f13 -> f14 : arg2'=arg2+arg1, [], cost: 1
     11: f14 -> f5 : [], cost: 1
     10: f5 -> f8 : [ arg2>=1 ], cost: 1
     20: __init -> f1 : arg1'=arg1P_21, arg2'=arg2P_21, arg3'=arg3P_21, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     29: f9 -> f5 : arg2'=arg2+arg1, [ arg2>=arg3 ], cost: 3
     30: f9 -> f9 : arg1'=1+arg1, arg3'=-1+arg3, [ arg2<arg3 ], cost: 4
     25: f5 -> f9 : arg1'=-1+arg1, [ arg2>=1 ], cost: 2
     24: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [ arg1P_1<=10000 && arg1P_1>=-10000 && arg2P_2<=10000 && arg3P_3<=10000 ], cost: 5

Accelerating simple loops of location 5.
   Accelerating the following rules:
     30: f9 -> f9 : arg1'=1+arg1, arg3'=-1+arg3, [ arg2<arg3 ], cost: 4

   Accelerated rule 30 with backward acceleration, yielding the new rule 31.
[accelerate] Nesting with 1 inner and 1 outer candidates
   Removing the simple loops: 30.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     29: f9 -> f5 : arg2'=arg2+arg1, [ arg2>=arg3 ], cost: 3
     31: f9 -> f9 : arg1'=-arg2+arg3+arg1, arg3'=arg2, [ -arg2+arg3>=0 ], cost: -4*arg2+4*arg3
     25: f5 -> f9 : arg1'=-1+arg1, [ arg2>=1 ], cost: 2
     24: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [ arg1P_1<=10000 && arg1P_1>=-10000 && arg2P_2<=10000 && arg3P_3<=10000 ], cost: 5

Chained accelerated rules (with incoming rules):
   Start location: __init
     29: f9 -> f5 : arg2'=arg2+arg1, [ arg2>=arg3 ], cost: 3
     25: f5 -> f9 : arg1'=-1+arg1, [ arg2>=1 ], cost: 2
     32: f5 -> f9 : arg1'=-1-arg2+arg3+arg1, arg3'=arg2, [ arg2>=1 && -arg2+arg3>=0 ], cost: 2-4*arg2+4*arg3
     24: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [ arg1P_1<=10000 && arg1P_1>=-10000 && arg2P_2<=10000 && arg3P_3<=10000 ], cost: 5

Eliminated locations (on tree-shaped paths):
   Start location: __init
     33: f5 -> f5 : arg1'=-1+arg1, arg2'=-1+arg2+arg1, [ arg2>=1 && arg2>=arg3 ], cost: 5
     34: f5 -> f5 : arg1'=-1-arg2+arg3+arg1, arg2'=-1+arg3+arg1, arg3'=arg2, [ arg2>=1 && -arg2+arg3>=0 ], cost: 5-4*arg2+4*arg3
     24: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [ arg1P_1<=10000 && arg1P_1>=-10000 && arg2P_2<=10000 && arg3P_3<=10000 ], cost: 5

Accelerating simple loops of location 11.
   Accelerating the following rules:
     33: f5 -> f5 : arg1'=-1+arg1, arg2'=-1+arg2+arg1, [ arg2>=1 && arg2>=arg3 ], cost: 5
     34: f5 -> f5 : arg1'=-1-arg2+arg3+arg1, arg2'=-1+arg3+arg1, arg3'=arg2, [ arg2>=1 && -arg2+arg3>=0 ], cost: 5-4*arg2+4*arg3

   Failed to prove monotonicity of the guard of rule 33.
   Accelerated rule 34 with backward acceleration, yielding the new rule 35.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 34.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     33: f5 -> f5 : arg1'=-1+arg1, arg2'=-1+arg2+arg1, [ arg2>=1 && arg2>=arg3 ], cost: 5
     35: f5 -> f5 : arg1'=-1, arg2'=-1+arg3-2*k_2, arg3'=arg3-2*k_2, [ -arg2+arg3>=0 && 1+arg2-arg3-arg1>=0 && k_2>=1 && arg3-2*k_2>=1 ], cost: 18*k_2
     24: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [ arg1P_1<=10000 && arg1P_1>=-10000 && arg2P_2<=10000 && arg3P_3<=10000 ], cost: 5

Chained accelerated rules (with incoming rules):
   Start location: __init
     24: __init -> f5 : arg1'=arg1P_1, arg2'=arg2P_2, arg3'=arg3P_3, [ arg1P_1<=10000 && arg1P_1>=-10000 && arg2P_2<=10000 && arg3P_3<=10000 ], cost: 5
     36: __init -> f5 : arg1'=-1+arg1P_1, arg2'=-1+arg1P_1+arg2P_2, arg3'=arg3P_3, [ arg1P_1<=10000 && arg1P_1>=-10000 && arg2P_2<=10000 && arg3P_3<=10000 && arg2P_2>=1 && arg2P_2>=arg3P_3 ], cost: 10
     37: __init -> f5 : arg1'=-1, arg2'=-1-2*k_2+arg3P_3, arg3'=-2*k_2+arg3P_3, [ arg3P_3<=10000 && k_2>=1 && -2*k_2+arg3P_3>=1 ], cost: 5+18*k_2

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     37: __init -> f5 : arg1'=-1, arg2'=-1-2*k_2+arg3P_3, arg3'=-2*k_2+arg3P_3, [ arg3P_3<=10000 && k_2>=1 && -2*k_2+arg3P_3>=1 ], cost: 5+18*k_2

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     37: __init -> f5 : arg1'=-1, arg2'=-1-2*k_2+arg3P_3, arg3'=-2*k_2+arg3P_3, [ arg3P_3<=10000 && k_2>=1 && -2*k_2+arg3P_3>=1 ], cost: 5+18*k_2

Computing asymptotic complexity for rule 37
   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),?)