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, [ arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1
     12: f3 -> f4 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg2>0 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
     13: f3 -> f5 : arg1'=arg1P_14, arg2'=arg2P_14, [ arg2<=0 && arg1==arg1P_14 && arg2==arg2P_14 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, arg2'=arg2P_3, [ 0==arg1P_3 && arg2==arg2P_3 ], cost: 1
      6: f11 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      3: f9 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1P_4==1+arg1 && arg2==arg2P_4 ], cost: 1
      7: f12 -> f10 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      4: f7 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>arg2 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f7 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1<=arg2 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
     10: f10 -> f4 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
      8: f4 -> f7 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1<arg2 && arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      9: f4 -> f7 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1>arg2 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
     11: f4 -> f13 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg1==arg2 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
     14: f13 -> f6 : arg1'=arg1P_15, arg2'=arg2P_15, [ arg1==arg1P_15 && arg2==arg2P_15 ], cost: 1
     15: f5 -> f6 : arg1'=arg1P_16, arg2'=arg2P_16, [ arg1==arg1P_16 && arg2==arg2P_16 ], cost: 1
     16: __init -> f1 : arg1'=arg1P_17, arg2'=arg2P_17, [], cost: 1

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     16: __init -> f1 : arg1'=arg1P_17, arg2'=arg2P_17, [], cost: 1

Removed unreachable and leaf rules:
   Start location: __init
      0: f1 -> f2 : arg1'=arg1P_1, arg2'=arg2P_1, [ arg2==arg2P_1 ], cost: 1
      1: f2 -> f3 : arg1'=arg1P_2, arg2'=arg2P_2, [ arg1==arg1P_2 ], cost: 1
     12: f3 -> f4 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg2>0 && arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
      2: f8 -> f11 : arg1'=arg1P_3, arg2'=arg2P_3, [ 0==arg1P_3 && arg2==arg2P_3 ], cost: 1
      6: f11 -> f10 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      3: f9 -> f12 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1P_4==1+arg1 && arg2==arg2P_4 ], cost: 1
      7: f12 -> f10 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      4: f7 -> f8 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1>arg2 && arg1==arg1P_5 && arg2==arg2P_5 ], cost: 1
      5: f7 -> f9 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1<=arg2 && arg1==arg1P_6 && arg2==arg2P_6 ], cost: 1
     10: f10 -> f4 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
      8: f4 -> f7 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1<arg2 && arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      9: f4 -> f7 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1>arg2 && arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
     16: __init -> f1 : arg1'=arg1P_17, arg2'=arg2P_17, [], 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
     12: f3 -> f4 : [ arg2>0 ], cost: 1
      2: f8 -> f11 : arg1'=0, [], cost: 1
      6: f11 -> f10 : [], cost: 1
      3: f9 -> f12 : arg1'=1+arg1, [], cost: 1
      7: f12 -> f10 : [], cost: 1
      4: f7 -> f8 : [ arg1>arg2 ], cost: 1
      5: f7 -> f9 : [ arg1<=arg2 ], cost: 1
     10: f10 -> f4 : [], cost: 1
      8: f4 -> f7 : [ arg1<arg2 ], cost: 1
      9: f4 -> f7 : [ arg1>arg2 ], cost: 1
     16: __init -> f1 : arg1'=arg1P_17, arg2'=arg2P_17, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     22: f7 -> f10 : arg1'=0, [ arg1>arg2 ], cost: 3
     23: f7 -> f10 : arg1'=1+arg1, [ arg1<=arg2 ], cost: 3
     10: f10 -> f4 : [], cost: 1
      8: f4 -> f7 : [ arg1<arg2 ], cost: 1
      9: f4 -> f7 : [ arg1>arg2 ], cost: 1
     19: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, [ arg2P_2>0 ], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     10: f10 -> f4 : [], cost: 1
     24: f4 -> f10 : arg1'=1+arg1, [ arg1<arg2 ], cost: 4
     25: f4 -> f10 : arg1'=0, [ arg1>arg2 ], cost: 4
     19: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, [ arg2P_2>0 ], cost: 4

Eliminated locations (on tree-shaped paths):
   Start location: __init
     26: f4 -> f4 : arg1'=1+arg1, [ arg1<arg2 ], cost: 5
     27: f4 -> f4 : arg1'=0, [ arg1>arg2 ], cost: 5
     19: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, [ arg2P_2>0 ], cost: 4

Accelerating simple loops of location 9.
   Accelerating the following rules:
     26: f4 -> f4 : arg1'=1+arg1, [ arg1<arg2 ], cost: 5
     27: f4 -> f4 : arg1'=0, [ arg1>arg2 ], cost: 5

   Accelerated rule 26 with backward acceleration, yielding the new rule 28.
[test] deduced pseudo-invariant -arg1<=0, also trying arg1<=-1
   Accelerated rule 27 with non-termination, yielding the new rule 29.
   Accelerated rule 27 with non-termination, yielding the new rule 30.
   Accelerated rule 27 with backward acceleration, yielding the new rule 31.
[accelerate] Nesting with 2 inner and 2 outer candidates
   Removing the simple loops: 26.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     27: f4 -> f4 : arg1'=0, [ arg1>arg2 ], cost: 5
     28: f4 -> f4 : arg1'=arg2, [ arg2-arg1>=0 ], cost: 5*arg2-5*arg1
     29: f4 -> [14] : [ arg1>arg2 && 0>arg2 ], cost: NONTERM
     30: f4 -> [14] : [ arg1>arg2 && -arg1<=0 && 0>arg2 ], cost: NONTERM
     31: f4 -> f4 : arg1'=0, [ -arg1<=0 && k_2>=1 && 0>arg2 ], cost: 5*k_2
     19: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, [ arg2P_2>0 ], cost: 4

Chained accelerated rules (with incoming rules):
   Start location: __init
     19: __init -> f4 : arg1'=arg1P_1, arg2'=arg2P_2, [ arg2P_2>0 ], cost: 4
     32: __init -> f4 : arg1'=0, arg2'=arg2P_2, [ arg2P_2>0 ], cost: 9
     33: __init -> f4 : arg1'=arg2P_2, arg2'=arg2P_2, [ arg2P_2>0 && arg2P_2-arg1P_1>=0 ], cost: 4+5*arg2P_2-5*arg1P_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     33: __init -> f4 : arg1'=arg2P_2, arg2'=arg2P_2, [ arg2P_2>0 && arg2P_2-arg1P_1>=0 ], cost: 4+5*arg2P_2-5*arg1P_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     33: __init -> f4 : arg1'=arg2P_2, arg2'=arg2P_2, [ arg2P_2>0 && arg2P_2-arg1P_1>=0 ], cost: 4+5*arg2P_2-5*arg1P_1

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),?)