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

Checking for constant complexity:
   The following rule is satisfiable with cost >= 1, yielding constant complexity:
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, [], 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
     10: f3 -> f4 : arg1'=arg1P_11, arg2'=arg2P_11, [ arg2<0 && arg1==arg1P_11 && arg2==arg2P_11 ], cost: 1
     11: f3 -> f4 : arg1'=arg1P_12, arg2'=arg2P_12, [ arg2>0 && arg1==arg1P_12 && arg2==arg2P_12 ], cost: 1
      2: f4 -> f5 : arg1'=arg1P_3, arg2'=arg2P_3, [ arg1==arg1P_3 ], cost: 1
      3: f5 -> f6 : arg1'=arg1P_4, arg2'=arg2P_4, [ arg1P_4==-1+arg1 && arg2==arg2P_4 ], cost: 1
      6: f6 -> f7 : arg1'=arg1P_7, arg2'=arg2P_7, [ arg1>=0 && arg1==arg1P_7 && arg2==arg2P_7 ], cost: 1
      7: f6 -> f8 : arg1'=arg1P_8, arg2'=arg2P_8, [ arg1<0 && arg1==arg1P_8 && arg2==arg2P_8 ], cost: 1
      4: f7 -> f10 : arg1'=arg1P_5, arg2'=arg2P_5, [ arg1==arg1P_5 && 1==arg2P_5 ], cost: 1
      8: f10 -> f9 : arg1'=arg1P_9, arg2'=arg2P_9, [ arg1==arg1P_9 && arg2==arg2P_9 ], cost: 1
      5: f8 -> f11 : arg1'=arg1P_6, arg2'=arg2P_6, [ arg1==arg1P_6 && 0==arg2P_6 ], cost: 1
      9: f11 -> f9 : arg1'=arg1P_10, arg2'=arg2P_10, [ arg1==arg1P_10 && arg2==arg2P_10 ], cost: 1
     12: f9 -> f3 : arg1'=arg1P_13, arg2'=arg2P_13, [ arg1==arg1P_13 && arg2==arg2P_13 ], cost: 1
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, [], 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
     10: f3 -> f4 : [ arg2<0 ], cost: 1
     11: f3 -> f4 : [ arg2>0 ], cost: 1
      2: f4 -> f5 : arg2'=arg2P_3, [], cost: 1
      3: f5 -> f6 : arg1'=-1+arg1, [], cost: 1
      6: f6 -> f7 : [ arg1>=0 ], cost: 1
      7: f6 -> f8 : [ arg1<0 ], cost: 1
      4: f7 -> f10 : arg2'=1, [], cost: 1
      8: f10 -> f9 : [], cost: 1
      5: f8 -> f11 : arg2'=0, [], cost: 1
      9: f11 -> f9 : [], cost: 1
     12: f9 -> f3 : [], cost: 1
     14: __init -> f1 : arg1'=arg1P_15, arg2'=arg2P_15, [], cost: 1

### Simplification by acceleration and chaining ###

Eliminated locations (on linear paths):
   Start location: __init
     10: f3 -> f4 : [ arg2<0 ], cost: 1
     11: f3 -> f4 : [ arg2>0 ], cost: 1
     17: f4 -> f6 : arg1'=-1+arg1, arg2'=arg2P_3, [], cost: 2
     20: f6 -> f9 : arg2'=1, [ arg1>=0 ], cost: 3
     21: f6 -> f9 : arg2'=0, [ arg1<0 ], cost: 3
     12: f9 -> f3 : [], cost: 1
     16: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     22: f3 -> f6 : arg1'=-1+arg1, arg2'=arg2P_3, [ arg2<0 ], cost: 3
     23: f3 -> f6 : arg1'=-1+arg1, arg2'=arg2P_3, [ arg2>0 ], cost: 3
     24: f6 -> f3 : arg2'=1, [ arg1>=0 ], cost: 4
     25: f6 -> f3 : arg2'=0, [ arg1<0 ], cost: 4
     16: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Eliminated locations (on tree-shaped paths):
   Start location: __init
     26: f3 -> f3 : arg1'=-1+arg1, arg2'=1, [ arg2<0 && -1+arg1>=0 ], cost: 7
     27: f3 -> f3 : arg1'=-1+arg1, arg2'=0, [ arg2<0 && -1+arg1<0 ], cost: 7
     28: f3 -> f3 : arg1'=-1+arg1, arg2'=1, [ arg2>0 && -1+arg1>=0 ], cost: 7
     29: f3 -> f3 : arg1'=-1+arg1, arg2'=0, [ arg2>0 && -1+arg1<0 ], cost: 7
     16: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Accelerating simple loops of location 2.
   Accelerating the following rules:
     26: f3 -> f3 : arg1'=-1+arg1, arg2'=1, [ arg2<0 && -1+arg1>=0 ], cost: 7
     27: f3 -> f3 : arg1'=-1+arg1, arg2'=0, [ arg2<0 && -1+arg1<0 ], cost: 7
     28: f3 -> f3 : arg1'=-1+arg1, arg2'=1, [ arg2>0 && -1+arg1>=0 ], cost: 7
     29: f3 -> f3 : arg1'=-1+arg1, arg2'=0, [ arg2>0 && -1+arg1<0 ], cost: 7

   Failed to prove monotonicity of the guard of rule 26.
   Failed to prove monotonicity of the guard of rule 27.
   Accelerated rule 28 with backward acceleration, yielding the new rule 30.
   Failed to prove monotonicity of the guard of rule 29.
[accelerate] Nesting with 4 inner and 4 outer candidates
   Removing the simple loops: 28.

Accelerated all simple loops using metering functions (where possible):
   Start location: __init
     26: f3 -> f3 : arg1'=-1+arg1, arg2'=1, [ arg2<0 && -1+arg1>=0 ], cost: 7
     27: f3 -> f3 : arg1'=-1+arg1, arg2'=0, [ arg2<0 && -1+arg1<0 ], cost: 7
     29: f3 -> f3 : arg1'=-1+arg1, arg2'=0, [ arg2>0 && -1+arg1<0 ], cost: 7
     30: f3 -> f3 : arg1'=0, arg2'=1, [ arg2>0 && arg1>=1 ], cost: 7*arg1
     16: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3

Chained accelerated rules (with incoming rules):
   Start location: __init
     16: __init -> f3 : arg1'=arg1P_1, arg2'=arg2P_2, [], cost: 3
     31: __init -> f3 : arg1'=-1+arg1P_1, arg2'=1, [ -1+arg1P_1>=0 ], cost: 10
     32: __init -> f3 : arg1'=-1+arg1P_1, arg2'=0, [ -1+arg1P_1<0 ], cost: 10
     33: __init -> f3 : arg1'=-1+arg1P_1, arg2'=0, [ -1+arg1P_1<0 ], cost: 10
     34: __init -> f3 : arg1'=0, arg2'=1, [ arg1P_1>=1 ], cost: 3+7*arg1P_1

Removed unreachable locations (and leaf rules with constant cost):
   Start location: __init
     34: __init -> f3 : arg1'=0, arg2'=1, [ arg1P_1>=1 ], cost: 3+7*arg1P_1

### Computing asymptotic complexity ###

Fully simplified ITS problem
   Start location: __init
     34: __init -> f3 : arg1'=0, arg2'=1, [ arg1P_1>=1 ], cost: 3+7*arg1P_1

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),?)